Oscar Serrate
email: oscar.serrate@meletu.univ-valenciennes.frthierry.berger

Thierry Berger

Dimitri Tabary

Christophe Kolski
email: christophe.kolski@univ-valenciennes.fr

Towards context-aware interactions between humans and a self-organized cybercar system

Keywords: Human-Computer Interaction (HCI), Self-Organization, Context Awareness, UsiXML, cybercar

The rising number of vehicles in many cities in the world lead to numerous nuisances such as pollution, safety, noise, traffic jams… During the last decade, many companies and research organizations have been developing a new concept of automated vehicle called: cybercars. The "cybercar" system inside the city must be flexible, robust and decentralized. We use self-organization principles to achieve this. Furthermore, with the purpose of having user-friendly human-computer interactions, for a range of different users, the system must be context-aware. In this paper, a general model and principles for modelling human-cyber interactions using UsiXML are proposed.

Introduction

Many cities in the world have problems with private vehicles. There are traffic jams, pollution, security problems and nuisances. The cybercar is a potential solution to these problems. Our research is focused on Human-cybercar interactions. Cybercars also aim to improve to quality of life by reducing the use of traditional vehicles. The cybercar is a safe mean of transport that any one can use (CyberMove, 2001). Also, with these vehicles, one hopes to reduce costs because there will not be any drivers. The cybercars must be integrated to the city's public transportation. They must complement the transportation system that already exists in a particular city. This aspect will be discussed in the following section. The user is a main element of the cybercar system. This system has to take into account who the user is, the environment that surrounds him/her, and which device he/she is using at the time of his/her request for the cybercar. Therefore, the display on the device, used by the user, has to be sensitive to the context or context-aware. It is the main objective of our ongoing research. The article begins with a description of cybercars. After this, we examine the cybercars' place with respect to the ITS (Intelligent Transport Systems). We then discuss the main principles brought by self-organization and how these characteristics will allow the "cybercar" system to be flexible, robust and decentralized. Following this, we direct our attention to "context-awareness" and how our system will be sensitive to context. A model unifying the selforganized cybercar system, context-awareness, and a user interface is proposed. Different scenarios are then discussed where the user can be inside or outside the city and how he/she asks for a cybercar. Finally, a task is presented for requesting a cybercar outside the city. We model this task and then show an example of a website, created using UsiXML (proposed as modelling language), where the user can reserve the vehicle.

State of the Art

2.1 Cybercars with respect to the ACTIF model and the ITS Cybercars are road vehicles with the capacity of complete automated driving. A fleet of these vehicles form a transport system, for passengers or merchandise, on a road network with the capacity of services on demand. Cybercars offer the advantage of functioning on any infrastructure which means that they are cheaper and more flexible [START_REF] Parent | Cybercars : Review of First Projects[END_REF]. Many private societies and research institutions/laboratories study the technological aspects of cybercars and their impact inside the city. These projects include: (CyberCars, 2006), (CyberMove, 2001), (EDICT, 2007), (NetMobil, 2005), (CyberC3, 2007), (CityMobil, 2008). For cybercars, as for any means of transport, we have to take into account many classical aspects, like the price, safety, maintenance, travel demands… FRAME (Framework Architecture Made for Europe) (FRAME, 2008) developed the first version of the European ITS Framework Architecture. They provided seminars, international meetings, technical documents to promote the Framework Architecture to different countries. France, as well as other countries in Europe, used these ideas to create their own ITS architectures. The ACTIF (ACTIF, 2007a) (Aide à la conception des systèmes de transports interopérables en France) model incorporates all of these aspects. ACTIF is used here as a generic model of an infrastructure of different means of transport; complete enough to allow the positioning of the cybercar system with respect to the aforementioned aspects. ACTIF also is associated with a method and software (ACTIF, 2007b) to do the above. In the ACTIF model there are 9 functional areas: (FA1) Provide electronic means of payment; (FA2) Manage emergency and safety services; (FA3) Manage transport infrastructure and traffic; (FA4) Operate public transport; (FA5) Provide advanced systems for driver assistance;

(FA6) Provide information on and manage multimodal mobility; (FA7) Enforce regulations; (FA8) Operate freight and fleets; (FA9) Manage the shared data. The functional area "Operate public transport" is particularly adapted to introduce the cybercar system. We are not going to into details in this article (for the lack of space) on how this is done. But in summary, this placement with respect to the ITS, via the ACTIF model, allows to encompass the outline of the cybercar system and link them with the other systems/areas surrounding the public transportation.

Self-Organization

Self-Organization is: "a process in which pattern at the global level of a system emerges solely from numerous interactions among the lower-level components of the system. Moreover, the rules specifying interactions among the system's components are executed using only local information, without reference to the global pattern" [START_REF] Camazine | Self-Organization in Biological Systems[END_REF]. Self-organization is based on studies on biological systems. The main idea is not to have a centralized system, but to have "individuals" which work together towards a common goal. The characteristics of self-organized systems are robustness, flexibility, and decentralization. Bonabeau and colleagues [START_REF] Bonabeau | Swarm Intelligence. From Natural to Artificial Systems[END_REF] suggest that using self-organization on artificial systems will reduce its costs and make them simpler. Self-organization is the main source of inspiration to conceive the cybercar system as a "naturally" autonomous group capable of adapting itself and able to face the different perturbations of a road network (i.e. traffic) without explicit configuration. This is possible due to the capacities of the cybercars which can communicate/interact locally with other cybercars, users and with the immediate environment. Routing protocols using self-organization have already been proposed in [START_REF] Melki | Interactions des transports publics et des cybercars dans un contexte urbain[END_REF] which are part of the PPF project. In section 3, we will propose a general model where we include the self-organized system of cybercars. As said before, this system will use routing protocols based on self-organization, and also will communicate locally with its environment (cybercars, users, interactive terminals…).

Context-Awareness

A user of the transportation system for cybercars must be able to call or reserve a cybercar according to his/her profile, the environment in which he/she is in and the interaction devices at his/her disposal. The system must be context-aware (User, Environment, Interaction Platform). A definition of context is given by A.K. Dey [START_REF] Dey | Providing architectural support for building context-aware applications[END_REF][START_REF] Dey | A conceptual framework and a toolkit for supporting the rapid prototyping of context-aware applications[END_REF]: "Any information that can be used to characterize the situation of entities (i.e. whether a person, place or object) that are considered relevant to the interaction between a user and an application, including the user and the application themselves. Context is typically the location, identity and state of people, groups and computational and physical objects".

Thevenin [START_REF] Thevenin | Adaptation en Interaction Homme-Machine : le cas de la plasticité[END_REF] describes context as a triplet {user, platform, environment}: (1) User (Type of user or profile) -Age, Occupation (Tourist, Professional…), Handicap, …; (2) Platform (material support and software that allows the interaction) -PDA, Cell phone, PC, … ; (3) Environment (place where Humancomputer interaction (HCI) is exercised) -Geographic place (home, on the street…), Day/Night, Ambient (noisy, crowded…)…

The goal of our HCI system with the cybercars is to take into account this information concerning the user, the physical environment, the properties of the platform, the noise level, the user's location, etc. We consider also that these interfaces of the system must be able to migrate to another interaction device while preserving usability [START_REF] Calvary | Plasticity of User Interfaces : A revised Reference Framework[END_REF][START_REF] Thevenin | Plasticity of User Interfaces: Framework and Research Agenda[END_REF].

Proposition of general model of user-cybercar system

Our system is composed in one part with a fleet of self-organized cybercars and in another part of a transportation system. These two elements define the application domain. The user must be able, with the appropriate context, to interact with the system in a natural way or by using a device (via a HCI platform). Our model, which is adapted from [START_REF] Coutaz | An MDE-SOA Approach to Support Plastic User Interfaces in Ambient Spaces[END_REF], is composed of a domain model, context model, and a user interface model (Figure 1). The domain describes the objects in the application. The cybercar model corresponds to every cybercar that is in the city. This model uses the notion of self-organization. Therefore each cybercar uses local information to accomplish a particular task. Cybercars are capable of communicating with themselves, with the transportation system, with the environment and with the user (Please note that different techniques have been proposed in the research projects in section 2.1). The transportation system is a model which describes how cybercars are distributed and how they will arrive at their destination according to the routing protocol. In this article we will not go into the details of this model. The management of public transportation and cybercars as well as the routing protocols are illustrated in [START_REF] Melki | Interactions des transports publics et des cybercars dans un contexte urbain[END_REF].

Figure 1. General Model

The user interface model describes the human-computer interactions which will be distributed on the interaction platforms which are available to the user. The task model is a formal or semi-formal transcription of a user activity. The abstract model defines interaction spaces (task distribution between windows, pages…) and the concrete model describes the presentation (widget, layout…). This concrete model must be distributed, automatically in principal, to the corresponding platform with the appropriate context. The context contains the triplet {user, platform, and environment}. The user model defines the different profiles that were discussed in the preceding section. The HCI platform model defines the different available devices that the user can use to request a cybercar. The environment is very important to the cybercars because they have to take into account if it is raining, if it is noisy… This general model allows taking into account the user inside an environment to adapt the user interface of the cybercar. If the user is inside the city, he/she can request a cybercar by using his/her PDA; he/she then can communicate directly with the nearest vehicle. If the cybercar is busy, this vehicle must inform the user and request another cybercar to take care of the passenger. The cybercars communicate with the "Transportation System" in the case there is a reservation that was done in advance by a user outside of the city. The transportation system with all of the users' information transfers these to the cybercar in the moment it has to pick up the user at a particular time and a particular place. In the next section, we define two scenarios: one where the user is inside the city and the other where the user is outside the city.

In: 27th European Annual Conference on Human Decision-Making and Manual Control, EAM'08, Delft, The Netherlands, june.

Scenarios

Our research is part of a project called PPF (Plan Pluri-Formation) "Coeur de Ville" which is associated with the French laboratories LAMIH, LAGIS and LGI2A. This project has the goal to treat urban transport problems by using cybercars inside the city. It will take into account problems of request management, allocation of cybercars, reallocation of cybercars after it arrived at a destination of a passenger, prices, constraints between the cybercar system and the other means of transport, perturbations. Figure 2 shows how the user interacts with the cybercars according to the two ways of utilization.

Figure 2. Main types of interactions

In the first case, the user is inside the city (where the cybercars are nearby), he/she can request a cybercar to arrive at a particular destination. The user can request a cybercar by using a mobile device (PDA, Cell phone…) or an interactive terminal. When the user uses this device, the user identifies himself/herself and is located. The authentication allows the system to recuperate the user's profile. The location assures, via the cybercar, the quickest arrival of the nearest available cybercar. Inside the vehicle, the screen (particular platform) will be configured according to the user's profile and the environment. The user will be able to view, for example, the museums, restaurants, train stations that are nearby in a city map. In the second case, the user is not inside the city and wishes to reserve a cybercar for a specific place inside the city at a certain date at a particular time. In this case, the user accesses the transportation system via a website. First of all, the user must register himself/herself if he/she is not already registered. The user profile allows the system to personalize the HCI.

Application

Interactions between cybercars and users imply potentially various tasks. Here we will provide a representative example by modelling an extract of the user interface which is context-aware.

Context and Task Modelling

The case study concerns the task "request cybercar from outside the city" by using a website. The user will use the website to reserve a cybercar. To begin, we will exploit CTT Environment [START_REF] Mori | CTTE : Support for Developing and Analyzing Task Models for Interactive System Design[END_REF] which is a task modelling environment based on

In: 27th European Annual Conference on Human EAM'08,Delft,The Netherlands,june. CTT (ConcurTaskTrees) [START_REF] Paterno | Model based design and evaluation of interactive applications[END_REF]. The task model plays a very important role because it indicates the logic of the activities that the application must support; each task represents an activity that must be implemented to arrive at a goal. Figure 3 shows how the task to request a cybercar is decomposed. According to this model, to request (or reserve) a cybercar, the user gets in contact with the transportation system. The user must identify himself/herself, must include the date, place and time that he/she wishes to be picked up by a cybercar. The user also must choose which type of service he/she wants. The system permits two types of service: (1) Regular -This service is the more classic one and the cheaper one. The user here states his destination. If there are other users that are close (at the time the user is using the cybercar) and that go on the same direction, the cybercar will stop and pick up these people; (2) Premium: The passenger will have his/her own cybercar and the vehicle will take the user directly to the destination by using the shortest path. With this information concerning the user and at the time the passenger is at the place and time that he reserved, the nearest available cybercar will show up to pick him/her up.

Context-aware user interface modelling using UsiXML

To develop a prototype of an interface that is context-aware, we have chosen UsiXML (User Interface Extensible Markup Language) (UsiXML, 2008); this language which is based on XML allows us to describe user interfaces capable of considering different contexts by using different levels of details and abstraction. UsiXML is a declarative language that captures the essence of an interface independent of the physical characteristics of the platform. This is done by using an abstract description of the elements that describe the particular interface. These elements are regrouped in different models (User, transformation, tasks, concepts, and others; for more details, see (UsiXML, 2008)). It is very important that the user identifies himself/herself, so that the adapted user interface is generated, according to the appropriate context. By using UsiXML, a simple first prototype was created; for lack of place in the article, we will only describe the part where we request a cybercar outside the city. Figure 4 shows a small extract on how the simplified interface was modelled. Three languages have been chosen at the moment for the interfaces (English, French and Spanish). By inspecting the code in figure 4, we see that the same interface is created easily for the three different languages (for example, we see the same button called "cancel" in English, "annuler" in French and "cancelar" in Spanish). In this same way, the rest of the interface was created. This is a first prototype and in the future the interface will take

In: 27th European Annual Conference on Human EAM'08,Delft,The Netherlands,june. into account other aspects for international users such as time formats, symbols,… [START_REF] Russo | How Fluent is Your Interface? Desinging for International Users[END_REF]. In figure 5, we see the result of the simplified interface on a website for a user who wants to reserve a cybercar. The user can choose his/her language of preference. If the user is registering, he/she must indicate his/her name, age, occupation, handicap, email, telephone. After the user is registered, he/she chooses which type of service he/she wishes for his/her journey. He/she indicates the date, time and place for the reservation of the cybercar. The transportation system will pass the information to the nearest available cybercar at this particular time and the vehicle will arrive at the location of the user. The user's information will be confidential and will not be accessible to external parties as established by the European Community (European, 2007). The interface in figure 5 was generated by using GrafiXML (based in UsiXML) which is a tool to develop interfaces for different interaction platforms (GrafiXML, 2008). This development environment offers also different plugins to export the UsiXML code to XHTML, Java and XUL. By using these plugins, we will be able to test different versions of this interface in PDAs, cell phones, PC, etc. <cioRef cioId="button_component_10"> <resource content="Annuler" contextId="CyberVal3-context-fr_FR_29"/> <resource content="Cancel" contextId="CyberVal3-context-en_US_29"/> <resource content="Cancelar" contextId="CyberVal3-context-es_ES_19"/> </cioRef> </resourceModel> </uiModel> 6a shows the scenario where the user is using a PDA inside the city to request a cybercar. Figure 6b shows the message that would be sent from the cybercar to the user in the case another regular passenger is going in the same direction as the first regular user.

Three languages for the button "cancel"

Conclusion

Cybercars are automated vehicles that intend to improve the quality of life (more flexibility in the transportation, less pollution, less noise, etc.). These cybercars can be integrated with the current public transportation system by using the ACTIF model. The conception of a transportation system composed of cybercars along with the principles of self-organization give the system robustness, flexibility and decentralization (concepts treated in the PPF project which we are a part of). The aspect that interests us the most concerns the interactions between the cybercars and the user, with the aid of a user interface that is context-aware; taking into account the user, the environment and the devices used during these interactions with the vehicles (including if these interactions are between cybercars, or between cybercars and the transportation system). Concerning the passenger, the system intends to integrate different types of users (children, adults, people with sensory handicaps…), that are inside or outside the city. A simplified first prototype was created in UsiXML was developed. In terms of research perspectives, other than the fact of going deeper on the development and testing of the prototype, we wish to integrate other types of human-computer interactions (i.e. vocal, sound) staying sensitive to the context of the user. Links between the cybercars and the other means of transport have to be taken into account also (i.e. information about other means of transport provided by the cybercar).

Figure 3 .

 3 Figure 3. Task "Request Cybercar outside the city"

Figure 4 .

 4 Figure 4. UsiXML code for the button cancel in three languages.

Figure 5 .

 5 Figure 5. Website to request a cybercar Figure6ashows the scenario where the user is using a PDA inside the city to request a cybercar. Figure6bshows the message that would be sent from the cybercar to the user in the case another regular passenger is going in the same direction as the first regular user.

  In: 27th European Annual Conference on Human Decision-Making and Manual Control, EAM'08, Delft, The Netherlands, june.

Figure 6

 6 Figure 6 (a) PDA example for requesting a cybercar (b) Alert message indicating to the user that another passenger will be in the cybercar.

Acknowledgements

The authors would like to thank the French Research Ministry, Jean Vanderdonckt and the participants of the PPF project for their support in this project.


Soulier Mathias

Laurent Gallais

Julien Lumeau

Hélène Krol

Emilie Steck

Mathieu Boutillier

Measurement of optical coatings absorption at 1570 nm and simulations of photo-induced modifications of spectral function under high power laser exposure

Keywords: Absorption, Free space communication wavelengths, photo induced effects, thin film

Free space communications between ground stations and geostationary satellites offer high-speed and secure data transmission, but compensating for atmospheric absorption poses a significant challenge. The need for high levels of beam power to overcome atmospheric losses calls for optics that can withstand strong flux, especially in the continuous wave (CW) regime. In this context, the absorption of optics at 1.5 µm is a critical parameter that must be accurately measured and understood to develop efficient and reliable photonic systems.

This study focuses on the absorption of optical coatings at 1570 nm. Lock-In Thermography (LIT) has been developed to measure the total absorption of the coatings with high sensitivity under 1 ppm. A modulated 100 W CW laser is used to induce heating into the coating stack, and the resulting rise in internal temperature is measured with a thermal camera. The LIT experimental setup offers a non-destructive and non-contact measurement technique, making it ideal for assessing the absorption of delicate thin-film coatings.

To understand the photo induced effects in a stack of thin film layers subjected to high-power laser heating, a finite element model is developed using COMSOL. The model simulates the index and thickness variations of each layer and predicts the shift in optical function resulting from photo induced effects. The results offer valuable insights into the impact of laser-induced heating on the optical properties of the coatings and provide guidelines for designing robust and reliable photonic systems.

INTRODUCTION

This section outlines the measurement method that aims to measure the absorption of thin-film components at a wavelength of ~1.5 µm. These absorption values are crucial input data required for evaluating the heating of a component exposed to a laser power flux at 1.5 µm. The literature is limited when it comes to continuous laser exposure at this wavelength, and these measurements will contribute to filling this knowledge gap. Another objective is to model the thermal and spectral behavior of multilayer components under laser flux and validate/recalibrate this model using an operational filter. The model, based on laser parameters, materials, and operating conditions, should enable the assessment of temperature gradients, surface deformations of the component, index variations in the substrate, and resulting surface wave deformations and spectral function variations.

METHOD

We have opted to employ a lock-in thermography technique to carry out absorption measurements. This method has been under development for several years within the laboratory. The primary advantage of this method lies in its relative ease of implementation compared to other techniques, as well as its ability to directly generate absorption maps for a given sample. However, it requires the use of a high-power laser source and a high-performance thermal camera to achieve high sensitivity and detect the desired levels of absorption.

Description of the absorption measurement method

To carry out the absorption measurement at 1.5 µm using thermography, the components are exposed to a continuous high-power laser flux. As the laser passes through the sample, a fraction of the power is absorbed, resulting in localized heating. This temperature variation is quantified by a thermal camera. Through the application of a calibration, it is possible to establish a correlation between this temperature increase and the absorption of the component. Figure 1 illustrates the principle of the employed method.

Thermal measurement

The thermal camera and its dedicated software enable thermography measurements and post-processing through lock-in detection. During signal acquisition, multiple images are captured and processed using the manufacturer's software. The outcome of this measurement process is a Lock-In Thermography (LIT) image. At the end of the measurement sequence, the thermal image generated by the camera represents surface temperature variations observed within the field of view. Each pixel is consequently linked to a temperature increment in Kelvin, relative to the surface temperature before the measurement.

Figure 2 illustrates the advantage of lock-in detection in signal extraction. On the left, the image is a thermal photograph corresponding to the maximum signal recorded during acquisition. On the right, the result of LIT for the same measurement sequence is depicted.

Figure 2. Extraction of the useful signal using synchronous detection

Calibration method

A calibration process has been established using a reference sample with a high absorption level and thermal parameters close to those of the samples. This process involves depositing particular single layer of Ta2O5 onto Corning C7979 substrates. The objective is to obtain absorption values that can be measured with a calibrated device with a resolution exceeding 10 -2 %. To achieve this, a deposition strategy has been developed to modify the layer's stoichiometry, reducing its oxygen concentration. Spectrophotometric measurements were carried out. For this calibration sample, measurements of transmittance (T) and reflectance (R) were conducted, allowing the calculation of losses (1-R-T). At these levels of absorption, scattering can be considered, in a first approximation, as negligible in the overall loss assessment. Under these conditions, the loss measurement allows quantifying the sample's absorption. The data and absorption values presented in this paper are calibrated using this method. Figure 3 shows the measured losses for the reference sample. The obtained amplitude value during a measurement is multiplied by both the calibration factor and the laser power, yielding an absolute absorption value.

It is important to note that each calibration is specific to the thermal parameters and the thickness of the corresponding substrate. The calibration presented in this context is applicable exclusively to coating depositions made on 2 mm-thick Corning C7979 glass substrates.

MODELS

Within the scope of this work, two models have been developed. The first one enables numerical calculations for simulating the response of a thin-film stack. The second is a finite element model that simulates the heating of an optical component and the subsequent phenomena that occur.

By combining both models, it is possible to calculate the spectral shift of a thin film stack induced by the absorption of a high power laser beam.

Optical coating model

A thin film stack absorption model has been developed with the objective of predicting absorption values for thin-film components of varying designs. This analysis is based on the knowledge of the absorption properties of the constituent materials and the distribution of the electric field within the multilayer stack. This model relies on matrix calculations and complex admittances. [START_REF] Macleod | Thin-film optical filters[END_REF] To implement this model, it is necessary to know the values of extinction coefficients of each layer type. This entails conducting absorption measurements on single layers of materials representative of those used in the filter, using the same coating method. When a specified stack design is provided, the model generates output values for absorption as a function of wavelength. It is important to note that this approach assumes that absorption is intrinsic to the materials and not related to the interfaces within the multilayer structure.

To compare the model with experimental data, an absorption measurement campaign was conducted. It involves performing absorption measurements at different angles of incidence using a rotation stage attached to the sample holder. The objective of this campaign was to validate the model using a dedicated single cavity Fabry-Perot filter developed within the framework of this work.

Absorption measurements at various angles of incidence are of interest due to the Fabry-Perot cavity filter's structure : (HL) ^4 2H (LH) ^4. Indeed, the optical response of the filter undergoes rapid changes as the angle deviates from angle associated with the cavity resonance. Outside of the resonance, the filter no longer transmits but behaves like a mirror. Therefore, an increase in the angle of incidence is expected to lead to a decrease in absorption. The measurements and the model's anticipated result are presented in Table 1.

Angle of incidence (deg) Model Measurement

-10 242 210 2 189 166 10 242 205

Table 1.

Comparison between the model and angular absorption measurements

The observed behavior of these results is due to the fact that the filters were designed to operate at a specific angle of incidence and are not precisely centered on the wavelength of the pump laser. The discrepancy between the experimental and theoretical values may stem from uncertainties in the absorption measurements. It is worth noting that the model derives the extinction coefficients of the layers it uses from these measurements. Additionally, it is possible that the layers within the filter do not have precisely the same extinction coefficient as their corresponding single layers.

COMSOL finite element model

The optical parameters that influence the spectral response of a thin-film stack include the refractive indices and thicknesses of each layer, as well as the refractive index of the substrate. It is important to note that these parameters are modified by the temperature increase and the emergence of thermomechanical stresses. [START_REF] Suhir | An approximate analysis of stresses in multilayered elastic thin films[END_REF] The model was specifically developed to simulate the thermal phenomena involved in establishing the relationships between the heating induced by the optical flux and the changes in mechanical and optical properties of thin films. Numerous input parameters are required for simulation [START_REF] Tien | Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry[END_REF] , and they are detailed in table 2.

Table 2. Input parameters of the COMSOL finite element model

Based on these parameters, the model simulates surface heating above the optics. Then it calculates the temperature rise and induced stress at every node of the mesh. As an output, the model delivers the variations in refractive index and thickness for each layer of the thin-film stack (Figure 5).

Absorption level

Coating properties

Laser beam properties

Mechanical parameters

Thermal parameters

STUDY OF SPECTRAL SHIFT ON FABRY PEROT FILTER

This section provides a comprehensive description of the conditions for measuring the reflection/transmission of a filter as a function of temperature. It also presents the results obtained for the spectral filters manufactured by CILAS within the temperature range of 20-80°C.

Measurement and method

Spectral measurements of the filter subjected to uniform and controlled heating were conducted. These measurements were carried out by mountung a sample onto a mount equipped with a heating module. The filter was then placed in a spectrophotometer. Using this setup, spectra of the heated component at various temperatures were acquired. The purpose of this experiment was to characterize the effects of heating on the spectral response of the Fabry-Perot filter and to compare them with the results from the COMSOL model. Figure 6 show the experimental set-up: Figure 6. Simulated temperature increase of a 1550 ppm absorption filter

Model/measurement comparison

The spectral measurement of the Fabry-Perot filter exhibits a shift of 12 pm/°C around the filter's resonance. This value is determined by determining the spectral deviations at 50% transmittance for different temperatures. In a first approximation, it can be considered that this wavelength shift remains constant within the studied spectral range. The model anticipates the same spectral shift as shown in table 3.

Spectral

Figure 1 .

 1 Figure 1. Schematic representation of the lock-in laser thermography system.

Figure 3 .

 3 Figure 3. Calculation losses for the reference sample around the laser wavelength (dotted line) From this absorption value, it becomes possible to calculate the power absorbed by the reference sample based utilizing the laser setpoint power. Calibration is achieved by aligning this value with the amplitude of the Gaussian curve derived from the LIT image. A calibration coefficient is established from the curve in Figure 4.

Figure 4 .

 4 Figure 4. Calibration curve for the determination of a calibration factor.

CONCLUSION

In this study, we developed a COMSOL finite element model to simulate photo induced effects in thin film layers under high-power laser heating. This model is based absorption measurements obtained from single layer. This simulation accurately predicted changes in optical properties due to temperature changes, providing valuable insights for the design of photonic components. Additionally, we focused on evaluating the absorption of optical coatings at 1570 nm using Lock-In Thermography (LIT), achieving high-sensitivity measurements down to 1 ppm. Through controlled heating with a modulated 100 W CW laser, absorption measurement on a Fabry-Perot filter and single layers have been carried out.


Abdelwaheb Trabelsi
email: abdelwaheb.trabelsi@fss.rnu.tn

Houcine Ezzedine
email: houcine.ezzedine@univ-valenciennes.fr

Christophe Kolski
email: christophe.kolski@univ-valenciennes.fr

Evaluation of agent-based interactive systems, application to an information assistance system: first results

Keywords: evaluation, Human-Computer Interaction, Human-Machine Interface, Electronic informer, travellers information system, traffic regulation

The evaluation of interactive systems is a wide and rich research domain. In this paper, we are focused on agent-based interactive systems. We propose an evaluation approach based on three complementary techniques: assistance evaluation tool, questionnaire, verbalization. The validation of our approach occurred within the framework of a project involving an industrial partner which is running the current urban transport network (tramway and bus) in the town of Valenciennes. The main results of the evaluation of an agent-based Information Assistance System (IAS) will be presented. This evaluation has been conducted in laboratory.

Introduction

The evaluation of interactive system consists in ensuring that the users are able to carry out their task by using it; it must therefore meet their needs. The methods and tools currently available for evaluating interactive systems are numerous and various; we quote for instance: observations, eye tracking, interviews, electronic informers, questionnaires, user tests, inspection methods, knowledge based automated systems, an so on [START_REF] Ivory | The State of the Art in Automated Usability Evaluation of User Interfaces[END_REF][START_REF] Jacko | The human-computer interaction handbook[END_REF][START_REF] Nielsen | Usability Engineering[END_REF]Senach 1990). Each of them presents some advantages and drawbacks.

In this paper we are particularly interested in the evaluation of agent-based interactive systems. Indeed agent-based architectures of interactive systems have been proposed since the eighties in the literature. Such architectures lead to new needs concerning the evaluation of the interactive systems concerned [START_REF] Kolski | Agent-based architecture for interactive system design: current approaches, perspectives, evaluation[END_REF][START_REF] Tran | Vers un environnement générique et configurable pour l'aide à l'évaluation des systèmes interactifs à base d'agents, Application à un Système d'Aide à l[END_REF].

Thus, we propose an evaluation approach based on several complementary techniques: assistance evaluation tool, questionnaire and verbalization. Urban transport networks, and in particular the system which provides information for the passengers (IAS: Information Assistance System (Ezzedine et al. 2008)), will be used as an example of the application of our approach.

We will present the main results obtained from the evaluation of the Information Assistance System (IAS). Indeed, the evaluation in the laboratory has initially enabled us to technically test the proposed assistance evaluation system, and secondly to detect a prior representative set of utility and/or usability problems, inherent to the IAS exploitation.

Agent oriented specification and design of the Information Assistance System

Agent oriented architecture is used for the design of the IAS [START_REF] Ezzedine | Agent oriented design of human-computer interface. Application to supervision of an urban transport network[END_REF][START_REF] Ezzedine | Modelling of an interactive system with an agent-based architecture using Petri nets, application of the method to the supervision of a transport system[END_REF]. The application agents are intended to manage the passenger information in the vehicles and stations and to calculate the information to be displayed (delays, timetable and route modifications, etc.). According to the traffic context, each agent possesses rules enabling it to act correctly in its environment. Concerning the specification of the interface agents, we have identified six types of interface agent responsible for direct interaction with the human regulator. These agents are represented in the form of interactive windows. The regulator can interact with these agents via the various functions possible in the windows, for example: the buttons, the edition zones, the pictures, etc. These agents are:

-The State of the traffic interface agent: it gives a synthetic representation of all the delays concerning mobile units travelling on the network. Thus, with the help of the network support system, it ensures the real time surveillance of vehicle delays on the network supervised.

-The State of the line interface agent: the view of the State of the line interface agent is made up of graphic elements such as stations, route sections, vehicles, etc. (see figure 1a).

A click on a vehicle directly displays the view (window) of the Vehicle agent which will deal with any further interaction with the regulator (see figure 1b). The principle is the same when the operator clicks on a station (see figure 1c).

-The Station and Vehicle interface agents: the view of these two interface agents is accessible by acting on their associated representations in the State of the line interface agent view (vehicle and station). It shows the regulator the information contained in the running plans in the form of a set of thumbnails depending on a direction which can be selected on a drop-down scroll list.

-The Message interface agent: the view of the Message interface agent enables the regulator to obtain a synthetic view of all the messages being sent to vehicles and stations.

-The Overall View interface agent: in order to make the task of supervising the traffic easier for the regulator, we created an Overall View interface agent. As its name implies, the view given by this agent provides the regulator with a global view of the traffic on the network. This view encompasses all the lines to be supervised and facilitates access to line, stations and vehicles.

A survey of the interfaces related to these agents is available in [START_REF] Trabelsi | Contribution à l'évaluation des systèmes interactifs orientés agents : application à un poste de supervision du transport urbain[END_REF].

Experimental device

The experimental device of the IAS evaluation consists of several techniques and tools: an assistance evaluation tool integrating an electronic informer called MESIA1 (Trabelsi et al. 2006), questionnaire and verbalization. The use of each of them is presented hereafter.

Assistance evaluation system

The assistance evaluation system was conceived in order to help and assist evaluators of agent-based interactive systems. It is composed of three main modules (Trabelsi et al. 2006):

-The electronic informer module: it ensures the collection of the actions/reactions of the user and the system. The collection of the data is ensured via a coupling between the IAS and the electronic informer. These collected data are very important insofar as the models of the tasks really carried out by the operator can be reconstituted and compared with the task models to be carried out.

-The generating Petri nets module: this module uses the data given by the electronic informer, in order to generate Agent Petri nets (Ezzedine and Kolski 2008) representing the model of the performed task and the model of the task to be realized. Up to now, this module provides results in textual form.

-The Simulation/Confrontation/Specification of the Petri nets module: This module offers the evaluators/designers the three following functionalities: the simulation of Agent Petri nets, the confrontation and the confrontation of these Petri nets.

Explanation about a specific tool ensuring the generation, the simulation and the confrontation of Petri nets can be found in (Tran et al. 2008a and2008b;[START_REF] Tran | Vers un environnement générique et configurable pour l'aide à l'évaluation des systèmes interactifs à base d'agents, Application à un Système d'Aide à l[END_REF]).

In addition to the verbalization, the use of the electronic informer as a tool for the evaluation of the IAS is enriched by subjective user answers to a questionnaire.

Questionnaire

The questionnaire prepared specifically for this evaluation is basically inspired from [START_REF] Ravden | Evaluating usability of human-computer interfaces: a practical method[END_REF]. It is composed of three parts: the first presents questions about the interface general aspects (such as the response time); the second gathers specific questions about each IAS view (window); and the third part presents a total ergonomic evaluation of the interface. The complementary technique to the questionnaires is the verbalization.

Verbalization

The verbalization is an easy and direct means to collect information about the quality of the system and particularly the interface. Contrary to the questionnaire, the verbalization has the advantage of being more flexible insofar as it allows the orientation of the questions towards the information sought by the evaluator.

Population implied in the evaluation

According to [START_REF] Nielsen | A mathematical model of the finding of usability problems[END_REF]Virzi, 1990), it is possible, with 4 or 5 participants, to detect nearly 80 to 85% of the utilisability problems which an interface could present. Hence, for this first evaluation of the IAS in laboratory, the population is made up of five subjects. They have an average age of 29 years. All the subjects are computer science PhD students. The fact that the subjects are experts in computer science can compensate, to some extent, their lack of experience in regulation. Indeed, the familiarity of PhD students with the computer software and the human-machine interfaces handling can put them draw sheet with the use of the IAS. However, it is clear that the results obtained within the framework of this first evaluation will never be as consistent as those which could be obtained with professional users of the regulation.

Experimental protocol

Each experiment lasts approximately an hour and half and comprises four phases. During the first phase of the experiment, which lasts fifteen minutes, the IAS and its global functioning are explained to the subject. The participant to the experimentation is then familiarized with the various views of the IAS during approximately ten minutes before undergoing truly the experimental tests. The right handling proceeds in twenty minutes and relates to two scenarios. Ten minutes are devoted to each scenario. The last phase of the evaluation relates to the filling of the questionnaire and the verbalization; it lasts approximately forty-five minutes.

Tasks to be realized

Scenario 1

To make sure that the user (the subject) easily succeeds in interacting with the IAS by sending messages to the station(s) and the vehicle(s), we propose a first evaluation scenario made up of four tasks described in table I (b).

Scenario 2

In the second scenario, the subject has to perform four preset tasks. Contrary to the first scenario, the execution of the tasks is not sequential. Indeed, the beginning of each task is announced by an alarm or warning message. Therefore, the user (subject) can execute a task concerning the appearance of a message, and receive another at the same time. Let us note that theoretical durations necessary to the realization of the tasks (see table 1 (c)) are approximate durations. They are determined by a supervision expert initiated with the SAI.

Results

The five subjects carry out the various tasks envisaged with the two scenarios. The experimental device used enables us to collect objective data by means of the electronic informer MESIA and of the subjective data via the verbalization and the fillings of the questionnaire. We present in what follows some relevant results.

The table I presents a summary of the real average duration of each task in the first scenario (d) as well as the success rate of its realization (e). The results displayed in this table 1 indicate that all the subjects carried out well the first and the second task with an acceptable realization average time; whereas, for the third and fourth task, only three subjects out of five could complete them. We also notice that the real realization duration of these two tasks exceeds the average. Indeed, this can be explained by the fact that the subjects are not experts in regulation.

Other results are available in [START_REF] Trabelsi | Contribution à l'évaluation des systèmes interactifs orientés agents : application à un poste de supervision du transport urbain[END_REF]. They lead to several improvements resumed below.

First IAS improvements

Regarding the results of the IAS evaluation obtained with the two suggested scenarios, the answers to the questionnaire and the verbalization, we propose improvements of the IAS mainly relating to the views of State of the Traffic, State of the Line and Message interface agents.

Improvement relating to the view of State of the Traffic interface agent

For a better usability, we propose to introduce (in top of the window) a specific zone to the alarm, anomaly and warning messages. In fact, when a message appears, the user takes note of it and validates it. Thus, instead of being lost, the message could be placed automatically in the message planned zone. In this way, the user would not need more to memorize messages or to note them on paper. This way of presenting the messages would make it possible the user to one by one treat them and to remove them once treated.

Improvement relating to the view of State of the Line interface agent

To solve the problem related to the message sent to the stations and the vehicles, we propose to introduce with the view of State of the Line interface agent a specific zone for the sending of message (see figure 2). This zone would make it possible the user to reach directly the Message view without having to pass by the view Station or the view Vehicle.

Improvement relating to the view of Message interface agent

After the changes carried out on the view of State of the Traffic, the view of Message interface agent should be also changed. Indeed, if the user wishes to send a message to the whole of the stations of a specific line, it would be interesting to mask the information relative to the unconcerned lines.

Other possible improvements

In addition, we note, during the evaluation, that the messages edited by the user are not recorded by the IAS. Indeed, if the user wishes to send the same message twice, he or she has to reedit it.

Conclusion

We have presented in this paper the results of a first evaluation of an Information Assistance System. This system is based on an agent-based architecture. This evaluation has been performed in laboratory and provided us with interesting results. The evaluation dealt with two different scenarios. It was then possible to deduce from it first proposals for an improvement of the IAS.

Our further research aims, on the one hand, to the improvement of the Simulation modules/Confrontation/Specification and generation of Petri nets (see (Tran et al. 2008a and2008b;[START_REF] Tran | Vers un environnement générique et configurable pour l'aide à l'évaluation des systèmes interactifs à base d'agents, Application à un Système d'Aide à l[END_REF]) and, on the other hand, a second evaluation on the ground which proves to be necessary for the detection of the problems of utility and/or usability not detected during the first evaluation.

  Figure 1: (a) view of the State of the line interface agent, (b) the view of a Vehicle interface agent, (c) view of a Station interface agent

  Figure 2: Improvement given to both interfaces: State of the Traffic and State of the Line

Table 1 :

 1 The real average duration of each task and the success rate of its realization

	(a)	(b)	(c)	(d)	(e)
	Tasks to be realized	Task description	Theoretical duration of the task	real average duration of the task	Success rate of the task realization
		Send a message to the
	T1	"SNCF railway station"	45 seconds	41 seconds	100 %
		of the tram line
	T2	Send a message to the tram 6 driver	45 seconds	39 seconds	100 %
	T3	Send a message to all the stations of line 16	60 seconds	67 seconds	(3 subjects out of 5)
	T4	Send a message to all the vehicles	60 seconds	75 seconds	(3 subjects out of 5)

MESIA: Mouchard électronique dédié à l'Evaluation des Systèmes Interactifs orientés Agents; translated by: Electronic informer dedicated to the Evaluation of Agent-Based Interactive Systems.

Acknowledgements

The present research work has been supported by International Campus on Safety and Intermodality in Transportation, the Nord-Pas-de-Calais Region, the European Community (FEDER). The authors gratefully acknowledge the support of these institutions.


Victor Almanza

Sandie Le Conte

Stéphane Vaiedelich

Emmanuel Foltête

Romain Viala

Andrés Felipe

Arciniegas Mosquera

Loïc Martinez

Nicolas Wilkie-Chancellier

Stéphane Serfaty

Vincent Placet

Scott Cogan

Physics-based simulations for assessing the playability of heritage musical instruments : Impact of the soundboard assembly process on its low frequency behavior

Keywords: Numerical simulations, experimental studies, decision-making support, heritage musical instruments, soundboard assembly process, mechanical behavior. Highlights

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Historical musical instruments, which have been in use for musical presentation up to the present day, are the subject of research and study in various countries of the world [START_REF] Tafura | Historické organové pozitívy na Slovensku: Historical positive organs within the territory of Slovakia[END_REF].

All museums that host a collection of musical instruments face several problems, such as, how best to describe the story of music through its instruments, how to preserve and restore heritage musical instruments and how to assess their playability. In regard to playability, the musée de la Musique de la Philharmonie de Paris houses a collection of more than 7000 instruments but only 5% of this collection is in a playable state. Indeed, heritage musical instruments present many cultural values including, historical, technical, acoustic and aesthetic. These cultural values are subjectively compared and hierarchized. The aim of this work is to provide an objective and quantiable response to assessing the playability of a heritage musical instruments.

Regarding wooden stringed musical instruments and more particularly their soundboards, the materials chosen are extremely varied including, skins, woods, metals, glass. The present work focuses on wooden soundboards.

Assessing the playability of wooden stringed musical instruments raises many questions. Indeed, a variety of factors inuences the mechanical state, stress and strain state, of wooden stringed musical instruments.

A distinction is made between the mechanical state induced by the string tension under normal playing conditions from that induced by the instrument maker during the construction of the instrument and in particularly the methods of assembling the instrument parts. So, a curator might wonder whether the state of internal stresses, intentionally introduced by the luthier in the process of making and assembling of a stringed musical instrument, has a signicant impact on the vibroacoustic behavior of the instrument and therefore should be restored after it has relaxed over time given the viscoelastic behavior of wood. In this work we will focus on the impact of the mechanical state induced by the instrument makers during the construction and assembly of the soundboard on its low frequency vibratory behavior.

A brief look at the chronological evolution of the guitar shows that the making gestures, particularly those concerning the reinforcement systems most often referred to as "bracings", have become increasingly complex and sophisticated (g.1). The techniques and assembly methods used to design these structures play a key role in their artistic inspiration, as changes in their mechanical behaviour inuence their intangible values, i.e. the acoustic qualities intrinsically present in these works. However, the initial state of these voluntarily added constraints is inevitably subject to change over time, given the viscoelastic behavior of wood.

Figure 1: Evolution of guitar bracing : from the 17th to the 20th century, guitar structural systems became extraordinarily complex. Adapted from D. Friedrich, Citéscopie : la guitare, Cité de la musique, 1995 [START_REF] Friederich | Les tables des guitares classiques et leurs barrages[END_REF] The types of bracing and their assembly methods dier according to instrument families, historical periods, schools and making styles. Although they vary widely in the detail of their execution, bracing techniques can be grouped into two categories, according to common mechanical criteria: those using external forces and those using the mechanosorptive behavior of wood [START_REF] Colmars | Précontraintes de fabrication dans les tables d'harmonie d'instruments de musique en bois[END_REF].

Several approaches have been used to study the mechanical behaviour of musical instruments, including experimental approaches using direct [START_REF] Jones | Holographic and speckle interferometry[END_REF][START_REF] Castellini | Laser Doppler Vibrometry: Development of advanced solutions answering to technology's needs[END_REF][START_REF] Viala | Towards a model-based decision support tool for stringed musical instruments making[END_REF][START_REF] Bakarezos | Laserbased interferometric techniques for the study of musical instruments[END_REF] or indirect [START_REF] Le Moyne | Couchet harpsichord soundboard vibroacoustics behaviour: An application of the impact neareld acoustical holography (IPNAH)[END_REF][START_REF] Le Moyne | Restoration of a 17th-century harpsichord to playable condition: A numerical and experimental study[END_REF] vibration measurement methods, analytical approaches [START_REF] Woodhouse | On the bridge hill of the violin[END_REF][START_REF] Ablitzer | Static model of a violin bow: Inuence of camber and hair tension on mechanical behavior[END_REF][START_REF] Chadefaux | A model of harp plucking[END_REF][START_REF] Trévisan | Vibroacoustics of orthotropic plates ribbed in both directions: Application to stiened rectangular wood panels[END_REF][START_REF] Trévisan | Vibroacoutsic Modelling of Piano Soundboards through Analytical Approaches in Frequency and Time Domains[END_REF] and virtual prototyping approaches [START_REF] Konopka | Numerical modelling of wooden structures[END_REF][START_REF] Kaselouris | A Review of Finite Element Studies in String Musical Instruments[END_REF] using the nite dierence method (FDM) [START_REF] Välimäki | Discrete-time modelling of musical instruments[END_REF][START_REF] Bilbao | Numerical sound synthesis: nite dierence schemes and simulation in musical acoustics[END_REF], the boundary element method (BEM) [START_REF] Richardson | Numerical modelling of stringed musical instruments[END_REF][START_REF] Le Pichon | Methode de prediction du rayonnement acoustique de structures volumiques. Composees d'une ou plusieurs faces planes vibrantes[END_REF][START_REF] Moosrainer | Application of BEM and FEM to musical instruments[END_REF] or the nite element method (FEM) [START_REF] Viala | Towards a model-based decision support tool for stringed musical instruments making[END_REF][START_REF] Le Moyne | Restoration of a 17th-century harpsichord to playable condition: A numerical and experimental study[END_REF][START_REF] Gough | Vibrational modes of the violin family[END_REF].

The vibration behavior of structures with an initial state of non-zero strains and stresses has been widely studied [START_REF] Raju | Free vibration behavior of prestressed beams[END_REF][START_REF] Addessi | On the linear normal modes of planar pre-stressed curved beams[END_REF]. The interpretation of the observations strongly depends on the structure, but also on how the initial state has been introduced. Despite the rich literature, the immediate knowledge transfer of these observations to wooden soundboards is not immediate. Indeed, very few studies exist concerning the impact of the initial mechanical state of a musical instrument on its vibratory behavior. This question has been studied concerning the eects of nonlinearities due to the static load of piano strings [START_REF] Mamou-Mani | Précontraintes et vibration des tables d'harmonie: vers une modélisation du savoirfaire des fabricants d'instruments de musique[END_REF]. More recently, the presence of manufacturing pre-stress in wooden soundboards has also been highlighted [START_REF] Colmars | Précontraintes de fabrication dans les tables d'harmonie d'instruments de musique en bois[END_REF].

Over the last decade, the introduction of structural calculations to support the conservation-restoration program to maintain instruments in a playable state has provided new methodological and practical perspectives [START_REF] Le Moyne | Restoration of a 17th-century harpsichord to playable condition: A numerical and experimental study[END_REF][START_REF] Vaiedelich | Maintenir en état de jeu: le cas du clavecin de I. Couchet, Anvers 1652[END_REF][START_REF] Conte | Using mechanical modelling and experimentation for the conservation of musical instruments[END_REF]. Moreover, numerical and experimental studies have already been carried out to investigate the impact of the string tension and of the assembly process on the vibratory behavior of a piano soundboard or simplied soundboards, for example [START_REF] Mamou-Mani | Numerical simulation of a piano soundboard under downbearing[END_REF][START_REF] Mamou-Mani | Prestress eects on the eigenfrequencies of the soundboards: Experimental results on a simplied string instrument[END_REF].

In spite of these studies, many unknowns remain given the unique nature of each instrument including the uncertainties inherent to the manual fabrication process as well as the spatial and temporal variability of the wood material.

In parallel, virtual prototyping has become a standard tool in the industrial world. In the eld of structural mechanics, numerical models are most often produced using the nite element method. For the last twenty years, an approach known as "Verication and Validation of Simulations" (V&V) has been developed, which consists in developing guidelines and decision support tools based on numerical simulations, or how to estimate the condence that can be placed in a numerical simulation given the presence of uncertainties [START_REF] Viala | Towards a model-based decision support tool for stringed musical instruments making[END_REF][START_REF]Guide for verication and validation in computational solid mechanics[END_REF][START_REF] Oberkampf | Verication and Validation in Scientic Computing[END_REF][START_REF] Viala | Model-Based Eects Screening of Stringed Instruments[END_REF].

The work carried out in this paper aims to develop a decision support methodology usable in a museum context and based on the virtual prototyping paradigm to study the static and dynamic behavior of historical musical instruments to optimize its conservation and its preservation in playing conditions but also to anticipate costly or time-consuming experimental campaigns. To illustrate this decision support methodology, a procedure was set up to determine if an unvalidated numerical model is able to predict useful trends for decision support in a museum context. The numerical and experimental studies are carried out on a facsimile of the soundboard of the Christoph Koch's archlute of 1654 (E.546) in order to evaluate the impact of its assembly process and gluing on its low frequency vibratory behavior.

The methods used for this procedure are presented in the next section, followed by the results and a discussion section. Finally, the conclusion and perspectives will be presented.

Methods

This section presents the studied case, the numerical simulations, the experimental protocol and the features and metrics.

Case study

Within the framework of this study, a facsimile of the soundboard of Christoph Koch's archlute was made by an expert in conservation and restoration. The soundboard and bars are made of spruce, Picea abies, while the bridge is made of pear tree, Pyrus communis. The table has a height of approximately 420mm and a maximum width of approximately 305mm. The facsimile can be seen on gure 2.a. The soundboard is glued to the body of the instrument all over its edge. To reproduce these boundary conditions, a MDF (Medium Density Fiberboard) block was manufactured (gure 2.b) on which the facsimile is glued with an animal glue. The resulting structure is shown in gure 2.c.

Regarding the bracing process, at bars are glued to the soundboard using a curved working counterform.

A curved working counterform was designed with a 3 mm gap between its center and ends.

Moreover, after the assembly of the table with the brace, the soundboard is glued to the body of the instrument, which is generally not at, modifying again its mechanical state. In order to study this assembly step, two types of MDF blocks were used: a at MDF block and a carved MDF block with the curvature of the instrument body. In order to design the carved MDF block, the arch of the ribs (body) of Christoph Koch's archlute was measured with relaxed strings by surface scanning. In order to dissociate the impact of the table assembly with its brace on the low frequency behavior of the soundboard from the eect induced by the assembly of the soundboard with the body of the instrument, a strategy was developed based on three dierent congurations:

A rst reference conguration in which the soundboard is braced with the at bars without using the counterform (its mechanical state is therefore unchanged) and the soundboard is glued to the at MDF block (conguration C0).

A second conguration in which the soundboard is braced with the at bars without using the counterform, and the soundboard is glued to the carved MDF block (conguration C1).

A third conguration in which the soundboard is braced with the at bars using the curved counterform and the soundboard is glued to the carved MDF block (conguration C2).

Moreover, since these operations require the gluing and ungluing of the soundboard, it was necessary to evaluate the impact of the gluing on the vibratory behavior of the soundboard in order to be able to dissociate it from the one of the assembly steps.

Numerical simulations

SolidWorks ® 3D computer-aided design software was used to create the geometric models of the soundboard and the at and carved MDF blocks. The 3D model of the soundboard was designed from the drawings that were used to make the soundboard.

ABAQUS nite element software was used for all structural calculations, including static calculations for the determination of the mechanical state resulting from the assembly steps and modal analyses for the determination of the natural frequencies and the corresponding mode shapes of the system. It has been observed that, for wooden stringed musical instruments, modal damping is very low [START_REF] Viala | Towards model-based approaches for musical instruments making: validation of the model of a Spanish guitar soundboard and characterization features proposal[END_REF], so our model is assumed to be undamped. The eigenvalue problem for the natural frequencies is given by:

-

ω 2 i M + K ϕ i = 0 (1)
where M, K ∈ R N,N are the mass and stiness matrices and ω i , ϕ i the i th eigensolutions.

The soundboard and the MDF blocks were modeled with C3D10 tetrahedral elements. Due to the presence of the rosette, and after a mesh convergence study, the structure studied is made up of 216802 elements of 3mm. The meshes of the facsimile and the MDF block are shown in gure 3.

Since the aim of this study is to assess the ability of an uncalibrated numerical model to predict trends that may be useful for decision making, wood is modeled with orthotropic linear elastic behavior, and the

Parameters

Values Modal analyses were performed under free condition between 10 and 1200 Hz for the C0 conguration and between 10 and 1500 Hz for the others.

ρ (g/cm 3 ) 0.38 E L (MPa) 10200 E R (MPa) 850 E T (MPa) 500 ν LR (∅) 0.39 ν LT (∅) 0.43 ν RT (∅) 0.50 G LR (MPa) 750 G LT (MPa) 675 G RT (MPa)
To model the conguration C0, the nodes of the soundboard and the at MDF block are linked, and a modal analysis is performed.

To model the conguration C1, a load is applied around the perimeter of the soundboard until it matches the arch of the carved MDF block. Then, the nodes of the soundboard and the carved MDF block are linked and the load is removed to obtain an elastic return. A modal analysis is then performed in this state.

To model the conguration C2, a load is applied to the bars of the soundboard until it matches the arch of the concave worktable. Then, the nodes of the table and the bars are linked and the load is removed in order to obtain an elastic return. A load is then applied around the perimeter of the soundboard until it matches the arch of the carved MDF block. Finally, the nodes of the soundboard and the carved MDF block are linked and the load is removed in order to obtain an elastic return. A modal analysis is performed in this state.

Several parameters can inuence the gluing, such as the mechanical properties of the glue, its thickness or the gluing surface. In our case, we are interested in the impact of the latter on the soundboard's vibratory behavior. To study this impact, we compared two congurations in which a 0.15 mm thick lm of glue [START_REF] Kurt | Eect of glue line thickness on shear strength of wood-to-wood joints[END_REF] is introduced between the soundboard and the MDF block. The adhesive lm is modeled with C3D10 tetrahedral elements and with an isotropic linear elastic behavior. The material properties of the latter were obtained from the literature [START_REF] Melià-Angulo | Study of the mechanical properties of selected animal glues and their implication when designing conservation strategies[END_REF] and are presented in table 3. The nodes on the surface of the glue lm in contact with the facsimile are bonded to it, and those on the surface of the glue lm in contact with the MDF block are also bonded to it. The rst conguration, referred to as "C3" in the following, has a glue lm covering the entire gluing surface. The second conguration, referred to as "C4" in the following, has a glue lm covering only a portion of the gluing surface. To achieve this, a percentage of the glue lm elements in conguration C3 were randomly removed. Two models of this conguration have been studied, one where the glue lm covers 85% of the gluing surface and a second where the glue lm covers 70% of the gluing surface.

In the following, these models will be referred to as "C4-85" and "C4-70" respectively. Since element removal is random, 10 dierent simulations were carried out for each of these models.

Experimental protocol

The dynamic behavior was studied by laser vibrometry using a Polytec PSV-500-3D scanning vibrometer.

The vibrometer's three-dimensional calibration process allows us to dene a reference coordinate system, and to precisely determine the positions and orientations of the three laser heads and the studied part within this coordinate system. The XY plane was dened as coincident with the front face of the facsimile. Measurements taken at each point in three dierent directions are used to reconstruct the three-dimensional velocity vector.

Only the -→ Z component was used for modal identication and computation-test correlation. Its amplitude is 1 to 2 orders of magnitude greater than that of the other two components. This limits the pollution of data by low signal-to-noise ratio measurements, while ensuring rigorous computation-test correlation. The use of a 1D vibrometer could lead to similar results, but the measurement direction is generally assimilated to the optical axis, and its variation during the scan is usually neglected. The experimental setup is shown in 5. The measurements lasted approximately 30 minutes and were carried out between 10 and 2000 Hz with a frequency resolution of 0.6 Hz. Three averages were made for each measurement. Since the impact hammer signal decreased by 10 dB after 1200 Hz, modal analyses were performed between 10 Hz and 1200 Hz. The dierent experimental measurements were carried out in a room maintained at 22°C ± 1°C with a relative humidity of 55% ± 5%.

Firstly, an experimental campaign was carried out in conguration C0. For this, the soundboard was glued to the at MDF block. This campaign was also used to study the repeatability of measurements over a day. Nine measurements were made throughout a day in this conguration.

To study the impact of the assembly of the soundboard with the body of the instrument, four new measurements were performed in conguration C0. Then, an experimental campaign was carried out in conguration C1. For this, the soundboard was unglued from the at MDF block and reglued to the carved MDF block (gure 7). Then, four measurements were conducted in this conguration and these measurements were compared to those obtained in conguration C0.

To study the impact of the assembly of the table with its braces, four new measurements were performed in conguration C1. Then, an experimental campaign was then carried out in conguration C2. For this, the soundboard was unglued from the carved MDF block and the bars of the soundboard were unglued from the table in order to be able to reglue them to the table by forcing them on the concave worktable (gure 8). Finally, the soundboard was reglued to the carved MDF block and four measurements were made in this conguration. These measurements were compared to those obtained in conguration C1.

Since the soundboard has been unglued from the MDF block and reglued between each of these experimental campaigns, it is necessary to study the impact of the gluing on the vibratory behavior of the soundboard in order to distinguish the variations observed due to the assembly steps from those resulting from the gluing. Hence, another experimental campaign was performed to study the impact of the gluing.

Three dierent gluing operations were therefore carried out by three dierent experts and measurements were made for each of the gluing operations. Six measurements were made for the 1st gluing, two measurements for the 2nd and nine measurements for the 3rd.

Features and metrics

To study the impact of the dierent stages of assembly of the soundboard on its low frequency behavior, we have chosen to focus on the soundboard's eigenfrequencies, since the characterization and the modelization of the damping remain a real challenge given its multiple origins, such as the damping relative to the wood material, which is inhomogeneous, or the damping in the links due to the gluing of the various parts of the instrument. However, as previously stated, the purpose of this study is not to match the frequencies obtained numerically and experimentally but to see if the numerical model, although imperfect, is capable of predicting the trends observed experimentally.

Regarding the experimental results, the frequency response functions were obtained from the Polytec PSV-500 software and the modal analyses were performed with the in-house software MODAN using the PolyMAX frequency-domain method [START_REF] Peeters | The PolyMAX frequency-domain method: a new standard for modal parameter estimation?[END_REF].

The post-processing of the numerical and experimental results was performed using MATLAB.

The matching of the eigenmodes is based on the modal assurance criterion (MAC) which leads to a correlation matrix between two modal bases whose component values are normalized between 0 and 1, with 1 indicating the modal vectors are colinear and 0 indicating they are orthogonal [START_REF] Allemang | A correlation coecient for modal vector analysis[END_REF]. Here, we consider that two modes are matched if they present a MAC > 0.7.

In order to compare numerical and experimental results, a common variation criterion must be chosen.

Given the small populations of results, we opted for a normalized range (N R). For each considered eigenmode, this criterion is dened as follows:

N R = f max -f min f cv (2)
with,

f cv = f max + f min 2 (3)
where f max is the maximum eigenfrequency, f min the minimum eigenfrequency and f cv the center eigenfrequency of the studied population.

Results

This section presents the numerical and experimental results.

Numerical results

First, in order to focus only on modes that mainly solicit the facsimile, a criterion based on elastic strain energy is used. The modes of interest will be those for which the strain energy within the facsimile represents more than 80% of the total strain energy. The percentage of total strain energy within the facsimile according to the eigenmodes identied, and the nal numbering, are shown in gure 9. As a result, only 11 eigenmodes will be retained for further analysis, compared to 20 initially.

Regarding the impact of the assembly of the soundboard with the instrument body, the correlation of the eigenmodes obtained with the modeling of the C0 and C1 congurations has been carried out. The resulting normalized ranges are presented in table 4. The maximum value is 0.64% for mode 4.

Regarding the impact of the assembly of the table with its brace, the correlation of the eigenmodes obtained with the modeling of the C1 and C2 congurations has been carried out. The resulting normalized ranges are presented in table 4. The maximum value is 0.03% for mode 1.

Regarding the impact of the gluing, the correlation of the eigenmodes obtained with the modeling of the C0, C3, C4-85 and C4-70 congurations was carried out. For the C4-85 modeling, the resulting normalized ranges are presented in table 5.The maximum value is 1.56% for mode 7. For C4-70 modeling, the resulting normalized ranges are presented in table 5. The maximum value is 2.56% for mode 7.

Experimental results

For the measurements performed on the C0 conguration, eleven eigenmodes were identied during the modal analysis. In order to compare the numerical and experimental results, the eigenmodes obtained with the modeling of the conguration C0 and those identied from the measurements performed on the conguration C0, were rst matched using the modal assurance criterion and the results are shown in gure 10. A change can be observed in the order of the eigenmodes. The numerical mode 2 corresponds to the experimental mode 3 and inversely. The numerical mode 5 corresponds to the experimental mode 6 and inversely. The numerical mode 9 corresponds to the experimental mode 10 and inversely. In the following, the numerical numeration is maintained.

Regarding the repeatability of the measurements during a day, the frequency response functions, averaged over all the measurement points, for the nine measurements performed on the C0 conguration, are shown in gure 11. During the modal analysis, eleven eigenmodes were identied for the measurements performed on the C0 conguration. The resulting normalized ranges of the identied modes have been studied and are presented in table 6. The maximum value is 1.20% for mode 5.

Regarding the impact of the assembly of the soundboard with the instrument body, eleven eigenmodes were identied during the modal analysis of the measurements performed on conguration C1. The matching of the eigenmodes identied with the measurements performed on congurations C0 and C1 was performed and the resulting normalized ranges of the identied modes were studied and are presented in table 7. The maximum value is 6.36% for mode 4.

Regarding the impact of the assembly of the table with its brace, eight eigenmodes were identied during the modal analysis of the measurements performed on conguration C2. The matching of the eigenmodes identied with the measurements performed on congurations C1 and C2 was performed, and modes 7, 8 and 10 were not identied for the measurements performed on conguration C2. The resulting normalized ranges of the identied modes were studied and are presented in table 8. The maximum value is 3.84% for mode 3.

Regarding the impact of the gluing, eight eigenmodes were identied during the modal analysis of the measurements performed for the 1st and 2nd gluing operations, compared with eleven for the 3rd gluing operation. The matching of the eigenmodes identied with the measurements performed for the dierent gluing operations was performed and modes 7, 8 and 10 were not identied for the 1st and 2nd gluing operations. The resulting normalized ranges of the identied modes were studied and are presented in table 9. The maximum value is 8.97% for mode 4.

Discussion

Firstly, in gure 12, a comparison of the numerically and experimentally obtained eigenfrequencies for the C0 conguration is presented. Whatever the eigenmode, one can observe that the numerical results are higher than the experimental ones. One way of minimizing this dierence would be to calibrate the model by identifying the material parameters of the wood species used during the making of the facsimile. However, as previously stated, the purpose of this study is to evaluate the capacity of the unvalidated numerical model to predict trends.

Figure 13 presents a comparison of the normalized ranges obtained numerically and a comparison of the mean value of these normalized ranges. The assembly steps are seen to have a very low impact on the studied eigenfrequencies. Moreover, the assembly of the soundboard with the body of the instrument is seen to have a higher impact on the eigenfrequencies than that induced by the assembly of the table with its brace.

However, whatever the mode, the gluing appears to have the predominant impact compared to the assembly steps. The gluing has the strongest impact on the 7th and 4th mode. the mean value of these normalized ranges. The variability specic to the study on the repeatability of the measurements is seen to be the lowest. Furthermore, we can observe that the gluing has a greater overall impact than that induced by the assembly steps. Also, although no information are known about the 7th mode, the 4th mode is still observed as the most impacted eigenmode. Finally, it should be noted that the study of the soundboard assembly process requires its gluing and ungluing from the MDF block. The gluing has been seen to have a signicant impact on the eigenfrequencies of interest and are no doubt responsible for the dierences we have observed on the low frequency soundboard behavior. This impact is smaller, since more than two measurements were taken during the gluing study. Thus, this result tends to show that the assembly steps have a very low impact on the soundboard's low-frequency vibratory behavior. Despite the dierence between numerical and experimental results, all these similar observations illustrate the capacity of the unvalidated numerical models to provide useful predictive trends in a museum context and to prevent the realization of costly experimental campaigns, in terms of time or equipment, that would not give signicant results. Furthermore, these results tend to demonstrate that, for this instrument, the assembly steps have a low impact on the low-frequency vibratory behavior of the soundboard, which was not intuitive. Thus, the curator can assume that it will not be necessary to reintroduce the internal stresses induced by the assembly process, given these results.

Conclusion

Object of use as much as object of art, the musical instrument undergoes multiple transformations throughout its life. Its material history and its structural transformations are rarely well understood. The analysis of the state of conservation and the history of restoration conrm that the disassembly of soundboards has been a common practice since at least the beginning of the 19th century.

A variety of factors inuence the mechanical state of wooden stringed musical instruments. A distinction is made between the mechanical state induced by string tension under normal playing conditions and the one induced by the instrument maker during the instrument assembly process. The work presented here focuses on the impact of the initial mechanical state induced by a particular assembly method on the low-frequency vibratory behavior of a real wooden soundboard. This study had the double objective of evaluating the impact of the assembly process on the low-frequency vibratory behavior of the soundboard, and also of assessing the ability of an unvalidated numerical model to predict trends that may be useful for decision support in a museum context. This work has led to numerical and experimental studies carried out on a facsimile of Christoph Koch's archlute soundboard of 1654. The numerical study, performed with an unvalidated model, demonstrated a greater impact of the gluing on the vibratory behavior of the soundboard than its assembly steps. The experimental campaign validated this trend, although the experimentally observed impact is higher than the one observed numerically. Thus, this study highlighted two observations: the capacity of an unvalidated model to predict useful trends in a museum context, and the higher impact of the gluing compared to that induced by the assembly process on the low frequency behavior of the soundboard. It should be borne in mind that this study was carried out on a facsimile. In the context of historic heritage instruments, all the constraints specic to the latter must be taken into account, i.e. the use of global, nonintrusive methodological approaches. In addition, the history, material properties and current mechanical state of the instrument will be uncertain. Ageing and visible and non-visible damage will also have to be taken into account. So, in this context, uncertainties will be numerous, severe and dicult to quantify. These factors led us to carry out a study based on an unvalidated model.

In order to validate the transfer of these observations to an entire instrument, the same experimental campaign should be carried out on a facsimile of the complete Christoph Koch archlute. Moreover, due to the unique aspect of each instrument, the methodology implemented here could be applied to other types of instruments using dierent assembly methods than those studied.

Figure 2 :

 2 Figure 2: Pictures of (a) Christoph Koch's archlute soundboard facsimile, (b) MDF block and (c) resulting structure

Figure 3 :

 3 Figure 3: Facsimile and MDF block meshes

Figure 4 :

 4 Figure 4: Material orientations used for the various facsimile components

Figure 5 :Figure 6 :

 56 Figure 5: Experimental setup

Figure 7 :

 7 Figure 7: Pictures of the (a) ungluing and (b,c) regluing of the soundboard on the carved MDF block

Figure 8 :

 8 Figure 8: Pictures of bars forcing on the soundboard using the curved working counterform

Figure 9 :

 9 Figure 9: Percentage of total elastic strain energy within the facsimile according to identied eigenmodes and nal numbering

Figure 11 :

 11 Figure 11: Frequency response functions of the measurements performed on conguration C0

Figure 14

 14 Figure 14 presents a comparison of the normalized ranges obtained experimentally and a comparison of

Figure 12 :

 12 Figure 12: Comparison of numerical and experimental eigenfrequencies for the C0 conguration

Figure 13 :Figure 14 :

 1314 Figure 13: Comparison of normalized ranges and mean value of normalized ranges for each eigenmode obtained numerically

75 Table 1 :

 751 Material properties of the various facsimile components

	Parameters	Values
	ρ (g/cm 3 )	0.75
	E (MPa)	4000
	ν (∅)	0.3

Table 2 :

 2

Material properties used for the MDF block values applied for the parameters governing this behavioral model have been obtained from the literature

[START_REF] Viala | Towards a model-based decision support tool for stringed musical instruments making[END_REF][START_REF] Guitard | Mécanique du matériau bois et composites[END_REF]

. The material properties used for the various facsimile components are shown in table 1 and those used for the MDF block in table 2. In addition, given the orthotropic nature of the wood material constituting the facsimile, the material orientation has been implemented for each component of the facsimile and is presented in gure 4.

Table 3 :

 3 Material properties used for the glue lm

Table 4 :

 4 Frequencies and normalized ranges of identied eigenmodes (modeling of C0, C1 and C2 congura-

	1	296.95	298.42	0.49	1	298.42	298.52	0.03
	2	440.63	442.85	0.50	2	442.85	442.94	0.02
	3	447.80	449.96	0.48	3	449.96	449.93	0.01
	4	638.87	642.94	0.64	4	642.94	643.08	0.02
	5	706.12	705.12	0.14	5	705.12	705.26	0.02
	6	742.78	742.59	0.03	6	742.59	742.68	0.01
	7	846.79	848.12	0.16	7	848.12	848.10	0.00
	8	894.32	895.37	0.12	8	895.37	895.43	0.01
	9	941.79	940.60	0.13	9	940.60	940.71	0.01
	10	959.37	961.33	0.20	10	961.33	961.42	0.01
	11	1134.63	1136.13	0.13	11	1136.13	1136.37	0.02
		Mean value	0.27		Mean value		0.02
	tions)
	Mode	fC3 (Hz) fC4-85 (Hz) N R (%)	Mode	fC3 (Hz) fC4-70 (Hz) N R (%)
	1	294.68	291.89	0.95	1	294.68	289.44	1.80
	2	437.36	433.19	0.96	2	437.36	429.59	1.79
	3	444.46	440.97	0.79	3	444.46	438.91	1.26
	4	631.02	622.65	1.34	4	631.02	616.42	2.34
	5	702.11	697.08	0.72	5	702.11	693.23	1.27
	6	738.13	731.72	0.87	6	738.13	727.01	1.52
	7	834.19	821.26	1.56	7	834.19	813.09	2.56
	8	888.87	881.86	0.79	8	888.87	879.31	1.08
	9	937.75	931.32	0.69	9	937.75	926.92	1.16
	10	955.08	948.00	0.74	10	955.08	944.05	1.16
	11	1129.10	1121.67	0.66	11	1129.10	1116.58	1.12
		Mean value		0.92		Mean value	1.55

Mode

fC1 (Hz) fC2 (Hz) N R (%)

Table 5 :

 5

	1	238.60	2.21	0.93
	2	401.30	4.49	1.12
	3	375.11	3.60	0.96
	4	517.03	5.16	1.00
	5	637.65	7.65	1.20
	6	624.10	4.59	0.74
	7	674.52	5.07	0.75
	8	771.00	4.39	0.57
	9	867.68	5.97	0.69
	10	784.22	4.03	0.51
	11	1086.79	5.64	0.52
		Mean value		0.82

Frequencies and normalized ranges of identied eigenmodes (modeling of C3, C4-85 and C4-70 congurations) Figure 10: MAC matrix (C0 modeling/C0 measurement) Mode fcv (Hz) fmax -fmin (Hz) N R (%)

Table 6 :

 6 Central values, frequency dierences and normalized ranges of identied eigenmodes (measurements

	of C0 conguration)

Table 7 :

 7 Central values, frequency dierences and normalized ranges of identied eigenmodes (measurements

	1	239.91	3.61	1.50
	2	399.64	3.79	0.95
	3	369.61	3.03	0.82
	4	527.03	33.51	6.36
	5	641.29	19.24	3.00
	6	620.58	3.79	0.61
	7	680.58	19.42	2.85
	8	773.86	10.02	1.29
	9	867.65	7.59	0.87
	10	783.54	9.29	1.19
	11	1086.35	10.26	0.94
		Mean value		1.85
	of C0 and C1 congurations)
	Mode	fcv (Hz) fmax -fmin (Hz) N R (%)
	1	236.01	5.12	2.17
	2	401.18	7.00	1.74
	3	364.22	13.99	3.84
	4	549.00	9.95	1.81
	5	649.44	3.80	0.59
	6	627.39	14.93	2.38
	7	-	-	-
	8	-	-	-
	9	870.27	9.82	1.13
	10	-	-	-
	11	1097.59	21.76	1.98
		Mean value		1.96

Table 8 :

 8 Central values, frequency dierences and normalized ranges of identied eigenmodes (measurements

	of C1 and C2 congurations)
	Mode	fcv (Hz) fmax -fmin (Hz) N R (%)
	1	241.12	7.26	3.01
	2	404.00	9.90	2.45
	3	379.79	12.96	3.41
	4	538.61	48.31	8.97
	5	648.90	30.16	4.65
	6	632.96	22.32	3.53
	7	-	-	-
	8	-	-	-
	9	871.30	13.22	1.52
	10	-	-	-
	11	1099.76	31.58	2.87
		Mean value		3.80

Table 9 :

 9 Central values, frequency dierences and normalized ranges of identied eigenmodes (gluing)

Acknowledgments We thank the Fondation des Sciences du Patrimoine and the Domaine d'Intérêt Majeur (DIM) Matériaux anciens et patrimoniaux for their generous support of this research project. We also thank Joël Dugot for his help in fabricating the facsimile of the soundboard.