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Keywords: Complex Engineered Systems, Mechatronics, CPS, CPPS, MBSE, Knowledge Management, Collaborative Design, Digital Twin, Articial Intelligence

Hammami, Professeur à l'ENSTA-ParisTech qui m'ont fait l'honneur de participer au jury et d'avoir accepté d'examiner ce travail. Enn, je souhaite remercier tous mes collègues du laboratoire Quartz, et particulièrement l'équipe IS2M qui, par leurs nombreuses discussions et leur amitié, nous permettent de travailler dans une ambiance conviviale. ii Préambule Le présent document décrit mes activités universitaires d'enseignant-chercheur depuis ma soutenance de thèse en 2012 eectuée au Laboratoire d'Ingénierie des Systèmes Mécaniques et des Matériaux (LISMMA) à ISAE-Supméca. Les thèmes développés en recherche concernent la formalisation des cadres de modélisation et de conception an de maîtriser la complexité croissante des produits et des processus de production en raison d'une importante intégration multidisciplinaire au c÷ur même des produits et des processus de production. Plus précisément, notre travail porte sur le développement d'approches méthodologiques, fondées sur une intégration Mécatronique an de garantir a priori le respect des diérentes exigences de conception. Notre projet de recherche propose une action centrale visant à dénir un cadre formel pour un processus de conception dans un contexte d'ingénierie système, permettant une conception collaborative multidisciplinare appliquée aux systèmes complexes de types Mécatronique, CPS et CPPS. Ce manuscrit contient la partie scientique du rapport HDR. Dans la première partie, je présente une synthèse de nos activités de recherche et de nos contributions. La deuxième partie détaille notre projet de recherche et les axes à développer.

The term "Mechatronics" was rst introduced in 1969 by an engineer from the Japanese company Yaskawa Electric Corporation. The denition of mechatronics is given in the NF E01-010 standard (NF 2008) as "an approach aiming at the synergistic integration of mechanics, electronics, automation and computer science in the design and manufacture of a product in order to increase and/or optimize its functionality".

This denition highlights the fact that functional performance of physical products is achieved through a synergistic integration of components based on heterogeneous technologies. These products are commonly called mechatronic systems, complex systems or complex engineered systems, to distinguish engineered systems from other complex systems such as natural, biological or economic systems. The mechatronics denition highlights also the fact that mechatronics is a design approach that takes into consideration the manufacturability, and more broadly speaking producibility, of the product. Finally, the denition of mechatronics emphasizes the multidisciplinary design optimization of the mechatronic system.

The terms used above are the main keywords around which my research activities have been built.

The applications concerned by mechatronics touch various complex engineered systems including automobile, aerospace, naval architecture, electronics, electricity distribution, production systems, assembly/disassembly lines, just to name a few.

Modern engineered systems include mechatronic modules in order to increase and optimize their functionalities. The objective is to meet the needs of increasingly demanding customers who want products cheaper, more customized, higher quality and more reliable, while at the same time being increasingly smart and innovative with high added value, while development times must be ever shorter. The design process of mechatronic systems includes activities of modeling, simulation, optimization, prototyping and deployment.

Modeling is a preliminary step that allows to create a representation of the considered system, and to appropriate its properties and specicities. Models are developed from dierent points of view, for dierent levels of abstraction, for dierent disciplines and physics, with dierent languages and tools, and by dierent developers from dierent engineering domains.

Simulation models have the particularity of allowing the analysis of the model in action, being able to inspect the behavior of the system, study its elements, analyze the processes and interact with the simulation model in action.

The physical behavior of these systems is complex because it is due to the coupling of several 1.1. Context,scientic background,positioning and research issues 15 physics. Multiphysics is a practice built on mathematics, physics, application, and numerical analysis. The mathematics involved usually contains partial dierential equations, ordinary dierential equations and/or dierential algebraic equations.

The optimization of a multidisciplinary system requires incorporating all relevant disciplines simultaneously, because the optimum of the simultaneous design problem is not equal to the design found by optimizing each discipline sequentially, since we can exploit the interactions between the disciplines. However, including all disciplines simultaneously signicantly increases the complexity of the design problem.

Prototyping aims to make an original model that has all the technical qualities and operating characteristics of a new product. It allows to validate the choices made during the design of the units. It also allows to exchange or acquire experience on a concept or material product. As well as to test the reactions of future users or consumers and to prepare the technical specications of the product.

The process of designing complex engineered systems requires also collaboration and knowledge management to perceive, identify, analyze, organize, memorize and share the knowledge of the members implied in the design process.

Looking at the set of design activities below, it is easy to deduce that the design process of mechatronic systems is a complex process that requires the implementation of ecient design methods and the development of new tools to manage this complexity. To achieve this, the main issue is the numerical continuity between the design stages, taking into account the evolution of the requirements throughout the design process, while facilitating collaboration between teams and engineering members.

The issue of managing the design of complex systems is not new. Classical system design cycles cover the phases of customer needs analysis, system requirements generation, functional analysis leading to functional architecture, then logical and physical architecture, as well as simultaneous pre-sizing activities allowing the evaluation of dierent architectures for the selection of a solution. This classical approach reveals many discontinuities when moving from one step to the next.

These discontinuities are due to several factors, including the type of model needed at each level of abstraction, the level of detail of the models, the languages and tools used to develop the models, the interoperability problems between the models and the tools that support them, the diculty of getting design members and teams with dierent engineering cultures to work together, etc. Thus, a disjunction is reected in the disciplinary "Silos" in which engineers are trained, think and work.

Notable improvements over the past twenty years include the development of languages and tools for Model-Based Systems Engineering (MBSE) and Chapter 1. Collaborative multidisciplinary design of mechatronic systems simulation.

For example, the Systems Modeling Language (Systems Modeling Language (SysML)) oers systems engineers several notable improvements over the more software-oriented Unied Modeling Language (UML). The semantics of SysML are richer and more exible, imposing fewer restrictions related to the UML view, and adding new types of diagrams, such as the requirements diagram, which can be used for requirements management, while the parametric diagram can be used for performance analysis and quantitative analysis.

However, parametric diagrams only support simple mathematical models dened by algebraic equations. They do not allow, for example, the modeling of dynamic systems dened with dierential equations.

Modelica is also an object-oriented modeling language for the practical modeling of complex systems. It allows a system to be described in the form of a set of equations. The associated simulator has the task of solving the system of equations at each time step. Modelica is able to describe the evolution of dynamic systems that are described by ordinary dierential equations, algebraic equations and discrete equations.

The Modelica solver, on the other hand, does not support partial dierential equations, which are necessary to describe the mono-physical or multi-physical behaviors of system's components. For this type of modeling, it is more appropriate to use modeling tools based on discretization methods (nite elements, nite dierences and nite volumes).

Furthermore, Multidisciplinary Design Analysis and Optimization (Multidisciplinary Design Analysis and Optimization (MDAO)) is a methodology that enables the analysis and optimization of a complete complex system by explicitly considering the important interactions and synergies between disciplines.

MDAO helps in creating automated workows that incorporate analysis tools and processes from dierent disciplines. These workows can be run repeatedly to quickly explore and quantify the performance, costs and risks of many dierent design solutions. MDAO also allows sensitivity analysis to nd the most important variables. In addition, MDAO workows can be automated using optimization algorithms to nd the best designs. Finally, probabilistic analyses can be performed to evaluate the robustness and reliability of the designs.

However, the implementation of MDAO workows to automate multidisciplinary analysis and optimization is often costly. In addition, it is often necessary for decisions to be made by experts and not automatically by algorithms. This requires the implementation of eective collaborative approaches to integrate the MDAO discipline into the mechatronics design process.

Prototyping allows the designer to validate the functionality and performance of the mechatronic design, but also to verify its manufacturability, producibility, reliability, etc. Indeed, for most companies, the manufacturing system is a valuable asset that is more or less xed and allows only minor modications. Therefore, 1.1. Context,scientic background,positioning and research issues 17 the mechatronic product design must be adapted to the manufacturing system.

However, trade-os must be made when the functionality and the performance objectives of the product are aected. To make these decisions, the designer must know the existing and future manufacturing system and understand the implication of the manufacturing system on the product design. Incorporating manufacturing, production and more globally DFX constraints into the preliminary design phases of the mechatronic product will give the designer a better chance of achieving an optimal design. This will require a good specication of the mechatronic product according to the dierent points of view related to its functionality, performance, manufacturability, producibility, etc. It also requires eective collaboration between dierent multidisciplinary stakeholders, using a platform allowing ecient communication and knowledge sharing.

Scientic background

Our contributions in the last 10 years have focused on the development of methodologies for the design of mechatronic systems. A methodology is dened as a collection of related processes, methods and tools to solve a specic problem [Martin, 2020]. For this purpose, I have divided my research activities in this manuscript into three interrelated lines of research:

MBSE-based approaches for the integrated design of mechatronic systems. Multiphysics simulation methods for mechatronics design.

Interdisciplinary collaborative design of mechatronic systems.

Mechatronic systems here include mechatronic products and their manufacturing/production systems. The goal of the integrated design for us is to ensure continuity in the design process between the systems engineering level and the do- With the goal of replacing paper documents with digital and data models, the use of Model-Based Systems Engineering (MBSE) has become widespread in industrial processes, and has thus improved reuse and collaboration between the dierent actors. Indeed, often used by system architects, it eectively encourages communication and collaboration between disciplinary experts during the dierent design stages. The integration of these dierent multidisciplinary points of view in the numerical models then contributes to the decision arbitrations. In addition, MBSE approaches increase data model consistency between disciplines, improve traceability to requirements and also promote model reuse.

However, system architects need a language that allows them to specify all system requirements and architectures, regardless of the discipline or technical team they are addressing.

For this purpose, SysML is generally used to implement the essential aspects of the MBSE approach. Indeed, this graphical notation language, based on UML [Hause et al., 2006]. Today, SysML is recognized by the systems engineering community as the most suitable language for implementing MBSE approaches.

Mainly dedicated to systems modeling, it replaces the numerous spreadsheets used in the industry, whose consistency and updating are often dicult to maintain.

Indeed, SysML allows to specify and analyze the structure and the functionality of the system and then dene the system and its subsystems. Moreover, SysML allows to verify and validate the feasibility of a system before its realization by oering a unique model at the system level. In this context, each designer can refer to a single model throughout the design cycle, and has an automatic update of the data shared by all the other actors of the design. This language has the advantage of oering a great semantic richness, as it allows to represent dierent views of the system thanks to its dierent diagrams and is particularly ecient to model the requirements, structure, behavior, allocations and constraints of the system [START_REF] Mhenni | A sysml-based methodology for mechatronic systems architectural design[END_REF]. Three groups of diagrams make up the SysML language:

behavior diagrams, requirements diagrams and structure diagrams (gure 1.2).

These diagrams allow multi-view modeling with dierent representations of the system linked together to ensure consistency and traceability. SysML thus enables Unfortunately, SysML is not practical enough to be used in real-world engineering projects. SysML is designed to express generic systems and requires specialized knowledge of specic engineering disciplines.

Thus a model written in SysML is less able to support communication between a systems engineer and engineers from specic engineering disciplines such as Mechatronic system design, 3D design, The aim of Mechatronics is the synergistic integration of mechanics, electronics, automation and software in the design and manufacture of products. The synergistic integration can be achieved with a strong functional-physical system integration.

Functional integration is the simultaneous implementation of several functions within the mechatronic system. It consists in integrating as many functions as possible in a product, either by combining several functions in a single component, or by dematerializing some functions by using programmable computer technologies, which provide the system with additional sensing, communication, information processing and feedback functions to the basic mechanical functions.

Physical integration allows a set of components to be spatially integrated to form a complex functional unit. This will allow a greater reliability for a smaller installation space due to reduced interfaces and, consequently, faster data transmission. The power output will also be higher with reduced assembly eort.

The gure 1.3 shows an example of physical and functional integration concerning an electric wheel drive system where the motor, the sensors, and the power electronics are spatially integrated. https://schaeffler-events.com/)

1.1. Context, scientic background, positioning and research issues 21

However, the spatial proximity of the components will generate undesirable interactions, such as heating, stray magnetic elds, vibrations, noise and voltage spikes, which must be taken into account as early as possible in the design process. Electronic components must be adapted to the operating environment (temperature, humidity, vibrations, etc.) and thus, under certain circumstances, additional measures such as encapsulation or cooling may be necessary to ensure component reliability.

System (functional-physical) integration therefore requires a systematic design procedure and modeling support with computer tools to analyze the system integration. Thus, to achieve a high degree of integration, the compatibility of operating principles and solution elements must be veried, taking into account benecial and disruptive functions, and the interfaces for further integration (rough sizing) must be formulated in the system design step. The possible incompatibilities must therefore be detected and eliminated during the preliminary system design and analysis. Otherwise, there may be costly changes during the specic-domains ne design.

In traditional mechanical engineering, the problem of system integration lies in a good denition of the part's shapes and their properties determining for a mechanical assembly design. In mechatronic system design, however, various interactions (e.g. behavior, electromagnetic compatibility, etc.) have to be taken into account to verify the incompatibilities.

Today, several multi-domain modeling and simulation software tools, such as Simcenter/Amesim, Matlab/Simscape, Modelica/Dymola, etc., allow the study of multi-domain and multi-physics interactions in a mechatronic system before embarking on a detailed geometric design, which is usually costly. These software tools provide a 0D/1D simulation suite for modeling and analyzing multi-domain systems and predicting their multi-disciplinary performance. At the lowest level, the dynamic behavior of the components is described by mathematical equations or algorithms. Domain-specic knowledge is represented by libraries containing components for mechanical, electrical, control, thermal, pneumatic, hydraulic, power train, thermodynamics, vehicle dynamics, air conditioning, etc.

Nevertheless, the multi-physics behavior is often very dependent on the geometry of the components and the geometric interfaces. This requires the development of compact models coupling simple geometry and physical behavior, such as vibration and thermal behavior, to analyze the location of components on the choice of a mechatronic system architecture.

In addition to the use of 0D/1D computer tools to simulate the interactions and multiphysics compatibilities, close cooperation between domain specic disciplines is necessary, as the evaluation of these interactions requires detailed technical knowledge.

Chapter 1. Collaborative multidisciplinary design of mechatronic systems 1.1.2.3 Multiphysics Simulation (MPS) When modeling multi-physics systems, each physics is represented, in general, as a system of nonlinear, time-dependent equations. These equations can be a combination of Partial Dierential Equations (PDE), Ordinary Dierential Equations (ODE) or Dierential Algebraic Equations (DAE). Multiphysics applications require a way to exchange information between physical components. Indeed, multiphysics problems require the computation of interacting elds that may have dierent time and/or space scales and may also be dened over dierent spatial regions.

Space-dependent multiphysics systems can be modeled using a single-domain or multi-domain approach.

For a single-domain approach, the coupled system is considered globally, and the state variables are dened over the entire spatial domain of the problem. A simple example for single-domain approach is a thermomechanical system whose solution consists of the temperature and displacements.

For a multi-domain approach, dierent sets of state variables and/or models may be considered on dierent spatial or physics domains. A simple example for dierent spatial domains is Fluid Structure Interaction (FSI), where the uid velocity and pressure are dened in the uid domain and displacements are dened in the solid domain. Multi-domain coupling, must respect the mathematical formulation of the coupled problem and must account for dierent meshes and discretizations used in each domain [START_REF] Keyes | Multiphysics simulations: Challenges and opportunities[END_REF].

Time-dependent multi-physics systems can be modeled using a monolithic or partitioned approach. In a monolithic approach, the physics are naturally and intrinsically coupled. The system is represented by a single system of ODEs or DAEs, and the time integration is accomplished with a single solver; all quantities are determined simultaneously and the coupling between the state-variables in this case is strong. In a partitioned approach, the system is decomposed into a set of subsystems, each of which is represented by a partition that is then coupled to other subsystem partitions via partition input-output relationships. The strategies used to solve coupled sets of physics equations can be generally categorized as tight coupling (or strong partitioned coupling) and loose coupling. Figure 1.4 illustrates the dierent multiphysics couplings.

In tight coupling solution methods, a single system of equations is assembled and solved for the full set of coupled physics. The nonlinear iterations operate on the full system of equations simultaneously, taking into account the interactions between the equations for the coupled physics in each iteration. In cases where there is strong coupling between the physics, this approach can have faster convergence rates than loose coupling. The primary disadvantage of this approach is that it necessitates tighter coordination between the codes to solve the individual physics [START_REF] Hales | Advanced multiphysics coupling for lwr fuel performance analysis[END_REF]. Loose coupling allows for the use of existing software modules such as dedicated uid-dynamics and structural-dynamics software. Loosely coupled partitions can be coupled either explicitly or implicitly. Under explicit loose coupling, advancement of all partition solutions from time t to t + ∆t is accomplished based on shared information at t. Alternatively, implicit partition coupling is formulated such that one or more partitions require other-module data in (t; t + ∆t) before the solution can be advanced; the partitions are thus tied together in a linear or nonlinear system that must be solved for time advancement [START_REF] Gasmi | Numerical stability and accuracy of temporally coupled multi-physics modules in wind turbine cae tools[END_REF].

It is necessary here to distinguish between physical and numerical couplings.

Indeed, the physical phenomena can be strongly or weakly coupled, from a physical point of view. The resolution methods on their side can be tightly or loosely coupled, from a numerical point of view. Nevertheless, a strong multiphysics coupling could be modeled and solved with a loose coupling. In the same way, a weak multiphysics coupling could be modeled and solved with a tight numerical coupling.

There is therefore no one-to-one correlation between physical and numerical couplings. All depends on the physical phenomena and the numerical means of resolution.

Simulating complex multiphysics systems can be very expensive, and sometimes is even infeasible due to the wide range of scales. In particular, in the mechatronic design process, simulations must be run many times to perform parameter studies, design optimization or for system control design and analysis. In addition, Chapter 1. Collaborative multidisciplinary design of mechatronic systems using full order models such as Finite Volume Method (FVM), Finite Dierence Method (FDM) and Finite Element Method (FEM) causes to large algebraic systems and high computational times.

It is therefore necessary to search for methodologies to exploit the potentials of multiphysics simulation and adapt them to the needs of mechatronic design. The use of compact 0D/1D models and reduced order models techniques are ways to reduce the computational complexity in such contexts.

Collaboration between multiphysics/mechatronics interdisciplinary groups is also one of the most important barriers to multiphysics applications for mechatronics system design. Indeed, the move to a multiphysics framework for mechatronics and thus to more complex simulations, will require the input of code and model developers to optimize eciency, the input of mathematicians to study stability and accuracy, and the input of the mechatronics engineers to ensure the integration and the overall analysis of the mechatronic system.

It is thus necessary also to have interdisciplinary collaborative frameworks that allow for knowledge sharing and communication to understand the problems of simulation and the assumptions behind the underlying models. Without this input, it is likely impossible to perform a complete analysis or optimization of the mechatronic system, and time will be lost as assumptions or necessary physical conditions may be violated during development. All members of the interdisciplinary team must understand both their role and that of the other participants. The most successful collaborations will produce multiphysics simulations that yield new physical knowledge with computational eciency and mathematical accuracy [START_REF] Keyes | Multiphysics simulations: Challenges and opportunities[END_REF]. 1.1.2.4 Design for X (DFX)

Eorts to reduce total product life-cycle costs through design innovation have always been a critical issue of the manufacturing industry. As a result, researchers have focused on integrating development constraints, methods, and costs in the preliminary design phase of complex products. Hence the emergence of design for assembly (DFA), design for manufacture (DFM), design for manufacture and assembly (DFMA), design for disassembly (DFD), design for environment (DFE), design for recycling (DFR), design for quality (DFQ), design for life cycle (DFLC), etc. These design methodologies are often referred as design for X (DFX).

For instance, Design for Manufacture and Assembly (DFMA) is an engineering methodology that integrates Design for Manufacture (DFM) and Design for Assembly (DFA) [START_REF] Boothroyd | Product design for manufacture and assembly[END_REF]. Beginning in the early design phases of the product life cycle, DFMA aims to reduce time-to-market and total production costs by prioritizing the ease of manufacturing product parts (DFM) and simplied assembly of parts (DFA) into the nal product.

DFM is dened as "the set of policies, techniques, practices, and attitudes 1.1. Context, scientic background, positioning and research issues 25 that cause a product to be designed for optimal manufacturing cost, optimal manufacturing quality, and optimal life cycle support, serviceability, reliability, and recyclability" [START_REF] Kuo | Design for manufacturability and design for" x": concepts, applications, and perspectives[END_REF]. The objectives of the DFM approach are to: (1) identify product concepts that are inherently easy to manufacture,

(2) focus on component design for ease of manufacture and assembly, and

integrate manufacturing process design and product design to ensure the best match between needs and requirements. DFM seeks to identify appropriate materials and manufacturing processes for the components considered in a product design, based on the combination of various product capabilities and limitations. Typically, DFM focuses on a particular manufacturing process, e.g., machining, stamping, injection molding, assembly, etc., and seeks to incorporate measures into the early design of the product that can prevent manufacturing problems and greatly simplify the production process [START_REF] Kuo | Design for manufacturability and design for" x": concepts, applications, and perspectives[END_REF].

Manufacturability is a DFM metric to measure how dicult or easy the design is, from manufacturing perspective. Similarly, producibility is a metric to measure how dicult or easy the design is, from production perspective. Therefore, the dierence between the two metrics manufacturability and producibility is related to the dierence between manufacturing and production. Indeed, manufacturing is generally dened as the process that involves the conversion of raw materials into nished products using machinery. Production, on the other hand, refers to the conversion of inputs, including raw materials and partially nished products, into nished products. Therefore, production is a broader term that encompasses the nancial activities of a company as well as other non-tangible elements.

To illustrate the dierence between producibility and manufacturability, let us consider the example of an Electronic Throttle Body (Electronic Throttle Body (ETB)), as illustrated in gure 1.5. This example will be used later in the contributions section as an example to validate some our research work.

As a mechatronic system, the ETB includes mechanical parts, electrical power, electronic sensors and a control system. The ETB is used in automobiles with combustion engines to control the air supply to the internal combustion engine (ICE). Air enters through the air intake and is admitted into the engine through the ETB air outlet after being regulated by the throttle valve according to the control of the power control module (PCM). A mechanical fail-safe system is incorporated in the ETB so that the air ow to the internal combustion engine is not completely shut-o in case of a problem with the ETB or its control.

A company that produces ETBs may only need to manufacture the body. The other parts must be purchased and assembled. Thus, in this case of ETB production, the company can use the manufacturing for some parts, but not for all. Hence, producibility metric can be viewed as the aggregation of several metrics, including manufacturability and assemblability. Indeed, assembly processes are adapted to assess implementation of mechatronic products in conditions of high volume and mass production. systems process has led to extensive eorts to improve the eciency and cost eectiveness of assembly operations [START_REF] Sanderson | Assembly sequence planning[END_REF]]. An assembly sequence plan is a high-level plan for building a product from its components. It indicates which sets of parts form sub-assemblies, the order in which the parts and sub-assemblies are to be inserted into each sub-assembly, and the nominal paths along which these insertions are to be made [START_REF] Chakrabarty | A structure-oriented approach to assembly sequence planning[END_REF]. Indeed, there are many possible assembly sequences for a product. Optimal sequence selection eectively reduces the cost and time of the assembly process [Kanai et al., 1996]. This method takes into account the shape of the parts, the connection typologies, the manual handling operations, as well as the calculation time and cost and the diculties of assembly between parts. Assemblability is a DFA metric to evaluate the quality of a product design from the assembly producibility point of view [START_REF] Ohashi | Extended assemblability evaluation method (aem)(extended quantitative assembly producibility evaluation for assembled parts and products)[END_REF].

Assemblability assessment allows to reduce the number of parts, to merge the parts when possible and to simplify manual, xed automation, or programmable automation of systems assembly operations [START_REF] Favi | A method to optimize assemblability of industrial product in early design phase: from product architecture to assembly sequence[END_REF].

For automated assembly operations, Assembly Sequence Planning (Assembly Sequence Planning (ASP)) provides feedback to the designer on the suitability of the product for robot assembly. On the other hand, assembly planning is the basis for the automatic generation of robot programs. The requirements for the design of new robot types can also be obtained from the ASP, e.g. the number of Degree Of Freedom (DOF), joint angle ranges, etc [START_REF] Thomas | Efcient assembly sequence planning using stereographical projections of c-space obstacles[END_REF]. 1.1. Context,scientic background,positioning and research issues 27 Products can be disassembled to allow maintenance, improve serviceability, and to meet end-of-life objectives such as product reuse, remanufacturing, and recycling.

In this age of environmental awareness, end-of-life goals such as component reuse, remanufacturing, and recycling are some of the most important reasons to disassemble products [START_REF] Desai | Evaluation of disassemblability to enable design for disassembly in mass production[END_REF]. As for assemblability, disassemblability is a Design for Disassembly (DFD) metric to evaluate the degree of easiness of disassembly. Disassemblability can be evaluated by measuring or calculating indicators such as the disassembly time, the eort and/or the energy/entropy required to accomplish the disassembly operation [START_REF] Vanegas | Ease of disassembly of products to support circular economy strategies[END_REF]. Automating the generation and the optimization of Disassembly Sequence Planning (Disassembly Sequence Planning (DSP)) is one of main challenge issues for disassemblability assessment.

ASP and DSP activities are proven to be NP-hard and thus their eective and ecient solutions have been a challenge for the researchers in this eld.

Indeed, ASP and DSP of a complex product easily runs into the combinatorial explosion, as the number of assembly/disassembly sequences is exponentially proportional to the number of parts or components in the product. Thus, several soft computing/metaheuristic algorithms were developed to solve the problem, such as Simulated Annealing [Motavalli andIslam, 1997, Hong andCho, 1999],

Articial Immune System [START_REF] Cao | Assembly planning using a novel immune approach[END_REF], Genetic Algorithms, Ant Colony

Optimization [START_REF] Wang | A novel ant colony algorithm for assembly sequence planning[END_REF], Guo et al., 2007], Articial Neural Networks [Chen, 1992, Hong and Cho, 1995, Sinano §lu and Börklü, 2005, Chen et al., 2008],

Particle Swarm Optimization [START_REF] Zhang | Research on a kind of assembly sequence planning based on immune algorithm and particle swarm optimization algorithm[END_REF][START_REF] Lv | An assembly sequence planning approach with a discrete particle swarm optimization algorithm[END_REF], Wang and Liu, 2010, Tseng et al., 2011]. In most of these research works the assembly was represented either with graphs and diagrams [De Fazio and Whitney, 1987, De Mello and Sanderson, 1991, Santochi and Dini, 1992, Gu et al., 2008] or with 3D CAD models [Hadj et al., 2018, Said et al., 2019, Bedeoui et al., 2019, Belhadj et al., 2020, Belhadj et al., 2021]. However, most of previous research works focused on detailed product geometry, which essentially introduces combinatorial problems in an ASP-DSP phase due to the product design complexity. Besides, traditional well-known DFA/DFD approaches can be considered as reactive, since they work on a detailed product geometry after all design decisions made, hence they lead to redesigns and delays due to late decisions changes. These approaches therefore result in late decision support and missing a true opportunity for an ecient product development process [START_REF] Demoly | An assembly oriented design framework for product structure engineering and assembly sequence planning[END_REF]. Therefore, more systematic approaches to the analysis, design, and planning of the assembly/disassembly operations or systems are needed to enhance their performance and enable their cost-eective implementation. In Chapter 1. Collaborative multidisciplinary design of mechatronic systems data [Belhadj et al., 2020] particular, it is necessary to dene the ASP-DSP in the preliminary stages of design by introducing and applying knowledge about the assembly/disassembly process in order to provide knowledge about the product/production context to support the systems engineering development process, especially for product structuring. Thus, there is value in integrating assembly/disassembly process engineering information and knowledge into the early phases of the product development process in a topdown, proactive manner to provide designers with an MBSE-based assembly context.

The denition of the product and its assembly/disassembly sequence requires both the improvement and the complete understanding of the relationships between the dierent components of the product and the associated assembly logic. Therefore, a new modeling approach is required to integrate the views of the dierent stakeholders involved in the early stages of the product life cycle. 1.1.2.5 Multidisciplinary Design Analysis and Optimization (MDAO)

For the design of complex engineering systems, multidisciplinary models are used in the design cycle with a strong interaction between them. Therefore, optimizing a model without taking into account the other models will generate integration problems in the nal product. The optimal design may even tend to converge on an absurd solution for the system [START_REF] Chapman | The application of a knowledge based engineering approach to the rapid design and analysis of an automotive structure[END_REF]. Given this state, Multidisciplinary Design Analysis and Optimization (MDAO) has been recognized as a promising solution to optimize globally the complex engineering systems [Alexandrov, 2005].

Multidisciplinary Design Analysis and Optimization (MDAO) or , for short, Multidisciplinary Design Optimization (MDO) is a methodology for the design of 1.1. Context, scientic background, positioning and research issues 29 complex engineering systems that are governed by mutually interacting physical phenomena and made up of distinct interacting subsystems in their design, everything inuences everything else [Sobieszczanski-Sobieski, 1995].

To express the MDO/MDAO problems, the basic formulation is the All-At-Once formulation (AAO), as dened in the Figure 1.7. This formulation contains all the coupling variables, their copies, state variables, consistency constraints and residual equations. Other formulations are derived from this denition. For the details about this formulation, readers can refer to [START_REF] Cramer | Problem formulation for multidisciplinary optimization[END_REF].

The term MDO architecture identies how the simulation blocks, analysis ele- In all the engineering domains, designers use computationally expensive numerical models. The optimization process based on the integration of such models can take long time due to the signicant number of iterations. Surrogate modeling is used in this case to make an approximation of the expensive model and then use it in the optimization process.

In the eld of surrogate modeling, three steps are required as we can see in As indicated in this section, the workow of analysis and optimization of the design process of a complex system is specied with an XDSM diagram for MDO specialists. However, the trend today is aligning people, processes, and technology around a single vision of a product promised by MBSE. Indeed, the use of a system architecture model as a single source of truth for describing the evolving system design throughout its product life-cycle reduces the development cost and risk of complex systems. The issue is the disconnection between systems engineers and engineering analysts that prevents MBSE from achieving its full potential.

Interdisciplinary Collaborative Design and Knowledge Management (ICDKM)

To improve interoperability between disciplinary engineering tools, many prod- CM is a managerial discipline that aims to ensure consistency and accuracy in product knowledge throughout its life cycle and for the same purpose, it is used to varying degrees in most organizations [START_REF] Niknam | Towards higher conguration management maturity[END_REF].

CM is dened in ISO 10007: 2003 releases as:

Conguration: interrelated functional and physical characteristics of a product dened in the product conguration information.

Product conguration information: requirements for the design, implementation, verication and support of a product.

Product conguration ensures the consistency through the design process by managing conguration information organized into Conguration Items. All the conguration items must be coherent over all the design process following the evolution into an iterative process and keep traceability of any changes.

Conguration management can be particularly interesting to manage parameters and rules used in several CAD/CAE models.

The rst objective of KCM is to enable designers to use parameters consistently in collaborative design. In fact, the lack of communication among dierent steps of the design cycle causes consistency problems in parameters. In Concurrent Engineering (CE), all participants need to access all relevant up-to-date product Chapter 1. Collaborative multidisciplinary design of mechatronic systems information. This methodology is based on the concept of crucial knowledge to keep the design models consistent with each other [START_REF] Monticolo | A meta-model for knowledge conguration management to support collaborative engineering[END_REF]. Crucial knowledge refers to the sucient and necessary knowledge that needs to be shared for the activity of a company [START_REF] Saad | A decision support for identifying crucial knowledge requiring capitalizing operation[END_REF]. Here, the knowledge consists of contextualized parameters and rules that are critical for the collaborative product development. Therefore, this crucial knowledge is structured and has its own lifecycle according to the Global Analysis Methodology (GAMETH) framework [START_REF] Grundstein | Gameth®, a decision support approach to identify and locate potential crucial knowledge[END_REF]. This framework denes a cycle with four facets which are: identify, formalize, value and update.

The principle is the capitalization of critical knowledge extracted from dierent expert models, into an abstract generic information entity called an Information Core Entity (ICE). The ICEs are grouped in a Knowledge Conguration (KC).

Then each stakeholder instantiates the necessary ICEs in his Usage Conguration (UC). This principle is illustrated in Figure 1.12. -KCM metamodel: The KCM UML metamodel is shown in Figure 1.13. The gure shows the links between the dierent concepts discussed above.

Particularly, KCM manages:

Technical data: the parameters and expert rules extracted from disciplinary models.

Information: the data identied, structured and organized into a specic entity to construct a technical and generic product information baseline.

Chapter 1. Collaborative multidisciplinary design of mechatronic systems -KCM use: Each user, working on very dierent expert models (design and simulation domain, dierent tools, dierent components, etc.), exports data from multiple product architectures into their congurations simultaneously. The consistency management between congurations is a main utility of KCM, because users can be warned if conicts occur between data shared by several expert models.

Two kinds of consistency checking can be considered:

Consistency in UC level: parameters must respect all the rules dened in the UC Consistency in KC level: Instances of the same ICE must contain the same values.

Positioning

My thesis, defended in January 2012, focused on a contribution to the integration of multiphysics simulation in the design process of mechatronic systems [Hammadi, 2012]. Following this, I continued to work on the development of In the literature, we can nd works that have dealt with this theme. For instance, [van Amerongen, 2003] discussed the need for an integrated approach when designing the mechanical and control parts of a mechatronic system. Mechatronic design requires models that, in addition to the controller parameters, retain all relevant physical parameters of the construction itself.

Likewise, [START_REF] Cabrera | Towards automation of control software: A review of challenges in mechatronic design[END_REF] Chapter 1. Collaborative multidisciplinary design of mechatronic systems identied a set of challenges related to the design of mechatronic systems. The challenges are mostly related to integration of design and analysis tools, and automation of current design practices. Addressing these challenges enables the adoption of a concurrent development approach in which the synergetic eects that characterize mechatronic systems can be taken into account during design. The main argument is that there is a need to consider the complex interdependencies among subsystems and the designers that develop them. In addition, [START_REF] Hehenberger | Con-References[END_REF] presented an approach for consistency checking of mechatronic design models based on the development of specic-domain checking rules. However, the granularity of modeling information aects the writing of consistency rules. So that, the approche is limited for consistency rules of elements at the same level of granularity (same level of abstraction). Furthermore, [START_REF] Torry-Smith | Challenges in designing mechatronic systems[END_REF] believed that a common language is essential in developing mechatronics, and should be evaluated based on: its capability to represent the desired views eectively, its potential to be understood by engineers from the various domains, and its eect on the eciency of the development process. In the same way, [Thramboulidis, 2013] addressed the main challenges in mechatronic system development including synergistic integration, size and complexity, reuse, as well as requirements handling and traceability, support for decision making, and maintaining consistency. The authors proposed SysML-based approach to address these challenges. Moreover, [START_REF] Budinger | Scaling-law-based metamodels for the sizing of mechatronic systems[END_REF] presented a metamodel form and associated construction procedure adapted to the sizing tasks of mechatronics systems. The scaling-lawbased metamodels have the advantage of a compact form with a good predictive accuracy.

More recently, [START_REF] Ma | Parameter space optimization towards integrated mechatronic design for uncertain systems with generalized feedback constraints[END_REF]] treated the integrated mechatronic design problem as a controller optimization problem with structural constraints.

The design problem is reformulated as minimizing the H2-norm upper bound of the closed-loop system transmittance from the exogenous disturbance to the regulated variables over the intersection of convex and non-convex domains.

On our side, we were interested in proposing methodologies for integrated design of mechatronic systems based on SysML language.

We have found it useful to integrate the DFX metrics, namely manufacturability, assemblability, disassemblability, recongurability, producibility, etc. in the preliminary design process of mechatronic systems. To evaluate and optimize the mechatronic design, it was also deemed necessary to integrate the possibilities of multiphysics simulation and multidisciplinary optimization.

For the third research activity, our objective is to develop an interdisciplinary collaboration framework allowing the management of knowledge shared between the dierent design domains: MBSE, MPS, MDAO and DFX. Figure 1.15 shows an overview on the specic domain knowledge that the mechatronics development engineer must share with other design members.

Research to improve the eectiveness and eciency of product develop- For mechatronic products design, [START_REF] Dawson | Schemebuilder: computer aided knowledge based design of mechatronic systems[END_REF] introduced the need for engineering knowledge management tools for storing past solutions and expert knowledge for the design of automatic precision machinery. Similarly, [START_REF] Larses | Drivers for model based development of mechatronic systems[END_REF] discussed the model based development from knowledge management perspective. Thus, a model of competence integration for the design of mechatronic systems was derived. The model describes how integration can be performed; it also supplies a dichotomy of two explicit strategies and a set of drivers for a given strategy.

[ [START_REF] Karayel | General framework for distributed knowledge management in mechatronic systems[END_REF] applied a knowledge management approach to mechatronic systems. Indeed, a knowledge management model of an internet-based CNC machining center has been developed and applied. [START_REF] Gardan | Enhancing knowledge management into systems engineering through new models in sysml[END_REF] developed new models into a SysML diagram to answer knowledge management needs for complex systems engineering. Therefore, the requirements satisfaction and decision-making process can be performed using new SysML diagrams modeling the organization, coordination and decision making. More recently, [START_REF] Yang | A knowledge management approach supporting model-based systems engineering[END_REF] proposed a knowledge management approach to support an intelligent question answering scenario when implementing MBSE in system lifecycle. Authors make use of the Graph, Object, Point, Property, Role, and Relationship (GOPPRR) approach to support MBSE formalisms which are transformed to knowledge graph models.

For our part, we believe that knowledge capitalization for mechatronic design is at the crossroads of knowledge sharing between mechatronics design domain and engineering disciplines related to MBSE, DFX, MPS and MDAO. For this reason, 40

Chapter 1. Collaborative multidisciplinary design of mechatronic systems it is necessary to develop collaboration tools that not only allow the mechatronics engineer to collaborate well with other specialists from dierent engineering disciplines, but also allow them to coordinate their activities with the specic needs of mechatronics design. Indeed, knowledge sharing is not limited to the knowledge models to be shared, but also to the collaborative process to solve multidisciplinary design problems in a collaborative manner.

Research issues

In the previous section, I presented our three research themes related to integrated and collaborative design of mechatronic systems. However, several issues have been identied that need to be addressed to achieve the research objectives.

These issues can be summarized by the three research questions below:

Issue 1: How can we integrate and evaluate the DFX metrics at the preliminary phases of mechatronic design using MBSE?

Issue 2: How can we integrate compact models for multiphysics simulation to verify mechatronics design?

Issue 3: How can we manage the knowledge for eective and ecient collaboration between the mechatronic system engineer and other engineers from specic engineering domains related to MDAO, multiphysics simulation and manufacturing?

In the following sections of this chapter, I will detail our contributions to address the above issues.

MBSE-based approaches for the integrated design of mechatronic systems

The integrated design of a mechatronic system requires the development of an approach that allows, on the one hand, the simultaneous development of product models and modeling processes of the mechatronic system, and on the other hand, the integration of DFX metrics and their evaluation. Thus, this part of the contribution will be divided into two sub-sections:

Integrating product model with production process model for mechatronics design.

MBSE approaches to integrate DFX for mechatronics design 1.2.1 Production process modeling for mechatronic product design

The goal of a mechatronic design is not only to develop a product that meets the requested functionalities and the desired performance requirements, but also a product that can be manufactured with the available means, which are generally dicult 1.2. MBSE-based approaches for the integrated design of mechatronic systems 41

to modify. However, for the design of innovative mechatronic products, it is often necessary to adapt the means of production to achieve innovative design solutions.

Moreover, modern production systems are more complex and sophisticated oering more production possibilities with a capacity of adaptation of the production system with the products to be realized by taking advantage of their recongurability.

Thus, it is necessary to model the production system together with the mechatronic product in the upstream phases of design of the mechatronic product.

The objective of this section is to address the following two issues:

How can the production system be jointly modeled with the mechatronic product?

How can we develop a simulation model to verify the recongurability of a recongurable manufacturing system?

These two questions are the subject of the following two contributions.

1.2.1.1 Co-joint modeling of the mechatronic product with the manufacturing process

Background

The link between the development of a product and its production process is a key In addition, [START_REF] Mhenni | Systems engineering approach for the conjoint design of mechatronic products and their manufacturing systems[END_REF] proposed an approach for the joint design of mechatronic products with their production systems. The proposed system engineering approach is based on SysML and it allows taking into account the interdependence between the mechatronic product and its production system.

Several other research works have addressed the problem of how the design team constructs the decision making schedule during the design process. Most of these As designs converge, participants agree to stay within the boundaries of the sets, except in extreme circumstances, so that others can rely on their communication.

Compared to working with one idea at a time, SBCE embraces the principle that processing sets of ideas leads to more robust and overall ecient optimized systems.

Because SBCE can be performed without feedback or rework, development time and costs can be signicantly reduced. However, there are several problems with implementing the SBCE approach in companies. A rst problem is related to how companies determine how many design ideas to pursue, an important step in the early design process. Another problem is how rms organize themselves for the overall design by assigning teams to develop design ideas and ultimately design an architectural system [Ammar et al.].

Proposed approach

The systems engineering design process is illustrated in Figure 1. 16. System architects propose concepts that meet the functional requirements of the product to be developed. The SysML modeling language is proposed to specify these concepts. Therefore, SysML is used to specify all traceability links and attributions between the developed system models.

In addition, SysML is used to specify the appropriate manufacturing capabilities for the product design features. The company's manufacturing knowledge can be formalized as a set of SysML diagrams by the manufacturing engineers. In this way, the initial manufacturing constraints of the production system are identied and the rst set of production system requirements are dened.

Figure 1.17 shows how the design team builds the decision making schedule, based on the SBCE method.

As the design of the mechatronic product evolves to dene the preliminary architecture, taking into account the results of the conceptual and functional development of the product and its production system, the development process of the production system design also evolves to dene the possible design solutions.

The mapping of the design space includes the denition of the dierent alternatives of each subsystem of the mechatronic product and the possible production solutions.

The resulting set of possibilities is communicated to the other design collaborators to incorporate other specic design constraints (DFX), such as cost, quality, manufacturability, maintainability, safety, etc. To get closer to detailed system design, assemblies are integrated in an inter-sectional manner by seeking the intersection of feasible assemblies, imposing minimal constraints, and seeking design robustness.

During this design process, the principle of inter-sectional integration is managed by 1.2. MBSE-based approaches for the integrated design of mechatronic systems 43

Figure 1.16: Systems engineering process for the joint design of a mechatronic product and its production system For the evaluation of DFX metrics, mathematical evaluation models and algorithms to reduce the design space are required. The integration and evaluation of the DFX metrics will be detailed in the dedicated contribution.

Validation of the proposed approach: Case-study of an electronic throttle body

The proposed approach was applied to the case study of an electronic throttle body (ETB). Figure 1.18 shows the components of the ETB. The functional decomposition can be performed at dierent hierarchical levels until the subsystems and components needed to perform the dierent functions can be identied. In this case, we have identied 4 subsystems and 8 components as shown in Figure 1.20. The rst subsystem is composed of the body (1), the cover (7), the air ow control system (3), the gearing system to adapt the mechanical energy [START_REF] Hamza | An analytical approach for modeling a multibody system during pre-design with application to the railway system[END_REF] and the springs (4). The second subsystem is the actuator [START_REF] Guizani | Multidisciplinary optimization of mechatronic systems: Application to an electric vehicle[END_REF]. The third subsystem is the sensing system [START_REF] Hammadi | A new multi-criteria indicator for mechatronic system performance evaluation in preliminary design level[END_REF] to measure the opening/closing angle, and the last subsystem is the controller [START_REF] Hammadi | Multidisciplinary approach for modelling and optimization of road electric vehicles in conceptual design level[END_REF].

The feasible design region, dened as the set of possible solutions, is determined by selecting the possible alternatives for each subsystem or component based on its properties. For example, the possible alternatives for the body (1) can be obtained by considering dierent possibilities for its properties, such as geometry, material and manufacturing process. In this case, the geometry of the ETB body can consist of one block, two blocks or three blocks. The material of the body may be metal or plastic, and in the case of a plastic body, it may consist of one plastic or two plastics (bi-plastic). The manufacturing process of the body can be molding or 1.2. MBSE-based approaches for the integrated design of mechatronic systems 45 By looking at the dierent ETB components that can be produced by manufacturing, we can determine the dierent manufacturing processes and the machines that match with them. Using the same approach as for the ETB components, a SysML diagram can be drawn up containing the dierent alternatives for producing the ETB components. Figure 1.23 shows a SysML diagram representing the design space for choosing production processes and machines.

Once the two design spaces of the product and the production process have been identied, the next step in the SBCE method is to apply the principle of integration by intersection.

The number of solutions is rst reduced by eliminating those outside the intersection. Then, by adding additional constraints and requirements, the sets are reduced more and more until only one solution remains for the ETB as a product and for its production process. Figure 1.24 shows the SysML model of the nal production process of the ETB.

Having dened the traceability links between the objects in the model relating to the product and those relating to its production system, the system architects can easily identify the parts impacted in the case of a change in requirements.

Therefore, it will help them making appropriate decisions to update the product and production system architectures [START_REF] Mhenni | Systems engineering approach for the conjoint design of mechatronic products and their manufacturing systems[END_REF]].

Conclusion of the contribution

In this contribution, we have proposed an approach for the joint design of mechatronic products with their production process in order to take into account the interdependence between them. This approach is based on a systems engineering methodology using SysML as a modeling language and the SBCE method.

By having a single model containing both the product and its production system, all actors in the product design and production process can communicate around this single model. They can dene a design space made up of a set of possibilities, and then add design requirements and manufacturing constraints during the development process until a single solution is reached. This allows the design of the product and its production system to be optimized while reducing iterations in the design process. The developed model also allows to easily evaluate the impact of changes occurring during the design of the product or its production system.

1.2. MBSE-based approaches for the integrated design of mechatronic systems 47 Indeed, manufacturing system conguration has a high impact on system productivity.

Rigorous verication of manufacturing system recongurability through the development of simulation models could reduce infeasible or uneconomic investments. As manufacturing systems become more complex and sophisticated, it is very dicult to easily obtain an executable model from huge system specications. This contribution presents a methodology and a framework to model and verify a Recongurable Manufacturing System (RMS) by simulating conguration alternatives. Figure 1.25 shows the proposed methodological framework for the design of a recongurable manufacturing system.

The idea behind this methodology is that multi-agent systems are the best suited paradigm to simulate the recongurability of RMSs. In a context of model-based systems engineering with SysML language, where one seeks to centralize the specication and verication while keeping traceability during the development cycle, the issue is that it is dicult to model a multi-agent system of a recongurable manufacturing system from SysML specications. Hence the need to make 1.2. MBSE-based approaches for the integrated design of mechatronic systems 49 transitions to ensure continuity between specication, modeling and simulation.

Thus, we propose in this methodology to add a phase of modeling of a holonic architecture from the specications modeled according to a classical approach of systems engineering (supported for example by the standard ISO/IEC 15288).

Then, we detail this holonic architecture to dene a multi-agent system that can be easily implemented in an agent-based simulation environment. Indeed, the holon concept and the agent concept are very similar in many aspects such as autonomy, reactivity, rationality, etc. Other details on multi-agent systems will be given in the section 1.4.2 about collaborative design.

The proposed framework, therefore, allows the designer to progress from the conceptual modeling level to the simulation level through a suggested mapping and transformation process. This process consists of 4 phases to be realized within the specication and modeling environment based on the SysML language which are: 1) the specication of the key characteristics of the RMS; 2) Denition of a holonic architecture of the RMS; 3) Detailing the simulation model of the RMS as a multi-agent system; and 4) implementation of the multi-agent system model in an agent-based simulation tool.

In the rst phase of the methodology, the idea is to use a systems engineering approach based on SysML, as illustrated in section 1.2.1.1, to specify both the product and the production system. Thus, in this phase we specify the requirements of the product, its behavior, its structure, etc. In the same way, for the production system, we specify the attributes of its structure, behavior, capabilities, etc. This phase is performed in a top-down way to get a set of SysML diagrams that model the product and the production system in a hierarchical manner. The models are established in such a way as to ensure traceability between the product and production requirements, on one hand, and the behavioral and structural modeling elements, on the other.

As mentioned above, the obtained SysML models do not allow a simulation of the production process to analyze the recongurability of the RMS. Therefore, in the second phase of the proposed methodology, the obtained system models from The proposed Holonic SysML prole is based on the ADACOR (ADAptive holonic COntrol aRchitecture for distributed manufacturing systems) [START_REF] Leitão | Adacor: A holonic architecture for agile and adaptive manufacturing control[END_REF]. ADACOR is one of the architectures suggested in literature to implement manufacturing control systems that require a dynamic and reactive reconguration based on distributed and intelligent control approaches.

ADACOR merges respectively the benets of hierarchical and heterarchical control structures using an adaptive mechanism. The product holon (PH): used to dene the necessary knowledge for the general operation of the manufacturing system and for selecting the general strategies that respect the planned objectives. The product holons represent the products of the RMS.

The task holon (TH): used to specify the knowledge to manage the execution of the strategies to attend the market demands.

The supervisor holon (SH) : used to describe all the knowledge to coordinate the holons of lower hierarchical levels, such as the coordination of the holon's operations.

The operational holon (OH): used to represent the RMS physical resources that have specic control devices for its automatic operation. It is also used to model the behavior of these resources in accordance with their objectives and capabilities.

The third phase consists in the denition of a metamodel of the multi-agent system using SysML. Indeed, the multi-agent system has the same architecture as the holonic architecture. However, the multi-agent metamodel has more attributes and details that are required for simulation purpose. Thus, we specify the parameters of each agent, the variables (which will vary during the simulation), the operations that represent the functions, etc.

MBSE-based approaches for the integrated design of mechatronic systems 53

The fourth and last step of the methodology is the implementation of the multi-agent simulation model in an agent-based simulation environment. The implementation is dependent on the details specied in the multi-agent system metamodel and the software tool supporting the multi-agent simulation.

To validate this approach, a case-study of an industrial manufacturing system is considered to simulate its recongurability for the purpose of analyzing its productivity. The considered case-study is based on a steel converter process as illustrated in gure 1.27. The nal product of this process is simple steel bars, but as we will see in this example the production system is not so simple to model and simulate. For this reason, we preferred to validate the approach on a simple mechanical product and not a complex mechatronic product. The traceability between the physical elements of the production system and the requirements could be ensured with a requirements diagram that can link structural elements with requirements via "satisfy" relationships. The traceability relations between the requirements themselves could be of the "derive requirement" type as illustrated in the gure 1.30.

The nal simulation of the production system requires the modeling of the behaviors of the dierent parts forming the system. Thus, the behavior of the continuous casting machine has been modeled with a state-machine as shown in gure 1.31. The second phase of the proposed methodology consists in dening the holonic architecture of the production system using the holonic prole dened previously.

MBSE-based approaches for the integrated design of mechatronic systems 55

Figure 1.32 shows the elaborated holonic architecture.

The third phase of the proposed methodology is to dene a multi-agent system of the production system with SysML. Figure 1.33 shows the SysML metamodel of the multi-agent system model to be implemented for the recongurability simulation.

The SysML metamodel contains details about the agents. For instance, the crane agent contains details such as crane position for 3D animation, maximum horizontal speed, maximum weight, etc. We can also nd the list of operations associated to each agent. For the case of the crane agent, operations like make rst move, set task parameters, wait task, etc. are declared.

These operations are implemented using the AnyLogic software, which supports multi-agent simulation. The gure 1.34 shows the simulation results for the steel converter process with two cranes and three continuous casting machines.

The verication process is based on the productivity ratio, throughput rate, machine utilization rate and discontinuity time.

In this way, the operation discontinuity rate of each physical resource is veried. The simulated congurations were with 1, 2 and 3 cranes combined with 1, 2 and 3 continuous casting machines. The best conguration obtained by simulation is the solution with 2 cranes and 3 continuous casting machines, which reduces the discontinuity time 1.2. MBSE-based approaches for the integrated design of mechatronic systems 57 To conclude this contribution, the design issue for this work was how to simulate recongurability of manufacturing systems under the constraint of requirement modications during the design process. For this, a SysML-based methodology was developed in order to reduce the gap between the specication level supported by MBSE and the verication phase supported by multi-agent simulation, while ensuring traceability between requirements and simulation results. This methodology is based on the adaptation of a systems engineering approach using SysML by adding a phase to describe the holonic architecture of the production system and then adding the specication details of a multi-agent simulation model. The last phase is to implement the simulation model in a multi-agent simulation tool. Finally the approach has been validated with a case study of steel converter process.

MBSE approaches to integrate DFX for mechatronics design

DFX allows the integration of production constraints in the upstream phases of mechatronics design. In a MBSE-based design methodology, this requires modeling of DFX metrics and linking their components with the Key Value Attributes (KVA)s 1.2. MBSE-based approaches for the integrated design of mechatronic systems 59 specied with the MBSE. Thus, in this section we will detail the following two contributions:

a MBSE approach for integrating manufacturability and reliability in the design process of mechatronic systems.

a contribution to the integration of assemblability in a MBSE approach.

MBSE approach for integrating manufacturability and reliability in the design process of mechatronic systems

This contribution is part of the thesis of Mohamed Firas BORCHANI [Th5],

which objective is to develop an approach allowing to reduce the number of possible solutions of a mechatronic product based on the two criteria reliability and manufacturability in the preliminary phases of design.

A review of works incorporating manufacturability and reliability in the literature showed several shortcomings:

Use of several types of standards for data exchange between engineers and experts, which delays product development time.

Developing a manufacturability analysis system or software is expensive and requires complex coding to extract manufacturing entities and compare them to geometric rules. In addition, when dealing with a complex shaped part, the system may misinterpret the design information.

The product development framework does not allow stakeholders to exchange ideas and areas of analysis to optimize the part design.

The manufacturability analysis is often based only on a single manufacturing process, which in most cases is machining. Other processes may oer good value for cost.

Constraints related to the manufacturing resources available at the production sites are not taken into account in the manufacturability study.

To overcome these shortcomings, the objective of this contribution is to develop an approach integrating the evaluation of manufacturability and reliability in the design process based on the SBCE principles and using SysML language. gure 1.35 illustrates the idea of the approach.

Compared to a classical systems engineering approach using MBSE tools, the approach proposes to use a new SysML prole (gure 1.36) allowing experts from dierent domains (manufacturing, reliability, etc.) to bring their contributions at dierent design levels according to the SBCE principles. In this diagram we dene the new KVA associated to DFX metrics: manufacturability, reliability, durability, cost, etc. For instance reliability attributes are associated to the 1.2. MBSE-based approaches for the integrated design of mechatronic systems 61

Figure 1.35: Interdisciplinary collaborative mechatronics design using MBSE and SBCE system/sub-system activities that could represent the system functionalities. On the other hand, manufacturability attributes are associated to both system activity and process features, which could represent a manufacturing operation. To create the solution set, we use the allocation possibilities of SysML (allocation Chapter 1. Collaborative multidisciplinary design of mechatronic systems matrices) to associate a set of physical solutions to a system functionality and a set of realization processes for the physical components.

The design process starts by associating values to the KVAs components either from the capitalized experience of the company, or by consulting experts or simply by looking in the catalogs of the suppliers to seek information, such as failure probability for reliability assessment. Next, the KVAs are sorted using an analytical hierarchy process (AHP), where the sorting criteria are set in advance according to the company's needs and the recommendations of the various stakeholders.

To map the design space, design participants and subsystem teams dene the scope of the design work required as well as the feasible design options/regions.

The design solution set is exported in the form of a graph (GraphML format) for the evaluation of the DFX metrics and the reduction process of the number of solutions.

The evaluation of DFX metrics is done using mathematical models and algorithms to calculate the values of the metrics from the KVAs. Specically, for the reliability assessment, a Failure Modes and Eects Analysis (FMEA) method was used in this work. The idea is to outline Severity (S), Occurrence (O) and Detection (D) rating scales. Severity indicates the gravity of the eects of a failure mode, occurrence denotes the probability of a failure occurring, and detection measures a failure's visibility that is the attitude of a failure mode to be identied by controls or inspections. Each parameter is correlated to a score range (chosen to be from minimum of 1 to a maximum of 5 in this work). To calculate and compare subsystem's criticities, each component criticity is calculated using risk priority number (RPN), which is dened as the product of the three components (parameters) S, O and D:

RP N = S × O × D (1.1)
Once the reliability metric is evaluated for each solution in the solution set, a developed algorithm is used to reduce the solution set by eliminating weak solutions and those that do not meet the design criteria.

The owchart describing the reliability assessment process is presented in gure 1.37

Thus, for each DFX metric, mathematical models and a solution reduction procedure need to be established.

To validate this approach, an electric compressor system was considered as a mechatronic product used for air conditioning application in automotive. Figure 1.38 shows a picture of the considered system and its components.

Electric compressors have the advantages of low refrigerant emissions, exible packaging, and ecient variable-speed operation. This automotive module constitutes the interface between the low and high-pressure sides of the refrigerant circuit.

The design space in this case study is limited to 15 solutions obtained by combining 3 possibilities of motors (Brushless, step by step and DC motor) with 5 possibilities of compressing techniques (Scroll, axial, lobe, screw and centrifugal). For the other compressor components, we have made the assumption that there is one unique 1.2. MBSE-based approaches for the integrated design of mechatronic systems 63 After applying the proposed methodology only three nal solutions were retained.

The nal decision could be made with a trade-o by comparing the three solutions using, for example, a radar chart as illustrated in gure 1.39 and reliability. This will allow the dierent actors of the mechatronic product development cycle to add their knowledge about the product in the preliminary design phases. For each metric, mathematical models and logic rules for evaluation are needed, and algorithms to reduce the design space must also be developed. The nal choice of the solution could be made based on a trade-o analysis comparing the dierent DFX metrics with the system performance metrics.

Contribution to the integration of assemblability in the MBSE appraoch

This work is part of the thesis of the doctoral student Rihab Brahmi [Th7]. We position ourselves in the context of the development of a complex mechanical or mechatronic product where assembly plays an important role in the design. In this 1.2. MBSE-based approaches for the integrated design of mechatronic systems 65 situation, a collaboration between the system engineer and the 3D CAD expert is necessary to analyze the impact of assemblability on functionality. Indeed, before embarking on the manufacture of such complex products, it is necessary to perform a functional verication of the assembly, which determines whether individual components are required and verify their functions. Functional analysis also allows the verication that all product functions are achieved by the design and that all the design requirements are met. The analysis of the assemblability, on its side, allows the systems engineer to determine:

whether the number of components can be reduced, whether some components can be replaced by others allowing self-positioning and self-inserting, the ease of assembly of parts with clearance if the need for reorientation during assembly can be minimized if parts that cannot be installed incorrectly can be eliminated if symmetrical parts can be maximized etc.

In this contribution, we propose an approach aiming at improving the collaboration between the systems engineer and the CAD expert.

The proposed approach is based on three phases which are :

Phase 1 -a preliminary MBSE study: in this step, a global study of the product from a functional point of view is performed by the systems engineer, with a global specication of the assembly requirements.

Phase 2 -a 3D CAD design development: in this step, the designer proposes a 3D design that could meet the need, with a the preliminary results of the assembly analysis.

Phase 3 -enrichment of the MBSE and validation of the design: in this step, the systems engineer checks if the proposed design solution is satisfactory by verifying the compatibility between the system functionality and its assemblability.

The proposed methodology is illustrated directly on a case study of a bicycle pedal with ashing LED lights. The product need can be described as following:

to reassure parents who want their children to remain visible, even if their dynamo lamp does not work, we need to develop a pedal that increases the cyclist's visibility and requires no maintenance: no batteries, no wires, no moving parts and no risk of failure. The illustrative example is inspired from an industrial example designed Chapter 1. Collaborative multidisciplinary design of mechatronic systems This product will be considered as a baseline for the development of a simpler, more ecient and innovative mechatronic product. The functional specications can be presented as following: when pedaling, a small generator integrated to each pedal produces current and powers the ashing lights. The surplus energy produced will be stored and then released when the cyclist is not pedaling (downhill, at a standstill, etc.). The battery life should be at least 5 minutes.

The rst step of the rst phase (preliminary MBSE study) consists in deciphering all the needs. For instance, the primary need of the pedal is to improve road safety by increasing the visibility of cyclists at night, even in adverse weather conditions.

The second step of the rst phase is the denition of the functional requirements.

The functional description must be complete, coherent and have a very clear structure in order to be understandable during the validation phase. MBSE with

SysML were chosen for their potential to describe the product from several points of view. For the example discussed, a functional requirements diagram is developed as illustrated in gure 1.41 to present a part of the requirements related to the transmission of mechanical energy.

After studying the product from a functional point of view, the systems engineer can propose an initial structure of the assembly. Modeled with SysML block denition diagram "BDD", this structure essentially contains the parts that are the basis of the system's operation. As illustrated in gure 1.42, the initial structure of the example treated can be composed of ve essential parts which are: a pedal body and a pedal axle used to transmit the mechanical energy provided by the cyclist during pedaling; a double intermediate wheel that multiplies the rotation of the axle; a generator to convert the kinetic energy into electrical energy to have light ashes and an integrated circuit used to store the surplus of energy produced.

The last step of the rst phase is to dene the assembly requirements and their traceability with other design specication (requirements, functional, structure and behavior). This step has a major importance in improving the quality of the assembly, because it allows the system engineer to quickly identify the impact of any 1.2. MBSE-based approaches for the integrated design of mechatronic systems 67 The proposed design solution must be evaluated from an assembly point of view.

For this, we propose to investigate three KVAs, which are: the maximum number of parts, total assembly time (TAT) and assembly eciency (AE). With the Maximum number of parts KVA, the 3D CAD designer analyzes the assembly by checking whether the total number of parts is optimal or can be reduced.

The proposed KVA is based on a procedure that attempts to minimize the total number of parts. According to Boothroyd [START_REF] Boothroyd | Design for assembly and disassembly[END_REF], the optimal number of parts in the assembly design can be calculated using a procedure

based on the answer to four main questions:

1. Is the part a base?

2. Is there a functional relative movement between the part and the others already assembled?

3. Does the part need to be made of dierent materials or be isolated from other parts already assembled?

4. Does the part need to be separated from other parts to allow for its assembly or disassembly?

For each part of the assembly, if the answer to all four questions is "no", the part in question is not needed and can be eliminated from the assembly design. This will determine the minimum number N min of parts needed for assembly.

The second step of the assemblability analysis is to evaluate the possible assembly sequence plans (ASPs). Figure 1.45 shows a list of possible ASPs.

The evaluation of the ASPs is performed by determining the total assembly time T AT and the assembly eciency (AE). systems

AE(%) = T min × N min T AT × 100 (1.2)
Where:

T min : Minimum assembly time in the industry's assembly line.

N min : Minimum theoretical number of parts.

T AT : Total Assembly Time of the product.

The current work of this thesis focuses on developing algorithms to automate the reduction of assembly sequence plans and to enrich the SysML model with new assembly data and with the results of the assembly analysis. For the example discussed, the updated structure and a zoom on the pedal axle part are shown in gure 1.46.

The last phase on the proposed approach is to validate the design assembly from a functional and assembly point of views. This work is in progress for the development of algorithms to evaluate a set of assembly sequences, by taking into account the functionality and performance of the system, and automatically reduce the number of solutions to keep only the most ecient ones.

To conclude this contribution, the objective is to validate the 3D design solutions proposed to meet a specication prescribing the functionality of a mechanical or mechatronic product. The evaluation criteria considered here are the functionality of the system and its assemblability. This work is in progress with a thesis defense planned for 2022. The outcome of this work could be coupled with the two previous contributions to propose a DFX platform for mechatronic products. ignoring the details of the geometry. However, for a good choice of the mechatronic system architecture solution in the preliminary design phases, some physics require a level of detail requiring the consideration of a certain dimension of the geometry. This is the typical case of the vibration of exible structures which could have an impact on the decision of choosing the mechatronic design solution.

This contribution is part of the work of Ghazoi HAMZA [Th1], whose objective is to develop compact models to model the vibration to simulate the vibration in the upstream phases of mechatronic design.

The main contribution of this work is to propose a method for the preliminary design of mechatronic systems based on an analytical approach, taking into account the eect of vibrations. For this, compact analytical models have been developed and implemented in Modelica/Dymola to study the vibration behavior of mechatronic systems. The idea is to develop libraries of Modelica components for multiphysics modeling that are stable and ecient for the preliminary design Chapter 1. Collaborative multidisciplinary design of mechatronic systems of a mechatronic system. This approach should provide the designer with a large space of solutions to choose from. We illustrate this approach with a case-study of a mechatronic system which is a wind turbine. as follows [START_REF] Bambill | Forced vibrations of a clamped-free beam with a mass at the free end with an external periodic disturbance acting on the mass with applications in ships' structures[END_REF]:

EI ∂ 4 w(x, t) ∂x 4 + ρS ∂ 2 w(x, t) ∂x 2 = 0 (1.3)
The beam has a length L, second moment of the cross section I and Young's modulus E. M is the concentrated mass, M t is the mass of the beam, ρ is the density of the material and S is the cross-sectional area. We assume that the beam is subjected to an unbalanced force applied to the concentrated mass, through a cyclic force F (x, t), with:

F (x, t) = p 0 cos(Ωt) = meΩ 2 cos(Ωt)

(1.4)

Multiphysics simulation methods for mechatronics design 73

Where, p 0 is the excitation amplitude, m is the imbalance mass, e is the imbalance radius and Ω is the rotational speed. Solution to equation 1.3 must comply with the following boundary conditions:

w(0, t) = 0; ∂w(0, t) ∂x = 0; ∂ 2 w(L, t) ∂x 2 = 0; -[-EI ∂ 3 w(L, t) ∂x 3 ] = M ∂ 2 w(L, t) ∂t 2 -p 0 cos(Ωt) (1.5)
A separation of variable method is followed to nd the solution of equation 1.3, which gives:

w(x, t) = W (x)T (t) = W (x)cos(ωt) (1.6)
By substituting equation 1.6 into equation 1.3, we obtain:

W (x) (IV ) W (x) - ρS EI Ω 2 = k 4 (1.7)
By assuming the solution of W (x) in the form:

W (x) = Acos(kx) + Bsin(kx) + Ccosh(kx) + Dsinh(kx) (1.8)
where, sinh and cosh are hyperbolic functions, and A, B, C and D are to be determined from the boundary conditions of the beam with:

k 2 = ω ρS EI (1.9)
The fundamental angular frequency is:

ω 1 = α 2 1 L 2 EI ρS (1.10)
where, α 1 is the fundamental eigenvalue, it depends on the value of the mass ratio r = M Mt .

Applying the boundary conditions:

W (0) = 0; dW (0) dx x=0 = 0; -EI d 3 W (x) d 3 x x=L = p 0 + M Ω 2 W (L) (1.11)
The deection expression gives the following relation for the beam deection amplitude: 12) with:

W (x) = - p 0 L 3 EI β 1 α 3 1 ( Ω ω 1 ) 3/2 + β 2 mα 4 1 ( Ω ω 1 ) 2 sin(kx)-sinh(kx)- sin(kL) + sinh(kL) cos(kL) + cosh(kL) (cos(kx)-cosh(kx)) (1.
β 1 = -sin(kL) + sinh(kL) cos(kL) + cosh(kL) (sin(kL) -sinh(kL)) -cos(kL) -cosh(kL) (1.13) and:

β 2 = sin(kL) -sinh(kL) -sin(kL) + sinh(kL) cos(kL) + cosh(kL) (cos(kL) -cosh(kL)) (1.14) Chapter 1. Collaborative multidisciplinary design of mechatronic systems

Analytical model of a rotating exible beam

The rotating beam considered in this contribution is assumed to be a prismatic cantilever of length L with a hollow rectangular cross section as shown in gure 1.48. Depending on the Euler-Bernoulli theory, the governing dierential equation for the rotating beam under ap wise vibration is given by [START_REF] Arrigan | Control of apwise vibrations in wind turbine blades using semi-active tuned mass dampers[END_REF]:

µ(z) ∂ 2 u ∂t 2 + ∂ 2 ∂z 2 E b I b ∂ 2 u ∂z 2 - ∂ ∂z T (z) ∂u ∂z = p(z, t) (1.15)
The centrifugal tension force T (z) at a distance z from the origin is given by:

T (z) = Ω 2 L z yµ(y)dy (1.16)
where, u is the relative movement of a point with respect to its static deected location. The applied force per unit length p is the unit mass of the beam per length, Ω is the rotational speed of the beam, which is assumed to be constant, E b is the modulus of elasticity, I b is the area moment of inertia of the beam crosssection. The impact of gravity on the rotation of the beam is considered to be negligible compared to centrifugal impact.

The clamped and free boundary conditions for the rotating beam are given as follows:

u = ∂u ∂z = 0 at z = 0; ∂ 2 u ∂z 2 = ∂ 3 u ∂z 3 = 0; at z = L (1.17)
The mode summation method is considered for the solution, that is :

u(z, t) = n i=1 Φ i (z)q i (t) (1.18)
where, Φ i (z, t) are the shape functions and q i (t) are the generalized coordinates.

The shape functions must be linearly independent and must satisfy the geometric

M = L 0 µ(z)Φ(z)Φ T (z)dz (1.19)
The potential energy of the system is:

U d (q) = 1 2 q T (t)Kq(t) -q T (t)F (t) (1.20)
where, K is the generalized stiness matrix of the blade which is:

K = K e + K g ,
where K e is the elastic stiness matrix, dened by:

K e = L 0 EI(z) d 2 Φ(z) dz 2 d 2 Φ(z) dz 2 T dz (1.21)
and K g is the geometric stiness matrix dened by:

K g = L 0 T (z) dΦ(z) dz dΦ(z) dz T dz (1.22)
The dynamic load vector F (t) is dened by:

F (t) = L 0 Φ (z)p(z, t)dz (1.23)
The dynamic model is formulated using the Lagrangian formulation expressed by:

d dt ∂L ∂ qT - ∂L ∂q T = F (t) = -C q (1.24)
where,

L( q, q) = T d ( q) -U d (q) = 1 2 q T M q - 1 2 q T Kq + q T F (t) (1.25)
By substituting the equation 1.25 into the Lagrangian formulation 1.24, we obtain:

M q + C q + Kq = F (t) (1.26)
where, q, q, q are the acceleration, velocity and displacement vectors and C is the damping matrix.

The beam is considered to be vibrating in its fundamental mode and a quadratic mode shape is assumed. This allowes the continuous beam to be reduced to a single degree of freedom (SDOF). The bending motion of the beam in the yz plan is only of interest, where this motion is called apping motion.

The relative displacement of the beam u(z, t) can be expressed as:

u(z, t) = φ(z)q(t) (1.27)
The shape function is taken as:

φ(z) = 3 2 z L 2 1 - 1 3 z L (1.28)
Chapter 1. Collaborative multidisciplinary design of mechatronic systems

The generalized mass matrix and stiness matrix are then:

M = 3 140 µL; K e = 3 EI L 3 ; K g = 81 280 µLΩ 2 (1.29)
The angular eigen-frequency at Ω = 0 can be expressed as:

ω 1,0 = K e M = 140 11
EI µL 4 = 3.5675 EI µL 4
(1.30)

and the angular frequency at Ω > 0 becomes:

ω 1 = K e M + K g M = ω 1,0 1 + K g K e = ω 1,0 1 + 27 22 Ω 2 ω 2 1,0 (1.31)
We consider that the applied load is a triangular harmonic distributed by unit, the frequency of this sinusoid being equal to the rotation frequency as shown in gure 1.48. This load can be expressed as follows:

p(z, t) = p 0 (t) z L = p 0 cos(Ωt) z L (1.32)
For a zero initial condition and without taking into account the damping eect, the analytical solution in steady state is then :

u(z, t) = 11Lp 0 40M (ω 2 1 -Ω 2 ) cos(Ωt) × 3 2 z L 2 1 - 1 3 z L (1.33)
1.3.1.3 Implementation of the exible structures in Modelica and application to case-study of a Wind Turbine

The previously developed equations for a exible beam with a mass and a rotating exible beam were implemented using the object-oriented and equation-based language Modelica. Every model is encapsulated with a Modelica object and the coupling between the components is ensured with connectors. Modelica connectors are instances of connector classes, which are used to connect the models of components to each other to dene a model of a complex system.

Two kinds of variables are used in connectors: Non-ow variables which are also called potential variables, and ow variables which represent some kind of ow.

Modelica generates automatically the coupling equations when components are connected:

Equality coupling, for non-ow variables Sum-to-zero coupling, for ow variables

The value of a ow variable is positive when the ow is into the component.

Frame connector of the Multibody Modelica library was used in this work for the two components: exible beam with a mass and the rotating exible beam. Frame To validate the modeling approach a case-study of the vibration analysis of a wind turbine was considered. It is known that wind turbines operate in hostile environments. The variable loads with an elastic structure create an ideal ground for induced vibrations. The wind turbine structure is idealized by replacing it with an assembling of a exible tower with a rigid mass at the top representing the nacelle, and the blades modeled with rotating beams. It will be assumed that the tower is subjected only to a load which represents the eect of rotor imbalance. The Modelica model of the study is illustrated by the gure 1.50.

In this analysis, the rotor is subjected to a thrust force caused by the wind, which in turn is transferred by the nacelle component on the top of the tower. The deformation of the blade and the tower occurs in the same plane. This model thus allows to study the dynamic interaction between the tower and the blade.

For the validation purpose, the vibration analysis results generated by the analytical models developed in this study and implemented with Modelica were compared to the analysis results generated using the components of the commercial FlexibleBodies Modelica library developed by BAUSCH-GALL GmbH and Dassault Systèmes in Dymola software. The comparison of the results shows a strong dierence between the two models in the transient phase which is 33%, but it is only 5% once the steady state regime is established. Since the purpose of the model is to be used in the preliminary design phase allowing the quick analysis of the interactions of the dierent disciplines and physics of mechatronics, it can be stated that the developed models allow to provide this utility to mechatronic designers to make the right decisions before embarking on detailed studies with expensive 3D CAD models and nite element calculations.

Finally, the proposed methodology of developing compact models using analytical approach with Modelica implementation can be easily applied to other physics such thermal and electromagnetic compatibility. share and exchange skills and knowledge. This requires, on the one hand, some kind of database to capitalize knowledge and its instantaneous reuse, but also to develop software means to assist designers during the design process.

In this context, we will present in this section two contributions. The rst one concerns the development of a methodology allowing to formalize the knowledge related to both the mechatronic product and its design process. The second contribution concerns the development of a collaborative design approach where designers are assisted by a multi-agent system.

Collaborative Design Process and Product Knowledge (CDPPK) Methodology

This contribution is part of the thesis of Mehdi MCHAREK [Th3] about the knowledge management of the mechatronic design: product and process.

Indeed, the success of any collaboration framework is strongly linked to the need to share knowledge between actors to ensure a common representation of the problem to be solved. However, the shared knowledge is composed of fragments that are Chapter 1. Collaborative multidisciplinary design of mechatronic systems created by various actors according to their expertise domain. An important aspect to be considered is then the adaptation to these dierent viewpoints between three types of actors : System engineer or system architect, and specialists in simulation and optimization.

One may wonder how we can adapt the already available knowledge conguration management (KCM) approaches in a way that covers the entire design cycle.

Our goal is to manage and communicate knowledge between the decomposition phase and the integration phase of the development cycle of a mechatronic product. Our framework aims at overcoming collaboration and reuse issues. For collaboration, a new way of viewing the product is necessary to nd solutions that lie across disciplinary boundaries. For the reuse, the previously proposed KCM model, presented in section 1.1.2.6, focuses on declarative knowledge (know-what).

It is important that this knowledge helps to understand the product, but it must be complemented by process intentions (know-how) to facilitate the reuse of a design project.

The new KCM model that we proposed, illustrated in gure 1.52, is inspired by KCM structure and the new contribution lies rstly on reorganizing parameters in order to facilitate collaboration. In fact, all parameters involved must be reected in a well formalized conceptual infrastructure to ensure an eective collaboration between the system architecture (SA) and specialists in modeling and simulation (MS). On the one hand, we propose the use of ICEs as a point of reference for SA actors. On the other hand, MS actors have only to instantiate the parameters that they need from specic ICEs. Subsequently, the MS engineers become detached from the conceptualization task of the ICEs.

Additionally, for each parameter an in/out ow attribute is added to facilitate the connection between the UCs of MS engineers, and create a collaborative network that will be used later for MSMDAO collaboration. The main concepts of the new model and the methodology to connect SAMS and MSMDAO will be detailed in the next sections.

CDPPK Main concepts

Information Core Entity (ICE)

The concept of ICE is kept in this methodology to capitalize knowledge. The dierence with the previous methodology presented in the background section 1.1.2.6 is that the ICE is considered here as an organizational structure only for the decomposition phase. System engineers use ICE to decompose the system into functional subsystems and save the associated parameters and constraints.

Therefore, ICE is used here to transform product data into product information.

The parameters can be: reals, intervals, vectors and matrices to give more exibility to the stakeholders. For the constraints, we consider only interval constraints in Stakeholders can add here the parameters and the constraints. DPK can be considered in this stage as a product information base. When the collaboration starts, stakeholders refer to this base which represents the system level. DPK also plays an important role in conict management, as we will explain later. After the collaboration, ICEs will contain the nal product results. Thus, DPK generates product knowledge from information stored in ICEs.

Usage Process Conguration (UPC)

This new class diers from the UC dened in KCM. Instead of aecting a block of parameters in the form of ICE instances, we propose to break ICEs and give the exibility to disciplinary engineers in the choice of parameters that they need. Our contribution is to dene input/output ows for the instantiated parameters. This considerably facilitates the collaboration and data exchange between stakeholders and helps to construct a collaboration network.

Collaborative Design Process (CDP)

It groups the Usage Process Conguration (UPC)s present in the collaboration.

Chapter 1. Collaborative multidisciplinary design of mechatronic systems

In Collaborative Design Process (CDP), we can generate a global collaboration process. It characterizes the originality of this approach by achieving the traceability of the collaboration evolution for reuse perspective. This collaboration graph presents the design process knowledge.

Project Domain (PD)

The concept of Project Domain (PD) makes it possible to dene a macroscopic context for the denition of the basis of ICEs and the use of congurations. Indeed, we can qualify a PD as a global usage environment. For example, a system can be dened in PD and can be decomposed into major subsystems. In this way, we capitalize the respective knowledge to each subsystem and reduce complexity in collaboration and traceability. Each Knowledge Domain has its own base of ICEs and congurations to facilitate the reuse.

CDPPK metamodel

This new model is adapted to the decomposition phase. Each functional subsystem is represented by an ICE. Then, in the integration phase, each specic domain tool is represented by a UPC. We notice that the knowledge cycle (data-informationknowledge) for the design process and product is respected The standard denes also conguration items that are components of the global conguration to ensure the nal use of information and allow users to converge to a single product. In our model, these items are the UPCs.

CDPPK process

Actors in the design cycle are submerged in a heterogeneous tools environment and information ow. They collaborate with traditional and informal ways (email, meeting...). These ways are error-prone and dicult to trace for reuse perspectives.

Whereas, if we have eective collaboration we can acquire not only short-term benets, during the product development, but also long-term ones, during the reuse process. Knowledge Management (KM) was proposed to improve collaboration performance in mechatronic design. Nevertheless, it is not limited to its technological aspect for it, also, includes a sociotechnical facet which considers knowledge as a resource participating in companies' performance [START_REF] Arduin | From knowledge sharing to collaborative decision making[END_REF]. A very common problem of a failed collaborative framework is that it does not meet the users' real tasks. Therefore, the CDPPK's methodology is proposed with regards The process is summarized as follows:

Step1: Project Requirements:

The project manager analyses the customer requirements. Accordingly, they create a knowledge conguration KC and identify the actors needed for each step. Their main objective is to lead the team towards accomplishing the project.

Step2: Conceptual Design:

Based on customer requirements, system engineers dene the functions of the system. They can explore several architectures according to the dened functions, in this work, we will focus on the development of one architecture. Our hypothesis is to decompose the system into functional subsystems. Each one of the latter is represented by an ICE. The available parameters and constraints (from requirements and previous works) are added in this phase to the ICEs.

Step3: Detailed Design:

Here, the previously created ICEs are enriched with all the crucial parameters necessary for the integration phase. To do so, we recommend a meeting between the dierent stakeholders. A knowledge expert can also capitalize the crucial knowledge necessary for the collaboration. Semi-automatic extraction of parameters methods exists also. This step is a direct intermediate between the decomposition and the Chapter 1. Collaborative multidisciplinary design of mechatronic systems Step5: System Validation:

Thanks to the product knowledge in DPK and the process knowledge in CDP, the project manager has a holistic view of the design cycle. They need to check the collaboration state and the recorded conicts between system engineers and disciplinary designers in order to assess the situation and make decisions. The purpose of conict management is to detect inconsistencies and trace this Figure 1.55: System and interdisciplinary conicts management in CDPPK information back to users to allow them to iterate, make decisions and nally converge towards a common solution. Once the conicts are detected, it is a matter of putting the information back to the dierent users. In the case of interdisciplinary conicts, the conicts are listed in CDP and managed directly by disciplinary engineers. In the case of system conicts, it is the DPK that is responsible for displaying this information for system engineers. In this way, the traceability and coherence of manipulated knowledge is guaranteed in the entire cycle.

Validation of the CDPPK methodology

For the validation purpose, we developed a demonstrator using Python language to implement the CDPPK model. The gure 1.56 shows the implementation of ETB systems ICEs in the CDPPK demonstrator. We developed the dierent simulation models To sum up, with the CDPPK model, knowledge generated by the collaborative activity can be stored into product knowledge and design process knowledge in a way that it can be easily reused. On one side, the product knowledge serves as a source of information for system engineers and disciplinary engineers. The system engineers use this knowledge to decompose the product parameters and requirements. This is suitable for their system view. The disciplinary engineers select the parameters that they need to collaborate to search the optimal values. On the other side, the dynamic process knowledge breaks with the traditional predened design process which is not suitable for concurrent engineering. This contribution is part of the thesis of Amir GUIZANI [Th1] about a collaborative design approach, combining designers and virtual agents, to collectively nd optimal solutions that satises the constraints and performance requirements of a mechatronic design. The proposed approach is based on multi-agent system.

The objective is to adapt this technique with the distributed collaborative design to benet from its properties. We start by recalling the denition of multi-agent systems and their properties to detail the contribution.

Several denitions attributed to the notion of agent exist in the literature. However, the denition of the term agent proposed by Ferber and Perrot [Jacques, 1995] is widely used in the scientic community. Ferber and Perrot dene an agent as being a physical (hard) or software (soft) entity located in an environment (real or virtual)

which:

is able to act in its environment, can communicate with other agents of the same platform or dierent platforms, is able to perceive its environment in a limited way, has its own resources, has skills oers services, have a partial view of its surroundings, can possibly recur.

The denition which was given later by [Jennings et al., 1998] is: "an agent is a computer system, located in an environment and which acts in an autonomous and exible way to achieve the objectives for which it was designed".

In order to better understand the notion of agent, we can identify several properties that can be attributed to agents [START_REF] Wooldridge | The cooperative problem-solving process[END_REF]:

Autonomy: the ability of an agent to act alone to achieve these objectives, and is not subject to any control over his internal state, nor over the actions it performs.

Social capacity: the ability of an agent to interact with other agents and possibly with humans through communication languages.

Reactivity: the ability of an agent to perceive its environment and to respond in a timely manner to the various changes that occur in it.

Adaptability: the ability of an agent to learn and improve with experience.

Chapter 1. Collaborative multidisciplinary design of mechatronic systems

Pro-activity: the agents must not react only to stimuli coming from their environment, they must also be able to show behaviors directed by internal objectives and this by taking initiatives.

Continuous over time: it is a process that is continuously in execution.

Many software platforms exist for the development of multi-agent systems. The choice of a platform depends on how easy it is to implement the dierent types (models) of agent and how easy it is to use. Indeed, the internal characteristics of the agents are more or less easy to implement depending on the development platform used. Among the best known platforms, we nd: CORMAS, DoMIS, JACK, JADE, Jadex, Janus, Madkit, etc.

JADE for Java Agent DEvelopment is an open source Multi-Agent System (MAS) development framework based on the Java language. It oers in particular an advanced support of the FIPA-ACL standard, as well as tools for syntactic validation of messages between agents based on ontologies.

In our case, we chose the Java Agent Development (JADE) platform [START_REF] Bellifemine | Jadea pa-compliant agent framework[END_REF] The JADE application is deployed on one or more machines. It hosts a set of uniquely identied agents that can communicate bidirectionally with other agents.

Each agent runs in a secondary container that provides its execution environment;

it can migrate within the platform. Each platform must have a main container (mainContainer). The framework for the agent-based collaborative design is shown in gure 1.60.

The agent platform (AP) is the software environment in which multiple agents can be created, deployed, registered, located, and communicate. Each agent must be registered with the Agent Management References Model (AMRF) descriptions, which provide a standard infrastructure with well-dened functions, to provide specic services. The agent management system (AMS) is a registry directory that assigns a unique identier to each agent (white page service: automatically references agents by name when they enter the system). The directory facilitator (DF) is a registry directory that provides the yellow pages service (referencing agents Figure 1.59: Case of collaboration of two design agents through a JADE platform [Guizani, 2016] by their service(s)). Agent's services can be queried by the information stored in DF. The message transport system (MTS) coordinates the communication between agents of the same or dierent agent platforms.

To the default agents dened in JADE, we added to new types of agents:

The design agent (DA): which is the piece of software associated to disciplinary team or member participating in mechatronic design.

The coordinating agent: which is a JADE agent that coordinates the collaboration during a design problem resolution. The coordinating agent could be associated to a real physical designer or a project manager.

The denition of the number of design agents depends on how the multidisciplinary design problem will be decomposed into more solvable sub-problems (partitions). This decomposition can be done according to disciplines, use-cases, design tools, design knowledge, etc.

The coordinating Agent (CA) resides in a primary main-container, and each design agent (DA) is deployed in a secondary container. These containers can be placed separately in dierent machines and distinguished by dierent IP addresses.

Coordination protocols specify the sequence of messages between agents. They dene the messages to be sent by specifying: the performative, the content, the recipient(s) and establish the responses to these messages. For our approach, the message sent from a coordinating agent (CA) to a design agent (DA) is dened as the formulation of an optimization sub-problem of the design, in which the objectives, the constraints and the design variables are specied. The message sent from a design agent (DA) to the coordinating agent (CA) is a set of possible systems The design problem wa partitioned into two design sub-problems, one associated to the determination of the batterie parameters and the second for determining the other parameters of the propulsion system. Thus, two design agents DA 1 and DA 2 were implemented in JADE with a coordinating agent CA. After solving the two optimization sub-problems, each design agents returns a table of values containing the possible solutions. The coordinating agent then searches for common solutions of the design problem.

To conclude this contribution, a collaborative design methodology based on multi-agent systems has been proposed and a proof of concept has validated the proposal. For this, two types of agents, which are design agent and coordinating agent, were proposed. The diculty lies in the programming of the agents' behaviors. We proposed to associate a design agent to each design partition. The exchange of messages between the agents during the cooperative solution search phase is done on the basis of a query associated to a formulation of an optimization 96 Chapter 1. Collaborative multidisciplinary design of mechatronic systems sub-problem and the response is a set of design solutions.

As perspectives, we propose to develop a collaborative design platform integrating knowledge management, by extension of the ICE concept, with the mutli-agent system, where agents can learn during the collaborative design process, with deep learning for example, which allows virtual agents to assist designers, with the knowledge acquired, during the design process.

Conclusions and synthesis

In this chapter, I have presented 7 contributions in the eld of integrated and collaborative design of mechatronic systems.

The rst contribution concerned the co-joint modeling of the mechatronic product and the production process. In this contribution a systems engineering approach supporting the SBCE method has been proposed. The dierent attributes of both the mechatronic product and its production system are specied and modeled with SysML. The SBCE method allows to cascade decisions according to the availability of information. This allows to explore a large panel of design solutions and system architectures in the early design phases, integrating the production requirements, before deciding on the solution to be detailed.

The second contribution, which deals with the modeling and evaluation of the recongurability of manufacturing systems, aims at evolving the MBSE model of a manufacturing system developed with SysML into a simulation model allowing the verication of its recongurability. Indeed, the recongurability of the manufacturing system allows the designer to verify several architectures of a product in early design phases. For this purpose, a new SysML prole has been developed, using the DSL possibilities of UML/SysML, to model the structure of the manufacturing system according to the Adaptive holonic architecture (ADACOR).

This holonic architecture is therefore used by the designer to develop a metamodel of the multi-agent system that will be used for simulation. Indeed, holons and agents share various similar attributes allowing to model the recongurability of a manufacturing system. The metamodel of the multi-agent system developed in the SysML environment allows, on the one hand, to ensure traceability with the attributes of the manufacturing system and the product to be developed, and on the other hand, it will be used as a support for the implementation of the multi-agent simulation model in an agent-based simulation environment.

In the third contribution, about a MBSE approach for integrating manufacturability and reliability in the design process of mechatronic systems, a new SysML prole allowing the specication of reliability and manufacturability was developed. Also developped using the DSL possibilities of UML/SysML, this prole diagram allows experts from dierent domains (manufacturing, reliability, etc.) to 1.5. Conclusions and synthesis 97 bring their contributions at dierent design levels according to the SBCE principles.

The experts contributions are used to specify the KVAs used for the evaluation of DFX metrics. The evaluation is performed using computational models linking the DFX metrics with KVAs. Thus, a reliability assessment model was developed based on the FMEA method.

The fourth contribution, about the integration of assemblability in the MBSE approach, A methodology combining a MBSE model based on SysML and 3D CAD model has been proposed.

The method consists of 3 phases: a product specication phase with denition of assembly requirements; a 3D design and assembly analysis phase; and a validation of the design solution from the two points of view: functionality and assemblability. Assemblability evaluation is performed using KVAs: the maximum number of parts, total assembly time (TAT)

and assembly eciency (AE).

The fth contribution about the development of compact models for vibration analysis of mechatronic systems is linked to the second research theme of multiphysics simulation methods for mechatronic design.

In this contribution, analytical solutions of the partial dierential equations (PDE) modeling the vibration phenomenon have been deduced and implemented in a Modelica library.

The developed models concern a exible beam xed on one side and subjected to a mass on the other side, and a exible beam in rotation. The implementation of the models in Modelica allows the designer to combine them with other Modelica libraries to perform multiphysics simulation including vibration. The approach has been validated using a case study of a wind turbine.

The sixth contribution is about the development of the CDPPK methodology.

A new collaboration model integrating model knowledge and knowledge about the design process was developed. The model is based on the use of the concept of ICE but extends it to include information about the design workow. Indeed, we propose to add inputs/outputs in the ICEs to both compose a knowledge on the product from the data but also a knowledge on the collaboration workow.

The methodology has been validated with a case study of an ETB, for which a test bed has been realized for the experimental validation aspect and a proof of concept has been developed using Python. In this case study ICEs for multiphysics, control and MDAO were used to illustrate the eectiveness of the multidisciplinary collaboration. This work has been realized within the framework of the MIMe project and the contribution aims at extending the possibilities of the KARREN software of Digital Product Simulation (DPS) company.

The seventh contribution aims at integrating the use of virtual agent in the collaborative design process of mechatronic systems. For this, a multi-agent system was developped using JADE platform, by adding two types of agents to the default used agents in JADE. Big Data and the Cloud are its main tools. Therefore, the challenge for manufacturers is no longer so much to produce in large quantities, but to be able to adapt their production chain to the needs of their consumers in real time and in a exible manner.

On the other hand, manufacturing and transportation of goods will see a remarkable growth in the use of autonomous vehicles in the future, whether they are Automated Guided Vehicles (AGVs) or Autonomous Aerial Vehicles/Unmanned Aerial Vehicles (AAV/UAVs). Indeed, these autonomous vehicles (AVs) excel in applications with repetitive movement of materials over a distance or with a process where material tracking is important [START_REF] Caruntu | Bio-inspired coordination and control of autonomous vehicles in future manufacturing and goods transportation[END_REF].

Last but not least, the advent of Industry 4.0 will not happen without taking into account the ecological transition. Reducing the environmental footprint is already a major challenge for industrial groups.

Faced with these industrial upheavals, we are aware that our research must include new methods and tools in the design process of complex systems. New collaboration strategies between the designers need also to be implemented, so that product development companies are able to exploit the new I4.0 technology, to remain competitive and attractive to increase their oer.

New research challenges

With the advent of the Industry 4.0 concept, customers seek for highly personalized products which requires including customers with design team around a collaboration platform integrating new I4.0 technologies in the product design phase to meet. It also involves the development of new collaboration strategies allowing better use of data, information and knowledge.

The advent of the Industry 4.0 concept has also brought changes to the simulation and modeling paradigm. The new simulation and modeling paradigm evolves today to the concept of Digital Twin. This concept extends the use of modeling & simulation to all phases of the product lifecycle, where products are rst developed and tested in detail in a virtual environment, and subsequent phases use the information generated and collected by the previous product phases of the life cycle [Rodi£, 2017].

New research challenges 109

The way humans interact with engineered systems is also transforming, just as the internet has transformed the way people interact with information. Indeed with the integration of computation, networking and physical processes, engineered systems are transforming to Cyber Physical System (CPS). CPSs are a way to encompass the large spectrum of technologies including robotics, IoT, embedded systems, and so on.

The Autonomous driving and smart trac, emergency response, environmental monitoring, electric energy grids, space missions, medical applications, and so on are CPS systems that share the challenge of integrating articial intelligence and that require new design methodologies. Being composed of many heterogeneous elements, CPSs require complex models to dene each sub-system and its behavior. Current design tools need to be upgraded to consider the interactions between the various sub-systems, their interfaces, and abstractions.

The application of the CPS to industrial manufacturing leads to a specialization of them referred as Cyber Physical Production System (CPPS). CPS and CPPS should be able to address interoperability issues, since one of their intrinsic requirement is the capability to interface and cooperate with other systems.

The design and control challenges of CPSs are harder, since individual component autonomy must be glued by explicitly addressing interdependence and coordination, interoperability, distributed control and emergence of behaviors. A strong demand for address today to the implementation of swarm intelligence in CPSs which play an important role when there is not enough information to solve the design problem in a centralized way, when there are time constraints which do not allow to nd an analytical solution, and when the operation needs to be performed in a dynamically changing environment. Swarm Intelligence (SI) is a popular multi-agent framework that has been originally inspired by swarm behaviors observed in natural systems, such as ant and bee colonies.

Swarm intelligence is based on the principle of thinking globally and acting locally [START_REF] Dias-Ferreira | Biosoarm: a bio-inspired self-organising architecture for manufacturing cyber-physical shopoors[END_REF].

For instance, swarming uses the principle of collective intelligence for solving the problem of traveling in formations of AVs.

The vehicles can be considered as simple particles that cooperate while updating their velocities. Thus, bio-inspired techniques to control a eet of AVs could be applied to accommodate their operations in unexplored and uncertain environments.

The tasks of each entity are therefore derived from emergent cooperative biological systems. Consequently, this allows considering decentralized, self-organized formations, in which each participant can have a specic behavior [START_REF] Dias-Ferreira | Biosoarm: a bio-inspired self-organising architecture for manufacturing cyber-physical shopoors[END_REF].

This introduction leads us to formulate the scientic issues on which we are led to make contributions in the coming years. In the next section, we will detail our new research topics to consider the following three scientic issues: The digital twin aims to produce a virtual replica of a physical asset (machine, system, product) in order to obtain visualization, simulation / prediction and monitoring functionalities. In the context of the Factory, the Digital Twin is an approach making it possible to couple the physical world with digital tools, and this throughout the life cycle of the system concerned and at all levels (strategic, tactical, operational , real time). The concept is today at the heart of many attentions and many questions, research, organizational and technological are raised.

According to their typology, we can consider the development of digital twins for the two following research activities:

Multiphysics simulation of cyber-physical systems Design of cyber-physical production systems 2.4.1.1 Multiphysics simulation of cyber-physical systems

The elds such as Aeronautics, Space, Land Transport, Defense, Security and Digital Identity integrate electronic modules (digital cards, analogue cards, power supply cards, mixed digital/analogue cards, ...) with software programs (Signal Processing, Specic Wave-forms, Low Level Software, Secure OS, ...), all this supported and protected by mechanical structures (assembly, materials of various types and shapes, ...), for the development of their complex engineered systems considered today as CPSs. This imposes a set of design constraints dened according to the specications of the CPS to be developed.

In order to meet these constraints, Multiphysics Digital Twin (MPDT) is considered as an essential tool that helps at the same time: in the rapid denition of the architectures, the detailed exploration of the CPS equipment's in their environments and the reduction of the risks linked to a bad anticipation of certain physical or functional phenomena. MPDT also limits the costs by allowing 2.4. New research axis 111 the design to converge more quickly and reducing the number of physical prototypes.

To do so, a MPDT is currently being developed as a part of Grégoire GALIS-SON's Thesis [Th9], which has started in May 2021. It is expected that the digital twin will be able to handle both the simulation management and the simulation modeling activities.

The simulation management helps in taking control of simulation data and processes to avoid common problems, such as analyzes performed on stale data, poor visibility of simulation results, and their coming too late to aect performance.

Thus, form the specications of the equipment to be designed and the analysis needs, the MPDT should help the System Modeling Architect (SMA) of the product in developing the specications for the simulation model (inputs, outputs, functional and environmental elds of application, physics involved, exchange formats between physics, temporal aspects and tools). The MPDT should also help the system modeling architect in setting up the simulation workow and the coordination between the dierent stakeholders involved in the development and use of the simulation model, including verication and validation phases of the digital twin.

The simulation modeling will take into account the aspects of couplings between physics:

the weak or strong coupling between 3D simulation tools and physics, which often does not oer the possibility of going beyond two or three physics, the coupling of reduced models within a system simulation which opens up the possibility of a system multiphysics platform.

To do this, the thesis is stained with dening an evolving theoretical, methodological and application framework allowing the design of the MPDT, as well as its implementation and its coupling with experimental devices (prototypes of the real system). This framework is required to allow the digital twin to evolve throughout the product design process and its cycle of use.

The use of model reduction techniques to develop system simulation models is not recent, however classical model reduction approaches are essentially based on a global application of modal decomposition techniques. The major drawback of these techniques is that these methods often lead to inaccuracies and instabilities in the solution caused, among other, by certain truncated modes which may contain a signicant amount of information and system energy.

The contribution targeted in this thesis is to develop a systematic approach for model order reduction using adaptive partitioning and clustering techniques to customize partitions with properly chosen widths. Each partition characterizes a specic stage in the dynamics and evolution of the system. Partitioning can be done 112 Chapter 2. Research project and perspectives: Collaborative multidisciplinary design of Cyber Physical Systems on physical domains, state space, parameter space, and time domain. During the use phase of the MPDT, an automatic calibration of the DT conguration parameters will be required. For this, we propose to use a method assisted by surrogates models and space mapping to align the digiatl twin with the data measured from the real system. The trained surrogates should be re-optimized by updating the system conguration in order to maximize the consistency between the MPDT predictions and the measurements of the physical system sensors.

Design of cyber-physical (prodcution) systems

Personalized products and production require new development techniques to overcome the main hurdles of the customization of complex engineered systems.

Typically, production processes for various complex product groups struggle to respond to the dynamic situations that arise from complex production processes.

In this sens, Digital Twin already presents promising avenues to overcome these challenges.

CPS and CPPS are core concepts of the fourth industrial revolution. They are physical and engineering system that can overcome the limitations of the personalized products and production process, as they are designed to improve the performance of products and manufacturing systems [START_REF] Monostori | Cyber-physical systems in manufacturing[END_REF]. In the manufacturing sector, a digital twin can be dened as a virtual plant that reects the structure of a real plant and synchronizes information and functions related to the plant design, operation, and production [START_REF] Park | Digital twin-based cyber physical production system architectural framework for personalized production[END_REF]. However, several challenges are still hindering an eective development of digital twins for CPS and CPPS. Indeed, the collection of accurate customer requirements and the reduction of the time gap between product development stakeholders (customer, designer, manufacturer, etc) are main challenges to overcome.

For this, we propose in this research axis,to develop new methodologies allowing the eective integration of digital twins for CPS and CPPS design. For this, several challenges need to be considered, among them: The issues to be considered in this case could be:

How can we develop new knowledge using IoT and connected objects that improve decision-making in collaborative design?

How can big data help in automating the design collaboration process and provide design insights based on data analysis?

How the cloud can provide DFX data and information on production optimization opportunities?

How articial intelligence tools such as machine learning algorithms, natural language processing, text processing, etc., coupled with big data and advanced algorithms can be helpful in using unstructured data sources to help designers in codifying knowledge and address the missing links in their knowledge ow?

Therefore, by considering the Industry 4.0 enablers in the collaborative design, we believe that we can develop self-learning design and coordinating agents, using deep learning and reinforcement learning techniques, which allows both the automatic capitalization of knowledge and the eective assistance of virtual design agents to real design agents.

Thus, we intend to develop this research axis for the collaborative design of CPS and CPPS.

Conclusion

Our research project for the next few years is therefore based on the integration of Industry 4.0 technologies in the collaborative design process of more intelligent, communicating and collaborative systems, namely CP(P)Ss.

In this chapter I have presented the two axes of research that we wish to develop in the near future: Digital twin development for cyber physical systems and Interdisciplinary collaborative design of cyber physical (production) systems. This goes in the same direction of a continuity of the two main axes of research: integrated design and collaborative design, but considering new challenges on the integration of I4.0, and later I5.0, technologies such as IoT, big data analytics, cloud computing, digital twins and articial intelligence.

The objective is always to formalize modeling and design frameworks in order to 2.5. Conclusion 115 master the growing complexity of products and production processes, and to guarantee that the design requirements are respected.

  for bipedal robot inspired by human structure, in 21st International Conference on Research and Education in Mechatronics (REM), IEEE, dec 2020. , scientic background, positioning and research issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.1.2 Scientic background . . . . . . . . . . . . . . . . . . . . . . 17 1.1.3 Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.1.4 Research issues . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1.2 MBSE-based approaches for the integrated design of mechatronic systems . . . . . . . . . . . . . . . . . . . . . . . 40 1.2.1 Production process modeling for mechatronic product design 40 1.2.2 MBSE approaches to integrate DFX for mechatronics design 58 1.3 Multiphysics simulation methods for mechatronics design . 71 1.3.1 Contribution to the development of compact analytical models for vibration analysis of mechatronic systems . . . . . . . . . 71 1.4 Interdisciplinary collaborative design of mechatronic systems 79 1.4.1 Collaborative Design Process and Product Knowledge (CDPPK) Methodology . . . . . . . . . . . . . . . . . . . . . 79 1.4.2 Collaborative design assisted by multi-agent systems . . . . . 89 1.5 Conclusions and synthesis . . . . . . . . . . . . . . . . . . . . 96 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 My research activities started in 2008 during my cotutelle thesis which was carried out at LA2MP/ENIS-Sfax, Tunisia and LISMMA/ISMEP-Supméca, France, then they continued without interruption in LISMMA at ISMEP-Supméca and today within Quartz EA7393. In this chapter, I present the synthesis of the research works in which I participated, in order to highlight my scientic contributions.

  main specic engineering activities. Domain specic engineering activities in our researches concern the Multiphysics Simulation (MPS), Multidisciplinary Design Analysis and Optimization (MDAO) and design for X (DFX) activities. The objective of the Interdisciplinary Collaborative Design and Knowledge Management (ICDKM) research activities is to provide a framework for eective collaboration between systems engineers, mechatronics engineers and specic domain specialists in multiphysics simulation, MDAO and DFX.

Figure 1 .Figure 1 . 1 :

 111 Figure 1.1 shows a more general view on the research elds concerned by our research activities.In the following sections, I will start by presenting the background and the basic research issues concerning these topics and then I present our contributions. The concerned research topics are the following:

Figure 1

 1 Figure 1.2: SysML Diagram Types (Source: https://www.omgsysml.org/ what-is-sysml.htm)

Figure 1 .

 1 Figure 1.3: E-wheel drive: example of spatial and functional integration (Source:

1. 1 . 23 Figure 1 . 4 :

 12314 Figure 1.4: Multiphysics couplings

Figure 1 . 5 :

 15 Figure 1.5: Electronic throttle body system

Figure 1 .

 1 Figure 1.6 illustrates an example of DSP generation and quality assessment based on CAD data.

Figure 1 . 6 :

 16 Figure 1.6: Generation of disassembly plans and quality assessment based on CAD

Figure 1 .

 1 Figure 1.7: All-At-Once formulation (AAO) MDO problem formulation

Figure 1 . 8 : 31 CollaborativeFigure 1 . 9 :

 183119 Figure 1.8: XDSM diagram Block GaussSeidel multidisciplinary analysis (MDA) process to solve a three-discipline coupled system

Figure 1 . 10 .

 110 Figure 1.10. An initial set of sample points is generated using a statistical method of Design of Experiment (DoE). These points are then used as inputs to run the simulation model and get function evaluations. Finally, a surrogate model type is

Figure 1 . 10 :

 110 Figure 1.10: Surrogate modeling process

Figure 1 . 11 :

 111 Figure 1.11: Space mapping concept

  uct models are created to support the Product Lifecycle Management (PLM) approach through data and information management (Function-Behavior-Structure, Core Product Model, Product Process Organization, etc. ). However, these models do not focus on the knowledge management built into Computer Aided Design (CAD) and Computer Aided Engineering (CAE) models. In this context, Knowledge Conguration Management (KCM) has been proposed to manage knowledge encapsulated in disciplinary models. It ensures the consistency of parameters through several product design and simulation activities in a context of collaborative engineering using the concept of Conguration Management (CM).

Figure 1 . 12 :

 112 Figure 1.12: Knowledge Conguration Model principle

Figure 1 . 13 :

 113 Figure 1.13: UML meta-model of KCM[START_REF] Monticolo | A meta-model for knowledge conguration management to support collaborative engineering[END_REF]

1. 1 .

 1 Context, scientic background, positioning and research issues 37 methodologies for mechatronic integrated design that meets the Mechatronics objectives, as xed in the denition NF E01-010 introduced in section 1.1.1. As previously mentioned, this work is divided into three research activities: MBSE-based approaches for the integrated design of mechatronic systems. Multiphysics simulation methods for mechatronics design. Interdisciplinary collaborative design of mechatronic systems. This research work is consistent with the research activities of my research team IS2M: Ingénierie des Systèmes Mécatroniques et Multiphysiques, for Mechatronics and Multiphysics Systems Engineering, at Quartz EA7393 laboratory.The objective of the rst and second research activities is to ensure the synergy and integration of the mechatronic design approach, by adapting the MBSE/SysML method to integrate activities and knowledge related to the MPS, MDAO and DFX domains. The gure 1.14 gives an overview of the areas covered by our research on the development of integrated mechatronic design approaches.

Figure 1 . 14 :

 114 Figure 1.14: Integrated mechatronic system design approach

1. 1 .

 1 Context, scientic background, positioning and research issues 39

Figure 1 .

 1 Figure 1.15: Interdisciplinary collaborative mechatronics design

  issue for the development of mechatronic systems. It is a common subject for the members of the Ingénierie des Systèmes Mécatroniques et Multiphysiques (IS2M) team. Research on integrated product-process design approaches has been considered since the 1990s. Several approaches and frameworks for integrated product-process development have been considered by researchers. Most research has approached the problem from two perspectives: (i) how to decompose the complex product into disjointed subsets, and (ii) how the design team constructs the decision making schedule, based on the dependencies between the subsets and the solutions studied for each subset. Several works, related to systems engineering, have considered the rst problem of decomposition of the product into disjoint subsets. To this end, a number of authors have proposed SysML as a language supporting the systems engineering methodologies they have suggested. For example, SysML4Mechatronics is an approach that uses the port concept of SysML to represent and analyze the inuences of change in mechatronic production plants [Kernschmidt 2013].

Chapter 1 .

 1 Collaborative multidisciplinary design of mechatronic systems works were based on the Set-Based Concurrent Engineering (SBCE) (set-based concurrent engineering) method. The SBCE method starts by establishing a large set of possible solutions and gradually narrows this set of possibilities to converge on a nal solution [Sobek 1999]. Design members examine, develop, and communicate the set of solutions in parallel and independently. As the design progresses, they progressively narrow their respective solution sets based on additional information provided by the development and design stakeholders.

Figure 1 . 44 Chapter 1 .

 1441 Figure 1.17: SBCE steps for concurrent engineering

Figure 1 .

 1 Figure 1.18: Electronic Throttle Body (ETB) components

Figure 1 .

 1 19 shows the functional architecture model of the ETB system developed using SysML.

Figure 1 . 19 :Figure 1 . 20 :

 119120 Figure 1.19: Functional architecture model of the ETB system developed with SysML

Figure 1 . 21 : 48 Chapter 1 .Figure 1 . 22 :

 121481122 Figure 1.21: Possible solutions for each subsystem of the ETB

Figure 1 . 23 : 50 Chapter 1 .Figure 1 . 25 :

 123501125 Figure 1.23: The production process and the manufacturing machines of the ETB congurations represented by a SysML diagram

  the rst step are mapped to a holonic architecture. Indeed, Domain Specic Language (DSL) tools implemented with UML-SysML allow us to develop new diagram proles based on the classical SysML diagrams to customize their use. Therefore we used DSL to develop an extended holonic SysML prole as illustrated in gure 1.26.

52 Chapter 1 .

 521 Figure 1.26: Extended Holonic SysML prole

Figure 1 . 27 :Chapter 1 .

 1271 Figure 1.27: Case study: Steel converter manufacturing system

Figure 1 . 28 :

 128 Figure 1.28: Phase 1: SysML model of the steel converter system

Figure 1 . 29 :Figure 1 . 30 :Chapter 1 .Figure 1 . 31 :

 1291301131 Figure 1.29: Phase 1: Internal structure of the continuous casting machine

Figure 1 . 32 :Figure 1 . 33 :

 132133 Figure 1.32: Phase 2: Holonic architecture of the production system

Figure 1 . 34 :Chapter 1 .

 1341 Figure 1.34: Phase 3: Multi-agent simulation model implemented using AnyLogic software

Figure 1 . 36 :

 136 Figure 1.36: New SysML diagram prole for manufacturability and reliability analysis

Figure 1 . 37 :Figure 1 . 38 :Chapter 1 .

 1371381 Figure 1.37: Reliability assessment owchart

Figure 1 . 39 :

 139 Figure 1.39: The radar chart for the three nal retained solutions

Figure 1 . 40 :

 140 Figure 1.40: Bicycle pedal with ashing LED lights

Figure 1 . 41 :Figure 1 . 42 :

 141142 Figure 1.41: Pedal requirements diagram

Figure 1 . 43 :

 143 Figure 1.43: Allocation and traceability of the pedal

1. 2 .Figure 1 . 44 :

 2144 Figure 1.44: CAD and exploded views of the pedal bike design

Figure 1 . 45 :

 145 Figure 1.45: List of possible ASPs

1. 3 .Figure 1 . 46 :

 3146 Figure 1.46: Enriched structure of the pedal in the MBSE environment

1. 3 . 1 . 1

 311 Analytical model of a exible beam with a rigid massThe presented model focuses on the deection of the system shown in Figure1.47.

Figure 1 . 47 :

 147 Figure 1.47: Flexible beam with a rigid mass

Figure 1 . 48 :

 148 Figure 1.48: Flexible rotating beam

1. 3 .

 3 Multiphysics simulation methods for mechatronics design 77 connectors is a denition of a coordinate system that is xed to a mechanical component. The connector allows the denition of the position and orientation vectors of the component in relation to the absolute frame (World). Il allows also the denition of the cut-force and cut-torque vectors resolved in the connector frame. Figure 1.49 shows the implemented Modelica components of the exible beam with a mass (on the left) and the rotating exible beam (on the right). The gure shows also the connectors used to allow the coupling of the components to each other or to the other mechanical components of the Modelica library.

Figure 1 . 49 :

 149 Figure 1.49: Implementation of the Modelica components with their connectors: exible beam with a mass (left), rotating exible beam (right)

Figure 1 .Figure 1 . 50 :

 1150 Figure 1.50: Modelica model of wind turbine for the vibration analysis

1. 4 .Figure 1 . 51 :

 4151 Figure 1.51: Nacelle vibration amplitudes

1. 4 .Figure 1 . 52 :

 4152 Figure 1.52: Collaborative Design Process and Product Knowledge principle

  . The UML metamodel of Collaborative Design Process and Product Knowledge (CDPPK) framework is shown in gure 1.53. The dierent classes and connections are represented between the entities dened previously. This model is based on the concept of Conguration Management (CM) dened in ISO 10007:2015. CM carries the access to the adequate information relative to product design, realization, verication and use. This information is organized in a global conguration which is updated and versioned to trace the evolution of the product. In CDPPK, this organizational concept is the Knowledge Conguration (KC).

Figure 1 . 53 :

 153 Figure 1.53: UML metamodel of CDPPK

Figure 1 .

 1 Figure 1.54: Collaboration methodology between System architect and MS actors with CDPPK

  This methodology enables each stakeholder to access and use the right knowledge. In managerial terms, our methodology moves from the traditional predened collaboration process to a more dynamic and exible one. It provides a common basis of exchange that does not disrupt the tasks of the stakeholders.The main dis-1.4. Interdisciplinary collaborative design of mechatronic systems 85 advantage of such a methodology is the need to bring the dierent stakeholders together to formalize the knowledge, which can be very time consuming.1.4.1.2 Collaboration using CDPPK and management of conicts According to our methodology, conicts are generated when parameters' values do not respect the constraints. The constraints associated with the parameters can be system constraints (dened in an ICE) or interdisciplinary constraints (dened in UPC). Therefore, system constraints help us to manage requirements' changes and interdisciplinary constraints help us to manage conicts between disciplinary engineers (gure 1.55). We dened collaboration states for UPC and CDP in order to organize the conict resolution process.

Figure 1 .

 1 Figure 1.56: ICEs denition in DPK menu of the CDPPK model

1. 4 .Figure 1 .Chapter 1 . 2

 4112 Figure 1.57: The dierent UPCs involved in the collaborative scenario of the ETB design

  as a development environment for the collaborative design platform. JADE includes all components to manage the collaborative platform according to the Foundation for Intelligent Physical Agents -Agent communication Language (FIPA-ACL) standard. These components are: Agent Management References Model (AMRF), Message Transport System (MTS), Agent Management System (AMS) and Directory Facilitator (DF).

Figure 1 .

 1 Figure 1.59 represents a JADE application developed on 3 machines to assist the collaboration of two designers. The coordinating agent CA is deployed in the main container (mainContainer), and the design agents DA1 and DA2 are deployed in container 1 and container 2.

Figure 1 .

 1 Figure 1.62: MAS coordination algorithm

110Chapter 2 . 2 . 4

 224 Research project and perspectives: Collaborative multidisciplinary design of Cyber Physical Systems How to make classical modeling & simulation techniques of complex systems evolve to the digital twin concept? how to make mechatronic design methodologies evolve towards the design of complex systems becoming more and more into CPSs? and, how to develop new collaborative design platforms integrating I4.0 technologies and allowing both designers and clients to collaborate in an ecient manner. New research axis 2.4.1 Research axis 1: Digital twin development for cyber physical systems

Chapter 2 .

 2 the eective integration of CPS or CPPS customers' requirements in the Digital Twin. the evolvement of classical 3D CAD models towards a 3D digital twin integrating knowledge and articial intelligence the digitalisation of manufacturing based on the digital twin These research activities are already carried out in the framework of a collaborative project that I am piloting (Franco-Tunisian Hubert Curien Partnership (PHC) program -UTIQUE) with the mechanical engineering laboratory LGM of the National Engineering School of Monastir (ENIM) in Tunisia. This project deals with the digitization of manufacturing systems using I4.0 technologies, where 2.4. New research axis 113the digital twin will play a main role. Indeed, the Digital Twin is considered as a relevant solution for digitizing manufacturing. In this context, our aim is to develop new approaches allowing the evolution of traditional CAD models towards a form of Digital Twin representing manufacturing units. The digital twin will be able to learn by itself from data transmitted with dierent formats from several sources: sensors of the physical system, relevant knowledge of the industrial eld, other similar machines and the environment in which the physical system is making part.As second research activity, we planned to work on the development of new design methodologies for the assemblability assessment of smart products and CPSs. Indeed, the constantly growing needs of customized products impose use of sensors, which provide feedback information on CPS use, behaviors and states in real time. The few works done to date on assembly analysis methods do not take this constraint into account. It would therefore be a question to develop new methods of analysis of ASP/DSP for CPSs. As a third topic related to the design of CPS/CPPS, we started within the framework of the thesis of Khalil ALOUI [Th8], to work on the development of decentralized control systems based on swarm robotics and bioinspiration. The activities for this work concern the continuity of the design process starting from the description of swarm behaviors, such as swarm formation, to the functional design of swarm element, the structural and architectural design of robots, the development of bioinspired control algorithms and the implementation of programs. SysML language is already being used in this work for the systems engineering phase of the CPS/CPPS, and Robot Operating System (Robot Operating System (ROS)) is used for the verication and code implementation. The interoperability between SysML and ROS is one of the challenges to overcome. The main contributions of this work will concern methods and tools to integrate swarm intelligence for the design and control of CPS/CPPS. 2.4.2 Research axis 2: Interdisciplinary collaborative design of cyber physical (production) systems The work we have started on the collaborative design of mechatronic systems has allowed us to acquire skills in the eld of knowledge management (KM) and the use of articial intelligence (AI) through multi-agent systems. This opens the horizons for us to combine these skills to develop new methods of collaboration for the design of CPS and CPPS. Indeed, the extension of ICEs to include design knowledge formulated as an optimization sub-problem with the solution to the sub-problem presented as an array of discrete solutions can helps in reducing the development time, taking into account the new design constraints. On the other hand, if we examine more deeply into modern collaborative design practices, we can notice that the internet of things and connected objects, big data analytics, smart systems, etc. are increasingly being integrated into knowledge 114 Research project and perspectives: Collaborative multidisciplinary design of Cyber Physical Systems management processes. This stimulated the development of integrated software platforms to optimize knowledge management strategies. In this context, knowledge management practices in the design process require the technology capabilities that support Industry 4.0, such as digital enhancements and the implementation of CPS, which can facilitate the process of managing knowledge. A such approach will take into account the technological challenges that collaborative design is dealing with in an Industry 4.0 context. Therefore, these challenges involve diverse stakeholders' skills and creative capabilities.

  1.1. Context, scientic background, positioning and research issues 19 2.0, was initiated by the Object Management Group (OMG) and International Council on Systems Engineering (INCOSE) in 2001, and standardized since 2006

Table 1 .

 1 1 illustrates the nomenclature of the proposed solution.

	Rep	item	Nb	Rep	Item	Nb 1
	1	Pedal body	1	12	Screw	2
	2	Pedal axle	1	13	Contact	1
	3	Sealing ring	1	14	Electronic card	1
	4	Bearing	2	15	Mechanical belt	2
	5	Spacer	1	16	Insert	1
	6	Reector cover	2	17	Inner cover	1
	7	Reector	2	18	Outer cover	1
	8	CHC screw	2	19	Engine body	1
	9	Generator	1	20	Motor wheel	2
	10	Connector	1	21	Motor wheel 2	1
	11	Bearing bracket	1	22	Motor cover	1

Table 1 .

 1

1: Nomenclature of the pedal

  The rst agent type is a Design Agent (DA) which role sistency checking of mechatronic design models. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, volume 44113, pages 11411148. (Cited on page 38.) Cited on page 26.) multidisciplinary design of Cyber Physical SystemsThe factory of the future brings digital technologies closer to the industrial world. The industrial process of tomorrow will be built on new technologies and

	innovation. The production tool is transforming, it communicates continuously
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Chapter 1. Collaborative multidisciplinary design of mechatronic systems

Figure 1.60: The implementation of a JADE platform for collaborative design of mechatronic systems [Guizani, 2016] solutions. This set could contain many solutions (e.g. Pareto front), one solution, or no solution.

The proposed coordination process is realized in the agent-based system as follows:

1. Initialization: All the design agents needed for coordination are registered in the agent management system (AMS). The information of each design agent is stored in the directory facilitator.

2. Specication: The global objectives, global constraints and convergence conditions of the system are stored in coordinating agent (CA).

Information:

The coordinating agent (CA) species the design agents (DAs) involved in the coordination by querying the agent management system (AMS) and invites all the design agents to join the coordination process.

4. Coordination: the coordination process begins for the determination of the optimal solutions that meet all the requirements requested from the dierent design agents.

Figure 1.61 represents a communication workow during a design collaboration between two design agents with a coordinating agent.

The behavior of the agents is implemented using Java language within JADE framework. For instance, the coordination behavior between the agents is carried Agent [Guizani, 2016] out according to the algorithm dened in gure 1.62. During the collaboration process, the coordinating agent (CA) informs the design agents (DAs) through the message transport system (MTS) that the communication workow is starting.

The coordinating agent (CA) sends a request by sending ACLM essage.Request to each design agent to perform a local optimization and the content of the message is the formulation of the optimization sub-problem of the corresponding agent.

Each design agent receives a request to perform a local optimization and determine the optimal solutions with respect to the local objectives in order to satisfy the requested requirements. The optimization itself is made by physical designers.

Once the optimization is performed and the solutions are generated, each design agent sends a ACLM essage.AGREE message to the coordinating agent. The content of the message is the set of solutions found.

The coordinating agent (CA) waits for the reception of all the messages from the dierent design agents implied. Then, the coordinating agent (CA) reduced the search design space of the optimal solutions by eliminating the solutions that do not satisfy all the design agent's constraints. A MiniMax algorithm was developed for this purpose (See [Guizani, 2016] for details).

The common solutions found are communicated back to design agents (DAs) to conrm the solutions found with ACLM essage.CON F IRM or to follow the collaboration process if required.

Chapter 1. Collaborative multidisciplinary design of mechatronic systems is to receive requests in the form of an optimization sub-problem formulation, and to send a response in the form of a set of solutions dened by an array.

The optimisation it self is perfromed by a physical designer by using MDAO for example. The second type of agents is the Collaborative Agent (CA), which role is to send requests to DAs and receive the design solutions. The behavior of an agent is programmed with JAVA. Thus, an algorithm allowing to search for common solutions among the solutions sent by the DAs has been implemented.

The algorithm also allows reducing the number of solutions by deleting those that do not satisfy all the design constraints.

Introduction

In this chapter, I start by presenting the new industrial and research challenges that led us to dene our research project for the more or less long term. The two research axis: digital twin development for cyber physical systems and interdisciplinary collaborative design of cyber physical (production) systems will therefore be detailed.

New industrial challenges

For a long time, the industrial sector has focused on productivity issues, particularly through the triptych of costs, quality and deadlines. The digitization of processes, the demand for the right level of customer experience, the increase in competitive pressure and the development of technologies are forcing industrial groups to rethink their production processes and to change their paradigm.

General conclusion

The theme of collaborative multidisciplinary design of complex systems is still relevant today.

The research works of the last years have been focused on the methods of modeling and integrated collaborative design of mechatronic systems. In recent years and in the future this theme opens on the connected, communicating and collaborative systems, known as CPS and CPPS.

Thus to master the ever-increasing complexity of products whose requirements are evolving in an industrial environment itself in evolution, the methods and tools for modeling, verifying and validating the design of complex systems are also constrained to evolve to meet the new challenges of product and process development.

This research theme is very open and presents several major technological and methodological challenges that will need to be resolved in the years to come, notably regarding the integration of I4.0 technologies: IoT, big data, cloud computing, digital twins and articial intelligence.

Collaborative Multidisciplinary Design of Complex Systems

Abstract: In this HDR manuscript, I have presented a review on our research themes concerning the formalization of modeling and design frameworks in order to master the increasing complexity of mechatronics and CPS products, and production processes (CPPS).

Therefore, in the rst chapter I presented a synthesis on the work done to develop a formal framework of modeling and design allowing collaborative design and management of the knowledge related to the activities in systems engineering, mechatronic design, multiphysics simulation, DFX and MDAO, with applications to mechatronic products.

In the second chapter, I presented our research project which aims at integrating the systems. The objective is always mastering the growing complexity of such products and production processes, and to guarantee that the design requirements are respected.