Ali Mahmino
email: ali.mahmino@ensica.fr

Jérôme Lacan
email: jerome.lacan@ensica.fr

Christian Fraboul
email: christian.fraboul@enseeiht.fr

Enhancing Guaranteed Delays with Network Coding

Keywords: Network Coding, network calculus, worst-case delays, buffering

For networks providing QoS guarantees, this paper determines and evaluates the worst case end-to-end delays for strategies based on network coding and multiplexing. It is shown that the end-to-end delay does not depend on the same parameters with the two strategies. This result can be explained by the fact that network coding can cope with congestions better than classical routing because it processes simultaneously packet from different flows. In counterpart, additional delays like algebraic combinations of packets are added

Introduction

In networks providing quality of service (QoS) guarantees ( ATM, IntServ, Diff-Serv, . . .) input data flows verify constraints of burstiness and maximal throughput. On the other hand, the network ensures a level of quality of service (QoS) guarantee expressed in terms of end-to-end delays or minimal throughput. The different guarantees and constraints characterizing the network and the flows can be represented by using network calculus. Network Calculus is a framework providing deterministic bounds of QoS parameters such as end-to-end delays or backlogs by using Min-Plus algebra. This theory was introduced and developed in [START_REF] Boudec | Network Calculus A Theory of Deterministic Queuing Systems for the Internet[END_REF] by generalizing previous works such as [START_REF] Cruz | A Calculus for Network Delay, Part I : Network Elements in Isolation[END_REF].

In this paper, we focus on decreasing worst case end-to-end delays by using network coding techniques. Network coding is a concept introduced by Ahlswede et al. in [START_REF] Ahlswede | Network Information Flows[END_REF], consisting in combining packets in routing nodes instead of simply forwarding them as a classical routing strategy. In addition to the optimization of the utilization of the capacity of the network, this technique also allows to decrease average end-to-end delays. For a complete file, the evaluation of the delay performance gains of several network coding strategies was studied in [START_REF] Eryilmaz | On Delay Performance Gains from Network Coding[END_REF] in the context of a downlink transmission of files from a single base station to multiple receivers. In [START_REF] Ma | Queuing Model and Delay Analysis On Network Coding[END_REF], a queuing model introduced for network coding allows to estimate the average end-to-end delays of the packets for independent Poisson flows in whole networks.

The problematic considered here concerns also end-to-end delays like in [START_REF] Ma | Queuing Model and Delay Analysis On Network Coding[END_REF], but the flows are constrained and the network provide QoS guarantees. In this context, our main objective is to reduce the worst cases delays.

The main idea is based on the fact that, with network coding, the node processes several packets simultaneously. Compared to a classical routing approach dealing with packets in sequence, this allows to reduce the maximum time spent by packets in the buffers. In counterpart, other delays are added like the time needed to achieve the linear combination or the time spent by a packet while it waits the corresponding packets arriving from other links.

The network hypotheses and the network coding node strategy are detailed in Section 2. The QoS guarantees provided by the nodes/network are evaluated and compared with a classical routing strategy in Sections 3 and 4. Finally, Section 5 presents the main conclusions.

Network Hypotheses

Consider a communication network represented by an acyclic directed graph G = (V, E) with a vertex set V and an edge set E. The set of nodes is divided into three categories: source nodes, intermediate nodes and receiver nodes. Each Source node S i generates a flow F i of packets of fixed length L constrained by affine arrival curves γ ρi,σi where ρ i is the leak rate and σ i is the burstiness size (see [START_REF] Boudec | Network Calculus A Theory of Deterministic Queuing Systems for the Internet[END_REF]). Intermediate nodes are the nodes situated between the sources and the receiver nodes. The nodes, e.g. v i and v j , are connected by directed edges, denoted by e i,j , each of them having a given maximum capacity C i,j and a maximum transmission delay T i,j . The service provided by the link is represented by a rate latency service curve β Ci,j ,Ti,j (t) (see [START_REF] Boudec | Network Calculus A Theory of Deterministic Queuing Systems for the Internet[END_REF]). We assume that all the nodes are synchronized and that each node knows the maximum transmission delays between itself and the neighbors generating its input flows. We suppose that the capacity of every output edge of a node is greater or equal than the sum of capacities of all input edges. We assume that the time necessary to perform a linear combination of several packets does not depend on the number of packets and is upper-bounded by T lc . Each intermediate node N n+1 offers a service curve β Cn+1,T n+1 B i +T lc +τn+1 (t) where T n+1 Bi is the maximum time spent by a packet of flow i in the buffers while waiting for corresponding packets of others flows. τ n+1 is the service delay to transmit a packet. Each multiplexer node N n+1 offers a service curve β Cn+1,τn+1 (t) where τ n+1 is the service delay to transmit a packet of the aggregate flow and C n+1 is the output edge capacity (see Figure 1(a)).

The network coding strategy described here is based on a fixed network code determined a priori. To ensure that receivers decode all the received packets, the concept of packet generation is used, where each generation corresponds to a fixed-length time interval [t i , t i + ∆[ in which a source generates at most one packet of a flow. The linear network code only combines packets belonging to the same generation. To perform a linear combination of several packets, the node must wait all the packets of the same generation. Since the network provides delays guarantees, a node is able to compute a time limit for reception of a given generation. If a packet of a given generation is not received before the time limit, the node assumes that the source did not generate a packet in this time interval, and it performs combinations with the available packets. To evaluate the interest of using network coding compared with a classical routing/multiplexing approach, we proceed in two steps: Node Level and Network Level.

3 Multiplexing vs Coding: Delay analysis at Node Level We suppose that the FIFO multiplexer node N n+1 presented on Figure 1(a) offers a service curve β Cn+1,τn+1 to the aggregated flow. From [START_REF] Boudec | Network Calculus A Theory of Deterministic Queuing Systems for the Internet[END_REF] and the hypotheses (and notations) introduced in Section 2, it can be shown that the maximum delay experienced by a packet of the flow F i in this multiplexer node is

T mn i = τ n+1 +( n k=1,k =i σ k +ρ k T k,n+1 )/(C n+1 )+(σ i +ρ i T i,n+1 )/(C n+1 - n k=1,k =i ρ k ).
Then the arrival curve (see [START_REF] Boudec | Network Calculus A Theory of Deterministic Queuing Systems for the Internet[END_REF]) of the flow F i at the output of the multiplexer is equal

to γ ρi,σ * i where σ * i = σ i + ρ i (T i,n+1 + τ n+1 + ( n k=1,k =i σ k + ρ k T k,n+1 )/(C n+1 )).

Coding Delay

Let us now consider the node presented on Figure 1(a) as an intermediate node combining the flows F i , i = 1, . . . , n, respectively constrained by γ ρi,σi . Following the hypotheses and notations introduced in Section 2, it can be shown that the maximum delay experienced by a packet of F i in the node is

T nc i = T n+1 Bi + T lc + τ n+1 + σ i + ρ i T i,n+1 /C n+1 .
Note that this delay corresponds to the delay between an input packet and the corresponding encoded packet. An arrival curve of a subflow corresponding to F i at the output of this intermediate node is

γ ρi,σ * i where σ * i = σ i + ρ i T i,n+1 + ρ i (T n+1 Bi + T lc + τ n+1 ).
4 Multiplexing vs Coding: End-to-end delays analysis

The properties of the network calculus facilitate the generalization of the results at node-level to the network level.

From [START_REF] Boudec | Network Calculus A Theory of Deterministic Queuing Systems for the Internet[END_REF] and Section 3.1, it can be shown that a FIFO multiplexer node N k (see Figure 1(b), node N 2 ) offers to the i th input flow a service curve

β i C k,r -X k i ,τ k +Y k i (t) where X k i = m k s=1,s =i C s,k and Y k i = m k s=1,s =i σ s /C k,
= T i tot + σi C i tot where T i tot = T 1,1 + n-1 k=1 T k,k+1 + n k=1 τ k + Y k i and C i tot =min(C 1,1 , C 1,2 -X 1 , C 2,3 -X 2 , • • • , C n,n+1 -X n ).
For the coding case, from the results of Section 3.2, the maximum delay of the flow F i from the source to the output of this network is equal to

T cn i = T i tot + σi C i tot where C i tot = min(C 1,1 , C 1,2 , • • • , C n-1,n ) and T i tot = T 1,1 + n-1 k=1 T k,k+1 + n k=1 T B k i + T lc + τ k .
Even if the worst case delays of multiplexing and coding strategy are difficult to compare in the general case, the main interest of these formulas is to emphasize the parameters that must be taken into account to decrease the worst case endto-end delays.

Conclusion

This paper has presented a new interest of network coding. The worst case endto-end delays were determined for classical routing/multiplexing and network coding approaches in networks providing QoS guarantees. These results show that the two formulas do not depend on the same parameters. These results can be viewed as the first step toward the construction of networks using network coding providing optimal level of guaranteed end-to-end delays.

3. 1 Fig. 1 .

 11 Fig. 1. Node Level and Network Level examples.

  r and m k is the number of input flows to node k and C k,r is the output edge capacity. The maximum delay of the flow F i from the source to the output of this net-

	work is T mn i


Cédrick Béler
email: cedrick.beler@enit.fr

Xavier Desforges
email: xavier.desforges@enit.fr

EXPERIENCE FEEDBACK, FROM CASES TO KNOWLEDGE

Keywords: knowledge-based systems, knowledge representation, uncertainty, risk assessment

In this paper, we present experience feedback as an alternative solution to usual knowledge management systems. The main characteristics of the experience feedback process and architecture are presented. Then, several elements about the realization of experience feedback application are detailed. We especially insist on the core experience metamodel and the way expert analyses and uncertainties are integrated in the general frame of experience feedback.

INTRODUCTION

Since the early history, experience feedback has been a major concern aiming at improving the practices of human activities. It was already the subject of a strong concern in the agricultural field, with considerations on the taking into account of the implemented practices: "Accordingly, an attentive head of a household, whose heart is set on pursuing a sure method of increasing his fortune from the tillage of his land, will take especial pains to consult on every point the most experienced farmers of his own time; he should study zealously the manuals of the ancients, gauging the opinions and teachings of each of them, to see whether the records handed down by his forefathers are suited in their entirety to the husbandry of his day or are out of keeping in some respects." (Columella,42).

Nowadays, public and private organizations and firms increasingly consider knowledge as a major part of their assets, that should be manage as well as financial, material... assets. Indeed, in a world of movement where various changes continually impact organizations, managing these assets is a key factor of success, especially since ISO 9000 norm was released since this norm imposes to take measures to target continuous improvement.

With respect to the variety of organizations, firms and of their concerns in terms knowledge engineering, several approaches have been developed that mainly aim at modelling, capitalizing, storing and reusing knowledge to support and improve their practices in their various processes. The improvements brought by knowledge engineering can be of different types, such as: make well at first attempt to reduce costs of nonquality, face the internal or external turnover of their personnel, integrate new information technologies in processes, make new actors operational as fast as possible in the different expert domains.

Among the methodologies of Knowledge Engineering that were developed, we find classical "top-down" approaches such as the popular CommonKADS (Knowledge Acquisition and Design Structuring) methodology [START_REF] Schreiber | Knowledge Engineering and Management: The CommonKADS Methodology[END_REF], where knowledge modeling is at first highly conceptual and then applied to more specific processes. The main drawbacks of such approaches are, according to us: the high level of abstraction of models makes them difficult to be adopted, they are a time and human resources consumer [START_REF] Duribreux | Elicitation and Analysis of Expert Knowledge on the Operation of Gas Distribution Networks[END_REF], they generally require the intervention of a knowledge engineer whose role is to help the experts to describe their knowledge, the knowledge extraction is not contextualized, the knowledge maintenance and update requires regular knowledge acquisition sessions.

Since the dynamics of evolution and complexity of the companies accentuate the difficulties of knowledge persistence within companies, the changing environment imposes a capitalization of knowledge in real time. In this context, "bottom-up" approaches, where knowledge is built incrementally from useful cases, is a way to ensure partial knowledge preservation. The source can be a problem resolution process, a causal study of an event, the description of a good practice… This approach is defined by [START_REF] Bergmann | Experience Management: Foundations, Development Methodology, and Internet-Based Applications[END_REF] as experience management (EM). According to him, it is a kind of knowledge management confined to knowledge originating from experience. EM gathers the terms "experience feedback" (EF), "lesson learned" (LL) and has become a challenging research topic (see for instance [START_REF] Bickford | Sharing Lessons Learned in the Department of Energy, Intelligent Lessons Learned Systems Workshop[END_REF], [START_REF] Aha | Bridging the Lesson Distribution Gap[END_REF], [START_REF] Bergmann | Experience Management: Foundations, Development Methodology, and Internet-Based Applications[END_REF]). EM advantages come from the contextualization of knowledge which makes it useful for practical needs; hence it requires less manpower and time and the experience base updates are done gradually, when new event occurs. Among the interesting features of this approach, let us point out that there is a no need to build a formal model of the expert knowledge. On the opposite, generated information can be too sparse and/or too specific. It also sometimes lacks of abstraction, for instance textual representations (even in structured applications) are often used and whereas it is excellent to give explanations, it becomes difficult when it comes to knowledge extraction and reuse.

The second part of this paper is dedicated to the description of the processes and the role of the actors involved in experience feedback from the collect of cases and the exploitation of experiences. Although the organizations wish to address various problems in various contexts, the experience feedback processes show enough similar features to consider the development of an experience feedback application generator.

The third part is dedicated to modelling and processing experience according to the object oriented approach. It takes into account the subjectivity of the actors involved in the processes by considering uncertainty and incompleteness. The meta-modelling of the generator is also proposed as a way of representing and associating the analyses of the experts to the cases. Eventually, it defines mechanisms to exploit the experiences.

We conclude by briefly presenting an implementation of experience feedback process in a context of risk prevention in Pyrenees Mountains and by showing this frame can be applied to industrial concerns.

EXPERIENCE FEEDBACK

Experience Feedback (EF) can be considered as an organizational process aiming at using the experience of the actors involved in the processes to grow the knowledge bases of the organizations progressively. In the loop of EF, knowledge is generated from the direct capitalization of the experiences and the knowhow used by the actors in their activities, using the tools and the methods that they daily employ. Thanks to this continuous capitalization, the EF makes it possible to maintain the knowledge of the organization up to date without requiring extra activities. Rakoto, et al. (2004) define experience feedback as: "a structured method of capitalization and exploitation of information resulting from the analysis of negative and/or positive events. It implements a set of human and technological resources which must be managed to contribute to reduce the repetitions of errors and to support some best practices". Fig. 1. Experience feedback macro-process (Rakoto, et al., 2004) EF, as shown in fig. 1, is a macro-process made of two main sub-processes: Capitalization: this sub-process gathers the set of activities allowing to add new experiences to the Experience feedback database, Exploitation: this sub-process consists in the activities allowing the dissemination and the use of these experiences to support decision and problem resolution.

Fig. 1 also shows the five major components contributing to the experience feedback processes: process activities which result in capitalizing and in exploiting information, information handled throughout the activities, from experience to knowledge, and stored in the experience feedback database (EF database) which constitutes the keystone of the EF process, actors and therefore competences for the creation of knowledge, the tools implemented to instrument the experience feedback, the performance indicators of the process.

The set of identified components that support the experience feedback process (activities, information, actors, tools and indicators) shown in Figure 1 described in more details below.

Activities refer to the different steps in the experience feedback process. The first step corresponds to the description of the context of occurrence of an event (observation). This step may provide statistical information. The second level, called "experience", is where the described events are analysed and solved, generally by experts. Then the last step is to analyse sets of experiences in order to extract rules, procedures or practices that should improve the processes of the organization.

The step of analysis is fundamental. Indeed, it adds the basic layer of knowledge to the description of the context and is usually achieved by domain experts. This analysis relates mainly: to the definition of the factors that explain the event occurrence, and to the characterization of solutions.

Actors refer to the competences involved in the iterative knowledge creation and play a central role in the EF processes. During the capitalization subprocess experts having competences are solicited to solve the identified problems (elaboration of experiences) and to create knowledge. During the exploitation process, actors who have the ability to improve their activities using the results of the experience feedback need to be identified and trained to the results provided by the systems.

Fig. 2. Information layers

Information refers to data modelling so as to express experience and therefore knowledge. During an EF cycle, the actors gradually transform events into knowledge. As shown in Fig. 2, in an EF application, we consider three layers to express the relationships between data, experience and knowledge. The first layer is the description of the context of occurrence of the event, which is a pure descriptive part. The second layer is when values are added to the pure descriptive scheme by analyzing chosen aspects of it. This is properly an experience, i.e. an analysed contextualized description which can be built along a problem resolution process. Actually this is a knowledge encoding in some ways, but as specific to a case, a context, we call it experience. Finally, the last layer corresponds to general knowledge, where generic conclusion can be drawn from a certain set of experiences.

Tools refer to experience feedback applications, i.e. applications and techniques that support the whole E.F. process, actually both sub-processes capitalization and exploitation. They support on one hand, the information flow management and, on the other hand, the analysis of the results of the experience feedback done by the actors. Thus, we distinguish two types of tools: the standard tools used to improve communication, collaborative work and coordination in the processes, and the advanced tools which facilitate the access to relevant and useful information. For example, these tools can be based on Case-Based-Reasoning mechanisms (CBR) ( [START_REF] Kolodner | Case-Based Reasoning[END_REF], [START_REF] Aamodt | Case-based reasoning: foundational issues, methodological variations, and system approaches[END_REF], [START_REF] Ruet | Search and adaptation in a fuzzy object oriented case base[END_REF] and in particular rely on the concept of similarity which makes it possible to identify the past experiences potentially similar to the current experience.

Our general objective is to elaborate a framework for experience feedback applications. Such a tool should include all dimensions shown previously, but in the following section, we will focus on the experience modelling and processing aspects. Actors, according to their competences, are the users of these applications. Their role in the processes are converted into multiple uses cases and are the starting point in the development of specific applications. Several roles and activities need to be defined as the interactions between them but this will not be the point in this paper. Here, we focus on the experience element as an entity which is the central element of the E.F. process. Also, even if the system has been implemented as a web application, we will not describe in details the technical choice we made.

EXPERIENCE MODELING AND PROCESSING

Experience, as an entity, is the kernel of EF applications and consists in an organization of information carried out by events. We chose a flexible but structuring organization because, on one hand, the captured information comes from the real world and then need to be flexible enough to integrate the world"s "fuzziness", and on the other hand, the structuring organization should ease data processing, especially experience reuse.

The descriptor, an attribute model

An experience can be considered as a model of data coming from the real world and being interpreted by an expert actor during an EF process. That is why the term "descriptor" often used in CBR will be preferred to the term "attribute".

Considering this, an experience is composed of descriptors and describes, according to a given point of view the analysis of a particular event. For instance, let us consider the case of the height of a person. In a traditional Information System (IS), it could be an integer (180), a range (from 175 to 185) or a string representing a category, a classification ("tall"). Instead of this, a descriptor is an object that can"t be assumed to be of a primitive type. Its structure, as defined in the section 2.3, provides the model of descriptors, which are the lower level representation entity of an experience model. Hence, it can be considered like the foundation of the experience meta-model.

Modelling paradigm, an OO-based light ontology

Experience can be represented by a set of descriptors and there are several kinds of them. First of all, there is a String descriptor, called TextDescriptor, where the associated domain corresponds to a list of strings. They have little encoded semantics. Then, there are primitive descriptor types comprising more semantic like quantities, basically a number associated with a unit, dates and even external domain objects. To illustrate the difference between string and domain object, here is an example. Let us consider a descriptor for a list of activities; it can be either a string list with no semantics ("activity1", "activity2"…) or a list of activity objects associated with some ontological semantics and description.

Ideally, all descriptor primitive (input type) should be structured because they are carrying semantics. That is why we ban free text description (full sentences), except to expose remarks, comments, without taking them into account in the reasoning process.

What is proposed is actually a minimum ontology model ready to be computed. That is why the metamodel has to follow imperatively and declaratively principals that we grab from the fields of Object-Orientation (OO) and Ontologies. All these principals are illustrated in fig. 3. Ontology is a shared domain conceptualization consisting of entities, relations between entities, constraints, business rules. Ontology insists on the semantics whereas OO principals are more application-oriented. They nevertheless share a common kernel. Fig. 3. Relation between OO, and ontology [START_REF] Knublauch | An Agile Development Methodology for Knowledge-Based Systems Including a Java Framework for Knowledge Modelling and Appropriate Tool Support[END_REF] Pure Ontology language like Description Logics (DL), frames (RDF) are the most common modelling paradigm in Knowledge Based Systems but are too complex to handle, especially by software agent. This explains why we consider a simpler modelling framework in which uncertainty consideration (integration and processing) is provided (see 2.4). Therefore, the following section is devoted to the model of a descriptor, in other words the core metamodel of experience feedback applications.

Experience meta-model

As said previously, the descriptor model can be considered as the core metamodel of experience feedback applications. Below is presented a simplified version exposing the main modelling characteristics. An example is then given to illustrate how it"s instantiated.

Fig. 4. Experience core metamodel

To build this model, one very common design pattern known as the composite pattern [START_REF] Gamma | Design Patterns: Elements of Reusable Object-Oriented Software[END_REF] is used. It is used twice and allows to have a tree-like structure, first, to categorize descriptors and, second, to compose descriptors. Container allows to categorize descriptors and an experience usually possesses a context container which is also composed of others containers. Concerning descriptors, an ObjectDescriptor is a composed descriptor. The difference with the container is that it has its own value whereas the container does not. Descriptors other than ObjectDescriptor are TextDescriptor (a descriptor with little semantic) and primitive descriptor which is declined in several sub-types (quantity, date, ontology object…). TextDescriptor is the "simplest" EF data entry and the possibility to transform a TextDescriptor into a PrimitiveDescriptor or ObjectDescriptor should be considered later.

Value is actually an object that is presented in the section dedicated to uncertainty consideration because it incorporates the chosen uncertainty framework (see. fig. 5). This value is compulsory and corresponds to the interpreted data (by an actor). It can be totally unknown, precise, partially defined and even not filled.

Also, not all elements are presented here. For instance, descriptors possess an optional raw data equivalent to the classical attribute in traditional forms and are more or less unnecessary. They are useful in case of automatic transformation (expert rules) or sometime to ease the user input.

To illustrate this metamodel, here is an example concerning the weather conditions taken from the application we realized regarding mountain activity experience feedback. It is an ObjectDescriptor because composed of several other descriptors and eventually having its own value comprised in the set {good, bad, extreme}.

Uncertainty consideration

In the chosen model, the interpreted value even if compulsory can be totally unknown or imprecise (and even false) as the descriptor expresses an opinion coming from any human being"s part of subjectivity. Actually, the system should be able to capture an expert opinion thanks to an actor (the expert himself) in a quite natural way without changing the original semantics.

Thus, actors have the possibility to express their opinion through the choice of the value of a descriptor over a set of possible value (called frame of discernment). Considering the example again, let us try to express weather conditions knowing the possible values are "good", "bad" or "extreme". The expert can of course choose each value independently but he also has the possibility to express: "I don"t know", "certainly bad but can be "good"… Dempster-Shafer Theory (DST) was chosen because, first, its expressiveness allows to capture such opinions, and second, this is a theory that provides information fusion techniques through the Dempster rule of combination like information revision when new information occur [START_REF] Shafer | Mathematical Theory of Evidence[END_REF]. We actually chose the Transferable Belief Model (TBM) which is an evolution of the DST with a better axiomatic justification [START_REF] Ph | The transferable belief model[END_REF]. This other advantage of this theory is that it generalizes the other frameworks of uncertainty modelling ( [START_REF] Shafer | Mathematical Theory of Evidence[END_REF], [START_REF] Dubois | Possibility theory[END_REF]. Indeed, probability and possibility theories are both specific cases of TBM Without going deeper in the description, DST is based on a basic belief assumption (bba), a unit belief mass distribution on the power set of the frame of discernment traducing the agent belief over a set of possible values as targeted. Probability is equivalent to masses affected to each element of the set (instead of superset) and possibility corresponds to masses affected to consonant subsets of the powerset (overlapped sets). Such a theory allows to express the various ways of considering uncertainty like unknowing, partial and full knowledge. TBM enable to express the fact that the value does not belong to the frame of discernment. Also, the possibility to leave a descriptor unfilled is allowed and is taken into account in the reasoning process.

Fig. 5 Value model

The bba is the initial definition stored as the descriptor value and defined from the associated domain object. Methods are provided to convert in plausibility and credibility measures equivalent respectively to upper and lower probabilities [START_REF] Shafer | Mathematical Theory of Evidence[END_REF] and also to a possibility and necessity measure [START_REF] Dubois | Possibility theory[END_REF].

Experience analysis and processing

Analysis, as said in the section 1, is the essential part of the EF process. An experience is a conjunction of descriptors which are relevant enough to describe an experience, and then factual knowledge (expert analyses) can be expressed by relations involving some of the descriptors. Once this analysis is done, experience has its semantic set and is ready to be processed. Although quite straight, it provides very useful information that can be used for a better indexing or as in our case to extract some kind of knowledge.

The aim is to express a relation between an event aspect and a combination of descriptors. For instance, in a project, we work on interpreting the occurrence of an event by establishing relations with combinations of the most significant descriptors assigned by an expert.

To illustrate the analysis method, an experience composed of 4 descriptors is considered. Each descriptor Di has a domain i and a precise value di i. Without any analyses, this experience is purely descriptive and can be interpreted in the following way: "event occurs when D1 was d1 and D2 was d2 and D3 was d3 and D4 was d4". Once analysed, the information carried out could be something like:

"This event occurred because:

(1) descriptor1=aVal AND descriptor3= aVal (2) OR (3) descriptor4= aVal [aVal, aVal2] (4) and I"m nearly sure of it".

To model the analysis step, the TBM frame is again used adding a new information layer in the experience structure consisting in a belief mass distribution over the scalar product of all descriptors. "AND" convey a conjunction of information whereas "OR" an alternative analysis. Two kinds of analyses are possible, either the expert will directly point a value (1), or he will observe that the value belongs to a particular range (closed or opened) (3). Then each analysed attribute has its value (a mass distribution) copied in another instance variable and eventually modified to express (3). When not analysed, the value is not consider but in order to uniformize the distribution to be able to combine distributions later, we must proceed to a vacuous extension on the nonanalysed descriptors, i.e. considering that whatever the value of the descriptor is, it does not matter. Consequently, the previous analysis gives the following bba: This lookup is based on similarity calculation based on the algorithm developed by [START_REF] Ruet | Search and adaptation in a fuzzy object oriented case base[END_REF]. Each descriptor has a similarity strategy attached to it (a similarity matrix, a function…) as illustrated in fig. 5. In fact, the analysis step when pointing a particular range instead of a value can even adjust the similarity strategy associated to a descriptor. For instance, if the analysis says that the event happened because a value was in a sub-set, then all values of this subset are considered equal.

CONCLUSION

The general experience modeling framework proposed in this paper has been applied in the context of a European INTERREGIIIa project called SUP (Security and Emergency in the Pyrenees). One of the objectives of the project is to improve mountain safety for professionals through experience feedback.

The model proposed in this paper has been implemented and instantiated on this specific problem. The resulting application is a web based software that is currently under deployment. Of course, the applicability of the proposed concepts is not restricted to this project and the framework can be used to elaborate experience feedback processes in organizations. From a scientific perspective, several issues can be studied now such as the improvement of the reuse techniques and a better integration with the actors of the organization (with respect to their competences).

  are analyzed, the lookup phase can be launched and consists in comparing a present context to all analyzed experience contexts. This is what effectively gives the experience feedback.


Adrian Dietz

Azzaro-Pantel Catherine
email: catherine.azzaropantel@ensiacet.fr

Pibouleau Luc

Ecodesign of batch processes : optimal design strategies for economic and ecological bioprocesses

Keywords:

This work deals with the multicriteria cost-environment design of multiproduct batch plants, where the design variables are the equipment item sizes as well as the operating conditions. The case study is a multiproduct batch plant for the production of four recombinant proteins. Given the important combinatorial aspect of the problem, the approach used consists in coupling a stochastic algorithm, indeed a Genetic Algorithm (GA) with a Discrete Event Simulator (DES). To take into account the conflicting situations that may be encountered at the earliest stage of batch plant design, i.e. compromise situations between cost and environmental consideration, a Multicriteria Genetic Algorithm (MUGA) was developed with a Pareto optimal ranking method. The results show how the methodology can be used to find a range of trade-off solutions for optimizing batch plant design.

Introduction

Traditionally, system optimisation in chemical and process engineering applications has focused on maximising the economic objectives. Over the past 10 years, considerations for improving the environmental performance have started to be integrated into system optimisation alongside economic criteria. These included various waste minimisation approaches from the concept of mass pinch as a tool to derive cost-optimal Mass Exchange Networks with minimum emissions waste, through minimum waste water generation in process plants and waste treatments costs [START_REF] Gundersen | The synthesis of cost optimal heat exchangers networks: an industrial review of the state of the art[END_REF], to the concept of Zero Avoidable Pollution [START_REF] Linninger | Generation and assessment of batch processes with ecological considerations[END_REF]. More recently, life cycle thinking [START_REF] Azapagic | The application of life cycle assessment to process optimization[END_REF] has started to be incorporated into the process design and optimisation procedures, thus establishing a link between the environmental impacts, operation and economics of the process. In this context, this paper proposes a methodology for the integration of environmental aspect into the development process, i.e. process ecodesign that is important from both environmental and the economic perspective. Typically the approach involves three major steps. (i) Process modelling and carrying out a Life Cycle Assessment study; (ii) Formulation of the multi-objective optimisation problem in the LCA context; (iii) Multi-objective optimisation and choice of the best compromise solution. In this paper, biochemical plants are considered as an application of the proposed methodology, since they generate a wide range of liquid, solid, and gaseous waste streams that require treatment prior to discharge. The proposed work deals with the multi-criteria cost-environment design of multi-product batch plants, where the design variables are the plant configuration with equipment item sizes and parallel equipment number as well as the operating conditions. This article is organized as follows. Section 2 presents the general framework. Section 3 is devoted to the implementation of the proposed methodology. Typical results obtained on a biochemical plant are discussed in Section 4. Section 5 presents conclusions and suggests perspectives.

General framework

The framework for batch plant design proposed in this study (see Figure 1) integrates simple unit operation models into the batch plant wide model, which is then embedded in an outer optimization loop. The approach adopted in this work [START_REF] Dietz | Integrating Environmental Impact Minimization Into Batch Plant Design: Application To Protein Production ESCAPE-14[END_REF] consists in coupling a stochastic algorithm, indeed a Multicriteria Genetic Algorithm (MUGA) with a Discrete Event Simulator (DES). The DES was developed using C++ object-oriented language, keeping the approach proposed in [START_REF] Bérard | Towards an incremental development of discrete-event simulators for batch plants : use of object-oriented concepts[END_REF]. A four layer framework was proposed, resulting in the development of a standard library for the simulator classes that are general to any case, thus minimizing the task of treating different study cases or the variants of a given one (i.e. design or scheduling objectives). In this approach, at the lowest level, the common engine can be found. Most of the events at the next level are common to all batch plant simulations, but some case studies could need the definition of a particular event. Only few equipment items are common to all batch plants (i.e. storage vessels) whereas most of them are particular to each problem and must be defined. The upper layer is the supervisor, which must be generally adapted to each study case. The objective of the master GA involved is to propose several good and even optimal solutions, whereas the DES checks the feasibility of the proposed configuration and evaluates different criteria with both economic and ecological targets.

Figure 1. General methodology for optimal batch plant design

Indeed, engineering design problems are usually characterized by the presence of many conflicting objectives that the design has to fulfil. Therefore, it is natural to look at the engineering design problem as a multiobjective optimization problem (MOOP) [START_REF] Bhaskar | Applications of Multiobjective Optimization in Chemical Engineering[END_REF][START_REF] Coello | An Updated Survey of GA-based Multiobjective Optimization Techniques[END_REF][START_REF] Ehrgott | Lecture Notes in Economics and Mathematical Systems -Multicriteria Optimization[END_REF]. As most optimization problems are multiobjective by nature, there are many methods available to tackle these kinds of problems. Lately there has been a large development of different types of multiobjective genetic algorithms, which is also reflected in the literature. The big advantage of genetic algorithms over other methods is that a GA manipulates a population of individuals. It is therefore tempting to develop a strategy in which the population captures the whole Pareto front in one single optimization run. This approach was adopted in this study.

The MUGA developed in this study involves different procedures: 1. A method for encoding solutions in strings of digits (or chromosomes); here, a chromosome represents a workshop configuration and the corresponding operating conditions. The encoding procedure will be briefly presented. 2. An initial population has to be randomly generated.

3. An evaluation function which takes a string as input and returns different fitness values which measure the quality of the solution that the chromosome represents relative to each criterion. Since this work is related to minimization cases (investment cost, limitation of pollution), the individual fitness F i is calculated by:

F i = C max -C i
where C i is one of the objective function value for individual i, C max is the maximum objective function value computed on the current population for the corresponding criterion. 4. An adaptive plan involving evolution and mutation, based on string crossover and mutation operators. The cycle {Evaluation, Selection, Crossover and Mutation} is repeated until a stop criterion is reached. After this cycle, the Pareto sort is applied. Concerning selection and multicriteria aspects involved, it must be emphasized that for a given survival rate, the selection process is achieved via a classical Goldberg's biased roulette wheel [START_REF] Goldberg | Algorithmes Génétiques[END_REF], relative to each criterion. For this purpose, the initial population is randomly partitioned into sub-populations (the number of sub-populations corresponds to the number of criteria considered simultaneously). A same number of individuals is chosen for each subpopulation. A binary system was chosen for encoding, as it simplifies the genetic operators, i.e., crossover and mutation. This encoding method presented was developed for the cases where the equipment items are identical at a given stage. The continuous variables were discretized and encoded in a binary way by a variable change (Figure 2), using the same bit number (i.e., eight bits). Figure 3 shows a code part used for operating stage encoding. For each stage, the equipment item number was encoded by a binary way (part A in Figure 3). The number of bits reserved to this variable set the maximum equipment item at the stage. For equipment size (L for large, M for Medium, S for Small, a number of bits equal to the available sizes for the equipment items was reserved (part B in Figure 3): the chosen size takes a positive value whereas zero is allocated to the other places. When equipment items are composed of several parts, the same approach is repeated for each component (part B and B' in Figure 3).

Continuous variable

Binary variable

B inf B sup 0 2 (nbits) -1 Continuous variable Binary variable B inf B sup 0 2 (nbits) -1 Figure 2. Continuous variables encoding L M S L M S L M S L M S A B B'
Figure 3. Operating stage encoding method

Implementation

1 Presentation of the illustrative example

The previous methodology was applied to a batch plant for the production of proteins taken from the literature [START_REF] Salomone | Dynamic simulations in the design of batch processes[END_REF][START_REF] Montagna | The design of multiproduct batch plans with process performance models[END_REF][START_REF] Chiotti | Batch plants with adaptive operating policies[END_REF][START_REF] Asenjo | Strategies for the simultaneous optimization of the structure and process variables of a protein production plant[END_REF]. This is a multiproduct batch plant, with four products to be manufactured by fermentation and eight treatment stages. This example is used as a test bench since short-cut models describing the unit operations involved in the process are available. The batch plant involves eight stages for producing four recombinant proteins, on one hand two therapeutic proteins, Human insulin (I) and Vaccine for Hepatitis B (V) and, on the other hand, a food grade protein, Chymosine (C) and a detergent enzyme, cryophilic protease (P). The methodology is generic for any plant producing recombinant proteins from yeast.

Figure 4 shows the flowsheet of the multiproduct batch plant considered in this study. All the proteins are produced as cells grow in the fermenter (Fer). Vaccine and protease are considered as being intracellular, hence, for these two products, the first microfilter (Mf1) is used to concentrate the cell suspension, which is then sent to the homogenizer (Hom) for cell disruption to liberate the intracellular proteins. The second microfilter (Mf2) is used to remove the cell debris from the solution proteins.

V = vaccine V = vaccine V = vaccine V = vaccine C = C = C = C =
The ultrafiltration (Uf1), prior to extraction, is designed to concentrate the solution in order to minimize the extractor volume. In the liquid-liquid extractor (Ext), salt concentration (NaCl) is used to first drive the product to a poly-ethylene-glycol (PEG) phase and again into an aqueous saline solution in the back extraction. Ultrafiltration (Uf2) is used again to concentrate the solution. The last stage is finally chromatography (Chr), during which selective binding is used to better separate the product of interest from the other proteins.

Insulin and chymosin are extracellular products. Proteins are separated from the cells in the first microfilter (Mf1), where cells and some of the supernatant liquid stay behind. To reduce the amount of valuable products lost in the retentate, extra water is added to the cell suspension.

The homogenizer (Hom) and microfilter (Mf2) for cell debris removal are not used when the product is extracellular. Nevertheless, the ultrafilter (Uf1) is necessary to concentrate the dilute solution prior to extraction. The final step of extraction (Ext), ultrafiltration (Uf2) and chromatography (Chr) are common to both the extracellular and intracellular products.

Environmental Impact Evaluation

Several methodologies for environmental impact (EI) consideration are available in the literature. The most important concept refers perhaps to the Life Cycle Assessment (LCA) [START_REF] Burgess | The application of life cycle assessment to process optimization[END_REF] considering all the wastes generated in order to produce the different products in the upstream stages (i.e., raw material production, energy generation, etc.), in the study stage (i.e. solvents, non-valuable byproducts, etc) and in the downstream steps (i.e. recycling, incineration, etc). The aim of LCA is to consider the wide chain in order to prevent pollution generation and to compare the different alternatives to produce a product. Another concept used the Pollution Balance (PB) principle to carry out a pollution balance [START_REF] Cabezas | Pollution prevention with chemical process simulators: the generalized waste reduction (WAR) algorithm--full version[END_REF] equivalent to the balance made for mass or energy. It means that a process can not only pollute but also consume a polluting product and will be a benign process. Finally, the Pollution Vector (PV) methodology [START_REF] Stefanis | Minimizing the environmental impact of process Plants: A process systems methodology[END_REF] consists in evaluating the environmental impact by means of an impact vector over different environments (i.e. water, air, etc) defined as the mass emitted on an environment divided by the standard limit value in this environment. Given the production recipes for the different products and the general flow-sheet, the first step consists in applying the LCA methodology to determine all the products contributing to the environmental impact (fig. 4). For information availability reasons, the study was reduced to the process being studied, which is of course a limited application of LCA. Products (i.e. vaccine) and raw materials (glucose, NH 3 ) were considered not having an environmental impact. After that, a PB is applied, using the PV to quantify the environmental impact. In this case, an adapted definition of the pollution vector was introduced, because the standard limit values for the polluting product were not found in the literature. This vector has two components; the former is the total biomass quantity released and the latter concerns the PEG volume used. Even if the solvent can be recycled, it cannot be carried out at 100%, so the environmental impact is considered to be proportional to this quantity. The pollution indexes were thus defined as the emitted quantities divided by the mass of the manufactured products. Let us remark that the environmental impact minimization can be viewed a multicriteria problem in itself.

The global index of each environmental impact criterion is defined as weighted sum respect to the production of each product index (eq. 1). I is the k pollution index of i product defined as the kilograms of the pollutant k by kilograms of manufactured product i and P i is the total production the i product.

The cost criterion considered in this study is classically based on investment minimization because there was not enough information to evaluate the operational cost of the batch plant (raw material cost, utilities cost ...) and to embed it in a net present worth computation.

The optimization criterion involving investment cost for equipment and storage vessels ICost is calculated using (1):

      + +       + = ∑ ∑ ∑ = = = ki C sk k k SK N 1 k i C ij i i EQ N 1 j OP N 1 i V B A V B A ICost ( 2)
where N OP is the number of operations, N EQi is the number of equipment items (for operation i), N SV is the number of storage vessels, A i , B i and C i are the cost coefficients for operation i, A s , B s and C s are the cost coefficients for storage vessels, V ij is the volume of equipment ij and V sk is the volume of storage vessel k.

The models representing the operation units involved in the global process are presented in detail in [START_REF] Dietz | Framework for Multiproduct Batch Plant Design with Environmental Consideration[END_REF] and will not be recalled here.

The optimization problem considered can be formulated as follows:

( ) ( ) ( ) H x,y s.t. g x min f y min f 1 ≤ 2
where, f 1 represents the investment cost and f 2 the environmental impact. The x vector, Without going into further detail, the optimization problem involves 44 variables, which may be either continuous (i.e. the operating conditions) or discrete (parallel equipment number, equipment size). A set of data must be fixed by the user concerning the optimization problem definition before the implementation of the design methodology (see [START_REF] Dietz | Framework for Multiproduct Batch Plant Design with Environmental Consideration[END_REF]. For instance, the annual demand for each product is presented in Table 1. Three sizes are available for each equipment item: large (L), medium (M) and small (S). The classical expressions used for computing the investment cost of the equipment items follows a classical scaling law. Of course, a thorough economic study would also include the operating cost estimation and analysis of profitability. Since this kind of analysis only requires reliable economic data for a real process and does not induce additional difficulties in the chosen resolution strategy, a capital cost-based study was finally adopted for the preliminary economic evaluation of the project for manufacturing biological products.

Table 2 displays the parameters of the genetic algorithm used for multicriteria batch plant design. In this work, the generation number was fixed as twice the population size. The global survival rate is relatively low as compared to standard values for optimization of test mathematical functions [START_REF] Dedieu | Design and Retrofit of Multiobjective Batch Plants via a Multicriteria Genetic Algorithm[END_REF]. Moreover, a high mutation rate was set. Although a systematic study was not carried out to find these values, they were chosen from several preliminary tests and agree with previous works [START_REF] Dedieu | Design and Retrofit of Multiobjective Batch Plants via a Multicriteria Genetic Algorithm[END_REF] where similar problems were treated. The elitism was used in order to avoid losing the best solution for each criterion. Considering the stochastic aspect of GAs, several optimization runs were carried out for each multicriteria optimization. Given that solutions obtained in one optimization run could be dominated by solution of another one, a Pareto sort procedure is applied to the set of solutions obtained at each optimization run, and the non-dominated solutions are those proposed by the methodology.

Results and Discussion

Only typical results concerning bicriteria cases are presented in what follows. Two strategies were tested either monoproduct or multiproduct campaigns with a batch of each product to be produced. In the latter case, the starting order of the different batches was fixed altering intracellular and extracellular products The MUGA presented in this work was first used to demonstrate that the two EI criteria considered, that are respectively the total biomass quantity and the PEG volume, present antagonist goals (figure 5). Very similar results were obtained at each optimization run, so only the results after the final Pareto sort procedure are presented in figure 6. Moreover, it must be noted that slight differences are obtained between both production policies because the environmental impact depends only on the mass balance that is function of the continuous variables. This antagonist behavior can be explained at the liquid -liquid extraction stage. The more solvent is used, the more efficient the stage becomes and, consequently, the fewer products are lost, reducing the environmental impact index computed as Kg of biomass released by Kg of final product.

The same approach was also applied to the cost -environment criteria. First, the amount of solvent used and the investment cost were considered. For illustration purposes, figure 6 shows the results obtained at each optimization run for the monoproduct production policy, performed with an identical parameter set to guarantee the stochastic nature of the GA. In this case, the results are not superposed as it was the case for the bicriteria optimization biomass -solvent and show the need of carrying out several optimization runs for the same problem.

In figure 6, it can be seen that each optimization run is oriented to a section of the search region. The first optimization comes up with the better solution for the cost criterion, the second for the environmental criterion and the third is a compromise between both. The final Pareto sort procedure is carried out over these solutions. The final results for both production policies are presented in figure 7. Let us note that the Pareto zone is constituted of sparse points, since the adaptation function related to the investment cost takes discrete values. Slight differences were found between both production policies. The antagonist behavior between these two criteria, investment cost -amount of solvent used, can be explained by a compromise between the solvent yield and the process global yield. When process yield is penalized, a bigger, and consequently more expensive, batch plant is required.

In order to evaluate the search performance of the GA, table 3 presents the best solution obtained at each optimization run for each criteria considered as well as the best solution obtained with a monocriterion approach. Even though the methodology was not able to find the best solution, the values are relatively near (around 5% more expensive for the investment cost criterion). It must be noted that in the monocriterion optimization (not presented here), the best value was obtained only once and, in the other cases, the solutions were around 2%-3% more expensive, which justifies the results when several criteria are taken into account simultaneously. The number of solutions obtained in each optimization run was around of 25. It is important to note that in each case, the solutions are uniformly distributed in the search space; this means that there is no preferential search region in the multicriteria search as shown in Figure 6. They have the same order of magnitude for both policies. Moreover, the minimal value of the range is close to the best value obtained in monocriterion optimization value which allows to predict less antagonism between investment cost and biomass released criteria. The last bicriteria optimization considers the investment cost and biomass released. As for the previous case, three optimization runs were carried out for each production policy. The results obtained after the final Pareto sort procedure are presented in Figure 8 and are similar for both production policies as it was shown for the cost-solvent criteria.

Conclusions

A methodology was proposed for batch plant design, considering both investment cost and environmental impact minimization. An optimization scheme has been implemented using a multiobjective genetic algorithm with a Pareto optimal ranking method. This technique is ideally suited to this type of problem, where a number of conflicting considerations must be taken into account. The use of MUGA makes possible a robust optimization technique, across a non-linear search space (the objective functions are computed by the use of a discrete event simulator (DES) integrating shortcut unit operations models) linking multiple variables and objectives. The paper clearly shows that opportunities for process optimization and environmental impact minimization must be considered at the early stages of process development before the process is frozen due to regulatory reasons.

Figure 4 .

 4 Figure 4. Multiproduct batch plant for proteins

Figure 5 .

 5 Figure 5. Pareto's optimal solutions for biomass released -solvent amount criteria (bicriteria case)

Figure 6 .

 6 Figure 6. Pareto's optimal solutions for solvent usedinvestment cost (bicriteria case) Figure 7. Pareto's optimal solutions for solvent usedinvestment cost (bicriteria case)

Figure 8 .

 8 Figure 8. Pareto's optimal solutions for biomass released -investment cost (bicriteria case)

Table 1 .

 1 Product demands

	Product	Production (kg/year)
	Insulin	1500
	Vaccine	1000
	Chymosin	3000
	Protease	6000

Table 2 .

 2 Genetic algorithm parameters

		Bicriteria	Bicriteria	Bicriteria	Tricriteria
		Solvent-biomass	Cost-Solvent	Cost-Biomass	Cost-EI
	Population size	300	450	450	600
	Generation number	600	900	900	1200
	Survival rate	0.5	0.5	0.5	0.5
	Mutation rate	0.4	0.4	0.4	0.4
	Elitism by criterion	1	1	1	1

Table 3 .

 3 Bicriteria Cost-Solvent optimization resultsIt is also interesting to see where the results are placed whit respect to the criterion not considered here, in this case the amount of biomass released. Table4presents the range of values for this criterion for both production policies.

			Monoproduct			Multiproduct
		Cost	Solvent [10 3 ]	Solutions	Cost	Solvent [10 3 ]	Solutions
	Run 1	1221890	4,445	32	1303730	5,070	21
	Run 2	1290490	4,779	23	1211100	5,006	28
	Run 3	1238050	4,415	23	1257200	4,406	23
	Best	1140990	4,386	---	1139100	4,386	---

Table 4 .

 4 Values range for the not considered criterion

		Biomass for Cost-Solvent	Solvent for Cost-Biomass
		Minimum	Maximum	Minimum	Maximum
	Monoproduct Multiproduct	14,393 14,261	20,3691 22,889	36,0292.10 -3 34,9659.10 -3	40,581.10 -3 41,877.10 -3


Loïc Cadoret

Nicolas Reuge

Sreekanth Pannala
email: pannalas@ornl.gov

Madhava Syamlal
email: madhava.syamlal@netl.doe.gov

C Rossignol

J Dexpert-Ghys

Carole Coufort

Brigitte Caussat
email: brigitte.caussat@ensiacet.fr

SILICON CHEMICAL VAPOR DEPOSITION ON MACRO AND SUBMICRON POWDERS IN A FLUIDIZED BED

Keywords: Fluidized Bed, Chemical Vapor Deposition (CVD), Submicron powders, Silicon, Process modelling

Titanium oxide (TiO2) submicron powders have been treated by Chemical Vapor Deposition (CVD) in a vibro fluidized bed in order to deposit silicon layers of nanometer scale on each individual grain from silane (SiH4). Experimental results show that for the conditions tested, the original granular structure of the powders is preserved for 90% of the initial bed weight while the remaining 10% consisted of agglomerates in millimetre range found near the grid of the reactor. A comparison between experimental and modelling results using the MFIX code shows that for Geldart's group B alumina particles (Al2O3), the model represents both the bed hydrodynamics and silane conversion rates quite well. The future objective is to extend the simulation capability to cohesive submicron powders in order to achieve better predictability of the phenomena governing ultrafine particles.

INTRODUCTION

The Fluidized Bed Chemical Vapor Deposition (FBCVD) process represents one of the most efficient ways to modify the surface properties of micro-or nano-powders. The most important applications concern the coating of powders against corrosion and oxidation or the synthesis of supported catalysts.

When coating powders using FBCVD, one major consideration is the fluidizability of the particles. Micronic powders belonging to Geldart's group C [START_REF] Geldart | Types of gas fluidization[END_REF] are difficult to fluidize because the interparticle cohesive forces are often much greater than the drag force exerted by the fluid. Consequently when subjected to fluidization, they tend to agglomerate. These agglomerates have a dynamic behaviour: Hakim et al. [START_REF] Hakim | Aggregation behavior of nanoparticles in fluidized beds[END_REF] showed that the agglomerates form, break and reform and their size (up to 500 µm) and shape change with time.

To overcome this problem, activation of the fluidization process becomes necessary. Some authors ([3]- [START_REF] Jimin | Effect of agitation on fluidization characteristics of fine particles in a fluidized bed[END_REF]) propose to improve fluidization by using mechanical stirrers inside the bed or introducing a small amount of large particles into the fine powders. More recently, Alavi & Caussat [START_REF] Alavi | Experimental study on fluidization of micronic powders[END_REF] and Xu & Zhu [START_REF] Xu | Parametric study of fine particle fluidization under mechanical vibration[END_REF] showed that mechanical vibration increases the forces acting on particles and tend to break up agglomerates: both the average size and the segregation of agglomerates in the bed are thus reduced.

Due to its high complexity, the understanding and the prediction of fluidized bed (FB) dynamics is essential to design an optimal fluidization and coating strategy. Due to the rapid advances in computational capabilities, computational fluid dynamics (CFD) appears to be a promising tool. Due to the complex behaviour of gas-solid systems, the development of such multiphase flow simulation tools are still on going. For example, there is still no general agreement on the appropriate closure models [START_REF] Van Wachem | Comparative analysis of CFD models of dense gas-solid systems[END_REF], and terms such as the solid phase stresses or the interphase momentum transfer are still in the research and development phase.

Most of the works on simulation of gas-solids FB were carried out with particles of Geldart's group B ( [START_REF] Goldschmidt | Hydrodynamic modelling of dense gas-fluidised beds using the kinetic theory of granular flow: effect of coefficient of restitution on bed dynamics[END_REF], [START_REF] Taghipour | Experimental and computational study of gas-solid fluidized bed hydrodynamics[END_REF], [START_REF] Johansson | Experimental validation of CFD models for fluidized beds: Influence of particle stress models, gas phase compressibility and air inflow models[END_REF]). Due to the cohesive behaviour of Geldart's group C powders, the incorporation of cohesion into continuum models seems to have been rarely attempted [START_REF] Gidaspow | Equation of state and radial distribution functions of FCC particles in a CFB[END_REF]. Thus to correctly reproduce a cohesive FB, Weber [START_REF] Weber | Simulation of Cohesive Particle Flows in Granular and Gas-Solid Systems[END_REF] proposed to use a Lagrangian representation in which the interparticle forces are considered via a square-well or Hamaker model.

The implementation of kinetic models of CVD coupled with CFD codes also represents a challenging task. Indeed, chemistry is an essential part in calculations of reactive flows due to the wide range of length and time scales. The first step usually consists of establishing the grid independence to be sure that the bed hydrodynamics is accurately predicted before the reaction kinetics scheme can be implemented. At the present time, only Guenther et al. [START_REF] Guenther | Fourth International Conference on Multiphase Flow[END_REF] simulated the dynamics of silicon CVD on a FB of group B alumina particles.

The present work deals with silicon FBCVD on macro and submicron powders. The first part goes into the study of silicon deposition on group C powders (TiO 2 particles) in a vibrated fluidized bed. The objective is to form nanometer scale continuous layers around each individual grain and thus preserve the original size distribution. In the second part, we present results about silicon deposition on macro powders of non porous alumina Al 2 O 3 . These experimental results form a data base for the simulation of the FB hydrodynamics coupled with the CVD process. Numerical results such as the height of the bed and the conversion rate of silane are compared with the experimental data.

EXPERIMENTAL

Figure 1 illustrates the experimental setup. The cylindrical column was made of stainless steel with an internal diameter of 0.05 m and a height of 1 m. The reactor was externally heated by a threezone electrical furnace and the wall temperatures were monitored by three thermocouples. Several thermocouples were also placed into a tube of 6 mm in diameter inside the reactor as shown in Figure 1. An Inconel™ porous plate is used for the gas distribution. Silane and nitrogen were supplied to the bottom of the bed through ball rotameters associated to manometers. A differential fast response pressure sensor measured the total pressure drop across the bed; the high pressure tap was placed under the distributor and the other one was situated at the top of the column. The vibrated fluidization experiments were performed by fixing the reactor on a vibrating table as shown on Figure 1. Two vibro-motors were thus mounted on the opposite sides of the table to achieve the horizontal vibration of the column. Vibration frequency could be varied from 15 to 50 Hz and the vibration amplitude from 0.5 to 6 mm. An accelerometer measured the forces applied to the column by the vibration. A hydrogen detector (catharometer) provided the hydrogen concentration of the outlet effluents. A DasyLab® system enabled the on-line acquisition of the differential pressure, FB temperatures and H 2 outlet concentration. Some hydrodynamic measurements were performed in a glass transparent column of similar features using a video camera (Panasonic Tri CCD NV-GS400). Alumina (Al 2 O 3 ) particles of Geldart's group B and titanium dioxide (TiO 2 ) group C powder were used in this study. Their main characteristics are summarized in Table 1. The cohesivity (C) and the Hausner Ratio (HR) of the Geldart's group C particles indicate that these powders are not fluidizable [START_REF] Carr | Evaluating flow properties of solids[END_REF]; indeed we have verified that they form channels and slugs when fluidized resulting in a very poor gas-solids contact. Concerning CVD experiments, a theoretical thickness was deduced from the deposited silicon mass assuming that the particles were spherical and the deposition was uniform. The conversion rate of silane was deduced from the deposited mass and the hydrogen concentration at the outlet. The initial and final size distributions of the powders were measured by laser granulometer (MasterSizer2000). The deposition morphology was analysed by scanning electron microscopy (SEM) (LEO 435 VP). Some Raman spectroscopy measurements have been performed at the "Service de Spectroscopies Vibrationnelles" of the Paul Sabatier University (Toulouse) on a Labram HR800 from Jobin Yvon equipped with a laser He/Ne (ex: 632.8 nm). Some transmission electron microscopy (TEM), Infra Red (IR) spectroscopy and X Ray Diffraction (XRD) analyses have been performed respectively on a Philips CM20, a spectrometer (Perkin Elmer Series 100) and on a diffractometer (SEIFERT 3000TT) at CEMES.

VIBRO-FB CVD OF SILICON ON TIO 2 POWDERS OF 0.5 MICRON

Before beginning the first CVD experiments, a hydrodynamic study has been performed to identify the fluidization conditions (amplitude, frequency, total gas flow rate) that provide the best gassolid contact. We found that fluidization was improved for a certain range of vibration intensities. But the bed always fluidized under the form of dynamic agglomerates and not as ''single'' particles. Without vibration, segregation took place in the bed: stagnant agglomerates with an approximate diameter of 2 mm were present near the distributor whereas smaller ones were observed at the top part of the bed (600 -700 µm). We selected optimal conditions of vibration and gas flow rate involving minimal agglomerate size and maximal interphase contact all along the bed. In these optimal vibration conditions, segregation was much less significant with a mean agglomerate size varying from 300 µm at the top to 600 µm at the bottom of the bed. The influences of the distributor porosity, bed initial weight, gas velocity and direction of vibration were also examined. The qualitative results obtained were in good agreement with literature data [START_REF] Xu | Parametric study of fine particle fluidization under mechanical vibration[END_REF]. These hydrodynamic results allowed us to perform first experiments of vibro FBCVD on TiO 2 powders as detailed in Table 2. The objective was to form nanometer scale continuous layers of silicon around each individual grain and to avoid particles agglomeration due to CVD. We have then chosen to work in a high chemical reactivity regime, i.e. with low inlet percentages of silane in nitrogen and at relatively low temperatures. The initial weight of powders was always 450 g corresponding to a ratio between the initial fixed bed height and the reactor diameter H 0 /D close to 5. Due to the small SiH 4 inlet concentration and to the large specific surface area of powders, the silane conversion rate was always 100%. Then it is well known that silane SiH 4 begins to decompose around 370°C [START_REF] Caussat | Silicon deposition from silane or disilane in a fluidized bed -Part I : Experimental study[END_REF]. As a consequence, it is mandator to cool the zone below the grid to avoid its plugging by undesirable silicon deposition. This cooling is responsible for significant thermal gradients along the FB (from 40°C to 80°C) as detailed in Tab le 2. Such gradients have already been mentioned in previous studies ( [START_REF] Caussat | Silicon deposition from silane or disilane in a fluidized bed -Part I : Experimental study[END_REF], [START_REF] Tejero-Ezpeleta | Optimization of Reaction Conditions in a Fluidized-Bed for Silane Pyrolysis[END_REF]). They are not too detrimental to the deposition uniformity as the particles are circulated axially inside the bed. During experiments, no de-fluidization phenomenon was observed. As previously explained, the main challenge was to conserve the original size distribution of the powders. The results showed that only few stable and hard agglomerates larger than 1 mm were formed, representing less than 10% of the bed weight. Before granulometric measurements, those "big" agglomerates were separated easily by sieving. Figure 2(a) shows that the volume size distributions remained quite unchanged after CVD despite a small peak detected in the 1 -10 µm range, showing that some micronic hard agglomerates remained after sieving. Figure 2 Figure 3(a) presents the results obtained by Raman spectroscopy. The spectrum obtained before silicon deposition, exhibits four peaks at 144, 398, 516 and 639 cm -1 characteristic of anatase phase of TiO 2 [START_REF] Balachandran | Raman spectra of titanium dioxide[END_REF]. After CVD, the Raman spectrum is different. The peak at 612 cm -1 can be attributed to rutile phase of TiO 2 and the peaks at 154 cm -1 and 400 cm -1 are attributed, respectively to the anatase and rutile phase, although they are broadened and shifted relative to the corresponding features in bulk TiO 2 [START_REF] Balachandran | Raman spectra of titanium dioxide[END_REF][START_REF] Porto | Raman Spectra of TiO 2 , MgF 2 , ZnF 2 , FeF 2 , and MnF 2[END_REF]. It has been demonstrated [START_REF] Parker | Raman microprobe study of nanophase TiO 2 and oxidation-induced spectral changes[END_REF] that these shifting and broadening could be related to some oxygen vacancies, maybe due to a partial reduction of the material. A new peak appeared at 500 cm -1 characteristic of the presence of amorphous silicon [START_REF] Zwick | multiple order Raman scattering in crystalline and amorphous silicon[END_REF]. Figures 3(b) and 3(c) present TEM views of TiO 2 particles before and after CVD for run T7. In Figure 3(b) grains appear aggregated due to interparticles cohesive forces. In Figure 3(c) blobs of amorphous silicon can be observed and the film does not seem to be fully continuous. For this particle, the film thickness is approximately 10 nm which is in good agreement with the calculated value of Table 2.

FBCVD OF SILICON ON ALUMINA POWDERS OF 342 MICRONS Experimental study

The operating conditions tested and the corresponding results are listed in Table 3. The inlet volumetric percentage of silane in nitrogen has been varied between 0.5 to 10. First, the reproducibility of the results has been verified through runs A10 and A11. Thermal gradients are still present for these runs but they can be lowered to around 15-20°C for the lowest temperatures tested, which gave acceptable uniformity of deposition primarily due to the intense circulation of the particles inside the bed. The reason to increase the initial FB weight (run A12) is to decrease this gradient by taking advantage of better thermal transfers between the reactor walls and powders.

nm

Si-coated TiO2 Uncoated TiO2

The deposition rate varies between 30 to 120 nm/min. As previously observed in the literature [START_REF] Caussat | Silicon deposition from silane or disilane in a fluidized bed -Part I : Experimental study[END_REF][START_REF] Tejero-Ezpeleta | Optimization of Reaction Conditions in a Fluidized-Bed for Silane Pyrolysis[END_REF][START_REF] Kojima | Optimum process conditions for stable and effective production of a fluidized bed CVD reactor for polycrystalline silicon production[END_REF], this parameter and the silane conversion increase with temperature. The silane conversion logically increases with the initial FB weight (runs A6 and A12). For runs A3 to A5 and A7 to A12, the weights of injected silicon are high. For these runs, some reversible disturbances of the thermal profile and pressure drop along the FB have been observed. They are due to a partial de-fluidisation of the bed, probably related to the appearance of short-lived agglomerates; indeed silicon dangling bonds are probably formed on the surface of each particle during deposition, acting as glue for the surrounding particles [START_REF] Caussat | Silicon deposition from silane or disilane in a fluidized bed -Part I : Experimental study[END_REF]. Such disturbances have not been observed for TiO 2 particles because of the low amount of SiH 4 used.

For the conditions tested, the size distribution of the powders has not been modified by deposition. SEM analyses revealed that deposition seems uniform on powders and that for the highest weights of silicon injected, coating thickness of several hundreds of nanometers was achieved. Some Raman and XRD measurements have shown that when the FB temperature was lower than 610°C, silicon deposition was mainly amorphous whereas it was polycrystalline at higher temperature.

CFD modelling of the process

The CFD open-source code MFIX [23], a benchmark tool for the simulation of FB, was used for this study. 2-D axisymmetric and 3-D calculations were performed using the continuum model, the drag law of Syamlal-O'Brien [START_REF] Syamlal | Fluid dynamic simulation of O3 decomposition in a bubbling fluidized bed[END_REF], kinetic theory of granular materials with an algebraic form for granular temperature equation for the solid phase stress tensor in the viscous regime and the Schaeffer model [START_REF] Schaeffer | Instability in the Evolution Equations Describing Incompressible Granular Flow[END_REF] for the calculation of the solid phase stress tensor in the plastic regime. Concerning the alumina powder, a mean Sauter diameter of 330 µm and an internal angle of friction of 40° were considered. The latter value corresponds t o the repose angle (note that for non-cohesive powders, these two parameters are identical [START_REF] Terzaghi | Theoretical Soil Mechanics[END_REF]). Since we did not find any data in the literature about the coefficient of restitution for the collisions of alumina particles, the default value of 0.8 was used.

Some preliminary calculations showed that using the Superbee method for spatial discretization scheme (order 2), the grid independent results were achieved by using 200 cells along the axial direction for a height of 0.4 m, 15 cells along the radial direction for the half diameter, and for 3-D calculations, 6 angular cells. This result is true over all the range of the operating conditions studied.

As a first step only the pure hydrodynamic behaviour of the bed has been modelled. In this study, experiments were performed using 800 g of powder fluidized with air at ambient temperature in the glass column, using average superficial gas velocities, U g , between 5 and 40 cm/s. The fluidization plateau was reached at a minimum fluidization velocity (U mf ) of about 12.5 cm/s, the pressure drop across the bed being very close to the theoretical value of 4000 Pa. Then, the bed behaviour was more specifically studied for 3 gas velocities: 18, 25 and 30 cm/s, using the video camera. This allowed determining accurately minimum and maximum average heights of the fluctuating bed for each gas velocity.

The knowledge of U mf allowed adjusting the coefficients of the Syamlal-O'Brien drag correlation [START_REF] Syamlal | Fluid dynamic simulation of O3 decomposition in a bubbling fluidized bed[END_REF]. Then, 2-D axisymmetric and 3-D MFIX simulations were performed for the 3 gas velocities studied. Values of minimum, maximum and average bed expansions, H/H mf , obtained from experiments and from calculations are compared in Figure 4. All calculations overestimate bed expansions and fluctuations but results obtained with 3-D simulations are much closer to experimental data than results obtained with 2-D calculations. It appears that the best prediction of 3-D calculations is obtained for the highest velocity (U g =30 cm/s) with overestimations of average bed heights and fluctuations of about 7%. Note that this gas velocity was used for experiments of Si CVD. The second step aimed at modelling the silicon deposition process. First, thermal profiles existing along the FB and the presence of the tube of 6 mm in diameter along the column axis were included in the simulation. A chemical model was then implemented in MFIX to simulate the deposition of silicon from SiH 4 . The kinetic law of Furusawa et al. [START_REF] Furusawa | Chemical Vapor Deposition and Homogeneous Nucleation in Monosilane Pyrolysis Within Interparticle Spaces -Application of Fines Formation Analysis to Fluidized Bed CVD[END_REF] was chosen because it is one of the sole established for the FBCVD process for our conditions. In the present version of the model, only the overall reaction of silicon deposition from silane is considered, leading to the production of gaseous hydrogen:

4 2 2 SiH Si H → +
Runs A5 and A7 of Table 3 were then simulated in 3-D with an average bed temperature of 600°C, an increase of the axial temperature during deposition of about 50°C measured along the bed, the fluidization ratio being close to 4.5.

The coefficients of the Syamlal-O'Brien drag correlation have been adjusted considering a value of U mf equal to 7.5 cm/s at 600°C. Note that a preliminary modelling study showed that discrepancies of about 10% on bed expansions and fluctuations had no effect on the final conversion rates of silane calculated.

Instantaneous fields of void fraction and normalized silane mass fraction calculated after 7.1 s of deposition for run A7 are presented in Figure 5. Figure 5(a) shows that a slug of gas is present on about 60% of the FB height due to the high H 0 /D ratio used. Some millimetre scale bubbles of gas are present near the distributor but the bed is clearly in the slugging regime. Although Figure 5(b) shows complete conversion of silane in the exit gas, the average conversion is indeed much less than 100%. Note the low conversion in the gas at the center of the slug. When the slug erupts at the top, gases with low silane conversion will exit the reactor. The average silane conversion was found by time-averaging the instantaneous values.

Final conversion rates of silane measured and calculated for run A5 are of 81% and 79% respectively. For run A7, they are of 78% and 65% respectively. This agreement is quite good considering that only the heterogeneous phase reaction kinetics have been implemented in the model.

CONCLUSION

The first results of silicon deposition by vibro FBCVD on TiO 2 submicron powders show that the original granulometry is preserved for all the particles except for those present where fresh silane enters. In order to limit this phenomenon, new experiments are under progress, in particular using a sequential feeding of silane. CFD simulations of both FB hydrodynamics and of reactive mass transfers existing during silicon CVD are in good agreement with the experimental data. Our future work is to implement (i) the homogeneous reactions occurring during silane pyrolysis, (ii) the column vibrations and (iii) extend this code to represent beds of cohesive particles, to better understand the physical and chemical phenomena involved when treating submicron powders.

Figure 1 :

 1 Figure 1: Experimental set up.

Figure 2 :

 2 (b) presents size distributions in particles number. The hard agglomerates are not visible anymore indicating that they represent a very small proportion of the total mass of powders. Size distribution of uncoated and Si-coated TiO2 powders measured by laser granulometer. a) volumetric percentages, b) total number of particles percentages.

Figure 3 :

 3 (a) Raman spectra for uncoated and Si-coated TiO2 powders (run T3); TEM images of TiO2 powders (b) before silicon deposition; (c) after silicon deposition for run T7.

Figure 4 :

 4 Figure 4: Minimum, maximum and average bed expansions vs. relative gas velocity obtained from experiments and from 2-D and 3-D calculations

Figure 5 :

 5 Figure 5 : Void fraction (a) and silane mass fraction (b) calculated after t=7.1 s for run A7

Table 2 :

 2 Operating conditions and experimental results for silicon deposition on TiO2 powders

	Run	Temperatures (°C)	Weight of injected Si	Run duration	Calculated thickness of
		Distributor Top of the bed	(g)	(min)	Si deposition (nm)
	T1	550	605	3.7	72	1.4
	T2	550	610	7.8	61	3.9
	T3	550	610	3.8	72	1.4
	T4	560	600	1.4	63	0.5
	T5	505	585	1.7	64	0.6
	T6	565	600	2.7	116	1
	T7	560	610	31	60	15

Table 3 :

 3 Operating conditions and experimental results for silicon deposition on Al2O3 powders of Geldart's group B.

		Temperatures (°C)	U/Umf	Initial		Weight of	Run	Weight of	Silane	Calculated
	Run	Distributor	Top of the bed		weight of powders (g)	Ho/D	injected Si (g)	duration (min)	deposited silicon (g)	conversion rate (%)	thickness of deposited Si (microns)
	A1	575	640	4.2	800	4	6.74	21.5	5	74.18	0.6
	A2	605	630	4.4	800	4	7.14	21.5	5.9	82.7	0.73
	A3	580	660	4.6	800	4	25.1	21	17.8	70.9	2.1
	A4	550	620	4.2	800	4	24	21	17.5	72.9	2
	A5	570	615	4.2	800	4	20.3	25	16.4	80.9	1.95
	A6	550	570	4	400	2	5.5	22	3.6	65.3	0.87
	A7	560	610	4.5	800	4	30.9	21	24.2	78.3	2.9
	A8	515	530	4.28	400	2	21.9	13	3.2	14.6	0.78
	A9	520	535	5	600	3	38.8	22	6.6	17	1
	A10	550	580	4	800	4	40.7	40	24.2	59.4	2.7
	A11	550	580	4.1	800	4	41	40	24.4	59.5	2.7
	A12	552	576	4.1	1300	6.5	41.4	40	36.3	87.7	2.5

Acknowledgements: The MFIX simulations have been performed on the GridMip platform of the French Grid'5000 network.