Eleni Xirouchaki
email: kyrani-eleni.xirouchaki@univ-brest.fr

Jean-Marie Boilevin

Alice Guyon

Thomas Lorivel

Julie Milanini

Caroline Bouissou

The notion of time from a didactics' point of view. Conceptions of 5 to 7-yearsold students about time perception

Keywords: conceptions, students 5 to 7 years old, time, speed, methodology, qualitative analysis conceptions, élèves de 5 à 7 ans, temps, vitesse, méthodologie, analyse qualitative

The enigmatic question of time, essentially of a physical, psychological and social nature, occupied human since becoming aware of his existence and of the surrounding environment. Young students' conceptions may be a starting point for improving their understanding of the world. This research is interested in very young students who are in full "construction" of the concept of time. Conceptions related to time notion play a decisive role throughout learning procedure and are often incompatible with the scientific model. Conceptions' analysis is a tool for the advancement of a proximal development zone in which a first conceptual system can be built by students. We refer to the area of current or potential success of young students concerning the understanding of time notion. This paper presents findings on 5 to 7-year-old students' conceptions about the inverse relationship between time and speed.

I INTRODUCTION

Our current research project, concerning Precursor Models and Time Measurement Teaching, aims to enhance the understanding of how the application of the Precursor Model Concept in Science Teaching and Learning may help children overcome comprehension difficulties. Our study concerns Early Years Science Education and Science in Primary School, especially French students aged from 5 to 7 years old. There is a general agreement that, children's initiation to Science Education should start as early as possible [START_REF] Eshach | Should Science Be Taught in Early Childhool[END_REF][START_REF] Klaar | Arguments for Early Childhood Science Education; a Review of Research Articles 2006-216[END_REF]. PISA 2012 results, highlight the benefits students get form attending preschool in terms of future school performance (Eurydice, 2014). Children's comprehension of natural phenomena is developed through everyday life's experience [START_REF] Eshach | Should Science Be Taught in Early Childhool[END_REF]Sikder & Fleer, 2015). Various authors argue that, spontaneous children's representations are a starting point of instruction to improve pupil's understanding [START_REF] Siry | Children Explain the Rainbow: Using Young Children's Ideas to Guide Science Curricula[END_REF][START_REF] Boilevin | Rénovation de l'enseignement des sciences physiques et formation des enseignants[END_REF]. We are interested in identifying the conceptions of 5 to 7-year-old students about time characteristics. By taking into account the difficulties encountered by students on the notions of grandeur and measurement [START_REF] Munier | Mesure et incertitudes en mathématiques et en physique à la transition école-collège : éléments d'épistémologie et difficultés des élèves[END_REF], and in particular on the concept of time measurement [START_REF] Piaget | Le développement du temps chez l'enfant[END_REF][START_REF] Levin | The development of the concept of time in children: An integrative model[END_REF][START_REF] Samartzi | Étude développementale des notions de durée et d'âge : temps physique et temps biologique[END_REF][START_REF] Ravanis | Mental representations of 14-15 years old students about the light propagation time[END_REF], we make the assumption that students encounter difficulties on the notion of duration, of succession as well as on the notion of speed in relation to time. Through the analysis of students' conceptions, we aim to determine the elements that hinder the understanding of time measurement. These obstacles can be taken into account for the construction of a didactic engineering under the objective of teaching time measurement.

II THEORITICAL FRAMEWORK

The enigmatic question of time, essentially of a physical, psychological and social nature, has occupied human since becoming aware of his existence and of the influence of the surrounding environment. Different distinctions have been proposed for time aspects. Individual time (biological and psychological), collective time (religious, political), time in physics. To approach our object of study, we retain a distinction concerning time: objective time and subjective time. Subjective or psychological time brings together various feelings we have of time flow. It is about perception and intuition of individual personal experiences [START_REF] Tartas | La construction du temps social par l'enfant[END_REF]. Objective time is socially shared and recognized. It can be declined in cultural or social objective time and in objective time in physics. School time is considered to be an aspect of social time [START_REF] Masy | La temporalité, une disposition sociale et culturelle de construction de l'avenir[END_REF]. Social time, also called conventional time, groups the constructions of human to be able to identify and regulate his existence (Fraise, 1979). This time corresponds to the time measurement systems specific to each culture [START_REF] Coster (de | L'acquisition et la construction de la notion de temps chez les enfants de 5 à 9 ans[END_REF]. Time in physics obeys to logo-mathematical relations, this is time defined by Newton.

As part of our research, we are interested in the notion of time measurement, which is perceived here in concordance with the official prescriptions of the French national education curricula for students of primary school, including kindergarten and elementary school students. For this reason, time measurement finds its bases in the scientific model underlying the theory of mechanics nonrelativistic classic physics [START_REF] Matthews | Science Teaching: The Contribution of History and Philosophy of Science, 2 nd[END_REF] as well as in the psychological aspects of time [START_REF] Piaget | Le développement du temps chez l'enfant[END_REF][START_REF] Droit-Volet | How Emotions Colour our Perception of time[END_REF]Samatzi, 2011;[START_REF] Rattat | Temporal categorization of familiar actions by children and adults[END_REF], explored throughout primary school. In this perspective, time is considered as the indefinite continuous progress of existence and events that occur in an irreversible succession from the past through the present to the future [START_REF] Matthews | Science Teaching: The Contribution of History and Philosophy of Science, 2 nd[END_REF]. From the epistemological point of view, we refer to the measurement of a grandeur. Two main streams exist related to grandeurs and measurement: operationalism and realism [START_REF] Perdijon | La mesure, histoire, sciences et technique[END_REF]. From the point of view of the operationalism, grandeur is strongly related to measurement and makes no sense in the absence of measurement. From the point of view of the realism, grandeur exists, regardless to measurement. [START_REF] Munier | Réflexions sur l'articulation entre didactique et épistémologie dans le domaine des grandeurs et mesures dans l'enseignement primaire et secondaire[END_REF] emphasize the need of introduction of epistemological knowledge and elements of metrology in teaching to enable students give meaning to the concepts of grandeur and measure. We identify a strong presence of the realistic aspect in French curricula of the first cycle of learning, [START_REF] Xirouchaki | Les conceptions des élèves de 5 à 7 ans sur la mesure du Temps[END_REF]. At this level, curricula emphasize on the construction of the time concept in student's mind as a grandeur. Thus, we identify the gradual introduction of the operationalist aspect in the curricula at the beginning of the second cycle of learning concerning students 6 to 8 years old (Ibid).

We refer to the notion of duration, succession, and to the notion of speed related to time. Duration refers to a time interval. The estimation of a duration may depend on a number of changes perceived and memorized at the time of the estimation (Fraise, 1979). A duration is felt each time that a need generates a desire which, to be satisfied, an interval of time unfolds [START_REF] Zakopoulou | Jeux avec le temps pour enfant[END_REF]. The capacity to estimate a duration and the personal working memory capacity related to the speed of information processing have a reciprocal influence relationship [START_REF] Droit-Volet | Development of time[END_REF][START_REF] Montemayor | Conscious awareness and time perception[END_REF]. The succession of events corresponds to the temporal consciousness [START_REF] Samartzi | Conception, compréhension et construction du temps[END_REF]. The perception of changes, of the successive phases of an event, lead to the primitive awareness of the concepts "before" and "after" [START_REF] Zakopoulou | Jeux avec le temps pour enfant[END_REF]. The understanding of these concepts is essential for the temporal consciousness to be structured, in terms of past, present and future. The temporal consciousness is a key component of the general consciousness and determines largely the level of general consciousness (Samatzi, 2003). We also refer to the notion of the perception of speed in relation to time perception. [START_REF] Piaget | Le développement du temps chez l'enfant[END_REF] explains that the relationship between time and speed is a key element in the temporal structuring of children. This relationship consists on the fact that a fast movement corresponds to a short interval of time. Using a language suitable for students from 5 to 7 years, we would say that "faster" corresponds to "less time", what [START_REF] Piaget | Le développement du temps chez l'enfant[END_REF] describes as the inverse relationship between time and speed. Considering the elements explained above, we are interested in the conceptions of students on the notion of duration, succession, and speed related to time by assuming the existence of obstacles concerning these notions.

We now discuss elements of explication for the terms: conception, obstacle, and didactic engineering. Conception (often referred to as representation), is described as students' implicit ideas about scientific concepts [START_REF] Bachelard | La formation de l'esprit scientifique[END_REF][START_REF] Astolfi | Didactiques des sciences. Communication présentée au Colloque « Que sais-je ?[END_REF]Giordan & Vecchi, 1994;[START_REF] Ravanis | Représentations, Modèles Précurseurs, Objectifs-Obstacles et Médiation-Tutelle : concepts-clés pour la construction des connaissances du monde physique à l'âge de 5-7 ans[END_REF]. Obstacle, is described as the boundaries that constitute the domain of children' experience [START_REF] Martinand | Connaître et transformer la matière[END_REF][START_REF] Astolfi | Obstacles et construction des situations didactiques en sciences expérimentales[END_REF][START_REF] Ravanis | Représentations, Modèles Précurseurs, Objectifs-Obstacles et Médiation-Tutelle : concepts-clés pour la construction des connaissances du monde physique à l'âge de 5-7 ans[END_REF]. These obstacles may concern the word polysemy, children's psychogenetic levels, children's attitudes, or explanations [START_REF] Ravanis | Représentations, Modèles Précurseurs, Objectifs-Obstacles et Médiation-Tutelle : concepts-clés pour la construction des connaissances du monde physique à l'âge de 5-7 ans[END_REF][START_REF] Xirouchaki | Les conceptions des élèves de 5 à 7 ans sur la mesure du Temps[END_REF]. The identification of obstacles leads to setting objectives for a learning intervention applying a didactic engineering. To learn, students have to be actively involved in a didactical situation [START_REF] Sensevy | Le sens du savoir. Éléments pour une théorie de l'action conjointe en didactique[END_REF]Bachtold, 2012). The precursor model is described as an intermediate mental schema between students' conceptions and a scientific explanation [START_REF] Lemeignan | A Developmental Approach to Cognitive Change in Mechanics[END_REF]. This procedure can be facilitated by the action of the teacher as a mediator (Fleer & March, 2009, Delserieys, Jégou, Boilevin & Ravanis, 2017). The term mediator describes an intermediary between the world of knowledge, scientific practice and students [START_REF] Weil-Barais | Approche cognitive et développementale de la médiation en contexte d'enseignement apprentissage[END_REF]. The proposal of a didactic engineering, including the conception, the realization, and the analysis of teaching sequences [START_REF] Artigue | Ingénierie didactique. Recherches en didactique des mathématiques[END_REF], could help students overcome the obstacles they encounter in measuring time. In our current research, we are interested in the first phase of a didactic engineering [START_REF] Artigue | Ingénierie didactique. Recherches en didactique des mathématiques[END_REF], which is called preliminary analysis. This analysis contains the cognitive analysis of students' conceptions.

III RESEARCH OBJECTIVES

New French curricula pay attention to time measurement teaching. Curricula examination of the first cycle of learning, concerning students 3 to 5 years old, reveals that one of the main objectives is the construction of time landmarks and duration awareness. According to curricula of the second cycle of learning, concerning students 6 to 8 years old, students learn to question time more accurately, by applying a first scientific and thoughtful approach.

The development of temporal landmarks is considered as a transversal skill, essential to the cognitive structuring of students. Everyday teacher practice reveals that among students in the same class, regardless of grade level, differences are noticed in student's performance in both perception and time measurement activities. Difficulties encountered by students related to time measurement question us. Etienne [START_REF] Klein | Le facteur temps ne sonne jamais deux fois[END_REF] claims that to be situated in time, to be today in time, is to have a story, a past, a present and a future. It is in the present that we are and feel, yet it seems that it escapes us. Based on information cited above, we consider that time measurement teaching presents a social and cultural issue.

From didactics' point of view, the emergence of students' conceptions is a process advocated by the majority of constructivist theories in science education (see [START_REF] Baviskar | Essential criteria to characterize constructivist teaching: derived from a review of the literature and applied to five constructivist-teaching methods articles[END_REF]. [START_REF] Driver | Pupils and paradigms: a review of literature related to concept development in adolescent science students[END_REF] emphasize the importance of taking students' conceptions into account by comparing them to the accepted scientific knowledge. In this context, conceptions are characterized as "alternatives, built by students" (Driver & Easley 1978, 64 and 79). Bachtold (2012) considers student conceptions as an essential ingredient in science education. Conceptions have a double importance (Ibid). On the one hand, conceptions should be taken into account for the didactic transposition of scientific knowledge. Didactic transposition refers to knowledge reorganization and reformulation in order to be assimilated by students. On the other hand, the very recognition of the existence of the initial conceptions of students arriving in class may lead to a revision of the science teaching strategy. In particular, teaching process can consider conceptions as a starting point. [START_REF] Posner | Accommodation of a Scientific Conception: Toward a Theory of Conceptual Change[END_REF] state that for students' conceptions to be understood, they have to become explicit. In this context, these conceptions must be expressed in one way or another, orally or through a schema. diSessa (2017), claims that students' conceptions examination can lead to innovating teaching ideas which can motivate students' interest about learning science.

We formulate our research questions under the following terms:

• What are the conceptions of 5 to 7 years old students about the measurement of time, concerning the notion of duration, succession and speed in relation to time?

• What obstacles do students encounter about perception of duration, speed and succession notions related to time?

IV METHODOLOGICAL FRAMEWORK

To identify students' conceptions of the concept of time measurement, we propose situations that allow students express their initial ideas about time measurement. We now present methodologist tools set up for a student sample for conceptions of the notion of the inverse relationship between time and speed. The methodological framework applied is inspired by research existing in both didactics and psychology. The collection of data obtained pass through open discussions between the student and the researcher. These discussions take place through an individual semi-structured interview, as we present to the student an experimental support. The discussion takes place around the questions transcribed in advance on our interview guide. The interviews last about five minutes, they are filmed and take place in a room specially designed for this purpose inside the schools. This way of data collection, allows us to collect the ideas, responses and reactions of each student individually, without being influenced by other students. 63 subjects (33 boys, 30 girls) aged 5 to 7 years participated in this data collection. The population comes from 5 classes of different primary schools, urban and rural, of the department of Ille and Vilaine in France. Participants are children from mixed socio-cultural categories as the students questioned come from public schools of this region. The choice of sample collection from the same department is done in order to eliminate the social time perception variable [START_REF] Coster (de | L'acquisition et la construction de la notion de temps chez les enfants de 5 à 9 ans[END_REF]). As previously explained, time is not lived or organized in the same way according to cultures [START_REF] Troadec | Psychologie culturelle, le développement cognitif est-il culturel[END_REF]. The subjects of our sample have not previously received a didactic intervention organized on the understanding of the notion being treated. Collection of our data is carried out using digital equipment, a dictaphone and a camera on stand with microphone. The interviews are subsequently transcribed. The use of video allows us to identify communicative gestures (DeLoache, 2004), for students aged 5 to 7 who may not express themselves verbally. In this study we focus on the external systems of representation (Ibid) mimetics and language, by keeping a video trace.

Students are confronted to a problem situation. We will refer to the etymological explanation of the word problem, from the epistemological point of view, as indicated by [START_REF] Boilevin | Enseigner la physique par situation problème ou par problème ouvert[END_REF]. (The word problem, is formed by the prefix "pro" which means "in front" and the radical "ballin" which means "to throw". The essential idea is that of a difficulty, an intellectual challenge, for example -that we throw "βαλλω" in front of "προ" the student). We design our experimental support, in the form of a water clock. By using this support, we create our problem situation with the objective of identifying its resolution procedure [START_REF] Boilevin | Enseigner la physique par situation problème ou par problème ouvert[END_REF], as developed by the student. We aim to understand the student's reasoning, identify his or her initial idea and the potential obstacle that exists behind it. In the modern cognitive psychological context, the study of the notion of time is usually related to the ability of problem resolution [START_REF] Samartzi | Time as a problem to solve[END_REF]. This is the main ability that reflects the thought directed towards a goal (Ibid).

The water clock is presented by a water tank which flows downward through a Y-tube. The two branches of the Y have exactly the same flow (quite low but steady) and are controlled by a single tap handle, so that they will always begin to flow simultaneously and stop simultaneously. We then branch under the two branches from the Y two small jars of different shapes and equal volumes (A) and (B) and the experiment begins. We ask the following questions to the student: "Which of these jars will be filled more quickly? "Will it take a longer time for the one jar to fill up or less time than for the other jar? ". We turn the tap and let the jars fill up. We continue with the questions: "Which jar has been filled more quickly? », « Did it take a longer or less time than for the other? ". We hypothesize that 5-to 7-year-olds students think that the fastest water movement, in their opinion, is the one that corresponds to a longer time. To emit this hypothesis, we are inspired by the research of [START_REF] Piaget | Le développement du temps chez l'enfant[END_REF], but also from the epistemological perspective of the Knowledge in Pieces (CpM), (diSessa, 2017) which refers to students' prior conceptions and the role of these in the emergence of competence. (Vosniadou, 2013) and proposes a method of qualitative analysis of students' conceptions on especially difficult notions (diSessa, 1993). The "conceptual ecology" of students before they receive a teaching has to be finely analysed (Ibid), considering one by one the intuitions to understand learning. Students have a multitude of disorganized "intuitions", activated and effective in very specific contexts which are called phenomenological primitives, (noted as "p-prims" as follows), (Smith, diSessa & Rochelle, 1993)."P-prims" can be mental structures used without justification or related to causal relationships with a low level of interpretation (Ibid). These are elements of intuitive knowledge that constitute for subjects their "sense of mechanism". This way of thinking leads young students to consider certain facts as obvious, some as plausible, some as improbable and provide their real or imaginary explanations. For example: "an increased effort generates greater results", "the greatest is the stronger" [START_REF] Disessa | Towards an Epistemology of Physics[END_REF]. By taking into account research cited above, we make the assumption that students from 5 to 7 years old, participating in our interviews, can express themselves in a way similar to the following one: "the jar (x) is filled more quickly, it will take more time to fill". The CpM methodology takes into account students' different ways of thinking and a various vocabulary, which allows us to deal with the richness and diversity of student responses.

We also establish a grid of categorization of possible student responses prior to the interview [START_REF] Ravanis | A comparative approach to the representation of light for five-, eight-and tenyear-old children: didactical perspectives[END_REF] to better manage the possible heterogeneity of the students' reactions during our analysis. We expect three classes of responses to which we add the case of a possible lack of response. The first class concerns the satisfactory response of a scientific point of view, which corresponds to the correct, immediate solution of the problem proposed. The second class concerns the intermediate response, which includes some ideas that fit the intended knowledge. The student will provide answers sometimes accurate, sometimes false. S/he will momentarily understand the inverse relationship "faster = less time", but may not be able to generalize this report.

The third class concerns the insufficient answer. In this case, the student anticipates that the smallest (the one that seems to be the smallest) of the two jars (A) and (B) will be filled the faster. S/he imagines that the fastest water movement (in his/her opinion) is the one that corresponds to a longer time. We also contribute a class in the absence of an answer. We also constructed a class for the absence of an answer. In this case, the child gives no answer or starts to answer and do not finish his sentence or remain undecided.

V RESULTS

We now present the results of our study concerning the notion of the inverse relationship between time and speed by giving some examples of the student responses. We are interested in students' ideas expressed before realising the experiment. The analysis of the ideas expressed by the students allows us to infer their conceptions about the inverse relationship between time and speed. In the case of satisfactory answers, the student says that the jar which will be filled the fastest is the one for which it will take less time to be filled. We present the example of the answer of the subject 9, to the first and the second question asked: "the jar (A) will be filled faster than the jar (B), it will take less time to fill the jar (A) ". In the case of intermediate answers, the student understands momentarily the inverse relationship "faster = less time". We present the example of the answer of the subject 25, to the first and the second question asked: "the jar (A), not the jar (B) will be filled as quickly as possible, the jar (B) will take more time, oh no I think that the jar (A) will take longer to fill". In the case of insufficient answers, the student anticipates that one of two jars (A) and (B) will be the fastest to be filled and says that the one who is going to be the faster to be filled, will take longer. We give the example of the answer of the subject 26: "the jar (A) will be the first to be filled, it will take more time to fill the jar (A).

The results obtained during the analysis indicate that a large proportion of the students provide an insufficient answer. More specifically, 19% of students do not give any opinion on the question asked. 56% of students present an insufficient opinion. 22% of them give an intermediate response whereas only 3% give a satisfactory answer. Taking into account the large number of insufficient responses added to the rate of no response, we can conclude that one of the main barriers to understanding the notion of time perception among students of the ages examined is the misunderstanding of the inverse relationship between time and speed.

VI DISCUSSION

The study presented in this paper provides an answer to one of our initial questions regarding 5 to 7-year-old students' conceptions of the inverse relationship between time and speed. We make the choice to perform interviews with students aged 5 to 7 from different schools in the department of [START_REF] Coster (de | L'acquisition et la construction de la notion de temps chez les enfants de 5 à 9 ans[END_REF]. We focus on the collection of students' conceptions of time perception. We refer to time measurement from the point of view of classic non-relativistic physics (Matthews,2015). The experimental support that we propose, in a form that we call "water clock", allows us to approach time as a grandeur [START_REF] Munier | Réflexions sur l'articulation entre didactique et épistémologie dans le domaine des grandeurs et mesures dans l'enseignement primaire et secondaire[END_REF] from a realistic point of view [START_REF] Perdijon | La mesure, histoire, sciences et technique[END_REF] in concordance with the official curricula of the national education for students 5 to 7 years old [START_REF] Xirouchaki | Les conceptions des élèves de 5 à 7 ans sur la mesure du Temps[END_REF]. This experimental setup allows us to identify students' conceptions [START_REF] Bachelard | La formation de l'esprit scientifique[END_REF][START_REF] Astolfi | Didactiques des sciences. Communication présentée au Colloque « Que sais-je ?[END_REF], Giordan & Vecchi, 1994[START_REF] Ravanis | Représentations, Modèles Précurseurs, Objectifs-Obstacles et Médiation-Tutelle : concepts-clés pour la construction des connaissances du monde physique à l'âge de 5-7 ans[END_REF] on the inverse relationship between time and speed by eliminating as much as possible the influence of stimuli from other registers, the presence of a colour or an odour for instance. By using this support, we also eliminate any mechanical difficulties. We refer, for example, to the synchronization at the level of the flow of water, by setting up the functioning of one wrist to drive the water stream. The problem situation [START_REF] Boilevin | Enseigner la physique par situation problème ou par problème ouvert[END_REF] that we propose enhances students' attention thanks to its originality. Students verbalize their ideas in the most of the times. This problem situation also brings out the reasoning of students. We are interested in the phase of the preliminary analysis [START_REF] Artigue | Ingénierie didactique. Recherches en didactique des mathématiques[END_REF]) of pupils' conceptions, which allows us to proceed to a cognitive analysis. Identification of mimetic and language elements within students' reactions [START_REF] Xirouchaki | Les conceptions des élèves de 5 à 7 ans sur la mesure du Temps[END_REF] using video capture favours our analysis.

VII CONCLUSION

The theoretical register and empirical phenomenological primitives (diSessa, 2017), leads us validate our initial assumption. The inverse relationship between time and speed is one of the obstacles that students aged 5 to 7 can face. We take into account the richness and the diversity of students' responses. We focus our interest on the assumptions made by students when formulating our first two questions. The variable of the volume of the jars proposed let us identify the report of students to the inverse relationship between time and speed. Individual interviews allow us to identify the ideas of each student without the interference of other factors that could influence the results. We consider that these first results on the conceptions of 5 to 7-year old about the inverse relationship between time and speed constitute an interesting start regarding the obstacles that young students may encounter on time perception and measurement.

Figure 1 :

 1 Figure 1: the water clockThis theoretical and empirical framework deals within the framework of the "conceptual change"(Vosniadou, 2013) and proposes a method of qualitative analysis of students' conceptions on especially difficult notions[START_REF] Disessa | Towards an Epistemology of Physics[END_REF]. The "conceptual ecology" of students before they receive a teaching has to be finely analysed (Ibid), considering one by one the intuitions to understand learning. Students have a multitude of disorganized "intuitions", activated and effective in very specific contexts which are called phenomenological primitives, (noted as "p-prims" as follows),(Smith, diSessa & Rochelle, 1993)."P-prims" can be mental structures used without justification or related to causal relationships with a low level of interpretation (Ibid). These are elements of intuitive knowledge that constitute for subjects their "sense of mechanism". This way of thinking leads young students to consider certain facts as obvious, some as plausible, some as improbable and provide their real or imaginary explanations. For example: "an increased effort generates greater results", "the greatest is the stronger"[START_REF] Disessa | Towards an Epistemology of Physics[END_REF]. By taking into account research cited above, we make the assumption that students from 5 to 7 years old, participating in our interviews, can express themselves in a way similar to the following one: "the jar (x) is filled more quickly, it will take more time to fill". The CpM methodology takes into account students' different ways of thinking and a various vocabulary, which allows us to deal with the richness and diversity of student responses.

Figure 2 :

 2 Figure 2: students' responses

  Ille et Vilaine wishing to limit the variant of social time (


Fabien Mieyeville
email: fabien.mieyeville@ec-lyon.fr

Mohamed Ichchou

Gérard Scorletti

David Navarro

Wan Du

Wireless Sensor Networks for active vibration control in automobile structures

Keywords: Wireless Sensor Network, Active control, mechatronic, Design methodology

Wireless Sensor Network (WSN) are nowadays widely used in monitoring and tracking applications. This paper presents the feasibility of using Wireless Sensor Networks in active vibration control strategy. The active control method used is an active-structural acoustic control using piezoelectric sensors distributed on the car structure. This system aims at being merged in wireless sensor network whose head node collects data and process control law so as to command piezoelectric actuators wisely placed on the structure. We will study the feasibility of implementing WSN in active vibration control and introduce a complete design methodology to optimize hardware/software and control law synergy in mechatronic systems . A design space exploration will be conducted so as to identify the best Wireless Sensor Network platform and the resulting impact on control.

Introduction

Wireless monitoring has imposed during the last year as a promising technology due to its wireless connectivity removing many hardware constraints and paving the way for new implementation on mechanical elements. Furthermore collocating computational power with sensors opens new perspectives in mechanical domain where a centralized approach is often preferred.

Use of Wireless Sensor Networks (WSNs) in mechanical domain has already successfully been demonstrated, particularly in Structural Health Monitoring (SHM) [START_REF] Lynch | A summary review of wireless sensors and sensor networks for structural health monitoring[END_REF] where realizations are numerous and distributed computation possibilities offered by WSN are beginning to be explored [START_REF] Wang | Decentralized civil structural control using real-time wireless sensing and embedded computing[END_REF]. If numerous works put the emphasis on demonstrating the aptitude of WSN for active control with sometimes comparison between hardware platform [START_REF] Lynch | A summary review of wireless sensors and sensor networks for structural health monitoring[END_REF] or deployment of decentralized algorithms, very few works put the focus on hardware platform analysis [START_REF] Shamim | Design and implementation of scalable wireless sensor network for structural monitoring[END_REF] or on design space exploration.

This work is embedded in Mécatronique@Lyon (M@L) ‡ project focusing on intelligent structures and systems in mechatronic domain from the component to the integrated design methodologies. The main objectives of this project are the identification and the integration of new intelligent active technologies in automotive systems so as to improve internal comfort (noise and vibrations). For this article, we will focus on the top-down design approach of Wireless Sensor Networks for active vibration control that takes into account the hardware platform specificities at high level of abstraction. When most current works are based on physical deployment of one (sometimes more) hardware platform, well will present and demonstrate a design flow that enables, by simulation, the exploration of different WSN node's architecture choice for a mechatronic application. From this design space exploration, we are able to identify the best hardware and to precisely evaluate the pro and cons of every architecture so as to elaborate the control law in adequation. ‡ M@L is supported by Ingénierie@Lyon (I@L), an institute of Carnot Network.

Mechatronic is the domain where several separate domains are strongly implicated [START_REF] Isermann | Mechatronic Systems: Fundamentals[END_REF]. If technological solutions merging those domains are commonly developed, only synergy between those domains can enable significant technological breakthroughs. Design methodologies are the keystone of this synergy: every specificity of those separate domains must be considered at conjointly at high level of abstraction so as to perform a global optimization of the system and the optimal distribution of the specifications. This paper offers a new technological solution by removing the conventional wired sensors used in network for active control and replacing them by wireless connected smart sensors such as shown on figure 1. Mechatronics being a tight integration of mechanical, electronic and information-driven units a specific design approach will be adopted to integrate the choice and the evaluation of the deployed WSN in the core of the development of the control law. WSN are now widely used [START_REF] Nitaigour | Sensor Networks and Configuration: Fundamentals, Standards, Platforms, and Applications[END_REF] in industrial application areas such as traffic control, stock management, industrial process monitoring and control, environment and habitat surveillance (water pollution, . . . ), structure monitoring [START_REF] Chintalapudi | Monitoring civil structures with a wireless sensor network[END_REF] as well as in civilian area where they are the keystone of ambient intelligence and home automation [START_REF] Kim | The study of applying sensor networks to a smart home[END_REF] . Commonly deployed WSN are used for application requiring low data rate exchange (sampling rate are often below the hertz). In this paper, we use WSN for active control where the data flow rate generated by each node of the network exceeds the kilohertz. We will establish the feasibility of deploying WSN for high data rate automotive application.

If feasibility is validated, new approaches could be used for active control. Indeed, beyond the removing of the wires of the network, WSNs, by providing distributed smart sensors embedding local computation power, could pave the way for new distributed approaches in the active control of vibrations. The feasibility of using WSN in active control is a two-steps approach: first we establish the specification of the mechatronic system to design a preliminary Wireless Sensor Network and then we used a WSN framework named IDEA1 [START_REF] Du | IDEA1: A SystemC-based system-level simulator for wireless sensor networks[END_REF] to explore the design space and identify the bottlenecks in the use of WSN for active control. From resulting conclusions and synthesis figures extracted from the analysis, we then propose guidelines for control laws § that suit the best to the WSN based active control network.

Wireless Sensor Networks

Wireless Sensor Networks are highly distributed self-organized systems [START_REF] Yick | Wireless sensor network survey[END_REF]. A Wireless Sensor Network is made of a large number of scattered tiny low-cost devices featuring strong constraints in terms of processing, memory, communications and energy capabilities. Common applications of WSNs deployed on a given space are data collection from sensor nodes measurements that are transmitted (or not depending on the local decision process implemented in each node) to a specific node called the sink node. The sink node can be as simple as a node whose connectivity has been extended to enable the transmission of data to external or networked systems, or as complex as a PC motherboard able to achieve elaborated computations. The longevity of the deployed network (often inaccessible or barely accessible) being a strong constraint, power saving techniques are commonly implemented resulting in specific behaviour for every nodes. Indeed, nodes sleep most of the time, waking up only for RF transmission or data measurement and rely on low power communications mainly based on a multihop data transmission from sensor nodes to sink nodes and vice versa.

Typical deployment of wireless sensor network can be seen figure 2. In this work, we use a heterogeneous network composed of off-the-shelf nodes and home-made nodes based on Zigbee communication protocol. The following subsections will rapidly describe hardware architecture of the node and radio-frequency communication in WSNs so as to introduce design parameters before developing feasibility of WSN in active control.

Hardware architecture

The elementary part of a wireless sensor network is called a mote or a node and consists of one or more sensors associated with a small microcontroller, a radio transceiver and an energy source, usually a battery. A sensor node might vary in size from that of a card box down to one-cubic-millimeter sized box [START_REF] Johnson | Millimeter-scale computer targets environmental, medical monitoring[END_REF] although functioning "motes" of § Since this work does not focus on specific active control algorithms, generic guidelines will be given for active control laws in general : the offered strategy can be adapted for various kind of control algorithms. genuine microscopic dimensions need still some development. Sensor nodes aim at being deployed by thousands: then the cost of a node is generally quite reduced (tenths of dollars) yet expanding to hundreds of dollars for high performances specific motes.

Constraints on motes differ from commonly considered electronic system ones (even embedded domain) in two ways. First, the very limited amount of embedded energy coupled with the difficulty of accessing to motes when deployed results in constrained resources in memory, computational speed and bandwidth [START_REF] Culler | Guest editors' introduction: Overview of sensor networks[END_REF]. Secondly, due to their structure, WSNs belong to distributed systems in which the main actor is not the element itself but the network that performs a task (data collecting and processing) in collaboration (data-centric approach).

In this work we used both commercial product from Crossbow and internally developed node that will be described later.

Software in WSN

In wireless sensor networks, software is at stake at two hierarchical levels: on the mote itself and on the global network for the management of every node so as to achieve the targeted application. Software embedded in mote results in operating system development whereas software in network is more related to middleware concerns [START_REF] Chatzigiannakis | 50 ways to build your application: A survey of middleware and systems for wireless sensor networks[END_REF]. An exhaustive and deep analysis of those aspects can be found in the following works [START_REF] Yick | Wireless sensor network survey[END_REF][START_REF] Farooq | Operating Systems for Wireless Sensor Networks: A Survey[END_REF].

For our application, where local computation is limited (embedded software is reduced to the following loop: data acquisition -sending data -sleep), the need for operating system is limited. But shall we implement local algorithms for active control, we should then use operating systems. Among several existing operating systems for WSN, TinyOS [START_REF] Lester | System architecture for wireless sensor networks[END_REF] is the most used and offers support for most existing commercial off-the-shelves WSN nodes. Because of the high energy cost of dynamic reconfiguration in TinyOS, our final solution will be funkOS [START_REF] Nolte | Wireless automotive communications[END_REF] that enables modular description, is supported by many microcontroller architectures and reduces energy costs in dynamic reconfiguration. Furthermore, in the first stages of our approach where few nodes are used to demonstrate feasibility of WSN in active control, middleware is not needed. In further steps, the link will be created between the framework and the deployment of the application on hardware and the maintenance of this network: dynamic reconfiguration [START_REF]Zigbee Specifications[END_REF], extension of the network, . . . .

Zigbee, a Radio-frequency solution for mechatronic

Radio-frequency (RF) communications are the backbone of the wireless sensor network. Due to the limited available energy, commonly used RF solutions cannot be used for WSN. Many works have focused on developing specific protocols and medium access control (MAC) layers [START_REF] Yick | Wireless sensor network survey[END_REF]. A low-cost, low-power, wireless mesh networking proprietary standard exists today for WSN based on the IEEE 802.15.4 standard: Zigbee [START_REF] Nitaigour | Sensor Networks and Configuration: Fundamentals, Standards, Platforms, and Applications[END_REF][START_REF] Yick | Wireless sensor network survey[END_REF]. Among the wireless solutions (Bluetooth, Ultra Wide Band and Wifi) that can be used for automotive, Zigbee is considered as a good solution [START_REF] Zames | Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses[END_REF] despite its lack of realtime capacity. We adopted it because of his low power consumption that could enable us to deploy an autonomous vibration powered wireless sensor network in a long term approach . Many RF transceivers implement this standard in their hardware (no need to develop code on the microcontroller to manage the RF transmission, the transceiver takes in charge the whole communication automatically) enabling fast development of massive networks. While not being, by some aspects ¶, the best solution for high performances wireless sensor network (no standard still exists in this domain), our WSN will be based on this standard protocol .

From IEEE 802.15.4 to Zigbee : brief overview of key parameters

With a data rate of 250kb/s, Zigbee limits the number of nodes that will be supported by the network and the latency (time elapsed between sensing operation on the node and data collection on the coordinator) of the network will directly impact on the control law. A global knowledge of its structure and the way it works is necessary to be able to establish the constraints. This section will present the basics of the IEEE 802.15.4 Zigbee tailored to WSN for mechatronic systems. For an exhaustive description of IEEE 802.15.4, we will report to the norm [START_REF] Font | H ∞ control of a magnetic bearing[END_REF]. ¶ Zigbee protocol is optimized for low duty-cycle applications (<0.1%). Miwi protocol based on IEEE 802.15.4 developed by Microchip is another way of development while not being as widespread as Zigbee.

Since in this work, we use standard radio-frequency transceiver, the physical layer is set and cannot be a design parameter : we will then focus on the parameters of the MAC layer and on the overlayer that Zigbee adds to IEEE 802.15.4 at the network level: organisation of the node of the network, data circulation in the network and application in the network.

2.4.1.

At the network level : architecture parameters So as to transfer data from a node to another, five important aspects are to be considered :

• Topology of the network: among the different topologies supported by Zigbee, the star topology is the best choice for our application so this aspect won't be considered as a parameter of design in our approach.

• Device class: in our application, with a star topology, the collecting node is a Full Function Device and the other nodes are Reduced Function Devices. This aspect being set, we will not developed further this aspect neither.

• Frame structure: to the data to be transmitted, the IEEE 802.15.4 MAC will add bytes so as to be able to fulfil safely the transfer. This supplementary bytes are the address of the receiving node and some bytes necessary to the synchronization of the data and to check the integrity of the data. Typical structure of a data frame will be developed later since offering several design parameters.

• Access mode to the medium: non-beacon mode and beacon-mode have both been explored in this work.

• Data transfer: the star topology sets, in our application, the status of every node. Furthermore, so as to achieve the best latency results, optional acknowledgements will not be used.

Every of these aspect will have its impact on the number of nodes that can be supported and on the average latency. Parameters associated to these aspects will be described in the following subsections.

Beaconed and non-beaconed networks

The main access method to the media in IEEE 802.15.4 is the channel access mode Carrier Sense, Multiple Access/ Collision Avoidance (CSMA/CA). In IEEE 802.15.4, this channel access mode can be used in two ways: unslotted mode and slotted mode.

Both have been explored in this work. Since in beacon-mode, a superframe structure is used, we will briefly present its characteristics so as to introduce the design parameters for the MAC layer. The superframe structure divides time into different transmission periods: Beacon, Contention Access Period (CAP), Contention Free Period (CFP) and inactive period as shown figure 3. Beacon mode is selected when power-saving is a really hard constraint since every node can sleep between two beacons. Furthermore minimal latency can be guaranteed. The duration of each period (active and inactive) will determine dynamic performance of the network: maximal data rate and latency. They can be calculated as follows :

• The Superframe Duration (SD) is the total time duration of the CAP, CFP (GTS) and a Beacon; it does not include the inactive period and is composed of 16 slots. This duration can be calculated by the following formula

SD = aBaseSuperf rameDuration • 2 SO with 0 ≤ SO ≤ BO ≤ 14 (1)
The minimum duration of a superframe (aBaseSuperframeDuration) is fixed to 960 symbols (16 slots of 60 symbols) corresponding to 15.36 ms, assuming 250 kbps in the 2.4 GHz frequency band (BO and SO are respectively the Beacon Order and the Superframe Order).

• Beacon Interval (BI) is the time duration between two successive beacons: it is composed of the active period and the inactive period. It can be calculated as follows :

BI = aBaseSuperf rameDuration • 2 BO with 0 ≤ BO ≤ 14 (2)
When BO = SO, the inactive period is reduced to zero and then BI = SD.

For the superframe structure, BO and BI will be the two key parameters used in our design space exploration.

In this part, we presented the basis of the Zigbee and IEEE 802.15.4 protocol with emphasis on our mechatronic application. In addition each design parameter that can be used for optimal adaptation of Wireless Sensor Network to the targeted application has been presented. In the next section, we will establish the specifications of the Wireless Sensor Network that has to be deployed.

M@L: Wireless Sensor Network specification

The first part of our work was to design the Wireless Sensor Networks from the hardware specification of each part of the node to the size and topology of the global network. The starting point being the data that needs to be collected, we begin by extracting the mechanical specifications of our vibrating structure to establish the format of the data that have to be processed by the control law.

Mechanical specification extraction

Active vibration control in vehicles is a complex problem that often necessitate the isolation of particular transmission paths. In this work where the focus is not on the development of the control law itself but rather on the wireless aspect of the data sampling collection, we will limit ourselves to the hypothesis of the use of piezoelectric sensors and actuators. For active control of internal automotive vibrations, we will consider the first three modes resulting in a [10Hz,300Hz] range. The preliminary estimation of the needed sampling rate, based on the active control strategy to be deployed is about 1kHz. Those two elements will set both the sampling rate performances of every node of the WSN as well as the constraints on the wireless sensor networks that mus provide the necessary bandwidth resulting from the sampling data rate that must be respected.

Control law in active control vibration

Specifications for active control vibration are naturally expressed in the frequency domain. Unfortunately, up to recently, most of the efficient active control design methods focus on time domain specifications. Nevertheless, the H ∞ control method [START_REF] Obinata | Model reduction for control system design[END_REF] emerges as an efficient active control design method which directly handles frequency domain specifications. The active control of flexible systems using H ∞ control begun to be explored in the nineties [START_REF] Ichchou | A reduced energy supply strategy in active vibration control[END_REF], with a special emphasis on multi-actuators multisensors systems. Based on the know how developed on the application of this approach, the use of model reduction methods [START_REF] Lynch | Design of a piezoresistive mems-based accelerometer for integration with a wireless sensing unit for structural monitoring[END_REF] allow to design active control systems of the lowest complexity. Note that the necessary complexity of the active control system dramatically depends on the performance specifications under consideration. The active vibration control strategy that will be first implemented in the computer connected to the collector node of our WSN will be a global semi-active strategy [START_REF] Liu | Active damage localization for plate-like structures using wireless sensors and a distributed algorithm[END_REF] chosen for its focus on reduced energy since the WSN deployed in this work aims at being energy sufficient (energy harvesting) in a long term view.

Hardware architecture of the node

It has been previously established that every node of the WSN must at least perform a sensing operation every 1ms. Furthermore, the latency should be kept to minimal.

In this section we will deduce from specification the hardware architecture of the node that will meet the specification for the global Wireless Sensor Network performance.

Microcontroller specifications

From the previous sections, we can infer, as expected [START_REF] Atmel | ATmega128(L) Data Sheet[END_REF] [START_REF]Ultra-Low-Power MSP430 Microcontrollers[END_REF], that an 8-bits architecture based microcontroller is sufficient. Furthermore, judging by the quantification specification for the analog to digital conversion, a microcontroller's integrated ADC (Analog-to-Digital Converter) solution can be considered: indeed current 8-bits microcontroller offer 10-bits based analog-todigital conversion with a sampling rate up to 20 MHz with an acquisition time about 15-20 µs. A brief overview of commonly used microcontroller for WSN make appear that ATMEGA128 family from ATMEL [START_REF]Pin Enhanced Flash MCUs with nanoWatt Technology[END_REF] or MSP430 family from Texas Instrument [START_REF] Karki | 3-v accelerometer featuring tlv2772 -slva040[END_REF] meets the requirements. Microcontrollers from Microchip are also good candidates with PIC16F [START_REF] Galliere | A 2-D VHDL-AMS Model for Disk-Shape Piezoelectric Transducers[END_REF] family and their nanowatt technology.

Transceiver specifications

We have chosen two devices commonly used in WSN community: the first one is the Chipcon CC2420 that can be found in many commercial platforms and particularly in the MicaZ node from Crossbow. The second is the MRF24J40 from Microchip chosen because of its hardware support of IEEE 802.15.4 specification. For the chipcon CC2420, the MAC layer must be realised by the microcontroller and then sent to CC2420 by SPI wire whereas for MRF24J40, microcontroller just has to send data to the transceiver by SPI wire and MAC layer support is done by the transceiver itself.

Sensor and signal conditioning

From mechanical specifications, it has been deduced that a soft PZT would fit our needs. We have chosen a PIC255 from Picoceramic. Yet, the output voltage delivered by the piezoelectric sensor is about millivolts. A signal conditioning stage has then be realized using a classical charge mode amplifier circuit architecture (cf. figure 4) based on the TLV2772 MOS amplifier from Texas Instrument, a commonly used amplifier in piezoelectric conditioning circuit [START_REF] Buratti | A mathematical model for performance of IEEE 802[END_REF]. The TLV2772 is an operational amplifier with high slew rate and bandwidth, rail-to-rail output swing,a high input impedance, a high output drive and an excellent dc precision. This device provides 10.5 V/µs slew rate and 5.1 MHz gain bandwidth product. With a consumption of only 1 mA of supply current, this device is perfectly adapted for signal conditioning for WSN. Furthermore, the high output drive and the rail-to-rail output swing are perfect for driving the the analog-to-digital converter of the microcontroller. The amplifier exhibits typical value of 60 V input offset voltage, 17 nV/vHz input noise voltage, and 2 pA input bias current.

The signal conditioning system is a three stage band-pass amplifier: the first stage is a passive high-pass filter that rejects continuous value of the signal, the second stage is dedicated to the amplification of the signal and the last stage acts as a passive low-pass filter to reject high frequency signal.

Component Value R 1 1 MΩ R 2 1 MΩ R 3 10 kΩ R 4 1 MΩ R 5 1 kΩ C 1 0.22 µF C 2 2.2 nF C 3 0.22 µF
Table 1: Component values for signal conditioning interface circuit.

We used the spice electrical model of the TLV2772 to design our signal conditioning circuit. For the piezoelectric, we used a very simple charge model (classical inductancecapacitance model with values extracted from the datasheet): should it be necessary, we could use a more detailed 2D VHDL-AMS model [START_REF] Buratti | Performance analysis of IEEE 802.15.4 non beacon-enabled mode[END_REF]. The global transfer function of this system can easily be calculated:

G(jw) =   1 1 + 1 jR 2 C 1 ω   • 1 + R 4 R 3 • 1 1 + jR 4 C 2 ω • 1 1 + jR 5 C 3 ω (3)
The components values are summarized in table 1.

The Spice simulation results from figure 5 (bode diagram: gain and phase) show that we have a band-pass filter with low cut-off frequency equal to 720mHz and high cut-off frequency equal to 470Hz. The gain in the flat band is about 11.

The resulting circuit exhibits a 2V amplitude signal with adequate frequency bandwidth. This measurement was made on a beam whose parameters have been chosen identical with the car structure. The amplitude and responsivity fit at best with the full scale of the internal analog-to-digital converters of the two microcontroller we have chosen for this work. Furthermore, this results will be used to generate the sensor stimuli of our design framework IDEA1 [START_REF] Du | IDEA1: A SystemC-based system-level simulator for wireless sensor networks[END_REF]. The nature, number and properties of measured data are of relevance in the system performance. In our case, as low frequency vibration control is targeted, typically the control of first vibration modes of the given structure is considered. From a pure control point of view one can consider displacement, velocity or acceleration for the vibration monitoring. It is expected that the data quality, if reasonable, will not strongly affect the algorithm performance in the low frequency range. Finally the issue of sensors locations can be treated considering the structural mode shapes of controlled modes.

Network specification

Previously, all hardware specifications have been established. Since the node will be deployed in a network, we must determine the number of node that can be supported by our application and the latency that it will present. The topology of our network will be a star composed of a Full Function Device (the coordinator) that has the ability to initiate communication and can authorize node to join the network and of Reduced Function Device that will collect the data and transmit them.

MAC layer parameters

The choice between beaconed mode and non-beaconed mode will have influence on the data rate and the latency. Depending on the communicating mode, collision will occur more or less. Collision that occurs can necessitate to send again data that were not received. The CSMA-CA access mode used in IEEE 802.15.4 offers mechanism to prevent collision from happening: each node must verify that the channel is free before sending data. This is achieved by sensing the idleness of the channel at random time duration. If the channel is busy, the node will wait a random time before retrying to access channel: the time unit of this random time is called backoff period (aUnitBackoffPeriod) equal to 20 symbols in IEEE 802.15.4. The random time is a random value of aUnitBackoffPeriod chosen in 0, 2 BE -1 with BE, the Beacon Exponent, an integer set to a minimal value and increased each consecutive time the node cannot access to the channel. Hence, it is very difficult to estimate the average behaviour of the network with actual data rate and latency (integrating collisions and backoff). If some works exist on performances of IEEE 802.15.4 based network, they result in analytical study of particular case of the IEEE 802.15.4 [START_REF] Dopico | Analysis of IEEE 802.15.4 throughput[END_REF], [START_REF] Elbatt | Potential for intra-vehicle wireless automotive sensor networks[END_REF] or are linked to a specific node architecture [34]. In this work we want to design a wireless sensor network based on IEEE 802.15.4 (we will have to explore the different algorithms adequacy) and we want the best architecture for it. We will use a design framework to explore the design space at MAC layer level and hardware node level and to establish the best wireless sensor network adapted to our needs but we need a starting point for this exploration. If the models previously mentioned, can help us we will prefer more general case model to establish starting point configuration of our network.

Latency

The only IEEE 802.15.4 mode that can guarantee a latency is the GTS mode. El Tamar et al. [START_REF] Xbow | [END_REF], in their work on Intra-Vehicle Wireless Automotive Sensor Networks, established a formula for the worst case latency (in ms) for beaconed-mode with GTS. If IEEE 802.15.4 could support up to 40 nodes with a latency that not exceeds 100 milliseconds, the IEEE 802.15.4 cannot offer a latency smaller than 15.9 milliseconds for any star of network of any size. The first order approximation means, in the frame of our work, that the coordinator will receive samples 16 sampling periods later compared with the real sampling time. It will have to be taken into account in the control law. The consequences of such a delay will be developed later in this paper.

Data rate

The IEEE 802.15.4 supports a maximum over-the-air data rate of 250 kbps for the 2400-MHz band. In reality, due to the many mechanism implemented in a frame structure to ensure a robust data transmission, the effective data rate is lower. It will depend on the choice of the mode (beaconed or non-beaconed), the size of the payload, the number of nodes, . . . . In the hypothesis of a non-beacon enabled network where CSMA/CA algorithm never finds that the channel is busy and no retries are required (associated acknowledgement included), we obtain an effective data rate of 127kbps for a maximum payload of 114bytes. If we consider a more real case with a 25% probability of busy channel necessitating one retry, the effective data rate falls to 101kbps [START_REF] Riccobene | SystemC/C-based model-driven design for embedded systems[END_REF]. This effective rate, taken in the context of our work where we consider that the analog-to-digital conversion will be realised on one byte means that the maximum size of our network is about 16 nodes.

M@L Wireless Sensor Network: a summary

The Wireless Sensor Network that can be deployed for the active control of vibrations will be a star network composed of eight nodes based on a 8-bits microcontroller architecture and Zigbee-IEEE 802.15.4 compliant transceiver. Microcontroller of every node has internal analog-to-digital converter responsible for the digitalization of the data collected from the piezoelectric sensor after a signal conditioning based on a TLV2772 amplifier architecture. A first order analysis showed that a minimal 15.89ms latency is to be expected for a 1khz sampling rate of vibration data.

We have used our Wireless Sensor Network design platform to validate these results and to optimize the network. We used two different hardware platform for the node: a commercial platform MicaZ fron Crossbow [START_REF] Kurkowski | MANET simulation studies: the incredibles[END_REF] and an internally designed node named N@L (acronym for Node@Lyon). Both platforms will be evaluated.

Wireless Sensor Network optimization

WSN platform: IDEA1

IDEA1 (hIerarchical DEsign plAtform for sensOr Networks Exploration) is an internally developed framework for Wireless Sensor Networks [START_REF] Du | IDEA1: A SystemC-based system-level simulator for wireless sensor networks[END_REF]. It aims at simplifying the design of any wireless sensor network from global application specification downto hardware individual performance of every component of a node. Written in C++ and based on SystemC subset commonly used in electronic and network community [START_REF] Andel | On the credibility of manet simulations[END_REF], it enables to take into account hardware characteristics at a network level. This framework allows designer to evaluate the impact of hardware and software architecture of a node (microcontroller/transceiver choice, Operating System implementation, sensor . . . ) on the performances of the global network. The node system is a composite module divided into 2 sub-models, hardware model and software model. The hardware components of a sensor node generally include a processing unit, a RF transceiver, several sensors and a battery. The software model consists of operating system, middleware, protocol stack, and application implementation. We can then estimate performances impact at network level from two aspects: hardware modification or software modification. All the nodes are connected to a same network object via their proxy modules. At the initialization phase, every proxy registers its information in the network module such as position, TX power and RX sensitivity. During simulation, the network object reads the packet sent by nodes, calculates the distance between the source and its destination based on the parameters of relative nodes, and forwards the packet according to the radio propagation models. If two nodes in the radio range transmit at the same time, a collision will occur. The SystemC kernel acts as the simulation engine. It schedules the execution of processes and updates the state of all modules at every simulation cycle. All active processes are invoked orderly at the same simulator time, which creates an illusion of concurrency.

A Graphical User Interface IDEA1 is targetting an audience composed of

Wireless Sensor Network designer. We have then developped graphical user interface based on Qt platform to integrate all the parts, which can facilitate the system configuration, network topology visualization, simulation control and result analysis.

Users can use graphical interface to configure the network system and analyze the simulation results. The input parameters of IDEA1 are defined in an eXtensible Markup Language (XML) file, which is read by the executable simulation code during runtime. The input parameters and output results of IDEA1 are summarized in fig. 8. Many parameters of different-levels can be configured by users, including node level, protocol level, application level, etc.

A library

Many commercial off-the-shelf (COTS) hardware components have been modeled. The current library of hardware supported by IDEA1 is summarized in table 2. We are currently developping TI MSP430 microcontroller so as to have a 95% coverage of existing commercial node for WSN. [START_REF] Du | Idea1: A validated systemc-based system-level design and simulation environment for wireless sensor networks[END_REF], [START_REF] Jeongyeup Paek | A wireless sensor network for structural health monitoring: performance and experience[END_REF], WSN simulations tools results are indeed not representative of reality unless some precautions should be taken. IDEA1 has been developed according to these aspects and has been validated through experimental results [START_REF]CC2420 Data Sheet[END_REF] thus enabling us to use it for design space exploration for WSN pre-deployment analysis.

Design space exploration framework

Node target architecture

For this work we use two nodes architecture: MicaZ and N@L. MicaZ is a reference mote architecture in the WSN community and is often implemented in mechanical systems such as structural health monitoring systems [START_REF] Chen | Real-time Enabled IEEE 802.15.4 Sensor Networks in Industrial Automation[END_REF]. It is composed of an Atmel ATmega128 microcontroller [START_REF]Pin Enhanced Flash MCUs with nanoWatt Technology[END_REF] and a CC2420 transceiver from Texas Instrument [43], a monopole antenna and a number of peripherals such as leds, flash memory and a 51-pin connector. The communication between the microcontroller unit and the transceiver is realized by a Serial Peripheral Interface (SPI) and control pins such as Clear Channel Assessment (CCA) and Start of Frame Delimiter (SFD). The SPI is used for both packets and control signal since the CC2420 does not support fully the IEEE 802.15.4. The microcontroller unit is then responsible for the IEEE 802.15.4 MAC layer support. Both the fact that IEEE 802.15.4 must be software implemented and the limited throughput of the SPI link can be bottleneck to global network performances.

N@L is an internally developed node: it is composed of a PIC16LF88 microcontroller unit [START_REF] Galliere | A 2-D VHDL-AMS Model for Disk-Shape Piezoelectric Transducers[END_REF] and a the MRF24J40 transceiver [START_REF] Galliere | A 2-D VHDL-AMS Model for Disk-Shape Piezoelectric Transducers[END_REF] (both from Microchip), a monopole PCB antenna and peripherals such as leds and a piezoelectric sensing circuit interface. The communication between the microcontroller unit and the transceiver is realized by a Serial Peripheral Interface (SPI) and control pins such as the wake-up trigger (WAKE) and the interrupt pin (INT). The microcontroller was chosen for its nanowatt technology that ensure low power consumption and the MRF24J40 because of its full hardware support of IEEE 802.15.4 MAC layer. At first view, N@L node architecture is superior to MicaZ's architecture and should exhibit better performances when deployed in a network.

Definition of the metrics.

To evaluate the performances of the Wireless Sensor Network, we need metrics. According to our application, the metrics are defined as follows • Packet Delivery Rate (PDR): PDR is used to evaluate the network throughput.

It is the ratio of the number of packets successfully received by coordinator to the number of packets need to be sent by nodes. A single communications failure occurs when a device transaction fails to reach the coordinator, i.e., channel access failure after macMaxCSMABackoffs attempts and an acknowledgment is not received after macMaxFrameRetries attempts,

• Average Latency (AL): Latency of a packet is the duration elapsed between the time the sensor from the node reads data and the time when the data is received by the coordinator. AL is an average latency of all packets successfully received by the coordinator,

• Power consumption: due to the battery of every node, the lifetime of the network is limited. It is very important to estimate the power consumption at the node level. We will differentiate global power consumption, microcontroller power consumption (data measurement and processing cost) and transceiver power consumption (radiofrequency communication cost).

• Energy Consumption per Sample (ECSple): ECSple is the average energy consumed for successfully transmitting one sample: with packet delivery rate and average latency, this metric fully characterizes the performance of the network.

All these metrics will be used to evaluate the performance and the lifetime of the wireless sensor network.

M@L Wireless Sensor Network: design space exploration

The three MAC algorithms in IEEE 802.15.4 standard are implemented, including unslotted CSMA-CA, slotted CSMA-CA and GTS. Unfortunately, the maximum number of GTS slots in a superframe defined in the IEEE 802.15.4 standard is 7. Since our current application consists of 8 nodes, we used the TDMA-based GTS algorithm proposed in [44] : it is more suitable than the original IEEE 802.15.4 GTS algorithm for industrial applications which require low packet delivery latency.

For each algorithm, many cases with different configurations of parameters (e.g., payload, superframe length, the maximum number of the retries allowed after a transmission failure, . . . ) have been simulated. Payload presents the number of samples in a packet. A sample occupies one byte. The node sends the sensor data out if the data in the buffer is more than payload. In an ideal case, the payload should be reduced to one sample but due to the high sampling rate (compared with the effective IEEE 802.15.4 data rate) such a solution is impossible. A small payload will result in more packets to be sent, causing more collisions and thus lower PDR. Furthermore, when payload is small, the short packet causes a short latency and the big number of packets results in more energy consumption due to more attempts of channel access. In contrast, a big payload takes a longer time for transmitting a packet, which will increase the channel access failures and cause lower PDR too. The best PDR, hence, occurs in the case with a moderate payload as short as possible so as to minimize the latency in the network. Beyond this global results giving the performances at the network level, it is interesting to extract performances at node level so as to be able to identify the bottleneck of every node. In figure 9, energy consumption of node is represented split over the architecture: processing unit is separated from the communication unit so as to evaluate the most consuming part. For the processing unit, we have three main processes: analog to digital conversion (EnergyADCPerNode), SPI communication (EnergySPIPerNode) and data processing (EnergyCPUPerNode). For the communication unit, we have chosen to separate the energy consumption in two parts: consumption in active mode (EnergyTransActive) and consumption in sleeping mode (EnergyTransSleep).

Discussions

MAC algorithm best choice

The CSMA-CA algorithms are not appropriate for this industrial application due to low PDRs. The sample rate is so high that the system is overloaded and every node keeps trying to transmit the sensor data during whole application and they compete for channel usage. The PDRs are small as a result of large number of collisions.

Due to the constraints of the maximum GTS slots number of the IEEE 802.15.4 standard, the number of nodes in this simulation is set to 7. Furthermore the original IEEE 802.15.4 GTS algorithm requires a minimum length of CAP period of a superframe (440 symbols -7040µs for 250 kbps data rate): in our application, this period is not used resulting in a loss of performances. Each node can only be allocated for one slot. This algorithm is implemented by software in MicaZ mote and by hardware in N@L mote. If from a global point view, N@L is superior to MicaZ, for this configuration, the Energy (µJ) power consumption of the N@L node is surprisingly 50% higher than the MicaZ's power consumption. At the node level, it appears that for IEEE 802.15.4 GTS, the MRF24J40 transceiver is hugely consuming. This peak of consumption comes from the hardware of the IEEE 802.15.4 standard. Indeed, for MicaZ mote, after receiving a beacon packet, the microcontroller can set the transceiver to sleep mode until its GTS slot; however for N@L mote, the transceiver acts automatically and stays in active mode during the CAP portion of a superframe. Yet, N@L stays the best candidate because of its payload of 15 compared with the payload of 30 for the MicaZ. This IEEE 802.15.4 algorithm is not suited for application since it authorizes only 7 nodes but we have taken it into account to demonstrate the feasibility and the limits of a WSN with standard IEEE 802.15.4. It has to be noticed that it is the first algorithm that can ensure a nearly 100% Packet Delivery Rate.

For the TDMA-based GTS algorithm, the PDRs can attain 100%, which prove the reliability of TDMA-based GTS algorithm based on the MicaZ and N@L hardware platforms in transmitting the sensor data to the coordinator. Yet, this IEEE 802.15.4 based sensor network fails to meet the real-time requirement of this application (1 kHz sample rate) due to the large average latency of packet. Although the average latency of packets can be reduced to 7.0 ms (in contrast with the theoretical 15.3 ms mentioned in El Tamar's work [START_REF] Xbow | [END_REF]), minimal payload is 10 samples which means that sensor node must collect 10 samples before sending them. Thus the collector node receives 10 samples at the same time, the first being 17ms old. It is interesting to notice that for the TDMAbased GTS algorithm, the power consumption of the N@L's transceiver is reduced since the microcontroller is taking in charge the communication and then can set the RF transceiver in sleeping mode.

From there, mechatronic system designers have two obvious choices : first they consider that the 9 first samples are useless and process only the last sample (this is equivalent to downgrade the effective sampling rate to 100Hz) or on the other hand they consider that they must establish a control low robust to a 17ms latency with the advantage of knowing the following coming samples. A third solution can be found: a distributed control law enabling local calculation on every node will reduce the data rate between the node and could be an interesting alternative.

Choice of an architecture node

Figure 9 allows a straightforward classification of pro and cons of each architecture from a consumption point of view. MicaZ has a low consuming transceiver but its processing unit is consuming in two aspects: data processing and analog-to-digital conversion. N@L has a low consuming processing unit but exhibits average to bad performances in RF communication. The full hardware support of the IEEE 802.15.4 standard that should be an advantage results in a consuming electronic circuit. Yet, the Packet Delivery Rates (PDR) of N@L are better than those of MicaZ (at same parameters they are better or they offer same results for lower payload), because of the hardware implementation of the MAC algorithms in MRF24J40. Furthermore, the average latencies of N@L and MicaZ are in the same order with a slight advantage to the MicaZ. This slight advantage comes from the SPI communication between ATMEL ATMega128 and TI CC2420 that is than its counterpart between PIC16LF88 and MRF24J40. In order to transmit one packet of several bytes from PIC16LF88 to MRF24J40, the address needs to be sent before each byte. However, ATMega128 only has to transmit one address before the transmission of packet. For example, PIC16LF88 needs 410 µs to transmit a packet of 10 bytes to MRF24J40, but it only takes 47.47 µs for ATMega128.

The N@L node platform is the better choice since the energy per sample (ie. the energy efficiency) is 25% to 50% smaller than its counterpart (except for the IEEE 802.15.4 GTS algorithm that supports only 7 nodes).

The two node architectures studied in this work (MicaZ and N@L) permit the constitution of two networks presenting similar results with a slight advantage for the N@L platform for its reduced consumption. Furthermore, we could infer from the table 3 and figure 9 that a third architecture based on a PIC16LF88 and a CC2420 node won't be more performing because of the lack of hardware support for IEEE 802.15.4 standard. We can expect an equivalent power consumption because of the increased consumption from the microcontroller's software support of IEEE 802.15.4 standard and a resulting degraded latency. Indeed, if the PIC16LF88 realizes the communication process, the data that will be transmitted through the SPI wires between PIC16LF8 and CC2420 will be much larger and we saw previously that the SPI communication is one of the main drawback of the PIC16LF88 microcontroller.

Conclusion and perspectives

In this paper we have presented the design of a wireless sensor network for automotive active control, from system specifications downto hardware implementation of node. From mechanical specifications of the physical phenomena, we have established the specifications of the wireless sensor network to be deployed. Then, we have used our WSN design platform to validate the WSN network structure established based on two different node architecture: MicaZ and N@L. From the simulation results, we have demonstrated that the IEEE 802.15.4 standard used is hardly suited for our application: if the samplings can be routed to the collecting node at a nearly 100% rate, the average latency generated is really to high to establish an efficient real-time control law. We have also demonstrated that the two node architectures are surprisingly similar in terms of performance with an advantage for the N@L platform for the energy efficiency.

The wireless sensor network based on N@L platform is currently being deployed on an automobile structure so as to explore the possibilities of embedding distributed control law in the network. In parallel of this validation, the following scientific fields are under investigation as a consequence of the results of this work : distributed computation, energy harvesting and structural health monitoring applications. By offering a limited communication bandwidth, WSNs cannot offer support for centralized control law but with an embedded computation unit at every node, local computation at sensor level is possible. Then active control laws could take benefit from distributed computation that may be used with centralized approach : the design are then on the distributed control laws and on the balance to establish between local control and distributed control. In an extended vision, dynamic control could be introduced by acting on this balance in a real-time approach. Energy that can be collected from vibration is high enough to enable the possibility of using sensor both as sensor and energy collector in a similar way that is currently used in structural health monitoring.

In conclusion, WSN nodes equipped with piezoelectric sensor and actuators (providing energy through harvesting and enabling local control through dissipation) should offer a performant alternative to current solutions with dynamic strategies based on the local control/global control ratio and methodologies for optimal dynamic spatial control.

Figure 1 :

 1 Figure 1: M@L wireless sensor network infrastructure.

Figure 2 :

 2 Figure 2: Classical deployment of wireless sensor network.

Figure 3 :

 3 Figure 3: Superframe structure in beacon mode.

Figure 4 :

 4 Figure 4: Piezoelectric signal conditioning circuit architecture.

Figure 5 :

 5 Figure 5: Spice simulation of the signal conditioning circuit.

Figure 6 :

 6 Figure 6: Piezoelectric signal conditioning on M@L mote.

4. 1 . 1 .

 11 Architecture of IDEA1 IDEA1 is a component-based simulation framework. Every component is modeled as an individual SystemC module communicating with each other via channels. The architecture of IDEA1 is illustrated in fig. 7.

Figure 7 :

 7 Figure 7: Architecture of IDEA1

Figure 8 :

 8 Figure 8: IDEA1 input parameters and output results

Figure 9 :

 9 Figure 9: Power consumption anatomy of the node.

Table 2 :

 2 If commonly accepted, use of simulation tools in the WSN is a subject of controversy. It is now established that these tools are effective in the comparison of solutions but not for validation before deployment IDEA1 supported devices library physique. According to analytical works of Stuart Kurkowski

	Processing unit	RF Transceiver
	ATMEL ATMega128	TI CC2420
	Microchip PIC16LF88	TI CC1000
		Microchip MRF24J40

Table 3 :

 3 Simulation results of MicaZ and N@L node.We have proceeded to simulations based on the starting point previously established and taking into account the aforementioned parameters. For every MAC algorithms, we have kept only the best results with the biggest PDR (or lowest AL if two or more cases achieve the biggest PDRs): they are presented in table 3. Each case is the average over 2500 samples and is simulated 100 times with random seeds : each metric is the average of the corresponding metrics over the 100 simulations so as to take into account the statistical nature of the RF communication. The two different hardware platforms previously presented are exploited.

Acknowledgment

The authors would like to thank I@L Carnot Institute for his financial support on this work.