B Trajin

I Sakhraoui

F Rotella

Soft sensor design for estimation of thermal behavior of encapsulating materials in power electronic module

With the emergence of new semi-conductor technologies, an increasing number of high integrated power electronic modules are designed. The increase of reliability of power modules induces the precise knowledge of the local temperature, even if it cannot be measured at any location. In this paper, the design of a soft sensor, more precisely a linear functional observer, is proposed. It enables the estimation of the temperature at any location using measurements provided from thermal sensors located at a number of precise points. The aim is to design a reduced size observer that could be implemented on a real-time embedded target such as Digital Signal Processor. Consequently, it is necessary to obtain a minimal order observer to limit the computation complexity.

Introduction

The emergence of Wide Band Gap materials (SiC, GaN, C) and new generation hybrid integration techniques significantly enhances performances of power electronic modules. Such modules should be able to operate under severe environmental conditions and constraints: high temperature and high-power density, fast switching, etc. High temperatures provoke new constraints which become critical for power electronics assemblies. Thus, for power electronic modules, real time condition monitoring is a great subject of interest. It has been shown in [START_REF] Ciappa | Selected failure mechanisms of modern power modules[END_REF] that the evolution of local constraints in a power electronic module, which can be thermal or thermo-mechanical, have a negative effect on the lifetime of the module. Consequently, precise knowledge of the temperatures at specific locations in the module, such as the temperature of the semiconductor chips or of the encapsulating silicone gel around these chips, is necessary. However, the use of thermal sensors may be difficult at some locations inside of the power module. For these reasons the objective of the following work is to estimate this physical variable in a specific non-measured location, using measured data by a number of sensors. Some research deals with the thermal model of power module to estimate the temperature of semiconductor chips. In order to obtain an accurate thermal model of power modules, heat transfers are considered and a spatial discretized thermal model can then be introduced [START_REF] Haussener | Thermomechanical modeling and simulation of a silicone gel for power electronic devices[END_REF][START_REF] Van Der Broeck | A thermal modeling methodology for power semiconductor modules[END_REF]. Note that the heat equation is a partial differential equation (PDE) with continuous distribution of parameters leading to infinite order systems. The main method used to simulate these systems is to discretize PDE leading to finite order systems. This method leads to a high order linear time-invariant state space representation. In order to design an associated observer, many studies propose to reduce the size of the state space representation either of the system [START_REF] Van Der Broeck | Spatial Electro-Thermal Modeling and Simulation of Power Electronic Modules[END_REF] or the observer [START_REF] Rotella | Minimal single linear functional observers for linear systems[END_REF]. Reducing the size of the system while discretizing the heat equation leads to additional approximation on temperature. In this paper, a reduced order linear functional observer (LFO) is presented to estimate the state of high order systems. These observers offer the advantage of estimating local temperature without estimating the whole states [START_REF] Trinh | Functional observers for dynamical systems[END_REF].

From the seminal works of Luenberger [START_REF] Luenberger | An introduction to observers[END_REF] solutions of the observation problem for a linear timeinvariant system have been developed. Methods have been elaborated for the design of LFO of the full or partial state vector of the system leading to reduced order observers. Thus, in our application, local temperature may be estimated without estimating all states.

As a case study, this paper considers a simple one-dimensional thermal system. Its model is given in Section 2. Section 3 deals with the design of a minimum order linear functional observer. Application of the design methodology is given in Section 4 for the estimation of temperature in the system. The performances of the designed observer on a real thermal system are discussed and results are compared with experimental data to validate the principle of the observer. The noise sensitivity of the observer is discussed. Approximations and simplifications regarding the choice of the observer are also examined in the paper and its real time implementation on embedded computing target such as Digital Signal Processor is presented.

System modelling

Description of the studied system

This study deals with the case of a bar of silicone gel (Silgel 616) of length much larger than radius. Thermal phenomena occurring along different directions of the main dimension of the bar will be neglected. Thus, the bar will be considered as thermally insulated outside of its main dimension. Thermal expansion induced by thermal behavior will also be neglected. This means that all thermal parameters will be constant regardless of conditions. The modelling methodology is based on a discretization of the heat equation described in [START_REF] Haussener | Thermomechanical modeling and simulation of a silicone gel for power electronic devices[END_REF].

The material is cast and crosslinked in a glass tube of internal diameter d=1 . 10 -2 m over a length L0=16 . 10 -2 m. The tube is then placed vertically on a temperature-controlled heating plate of temperature Th(t) that is measured by a thermocouple. Ambient temperature Ta(t) is also measured. Thermocouples are inserted into the silicone gel at different positions along the length of the bar to measure the local temperature. All thermocouples are placed at the center of the bar along its radius. Finally, a thermal insulator composed of extruded polystyrene is positioned around the tube. It has a thermal conductivity approximately ten times lower than the silicone gel, avoiding heat transfer along the radius axis of the cylinder. To establish the model, the system is sampled into n=16 elementary volumes of length Dx=1 . 10 -2 m (see Figure 1). The centers of each elementary volume are called the nodes of the system. Thermal conduction is considered inside the cylinder along its main dimension. Convection is considered to air at ambient temperature along one base of the cylinder.

Thermal model

Conductive and convective heat transfers are governed by the heat equation expressed in a single spatial dimension [START_REF] Cannon | The One-Dimensional Heat Equation, Encyclopedia of Mathematics and Its Applications[END_REF]. The heat equation is spatially discretized with the finite centered difference method of order 2 [START_REF] Lambert | Numerical Methods for Ordinary Differential Systems[END_REF]. Using bond graph methodology on spatially discretized heat equation, it is clear that temperature at each node of the system can be considered as state variables of the systems [START_REF] Trajin | Bond graph multi-physics modeling of encapsulating materials in power electronic modules[END_REF]. Associated differential equations of order 1 can then be easily written in a matrix form (see Eq. 1 to 3) where T(t) is the state vector of the local temperatures and Tmes(t) is the measured temperature located at the 13 th node of the system that will be used for thermal estimation. Matrices Ath(n,n), Bth(n,p) and Cth(m,n) are given in Appendix A.

! " (#) = $ #% !(#) + & #% '(#)**** (1)
'(#) = , ! -(#) ! . (#) /**** (2)
! 012 (#) = 3 4-!(#)*** (3)

Linear functional observer

Design of a single LFO

The objective of this section is to describe the design of a single LFO to estimate the vector v(t)=L.T(t) where L(l,n) is a one-row vector i.e. l=1.

Firstly, the triplet (Ath, Cth, L) has to be functionally observable (Eq. 4) where O(Ath, Cth, n) is the observability matrix [START_REF] Rotella | A note on functional Observability[END_REF].

5678 9: ;($ 4-< 3 4-< 7) > ?@ = 5678(;($ 4-< 3 4-< 7))*(4)
Moreover, in order to avoid a trivial algebraic part in the observer, it is supposed without loss of generality that Cth and L are linearly independent:

5678 9: 3 4- > ?@ = A + B* (5)
The observation C D(#) of v(t) can be carried out by a LFO which is described by the state space equation (Eq. 6) [START_REF] Van Der Broeck | A thermal modeling methodology for power semiconductor modules[END_REF].

E F" (#) = G*F(#) + H*'(#) + I*! 012 (#) C D(#) = J*F(#) + K*! 012 (#) *** (6)
The constant matrices F(n,n), G(n,p), H(n,m), P(l,n), V(l,m) and the order n have to be determined such that lim 4LMN C(#) O C D(#) = P. This asymptotic tracking is ensured if F is a Hurwitz matrix, i.e. all the real parts of its eigenvalues are strictly negative (Eq. 7).

Q(RST(G)) U P (7)
The necessary and sufficient condition (Eq. 8) for the existence of an asymptotic observer (Eq. 6) are given by the following results [START_REF] Trinh | Functional observers for dynamical systems[END_REF].

V W*$ 4-= I*3 4-+ G*W > = J*W + K*3 4- H = W*& 4- (8)
where Q is a constant matrix such that lim 4LMN F(#) O WX !(#) = P.

Dynamic of the observer

As a preliminary, let q be the smallest integer such that:

5678YZ [ \ = 5678 ] Z [ >*$ 4- [ ^ (9)
with:

Z [ = _ à 3 4- > 3 4-*$ 4- >*$ 4- b 3 4-*$ 4- [cd >*$ 4- [cd 3 4-*$ 4- [ e f f f f f g
The design of the observer uses the successive derivations of v(t)=LT(t) that must be expressed only with v(t), Tmes(t), U(t). and their successive derivatives.

Realizing the obtained input-output differential equation [START_REF] Rotella | Minimal single linear functional observers for linear systems[END_REF] leads to a state equation for the observer (Eq. 10).

h j j j k j j j n F" (#) = o P p q q P r s r d b p r [cd t F(#) + o u s u d b u [cd t '(#) o v s + r s *v [ v d + r d *v [ b v [cd + r [cd *v [ t ! 012 (#) C D(#) = ( P w P p)F(#) + v [ ! 012 (#) (10)
If Sq is a full row rank matrix, the observer is realized through solving (Eq. 11) where Z [ x is the pseudo-inverse of Sq.

yv s r s w v [cd r [cd v [ z = >*$ 4- [ *Z [ x * (11)
As a contrary, if Sq is not a full row rank matrix i.e. the rank of Sq is lower than its number of rows, there exist some degrees of freedom in the design of the observer. The amount of degrees of freedom is denoted r and is defined by (Eq. 12). It means that r parameters in yv s r s w v [cd r [cd v [ z may be chosen depending on the desired dynamics of the observer [START_REF] Rotella | Minimal single linear functional observers for linear systems[END_REF]. This case will be detailed in Section 4.

= {SAY|R5(Z [

} )\ (12)

Procedure for implementing the design of the observer

In a practical way, q is determined through an iterative procedure leading to a possible minimum order for the LFO [START_REF] Rotella | Minimal single linear functional observers for linear systems[END_REF].

The whole procedure is given in Figure 2.

Design of thermal observer

The observer will be designed to estimate the temperature at a distance of 1cm from the heated plate. The estimation point corresponds to the average temperature of the first and the second node in the model i.e. to the functional matrix L: L=(0.5 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0) Fig. 2. Algorithm of the procedure for the design of the observer A thermocouple is inserted at the estimation position for the validation of the results of the observer.

Iterative procedure

Regarding the system modelling in Section 2 and the design procedure given in Section 3, preliminary checks (Eq. 4, 5) are carried out. As the system is functionally observable, an iterative procedure may be undertaken to find the smallest integer q such that (Eq. 9) is verified.

Integer q=8 leads to an observer of size 8 lower than the size of the system (n=16). However, in this case, r=1 meaning that a degree of freedom exists in the design of the observer. This degree of freedom is called G in the following. A root locus of the observer (see Figure 3) demonstrates that a parameter v ỹOPX•*€ *pPz leads to a stable observer satisfying (Eq. 7, 8).

Performances of the designed observer

Once designed, the performances of the observer are verified in terms of noise sensitivity and decay rate of the estimation error. Note that the noise sensitivity depends on the dynamic of the observer and then on the choice of the parameter G. This study is done by using gain behavior of transfer functions from state space representation of the observer regarding its inputs Th(t), Ta(t) and Tmes(t). The transfer functions H(s) of the system are obtained using (Eq. 13) where Iq is the identity matrix of size q. Associated Bode diagrams, especially gain diagrams are given in Figures 4 to 6.

I(•) = J*Y•*' [ O G\ cd yH*Iz + yP*P*Kz (13)
Regarding Th(t) and Ta(t), the transfer acts respectively as a first and fourth order low pass filter, thus avoiding the effects of high frequency measurements noise on the estimated variable. Considering Figure 5, due to direct action of Tmes(t) on the estimated variable (Eq. 6), a static gain at low and high frequencies is obtained. Note that resonant behavior should be avoided. Moreover, it can be remarked that static gains on Figures 5 and6 are lower for G=-0.2. This means that the observer becomes less dependent on input values Ta(t) and Tmes(t). As a consequence, G=-0.2 could be chosen.

Finally, the observer is realized. Matrices of the observer are given in Appendix B. Eigenvalues of F are then (-0.0013, -0.0059, -0.0138, -0.0228, -0.031, -0.0393, -0.0468, -0.0512). Conditions in (Eq. 7, 8) are then verified. The estimated temperature obtained with the observer is compared with that measured at the same position (see Figure 7). The applied boundary conditions are those defined (Eq. 2). The error rapidly decreases, in accordance with eigenvalues of the observer, resulting in good estimation properties.

However, it seems that a slight estimation error of about 2 °C exists even for long duration. This error is null when the observer output is compared to the model one. This may result from some hypothesis used to model the system such as constant parameters whatever the temperature or the absence of mechanical length variations due to temperature increase. Indeed, LFO has been applied to a system that is known to be non-linear. One can conclude that even using this strong simplification, estimation performances are fair enough to estimate potential degradation of the silicone gel.

In addition, it must be remembered that discretizing PDE may lead to static error between model and reality. Finally, even with these imprecisions, the estimated temperature could be validated in terms of decay rate of estimation error, given a good approximation of the local temperature in the silicone gel bar. It can be remarked that for t=0, the measured temperature increases whereas the estimated one decreases. This stems from unstable zeros (zeros with positive real part) in the transfer function of the observer regarding two of its inputs Th(t) and Tmes(t). This behavior is due to the fact that the dynamic of the observer may not be fully chosen except by choosing the parameter G that has been tuned according to noise sensitivity.

Real time implementation of the observer

In order to be used in real time embedded computing systems, it is necessary to implement the observer as a recursive equation.

Some methods have been detailed in [START_REF] Sakhraoui | Discrete linear functional observer for the thermal estimation in power modules[END_REF]. It has been demonstrated that the use of a classical numerical integration algorithm such as Euler or Runge-Kutta methods of order 2 and 4 provides the best results for implementing the observer by limiting the number of operations per time sample. For these methods, the maximum number of additions and multiplications to be done at each sample time in order to estimate the temperature can be evaluated and are presented (see Table 1). Moreover, regarding matrices given in Appendix B, it can be remarked that some values may be tuned to 0 without loss of estimation performances. This results in a reduction of the computation complexity of the observer on a real time target.

Conclusion

A thermal estimation approach was presented for a number of studied materials used in power electronic modules: the silicone gel used for encapsulation. The proposed approach is based on state space representation. The design of a single LFO has been presented and designed in order to estimate the temperature in any desired location using one measurement and the knowledge of thermal inputs.

This kind of observer results in a relevant reduction in the observer order compared to the initial system dimension. It has been demonstrated, using experimental data, that the observer was able to accurately estimate the temperature evolution of a desired location in the considered system. Moreover, the noise sensitivity of the observer has been detailed depending on its parameters, and real time implementation of the observer on embedded computing target has been discussed.

Several developments have to be investigated regarding the present work. One of our future work axes will be to validate linear functional observers on thermo-mechanical systems to estimate mechanical stress or elongation depending on thermal behavior. 3D thermo-mechanical behavior will be considered to be more representative of power electronic modules. The proposed method for design minimal order observers may be easily applied to these models. However, such models will be naturally of large dimension, and state space representations will be huge. Thus, it could be supposed that even the use of linear functional observer will not drastically reduce the order of the problem. In this case, the observer designed from experimentally identified transfers could be studied.

Time-varying systems can also be studied and corresponding observers could be designed. This point seems of particularly significant interest in the field of power electronics where parameters depend not only on temperature but also on aging of the material itself.

Finally, another axis of future research is to consider unknown inputs, such as thermal power dissipated by semiconductors or thermal perturbations from passive elements in the power module. The next step will be to design functional observers of unknown inputs to accurately monitor the temperature of semiconductors during the life cycle of the power modules.

G

J = (P P P P P P P p), V=-0.2 (20)

Fig. 1 .

 1 Fig. 1. Studied system.

Fig. 3 .

 3 Fig. 3. Root locus of the observer.

Fig. 4 .

 4 Fig. 4. Gain behavior of ƒ "(…) regarding Th(t).

Fig. 5 .

 5 Fig. 5. Gain behavior of ƒ "(…) regarding Ta(t).

Fig. 6 .

 6 Fig. 6. Gain behavior of ƒ "(…) regarding Tmes(t).

Fig. 7 .

 7 Fig. 7. Observer results.

Table 1

 1 Evaluation of number of operations to calculate C D(#)

	Euler	RK2	RK4
	Additions ultiplications † ‡ˆ † pPˆ † ‡ˆ † ppˆ † ‰ŠM † ‰‹ˆ

Acknowledgements

This work is executed and funded in the framework of ANR-CAPTIF project (ANR-14-CE05-0044).

Appendix A. Expression of thermal matrices

Regarding 1D discretized thermal equations using proposed methodology, matrices of the system have a particular form that is detailed below.

Appendix B. Expression of matrices of the observer

Matrices of the observer that are obtained through the proposed methodology are detailed below.


Abdourahim Sylla
email: abdourahim.sylla@grenoble-inp.fr

Thierry Coudert
email: thierry.coudert@enit.fr

Laurent Geneste
email: laurent.geneste@enit.fr

A Case-Based Reasoning (CBR) approach for Engineer-To-Order systems performance evaluation

Keywords: Complex systems design, Performance evaluation, Decision making, Engineer-To-Order, Case-based Reasoning

In Engineer-To-Order (ETO) industrial contexts, decision-making about which systems to offer for sales or which subsystems to integrate into the systems for sales is based on various performance indicators. However, the lack of relevant information to evaluate these indicators challenges the decision-making process. In this article, to face this issue, a CBR approach is proposed for the evaluation of the performances of ETO systems. The main contributions are : (i) an object-oriented case representation model which allows to store previous evaluated systems for an effective and time efficient similar systems retrieval, and (ii) a method that allows to compute similarity between two systems that can have different structures.

INTRODUCTION

In Engineer-To-Order (ETO) industrial situations, companies must totally or partially define novel or adapted systems in order to cover the customer requirements [START_REF] Sylla | Configuration knowledge modeling : How to extend configuration from assemble / make to order towards engineer to order for the bidding process[END_REF]. When defining such systems, called nonstandard systems, decision-making about which systems to offer for sales or which subsystems to integrate into the systems for sales is based on various performance indicators. They characterize the system and its development process. Some examples of performance indicators are cost, feasibility, complexity and risks. A reliable evaluation of these indicators is crucial in order to foster right decisions. However, most of the time, in ETO contexts, relevant information to the evaluation of a non-standard system is not fully available [START_REF] Sylla | Possibilistic Pareto-dominance approach to support technical bid selection under imprecision and uncertainty in engineer-to-order bidding process[END_REF]. In some companies, to overcome this issue, domain experts, based on their experiences, extrapolate the evaluation of standard (existing) systems in order to evaluate the non-standard (new) one. This may work when dealing with simple system with few subsystems and few integrations between subsystems. When dealing with complex systems, composed of numerous subsystems and integrations, the cognitive workload associated to the evaluation task is high and cannot be supported by a human brain. Moreover, a highly humandependent approach can lead to inaccurate or inexact evaluation. Therefore, a computerized approach capable of reproducing human reasoning is needed in order to support the evaluation of complex systems in Engineer-To-Order industrial situations.

To face this issue, a Case-Based Reasoning (CBR) approach is proposed in this article. As explained in several works as [START_REF] Kolodner | An Introduction to Case-Based Reasoning[END_REF] and [START_REF] Aamodt | Case Based Reasoning : foundational issues, methodological variations, and system approaches[END_REF], CBR approach is an artificial intelligence based approach which allows to solve a new problem by finding similar past problems and reusing knowledge and information from those problems. In a CBR terminology, a problem situation is referred as a "case" or an "experience". A past problem situation that has been studied so that its related knowledge and information can be reused to solve new similar problems is called "previous case" or "source case". Similarly, a new problem situation is called "new case" or "target case". CBR approach has been used for several evaluation problems, especially effort estimation in software development [START_REF] Wu | Case-based reasoning with optimized weight derived by particle swarm optimization for software effort estimation[END_REF], cost estimation in new product development [START_REF] Relich | A case-based reasoning approach to cost estimation of new product development[END_REF] and prediction of the roughness and residual stress of machined surface [START_REF] Xu | An improved case based reasoning method and its application in estimation of surface quality toward intelligent machining[END_REF]. In these works, all systems are considered to have the same structure, which means that all systems are defined by the same set of features. Consequently, the proposed CBR approaches do not consider situations where the system to be evaluated has different structure from the past existing systems. However, in Engineer-To-Order industrial situations, a nonstandard system maybe defined by adding non-standard values for standard features or adding non-standard features or subsystems to standard systems.

In this article, we consider Engineer-To-Order industrial situations and propose a CBR approach for the evaluation of complex systems in domains where systems may have different structures. The main contributions are: (i) a "complex system performance evaluation" case repre-sentation model which allows to model and store system evaluation situations in a way that fosters an effective and time efficient case retrieval, and (ii) a simple method that exploits the case base structure to retrieve the most similar cases from the case base, taking into account common and non-common features of the target case and the previous cases. The rest of the paper is structured as follows. Next section provides the fundamentals of CBR approach for problem solving. Section 3, 4 and 5 describe the proposed CBR approach. Section 6 presents an illustrative application dealing with the evaluation of the cost of a tower crane system. Finally, Section 7 presents conclusion and future research.

FUNDAMENTALS OF CBR SYSTEMS

A CBR system is generally described by a cycle composed of five main phases. They are described in the following [START_REF] Aamodt | Case Based Reasoning : foundational issues, methodological variations, and system approaches[END_REF].

• Define: a new problem is described in order to compare it to past problems stored in the case base. • Retrieve: using a similarity measure, most similar problems in the case base are searched and selected.

• Reuse: knowledge or information related to the selected cases are reused to propose an initial solution.

• Revise: if the initial solution is not suitable, it is revised to make it more convenient. • Retain: the new problem and its related information and knowledge are stored in the case base.

Two major challenges related to the development of an effective CBR system are to design a suitable case representation model and to define a relevant similarity measure. A case representation model is used to describe the problems. As explained in [START_REF] Bergmann | Representation in case-based reasoning[END_REF], it generally consists of a problem and its solution description. It makes it possible to compare two cases and to compute their similarity. It also allows to store already studied cases in a case base. An appropriate case representation model combined with a well-organized case base allow for an effective and time efficient case retrieval and reuse.

Various case representations have been proposed in the literature, namely feature vector, hierarchical, ontology, and object oriented [START_REF] Bergmann | Representation in case-based reasoning[END_REF]; [START_REF] Shaker | Case Based Reasoning: Case Representation Methodologies[END_REF]. With feature vector, each case is represented as a set of features (attributes-values) which describe the problem and its associated solution. In this setting, all cases must have the same structure. The similarity measure is based on the values of the attributes and the relative importance of each attribute. In an hierarchical representation framework, a case is represented at multiple levels of detail [START_REF] Bergmann | On the Role of Abstraction in Case-Based Reasoning[END_REF]. This allows, when finding similar cases to a new one, to retrieve appropriate cases at the same levels of detail [START_REF] Bergmann | Representation in case-based reasoning[END_REF].

With Ontologies, cases are represented with formal, explicit and sharable concepts and properties. Properties are used to describe the concepts and the relationships (hierarchical or non-hierarchical) between concepts [START_REF] Foguem | Knowledge formalization in experience feedback processes : An ontology-based approach[END_REF]. The similarity measure is generally based on the position of each case related concept in the hierarchy of concepts. With object-oriented representations, each case is represented as an object which is described by a set of attribute-value pairs [START_REF] Bergmann | Representation in case-based reasoning[END_REF]. In this work, as we consider ETO industrial contexts where systems may have different structures, we have chosen the object oriented representation to develop the CBR approach. It is based on the CBR inspired cycle shown in Figure 1. When a new system must be evaluated, it is represented using the case representation model proposed in Section 3. Then, it is mapped to the case base and the most similar cases are retrieved and selected using the method proposed in Section 4. Finally, knowledge and information related to the selected cases are used to evaluate the performance of the new system using the method proposed in Section 5. The new system, when evaluated, is added to the case base along with its related knowledge and information.

CASE REPRESENTATION FOR COMPLEX SYSTEMS EVALUATION

A complex system can be defined as a set of subsystems which are integrated through adequate interfaces Henderson and Clark (1990). Each system or subsystem is, on one hand, defined by a set of properties (example: length and stiffness of a crane jib) and, on the other hand, characterized by a set of performance indicators such as cost, feasibility, complexity and risks. Based on that and using object-oriented framework, a "complex system performance evaluation" case representation is defined as follows:

• a case is a specific "system evaluation situation" and it is represented by an object which is an instance of a class; • a class may be composed of one or several other classes and classes are organized in a class hierarchy; • an object's class determines its attributes which may be a property, a performance indicator or an object; • the collection of all objects represents the case base. For instance, CCC01 is a case of a cabin controlled crane system performance evaluation and Ca01 is a case of a cabin system performance evaluation. In the next section, the method that allows to retrieve similar previous system evaluations for the evaluation of a new system is presented.

CASES RETRIEVAL AND SIMILARITY MEASURE FOR COMPLEX SYSTEMS

We assume that one may use our CBR system to evaluate a system for sale (crane system in the example of Figure 2) or a system which is a part of the system for sale (Jib system in Figure 2). In the latter situation, the CBR system provides an evaluation of a part of the system for sale, which can be used through another evaluation method to evaluate the system for sale. This is particularly appropriate in ETO situations where few parts of an existing system must be modified to develop a new system.

In this article, we propose a generic approach which allows to retrieve the most similar cases in both situations (see Figure 3). The main steps are described in the following.

1.Relevant case retrieval. At the first step, the structure of the case base is exploited to directly retrieve relevant previous cases to the target case. In fact, as each ∩ Ω(C p ) inherited from their Direct Common Superclass (DCS). In addition, at least, one case has one or more attributes that the other case does not have, see lower part of Figure 4. Based on the similarity computation method in feature-vector approach, a simple, effective and easy to implement method is proposed to compute similarity of two cases in any of the above mentioned two situations. The global similarity of the two cases, noted Sim(C t , C p ), is a real number between 0 and 1. It is computed as a weighted average of the local similarities of attributes, noted Sim(att t i , att p i ), see Equation 1. The weight w i of an attribute indicates its relative importance to the performance indicator being evaluated. In order to take into account the two situations mentioned above, the following hypothesis are considered for the computation of the local similarities:

• For an attribute that characterizes both target and previous cases, the local similarity is a real number between 0 and 1. In fact, such an attribute tends to increase the global similarity of the two systems. If the values for the attributes for the two systems are the same, the total weight w i of the attribute is added to the global similarity. If not, a percentage (which corresponds to the local similarity) of w i is added to the global similarity.

• For an attribute that characterizes only one of both cases (target or previous) the local similarity is equal to 0. In fact, such an attribute tends to decrease the global similarity of the two systems. By setting the local similarity to 0, the weight w i of the attribute is not added to the global similarity. It is removed from the maximum global similarity which becomes 1 -w i . So that, if the attribute in consideration has a strong impact on the performance indicator to evaluate, the global similarity of the two cases will be low.

In the context of complex systems evaluation, the attributes may be simple or relational. The values of simple attributes can take multiple forms, namely crisp symbols and crisp numbers. In example of Figure 2, for the "jib system", the value of its attribute "stiffness" may be "strong" and the value of its attribute "length" may be "100 meters". The value of a relational attribute is an object. Depending on the form of an attribute, a different method is used to compute the local similarity. Let q pi and q ti denote the values of an attribute att i for a previous case C p and a target case C t . If q pi and q ti are in the form of crisp numbers, the local similarity is computed using equation 2. If q pi and q ti are in the form of crisp symbols, the local similarity is computed using a similarity matrix as shown in Figure 5. If q pi and q ti are objects (i.e. subsystems), the local similarity is recursively computed using equation 1.

Sim(C t , C p ) = k i=1 w i * Sim(att t i , att p i ) 0 < w i ≤ 1 and k i=1 w i = 1 ∀i ∈ Ω(C t ) ∩ Ω(C p ), 0 ≤ Sim(att t i , att p i ) ≤ 1 ∀i ∈ Ω(C t )\Ω(C p ), Sim(att t i , {}) = 0 ∀i ∈ Ω(C p )\Ω(C t ), Sim(att p i , {}) = 0 (1) sim(att t i , att p i ) = 1 - |q pi -q ti | max p∈φ {|q pi -q ti |}
φ is the set of the retrieved previous cases.

(2) One can notice that the weights of the attributes take a great place in this method. The efficiency of the similarity assessment strongly relies on what weights reflects the relative importance of the attributes with regards to the performance indicator being evaluated [START_REF] Doan | Determining Attribute Weights in a CBR Model for Early Cost Prediction of Structural Systems[END_REF]. Several methods have been proposed to determine the weights of attributes in CBR systems, namely Analytic Hierarchy Process (AHP), Artificial Neural Network (ANN) and optimization techniques. In this article, we use AHP method [START_REF] Saaty | The analytic hierarchy process[END_REF]. AHP is a systematic method which uses knowledge of domain experts to determine the weight (relative importance) of each attribute with respect to the performance indicator being evaluated. First, a pairwise comparison of the attributes is performed in order to have the input data. Second, the obtained pairwise comparison matrix is used to compute the weight of the attribute. Finally, a consistency ratio is computed to examine the consistency of the weights determination process. As AHP is a well-established method that has been described in many researches, we do not describe it in detail. More details can be found in numerous articles, especially [START_REF] Saaty | The analytic hierarchy process[END_REF].

3.Useful cases selection. After computing the similarity of the target case with each previous case, based on a "similarity threshold" and a "maximum number of useful cases", the most useful cases are selected for the evaluation of the target case. The similarity threshold allows to define a minimum similarity value under which a previous case is not considered similar enough to the target case in order to be considered for the evaluation. The maximum number of useful cases is used to limit the number of cases in the evaluation process. It allows to reduce the computational time, especially in situations where numerous previous cases are retrieved. In the following, we describe how to evaluate a new system using knowledge and information related to past similar systems.

EVALUATION OF THE TARGET SYSTEM

In this phase, the performance perf of the target case C t is evaluated using the evaluations of the m most similar previous cases retrieved and selected from the case base (C p j , j = 1 to m). We assume that one may want to revise the evaluations of the selected previous cases in order to make them conform to the evaluation context of the target case. This is particularly appropriate in situations where the time difference between the evaluations of previous and target cases is long. For example, when evaluating the cost a new system, the inflation factor due to the time difference must be considered. Let l be a factor that characterizes the evaluation context of the target case and K l its revision coefficient. The revised evaluation of the performance of a selected previous case C p j , noted E perf r (C p j ), is computed using Equation 3. In this equation, E perf (C p j ) is the original evaluation of the previous case C p j . Then, the evaluation of the target case is performed as the weighted sum of the revised evaluations of the previous cases (see Equation 4). The weight W j of each case being the normalized value of its similarity to the target case. It is computed using Equation 5.

E perf r (C p j ) = K l * E perf (C p j ) (3) E perf (C t ) = m j=1 W j * E perf r (C p j ) (4)
W j = Sim(C t , C p j ) m j=1 Sim(C t , C p j ) (5)
In the next section, an illustrative application is presented to show how the proposed approach can be used.

ILLUSTRATIVE APPLICATION

The aim of this section is to show how to use the proposed CBR system to evaluate a new system during an engineering design process. The example concerns the evaluation of the cost of a new crane. Following the proposed case representation model presented in Section 3, the new crane, called C t , is defined as follows. The attributes of the crane C t allow to identify the corresponding class in the case base class hierarchy. It is the class CC Crane, and C t has one "sisters' class" which is RC Crane (see Figure 2). Therefore, as explained in Section 4, only cases which are instances of the classes CC Crane and RC Crane are retrieved for further similarity computation. The other cases are not retrieved as they are not cranes. This enables to directly retrieve the relevant cases to the target case. Thus, it allows to reduce the computational time related to the retrieval and similarity computation process. In total, fifty previous cases is retrieved. A sample is shown in Table 1. After that, the similarity computation method presented in Section 4 is used to compute the similarity of each previous case with the target case. For the seek of clarity, all details about the similarity computation are not shown. Instead, we choose to present a sample of the final result in Table 2. In this table, weight 1 is the weights of the attributes when the target and previous cases are instances of the same class, whereas weight 2 is the weights when they are not instances of the same class. It is important to notice that the proposed method supports not only the similarity computation between two systems of the same structure (e.g. C t and case 1 in Table 2), but also the similarity computation between two systems of different structures (e.g. C t and case 4 in Table 2). For the evaluation of the cost of the new system, in order to select cases that have a great similarity to the target case, the similarity threshold was fixed to 0.90. Only three cases (case 12, case 14 and case 20) correspond to this requirement (see Table 2). As the maximum number of useful cases is set to 5, the costs of the three cases are used to compute the cost of the new system using the method presented in Section 5. The revision coefficient is supposed 1, which means that a revision is not necessary in this context. The final result of the evaluation of the cost of the target case is 192016.45.

CONCLUSION

In this article, a CBR approach has been proposed for the evaluation of the performance of engineer-to-order systems during engineering design process. It is based on an objectoriented case representation which allows to store previous cases for effective and time efficient similar cases retrieval. The proposed approach is applicable in domains where the system to evaluate can have different structure with the

Fig. 1 .

 1 Fig. 1. CBR inspired cycle for ETO system evaluationThe object-oriented framework contains powerful relations which allow to describe complex cases in domains where cases may have different structures.[START_REF] Bergmann | Similarity Measures for Object-Oriented Case Representations[END_REF] proposed two measures to compute the similarity of two cases (Intra-Class and Inter-Class) which are based on the class attributes.

  The upper part of Figure2depicts an UML class diagram which is an object-oriented case representation of a tower

Fig. 2 .

 2 Fig. 2. An example of object-oriented case representation crane system. In this diagram, a crane is a kind of system defined by the class Crane. It is composed of three subsystems (a tower, a jib and an engine) which are also kinds of systems described by the classes Tower, Jib and Engine, respectively. There are two kinds of crane system: Cabin Controlled Crane (CC Crane) and Remote controlled Crane (RC Crane). They are specializations of the class Crane. In addition to attributes (cost, lifting capacity, engine, jib and tower ) inherited from the class Crane, they have specific attributes: {Cabin} for CC Crane and {R Control } for RC Crane. At the lower part of Figure 2 are shown examples of previous system performance evaluation cases.For instance, CCC01 is a case of a cabin controlled crane system performance evaluation and Ca01 is a case of a cabin system performance evaluation. In the next section, the method that allows to retrieve similar previous system evaluations for the evaluation of a new system is presented.

Fig. 3 .

 3 Fig.3. The selection process of the most similar cases class of the case base is built based on a set of common properties of systems, the case base structure contains general knowledge about which systems are of the same type and which systems are not of the same type. For instance, CCC01 and RCC01 are of the same type, they are all cranes. In the contrary, CCC01 and CaO1 are not of the same type, CaO1 is a cabin and not a crane. Exploiting the case base structure allows to reduce the computational time related to search and similarity computation. Practically, once a new system must be evaluated, its properties are extracted in order to identify the relevant class in the case base class hierarchy. Only cases that are instances of the class of the target case and those that are instances

2.

  Similarity computation. After that, the similarity of the target case C t with each retrieved previous case C p is computed. The two situations that can be encountered are considered. In the first situation, the target case and the previous case are instances of the same class. The two cases have the same set of attributes Ω(C t ) = Ω(C p ), see the upper part of Figure4. In the second situation, the target case and the previous case are instances of different classes. The two cases have a set of common attributes Ω(C t )

Fig. 4 .

 4 Fig. 4. Two situations of similarity computation

C

  t = {lifting capacity = 15200 kg, cabin = Ca15 = {floor area = 2.5 m 2 , ergonomics = A+}, jib = Ji21 = {stiffness = strong, length = 96 m}, tower = To21 = {height = 108, section = 3.77 m 2 }, engine = En21 = {power = 1890, energy = solar}}.

  of its "sisters' classes" are retrieved. We define "sisters' classes" as classes that have a Direct Common Superclass (DCS). For example, in Figure2, CC Crane is a sister class of RC Crane. The DCS of CC Crane and RC Crane is the class Crane. Therefore, if the target case is an instance of the class CC Crane, all systems that are instances of the classes CC Crane and RC Crane are retrieved for further similarity computation. The other cases that are not instances of CC Crane and RC Crane, CaO1 for example, are not compared to the target case.

Table 1 .

 1 A sample of retrieved previous cases

		lifting c.	stiffness	length	height section	power	energy	floor area ergo.	precision	ergo.	cost
	case 1	24624	strong	83	105	3.91	1894	solar	2.5	A+	-	-	285721
	case 2	23542	strong	88	98	3.68	1811	gasoline	2	A	-	-	273378
	case 4	21966	strong	100	110	3.59	1690	solar	-	-	5	B+	259479
	...	...	...	...	...	...	...	...	...	...	...	...	...
	case 12	16075	strong	104	114	3.94	1237	electric	2.2	C	-	-	196304
	case 14	15792	strong	98	108	3.72	1195	gasoline	-	-	3	A	192022
	case 20	15254	strong	106	118	3.77	1173	electric	2.5	A+	-	-	187947
	case 25	7380	medium	50	60	2.84	568	gasoline	-	-	4	B+	91574
	case 43	897	low	32	42	2	69	gasoline	2	B	-	-	17700

previous evaluated systems. An illustrative application is presented to show how to use the proposed approach. As a future research, we intend to apply the proposed CBR system to use cases from industries in order to show its applicability and effectiveness.


F Rotella

F J Carr

M Llo
email: llo@enit.fr

Ayadi
email: aya.di@enit.fr

POLYNOMAL CONTROLLER. D.ESIGN BASED ON FLATNESS

Keywords: Flatness, two-degreP--S-Of-freedom control lers, linear systems, polynomial cont rollers

By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Pol yn omial controllers for fini te-dimensional linea:r systems can then be designed v. r ith very natural choices for high level pararueters design. This design leads to a Bezout equation whlch is independent. of the closed loop dyna.mlcs but depends onJy on the system -model.

INTRODUCTION

For fuùte-dimensional lin. ear systf-.ms, a well known control design t, ochnique is r.onstituted by pol yn omial two-degr�f-freedom controllers (Astrôm, and Witten.mark, 1990;[START_REF] Franklin | :kman[END_REF]Kuoera, 1991), w h lch b.ave been. in. troduced for ty years ago by [START_REF] Horowitz | Synthe. 'i7-9 of Feéd[END_REF]. Wbatever the cbosen design method, thls powerful method is based on pole placement and presents one defi cienc y: it neecls to know a priori where to place ail the pole. of the closed loop system. Foll owing [START_REF] Astrôm | Solution usin& robust adapth•e pole place ment[END_REF]: ''the key issue is to choose the closed loop poles. This choice requires consid erable insight ... ". This can be done, for instance, through. LQR design, but the p.roblem is then :replaced by the correct choioe of the weigbting matrioes in the cost functions.

In order to overcome the drawback of this design technique, it wïÏl be seen, in the following, that the use of a new method for system control, namely with a flatness point of view, enlightens the choice of the hlgh level para.meters and brings physical meanings t.o obtain a clear guideline for polynomial pole placement design. Followmg (Fliess, et al., 1995;Fliess, et al., 1999), ftatness is a very interesting p:roperty of processes to design a control, i,pecially for trajectory planning and traclring for nonlinear systems.

The paper is organized as follows. Section 2 and 3 are devoted to survey very quic:kly, the design of polynomial controllers for the first one and, for the second one, the fiat ness proper ty and the control design implied for a fiat system. At the end of the section 3, a methodology for the control of fiat systems is proposed and illustrated on finite-dimensional linear systems in the section 4. This point of vîew Ieads to propose a fiatness based two-degrees-0!-freedom r.ontroller which is rea.lized in the section_ 5. lu t.he fol iowing, the paper will be developed in a con. tinuous tirne formulation, but alJ the developments can be extended to discrete tirne linear systems. For n EN, the following not ations will be used , u.<n>(t) = dâ;l t l = p"u(t), where p denotes the dlfferential operator.

The paper will aLso be developed, for the sake of shortness, for S180 linear systems, but ail the reslllts can be adapted to MIMO linear systems.

POLYNOi\UAL CONTROLLERS

This section offers a short -descri-ption of lhe design principles of the polynolli.ial Lwo--<legrees of-free.dom controllers for linear systems. More detaîls are given in (Aslrom, ahd Wittenmark, 1990: Franklin, el al.. 1998;Kuoera, 1991) and the references therein, and in the following these controllers wfü be den.or. ed as RST controUers [START_REF] Landau | lde:n.ti fi.cation. el Communde des P.ror[END_REF].

Consider the finitwïmensionàl $ISO linear sys tem described by r.he input.-ouLpuL mode!:

Ay = Bu, (1)
where y and -u are the output and contrai signais, A is monic and A and B are coprime poly nornials.

For (1), the RST (two-de gr ees-of-freedom) con trol ler (Astrèim and Wittenmark, 1990) is given. by:

Rv.=-Sy+T-r, (2)
wbere r JS the reference to track, and R, S and T are pol y nom ials in r.he considered operator. These pol y nomials are given by the fol lowing rul es: R and Sare.solutions of the Diophantine ( or Be-rout) equation:

P=AR+BS,

whete the roots of the polynomial P are constituted by the desired closed loop and obsenrer poles, and P and R are monic; T is given by the desired cloeed loop transfer such that:

PBm=TBAm, (4)
When ail these conditions are fulfilled, t.he cloeed loop behavior is obt,ained:

Amy=Bm'r, ( 5)
Some remarks for the design: Ali these points, which have been for malized through the Lie-Backlund eqwvalente of systems in (Fli=, et al.. 1993;Fliess, et al. 1999 ), lead to propos e a nonlinea:r feedback which ensur e s a stabilized tracking of a desired motion for the flac output. This methodology bas bee.n applied on many industriaJ processes as 1t has beeo shov.11 previously, for instance, oo magnetics bearings [START_REF] Lévine | A nonlincar approach to the control of mag netic bearings[END_REF]. ehernical reactors (Roth.fuil et al., 1996), cranes or filght control (Lêvine, 1999) or t.urning process (Rotella, and Carrillo, 1998; Rotella, and [START_REF] Carrillo | proposed control to over come unoertainty in mode! pa:rameters[END_REF], arooog many other examples.

To be more precise the use of flatness leads to the following methodology t.o design a control.

The main objective of t;his control is to insure an asymptotic tracking of a desired trajectory and can be ensured through the followi.ng steps : (i) Explicit the flatness: namely, the analytic ex pression s are obtained. here�

-h( (lJ (<>) ) .Z - X, U s 'U. , ••• � 'U , x==A(z, ... ,z(�l), u=B(z, ... ,zUHIJ), (15) (16) (17)
where u is the chosen co11trol variables, and x, the whol e set of internat variables. lt must be noted here that the relationship which gives x wil1 not be use<l in th.e followi.ng, but it i. s neoes.sary to confum z as a flat output. I.ndeed, if one of the interna! variable is not de.fined by z, then z is not a flal output.

(ü) Linearization: by the control:

u = B(z, ... , z<P), v), ( 18
)
where v is a ne w control, the linear system z(BH) = v is obtained. It must be noted here that thls step is an intermedia.te one a.nd must be fol lowed by the next ones.

(ili) Motion planning: it coo sists in the design of a trajectory defined by Zd(t). whlc h must be d.ifferentiable at the or der (/3 + 1).

(iv) !viotion tracking: by the control:

v == z;f+ 1 )(t) + I)i,(z�')(t) -z { •)(t)), ( 19
) i,=O
where the k, ensUie that the _poly nomial K(p) = p o+ 1-t 2::� k;p' is Hurwitz, the complete control is tbeu as follows:

u= B(z .... ,z (Pl , {J z,r+11 ( t) + L k,(z�')(t) -z<•)(f)))

1-=0

= <P(z., • , z ( /1), K(p)zd(t)), ( 20) which leads to an asyroptotic traclcing of t.he desired tra.jectory. [START_REF] Bitaud | A flatness based oontrol syothesi s of li:near systemS and application to WÛldshield wipers[END_REF]Fliess, et al., 1998) and extended for infinite--dimensional ones (Fliess an.d Mounier, 1998). It will be seen, in this section, that .i.pply i ng the guideline .induced by a .B.atness based control to a linear system lea.ds to e.xpress it in a .natural RST form.

The previ ous methodology will be applied now to a linear lumped parameter SISO system defined by t,he transfer:

A (p)y( t) = B(p)u(t), (21)

where the notations have been previously defined but with:

n-1

A(p) ==p n + E a.p i == p" +A"(p), ( 22)

-n-J_ B(p)= Eb,p;.

(2 3 ) i=O Ftom coprimeness, it has been sbown in [START_REF] Bitaud | A flatness based oontrol syothesi s of li:near systemS and application to WÛldshield wipers[END_REF]Fliess, et, al,, 1999), that this system is fiat with a flat output defined by: The explicit expressions of the output y(t) and the control u(t) are given by:

  ( i) Denoting by deg P the degree of a. pol y nomial P. For realiza.bility conditions, the RST controller must be such that (Astrôm and Witqinmark, repui.rk is that it has been used, for the choioe of T, the point of view developed in(AstrôJD and Wittenmark, 1990), where (B m , A,,.) was a wodel-to-fol low, but it can be also chosen the proposed one î,n[START_REF] Landau | lde:n.ti fi.cation. el Communde des P.ror[END_REF], where r is given by:(8) where (B rn , A m ) defines a trajectory-to-follow or a trajccuiry generat, or of r(t). ln thls lasn point of view, T is designed such that: As a remark Ît can be noted that ail the design of a RST controller cap be performed with ail the pol y nQmials \l,Titten in rea.lizable opera.tors, as in[START_REF] Landau | lde:n.ti fi.cation. el Communde des P.ror[END_REF], and in this case, if:A(O) = R(O) = P(O) = 1,the realizability conditions (6 ) and (7) disappear. 3; SHORT SURVEY ON FLATNESS The fiat prope.rr.y, whlch has been introduced recently (F liess, et al., 1992; Fliess, et al., 1993; Fliess, et al., 1995} for continuous time nonlinear systems, leads to interesti ng points of vie.w for control design . In the following, a short revîew about fla.tness o[ systems and the application of thi$ property to design a controller will be given.. The .i nterested reader �Y .find more details in the quot.ed literarure and the references therein. A system described. .e:re is no unique ness. But, as it bas been obsei:ved on numerous e:x:ample s, the fiat output has a simple and physical meaning. Roughly speakmg, the implications of fiatness are of ve. ry importance in several ways for control For motion planning, by impoeing a desi:red trajector y on the fiat out.put, the neces.58. control to generate the trajectory, can be obtained e:x:plicitly (witbout any integration of the differential equa tions). The desired trajectory, zd(t), must be (J3 + 1)-times continuously differentiable. For feedback control whlch on ly cnsures a good stabilization around t, he desired motion Z'.t(t).

  p) and D(p) are the pol yn omial solutions of the following Bez.out equation: imeness, existence of N(p) and D(p) are gua.ranteed and the minimum degree solutfon is, for n > 1. such that degN = nl and degD =n-2.

  It must be noted here that the information needed by dùs cont.rol can be obtained through observers. and a major advao.tage of tlùs controller wit.h respect to other nonlinE'.ar strategies is that it overcomes the problems generatced by non st able zeros d yn amics(Isidori, 1989;[START_REF] Nijmeijer | Nonlin ear Dynamical ConGrol Systems[END_REF]

	der Scha.ft, 1990).
	4. IMPLICATION FOR LINEAR SYSTE: MS: TOWARDS RST CONTR. OLLERS
	Despite the fact that flatness bas been firstly developed for nonlinear systems, it bas been air plied to firute-dime.nsional linear system s

ll ( t) = A(p)z(t), y(t) = B(p)z(I )•

(26) (27) which allows to relar. e the fiai output of a. linear system to the partial state defined by several authors [START_REF] Kailath | Linear Systems[END_REF].

FoUowing the step (jY) of the meth, odology, the contrnl is given by: where: u ( t) = t•(t) + .4.(p)z(t), (28) n-l v(t) = z�">(t) + L k,(zJ 1 (t)-z ( •)(t)). ( 29

h is not realizable. The realization of this con troller will be the subject of the next part.

R.EALIZATION

To implement the control (31), ÎL can be� an.

observer of the vector

where: A direction of future works will be to atta.ck the problem of tbe numerical implement ation of su. ch controllers as it bas been_ underlined in (R.otel la


Brice Torti

Yannick Hallez

Benjamin Erable

Fabien Chauvet

SERS IN MICROCHANNELS FROM THE INTEGRATION OF A NANOSTRUCTURED SILVER LAYER BY ELECTRODEPOSITION AND STUDY OF THE PHOTHERMAL EFFECT

Keywords: SERS, Photothermal Effect, Electrodeposition, Chemical Imaging, Heat Transfer, Adsorption

A new method is described and used to integrate an immobilized Surface Enhanced Raman Spectroscopy (SERS) substrate in microchannels. This is based on the direct and fast electrodeposition of an adherent Ag layer on a microchannel wall. This layer exhibits a spatially uniform nanostructure allowing the enhancement of the Raman signal by an analytical factor of 2.10 4 for crystal violet molecules. The microsystem thus elaborated is used to examine the photothermal effect, induced by the laser used, on the SERS spectra under liquid flow.

INTRODUCTION

Microfluidic devices are developed and used for chemical analysis (detection, identification, and quantification) but also for the study of various physicochemical and biological phenomena under well controlled conditions: spatiotemporal control of the chemical composition, temperature, etc. Associated with this microfluidic control, chemical imaging (mapping of the chemical composition) inside microchannels enables new measurement strategies [1]. This requires a direct chemical imaging method (without labeling) with 3 qualities: sensitivity, spatial resolution and a wide range of addressable species. Among the methods already used in microfluidics, Raman spectroscopy has good spatial and spectral resolution but its sensitivity is too low. The latter can be significantly improved using nanostructured metallic substrates (Ag, Au) for which the plasmon resonance induces the enhancement of Raman scattering in the vicinity of their surfaces [2]. Unlike the usual way of synthetizing such SERS substrates, from metallic nanoparticles (requiring multiple steps, from the synthesis to the controlled deposition by favoring hot spots), here, the nanostructures are directly formed inside microchannels by the electrodeposition of Ag. The efficiency of the elaborated system for microfluidic SERS measurements is evaluated with crystal violet as a model molecule. The cooling effect of the liquid flow in the microchannel, on the SERS signal that comes from the laser-heated substrate, is also examined (photothermal effect [2]).

EXPERIMENTAL

The microfluidic device is elaborated from a double-sided adhesive layer (kapton, 75 µm, digitally cut) bonded between two glass plates (Fig. 1a). The electrodes are first deposited by gold sputtering on the bottom glass plate. A very thin gold layer (non-conductive) is also deposited, between these two electrodes, to favor the adhesion of the electrodeposit on the channel wall during its formation (as in [3]). The latter is performed by a constant current electrolysis of a AgNO3 solution inside the microchannel. A nanostructured, adherent and uniform Ag layer is obtained, Fig. 1c. The formation mechanism of this layer is related to the electrochemical growth of very dense branching deposits on thus gold metallized surfaces [3]. The growth proceeds by re-nucleation processes of nanoscale metal crystals, Fig. 1c. A Raman probe (Ocean Optics) is used to illuminate the Ag layer with a spot size of 158 µm (laser 532 nm, 100 mW), and collect the scattered light which is sent to a spectrometer to obtain Raman spectra, Fig. 1b. Measurements are performed in stagnant solution, or at a liquid flow rate !, and by recording the spectra over time. The heating, induced by the laser, is estimated by a micro-thermocouple located on the lower surface of the bottom glass plate and 1 mm behind the laser spot, downstream of the flow, Fig. 1b.

RESULTS AND DISCUSSION

In Fig. 2, the obtained SERS spectra and the corresponding temporal variations of the temperature are shown for a stagnant solution !=0 (Fig. 2a) and !=10 3 µL/min (Fig. 2b). We observe that the variation of the spectra is correlated with the variation of the temperature. For !=10 3 µL/min, a steady state regime is reached more rapidly and the temperature increase is lower than for !=0. From numerical simulation of heat transfer, it is estimated that 10% of the laser power is converted into heat and that the steady state temperature at the laser spot reaches 55°C and 41°C for !=0 and !=10 3 µL/min respectively. Such variations of temperature induce the desorption of crystal violet molecules from the Ag surface and thus the observed decrease of the SERS signal. A more detailed analysis of theses variations (with other concentrations and ! values) provides information on the adsorption of the probed molecules (heat of adsorption). The normal Raman spectrum of crystal violet, obtained with the same optical system but in a UV-Vis cuvette (without surface enhancement), is shown in Fig. 2c; this spectrum was constant over time. The peak intensities (~1000) are of the same order of magnitude as for the steady state SERS spectra (~2500), but the concentration and integration time are higher, Fig. 2c. From these data, we estimate an analytical enhancement factor ([4]) of at least 2.10 4 . Furthermore, an uniform SERS signal is measured over the Ag layer.

CONCLUSION

The microfluidic device elaborated, wherein a nanostructured Ag layer is integrated by electrodeposition, enables SERS measurements well suited for chemical imaging in microchannels. The application of a sufficiently fast flow allows to limit the heating of the SERS substrate and thus to maintain intense and stable SERS signals.

Figure 1 :

 1 Figure 1: Sketches of the assembly of the microfluidic device (a) and of the running experimental set-up (b) and SEM observations of the electrodeposited silver layer (c).

Figure 2 :

 2 Figure 2: (a,b) Temporal evolutions of SERS spectra of crystal violet and temperature ", after the start of the laser illumination, in stagnant solution (a) and with flow at !=10 3 µL/min (b); time step between each spectrum is 12 s. (c) Normal Raman spectrum of crystal violet obtained in a UV-Vis cuvette. Baselines have been subtracted. The concentration and integration time (IT) are indicated.