Keywords: Wireless sensor networks, informationcentric networking, content-centric networking, content caching, energy efficiency, duty-cycling, interest satisfaction rate

The Content Centric Networking (CCN) is an emerging paradigm that grounds networking primitives on content names rather than node locators. CCN targets seamless mobility, native muticast/multipath support, and content oriented security to better reflect the needs of today users. CCN could greatly improve the efficiency of content delivery also in Wireless Sensor Networks (WSNs). In such a context, we place our attention on the energy efficiency of caching content placement. Our objective is to save energy while achieving a high interest satisfaction rate by study the impact of certain parameters on caching strategy. To this end, we come up with a collaborative on path caching strategy that exploits the node degree and its distance from the source. Through extensive simulations, we demonstrate that our approach achieves a energy efficiency compared to a LCE (Leave Copy Everywhere) while ensuring a good cahe hit then an important interest satosfaction rate.

I. Introduction

The massive number of heterogeneous devices made the retrieval of the content by address a hard task and motivated the development of data-centric approaches to networking. Nowadays, people use their devices to share their own contents and they are interested in getting the requested content without having an idea about its location [START_REF] Lee | Proxy-based mobility management scheme in mobile content centric networking (ccn) environments[END_REF]. To face this new demand, the Information-Centric Networking (ICN) paradigm emerged [START_REF] Xylomenos | A survey of information-centric networking research[END_REF]. Many different ICN architectures have been designed so far, all grounded on the common rationale that networking primitives should be based on content names rather than node locators. WSNs represent a very relevant example of ICN system. They are made of wireless devices equipped with sensors that are able to monitor various interests within a target environment with a distributed approach [START_REF] Amadeo | Named Data Networking: a Natural Design for Data Collection in Wireless Sensor Networks[END_REF]. Whenever, a user is interested by querying the WSN to receive an update of some measurements, he does not care about the node that will ultimately reply to his query but to the actual information that will be returned by the sensor network. In other words, this means that WSNs are ideal candidate to experiment the benefits brought by ICN architectures, as proved by the recent literature [START_REF] Amadeo | Named Data Networking: a Natural Design for Data Collection in Wireless Sensor Networks[END_REF].

One of the major issues in WSNs is energy consumption because the nodes are usually battery powered. In ICN, distributed in-network caching can alleviate energy consumption due the presence of content copies within the WSN. Consequently, building ICN enabled-WSNs may also help in optimizing energy efficiency [START_REF] Saadallah | CCNx for Contiki: implementation details[END_REF]. In our work, we explore the node degree and its distance from the source in order to optimize content placement. To formalize our approach, we focus on CCN but we argue that our approach can be applied (with some modifications) to any ICN architecture that works as a network of caches in pull mode. In CCN, a user sends an interest to ask for a specific content and the node with the corresponding content object replies to provide the asked data. Each node maintains three tables: the CS to cache contents, the FIB to store forwarded interests and the PIT to record unsatisfied interests.

In this paper, our objective is to investigate the minimum energy consumption that CCN achieves while ensuring a high interest satisfaction rate (fraction between the satisfied interests and generated interests in the network). Thus, we come up with acollaborative Caching Strategy Degree and Distance aware (CSDD). To evaluate the energy consumption, we use the mathematical model for energy in CCN/WSNs that we proposed in [START_REF] Jaber | An adaptive duty-cycle mechanism for energy efficient wireless sensor networks, based on information centric networking design[END_REF]. Finally, we implement the proposed mechanism and through extensive simulations, we show that our mechanism enhances the energy efficiency compared to LCE and LCD.

The remainder of this paper is organized as follows: in the next section, we present the related work. Section III describes the content caching strategies in CCN. The proposed caching strategy is presented in section IV. Section V details the performance evaluation. Section VII summarizes and concludes the paper.

II. Related Works

Several contributions on caching in content-centric networking exists. In this paper, we present some as follows:

In [START_REF] Kim | Cache capacity-aware content centric networking under flash crowds[END_REF] In [START_REF] Wei | Cache less for more in informationcentric networks (extended version)[END_REF], the centrality of the node is used as a parameter to select appropriate node. Centrality is measure of importance of a node in communication model. More number of times a node will come on content delivery path more centrality of the node will be. BetwCent chooses a node with the highest betweenness centrality along the content delivery path to store contents.

Bo et al., [START_REF] Chen | Brr-cvr: A collaborative caching strategy for information-centric wireless sensor networks[END_REF] proposed a collaborative caching strategy for information-centric wireless sensor network (ICN-WSN). They proposed a strategy that consists of three parts: the node betweenness based cache size adjustment, the data replacement frequency based cache decision, and the content value based cache replacement algorithm.

To summarize, too many works investigated the problem of caching in CCN. Several works treated this in ICN-WSNs. However, to the best of our knowledge, no one proposed a caching strategy that combine at the same time the degree of a node and its position and aim to reduce energy consumption, traveled path and increase cache diversity. In this paper, we aim to combine these parameters in our strategy.

III. Content Caching in Content-Centric Networking A. Caching strategies

Optimal cache placement is strictly dependent on content placement, request routing, network topology, content replacement, interest arrival rate and caching size [START_REF] Hashim | Optimal placement of relay nodes in wireless sensor network using artificial bee colony algorithm[END_REF]. For the proactive content placement, several studies exists. However, the reactive content placement which is our case is more complex due to the behavior of every node when receiving a content from another node.

1) Existing Cache placement policies: In-network caching can present some decision challenges: the cache placement (where to cache), content replacement (which content is to evict from the cache) and request routing (how to redirect requests to optimal cache). In this paper, we treat the cache placement and replacement.

a) Leave Copy Everywhere: Cache management in LCE [START_REF] Suki | Cache replacement positions in information-centric network[END_REF] is defined by its operation of caching data in every node crossed. Part of the practice of the CCN is the ability to make information readily and easily accessible. As a user sends out a request using LCE, the nature of the network serves the interest using hierarchical search and ordering of nodes to acquire a cache-hit.

b) Leave Copy Down: The Leave Copy Down (LCD) [START_REF] Suki | Cache replacement positions in information-centric network[END_REF] is a cache management strategy similar to the drop at the first neighbor process. However, it requires minimal coordination among caching nodes as they can signal to other nodes downstream whether to cache the content or not by simply appending a flag to the delivered content [START_REF] Saino | On the Design of Efficient Caching Systems[END_REF].

2) Existing cache replacement policies: The design of cache replacement algorithms is realized for content distribution purposes. When the network becomes stable and the router cache is full, a replacement policy is applied to make room for a new arrived content.

a) Least Frequently Used (LFU): the probability of each item being requested is stationary over time and independent of previous requests. In this case, the optimal replacement policy is the least frequently used, which statically places in cache the C most frequently requested items [START_REF] Saino | On the Design of Efficient Caching Systems[END_REF].

b) Least Recently Used (LRU): LRU policy keeps the data recently used and replaces with the other data. LRU has two advantages that makes it very popular, it is very responsive to non-stationary trends, since its replacement decisions are exclusively based on recency and it cannot perform significantly worse than LFU because the ratio between optimal cache hit ratio and LRU cache hit ratio is bounded [START_REF] Saino | On the Design of Efficient Caching Systems[END_REF].

c) Random replacement (RR): RR simply replaces a randomly selected item.

IV. On Path Caching Strategy for CCN enabled Wireless Sensor Network

We consider a wireless sensor network consisting of sensor nodes that interact with the environment and sense the physical data. A sensor nodes that senses and holds the original copy of a data item is called source for that particular data item. Sensor nodes frequently access the data, and cache some data locally to reduce network traffic and data access delay.

A. Cache Admission Control

When a sensor node receives the requested data or a data item passes through it, a cache admission control is triggered to decide whether it should be stored into the cache of the node or not [START_REF] Chand | Cooperative data caching in wsn[END_REF]. Inserting a data item into cache might not always be favorable because incorrect decision can lower the probability of cache hits and also makes poor utilization of the limited storage.

In our strategy, the cache admission decision at a node is based on two conditions: (i) the percentage of path from the source is it greater than ∆ ? (ii) if yes, the nodes does it has a number of neighbors greater than x ? Therefore our strategy is a 'collaborative Caching Strategy Distance and node Degree aware in content-centric enabled wireless sensor networks' called CSDD. A trade-off exists between query latency and content accessibility. With a small ∆, the number of copies for each content is high and access delay for this content object is low. On the other hand, with a larger ∆, each content has a small number of copies in intermediate nodes, and the access delay can be longer [START_REF] Chand | Cooperative data caching in wsn[END_REF]. However, this depends on the position of the user.

Fig. 1 explains the first condition of our caching strategy and ∆ variation; from how much ∆ from the source, our strategy decides to cache? In the next section, we will see the impact of this parameter on our caching strategy.

B. Cache replacement policy

Once the CS is full, our replacement policy relies on replacing the less popular content in the node content store with the new content in the content store. It aims to keep popular contents in the CS. Then our replacement policy is Popularity-based. In addition to that, the interests follow the Zipf distribution.

In our replacement policy, we suppose that popularity denoted by P of content N 1 is bigger than the popularity of N 2. Then, P (N 1) > P (N 2) > P (N 3) > ..

. > P (N n).

Since the cache size is limited, the node only caches the most popular content and evicts the less popular. If two contents of the same popularity exist when applying replacement, our strategy evicts the content having the smallest index for example if N 8 and N 7 have the same popularity N 7 is evicted.

V. Performance Analysis

In this section, we examine the performance of CSDD under different degree values x and distance ∆. We then compare it to LCE and LCD, under two replacement policies FIFO and Popularity-based. Moreover, we varied the Zipf exponent α.

A. Simulation Set-up

To implement our scheme, we use CCNx Contiki framework [START_REF] Saadallah | CCNx for Contiki: implementation details[END_REF] and we extend it to follow the requirements of our mechanism. Contiki [START_REF] Gao | Energy efficient interest forwarding in ndn-based wireless sensor networks[END_REF] is an open source operating system for the Internet of Things with memoryconstrained embedded systems and WSNs. Simulations are conducted using Cooja simulator. Fig. 2 shows how our Fig. 2: Caching strategy. strategy works if a user send an interest for a content and if ∆ is equal to 50% and x >= 3. When the requested content object is found, it is sent back to the user. Meanwhile, it is cached in nodes that fulfill the two condition related to the degree x and position from the source ∆. For the sake of illustration, we take into account not only the energy consumption modeled in the previous section but also the energy consumed due to the interests forwarding. To evaluate the energy consumption, we adopt the example of power consumption of Tmote sky.

B. Evaluation metrics

We use four main performance metrics for evaluation:

• Energy consumption: the total energy consumed by the network [START_REF] Jaber | An adaptive duty-cycle mechanism for energy efficient wireless sensor networks, based on information centric networking design[END_REF].

E n i = K i=1 p i (1 -e -piτi ) (α t txi P tx + E n pi )
+ p i e -piτi ( t rxi P rx + S coi t cai P ca

+ t txi P tx + E n pi ) + (1 -p i ) E n pi ( 1
)
• Cache hit: measured on a path when looking for a content [START_REF] Bernardini | A comparison of caching strategies for content centric networking[END_REF] which reflects the interest satisfaction rate.

Cache hit = N i=1 hits i N i=1 hits i + N i=1 miss i (2)

C. Simulation Results

In this study, we implement two cache replacement policies: the FIFO and the Popularity-based strategies. Since our interests follow Zipf distribution, we consider that different α describes different scenarios. Fig. 3: Energy consumption for all the strategies when using FIFO and Popularity-based replacement policies for 80 nodes.

For both replacement policies, it is noticed that when α increases the energy consumption decreases for all the strategies under both replacement policies. Indeed, when α increases, popular contents will be more requested by users and they will be cached more in intermediate nodes. Consequently, most of the requests cross a shorter path. In low popularity scenarios, all the strategies consumes more energy. This is due to the fact that the contents are almost requested with the same rate. Then, the replacement happens frequently increasing energy consumption.

It is also worth to note that under the FIFO replacement policy, all the strategies consume more energy. This is explained by the fact that since the interests follow Zipf distribution in both cases, when using FIFO, the probability of replacement is the same for all the contents. Nevertheless, when using the Popularity-based policy, popular contents will be kept in the caches. Therefore, the network consumes less energy consumption since requested contents will be in the cache for longer time. For instance, for α = 0.4, under FIFO, LCE consumes about 1230 mJ and CSDD (x > 2 and ∆ = 30%) consumes slightly more than 950 mJ. Yet, under Popularity-based policy, CSDD (x > 2 and ∆ = 30%) dissipates just 890 mJ and LCE consumes 1050 mJ. For low popularities, CSDD with a node degree higher than 2 and a caching distance from 30% or 50% consumes less energy than LCE, LCD and CSDD with a degree of 3 or 4. Since nodes with a degree higher than 3 represents only 16% of the network nodes, contents will not be cached on a lot of nodes then, requests will be forwarded to many nodes to find the content. Then, CSDD with a degree of 3 or 4 consumes more energy.

Cache hit ratio: We also studied the cache hit ratio for all the strategies under different popularity distribution when using both FIFO and Popularity-based replacement policies. Fig. 4: Cache hit for all the strategies when using FIFO and Popularity-based replacement policies.

The results plotted in Fig 4 have shown that when the popularity increases, the cache hit increases when using FIFO and Popularity-based. Indeed, when the α increases, the popularity of certain contents increases and they will be more requested hence they will be more available on network node. In Fig. 4a, for α = 0.2 when FIFO is used, we observe that LCE outperforms almost all the strategies (except CSDD with x > 2 and a ∆ = 30% or ∆ = 50% ). This is due to the uniform distribution of interest and to the maximum caching in nodes. However, in high popularity, CSDD with x > 3 and a ∆ = 30% or ∆ = 50% reports better performance than LCE.

For Popularity-based replacement policy, for low popularity, this time LCE presents the worst result because it is caching everywhere the same contents. However, in high popularity, it is achieving the better results since during the rush hours, there are a lot of interests sent on the network requesting the most popular contents. So, it is better to make them available. However, LCE still does not outperform CSDD with an x > 2 or x > 3 in this case. Therefore, we notice that the values of the caching are low since, in a wireless network, the interests are widely diffused increasing the number of miss since the requested content is not cached in all the network node. Then, they will be recording cache miss and decreasing the cache hit ratio. Increasing cache hit will generate the increasing in the interest satisfaction rate.

Finally, we argue that the choice of the degree must be coherent with the percentage of nodes having this degree. For instance, the results showed that the degree x > 4 realized bad results since it just represents 4% of the network nodes. Then, the number of potential candidates on which caching is realized, is low.

VI. Conclusion

In this paper, we proposed a new caching strategy that aims to find an optimal way to cache the content in order to realize better network performance. For this, we started by presenting different existing caching strategy in the literature that we implemented further. After that, we proposed CSDD an on-path caching strategy in contentcentric enabled wireless sensor networks with two parameters to vary (node degree and its distance from the source node). Finally, we presented the simulation results in order to show the impact of CSDD on energy consumption and cache hit. An interesting direction for future work is to study the performance of our strategy in terms of replacement rate, cache diversity, and network lifetime. Besides, from an experimental view, we will implement our mechanism on a the real platform of neOCampus network.

Fig. 1 :

 1 Fig. 1: Caching condition.

  Energy consumption: Figure 3 plots the results of energy consumption for the different strategies under different variation of α for two replacement policies: FIFO and Popularity-based. and ∆ = 50% CSDD with x>2 and ∆ = 30% CSDD with x>2 and from source CSDD with x>3 and ∆ = 50% CSDD with x>3 and ∆ = 30% CSDD with x>4 and ∆ = 50% CSDD with x>4 and ∆ = 30% LCD (a) Energy consumption when using FIFO. and ∆ = 50% CSDD with x>2 and ∆ = 30% CSDD with x>2 and from source CSDD with x>3 and ∆ = 50% CSDD with x>3 and ∆ = 30% CSDD with x>4 and ∆ = 50% CSDD with x>4 and ∆ = 30% LCD (b) Energy consumption when using Popularitybased.

  and ∆ = 50% CSDD with x>2 and ∆ = 30% CSDD with x>2 and from source CSDD with x>3 and ∆ = 50% CSDD with x>3 and ∆ = 30% CSDD with x>4 and ∆ = 50% CSDD with x>4 and ∆ = 30% LCD (a) Cache hit when using FIFO. and ∆ = 50% CSDD with x>2 and ∆ = 30% CSDD with x>2 and from source CSDD with x>3 and ∆ = 50% CSDD with x>3 and ∆ = 30% CSDD with x>4 and ∆ = 50% CSDD with x>4 and ∆ = 30% LCD (b) Cache hit when using Popularity-based.

TABLE I :

 I Simulation parametersLet consider a WSN deployed on an area of 100×100 m. The number of nodes varies from 80 to 240. All the sensor nodes are static and have the same detection radius. In addition, all the communication links are bidirectional. Different types of content are generated by the network. Users are modeled by application agents which polls interests. Simulation parameters are detailed in TableI.

Acknowledgment

This work is supported jointly by the neOCampus research grant [1] and the Occitanie Province.


Adda Boualem
email: adda.boualem@univ-tiaret.dz

Marwane Ayaida
email: marwane.ayaida@univ-reims.fr

Cyril De Runz
email: cyril.derunz@univ-tours.fr

Hybrid Model Approach for Wireless Sensor Networks Coverage Improvement

Keywords: Wireless Sensor Networks, Clustering, Voronoi Diagram, Area Coverage, Connected Dominating Sets

The area coverage is a non-trivial problem in Wireless Sensors Network (WSN) due to the lack of knowledge in the minimum sensor nodes set that can cover an area of interest and limitation of energy reserve, monitoring and communication ranges. Coverage protocols address two fundamental questions: how can the coverage performance of deployed sensor nodes in a monitoring region be evaluated; and how can the coverage performance be improved when wireless sensor network cannot effectively satisfy quality of service requirements? Constructing sets of minimal nodes to optimize the coverage problem push researchers to use different techniques from different domains, such as Voronoï Diagram, Connected Dominating Set, Clustering, and others. Each technique deals with the problem by its own philosophy. Our approach aims to use a hybrid model combining Diagram of Voronoï, Clustering, and Connected Dominating Set in order to benefit from the advantages of these three models to optimize area coverage, keep connectivity, and minimize energy consumption. The simulation showed the ability of our approach to ensure optimal coverage with minimal power consumption for a longtime.

I. INTRODUCTION

I N the last decade, the exponential progress of wireless communication and embedded micro-sensing (MEMS) in technologies stimulate tiny and cheap wireless nodes. The Wireless Sensor Networks (WSNs) use innovative applications to enable sensing in hostile or difficult access areas such as environmental monitoring, rescue operations, pollution detection, battlefield surveillance, Health and home entertainment [START_REF] Yaghoubi | Connectivity issue in wireless sensor networks by using depth-first search and genetic algorithm[END_REF]. Moreover, each node is able to collect, to store, to process environmental information, and to communicate with neighborhood nodes. In general, WSNs could involve hundreds or even thousands of sensing nodes. It is suitable to make these nodes as energy-efficient as possible and to rely on their large numbers in order to obtain high quality of service (QoS) results. Since sensors may be spread in a random manner; a fundamental problem in a wireless sensor network is to ensure coverage and connectivity with minimal energy consumption.

Coverage is generally interpreted as the ability of a sensor network to monitor an area of interest. It can be considered as a measure of quality of service (QoS). Getting a better QoS is solving the coverage problem.

Coverage is usually interpreted as how well a sensor network will monitor a field of interest. That is to say; how to monitor a zone or an area with minimal sets of sensor nodes? This step requires an equitable deployment with good dispersion. Moreover, it impacts directly on connectivity, quality of service and lifetime of the sensor network.

The deployment is a step of dropping the nodes of sensors on the area of interest (AoI) in equitable way with instruments such as aircraft or robots, to intend a complete coverage of the geographic area. Obviously, the area coverage can be guaranteed if the deployed sensor network can retrieve the information at every point in the region. This step directly influences the coverage, the connectivity, the topology, the lifetime of the network, so the quality of service of applications to fulfill. Hence, the process of deployment and redeployment become a major necessity.

In recent years, a several researches were carried out to solve the coverage problem in wireless sensor networks based on mathematical methods (geometry as circles, triangles The grids and rhombuses), on the graph theory (as the Voronoi Diagram and the Deloney Diagram) and on the different methods of operational research domain (as scheduling techniques). The Voronoï Diagram and Delaunay Triangulation are used to solve the energetic problems, but they are not used to solve the K-coverage problems. The Clustering and Connected Dominating Sets (CDSs) are two basic techniques used to generate the backbone for wireless sensor and ad hoc networks. The clustering process divides the nodes of a network into sets of groups of nodes named clusters. In each cluster, there is a Cluster-Head (CH), which is the responsible of the coordination and the communication data between nodes in the cluster. The selection of Clusters-Head is done via a centralized strategy (by the base station) according to a certain protocols or via a localized strategy (the selection consists of a cooperation between the neighboring nodes to select the best CH) according to others. Besides these protocols as (localized and centralized protocols) use geometric methods such as Voronoï diagram or Delaunay triangulation to detect holes in the network and to create an optimal topology of 978-1-7281-9015-0/20/$31.00 c 2020 IEEE the sensors to eliminate the holes sensed. However, most of these methods do not consider in one hand the reality of the environment in which the sensor network is deployed, and do not take into consideration the energy consumption in the other hand. Our approach uses the clustering concept to divide the geographical area under subareas (clusters) of R s diameter to ensure full monitoring by a single node that can anyone receive in each cluster. The selected node is used as the Cluster-Head; i.e. supervise of the whole cluster node and to communicate the information to the base station. Communications within a cluster can be one-jump or a multi-jump based on backbone. The backbone could contain only cluster-heads or may include some gateway nodes to enable connectivity [START_REF] Hai Liu | Wireless Sensor and Actuator Networks[END_REF]. Calculating the connected dominating set is used for controlling the uncovered portions of areas and measuring the connectivity ratio in the network.

This paper presents a new approach based the benefits of using the Voronoï Diagram, Clustering and Connected Dominating Set in a hybrid model to achieve self-optimization for area coverage. The remainder of the paper is organized as follows. In the next section (Section II), we describe related work on coverage optimization strategies. Section III presents firstly the general assumptions, and secondly provides the description of the proposed model. Section IV presents the evaluation results of our approach, and we finish by conclusion in Section V.

II. RELATED WORK

There are several ways to define coverage in WSNs, each has its advantages and its disadvantages. This section discusses few existing methods, and presents other known applications of Delaunay Triangulation (DT) and Voronoï Diagram (VD) in WSN. The Coverage Calculation Methods: which consist of the division of the area of interest into a grid of small squares, each representing one sensible area that should contain at least one sensor, as used by authors in [START_REF] Razak | Deployment density estimation for a-covering problem in wireless sensor network[END_REF], [START_REF] Haining Chen | Grid-based approach for working node selection in wireless sensor networks[END_REF] is the simplest method for assuring sensing coverage on Area of Interest (AoI). The Delaunay Triangulation and Voronoï diagram are used to quantify the Quality of Coverage (QoC) in the empty spaces between sensors. They require a spatial segmentation algorithm whose characteristics reveal the QoC information. Among the possible techniques are the Voronoï algorithm, the Gabriel graph [START_REF] Ijaz | Hop-based approach for holes and boundary detection in wireless sensor networks[END_REF] and triangulation methods. Voronoï creates a polygon around each sensor. The Gabriel graph is a sub-graph of the Delaunay triangulation edge graph, so its edges divide the plane into larger polygons. A triangulation algorithm creates a graph of edges between sensors, which segments the plane into triangles, where many mathematical procedures could be used easier than on polygons with different numbers of vertices. Recently, Voronoï diagram was applied into coverage control for wireless sensor networks [START_REF] Guoyong Dai | A novel coverage holes discovery algorithm based on voronoi diagram in wireless sensor networks[END_REF]. The AoI can be divided into several Voronoï cells. Each cell contains one sensor node. Every node could cover the cell using its circler monitoring radius. The circles in AoI are the sensing range of these nodes. Obviously, the coverage ratio is quite low and there exist holes in this case. The relationship between the sensing range of a node and its corresponding Voronoï cell may vary among the following cases: (a) the sensing range covers the Voronoï cell, (b) the Voronoï cell covers the sensing range, and (c) the sensing range and the Voronoï cell overlapped.

There are already lots of works in the literature focusing on the topic of area coverage and area coverage control in WSNs in order to improve the quality of service. Many researchers have been concerned by: area 1-coverage, area k-coverage, discovery and repairing the area k-coverage holes. Author G. Yaghoubi in [START_REF] Yaghoubi | Connectivity issue in wireless sensor networks by using depth-first search and genetic algorithm[END_REF] discussed the types of coverage problem according to different standards. He identified the coverage problem during the network deployment and provided an early solution while generating the network. Author in [START_REF] Aslam | Distributed coverage and connectivity in three dimensional wireless sensor networks[END_REF] defined a study to identify various problems related to coverage in sensor network. He provided a solution to cover the network area with a generation group over the network. He divided the network into smaller zones and then performed the coverage analysis. He also proposed a study on geometric computationbased, grid-based, etc. He studied these approaches under cost and benefit estimation. Author of [START_REF] Vijay Chandrasekhar | Localization in underwater sensor networks : survey and challenges[END_REF] has defined the cover set generation based on disjoint set analysis. This kind of analysis is based on the cover set generation under disjoint set specification. He also defined an effective scheduling mechanism to set the order of cover set activation. The static environment and deterministic deployment are used since the location of each sensor can be predetermined properly. M AX_AV G_COV and M AX_M IN _COV are two gridbased algorithms proposed in [START_REF] Dhillon | Sensor placement for effective coverage and surveillance in distributed sensor networks[END_REF], where sensors must be placed on predefined grid points distributed on the whole sensing area. These algorithms focus on average coverage as well as on maximizing the coverage of the most vulnerable grid points. M AX_AV G_COV tries to place sensors such that the average coverage of grid points will be maximized. In M AX_M IN _COV , the coverage of grid point, that is less covered, will be maximized. In [START_REF] Shakkottai | Unreliable sensor grids: Coverage, connectivity and diameter[END_REF], authors consider an unreliable wireless sensor grid-network with nodes placed in a square of unit area. They derived sufficient and necessary conditions for the relations between coverage, connectivity and diameter. In [START_REF] Wang | Efficient deployment algorithms for ensuring coverage and connectivity of wireless sensor networks[END_REF], the sensing area was presented as an arbitrary-shaped polygon possibly with obstacles. The sensing area is partitioned into smaller sub-regions based on its shape, and then sensors are deployed into these regions systematically.

III. THE DESCRIPTION AND THE IMPLEMENTATION OF THE HYBRID MODEL

Our objective behind this hybrid model (Clustering, Voronoï Diagram, and Minimum Connected Dominating Set) is to benefit from the advantages and minimize the disadvantages of these three techniques in order to guarantee the coverage in WSN area. To apply our model, it is necessary to take some assumptions into consideration, such as:

• Each node has a N um_Cluster parameter to designate the working set (group), which will be considered as a cluster in our strategy. • We consider that each set of nodes occupying the same geographical subarea constructs a cluster of nodes that shares the same task, and each sensor node can be a Cluster-Head.

• Each node has one sensing range (R s ) and two communication ranges; it communicates the collected data using the short-range communication R s c to all neighboring nodes in the cluster, and it will transmit the data to the base station using the wide-range communication R l c , as described in the Fig. 1.

• The deployment of nodes is assumed to be dense and well dispersed on the area of interest. • The base station is located in the center of the area of interest in a way that each node can communicate information directly to base station using the wide-range communication R l c . This model consists of two selections, one at the level of each cluster (Sub-area) to choose the Cluster-Head and an another selection to construct the Voronoï diagram. The purpose of this diagram is to balance the new clusters (Voronoï Cells's) in the case where some sub-areas contain only exhausted nodes, that is to say the nodes of a cluster k which are all depleted. In this case, the voronoï cells would be considered as new clusters. The selection Clusters-Head in the new clusters (cells of voronoï) and which will play the role of cover is as follows:

After the nodes' deployment step on the AoI; all nodes send a Hello message to the base station using the widecommunication range R l c . The BS divides the AoI in sub-area zones and determines for each node their cluster and sends its their cluster numbers (Construction of the Clusters).

After each time period T , all Cluster i nodes calculate their standardized energy reserve (E N or i ) and send a Hello message containing E N or i measurement for the (Selection of Clusters -Head).

The base station constructs the Voronoï Diagram in the AoI and sends all geographic positions at all activate nodes on the AoI. If a voronoï diagram cell contains more than one node, then the node which has the large energetic reserve will be activated as cluster-head and will realize the coverage in the entire polygon (the entire voronoï diagram cell). This model consists of one step to select the clusters. Another step is to select one Cluster-Head in each cluster which will play the role of covering the entire cluster and communicate the collected information towards the BS. The third step consists of calculating the Connected Dominating Sets (CDSs). This step is necessary to control the connectivity within each cluster and to measure the ratio of uncovered portions (ρ j ) of each Cluster j. The fourth step is the construction of the Voronoï diagram. The purpose of this chart is to match the new clusters (Voronoï Cells) where some sub-areas contain only depleted nodes, that is to say that the nodes of a cluster k are all depleted. In this case, the voronoi cells would be considered as new clusters. Selected Cluster-Head in new clusters (Voronoï cells), has to play the same role than the precedent Cluster-Head.

the detailed description is as follows:

Step 1 : Construction of the Clusters After their initial deployment, each sensor node sends a Hello message that contains the position to the base station. Based on this information, the base station divides the geographical area of dimension D into sub-areas of dimension L, such as:

L = √ 2 × R s (1)
The base station repetitively sends just two points among the four corners of the square: the Cluster Number N um for each subarea and P 1 and P 4 or P 3 and P 4 , and deduct the others two points. Interested nodes execute the algorithm 1 to see if it belongs to this subarea. If so, then the nodes will update their Cluster number. The pseudo algorithm showed in Algorithm 1 illustrates how to know if a point P (x, y) is in the rectangle or not. If P (x, y) is greater than D1 then x <(y-D1.coorOri) /D1. Slope; 14: If (Test_IsInSubArea (P1, P2, P3, P4)) then Num_Cluster=Num;

The subdivision of the geographic area by R s diameter of subareas aims to ensure the whole monitoring of any node in the cluster, and to ensure connectivity (communication between nodes), as shown in Fig. 5 and Fig. 2.

Step 2 : Selection of Clusters -Head

We consider each subarea as a cluster and each sensor node can be a Cluster-Head. The neighbor node that has the largest energy reserve elected as a Cluster-Head (CH). The selection of CH works as follows:

The nodes i of each cluster j calculate their standard energy reserves (E ij N or ).

E ij N or = E ij Act E 0 (2)
Where:

E ij Act : Represents the energy reserve remained of the node (i.e. n ij ; the node i of the cluster j). E 0 : represents the initial energy of a sensor node. The CH is elected based on a highest metric that combines the Euclidian distance to the center and the remaining energy of the node.

The CH node communicates the data collected using the short-range communication R s c to to elected neighbor node (Cluster-Head). This node will transmit the data to the base station using the wide-range communication R l c to minimize the energy consumption and keep the perfect coverage of the area of interest.

Step 3 : Calculating the Connected Dominating Sets

This step is necessary to control the connectivity within each cluster and to measure the ratio of uncovered portions (ρ j ) of each Cluster j, i.e. see if there is in each cluster at least one Minimal Connected Dominating Set (M CDS). Therefore, if ρ j = 1, then, the Cluster j is uncovered; if ρ j ∈]0..1[, then, the cluster is partially uncovered; otherwise (ρ j = 0), the cluster is fully covered.

Step 4 : Construction of Voronoi Diagram

This step is necessary if there are some empty clusters or the ratio of uncovered portions clusters is not null ρ j = 0. The BS constructs the AoI Voronoï Diagram to delineate the new clusters. After that, it returns to each active node (probable Clusters-Head) on AoI all the positions and thus their cluster numbers that they contain. This aims to reach the full coverage on the whole interest area with the rest of the living sensor nodes in the network. Otherwise, the base station keeps the same old cluster structure. After a predetermined period T by the base station; all nodes will be activated and will they send a Hello message to the neighboring nodes in the cluster containing the information of the energy left using short-communication range (R s c ). The current CH sends more gathered information during its monitoring period using R s c to neighboring nodes. The nodes in each cluster compare their left energy with other neighbors. Then, the node that has the largest energy reserve will automatically be activated and be considered as the cluster-head. However, the other nodes will return to the passive state. New CHs send Hello messages to the base station (containing the geographical position and the collected information in the previous period) using the R l c . The BS calculates the ratio of the uncovered portion (ρ) and decides if it is necessary to construct the clusters by Voronoï Diagram. These steps will run until the exhaustion of the whole network. Fig. 2, shows an example of the subdivision of the geographic area, Clusters, CDSs and Clusters-Head.

IV. SIMULATION AND EVALUATION

In this step, we have defined the protocols used in the simulation, cited their strengths and weaknesses in order to make a good comparison. Then, we quoted the parameters of the simulation, and presented the simulator used. We ended this part by analyzing the results found in terms of the coverage rate, the rate of energy consumption consumed and in terms of the rate of nodes remaining alive.

A. Strengths and weaknesses of simulation protocols

• The NLAC protocol uses Clustering as a node activation planning technique (active / passive), but the one-time clustering application to allow for the proper distribution of the sensor nodes does not show a major benefit in the coverage. other planning mechanisms are needed to allow the network to be redistributed equitably. • The IDA-OFCA protocol is proposed to make a fully distributed decision to select the active nodes, but to ensure the good distribution of the sensor nodes in the network by the mechanism used by IDA-OFCA it is necessary that the network is very dense and well deployed. , the more it requires the mobility of sensor nodes as a condition to keep the distribution fair in the network. The thing that quickly depletes the network. • The VAC protocol is proposed to address weaknesses of protocols that rely on completion to equitable distribution. This protocol uses clustering, and Voronoï diagram to ensure maximum coverage, based on decision algorithms that use greedy calculation of the distribution, the thing that exhausts the network in the first rounds of application of this protocol.

B. Simulations Parameters

The experiments were conducted using MATLAB Simulator. All the sensor nodes are homogeneous(same widecommunication range, short-communication range and the same sensing range). The simulation parameters used are listed in Table I [START_REF] Guoyong Dai | A novel coverage holes discovery algorithm based on voronoi diagram in wireless sensor networks[END_REF].

C. Simulation illustration

The base station divides the area of interest using R s = 28.28m as diameter of each square cell (cluster). With a well dispersed deployment of 200 sensor nodes, each cluster can contain from 5 to 6 sensor nodes. The duration of the simulation is 1000s, which contains 50 Rounds. We scattered different five ( 5) trials (varying from 200, 400, 600, 800 and 1000 of sensor nodes) in the AoI with uniform density. We evaluated the average of the coverage ratio and the average of the energy consumption while varying the number of deployed sensor nodes on the AoI. We compare our proposed protocol denoted V D_C_CDS with three 4) tested protocols after 50 times of BS, according to number of deployed nodes within the 5 trials over the AoI. Our proposed protocol (V D_C_CDS) shows a full coverage progress of the AoI from 94% to 96.5% depending on the number of sensor nodes, which is fairly scattered on AoI, and for different densities of deployed networks, especially, when the density is dense knots of the long coverage lasts through Voronoï-based area coverage mechanism (V AC) protocol against the protocols: N LAC and IDA_OF CA show less coverage and they do not exceed 95%, 90% and 77.5% respectively for the V AC, N LAC and IDA_OF CA after 50 rounds, when the nodes density reaches 1000 nodes.

2) Energy Consumption Rate: Fig. 6.(b) shows the average energy consumption to ensure coverage of the four protocols after 50 times of BS according to the number of deployed nodes within 5 trials. Our proposed protocol (V D_C_CDS) shows a minimal and efficient energy consumption to ensure full area coverage by deployment of the sensor nodes, from 65% for 200 nodes to 15.5% for 1000 deployed nodes of the network total energy after 50 rounds. However, the three others protocols show energy consumption reduction at 18%, 32% and 58.5% respectively for the V AC, N LAC and IDA_OF CA even when the density of nodes arrived to 1000 nodes. 3) The Remained Active Rate: The Fig. 6.(c) shows the rate of remained active nodes of the four protocols after 50 times of BS a final according to the number of deployed nodes of 5 trials. Our protocol shows its effectiveness through the large number of remained sensor nodes. In fact, it reached a percentage of 80% at a density of 800 nodes after 50 rounds times. The V AC, N LAC and IDA_OF CA show a percentage reached to 70%, 48%, 40% for 1000 sensor network nodes. The main idea behind the use of clustering was to activate a single sensor node in each cluster; for playing a multiple role; a role of Cluster-Head, a role of coverage in the entire cluster and a role of communication sender of the information to the base station.

To check the connectivity in each cluster and to measure the portion rate of uncovered areas, we used the CDSs concept. If the rate of uncovered portions is not null, then the Voronoï Diagram reconstruction is required. Thanks to benefits of the proposed protocol, the application reach a coverage of 96.5% of AoI, as shown in the simulation results, and preserve the connectivity until the network depletion. As a future works, we intend to use the proposed hybrid technique to apply it into 3D WSN coverage study. We aim to study its efficiency in 3D cases.

Algorithm 1 3 : 4 : 9 :

 1349 Pseudo Algorithm for cluster construction 1: Test_IsInSubArea (P 1 , P 2 , P 3 , P 4 , Num) : Boolean 2: Step 1: The square ABCD, which passes through the four points (P1 (x1, y1, z1), P3 (x3, y3, z3), P4 (x4, y4, z4), P2 (x2, y2, z2)); Step 2: Consider x1 is the smallest abscissa, and y3 is the largest coordinate, such: x1=x2, x3=x4, y1=y3 and y2=y4; Step 3: The straight lines: Step 4: Check the position of the point (p) with respect to the line; 10: If P (x, y) is less than D2 then y <D1.pente * y + D1.CoorOri; 11: If P (x, y) is greater than D4 then y> D2.pente * y + D2.CoorOri; 12:If P (x, y) is lower than D3 then x <(y-D3.coorOri) /D3. Slope;13:

Fig. 1 .

 1 Fig. 1. Communication and Sensing ranges.

Fig. 2 .

 2 Fig. 2. Clustering Concept.

Fig. 3 .Fig. 5 .

 35 Fig. 3. {g, b}, {g, a, c} and {g, a, c, d} are CDSs, {f, d} is Minimum Connected Dominating Set.

( 3 )

 3 state of art works, namely N LAC[START_REF] Aslam | Distributed coverage and connectivity in three dimensional wireless sensor networks[END_REF], IDA -OF CA[START_REF] Vijay Chandrasekhar | Localization in underwater sensor networks : survey and challenges[END_REF] and V AC[START_REF] Selina Sharmin | Area coverage for clustered directional sensor networks using voronoi diagram[END_REF]. The simulation results of the average coverage percentage according to the number of deployed nodes after 50 rounds are shown in Fig. 6.(a) The simulation results of average energy consumption percentage of monitoring according to the number of deployed nodes after 50 rounds are shown in Fig. 6.(b) Simulation results showing the number of sensor nodes percentage remain active after 50 rounds are presented in Fig. 6.(c) D. Results Analysis 1) The Coverage Rate: Fig. 6.(a) shows the average percentage of AoI coverage of the four (

Fig. 6 .

 6 Fig. 6. (a.) The average coverage percentage VS the number of deployed nodes. (b.) The average energy consumption of monitoring percentage VS the number of deployed nodes. (c.) the number of sensor nodes percentage remaining active VS the number of deployed nodes.

  V. CONCLUSION The three techniques; (a) Voronoï Diagram, (b) Minimum Connected Dominating Set, and (c) Clustering are among the best optimization techniques already proposed in the area coverage in WSNs. Our contribution is to hybridize these techniques to gain the benefits and minimize the disadvantages of these techniques. A technical hybrid Model of: Clustering, Connected Dominating Sets and Voronoï Diagram is implemented to optimize a NP-Hard area coverage problem.


Abdelhak Mekahlia
email: abdelhak.mekahlia@vedecom.fr

Eric Semail

Franck Scuiller
email: franck.scuiller@ecolenavale.fr

Hussein Zahr
email: hussein.zar@vedecom.fr

M Abdelhak Mekahlia

Torque-Speed Characteristic Improvement in Nineteen-phase

Keywords: Multiphase Induction Machine, Pole-changing, Speed Range Extension, Stator Phase Connection, Torque Enhancement, Traction application

come

I. NOMENCLATURE

-N : Phase number.

p : Number of pole-pairs under 1 st stator supplying sequence. -I : Current in the inverter phase "k". -I : Amplitude of rated inverter output current. -S : Apparent power delivered by the inverter.

f : Frequency of inverter currents φ : Phase of inverter currents -I : Current in the stator phase "k".

-I : Amplitude of rated stator phase current. -V : Amplitude of rated stator phase voltage. -V : DC bus voltage.

-SH : shift between two connected phases.

u: stator sequence (injected current harmonic).

-EGB : "Electrical Gearbox" ratio.

II. INTRODUCTION

ultiphase induction machines have shown great advantages regarding torque density which can be improved thanks to simultaneous injection of different harmonics of stator current (non-sinusoidal currents) [START_REF] Abdel-Khalik | Optimum Flux Distribution With Harmonic Injection for a Multiphase Induction Machine Using Genetic Algorithms[END_REF]- [START_REF] Kong | Nonsinusoidal Power Supply Analysis for Concentrated-Full-Pitch-Winding Multiphase Induction Motor[END_REF], and speed range which can be extended thanks to the polechanging technique (sequential injection of harmonics) [START_REF] Patzak | ISCAD -Electric High Performance Drive for Individual Mobility at Extra-Low Voltages[END_REF]- [START_REF] Reddy | A five speed 45-phase induction motor drive with pole phase modulation for electric vehicles[END_REF]. Furthermore, multiphase machines are more adapted for A . Mekahlia and E. Semail are with Univ. Lille, Arts et Metiers Institute of Technology, Centrale Lille, HEI, L2EP -ULR2697, HESAM Université, F-59000 Lille, France (e-mail: abdelhak.mekahlia@ensam.eu and eric.semail@ensam.eu). fault-tolerant operations and offer more degrees of freedom regarding winding configurations [START_REF] Dajaku | Opportunities of advanced multiphase concentrated windings[END_REF].

For the inverter, high phase numbers allow a better use of the DC-Bus voltage by injection of different harmonics [START_REF] Levi | Analytical determination of DC-bus utilization limits in multiphase VSI supplied AC drives[END_REF], a reduction of the DC-link capacitor size [START_REF] Vujacic | Evaluation of DC-Link Voltage Switching Ripple in Multiphase PWM Voltage Source Inverters[END_REF] and of the inverter losses [START_REF] Kesbia | Impact of the number of phases on losses of a multiphase inverter for electric vehicle drive[END_REF].

In multiphase induction machine, different stator sequences can be used to supply the machine, while only one sequence is possible for three-phase machines, thanks to the separation of space harmonics into several -planes when the number of phases is greater than three [START_REF] Fudeh | Modeling and analysis of induction machines containing space harmonics: Part I: Modeling and Transformation[END_REF], [START_REF] Mekahlia | Reduced-Order Model of Rotor Cage in Multiphase Induction Machines : Application on the Prediction of Torque Pulsations[END_REF]. A stator sequence corresponds to the order of supply of stator phases. For example, the sequence "1" corresponds to the order: ph1, ph2, ph3 … and the sequence "2" to the order: ph1, ph3, ph5… Each stator sequence "u" generates a set of rotor current harmonics and induces a particular number of magnetic pole-pairs "u.p1" in the machine [START_REF] Jia-Qiang | Electronic pole changing technique of multiphase induction motor based on vector control[END_REF], [START_REF] Mekahlia | Impact of Winding Parameters on Torque Level under Harmonic Injection in Multiphase Induction Machine[END_REF].

With multiphase machines, this theoretical ability to electronic pole-changing by switching the stator supply sequences, can be used to enlarge the operating zone obtained classically by flux weakening in three-phase induction machines. The sequences inducing high polarities can be used for High-Torque-Low-Speed regions and the sequences inducing low polarities can be used for Low-Torque-High-Speed regions [START_REF] Osama | A new inverter control scheme for induction motor drives requiring wide speed range[END_REF].

The challenge is to obtain practically the pole-changing with efficiency. For a given power of Voltage Source Inverter, the windings factors of the machine associated to the used stator sequences (different polarities) must be sufficiently high [START_REF] Mekahlia | Impact of Winding Parameters on Torque Level under Harmonic Injection in Multiphase Induction Machine[END_REF]. It is also necessary to choose the adequate winding connection which allows to use efficiently the different polarities with a given peak amplitude of the VSI current [START_REF] Edelson | High phase order ac machine with short pitch winding[END_REF].

Switching between the supply sequences allows a better magnetic use of the machine iron. On the other hand, switching the supply sequences with phase-to-phase connections (like the Pentagon for five-phase machines) changes the amplitudes of stator currents and voltages for the same inverter power (as described in the section III of the paper). This aspect is the subject of "The Chorus Meshcon patent" [START_REF] Edelson | High phase order ac machine with short pitch winding[END_REF], [START_REF] Edelson | The Chorus Meshcon solution for starter-generators[END_REF].

This paper aims to investigate how to choose a stator phase connection allowing to improve the torque-speed characteristic in a multiphase induction machine with polechanging operation. Firstly, a mathematical representation of stator phase connection is provided with some examples of multiphase connections and their effects on stator current and voltage. Then, an application on nineteen-phase machine with special connection for traction application is presented, the torque-speed characteristic of this machine is obtained thanks to a Finite-Element approach and compared to a three-phase machine with the same global volume and the same inverter power.

III. MATHEMATICAL REPRESENTATION OF PHASE

CONNECTION

A. Three-phase machine

The connection between stator phases impacts the amplitudes of stator current and voltage. In the case of threephase machine, only two connections are possible: star and delta. For the star connection, the amplitude of the stator current I has the same value as the inverter current I and the amplitude of rated stator voltage V is equal to (if we assume a simple PWM control of the inverter). For the delta connection, I = √ and V = . √3.

The delta connection allows to obtain a higher voltage in stator phases and a lower current, it could be preferred for applications requiring high speed with a low torque. For example, the classical Delta/Star starting uses this property (using switches to change the connection).

B. Multiphase machine

In the case of multiphase machine, the number of possible connections is higher, a star connection is always possible, whatever the number of phases is. In the other hand different "phase-to-phase" or "polygonal" connections are possible, their number depends on the phase number.

For example, in the case of five-phase machine, three different connections are possible [START_REF] Sadeghi | Wide operational speed range of five-phase permanent magnet machines by using different stator winding configurations[END_REF]: star, pentagon and pentacle. As the case of three-phase machine, the star connection presents the same amplitudes of inverter and stator currents, and a maximum reachable peak stator voltage close to V = . With five phases, two "polygonal" connections are possible, pentagon by connecting each phase to the adjacent phase (1-to-2, 2-to-3, 3-to-4 …), and pentacle by shifting one phase to connect (1-to-3, 2-to-4, 3-to-5 …).

A five-phase machine can be supplied by different stator sequences (current harmonics), if the connection is "polygonal" (pentagon or pentacle), stator current amplitude depends on the connection and the sequence.

Fig. 1 shows how the stator current amplitude changes in function of the phase connection and the supply sequence. In the case of a five-phase machine, for example, if the current required under the 3 rd sequence is more important than the one under the 1 st sequence at a fixed inverter current, the "pentacle" connection should be chosen. On the other hand, with the pentacle connection, the rated stator voltage is higher under the 1 st sequence (adapted to reach high speeds). More generally, as described in the Chorus Meshcon patent [START_REF] Edelson | High phase order ac machine with short pitch winding[END_REF], for a given number of phases N , the number of possible "polygonal" connections is floor . A polygonal connection can be obtained by connecting each stator phase to another phase. The shift between two connected phases, called "SH ", can be defined as follows:

SH ϵ 1 ⋯ floor (1)
For example, the "pentagon" connection in a five-phase machine corresponds to "SH = 1", the "pentacle" connection corresponds to "SH = 2". SH = 2 is the maximum for a five-phase machine according to equation [START_REF] Abdel-Khalik | Optimum Flux Distribution With Harmonic Injection for a Multiphase Induction Machine Using Genetic Algorithms[END_REF].

In a multiphase machine with a "polygonal" connection and supplied by a sequence "u" (the stator current sequence), the rated stator current amplitude in function of the amplitude of rated inverter current can be expressed as follows:

I = . . . (2)
Therefore, the rated stator phase voltage can be defined as follows:

V = 2. sin SH . u. (3)
According to equations ( 2) and ( 3), the choice of a "polygonal" connection (parameter "SH ") and the use of different sequences (parameter "u") in order to supply the stator of a multiphase machine have an effect of "electrical gearbox" whose ratio can be defined as follows:

EGB = . . . (4)
If "EGB < 1" the stator current is lower than the inverter current, and the stator voltage is higher than , which is well adapted to the operating points at high speed and low torque (vice versa for "EGB > 1").

C. Examples and validation using Simplorer

The Table I shows some examples of "EGB " for different multiphase connections under different stator sequences. The maximum "EGB " that can be obtained raises with the phase number (1.15 for 7-phase, 1.93 for 12phase and 3.04 for 19-phase). For high phase numbers, the "electrical gearbox" effect is more important.

In some cases in Table I, "EGB " is equal to ∞, like the 12-phase connection with "SH = 6" and under even-order stator sequences. In fact, for these cases, the stator voltage V is null, which is a kind of short-circuit induced by the connection under some sequences. Hence, the combinations with "SH . u = N ", where all stator phases are shortcircuited, must be avoided. Thus, for prime phase numbers, like 7 or 19, this kind of short-circuit situation is not possible. The values shown in the Table I are verified using "Simplorer software". Fig. 2 shows an example of the modeling using this software (all the connections presented in Table I are modeled, only one example of 7-phase is shown). The inverter is controlled by PWM. The sequence used to supply the inverter phases is "u", so the current in a phase "k" can be expressed in equation ( 5):

I = I . sin 2π. f . t -k -1 . u. + φ (5)
As explained above, when the connection is "polygonal", switching the sequence "u" allows to change the amplitude of stator current and voltage, for the same amplitude of inverter current.

The inverter current, stator current and stator voltage are measured as illustrated in Fig. 2 (Amperemeters for Is and Iinv, Voltmeter for Vs). The "EGB " can be obtained by dividing the value of on the measured fundamental component of stator voltage V , or by dividing the measured fundamental of stator current I on the fundamental of inverter current I (according to equations ( 2) and ( 3)). The calculated values thanks to Simplorer simulations are the same as presented in the Table I.

IV. SPEED RANGE EXTENSION IN NINETEEN-PHASE INDUCTION MACHINE

A nineteen-phase induction machine, for traction application, is sized to operate under three different stator sequences. The connection chosen for this machine is "polygonal" with "SH = 4" (the last column of the Table I), as shown in Fig. 3. In a multiphase machine, operating under different sequences, hence different magnetic pole-pairs numbers [START_REF] Mekahlia | Impact of Winding Parameters on Torque Level under Harmonic Injection in Multiphase Induction Machine[END_REF], the sequences inducing high polarities are usually used for operating region with low speed and high torque. In fact, the high sequences (high polarities) allow a better use of the stator and rotor iron (yokes) which favors the torque density but with an important back-EMF, hence the maximum stator voltage is reached at low speed. Therefore, the low sequences (low polarities) are used for operating region with high speed and low torque.

The "polygonal" connection with "SH = 4" is chosen in order to use the sequences "u=3,4 and 5" in an optimal way. The 5 th sequence, naturally favoring high torque with low speed, has an "EGB " of 3.04, so the stator current is approximately three times the inverter current, but the maximum stator voltage is low ( * .

), this "EGB " is well adapted to deliver important torque. The 4 th sequence has an "EGB " of 1.05, so lower stator current and higher stator voltage than the 5 th sequence. The 3 rd sequence is used to reach important speed levels with low torque, thanks to its low polarity and its "EGB " of 0.55. This nineteen-phase induction machine with this special phase connection is compared to a three-phase induction machine, regarding operating Torque-Speed characteristic using F-E simulations (Maxwell Software).

A. Three-phase machine

The parameters of the three-phase induction machine, considered as reference for comparison, are listed in the Table II. This machine is simulated by F-E software (Maxwell), by imposing stator current and mechanical speed. The machine geometry with the poles distribution is illustrated in Fig. 4. In this kind of simulations, the stator current (amplitude, sequence and frequency) and the mechanical speed (slip) are imposed, so the stator EMF is determined by Maxwell (after achieving the numerical steady state). By increasing the imposed speed, the stator EMF raises. This EMF is limited to the maximum stator voltage (200 Vpeak for this machine), and this limit corresponds to the base speed. Therefore, to determine the base speed, simulations on different mechanical speed values are done. For each speed value, the stator voltage is determined by Maxwell, and the speed corresponding to the maximum stator voltage of 200 Vpeak is determined by extrapolation. For a given synchronous speed, the slip (so the rotor frequency) that maximizes the torque is found by parametric variation on Maxwell. Then, three simulations are done, to determine the base speed by extrapolation, as shown in Table III. Fig. 5 illustrates the voltage signals for the three operating points (maximum torque with different synchronous speeds).

B. Nineteen-phase machine

The parameters of the nineteen-phase induction machine are listed in the Table IV. This machine has the same global volume as the three-phase machine (considering the external stator diameter and active length).

The 19-phase inverter delivers approximately the same apparent power as the three-phase inverter, where: S = .

. I = 103.8 kVA (6) S = .

. I = 104.5 kVA

The chosen winding distribution allows to have important even order space harmonics, so the sequence 4 can be used to supply the machine and with a high winding factor of 0.99. In fact, unlike the three-phase machine, with 19 stator phases the space harmonics are separated into 9 different -planes, so the presence of even order harmonics has a positive effect. In fact, a pole-changing operation with even polarities, like this case of 3-4-5 pole-pairs, is smoother than the case without even sequences. On the other hand, under a given stator sequence the resulting magnetomotive force does not contain harmonics with important amplitudes, for example under the third sequences, the generated space harmonics are 3, 16, 22 … under this sequence the fundamental corresponds to the third space harmonic, and the other harmonics (16, 22 …) have a high order, hence their amplitudes are not important. Fig. 6 shows the machine geometry with poles distribution under the three imposed polarities. This machine is simulated by F-E software (Maxwell), by imposing stator current and mechanical speed, for the three stator sequences "u=3, 4 and 5".

Firstly, the maximum torques developed under the rated inverter current are determined by sweeping the slip (rotor frequency), for the three supply sequences (thanks to the chosen winding connection, stator current amplitudes are different from a sequence to another, for the same inverter current). Fig. 7 illustrates the maximum torque (with the optimal rotor frequencies) for the nineteen-phase induction machine under the three different polarities (sequences) compared to the three-phase machine maximum torque. Three simulations were done under each sequence, to determine the base speeds by interpolation, as shown in Table V for the stator sequence "3", Table VI for the stator sequence "4" and Table VII for the stator sequence "5". Fig. 8 illustrates the voltage signals under the three polarities, for the three simulations points (synchronous speeds).

Comparing to the three-phase machine, the nineteen-phase machine with its special connection of phases allows to extend the speed range thanks to the use of the third stator supply sequence whose base speed is 18000 rpm, more than two times the base speed obtained with the three-phase machine. On the other hand, the use of the fifth sequence, where the stator current is amplified thanks to the connection, allows to obtain higher torque at low speed for the same inverter current. The torque-speed characteristics (considering only the constant maximum torque region below the base speed) for both machines (3-phase and 19-phase with the three polarities) are illustrated in Fig. 9. On this figure, the nineteen-phase induction machine with its special connection, and the use of three different stator sequences, presents clearly a very important extension of the torque-speed characteristic comparing to the three-phase machine. The simulated operating points (shown in Table III, Table V, Table VI and Table VII) by Maxwell are marked with red crosses in Fig. 9. The torque and mechanical speed are specified in "p.u" in the figure considering the maximum torque and base speed of the three-phase machine (Table III) as reference.

The torque-speed characteristic, is extended vertically thanks to the use of the fifth stator supplying sequence where the torque can reach 300 N.m (maximum of 96 N.m for the three-phase machine), the values of stator current density (per conductor) are shown in the legend of Fig. 9, with the fifth sequence an important stator current supplies the winding, hence the current density is more important than the other sequences, which requires more sophisticated cooling system.

The torque-speed characteristic is also extended horizontally thanks to pole-changing operation. The nineteenphase machine with its lowest polarity reaches a base speed of 2.2 p.u (considering the base speed of the three-phase IM as a reference 1 p.u) which represents a very significant enhancement. It must be mentioned that this extension is obtained with almost the same inverter power as the threephase drive (as shown in the figure 103.8 kVA for the 3-phase inverter and 104.5 kVA for the 19-phase inverter). It should be noted that Fig. 9 does not consider the flux weakening regions (for the 4 characteristics) because the F-E simulations were done only for operating points at maximum torque. Of course, with flux weakening the three-phase induction machine can reach 2 to 3 times the base speed [START_REF] Fuchs | Analysis of criticalspeed increase of induction machines via winding reconfiguration with solid-state switches[END_REF]. However, the flux weakening can also be operated for the three polarities in the nineteen-phase machine, which can allow to provide constant power curves between the maximum power points for each polarity. Under the lowest polarity of the 19-phase IM (p = 3), which have an important base speed, the flux weakening operation can be operated to reach very high speeds (unreachable with the three-phase machine).

V. CONCLUSION

In this paper, the effect of stator sequence switching with specific phase connections on the stator current and voltage has been investigated. A mathematical representation of the stator connection has been provided and it allows to determine the amplitudes of stator current and voltage for a given inverter current and DC voltage.

An application on a nineteen-phase induction machine with a special stator phase connection allowing to extend the torque-speed characteristic has been presented. Thanks to Finite-Element approach, the torque-speed characteristic of this machine with pole-changing operation has been estimated and compared with a three-phase induction machine with the same global volume and the same inverter power.

The results show a very significant extension of the torquespeed characteristic vertically (improvement of torque density) and horizontally (improvement of speed range), thanks to the pole-changing operation and the chosen phase connection for the nineteen-phase induction machine.

This extension is obtained with the same machine volume as the three-phase machine, thanks to a better use of the machine iron with the multipolarity operation, and with the same inverter power thanks to the "electrical gearbox" effect presented in this paper, so there is no need to oversize the inverter components in order to reach more important torque (obtained here with the sequence "5"). Of course, even if this high torque is obtained with the same inverter current, the stator current density is higher than the other sequences, so the cooling system must be adapted. This torque speed-characteristic improvement is obtained with a fixed stator phase connection, so without dedicated switches to change physically the machine coupling and which increase the complexity of the drive.

Fig. 1 .

 1 Fig. 1. Stator current amplitude for pentagon and pentacle connections under 1st and 3rd sequences.

  1.15 0.63 1.93 0.71 0.5 3.04 0.81 u = 2 0.64 0.51 1 0.5 ∞ 1.54 0.51 u = 3 0.51 1.15 0.71 0.71 0.5 1.05 0.55 u = 4 0.51 1.15 0.58 ∞ ∞ 0.81 1.05 u = 5 0.64 0.51 0.52 0.71 0.5 0.68 3.04

Fig. 2 .

 2 Fig. 2. 7-phase connection with "SH = 1" modeled by Simplorer

Fig. 3 .

 3 Fig. 3. Polygonal connection with "SHph=4" for the nineteen phase machine.

Fig. 4 .

 4 Fig. 4. Poles distribution for the three-phase machineFirstly, the maximum torque developed under the rated stator current (346 Apeak) is determined by sweeping the slip (difference between the synchronous speed and mechanical speed).In this kind of simulations, the stator current (amplitude, sequence and frequency) and the mechanical speed (slip) are imposed, so the stator EMF is determined by Maxwell (after achieving the numerical steady state). By increasing the imposed speed, the stator EMF raises. This EMF is limited to the maximum stator voltage (200 Vpeak for this machine), and this limit corresponds to the base speed. Therefore, to determine the base speed, simulations on different mechanical speed values are done. For each speed value, the stator voltage is determined by Maxwell, and the speed corresponding to the maximum stator voltage of 200 Vpeak is determined by extrapolation.

Fig. 5 .

 5 Fig. 5. Stator phase voltage for the three-phase IM for three different synchronous speeds.

Fig. 6 .

 6 Fig. 6. Poles distribution for the nineteen-phase IM under three polarities (stator sequences)As seen in the Table IV all of the used sequences (3, 4 and 5) to supply the stator are characterized by important harmonic winding factors, which allow a good torque capability.This machine is simulated by F-E software (Maxwell), by imposing stator current and mechanical speed, for the three stator sequences "u=3, 4 and 5".Firstly, the maximum torques developed under the rated inverter current are determined by sweeping the slip (rotor frequency), for the three supply sequences (thanks to the chosen winding connection, stator current amplitudes are different from a sequence to another, for the same inverter current). Fig.7illustrates the maximum torque (with the optimal rotor frequencies) for the nineteen-phase induction machine under the three different polarities (sequences) compared to the three-phase machine maximum torque.

Fig. 7 .

 7 Fig. 7. Comparison of torque between three-phase IM with one polarity, and nineteen-phase IM with three polarities (the winding connection allows different stator current amplitudes for the same maximum inverter current).

Fig. 8 .

 8 Fig. 8. Stator phase voltage for the nineteen-phase IM, under the three polarities (three synchronous speeds for each polarity).

Fig. 9 .

 9 Fig. 9. Torque-Speed Characteristics comparison between 3-phase induction machine, and 19-phase induction machine supplied by 3 sequences.

  for 19 phase IM with the polarity p=3

TABLE II THREE

 II -PHASE INDUCTION MACHINE PARAMETERS.

	Parameter	Unit	Value
	Phase Number		3
	Pole-pairs		2
	Winding factor		0.96
	External stator diameter	mm	245
	Active length	mm	210
	Rated Power	kW	80
	DC Voltage	V	400
	Maximum inverter current	Apeak	346
	Connection		Star
	Maximum stator current	Apeak	346
	Maximum stator voltage	Vpeak	200
	Rotor Cage		Aluminum

Stator phase voltage (V)

Synchronous speed = 3000 / Mechanical speed = 2984 Synchronous speed = 15000 / Mechanical speed = 14984 Synchronous speed = 18000 / Mechanical speed = 17984 Stator phase voltage (V)


Amélie Beauville

Dit Eynaud

Nathalie Klement
email: nathalie.klement@ensam.eu

Lionel Roucoules

Olivier Gibaru

Laurent Durville

Risk and decision analysis for Reconfigurable Assembly System Design under uncertainties

Keywords: Changeability, Reconfigurability, Reconfigurable Assembly System, Decision Support Tool, Decision analysis

To face the variable demand of the market, modular and mobile equipment are integrated on production lines. Previous works proposed design and evaluation methodologies to build reconfigurable production systems. However, taking the right decision concerning investments and the choice of equipment may be complex. In this paper, we present RAS design from a risk and decision analysis perspective to support decision making. Market demand scenarios are associated with occurrence probabilities. A decision tree represents consecutive scenarios, for which the decision maker is proposed to make a choice regarding investments for the assembly line. The utility function is computed based on the decision makerâs attitude to risk. The objective function computing the final score of a scenario and a decision covers investments, reconfigurability rate and performance of the system. Implications of early investments towards reconfigurability can be identified. The approach is applied on a real use case from the automotive industry.

INTRODUCTION

To face a volatile and unpredictable customer demand, developments of a new generation of production systems, Reconfigurable Manufacturing and Assembly Systems (RMS and RAS), have been carried out. [START_REF] Koren | Reconfigurable Manufacturing Systems[END_REF] formalized the paradigm of reconfigurability in Production Systems (PS), and defined six core characteristics of production systems: scalability, modularity, integrability, customisation, convertibility and diagnosability.

Fluctuations of the market imply the need of a production system able to follow changes in terms of product type or production volume. Depending on the economical context, companies need to quickly configure and set adjustment parameters of the system. In order to achieve these quick changes, RMS and RAS integrate modular tools and machines, and easily movable equipment (Beauville dit [START_REF] Beauville Dit Eynaud | UMLbased reconfiguration rate analysis of assembly line depending on robot integration[END_REF]. An important point is also to integrate consideration of changeability at early stages of production system development [START_REF] Andersen | A participatory systems design methodology for changeable manufacturing systems[END_REF]. Companies are not familiar with changeable systems and research works focus on supporting the industry in the process of RMS integration. Furthermore, decision makers struggle with the evaluation of new generation PS on criteria which are hardly comparable on a same scale. Indeed, the comparison of performance metrics with reconfigurability indicators is questionable. We aim to support RMS Design by answering the question of how to invest and adjust in the best way the production system.

During the PS life-cycle, the economical context will change. In this paper, the demand is modeled by scenarios, for which are periods of time are corresponding to a market requirement, for which a configuration has to be selected. In the proposed Reconfigurable Production System Design Problem (RPSDP), consecutive scenarios are considered, and implications of early decisions in a previous scenario are taken into account in next scenarios. In this paper, a "scenario" corresponds to the succession of a decision step followed by a market evolution (event). The problem to solve is the choice to invest or not in a new resource for each time period, without knowing with certainty how the market will change.

STATE OF THE ART

Decisions in reconfigurable production systems design

Previous research focused on providing support tools for companies to choose appropriate resources and PS configuration in the design process. [START_REF] Andersen | A participatory systems design methodology for changeable manufacturing systems[END_REF] and [START_REF] Beauville Dit Eynaud | Framework for the design and evaluation of a reconfigurable production system based on mobile robot integration[END_REF] proposed RMS/RAS design methodologies, covering design steps from needs identification to final decision.

In order to support the design process, reconfigurability metrics have been investigated and developed based on the six core characteristics of reconfigurability [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF][START_REF] Rösiö | Towards an assessment criterion of reconfigurable manufacturing systems within the automotive industry[END_REF][START_REF] Beauville Dit Eynaud | Framework for the design and evaluation of a reconfigurable production system based on mobile robot integration[END_REF]. In particular, (Beauville dit Eynaud et al., 2020) defined quantitative metrics for reconfigurability evaluation of RAS, and compared obtained metrics with performance indicators evaluated by discrete event simulation (DES). Results are then made available on a dashboard for the decision maker.

However, during the design procedure, the company needs to evaluate various technical solutions (for example fixed, movable or mobile robots), several layout configurations, and different demand scenarios. Then, based on metrics evaluated for all these cases, a decision has to be taken. The decision maker faces many indicators with a complex imbrication: if a technology has been adopted in a first investment step, this decision will have consequences on investment decisions in the next steps, that is to say in the next scenarios. The problem can be modeled using a tree structure, where each node corresponds to an investment decision or to an event (market change).

Risk decision analysis

Decision analysis supports judgement in the case of complex, multi-criteria and multi-stages scenarios. It enables an objective, mathematical-based decision instead of a bias-distorted decision when conducted without methodology [START_REF] Tversky | Judgement under uncertainty: heuristics and biases[END_REF]. Risk decision analysis covers the study of alternatives, influences between parameters and their prioritisation. The scope of decision analysis is wide and covers the economic sphere, risk analysis in engineering, medicine, etc.

In the domain of floating production storage and offloading units, [START_REF] Lassagne | Applying a Decision-Analysis-Based Method to the Evaluation of Potential Risk Reducing Measures: The Case of a Floating Production Storage and Offloading Unit in the Gulf of Mexico[END_REF] studied the impact of the integration of risk-reduction measures on offshore installations on both technical and economical sides.

In the automotive sector, [START_REF] Tchoffa | Decision analysis in management of industrial incidents[END_REF] applied decision analysis on the management of industrial incidents. With their model, authors are able to evaluate the impact of the different incident causes, their inter-relations and their probabilities of occurrence.

The methodology to model a decision problem in an uncertain environment is the following [START_REF] Clemen | Making Hard Decisions with DecisionTools -3rd Edition[END_REF]:

1. Identification of the situation and objectives 2. Identification of alternatives 3. Problem modeling 4. Determination of the best alternative

Sensitivity analysis

The decision maker's attitude to risk is evaluated based on equivalent lotteries which enables to define the utility function. The principle of an equivalent lottery is to give the choice between two lotteries: for example, winning a high gain with 10 % chance and not winning at all with 90 % chance, or winning a small gain with 50 % chance. If the decision maker chooses the second lottery, he is risk-averse. In the case of conflicting objectives, the equivalent lotteries also support the definition of the multi-attribute utility function based on the company's priorities.

In the problem modeling step, an influence diagram is built to represent in a formal way decisions, uncertainties, values and inferences. It is an oriented acyclic graph with decision nodes and value nodes (deterministic nodes) [START_REF] Clemen | Making Hard Decisions with DecisionTools -3rd Edition[END_REF]. The influence diagram is an extension of Bayesian networks, as the nodes of the graph correspond to probability distributions and arcs between nodes to dependencies between those distributions. The decision tree is then built to represent the sequentiality of decisions and events in an explicit way. A decision tree is an oriented graph with uncertainty nodes, decision nodes and terminal nodes.

The resolution process is decomposed in two steps, with the objective to maximise the expected value of the profit [START_REF] Goodwin | Decision trees and influence diagrams[END_REF]. Using the decision tree, in the roll-forward step, the final payoffs of each alternative, corresponding to a branch of the decision tree, are calculated. Then, the rollback step consists in the computing of the profit value for each terminal node. The chosen decisions are the ones with the highest expected values.

Conclusion of the literature review

In a volatile environment, it is complex to take objective decisions regarding investments. Furthermore, decision makers can be influenced by a bias regarding MOSIM'20 -November 12-14, 2020 -Agadir -Morocco new technologies: mistrust or on the contrary blind trust.

The industry needs a decision support tool for the design of RMSs and RASs. Previous works fixed design methodologies and evaluation criteria to help design and rating of the integration of new technological solutions or configurations of the production system. However, the quantity of parameters to take into account while conceiving a manufacturing system (performance, reconfigurability, and costs metrics) makes the decision process complex. In addition, it is complex to have a clear overview of consequences of consecutive decisions over scenarios. By modeling uncertainty about future market trends, it is possible to simulate the system evolution following consecutive decisions.

Decision makers need an overview over market demand scenarios supporting multi-criteria evaluation of decisions.

DECISION ANALYSIS FOR RAS DE-SIGN

Case study: Multi-product assembly line

The case study is a multi-product engine assembly line in the automotive industry, facing a varying demand in both product mix and volume. To face changing market requirements, the new strategy of the company is to transform its production system into a RAS. However, taking decisions in this context is complex. Indeed, decision makers are not familiar with the new reconfigurable equipment, and in addition, the production system seeks contrary goals: being efficient, as well as rapidly reconfigurable and economically interesting.

The objective is to maximise the utilisation rate of machines, minimise investments and maximise reconfigurability of the system.

Alternatives offered to the decision-maker are, at the beginning of each scenario, to choose to invest in a new resource, or to abstain from investing. Each resource type has a different price, reconfigurability rate and utilisation rate. This last parameter is determined by running the same scenarios in a Discrete Event Simulation software, enabling assessment of the performance of the production system with the new machine. The price of resources is also known, and the reconfigurability metric of each resource is computed by means of the formula defined in (Beauville dit Eynaud et al., 2020), based on reconfigurability characteristics defined by [START_REF] Koren | Reconfigurable Manufacturing Systems[END_REF].

In this study, we propose two scenarios for the variations of the market demand: an increase and a decrease of the demand.

Model

The approach is implemented in the decision analysis software Decision Programming Language (DPL9) developed by Syncopation. The utility function is determined by equivalent lotteries generated with AS-SESS tool. The user indicates the attributes (decision parameters) of the problem, boundary values, and the tool supports the determination of the multiattribute utility function. In this problem, the four attributes are the investment level, the machine utilisation rate, the reconfigurability indicator and the maturity indicator. The maturity metric depicts the level or readiness of the proposed technological bricks.

Figure 1 depicts the influence diagram built in DPL9.

Two scenarios are represented. The squares correspond to decision nodes, ovals to chance nodes (events) and squares with rounded edges are value nodes. Arrows between nodes represent influences between them. The model includes two consecutive scenarios. At the beginning of a time period, a decision regarding purchasing of new resources is taken by the company. Then, a scenario run is materialized by the realisation of a market evolution. The same procedure occurs a second time to illustrate the second scenario.

The decision tree of the problem is symmetric. The four decision alternatives are illustrated Figure 2: no investment (no action), add a fixed robot, add a movable robot, or add a mobile robot.

A chance node can lead to four possibilities: strong market decrease, low decrease, low increase or strong increase of the demand. In the first scenario, depicting a rise of the market demand, the probability of strong decrease is 0 %, the probability of low decrease as well as low increase are 40 %, and the probability to face a strong increase is 20 %. The second scenario simulates a decline of the demand, and is modeled by a 70 % chance of strong market decrease, 30 % chance of low decrease and 0 % of chance of increase (for both low and strong possibilities).

Results

Figure 3 presents an extract of the decision tree after DPL9 simulation. Considering given probability distributions and values for the attributes, the multiattribute utility function is maximised when a movable robot is added to the system in the first time period, and no investments are done in the second period.

Indeed, in the first scenario, the market evolution is uncertain and is likely to increase or decrease. This explains why it is relevant to integrate on the line a resource which can be easily added or removed. In the second period however, a decrease is certain, and it is preferable not to increase unnecessarily the capacity of the system.

In the second scenario, the decision analysis suggests to add fixed resources on the engine assembly line. Indeed, as the demand increase is quite certain, the most reasonable choice is to invest in resources for a long-term high-throughput production.

In a second step, a sensitivity analysis is conducted to verify the robustness of the solution regarding input parameters. In this paper, we propose to conduct a sensitivity analysis on the maturity indicator of the mobile robot. For now, the value of this metric is M R = 0.48. The hypothesis we want to verify is if the increase of M R has an impact on the final decision proposed by DPL9. Figure 4 shows the results of the sensitivity analysis. The abscissa corresponds to the value of M R for the mobile robot, and the ordinate is the expected value. From this graph, we can read that above a value of 0.6 for the maturity index, there is a policy change in the model, and the solution "mobile robot" will be preferred.

Discussion

The contribution of decision analysis for RMS/RAS design concerns decision support in an industrial context where companies are divided between the urge to integrate new components to have state-of-the-art production facilities, but are limited by the high price of flexible solutions. We propose an approach to enable statistically-based objective decision in an uncertain environment.

The specificity encountered when designing a reconfigurable system is the inability to predict exactly sales and the need to assess the transformability potential of the line. Thus, expected production volumes and product mix can be formulated as scenarios defined by probabilities of occurrence. We are able to build a model taking into account the three axes to evaluate a reconfigurable system : costs, performance and reconfigurability.

Influence diagrams and decision tree are efficient tools to represent and communicate on various scenarios. They give a clear overview on relationships between decisions, events and relevant values, and illustrate at one sigh all possible alternatives.

Results obtained in this study are promising and give a new insight in the RMS/RAS design process. By enabling a sensitivity analysis on one of the input criteria, such as the maturity of a type of resource, this approach supports the industry to evaluate the right moment when to invest in a new type of resource. This way, the method helps the upgrade of production facilities regarding Industry 4.0. In this paper, we propose the application of decision analysis on the RPSDP. The utility function is built based on the parameters of the RMS/RAS, which are the reconfigurability, the productivity and the investment cost of the system. The attitude towards risk of the decision maker and the relative weights of the attributes are obtained by evaluation of equivalent lotteries. For the studied production scenarios, occurrence probabilities are defined and validated by experts. Based on this data, and by applying decision analysis on the RPSDP, we obtain a suggestion for the design strategy.

Our methodology provides an evaluation of many parameters of the problem, and aims to erase psychological bias in the design process. Furthermore, the summation of all relevant data and scenarios in a single decision tree supports communication in decision meetings.

The tool used for decision analysis is currently independent of other modules of the approach. Further research will focus on the automation of the analysis, by implementing gateways between the reconfigurability indicators calculation module, the DES software, optimisation module, and the risk decision analysis software.

Figure 1 -Figure 2 -

 12 Figure 1 -Influence diagram (DPL9)

Figure

  Figure 3 -Proposed alternative

ACKNOWLEDGMENTS

This work took place in the framework of the Open-Lab "Materials and Processes" combining ENSAM network, GeorgiaTech Lorraine and Groupe PSA.