Wanda Zhao

Anatol Pashkevich

Alexandr Klimchik

D Chablat

THE STABILITY AND STIFFNESS ANALYSIS OF A DUAL-TRIANGLE PLANAR ROTATION MECHANISM

Keywords: Tensegrity mechanisms, Equilibrium configurations, Stability analysis

The paper deals with the stiffness analysis and stability study of equilibrium configurations for dual-triangle tensegrity mechanism, which is actuated by adjusting elastic connections between the triangle edges. For this mechanism, the torquedeflection relation was obtained as a function of control inputs and geometric parameters. It was proved that the mechanism can has either a single or three equilibrium configurations that can be both stable and unstable. Corresponding conditions of stability were found allowing user to choose control inputs ensuring the mechanism controllability. The obtained results are confirmed by the simulation examples presented in the paper.

INTRODUCTION

Many modern robotic applications require new type of manipulators that possess high flexibility similar to an elephant trunk [START_REF] Rolf | Constant curvature continuum kinematics as fast approximate model for the Bionic Handling Assistant[END_REF] [START_REF] Yang | An elephant-trunk manipulator with twisting flexional rods[END_REF]. Such manipulators are usually composed of a number of similar segments based on varies tensegrity mechanisms, which are assembly of compressive elements and tensile elements (cables or springs) held together in equilibrium [3][4]. This paper concentrates on the stiffness analysis and equilibrium stability study, which are connected by a passive joint in the center and two elastic edges on each sides with controllable preload.

Some kinds of the tensegrity mechanisms have been already studied carefully in literature [START_REF] Duffy | A review of a family of self-deploying tensegrity structures with elastic ties[END_REF] [START_REF] Arsenault | Kinematic, static and dynamic analysis of a planar 2-DOF tensegrity mechanism[END_REF]. In particular, in [START_REF] Furet | Kinematic analysis of planar tensegrity 2-X manipulators[END_REF] [START_REF] Furet | Workspace and cuspidality analysis of a 2-X planar manipulator[END_REF], there were considered the cable-driven X-shape tensegrity structures, where each section was composed of four fixed-length rigid bars and two springs. For this mechanism, the authors investigated influence on the cable lengths on the mechanism equilibrium configurations, which maybe both stable and unstable. Special attention was paid to the work space and singularities analysis. Another group of related works [START_REF] Arsenault | Kinematic, static and dynamic analysis of a planar 2-DOF tensegrity mechanism[END_REF] deals with the mechanism composed of two springs and two length-changeable bars. The authors analyzed the mechanism stiffness using the energy method and demonstrated that the stiffness of this mechanism always decreases when it is subjected to external loads with the actuators locked, which may lead to "buckling". Some other research in this area [START_REF] Wenger | Kinetostatic analysis and solution classification of a planar tensegrity mechanism[END_REF] focus on the three-spring mechanisms, for which the equilibrium configurations stability and singularity were analyzed. Using these results the authors obtained conditions under which the mechanism can work continuously, without the "buckling" or "jump" phenomenon. There are also some research studying a four-legged parallel platform [START_REF] Moon | Position and force analysis of a planar tensegrity-based compliant mechanism[END_REF], which is based on the compliant tensegrity mechanisms. Here, each leg consists of a piston and a spring in series, which allows the platform to achieve in the desired position and orientation. The authors investigated the loaded equilibrium configurations and numerically computed the platform stiffness. However, the tensegrity mechanism based on dual-triangles were not studied in robotic literature yet.

This paper focuses on the stiffness analysis of a new tensegrity mechanism, which is composed of rigid dualtriangles connected by a passive joint that is actuated by adjusting elastic connections between the remaining triangle edges. This structure proved to be very promising for designing of multi-section serial chains possessing very high flexibility. For this mechanism, we concentrate on the equilibriums computing, the stability analysis and the selection of the geometric parameters and control inputs allowing to achieve the desired configuration while ensuring its stability. The results provide a good base of the study of the multi-segment manipulators in the future work.

MECHANISM

GEOMETRY AND EQUILIBRIUM EQUATION

Let us consider first a 1-d.o.f. (degree of freedom) segment of the total flexible structure to be studied, which consists of two rigid triangles connected by a passive joint whose rotation is constrained by two linear springs as shown in Fig. 1 To find mechanism configuration angle q corresponding to given control inputs F generated by the springs can be obtained from Hook's law as follows.

00 1 1 1 1 2 2 2 2 ( ); ( ) F k L L F k L L     (1)
where 1

L and 2 L are the spring lengths AD , BC corresponding to the current value of the angle q . These values can be computed from the triangles AOD  and BOC  using the formulas

22 1 1 1 2 1 2 1 22 2 2 1 2 1 2 2 ( ) 2 cos( ) ( ) 2 cos( ) L c c c c L c c c c           (2)
where q   ; 2 12 q   ; 12

1 1 2 2 atan( / ) + atan( / ) a b a b   The torques 1 1 1 M F h , 2 2 2 M F h    created by the forces 1 F , 2
F in the passive joint O can be computed using the triangle area relations 1 1

1 2 1 sin( ) L h c c   , 2 2 1 2 2 sin( ) L h c c   of AOD  and BOC  , which yield the following expressions 0 1 1 1 1 1 1 2 1 0 2 2 2 2 2 1 2 2 ( ) (1 ( )) sin( ) ( ) (1 ( )) sin( ) M q k L L c c M q k L L c c         (3)
where the difference in signs is caused by the different directions of the torques generated by the forces 1 F , 2 F with respect to the passive joint.

Further, taking into account the external torque ext M applied to the moving platform, the static equilibrium equation for the considered mechanism can be written as follows equation is highly nonlinear and cannot be solved analytically, so it is reasonable to apply the numerical Newton technique, which leads to the iterative scheme

  1 ( ) ( ) k k k k ext q q M q M M q      (5)
where

12 ( ) ( ) ( ) M q M q M q ,   () k M q dM q dq   .

STABILITY ANALYSIS OF THE MECHANISM

Let us now evaluate the stability of the considered mechanism at the equilibriums, which shows its reaction to the external disturbances. In general, this property highly depends on the equilibrium configuration defined by the angle q, which satisfies the equilibrium equation ( ) 0 ext M q M  . As follows from the relevant analysis, the function

()
Mq can be either monotonic or non-monotonic one, so the single-segment mechanism under study may have multiple stable and unstable equilibriums, which are studied in detail below.

To analyze the mechanism equilibriums, let us consider the torque-angle curves 12 ( ) ( ) ( ) M q M q M q  defined by Eq. 3 and presented in Fig. 2. It is clear that for the monotonic function () Mq with negative derivative (see Fig. 2a) increase of the external loading ext M always leads to higher mechanism resistance, so the equilibrium is unique and stable. However, in the non-monotonic case, while increasing the external loading, it is possible to achieve a point where the mechanism does not resist any more and suddenly changes its configuration as shown in Fig. 2b. It is worth mentioning that similar phenomenon can be observed in other robotic mechanisms and is known in mechanics as "buckling" [START_REF] Jones | Buckling of bars, plates, and shells[END_REF]. Hence, in the nonmonotonic case, there maybe three solutions of the equilibrium equation (two stables and one unstable).

As follows from the above presented figures, the static equilibrium defined by angle q is stable if and only if the corresponding derivative

  0 0 q Mq    (6)
which is easy to verify in practice. It should be noted that here the derivative represent the mechanism stiffness for the unloaded configuration.

To compute the desired derivative for any given q , it is convenient to represent the function () Mq in the following way

      00 12 1 2 1 1 1 2 2 2 1 1 2 2 1 sin 1 sin LL M q c c k c c k LL                       (7)
This allows us to express the mechanism stiffness in general case as follows

            00 12 1 2 1 1 1 2 2 2 2 2 0 2 2 0 22 1 1 1 2 2 33 1 2 1 1 1 2 2 2 12 1 2 2 11 () Mq LL LL c c k cos c c k cos c c k L c c k L sin si LL n                           (8)
For the special cases, when

0 q  and 12 q   (or 12 q   ),
the above expression is simplified respectively to

        00 1 1 2 2 1 2 12 1 2 12 2 2 2 0 0 12 1 2 1 1 2 2 1 0 2 3 () q k L k L c c cos k k sin c c k Mq L L L k L                   (9)       1 0 2 0 1 1 2 1 12 12 02 2 2 0 2 12 1 2 2 1 2 1 1 2 2 3 1 1 21 2 2 2 ( 1 ) q L c c k cos L sin c c k c c k L cc Mq L L                      (10)
where  

Mq q ck c q L          (12)
where the control input must satisfy the condition 0 02 Lb , which follows from the mechanism geometry (Fig. 1). To distinguish the monotonic and non-monotonic cases presented in Fig. 2, let us compute the derivative for the unloaded equilibrium configuration 0 q  ,which after simplification can be expressed in the following way

    0 2 2 0 2 () q Mq k b a L b     (13)
The latter allows us to present the condition (6) of torque-angle curve monotonicity as The monotonic and non-monotonic cases are also illustrated by Fig. 3b, which includes the energy curves  

2 2 0 1 1 ( ) ( ) 2 i i E q k L q L   
as the function of the rotation angle q. As follows from this figure, the energy () Eq has either a single minimum

q abk M q L c b a a b        (16)
which allows us to decide if the stable equilibriums in the nonmonotonic case are located inside of the interval of feasible rotation angles

  12 12
, q    

. It can be proved that the relevant condition can be expressed as follows

  2 0 2 22 2 ba L ba    (17)
and allows user to estimate if the energy minimum is achieved inside or on the border of the feasible region of q. A physical interpretation of this equation is shown in Fig. 4, where two cases are presented. In the first case, the mechanism is unstable in the desired configuration q=0 and jumps to one of two possible stable configurations e  that are located inside of mechanical limits. In the second case, the mechanism is also unstable in the equilibrium configuration q=0 but it jumps to one of the mechanical limits 12 q   (because the stable configurations are out of the limits). So, a static error appears in both cases, where q is equal to either 12   or e q  . For this reason, it is necessary to avoid in practice the parameters combinations producing non-monotonic torque-angle curves.

It is also useful to investigate the case when the control inputs are not equal, i.e. LL  , assuming that they produce the desired stable configuration with the output angle 0 q  . In this case, the torque and its derivative can be presented as follows.

  00 12 12 12 1 2

2 cos sin sin sin 22

qq M q ck c q L L          (18)
 

0 0 0 0 22 1 2 1 2 2 cos cos sin ) 22 ( 22
L L L L qq k b a q b Mq a            (19)
where all notations are the same as in the above expressions [START_REF] Furet | Kinematic analysis of planar tensegrity 2-X manipulators[END_REF] and [START_REF] Furet | Workspace and cuspidality analysis of a 2-X planar manipulator[END_REF]. It can be proved from the equilibrium equation that the control inputs

0 1 L , 0 2
L insuring the desired output angle q must satisfy the linear relation 00 , all three terms of (19) are negative, so the desired equilibrium configuration q is stable. -q e q e -q e

q a q b q L L b a q LL q cq                                 (
L b a a q q b a b b L b a a q q b a b b                         (22)
It is worth mentioning that in the case of 0 q  the above expressions give the stability condition Eq. 22.

Hence, to achieve the desired configuration q , it is necessary to apply the control inputs L are presented in Fig. 5, which clearly shows for which combination of inputs the desired configuration can be reached geometrically and it is statically stable, and where the angle q is constrained by the geometry conditions:

    2atan , 2atan , q a b a b q a b a b      (23)

CONCLUSION

The paper presents some results on the stiffness analysis of a new type of tensegrity mechanism, which is composed of two rigid triangles connected by a passive joint. In contrast to conventional cable driven mechanisms, here there are two length-controllable elastic edges that can generate internal preloading. So, the mechanism can change its equilibrium configuration by adjusting the control inputs length. Such design is very promising and convenient for constructing a multi-section serial structures with high flexibility, which are needed in many modern robotic applications.

For this mechanism, the main attention was paid to a symmetrical structure composed of similar triangles. In particular, the case of equal control inputs was investigated in detail and analytical condition of equilibrium stability was obtained, which allows user to select the control inputs ensuring the mechanism controllability. The relation between the external torque and the deflection was also obtained allowing to find loaded equilibriums. It was proved that depending on parameters combinations, the actuation can lead to either the desired mechanism configuration (corresponding to a stable equilibrium) or undesired configuration corresponding to shifted stable equilibrium or joint limits. Besides, similar analysis has been done for the case of nonequal control inputs, and equivalent serial structure was proposed where the passive joint was replaced by a virtual actuated joint with variable stiffness. In future, these results will be used for the stiffness analysis of multi-section mechanisms that may demonstrate unusual behavior under static load and suddenly change its configuration. L .

2 FIGURE 1

 21 FIGURE 1 MECHANISM GEOMETRY.

L

  , let us derive the static equilibrium equation. The forces 1 F , 2

, and the angles 1  , 2 

 12 are expressed via the mechanism parameters as follows[START_REF] Rolf | Constant curvature continuum kinematics as fast approximate model for the Bionic Handling Assistant[END_REF] 12

2 L

 2 and to the external torque ext M applied to the moving platform. It is clear that this

FIGURE 2

 2 FIGURE 2 THE TORQUE-ANGLE CURVES AND EQUILIBRIUMS FOR DIFFERENT COMBINATIONS OF MECHANISM PARAMETERS

FIGURE 3

 3 FIGURE 3 STABLE AND UNSTABLE REGIONS OF THE PARAMETER PLANE FOR UNLOADED EQUILIBRIUM 0 q  .

  q e <β 12 (b) q e >β 12 q e

FIGURE 4

 4 FIGURE 4 LOCATION OF STABLE "•" AND UNSTABLE "O" EQUILIBRIUMS WITH RESPECT TO GEOMETRIC BOUNDARY   12 12,  

  21) whose solution allows us to present the stability condition in the

  Fig. 5 Regions of equilibrium stability for different inputs 0 1 L , 0 2

ACKNOWLEDGEMENTS

This work was supported by the China Scholarship Council ( No. 201801810036 )


Oussama Meski

Farouk Belkadi

Florent Laroche

Mathieu Ritou

Benoit Furet

A generic knowledge management approach towards the development of a decision support system

The fourth industrial revolution is increasingly implemented in most fields and categories of industry. The use of several highly developed technologies generates huge amounts of heterogeneous data and knowledge, hence the need to manage it in order to facilitate its reuse. This article proposes a global approach of knowledge management, from the analysis and development of the knowledge base structuring models, to the implementation phase using knowledge engineering tools. This research work is part of a global knowledge-based decision support framework that ensures several axes of decision support, this article deals with the diagnosis axis. It provides analysis and comprehension of the failures occurring during production. The approach has been implemented as a first demonstrator tested in a real case study: the aeronautical mechanical machining industry. This article details the issues of this implementation and its interest for the validation of the approach.

Introduction

Since its appearance, the fourth industrial revolution has not ceased to affect most fields of activity and its implementation presents an interesting research topic in several disciplines. Nowadays, the strong aspect of this revolution is the expansion of the industry with the use of several technologies such as cyber physical systems, Internet of Things, digital twin, etc. [START_REF] Zuehlke | Smartfactory-towards a Factory-Ofthings[END_REF].

Production systems are among the most favourable areas for migration to industry 4.0 because manufacturing industries aim to provide an optimal and efficient product for their customers while maintaining as a main challenge the increase of competitiveness and the improvement of productivity [START_REF] Brynjolfsson | S t r e n g t h in Numbers: How Does Data-Driven Decision-Making Affect Firm Performance[END_REF]. Thus, these systems continue to work daily on findi g the best tips and tools for continuous production improvement.

Despite the emergence of new technologies and their ability to solve industrial problems, these tools need to remain under the control of the technicians and must be managed by human capacities and skills. The expertise of all industrial actors is crucial to ensure optimal use of available resources. This collaboration is the origin of artifici l intelligence, which can be considered as the digitisation of human know-how, skills and experience in order to automate the process of proposing solutions to reduce calculation times and reasoning efforts. Among the methods of artificial intelligence, decision support systems (thereafter, DSS) are used to analyse a problematic context and to propose a suitable solution to correct or avoid it (Teti 2015). These techniques have been too widespread for years and their usefulness is increasing with the appearance of new information technologies. As l o n ga st h e s es y s t e m sa r eb a s e do nb u s i n e s sr u l e sa n d industrial knowledge bases, they will generate reliable results.

Given all the resources used in industry, huge amounts of data and knowledge are available but unfortunately not widely exploitable. It is obvious that their reuse is constrained due to the heterogeneity of this knowledge. Several researches deal with the knowledge reuse issues in the field of production and manufacturing (Cochrane et al. 2009;Chungoora et al. 2013;U r w i na n dY o u n g 2013):theyallagreethereisaneedforaprocessofknowledge structuring and management in order to facilitate their exploitation.

This research work focuses on a specifi fiel of production: the machining of aeronautical mechanical parts. As these parts are very expensive and complex, the challenge of productivity is to manufacture good parts from the first try. Implicitly, it is necessary to avoid the occurrence of any problems or malicious phenomena that may affect the machining process (Teti 2015). Therefore, it's important to monitor the machining process [START_REF] Ferretti | Monitoring Systems for Zero Defect Manufacturing[END_REF] to improve its quality and its efficie y [START_REF] Grevenitis | AHybrid Framework for Industrial Data Storage and Exploitation[END_REF].

In addition to the two methods studied in this research, DSS and knowledge modelling and management approaches, the improvement of the performance of the manufacturing process can also be achieved through improving sustainability metrics (Raman et al. 2020). Several standards are working on characterising industry manufacturing processes for sustainabilityrelated decisions. For example, the subcommittee E60.13 of the American Society for Testing and Materials (ASTM) is focused on the issues of sustainable manufacturing.

T h i sa r t i c l ep r o p o s e sa ni n d u s t r i a lk n o w l e d g em a nagement strategy to help the development of a decision support system. The global framework being developed enables several decision-support axes: reporting, diagnosis, prediction and reaction. This work is mainly focused on the second axis.

Therefore, this article begins with a literature review on decision support systems and knowledge managemen t.N ext,thefir stst epso fthea p p r oac hco n structio n are presented; they consist of data and knowledge analysis and modelling. Finally, the scientific proposal ends with the presentation of the usefulness of the knowledge management approach for the development of the second decision support axis: diagnosis.

State of the art

This literature analysis begins by definin decision support systems, describing their usefulness, and detailing their processes. There are several categories of such systems, among them those based on knowledge managementprocesses.Theknowledge,aswellasthetoolsand methods needed for its structuring and management will be described in the second part.

Decision support systems

Research around designing technological solutions capable of supporting decision-making assistance to solve problems began since the 1970s [START_REF] Gorry | AF r a m e w o r k for Management Information Systems[END_REF]. The DSS consists of developing and implementing systems using information and communication technologies to ensure decision-making (Shim, Warkentin, and Courtney 2002).TheDSSareveryusefulforimproving and facilitating management at the different decision levels in the industry: the strategic level, which focuses on long-term planned actions to enhance productivity, the tactical level that manages processes and resources, and the operational level for the control and management of specifi operations (Klement, Silva, and Gibaru 2017). [START_REF] Drucker | Marketing and Economic Development[END_REF], [START_REF] Simon | Theories of Decision-Making in Economics and Behavioral Science[END_REF])andArcher(1980)define three essential phases of the decision-making process. T h efi r s ti s' t h ei n t e l l i g e n c ep h a s e 'w h i c hm a i n l yd e a l s with the definition of the problem. The second, intermediary, for structuring and defining the links between p r o b lem sa n dp r o posedso l u tio n s'th edesigna n dm odelling phase'. Finally, 'the choice phase' allows the decision-making and the proposal of a validated final solution.

The DSS process

Based on these 3 phases, several other works continue to define the steps of the decision support process, and the most frequently cited research remains that of (Shim, Warkentin, and Courtney 2002)w h i c hd e fi n e s seven steps. The fi st is always the problem identific tion. Foreachissue,thereisoneormoremethodtoeliminate or avoid its occurrence. To analyse these different alternatives, it is important to develop specific models that define the relationships between issues and proposed solutions as well as all the complementary parameters and business rules. These intermediate steps of analysis make it easier to choose the appropriate decision to be able to implement it in the last step.

Different categories of DSS

Along the technological evolutions, and the development of research on DSS, this field greatly evolved and several approaches and subfield emerged over time. [START_REF] Arnott | ACriticalAnalysisofDecision Support Systems Research[END_REF] deals with DSS and defines the main subfield and their evolution over time. It is hence possible to describe some types of DSS:

• Personal Decision Support Systems: as the name implies, these are often developed for a single manager or a group of independent managers. • Group Support Systems: are developed to improve the work and collaboration among a working group. The main objective of this system is to encourage decisionmaking based on all the suggestions proposed by the various members of the group. • Negotiation Support Systems: this type of system uses computer technologies to facilitate negotiation. There are two categories of these systems: problem-oriented and process-oriented. • Intelligent Decision Support Systems: this category of system introduces the use of artificia intelligence in decision support. They are classifi d into two generations: the fi st is rule-based systems and the second generation includes genetic algorithms, fuzzy logic and neural networks. • Knowledge Management-Based DSS: these systems allow the taking based on the capitalisation of knowledge and the development of knowledge repositories.

Also the manipulation, transfer and reuse of knowledge, for the purpose of decision-making and thus the creation of new knowledge.

The Decision Support System developed throughout this research work can be classified as both an Intelligent DSS and a Knowledge Management-Based DSS as it focuses on capitalising knowledge and expertise thanks to artifici l intelligence.

Knowledge management (KM)

Before beginning the management process, a literature review was essential, particularly concerning knowledge definitions. [START_REF] Davenport | Working Knowledge: How Organizations Manage What They Know[END_REF]defineknowledge as:

A fluid mix of framed experience, values, contextual information, and expert insight that provides a framework for evaluating and incorporating new experiences a n di n f o r m a t i o n .I to r i g i n a t e sa n di sa p p l i e di nt h e minds of knowers. In organizations, it often becomes embedded not only in documents or repositories but also in organizational routines, processes, practices, and norms.

Since the 1990s, many researchers have become strongly interested in knowledge management strategies as these methodologies has become crucial to increase productivity and competitiveness in production industries. Knowledge management can aff ct the organisation in several aspects: its structuring, behaviour, resources, and even organisational and economic strategies. Concerning DSS, several works have focused on the importance of KM to facilitate decision-making and to support knowledge creation processes [START_REF] Carlsson | Preface and Introduction in Proceedings of IFIP TC8/WG8.3 International Conference on Decision Support Through Knowledge Management[END_REF] Nowadays, with all the aspects of development and progress achieved, the challenge is not limited to the use of an effici t information system and developed technological resources: the real issue is to be able to adapt these resources to facilitate the creation of knowledge. [START_REF] Gunasekaran | K n o w l e d g e Management in 21st Century Manufacturing[END_REF];C h o we ta l .2005) defin knowledge management as the set of operations and activities that enable the creation and storage of knowledge for its distribution and application in organisations. In the same context, research continues to defin the basic functions of the knowledge management process. In 2017, Olson and Wu dealt with the KM processes in the service of the DSS and distinguished the following 4 core functions: the identification of the most important information and measures to support the decision-making, the acquisition of the data corresponding to these measurements and the storage in specifi databases for allowing the retrieval [START_REF] Olson | V iewofIJPRContributionstoKnowledge Management in Supply Chains[END_REF].

Using KM is very important in several field and especially in production and manufacturing. Berawi and Woodhead (2005) confi m that a good KM strategy helps to improve the overall production management system. Several research works deal with these themes in all the stages of the production process: purchasing [START_REF] Lau | A Knowledge-Based System to Support Procurement Decision[END_REF][START_REF] Zsidisin | AnInstitutional Theory Perspective of Business Continuity Planning for Purchasing and Supply Management[END_REF], planning (Gernhardt et al. 2016;Miltner,Vogel,andHemmje2014;[START_REF] Efthymiou | On Knowledge Reuse for Manufacturing Systems Design and Planning: A Semantic Technology Approach[END_REF], scheduling [START_REF] Kant | TheV aluesofUsingScheduling Information in Planning Material Requirements[END_REF][START_REF] Chryssolouris | K n o w l e d g eM a n a g e m e n t Paradigms in Selected Manufacturing Case Studies[END_REF], quality control (Muthu et al. 2001), etc. In the field of manufacturing and production, and more specifical y in the mechanical machining domain, t h ea n a l y s i so ft h ea v a i l a b l ed a t aa n dk n o w l e d g ea l l o w s the distinguishing the heterogeneities due to the variability of sources, types, natures, frequency, etc [START_REF] Grevenitis | AHybrid Framework for Industrial Data Storage and Exploitation[END_REF]. Thus, a challenge of adaptability and structuring is key to enable the aggregation, processing and extraction of knowledge from these information flows (Farhoomand and Drury 2002). Research on data and knowledge in the fiel of production has generally focused on the basic objects that compose the industry, i.e. the product, the resources used, the manufacturing process, the work context, the behaviour, etc. The modelling of industrial data and knowledge revolves around these basic objects. The analysis of the literature helps to distinguish several modelling approaches, for instance: The Product, Process, Resources approach (Cutting-Decelleetal .2007;Bo rjaRa misetal .2016), The Function, Behaviour, Structure -Product Process Resource External Effects approach [START_REF] Labrousse | FBS-PPRE, an Enter-priseKnowledgeLifecycleModel[END_REF].

Knowledge modelling must ensure a better visibility and understanding of the industrial knowledge fl ws to t h ee x p e r t( D e m o l ye ta l .2010). It is therefore essential to propose a well-structured and rich representation by adding semantics to relations and objects [START_REF] Belkadi | A Meta-Modelling Framework for Knowledge Consistency in Collaborative Design[END_REF]. Studies in the fiel of semantic modelling are, generally, connected to the semantic web (Berners-Lee, Hendler, and Lassila 2001). Hence the use of its languages, generally developed by The National Institute of Standards and Technology (NIST) for example: RDF (Resource Description Framework), XML (eXtensible Markup Language) and OWL (Ontology Web Language) [START_REF] Mclean | ShopData Model and Interface Specific tion[END_REF]McGuinness and Harmelen 2004).

Among the most effective methods for ensuring semantic understanding are ontologies (Pavel Vrba et al. 2011). An ontology is a method for representing and organising knowledge of a specifi field using reasoning and inference mechanisms [START_REF] Octaviani | RDB2Onto: An Approach for Creating Semantic Metadata From Relational Educational Data[END_REF][START_REF] Munir | T h eu s eo fO n t o l ogies for Effective Knowledge Modelling and Information Retrieval[END_REF]. [START_REF] Gruber | A Translation Approach to Portable Ontology Specific tions[END_REF] which define ontology as an explicit specification of a conceptualisation, he also describes all of its fundamental elements:

1. Concepts or classes: these notions allow the description of a task, a function, an action or a reasoning process. 2. Relationships: represent a type of interaction between two or more concepts. Examples of relations include 'subclass-of' or 'connected-to'. 3. Functions: are a special case of an n-element relationship where the last element of the relationship is unique for the fi st n-1 elements. 4. Axioms: are used to defin the semantics of terms (classes, relations), their properties and any constraints regarding their interpretation. 5. Instances: used to represent elements.

Two types of ontologies can be distinguished: storage ontologies and inference ontologies [START_REF] Fankam | OntoDB2: un Système flexible et Effici t de Base de Données à Base Ontologique Pour le Web Sémantique et les Données Techniques[END_REF].

The first, as its name suggests, allows to capitalise a maximum of knowledge on a given domain. The second allows, through the execution of a set of business rules, inference rules, restrictions and constraints, the automatic generation of new knowledge [START_REF] Milicic | PLM Ontology Exploitation Through Inference and Statistical Analysis A Case Study for LCC[END_REF].

Ontologies are used in several domains to ensure communication, structuring and reuse of knowledge [START_REF] Gruninger | Ontology Applications and Design[END_REF];S u r e e p h o n ge ta l . 2008;Schmidt et al. 2016). And to ensure interoperability [START_REF] Gunendran | An information and knowledge framework for multiple-perspective design and manufacture[END_REF] between the different subcomponent of an overall system. Thus, they are a good choice for the development of knowledge-based systems [START_REF] Sanya | A Framework for Developing Engineering Design Ontologies Within the Aerospace Industry[END_REF]. In each particular fiel , research work uses reference ontologies [START_REF] Annamalai | An Ontology for Product-Service Systems[END_REF]Borsato2014) which are considered highly generic domain ontologies, often resulting from merging several specifi ontologies [START_REF] Palmer | Interoperable Manufacturing Knowledge Systems[END_REF]). In the literature there are several examples of these reference ontologies, such as: DOLCE [START_REF] Masolo | S o c i a lR o l e sa n dt h e i r Descriptions[END_REF] Others have used standards for the development of ontologies, for example: OntoSTEP [START_REF] Krima | OntoSTEP: OWL-DL Ontology for STEP[END_REF] based on the Standard for the Exchange of Product model data (STEP). Also, standard languages such as The PSL ontology based on The Process Specific tion Language [START_REF] Schlenoff | ISO-18629 The Process Specific tion Language (PSL): Overview and Version 1.0 Specific tion, NIS-TIR 6459[END_REF]

;G r u n i n g e ra n dK o p e n a2005).

There is also the Standard MTConnect that, according to their website, 'off rs a semantic vocabulary for manufacturing equipment to provide structured, contextualized data with no proprietary format'.

There are several foundations whose objective is to centralise research on ontology development in each specifi field. In the area of digital manufacturing, the Industrial Ontologies Foundry (IOF), as stated on their website, tries to create a set of core and open reference ontologies that spans the entire domain [START_REF] Kulvatunyou | TheIndustrialOntologiesFoundryProof-of-Concept Project: IFIP WG 5.7[END_REF].

After the analysis of the ontological solutions proposed in the literature, and considering their interests for ensuring interoperability and communication of knowledge between the services of industry, it is noticeable that most of these works are oriented towards partial communication. It is insured just between the services directly involved in the realisation of the product: basically between the workshop and the design or manufacturing departments. This implies a lack of communication between the different services of the industry, which are closely or remotely related to the realisation of a product as well as the communication between the different information systems of the company. In addition, the proposed solutions do not manage all heterogeneous knowledge from different sources and formats. Another disadvantage is the lack of genericity of the identifi d solutions. This involves a difficult reuse in other fields compared to our ontological solution, which enables flex ibilityandadaptability,thankstoitslayeredstructureand the use of norms and standards.

This literature review raises three main issues: how to develop the best knowledge management approach, able to structure the variety of heterogeneous data and knowledge? How to implement such a knowledge repository? How to exploit it, to ensure the reuse of knowledge and to generate new ones in decision-support scenarios?

The analysis phase

A clear distinction between the different types of heterogeneous data and knowledge circulating in the industry is necessary for optimal capitalisation.

In order to build this classific tion of knowledge, the first step adopted in the proposed methodology was to develop process models to analyse all information flows in the manufacturing shop floor of mechanical parts. They were built based on literature survey and consolidated with the industrial partners of this research project in order to validate the adequacy of these formalised manufacturing processes (Meski et al. 2019b).

In addition to the output data flows generated from the various phases of product manufacturing, monitoring data are also traced using a specifi device composed of hardware components (such as sensors and acquisition cards) and software components that include monitoring database and processing algorithms.

Several sensors have been installed to monitor machining parameters: acceleration, temperature, vibration frequency, etc. These sensors allow the recording of representative data concerning the health status of the machine and its different components (spindle, cutting tools, platens, etc.). The machine's computer numerical control (CNC) provides additional information related to the operational context of manufacturing process (date and time of operation, working piece reference, program reference, operating mode, etc.). These heterogeneous data are then subjected to several aggregations and data mining operations to generate a new category of data called Smart Data [START_REF] Ritou | Knowledge-based Multi-Level Aggregation for Decision aid in the Machining Industry[END_REF]. The use of these processing methods adds a new semantic layer representing links between the initial raw data. New indicators are then created and allows for better evaluation, not only of the health status of the manufacturing resources, but also the quality of the manufactured workpiece and especially the potential malicious phenomena that may appearduringmachiningprocess.Boththeuseofsmart data and key performance indicators (KPIs) require additional knowledge from the expert who therefore acts like an additional knowledge source.

The capitalisation of this different knowledge allows t h ei m p l e m e n t a t i o no fs e v e r a ld e c i s i o ns u p p o r ts c e n a rios (Figure 1) .T h efi r s ta x i si st h e' R e p o r t i n g 'w h i c h provides several reports that describe malicious phenomena conducted to undesired impact (i.e. a degradation of the quality of the working piece due to the appearance of a chatter, a cutting tool breakage, a collision between the tool and the part, or others). These reporting operations are executed within a specifi mode (periodic, on-demand, after a phenomenon occurs) and are customised for particular business roles or departments in the company (quality control, maintenance, process planning, programmer, etc.). After reporting and studying the characteristics of detected problems and phenomena,adiagnosisprocessmustbecarriedouttodetectthe cause of their appearance. Finally, once the situation has been studied, solutions can be proposed to facilitate the decision-making process to improve the product quality or to prevent any future occurrences.

The separation between data and knowledge types conducts to two repositories. The first one includes raw and smart data (separated in three databases) while the second gathers all the available industry knowledge, the business rules, the set of KPIs and reports generated through the reporting processes. Thus, the four knowledge types distinguished in this work are raw data base, smart data base, traceability data base and knowledge repository (Meski et al. 2019a).

To structure these digital repositories, several categories of models have been created. First, data models were dedicated to clarify all the available industry data fl ws, in a standard format, then other models were developed to structure the traceability database.

Data-knowledge models construction

Before starting construction of the models, an in-depth study of the state of the art in the fiel of product and process-oriented modelling was made and coupled with an analysis of real industrial processes. The target was to draw inspiration from the models realised in the fiel . Following this literature review, several modelling approaches were identified. These models are strongly linked since they are all based on a common list of industrial objects and components. Among these components were identified four that match well with this project: product, process, context, resources, and people. While these objects represent essential elements for each industry and they are considered fundamental to model the global industrial knowledge base, previous modelling approaches do not cover all of these elements simultaneously. This leads to the development of the CR3P (Context, Resources, Product, Process, People) modelling approach. As its name suggests, it initially covers the entire context of the work and the whole set of significa n tkno wledg etha tca nco v erinf o rma tio na bo u t working conditions, references and identifie s of the different elements used, as well as information about risk assessment or even the constraints imposed by the end customer.Thisapproachalsoinvolvesknowledgerelated to the resources used, the product being manufactured o rt h ep r o c e s sf o l l o w e dt om a n u f a c t u r ei t( M e s k ie ta l . 2019b).

The specific ty of the approach is also linked to the integration of the 'People' object as a foundation element i nt h eg l o b a lk n o w l e d g em o d e l .T h eC R 3 Pa p p r o a c h emphasisesthehumanbyconsideringitasamainnodeof the overall industrial structure. An important amount of knowledge is provided by the expert and several decisions must be taken or supported by him and his expertise. This expert knowledge lies in what is called business rules.

Based on the analysis step, the knowledge models have been developed and enriched with high level of granularity and details using ontology modelling paradigm. Indeed, using ontologies is a practical solution given the large amount of heterogeneous knowledge to be considered, the relations and business rules to be integrated, and the reasoning to deduce new knowledge and decision to be created.

The proposed ontology is structured around several layers, gathered into three main groups, which have been formalised according to the specific ty, nature and origin of the knowledge acquired (Figure 2).

T h efi r s tl a y e rc o n t a i n st h ed i c t i o n a r i e so fr e s o u r c e s used in machining process, such as references of the cutting tools used with their specific cutting conditions, characteristics of the resources used for manufacturing, t y p e so fr a wm a t e r i a l su s e d .T h e r ei sa l s ot h ek n o w ledge related to the manufacturing process, the diff rent operations used, etc.

In parallel with this fi st layer, and in order to ensure thegenerici tyo fthekno wledgebasef o rfu t ur er eusein other fields, norms and standards have been analysed and the most appropriate ones have been considered for structuring the second layer of ontological models. In this research, part of the STEP-NC (14649-10: Data model for computerised numerical controllers -Part 10: General process data) is used. It includes all the parameters, names, concepts and relationships for the majority of manufacturing operations and features. STEP-NC is a data exchange standard for numerical control programming, and for communication between the diff rent parts of the physical industrial chain: design, industrialisation and manufacturing. It is based on the STEP standard (ST andardfortheExchangeofProductmodeldata)that use the data modelling language EXPRESS to develop several models and schematics. In addition, Step NC uses the graphical standard EXPRESS-G to represent the process model. This standard is widely used in the field of mechanical manufacturing.

The integration of this standard into the global knowledge base consists of transforming EXPRESS-G diagrams into an ontology composed of classes, relationships and attributes. The transformation of this standard into the ontology has resulted in the development of more than a thousand axioms (Figure 3).

The last layer groups all the knowledge necessary to support the decision process. It includes mainly business rules and the structure of a decision support case. In this research work, the business rules are very useful and essential for the implementation of the second development axis in this project: the diagnosis. As shown in the figure above, the three layers constituting the ontology are strongly interlinked. In general, the execution of a decision support scenario should begin by analyzing and identifying the context elements, characterising the situation or case to be treated. They are instantiated based on dictionaries and sometimes-standard layers.

Data and knowledge bases are in continuous collaboration: the execution of a scenario starts at the knowledge base level to retrieve the necessary structure then the reasoning system queries the databases to retrieve the corresponding data. The processing is then executed and it instantiates specifi elements in the knowledge base. For an event diagnosis scenario, these elements, also knownasindividuals,arerepresentedbycasesandthose are structured with the objects 'cause, effect, decision, context', which will be presented in the following section.

Framework application: the diagnosis process

In order to improve a company's productivity and competition, a diagnosis process is set up. It allows the analyse of distinguished failures and the detection of the causes of malicious phenomena appearance during machining process. Beyond that, the diagnosis scenario is based on a characterisation of the working context to propose the appropriate solution based on experiences. This will help improving quality and leading time of the entire production process, and especially to lighten the work of the quality department. The proposed solution aims also to support the maintenance department to be preventive and avoid the recurrence of similar undesirable phenomena in the future.

Proposed approach to diagnosis process

At the conceptual level, the proposed approach is based on the well-known FMEA (Failure Modes and Effects Analysis) method in order to set up the main criteria and parameters representing failures, causes and eff cts. F o l l o w i n gt h i sm e t h od ,n ewk n o wl e d g e( ru l e sa n dp r ocedures) has been integrated into the ontology in order to support the diagnosis process at the decision aid level. This knowledge is structured as a 'case' which is composed by the quadric 'Context-Cause-Effect-Decision'.

• The CONTEXT calls, from the other layers of the ontology, all the elements necessary to characterise the manufacturing environment, namely: the name and reference of the tool, the name of the program and subprogram, the date, etc. Additional characteristics of the machining resource can be reached from the resource library. These contextual elements depend strongly on the diagnosis case and can vary according to the related decision needs of the user. • The EFFECT characterisesthemainfailuretobediagnosed. In this project, it represents the malicious phenomenon that has appeared. The instantiation of this element can be either automatic following a direct detection of the problem or indirect following a fi st phase of in-depth analysis. This object has several featuresandoptions,namely:aneffectcanbetheorigin of another one, each effect can be generic or detailed, an effect can also be an element of context for another case, etc. • The CAUSE is the key element of the proposed knowledge-based diagnosis approach. It represents the origin of the malicious events that occurred during the machining of a mechanical workpiece. To be able to propose a cause to an event, the solution was to formalise human intelligence and the best practices in order to propose an artificial intelligence tool ready to be integrated into the machine. More precisely, in this project a set of business rules have been defin d to formalise the interpretation of expert about past incidents. So, the reasoning on the current incident can be made based on its connection to similar past situation were the appropriate business rules are applicable. The execution of business rules depends strongly on the contextual elements and the observed effect to generate the most reliable cause, hence the importance of the instantiation stage of the object 'context'. • The DECISION: once a new undesirable situation has been detected, its effects observed and its causes identified,thelastelementstobecomputedisaproposed solution and the related decisions needed to solve the problem. The notion of decision (or solution) includes all actions beyond the diagnosis process that aim to remove the observed consequences (reparation) or to anticipate/neutralise the problem causes (preventive). Explicitly, it regroups all the rules, actions and procedures that contribute to reset or maintain the manufacturing system in its normal working conditions. Given the specificity of this research work, the decision is represented by a solution, but it may have different forms in other cases of application, depending on the objective, and the need of the user. Therefore, the loop of the knowledge-based decision-aid framework is closed.

The global objects of the modelling strategy represented by the quadric defined above, are strongly linked and can depend on each other. More precisely, a first phenomenon 'A' (represented by an 'Effect1' with a 'Cause1') can be the cause of appearance of a second phenomenon 'B' (an 'Effect2' with a 'Cause2'), as shown in the Figure 4, and this induces a second diagnosis process.

More formally:

« Effect1 → Cause1 = Effect2 → Cause2 »
In this case, the context may be the same for both scenarios (referred as 'ContextGlob') or may be specifi to both (referred as 'Context1' and 'Context2'). More formally: Knowing that {Cause1, Effect1}∈Context1 {Cause2, Effect2}∈Context2 More technically, in order to structure diagnosis operations at the ontology level, these four objects have been defin d as classes. In addition, a list of relationships linking these classes and attributes has been specified. Progressively, as the ontology is implemented and real scenarios are run, these classes will be instantiated by creating the corresponding group of individuals. This instantiation is based on previously structured industrial databases (raw, smart and traceability); this highlight the utility of the knowledge management strategy, promoting the interaction with data to generate new knowledge.

Either: ContextGlob in which « Effect1 → Cause1 = Effect2 → Cause2 » Knowing that {Cause1, Effect1, Cause2, Effect2}∈Con- textGlob Either: ∃ (Context1; Context2) ∈ ContextGlob Such as « Eff ct1 → Cause1 = Effect2 → Cause2 »
To better illustrate this structuring methodology, a use case scenario is presented in the next section.

The use case

T h ei n i t i a ls t a g ew a sm a d ep r i o rt ot h i sr e s e a r c hw o r k and concerns the defin tion of specifi data mining algorithms to analyse raw data and extract smart data [START_REF] Wang | Comparison of K-Means and GMM Methods for Contextual Clustering in HSM[END_REF]. This leads to the generation of traceability data and the management of heterogeneous reports [START_REF] Ritou | Knowledge-based Multi-Level Aggregation for Decision aid in the Machining Industry[END_REF]). Together, these latter two publications explain the various operations required for the preliminary stage. Many research works define the criteria to be respected and the means to manage large-scale enterprisesoftwaresystems.Amultitudeoftechnologiesand standards exist to ensure software interoperability and systems integration in order to facilitate interaction with each other [START_REF] Andersson | Architectural Integration Styles for Large-Scale Enterprise Software Systems[END_REF].

In this research project, given the diversity of tasks, skills, and technologies handled by the different research teams, the need for a solution to ensure technical interoperability is necessary to develop a common global Framework. The solution chosen in this use case is the use of multi-agent systems. Thus, several agents have been developed over time (Computing Agent, Communication Agents, Databases Agent ...). In this article, a decision support agent is presented: the Diagnosis Agent.

Expertise analysis and scenarios definition

Operations of data mining were able to detect a set of very frequent phenomena: chatter, tool failure, and collision.T oensurethisdetection,afirstphaseofmachine learning was established to calculate specifi thresholds for several detection criteria and parameters. For example, to detect a chatter, it is sufficient to notice an overflow of the threshold for the 'N h ' parameter which is the sum of the amplitudes of the fiv dominant non-harmonic contributions of the vibration spectrum [START_REF] Godreau | Continuous Improvement of HSM Process by Data Mining[END_REF]. A tool failure is also likely due to the exceeding of the threshold defin d for the 'U b ' parameter which is computed as the vibration amplitude of the contribution at the spindle frequency, when the spindle is rotating without cutting (to prevent from false detection due to cutting forces). Several other aspects can be the cause of an abnormal phenomenon, such as significant power variations, which are good indicators of a collision. In addition, the variation of the machine-tool potentiometers is a practical KPI since it allows the detection of any human intervention that could delay productivity. After this first step of phenomenon detection, in order to understand the cause of appearance, a formalisation of all the business rules necessary for an analysis is essential. T orealisethissecondstep ,thesolutionistoholdin terviews with technicians and industrial experts and discuss possible causes. The recurrence of the phenomenon must be studied to understand the origin of the phenomenon.

This leads to the defin tion of an explicit list of business rules. Table 1 shows some of them. On each line, parameters necessary to detect a given eff ct and the rules applied to determine its cause of appearance are detailed.

Following this mapping phase, an algorithm of the diagnosis agent is defin d. It starts by an interaction with t h eu s e rt od e fi n et h es p e c i fi cc o n t e x ta n dt h ed i a g n osis operation to perform. The scenario category to be executed may depend on the user's profile, or on the importance and seriousness of the phenomena studied. Hence, the importance of defining a criterion or a criticalscore for each anomaly. This rating is measured based on the following table (Table 2).

The diagnosis agent is in continuous communication with the knowledge base and databases. Accessing the knowledge base, it retrieves a list of criteria, conditions, thresholds, etc. Afterwards, accessing the databases it recovers data needed to execute the necessary specific reasoning. Finally, it instantiates all the case at the ontology level with the context, effect, cause and decision respectively.

General view of the algorithm

To better illustrate these aspects, let's focus on a specifi scenario concerning the diagnosis of a tool breakage. Based on the previous list (Table 1), this scenario described in Table 3,willbetreated.

The following diagram (Figure 5)r e p r e s e n t st h e detection algorithm. It shows how the analysis of a particular scenario enrich the knowledge base, gradually improving the strength of this decision-support program.

Technical aspects and user interface (UI)

The Global Framework is developed using the Java language. The technological issue was to find the most suitable API to communicate with the ontology developed using the Web Ontology Language (OWL). The required solution is to use the Jena API. Apache Jena,a ss t a t e d o nt h eJ e n aw e b s i t e ,i saJ a v af r a m e w o r kt oc o n s t r u c t Semantic Web Applications. It provides a programmatic environment for:

• Resource Description Framework (RDF), a graph model for describing web resources and their metadata,sothatsuchdescriptionscanbeprocessedautomatically. Developed by the W3C, RDF is the basic language of the Semantic Web. • The Jena inference subsystem, designed to allow a range of inference engines or reasoners to be plugged into Jena. Such engines are used to derive additional RDF assertions, which are entailed from some base RDF together with any optional ontology information, and the axioms and rules associated with the reasoner. These developments are part of a global demonstrator that revolves around two decision-support axes: reporting and diagnosis. On the first part of Figure 6 there are the 3 functionalities enabling to do reporting by event detection, on demand or by planning. Concerning this use case, the user has to choose the fourth, 'Phenomena diagnosis'. Thus, a second interface appears, in which he can choose from a list the context elements (production line, machine tool_Id, period, type of phenomenon to be diagnosed, etc.). In this scenario, the user chooses the 'Tool failure' phenomenon.

Diagnosis process details

In the specific scenario of a tool failure, the first step is the verification of the possible exceedance of the threshold defin d for the detection criterion 'U b '. To do this, a threshold, calculated using machine learning algorithms, has been instantiated beforehand at the knowledge base level. This is the first manifestation of interaction between data and knowledge. Thequeryingoftheontologyfordataretrievalisdone using the SPARQL query language. The figure below shows an example of a query used in this demonstrator (Figure 7).

Once the threshold value is recovered, the monitoring databases must be analysed by comparing the U b variations with this threshold. An exceeding value means the appearance of a tool failure and thus initiates the diagnosis process. Currently, the smart database is in form of a CSV fil . Figure 8 shows an excerpt from a smart data fil .

The instantiation of the ontology starts with a new individual (Figure 9) called 'Case_tool_failure' and also individuals of type 'Cause' 'Context' and 'Eff ct'.

Subsequently a mapping phase is needed to make the link between these elements using 'Object properties'. And finally, by using 'Data Properties' the attributes of each individual are added.

In order to add the context elements (considered here limited to the instantiation of the tool, the program and the day), it is necessary to position on the line containing anexceedingofthethresholdofthe'Ub'criterion,andto recover all the necessary parameters.

The next step, 'searching for the cause', is the most important step, and is presented in the flowchart (see Figure 5)asaseparateprocess.

Concerning this scenario, a fi st business rule was formalised following the interviews with the industrial partners of the project:

The tool is the cause of the breakage when the measured cutting conditions are different from the reference cutting conditions.

Here, measured cutting conditions are those recovered using the monitoring tools and the reference cutting conditions are the ideal ones predefine by the methods office.

To implement this rule at the ontology level, a transformation step is needed to convert this rule from the naturalhumanlanguagetotheformalisedrulelanguage specifi to the JENA API, which is shown below: @prefix ns: < SpecificPrefix > . [rule1: (?a ns:hascontext?b)(?a ns:hascause?c)(?b ns:hastool?x)(?x ns:hasVf?d)(?x ns:hasVFReal?w) notEqual(?d,?w) → (?c ns:hascausedirect 'tool problem: non-compliant cutting condition')]

The execution of this business rule implies the verification and the comparison between the two categories After the automatic instantiation of the ontology, the user receives the result of the entire diagnosis operation in the interface shown in Figure 11 and is presented with solutions.

This scenario represents a simple execution of a single business rule; other scenarios require multiple rules and iterations to fin the origin of a single problem. Therefore, a typical scenario would not necessarily end at this stage since the determination of a first direct cause can lead to a new diagnosis process for the determination of indirect ones.

Conclusion

The implementation of the industrial knowledge management methodology proposed in this article, and the testing of several decision-support scenarios have shown the feasibility and the interest of the approach. However, there are some limitations to this approach, most notably the availability and accessibility of industrial knowledge. Suchatoolmustbeimplementedinafavorableindustrial c o n t e x tt h a to ff e r st h en e c e s s a r yr e s o u r c e sa n dm e a n s , and encourages collaboration between the digital system and the experts. The complexity of the development is hence mainly focused on the formalisation of the business rules base, through the transformation of the e x p e r t i s ea n da l lt h ei m p l i c i ta n dt a c i tk n o w l e d g ei n t o explicit formal rules. This aspect favors and highlights the importance of the human place in the context of digitisation and the fourth industrial revolution. The need for a first phase of direct interviews with the business experts highlights this crucial role. In a nutshell, the challenge is to promote the importance of collaboration between the system and users who remain masters and controllers of the operations: the initial objective of a decision support system.

Our approach is specifi in its layered structure and especially the separation between the domain ontology layers that regroup the generic knowledge sets and libraries, and the decision support layer. This in turn guarantees adaptability and modularity in various other research domains by changing the first layer with another reference ontology of another field. In addition, t h es t ru c t u r i n go fk n o w l e d g ea saq u a d ru p l e t' Co n t e x t -Cause-Effect-Decision' would allow several perspectives for the development of the system. For example, the of diagnosed cases and all the elements describing the work context would enables the elaboration of reasoning based on similarity indices. This wouldinturnfacilitatefuturediagnosisoperations,solution proposals, but also the prediction of the appearance of a phenomenon and the proposal of preventive actions.

Multiple perspectives could be envisaged for the continuation of this work. In the short term, the objective is to improve and enrich the business rules base, to be able to implement other diagnosis scenarios. Interviews with industrial experts continue to be held enabling the capitalisation of their expertise into an artificial intelligence embedded in the production machines. In this article, the use of the knowledge management methodology to implement a diagnosis process is demonstrated. Among the possible perspectives envisaged is the use of this strategy to implement other axes of decision support, especially, to provide reaction and prediction. Another perspective of this work consists in validating the adaptability and genericity of the methodology developed in other fields such as architecture and archaeology for example. This could demonstrate how the Context-Cause-Effect-Decision methodology is suitable on a comprehensive panel of knowledge-based diagnosis.

Disclosure statement

No potential conflict of interest was reported by the author(s).

  ; Sanfilippo and Borgo 2015) SUMO (Oberle et al. 2007)B F O( R o b e r t Arp, Smith, and Spear 2015). Some ontologies are more specifi to the manufacturing domain such as MASON (Lemaignan et al. 2006), Onto-pdm (Panetto, Dassisti, and Tursi 2012), etc.

Figure 1 .

 1 Figure 1. Execution phases analysis.

Figure 2 .

 2 Figure 2. Knowledge base structure and layers interconnection.

Figure 3 .

 3 Figure 3. STEP-NC from Express-G to ontology with Protégé software.

Figure 4 .

 4 Figure 4. Dependencies of diagnosis elements.

Figure 5 .

 5 Figure 5. Detection algorithm flow chart.

Figure 6 .

 6 Figure 6. UI diagnosis launch.

Figure 7 .

 7 Figure 7. SPARQL query example.

Figure 8 .Figure 9 .

 89 Figure 8. Smart data file extract

Figure 10 .

 10 Figure 10. The Automatic instantiation of ontology.

Figure 11 .

 11 Figure 11. The final interface representing the result of the diagnosis.

Table 1 .

 1 List of possible diagnosis scenarios.

	Detection criteria	Effect	Cause	Rules
	U b > threshold	Tool failure	-Cutting conditions problem	Compare with reference cutting conditions
			-Tool life badly defined	Tool often broken at the end of its life
	Power variation	Collision	-Program error (during machining).	Checking program and subprogram names (ex: CHANG_OUT.SPF
			-Tool gauge or probing error.	for tool change) + machining time = 0 ...
			-Wrong operator manipulation (manual mode)
			-Problem returning the tool to the magazine
	Nh > threshold	Chatter	-Either the tool or the workpiece
			-bad programming
			-bad workpiece clamping

Table 2 .

 2 The measurement elements of the criticality criterion.

	Criteria	Rating
	Failure severity rating grid G
	Minor defect without performance degradation	1
	Fault can be repaired on site without performance degradation	2
	Fault can be repaired on site with impaired performance	3
	Non-repairable fault	4
	Rating grid for the frequency of appearance F
	Very low	1
	Low	2
	Frequent	3
	Very frequent	4
	Non-detection rating grid D
	Effective preventive detection (measurement, optimised	1
	threshold, action)
	Preventive detection (measurement, non-optimised threshold,	2
	action)
	Preventive detection not used	3
	Not detected	4

Table 3 .

 3 The diagnosis scenario selected for the implementation.

	Detection criteria	Effect	Cause	Rules
	U b > threshold	Tool breakage	-Cutting conditions problem	Compare with reference cutting conditions
			-Tool life badly defined	Tool often broken at the end of its life

Funding

This work was supported by Agence Nationale de la Recherche [grant number ANR-16-CE10-0005].

Notes on contributors

Dr Oussama Meski i saP h Ds t u d e n t in industrial engineering at the University of Nantes (at LS2N: Laboratory of Digital Sciences of Nantes, IS3P team). He received his engineering degree in robotics in 2017 from the Polytechnic School of Montpellier France. Currently he is involved in the SmartEmma research project in which he is working on the challenges of digital transformation of companies and the industry 4.0 issues. He is mainly specialised in knowledge management for the development of decision support systems. Despite his very recent career inthefieldofscientificresearch,hehasmanagedtopublishhis research in 3 international journals and several national and international conferences.

Dr Farouk Belkadi is an associate professor atEcoleCentraledeNantes(researcherat LS2Nlaboratory ,IS3Pteam).Hereceived his PhD in Industrial Engineering from the University of Franche Comté in 2006. The PhD thesis treats the problematics of knowledge and skill management in design projects. During his career, he was involved in several research projects at national and European level, dealing with various topics: Product-service systems, system engineering, information systems and PLM, knowledge engineering and management, and, recently industry 4.0 related technologies. His research results were disseminated in 30 international journals and more than 70 national and international conferences Dr Florent Laroche is assistant professor at EcoleCentraledeNantes(France).Aftera engineering diploma in 2003 and his PhD in 2007, he was empowerment for driving his own researches in 2017. At university, Florent Laroche is the head of Mechanical Department for design and production product and system; Florent Laroche is doing his research at the laboratoryLS2N (Digital Science Laboratory, Nantes, France-UMR CNRS6004). He works on the translation of knowledge of the past in contemporary knowledge, readable and understandable in the present sociotechnical system. One objective of this research is to reuse the technical heritage as a basis for innovation. His research topics are KM, PLM, information system modelling, interoperability, enterprise modelling, virtual engineering, reverse engineering. He is active in 21 scientifi networks from all over the world. He is author, co-author or invited speaker in more than 230 scientifi communications quoted more than700 times; director of 12 PhD, 26 masters. He is expert for Museums and ICOMOS.

Pr

ORCID

Oussama Meski http://orcid.org/0000-0002-3017-0954 Farouk Belkadi http://orcid.org/0000-0003-2783-4147


E Guilmineau

G B Deng

A Leroyer

P Queutey

M Visonneau

J Wackers

Influence of the Turbulence Closures for the Wake Prediction of a Marine Propeller

Keywords: Propeller, Open water, Numerical simulations, Turbulence models, DES approach, RANS models

Results of computational fluid dynamics validation for flow around a marine propeller are presented. Computations were performed for various advance coefficients following experimental conditions. The objectives of this study are to establish capabilities of various turbulent closures to predict the wake of a propeller, and to predict the instability processes in the wake. Two RANS models are used: the k-ω SST of Menter and an anisotropic two-equation Explicit Algebraic Reynolds Stress Model (EARSM). A DES approach based on the k-ω model is also used. Computational results for both global and local flow quantities are discussed and compared with experimental data. The predicted thrust and torque are in good agreement with the measured values for all turbulent closures. With the RANS turbulence models, the wake of the propeller is too dissipated and then the instabilities of the wake are not predicted. On the contrary, DES approach can allow to capture the evolution of the tip vortices and predicts the onset of instabilities in the wake. The main difference between these various turbulence closures is that the flow in the core of the vortex is characterized by rotation, streamline curvature effects which are not adequately modelled by RANS turbulence models.

INTRODUCTION

The prediction of the fluid dynamics interaction between propellers and the hull is very important for the improvement of ship performance since the interaction is directly related to vibrations, noise and propulsion performances. In this context, the demand for the improvement of performance implies a rising interest in the development and application of detailed numerical tools

The physical mechanisms that characterize the interaction between the propeller and the hull are very complex. However, even in the simpler case of an isolated propeller in a uniform flow, called open water conditions, we are confronted with several numerical and physical challenges. In the propeller field, a number of viscous phenomena can be identified including blade and hub boundary layers, flow separation on the blade, viscous-inviscid interaction, hub and tip vortices, viscous wake. Therefore, study of these flow characteristics is essential for accurate prediction of the propulsion performance. In this paper, we only focus on the open water conditions. In this case, the flow is characterized by two vortex systems: one generated by the tip of the blade and the second emanated from the hub. A comprehensive description of the state of the art can be found in [START_REF] Felli | Mechanisms of Evolution of the Propeller Wake in the Transition and Far Fields[END_REF], who experimentally investigated the flow around a propeller in water tunnel. These authors studied the mechanisms that trigger the instability of wake and investigated the dependence of the vortex pairing and grouping on the mutual vortex distance.

Based on a numerical point of view, the reliability of the such numerical predictions can be questioned. It is difficult to control numerical diffusion when intense and localized three-dimensional structures are concerned. The flow in the core of the vortex is characterized by rotation, streamline curvature effects which are not adequately modeled by classical eddy-viscosity based turbulence models. Unsteady hybrid LES turbulence closures like DES appear attractive, see [START_REF] Muscari | Modeling of Vortex Dynamics in the Wake of a Marine Propeller[END_REF].

The purpose of this paper is to conduct such a validation of the flow around an isolated propeller to compare statistical turbulence closures and an hybrid LES methodology to draw conclusions about the requirements in term of physics. The present paper is organized as follows. The test-case is presented followed by the numerical method. The CFD results are presented for comparison and validation, as well as flow field analysis. Lastly, some concluding remarks are made.

characterized by a nominally constant pitch distribution and a very low skew angle. The propeller is presented in Figures 1 and2 and the main geometrical features are reported in Table 1. The solver is based on the finite volume method to build the spatial discretization of the transport equations. The unstructured discretization is face-based. While all unknown state variables are cell-centered, the system of equations used in the implicit time stepping procedure are constructed face by face and the contribution of each face is then added to the two cells next to the face. This technique poses no specific requirements on the topology of the cells. Therefore, the grids can be completely unstructured: cells with an arbitrary number of arbitrarily-shaped faces are accepted. Pressure-velocity coupling is enforced through a Rhie & Chow SIMPLE type method: at each time step, the velocity updates come from the momentum equations and the pressure is given by the mass conservation law, transformed into a pressure equation. In the case of turbulent flows, transport equations for the variables in the turbulence model are added to the discretization Free-surface flow is simulated with a multi-phase flow approach: the water surface is captured with a conservation equation for the volume fraction of water, discretized with specific compressive discretization schemes, see [START_REF] Queutey | An Interface Capturing Method for Free-Surface Hydrodynamic Flows[END_REF]. The technique included for the 6 degrees of freedom simulation of ship motion is described by [START_REF] Leroyer | Numerical Methods for RANSE Simulations of a Self-Propelled Fish-like Body[END_REF]. Time integration of Newton's law for the ship motion is combined with analytical weighted analogy grid deformation to adapt the fluid mesh to the moving ship. To enable relative motions of appendages, propellers or bodies without having recourse to overlapping grids, a sliding grid approach has been implemented. Propellers can be modeled by actuator disc theory, by coupling with boundary element codes (RANS BEM coupling, see [START_REF] Deng | Ship Propulsion Prediction with a Coupled RANS-BEM Approach[END_REF]) or with direct discretization through e.g. the rotating frame method or sliding interface approaches

Finally, an anisotropic automatic grid refinement procedure has been developed which is controlled by various flowrelated criteria, see [START_REF] Wackers | Combined Refinement Criteria for Anisotropic Grid Refinement in Free-Surface Flow Simulations[END_REF]. Parallelization is based on domain decomposition. The grid is divided into different partitions, which contain the cells. The interface faces on the boundaries between the partitions are shared between the partitions; information on these faces is exchanged with MPI (Message Passing Interface) protocol.

The method works with the sliding grid approach and the different sub-domains can be distributed arbitrarily over the processors without any loss of generality. Moreover, the automatic grid refinement procedure is fully parallelized with a dynamic load balancing working transparently with or without sliding grids

NUMERICAL SIMULATION SET-UP

The computational domain consists of a cylindrical domain, whose diameter is 3 times the propeller diameter, and length is 9.18 times the propeller diameter. It starts 3.96R before the propeller plane and it extends until 15.4R after the propeller plane. The computational domain with the boundary conditions is presented in Figure 3. The computational mesh is created with HEXPRESS, an automatic unstructured mesh generator. This software generates meshes containing only hexahedrons. The mesh consists of 21.4×10 6 cells. The number of faces for each blade is approximately 38,100. The average wall normal resolution on the blades is y + = 0.6 with a maximum around the tip, in the order of 1.8. A box including the propeller and extending up to 6 diameters in the wake is added to capture the vortices. In this box, the cells are isotropic and the size is 0.0105R, see Figures 4 and 5 The RANS equations are written in the moving reference frame but written in terms of absolute reference quantities.

For the RANS turbulence models (k-ω SST and EARSM), the solution is a steady solution while for DES computations, this approach is unsteady and the time step is 3×10 -5 seconds. This time step corresponds to a rotation of 0.27 degrees. The time-averaged flow is obtained in approximately 9 flow-times for DES computations.

The numerical simulation is distributed on 96 processors on a SGI Altix ICE 8200. For the RANS simulations, the CPU time per processor is 23 hours while for the DES approach, it is 300 hours

Flow field in the wake

However, it is crucial to evaluate the ability of the turbulence model to reproduce some of the findings of [START_REF] Felli | Mechanisms of Evolution of the Propeller Wake in the Transition and Far Fields[END_REF]. The analysis of the flow field is carried out for three values of the advance coefficient, J = 0.71, 0.45 and 0.20. All results obtained with a RANS turbulence model are steady results while for the DES results, if not explicitly mentioned, the results are issued from an averaged flow.

J = 0.71

A general view of the wake of the propeller, for the advance coefficient J = 0.71, is given in Figure 7 which presents an isosurface of the dimensionless value λ2 = -2 of the second largest invariant of S 2 +Ω 2 (S and Ω being the symmetric and antisymmetric component of ∇u) colored by the helicity. The acceleration of the flow behind the propeller causes a slight reduction of the radial position of the vortex cores. Then, the helices formed by the tip vortices remain located on a circular cylinder. RANS model yield tip vortices but they vanish more or less rapidly in the wake depending on the turbulence model used and the level of anisotropy associated with the turbulence model. With the DES approach, the tip vortices are maintained much further in the wake. These remarks are also observed by [START_REF] Muscari | Modeling of Vortex Dynamics in the Wake of a Marine Propeller[END_REF].

In order to have a qualitative idea of the level of mesh resolution, a view of the DES function is presented in Figure 8. The blue area corresponds to F DES ≤ 1, which represents the RANS area, while F DES > 1 for the LES area, the red region in the figure. the resolution of propeller wake is suited to a LES approach Figure 9 presents a comparison of the turbulence kinetic energy (TKE) and the y-component of the vorticity for the three turbulence models used. the RANS simulations, Figure 9(a) and 9(b), predict a small value of the TKE near the tip of the blade which grows rapidly in the vortex core. The values around the vortex core increase along the filament. On the contrary, the DES approach produces a high TKE near the tip but the level vanishes quickly and the level is lower than those observed with a RANS approach.

Then, the level of vorticity, which is similar for all numerical simulations close to the propeller, decreases very quickly for the RANS simulations whereas for the DES the decay is more progressive The detailed frequency analysis performed in the experimental work illustrates the process of energy transfer from the blade harmonic to the shaft at nearly at x =7R, owing to vortex grouping. In the numerical simulation with the DES approach, the vortex grouping, marked by red ellipse, appears nearly 7.2R.

J = 0.45

The figure 11 presents an instantaneous view of the vortical structure obtained with the DES approach and the visualization in [START_REF] Felli | Mechanisms of Evolution of the Propeller Wake in the Transition and Far Fields[END_REF]. These figures are very similar and present the pairing of the vortices due to the instability of the tip vortices and the beginning of the instability of the hub vortex. The tip vortices deform from the helical path and trend to interact mutually and form a group. Then, the hub vortex undergoes a sudden deformation from a straight to a spiraling geometry. The difference between the numerical result and the experimental visualization is the spiral-to-spiral distance. In the numerical simulation, this distance is shorter than that observed in experiments. However, the numerical spiral-tospiral distance is in agreement with the numerical simulations of Musca ri et al. ( 2013). To compare all turbulence models, the averaged flow for the DES approach is presented with the RANS results in Figure 12. For the RANS results, the characteristics of the flow are the faster deformation of the wake and the stronger tip vortices. Even if the tip vortices are stronger than those predicted with the previous advance coefficient, they are resolved over a shorter distance. This trend is also confirmed by the numerical results of [START_REF] Muscari | Modeling of Vortex Dynamics in the Wake of a Marine Propeller[END_REF].

The DES model permits to predict more extended vortices and shows both the onset of the vortex instability and the start of the pairing process.

J = 0.20

The last value of the advance coefficient is J = 0.20 which corresponds to a condition of very high blade loading. The wake evolution of the tip vortices decreases quickly, even for the DES approach, see Figure 14. approach, more structures are predicted. Even if a RANS simulation yields a good prediction of forces and moments, this approach fails to give information about the wake evolution which may be important, like for the prediction of noise or if a body like another propeller or a rudder is in its wake.

CONCLUSIONS AND FUTURE WORK

The capabilities of numerical simulations with various turbulence closures (RANS and DES), using ISIS-CFD flow solver, to predict the complex flow past an isolated propeller have been presented in this paper. A marine propeller called INSEAN E779A was selected for the present study. Computations were performed for various advance coefficients following experimental conditions.

Computational results are discussed and compared with experimental data. The predicted global quantities, such as thrust and torque, obtained with various turbulence closures, are in good agreement with the measured data. For the prediction of the wake, a comparison between the RANS models and the DES approach shows that the RANS approach dissipates the tip vortices very quickly due to the high level of the turbulence kinetic energy in the core of the vortices. On the contrary, the DES approach allows to capture the evolution of the tip vortices. The initial stages of the instability pattern, with two consecutive filaments grouping their relative position, can also be reproduced and agree reasonably well with the flow visualization. The hybrid LES model performs better than the eddy-viscosity based turbulence closures since it is able to predict the relaminarization of the core of the tip vortex in the wake of the propeller.

The overall results suggest that the RANS approach is sufficient to predict the thrust and the torque. But if the prediction of the propeller wake is necessary, a DES approach should be used. Nevertheless, the cost of this approach is still prohibitive to be used as a matter of routine architecture design offices. However, for the propeller design to predict the cavitation risk, the DES approach has still to demonstrate its ability in predicting a better tracking of the ventilated tip vortex father downstream.

Figure 1 :

 1 Figure 1: Front view of the propeller model.

Figure 2 :

 2 Figure 2: Side view of the propeller model.

Figure 3 :

 3 Figure 3: Computational domain with the boundary conditions.

Figure 4 :Figure 5 :

 45 Figure 4: View of the mesh in the symmetry plane

Figure 6 :

 6 Figure 6: Open-water characteristics of the E779A propeller.

  Figure 7: J = 0.71 -Vortical structures visualisations (λ2 = -2).

Figure 8 :Figure 9 :

 89 Figure 8: J = 0.71 -Visualisation of the DES function (red: LES region, blue: RANS region).

Figure 10 :

 10 Figure 10: J = 0.71 -Instantaneous visualization of the vortical structures (λ2 = -2).

  (a) Experimental view (Fig. 8 in Felli at al. (2011)) (b) Numerical results

Figure 11 :

 11 Figure 11: J = 0.45 -Instantaneous visualization of the vortical structures.

Figure 12 :

 12 Figure 12: J = 0.45 -Vortical structures visualisations (λ 2 = -2).

  Figure 14: J = 0.20 -Vortical structures visualisations (λ 2 = -2).

Figure 15

 15 Figure 15 represents a view of the instantaneous isosurface of the invariant λ2 obtained with a DES approach. We can compare this figure with Figure 14(a) or 14(b) which represent a view with the RANS model. With the DES

Figure 14 :

 14 Figure 14: J = 0.20 -Instantaneous vortical structures visualization (λ2 = -2).

Table 1 :

 1 Propeller parameters of INSEAN E779A model.

	Diameter	D = 0.227 m
	Number of blades	Z = 4
	Pitch ratio	P/D = 1.1
	Rake	4°35' (forward)
	Expanded area ratio	0.689
	Hub ratio	0.200
	In this paper, the rotational speed of the propeller is kept
	fixed to a value of n = 25 rps and the different advance
	coefficients J = U∞/(nD) are obtained by changing the
	inflow velocity U∞. The Reynolds number Re = 1.78×10 6 is
	based on the radius of the propeller (L ref = R = 0.1135 m)
	and the velocity of the tips of the blades (U ref = nπD ≈
	17.829 m/s)

3 ISIS-CFD AT GLANCE

	The solver ISIS-CFD, available as a part of the
	FINE TM /Marine computing suite, is an incompressible
	unsteady Reynolds-averaged Navier-Stokes (URANS)
	method mainly devoted to marine hydrodynamics. The
	method features several sophisticated turbulence models:
	apart from the classical two-equation k-ε and k-ω models,
	the anisotropic two-equation Explicit Algebraic Reynolds
	Stress Model (EARSM), as well as Reynolds Stress
	Transport Models (RSM), are available, see Deng &
	Visonneau (1999) and Duvigneau et al. (2003), with or
	without rotation corrections. All models are available with
	wall-function or low-Reynolds near wall formulation.
	Hybrid LES turbulence models based on Detached Eddy
	Simulation (DES) are also implemented and have been
	validated on automotive flows characterized by large
	separations, see Guilmineau et al. (2011). Additionally,
	several cavitation models are available in the solver.

TEST-CASEThe propeller geometry is the INSEAN E779A model, i.e. a four bladed, fixed-pitch, right-handed propeller

ACKNOWLEDGMENTS

This work was granted access to the HPC resources of CINES/IDRIS under the allocation 2014-2a0129 made by GENCI.

DISCUSSION

Question from Douwe Rijjpkema

Did you already investigate the pressure inside the core of the vortex? This is of good interest when calculating cavitation.

Authors' Closure

Thank you for your question and your suggestion. Since we also consider the cavitation risk, the evolution of pressure was investigated. The evolution of pressure for J = 0.71 in the plane Y = 0 mm for is presented in Figure I. The most significant modeling effect is a high dissipation of the intensity of vortices, and of minimum pressure levels, with RANS models. With DES, the lowest pressure level is maintained further downstream. This is what we expect from the physics. However, if this trend is encouraging, it remains to validate a DES simulation including the cavitation modelling.

Question from Antoine Ducoin

You use two turbulence RANS models that predict different level of turbulent kinetic energy in the wake/tip vortex. Is it an important parameter to avoid the diffusion of the vortex in the wake? If no, how do you analyze the differences on the λ 2 plots?

Authors' Closure

Thank you for your question. For both RANS models, there is no parameter to avoid the diffusion of the vortex in the wake. Both RANS models predict an increase of the turbulence kinetic energy in the wake that destroys the tip vortex. With the DES approach, the prediction of the turbulent kinetic energy in the wake is lower than that predicted with the RANS models.

Question from Tobias Huuva

How did you model the rotation of the propeller in the computation? How will you do when including the rudder? How much longer time step for DES? For RANS?

Authors' Closure

Thank for you question. The equations are written in the moving reference frame but written in terms of absolute reference quantities. When a rudder will be present, two solutions are available. The first is the use of the sliding grid. It depends on the position of the rudder with regard to the propeller and the hull. The second option is the use of overset. The number of time steps for DES is approximately 16,200 and the CPU time per processor is 300 hours. For RANS, the number of time step is approximately 4,000 time steps and the CPU time per processor is 23 hours. All simulations are distributed on 96 processors.