Keywords: Pickup and Delivery Problem, Transportation, metaheuristic, algorithm

The pickup and delivery problem (PDP) is a problem of optimization of vehicles routes, in order to satisfy the demands for carriage of goods between suppliers (pickup locations) and customers (delivery locations) using a set of vehicles. In this paper, we discuss a variant of PDP which is the SPDPTWPD (Selective PDP with Time Windows and Paired Demands). In this type of problems, a set of constraints must be respected. Those constraints are related to the capacity of the vehicles, the opening and closing times of each site (occurrence of time windows), the precedence (paired demands), and the choice of sites to be visited (selective aspect). We proposed a new metaheuristic to solve the SPDPTWPD, then we tested our method on benchmark instances, and its efficiency is shown by obtained results.

I. INTRODUCTION

The pickup and delivery problem (PDP) aims at constructing a set of routes in order of establishing a transportation network to satisfy a set of pickup and delivery requests under specified constraints. Each constructed route is traveled by a vehicle with limited capacity, which is, among other available vehicles, based at a starting depot. The vehicles must also return to depot at the end of their routes. In our problem, each pickup or delivery site has a time window to be respected, which means that the site must be visited either between its opening time and its closing time or before its opening time. In this last case, the vehicle must wait until the beginning of service time. In addition, the paired demands constraints included in our problem ensure that each vehicle route satisfies the precedence constraints, so the customer must be served only after its supplier. In the urban context, taking into account all the above constraints becomes more critical because of the applied policies by the public authorities in some cities. For example, limiting transportation hours per day to reduce the noise, or the regulation of parkings and street access. The variant of the classic PDP studied in this paper is the selective PDP with time windows and paired demands (SPDPTWPD). This variant is a generalization of the standard PDP where in addition of constraints related to time windows and paired demands, it is not obligatory to visit all nodes.

In fact, sometimes it is impossible to visit all nodes in the transportation network in a given period, so we must choose nodes which will be served in this period. Hence, a profit is associated to each site to represent its priority and the goal of our variant is to maximize the total profit then to minimize the distance.

Figure 1. Example of the SPDPTWPD

Fig. 1 represents an example of our variant with 5 suppliers and 5 customers. The fleet is composed of 2 vehicles. Each paired demand (between a supplier and its customer) can be identified thanks to the same color and the same number. The green triangle represents a supplier paired with the depot (the goods picked up from this site are delivered to the depot). And the green circle represents a customer paired with the depot. In the shown solution, the nodes numbered 4 were not selected. The next sections of this paper are organized as follows: a literature review is provided in section II. Then, the section III defines the SPDPTWPD with a mathematical formulation. In section IV, we explain our new metaheuristic to solve the SPDPTWPD. After that, section V is dedicated to the experimental results. Finally, section VI concludes this paper and gives direction for further research.

II. LITERATURE REVIEW

In this section, we provide a state of the art of various methods used to solve different variants of the PDP.

The PDP is considered as a variant of the combinatorial optimization problem VRP (Vehicle Routing Problem). It consists in establishing an optimal set of routes traveled by a fleet of vehicles in order to visit a specified set of customers. A taxonomic literature review of the VRP was made between 2009 and June 2015 and has been published in [START_REF] Braekers | The vehicle routing problem: State of the art classification and review[END_REF].

A New Metaheuristic to Solve a Selective Pickup and Delivery Problem

Zaher Al Chami, Hamza El Flity, Hervé Manier, Marie-Ange Manier Univ. Bourgogne Franche-Comté FEMTO-ST Institute/CNRS, Rue Thierry-Mieg (UTBM), 90 010 Belfort Cedex, France (Zaher.al-chami@utbm.fr, hamza.el-flity@utbm.fr, herve.manier@utbm.fr, marie-ange.manier@utbm.fr)

The PDP involves a collection of suppliers and a collection of customers geographically located. Over the few past decades, many studies concerning the variants of this problem have been achieved. For more details, see book [START_REF] Toth | The vehicle routing problem[END_REF] and a number of surveys [START_REF] Parragh | A survey on pickup and delivery problems. part i: Transportation between customers and depot[END_REF][10] [START_REF] Savelsbergh | The general pickup and delivery problem[END_REF]. Many exact methods have been elaborated to solve the PDPTWPD. Among those methods, Ropke and Cordeau have accomplished a branch-and-cut-and-price algorithm in which the column generation algorithm is used to calculate the lower bounds [START_REF] Ropke | Branch and cut and price for the pickup and delivery problem with time windows[END_REF]. Moreover, another exact algorithm based on a branch-and-cut-and-price approach has been proposed to solve the m-PDPTW (multi vehicles PDPTW) with two different objective functions: minimizing the total vehicle fixed costs, and minimizing the route costs [START_REF] Baldacci | An exact algorithm for the pickup and delivery problem with time windows[END_REF]. Furthermore, researchers have elaborated a new formulation to solve the Mu-PDPTWPD (Multi-periods PDPTWPD) where each site can be visited in one or several periods [START_REF] Manier | Shippers' collaboration in city logistics[END_REF]. The period can be represented as one day or any time slot and their model is solved by using CPLEX.

Due to the combinatorial complexity of the PDPs, the efficiency of exact solving methods has been proved mainly for simple problems, but not for the complex problems with great size. For this reason, many studies applying metaheuristic algorithms have been carried out in the literature. Authors have developed a "Squeaky wheel" method which solves the m-PDPTW using a local search [START_REF] Lim | Solving the pickup and delivery problem with time windows using squeaky wheel optimization with local search[END_REF]. Another method to solve this problem has been presented in [START_REF] Quan | A new insertion-based construction heuristic for solving the pickup and delivery problem with time windows[END_REF]. It is a construction heuristic method based on the integration principle. Moreover, a hybrid metaheuristic, which combines tabu search and simulated annealing, has been developed by researchers in [START_REF] Li | A metaheuristic for the pickup and delivery problem with time windows[END_REF]. A memetic algorithm has been introduced in [START_REF] Liao | Solving the biobjective selective pickup and delivery problem with memetic algorithm[END_REF] to solve the biobjective selective PDP (SPDP) where the demands are unpaired.

Concerning the selective aspect of the PDPTWPD, researchers have proposed a linear programming model, based on three-index formulation, to solve this problem [START_REF] Chami | New model for a variant of Pickup and Delivery Problem[END_REF]. Moreover, a lexicographic approach to solve the biobjective SPDPTWPD has been presented in [START_REF] Al Chami | A lexicographic approach for the bi-objective selective pickup and delivery problem with time windows and paired demands[END_REF]. Recently, a hybrid genetic algorithm to solve the multi-objective SPDPTWPD has been published in [START_REF] Al Chami | A hybrid genetic algorithm to solve a multi-objective Pickup and Delivery Problem[END_REF] where the aim of our method was to maximize the profit and minimize the distance in the same time. In this paper, we propose a new metaheuristic method to solve this variant.

III. MATHEMATICAL FORMULATION

A. Notations

In this part, we introduce a mathematical formulation for SPDPTWPD. In this purpose, we define the following parameters useful in our problem: Data: -1 if vehicle k moves from site i to site j, -0 Otherwise,

 V:

B. Mixed Linear Program for the SPDPTWPD

A mathematical formulation for the SPDPTWPD could be as follows: Minimize/Maximize F (1)

Subject to:

∑ ∑ 𝑋 𝑖𝑗 𝑘 𝑘 ∈ 𝑉 𝑗 ∈𝑁 ≤ 1 i ∈ Nodes (2) ∑ ∑ 𝑋 𝑖𝑗 𝑘 𝑘 ∈ 𝑉 𝑖 ∈𝑁 ≤ 1 j ∈ Nodes (3) ∑ 𝑋 𝑖𝑢 𝑘 𝑖 ∈𝑁 -∑ 𝑋 𝑢𝑗 𝑘 = 0 𝑗 ∈𝑁 k ∈ V; u ∈ Nodes (4) ∑ 𝑋 𝑗𝑤 𝑘 𝑁𝑜𝑑𝑒𝑠 𝑗=1 = 1 k ∈ V; w ∈ W (5) ∑ 𝑋 𝑤𝑖 𝑘 𝑁𝑜𝑑𝑒𝑠 𝑖=1 = 1 k ∈ V; w ∈ W (6) 𝑄 𝑘 ≥ 𝑌 𝑖 𝑘 ≥ 0 i ∈ N; k ∈ V (7) 𝑌 𝑗 𝑘 ≥ 𝑌 𝑖 𝑘 + 𝑞 𝑖 -𝑀(1 -𝑋 𝑖𝑗 𝑘 ) i, j ∈ N; k ∈ V (8) 𝑌 𝑗 𝑘 ≤ 𝑌 𝑖 𝑘 + 𝑞 𝑖 + 𝑀(1 -𝑋 𝑖𝑗 𝑘 ) i, j ∈ N; k ∈ V (8 bis) 𝑋 𝑤 𝑘 = ∑ (-𝑞 𝑖 * ∑ 𝑋 𝑗𝑖 𝑘 𝑗∈𝑁 ) 𝑖 ∈𝐶 k ∈ V ; w ∈ W ; j ≠ I; Supplieri = w (9) 𝐷 𝑤 𝑘 = 0 k ∈ V; w ∈ W (10) 𝐷 𝑖 𝑘 ≥ 𝐴 𝑖 𝑘 + 𝑆 𝑖 -𝑀(1 -𝑋 𝑖𝑗 𝑘 ) i, j ∈ N; k ∈ V (11) 𝐷 𝑖 𝑘 ≤ 𝐴 𝑖 𝑘 + 𝑆 𝑖 + 𝑀(1 -𝑋 𝑖𝑗 𝑘 ) i, j ∈ N; k ∈ V (11 bis) 𝑒 𝑖 * ∑ 𝑋 𝑖𝑗 𝑘 𝑁 𝑗=1 ≤ 𝐴 𝑖 𝑘 ≤ 𝑙 𝑖 * ∑ 𝑋 𝑖𝑗 𝑘 𝑁 𝑗=1 i ∈ N; k ∈ V (12) 𝐴 𝑖 𝑘 ≥ 𝐷 𝑖 𝑘 + 𝑑 𝑖𝑗 𝑆𝑝𝑒𝑒𝑑 𝑘 -𝑀(1 -𝑋 𝑖𝑗 𝑘 ) i, j ∈ N; k ∈ V (13) 𝐷 𝑓 𝑘 ≤ 𝐴 𝑐 𝑘 f ∈ B; c ∈ C such as Supplierc = f (14)
Our objective function is represented by [START_REF] Al Chami | A lexicographic approach for the bi-objective selective pickup and delivery problem with time windows and paired demands[END_REF]. The main objectives are expressed by the following functions:

-Maximizing profit: 2) and (3) ensure that each site is visited at most once by a single vehicle. Constraints (4) ensure the routing continuity by a vehicle. Constraints ( 5) and ( 6) guarantee that each vehicle begins its route and finishes it at the depot, even if they do not visit any site. The capacity constraints are ensured by ( 7), ( 8), (8bis) and [START_REF] Parragh | A survey on pickup and delivery problems. part i: Transportation between customers and depot[END_REF]. Moreover, the time windows constraints are guaranteed by ( 10), ( 11), (11bis), ( 12) and [START_REF] Savelsbergh | The general pickup and delivery problem[END_REF]. Constraints [START_REF] Toth | The vehicle routing problem[END_REF] ensure that the supplier is visited before its customer. In the next section, we present our approach to solve the considered problem.

𝐹1 = ∑ ∑ ∑ 𝑃 𝑖 𝑋 𝑖𝑗 𝑘 𝑘 ∈ 𝑉 𝑗 ∈ 𝑁 𝑖 ∈ 𝑁 -Minimizing distance: 𝐹2 = ∑ ∑ ∑ 𝑑 𝑖𝑗 𝑋 𝑖𝑗 𝑘 𝑘 ∈ 𝑉 𝑗 ∈ 𝑁 𝑖 ∈ 𝑁 Constraints (

IV. PROPOSED METAHEURISTIC

In this section, we introduce our new metaheuristic which solves the SPDPTWPD. Our approach could be considered as an extension of the tabu-embedded simulated annealing algorithm proposed by Li & Lim to solve the PDPTWPD [START_REF] Li | A metaheuristic for the pickup and delivery problem with time windows[END_REF].

A. Approach of Li and Lim

In their study, authors have considered an unlimited number of vehicles. The objective of their method is defined as follows, respecting the following priority order:

1-Minimization of number of vehicles 2-Minimization of total travel cost 3-Minimization of total schedule duration (the sum of waiting time, travel time and service time) 4-Minimization of total waiting time to start service The metaheuristic developed by Li and Lim is principally based on three permutation operators used for several iterations allowing to restructure the routes in the purpose of reaching the objective earlier mentioned and obtaining the best possible solution. The first routes are obtained using the insertion heuristic proposed by Solomon [START_REF] Solomon | Algorithms for the vehicle routing and scheduling problems with time window constrains[END_REF]. An explanation for those operators is given by the following description:

1-PD-Shift Operator

This operator moves a pickup-delivery pair from a route to another. In fig. 2, the PD-Shift operator is used to move the pair Pi-Di from route Ri to route Rj. Pi and Di are originally in route Ri, so first the PD-Shift operator removes Pi and Di from the route Ri, and then inserts them at a feasible position in route Rj, subject to the constraints imposed on PDPTWPD. Infeasible shifts are forbidden.

3-PD-Rearrange Operator

Figure 4. PD-Rearrange operator

The PD-Rearrange operator repositions the pickupdelivery pairs within the same route. Its objective is to move each pair in a route to the best position that maximally ameliorate the route in order to reach the objective early mentioned. In fig. 4, the PD-Rearrange operator removes the pair Pi-Di which is in the route Ri, and then inserts them at another feasible position in the same route. Infeasible insertions are also not allowed.

B. New extension

As mentioned above, our study is principally based on the approach published in [START_REF] Li | A metaheuristic for the pickup and delivery problem with time windows[END_REF]. Due to the difference in objectives and criterions between our study and the one in [START_REF] Li | A metaheuristic for the pickup and delivery problem with time windows[END_REF], we adapted this method to the context of our problem, where the objective functions are the following:

1-Maximization of the total collected profit. 2-Minimization of the total traveled distance.

First, we added the profit attribute to each site, which doesn't exist in [START_REF] Li | A metaheuristic for the pickup and delivery problem with time windows[END_REF]. Then, as early mentioned, in [START_REF] Li | A metaheuristic for the pickup and delivery problem with time windows[END_REF] an unlimited number of vehicles is used to solve the problem, contrary to our case where we use a limited number of vehicles. Therefore, we added to the algorithm a new function which creates a solution with a limited number of vehicles from a solution with unlimited number of vehicles.

In the purpose of respecting the objective functions, the solution generated must be the solution with maximal possible profit. To do so, the principle used is to keep removing the routes having the minimal profit among the set of routes in the solution one by one, until having a solution with the considered number of routes which is equivalent to the number of available vehicles.

In addition, we ameliorate the solution by trying to insert nodes from removed routes in the remaining routes. For each node, if the insertion is not feasible, with regard to the problem constraints, we try to exchange it with a node in the remaining routes having a lower profit. This explanation could be shown in figure 5.

Figure 5. Solution optimization procedure

In Fig. 5, S is the current solution, NV is the number of vehicles used in S, and real NV is the real number of available vehicles that we must have in the solution.

To compare two solutions into the algorithm, we used a comparison method that we called F described as follows: In Fig. 6, we the function F on each of the two solutions we want to compare, to have two solutions with the real number of vehicles. For the obtained solutions, the best is the one with the higher profit. If the two solutions have the same profit, the best is the one with the lower distance. If the two solutions have different number of routes after applying F, we decided to consider that the best is the one which needs the lower number of vehicles, ignoring the profit and the distance. Indeed, we remarked that this consideration helped us to get better solutions at the end. Finally, we choose among the solutions to compare initially, the one which created the best solution when applying F.

In the next section, we present the experimental results obtained by this study, comparing to the results of a lexicographic approach previously elaborated.

V. EXPERIMENTAL RESULTS

In this part, we test our new metaheuristic on benchmark instances for the SPDPTWPD (accessible via this link: https://www.dropbox.com/sh/zpfyjo1l4etfuqe/AAAHUB MYfTfbKau0Nmc0yAOWa?dl=0).

Each instance is labeled SPDPTWPDxyz, x is the type of instance (R: nodes are randomly distributed, C: nodes are totally clustered, and RC: nodes are partially clustered and partially randomly distributed), y is the number of nodes (20, 50 and 100) and i identifies the distribution of profit (1: nodes have the same profit and 2: each site have a different value of profit). The hybrid genetic algorithm, presented in [START_REF] Al Chami | A hybrid genetic algorithm to solve a multi-objective Pickup and Delivery Problem[END_REF] to solve the same variant, provides a set of non-dominated solutions that maximize the profit and minimize the distance. The authors have proved that the gap between the obtained solutions and the optimal Pareto front was acceptable. On the other hand, our proposed metaheuristic focus on giving only one non-dominated solution for each tested instance (the one with the maximal profit). In this section, we will prove that the gap between the obtained solution and the optimal Pareto front is very small. For that, we compared the results of our method with the results of a previous lexicographic approach solving the same variant in which the authors maximize the profit then minimize the total traveled distance [START_REF] Al Chami | A lexicographic approach for the bi-objective selective pickup and delivery problem with time windows and paired demands[END_REF]. The comparison also involves the CPU time to find the difference between the two approaches at the level of performance. Table 1 shows the results for each method, as well as the gap between them concerning each criterion.

As shown in table 1, we can find out 3 kinds of results:

Case 1: The results obtained by the new metaheuristic are the same as the results of the lexicographic approach, as in the case of the instance SPDPTWPD-C20. In this case, the metaheuristic gives the best possible solution and we can notice that this concerns the majority of tested instances with a percentage of 60.87%.

Case 2: For 17.39% of tested instances, the metaheuristic cannot give a solution with the same profit as the solution given by the lexicographic, but it gives a solution with a better travel distance, such as for example the instance SPDPTWPD-RC1001. In this case, it could be that the metaheuristic solution belongs to the Pareto front. To ensure that, we run our MILP to get the minimal distance for the obtained profit value. We remarked that 25% of obtained solutions in this case belongs to Pareto front. Case 3: The solution given by the metaheuristic is worse than the one given by the lexicographic approach in terms of profit and distance, as for the instance SPDPTW-RC502. This case occurred in 21.74% of tested instances.

In average, the gap between our new metaheuristic and the lexicographic approach is 1,14 concerning the profit, and -0.04 concerning the distance. For the solving time, it could be noticed that our proposed metaheuristic is more performant for the majority of tested instances compared to the lexicographic approach. This time depends on several elements for example: the number of nodes, the time windows and the number of vehicles used. It can also depend on other characteristics like the distribution of the time intervals, the geographical distribution of the nodes…

VI. CONCLUSION

In this paper, we have presented a new metaheuristic to solve the SPDPTWPD. The results show that this new approach gives us very good solutions in a reasonable computational time.

In our future works, we will focus on improving our approach to achieve better results and we will add more constraints to our variant to match more real life cases.

  Collection of available vehicles,  C: Collection of all customers,  B: Collection of all suppliers,  Nodes: Collection of all suppliers and customers (Nodes = C ∪ B),  W: Collection of all depots,  N: Collection of all depots, suppliers, and customers (N = Nodes ∪ W),  M: a great number  Supplieri: Collection of all suppliers related to customer i,  Q k : Capacity of vehicle k,  Speed k : Average speed of vehicle k,  dij: Distance between site i and site j,  Pi: Profit characterizing the site i,  [ei, li]: Time window of site i,  Si: Service time at site i,  qi: Goods quantity requested by site i -If i ∈ B then qi > 0, -If i ∈ C then qi < 0, Variables:  Ai k : Starting service time of vehicle k in site i,  Di k : Departure time of vehicle k from site i,  Yi k : Goods quantity in vehicle k visiting site i,  Xij k :

Figure 2 .

 2 Figure 2. PD-Shift operator 2-PD-Exchange Operator

Figure 3 .

 3 Figure 3. PD-Exchange operatorThe PD-Exchange operator swaps pickup-delivery pairs of two routes. In other words, it moves one pair from each route to the other. For example, in fig.3, the pair Pi-Di is originally in route Ri, and Pj-Dj is originally in route Rj. The PD-Exchange operator first removes Pi-Di from route Ri and Pj-Dj from route Rj, and then inserts Pi-Di at a feasible position in route Rj, at the same time of inserting the locations Pj and Dj at a feasible position in route Ri. The infeasible insertions are not allowed.

Figure 6 .

 6 Figure 6. Comparing solutions

Table 1 .

 1 Experimental results

										GAPs (%)
	Instance
			Profit	Distance	CPU Time (s)	Profit	Distance	CPU Time (s)	Profit	Distance
	SPDPTWPD-C201	1	180	275,19	0,3	180	275,19	11	0,00	0,00
	SPDPTWPD-C202	1	144	167,99	19,88	144	167,99	7	0,00	0,00
	SPDPTWPD-C202	2	217	212,94	52,15	217	212,94	8	0,00	0,00
	SPDPTWPD-R201	4	190	398,25	0,35	190	398,25	6	0,00	0,00
	SPDPTWPD-R202	6	213	378,95	12,2	213	378,95	6	0,00	0,00
	SPDPTWPD-RC201	2	160	233,2	0,33	160	233,2	6	0,00	0,00
	SPDPTWPD-RC202	2	180	235,09	0,52	180	235,09	6	0,00	0,00
	SPDPTWPD-C501	5	480	363,28	9,67	480	363,28	57	0,00	0,00
	SPDPTWPD-C502	1	437	431,25	28,31	436	386,08	433	-0,23	-10,47
	SPDPTWPD-C502	2	656	525,87	204,44	656	525,87	401	0,00	0,00
	SPDPTWPD-R501	13	490	1075,77	14,86	490	1075,77	21	0,00	0,00
	SPDPTWPD-R502	10	576	834,92	17,24	576	834,92	20	0,00	0,00
	SPDPTWPD-RC501	4	320	481,37	1629,02	310	489,4	28	-3,13	1,67
	SPDPTWPD-RC502	4	420	527,76	151,37	400	518,14	26	-4,76	-1,82
	SPDPTWPD-RC502	5	500	686,69	1352,38	480	677,07	27	-4,00	-1,40
	SPDPTWPD-RC502	6	562	758	4505,16	547	801,64	28	-2,67	5,76
	SPDPTWPD-C1001	6	690	437,04	928,93	680	469,58	290	-1,45	7,45
	SPDPTWPD-C1002	7	770	542,15	621,54	760	575,08	233	-1,30	6,07
	SPDPTWPD-R1001	7	500	639,64	3540,04	500	639,64	138	0,00	0,00
	SPDPTWPD-R1002	6	514	679,44	1391,96	512	687,81	157	-0,39	1,23
	SPDPTWPD-RC1001	1	120	140,35	382,23	110	127,22	151	-8,33	-9,36
	SPDPTWPD-RC1002	1	138	125,68	103	138	125,68	109	0,00	0,00
	SPDPTWPD-RC1002	1	252	274,49	7000	252	274,49	145	0,00	0,00

Lexicographic approach Number of vehicles Proposed metaheuristic

ACKNOWLEDGMENT

This work is supported by the ANR (French National Research Agency) in the framework of the project TCDU (Collaborative Transportation in Urban Distribution). This project ANR-14-CE22-0017 is labelled by the Pôle Véhicule du Futur, and is jointly performed by four partners, the three french universities of technology (UTT, UTBM, UTC) and the society Share And Move Solutions.


Philippe Canalda

Mohamed Hassine

Idriss Hassine

Idriss Hassine Le

Le covoiturage évolue avec la prise en compte des transbordements et des reports modaux, et la complexification des rôles de passager ou de chauffeur

teaching and research institutions in France or abroad, or from public or private research centers.

FUTURMOB'17

Le covoiturage évolue avec la prise en compte des transbordements et des reports modaux, et la complexification des rôles de passager ou de chauffeur Canalda 1 , P. Hassine, M. Hassine, I.

(1) Institut femto-st (UMR CNRS 6174) Centre de Développement Multimédia NUMERICA 1, Cours Louis Leprince-Ringuet, 25200 Montbéliard, France. E-mail: philippe.canalda@femto-st.fr Mots-clés : covoiturage dynamique, N-intra-modalité, fenêtres de temps, itinéraires avec Vias, reports modaux.

Keywords: dynamic carpooling, N-intra-modality, time windows, itineraries with Vias, modal shifts.

Résumé Le covoiturage qui se démocratise se résume soit à un système d'information pour préparer la mise en contact (Bla-bla-car), soit l'intégration d'un accompagnement de prise en charge à-la-taxi (ou uber). Pourtant différentes offres avancées sont opérationnelles et proposent du transport mutualisé dynamique. Une évolution de rupture s'annonce avec la prise en compte des reports intra-modaux, la variabilité des rôles avec des rôles préférentiels (plutôt passager ou plutôt chauffeur) mais pas tranchés, et donc la prise en compte intelligente du report de charge.

Nous proposons une formalisation du problème du covoiturage dynamique N-intramodal avec transbordements, ainsi qu'une première implémentation d'une version de résolution de ce problème combinatoire. La N-intra-modalité permet d'organiser les reports de charge d'un véhicule sur un autre véhicule. Un usager du covoiturage peut ainsi formuler son acceptation d'utiliser un seul moyen de transport ou bien un nombre maximal de reports modaux. Le transbordement, dans sa mise en oeuvre la plus générale, autorise qu'un chauffeur devienne passager. L'application de la Nintra-mdoalité et du transbordement permet ainsi de réduire le nombre de véhicules sur les routes et d'augmenter le taux d'occupation des véhicules en circulation. Il est alors nécessaire d'introduire de nouvelles contraintes opérationnelles comme celle de formuler le trajet retour dès la formulation du trajet aller de façon à organiser la récupération pour un chauffeur, de son véhicule, lorsqu'il a accepté de réaliser son transbordement. L'évaluation est réalisée sur des jeux de tests réalistes.

Un travail antérieur a porté sur le covoiturage dynamique 1-intra-modal [START_REF] Canalda | Covoiturage Dynamique et Incrémental : formalisation, algorithme de programmation dynamique Cut,Price and Share, et évaluations[END_REF]. C'est une extension au problème classique du covoiturage consistant à affecter la demande de nouveau(x) passager(s) à un ou plusieurs véhicules dont leur(s) propriétaire(s) propose(nt) des itinéraires flexibles. Cette mission d'affectation, classiquement, se cantonne à de la mise en contact basée sur l'origine et la destination qui doivent être communes. Ainsi, le covoiturage dynamique le plus avancé [START_REF] Hassine | Dynamic Intra-Modal Carpooling with Transhipment : Formalization and Combinatorial Solution[END_REF], dans sa formulation L'exemple du schéma illustre la rupture servicielle du covoiturage dynamique N-Intra-modal. L'offre d'un acteur plutôt chauffeur, et pour un nombre de reports modaux (RM) nul, permet à celui-ci de prendre ou de ne pas prendre son véhicule. L'appariement en gris est sous-optimal si le nombre de reports modaux est égal ou supérieur à 1. Ainsi, lorsque l'offre du chauffeur précédent accepte un RM supérieur à un, alors le transbordement est autorisé et une économie de véhicule peut-être réalisée (l'appariement en beige). Il est avisé que le chauffeur réalisant le voyage le plus long lors du trajet aller, utilise son véhicule en garantissant un itinéraire retour (en violet). Une première implémentation d'une version exacte de ce problème de covoiturage N-intra-modal avec transbordement est réalisé en JAVA. Les simulations effectuées ont permis de satisfaire à 3840 demandes et 1920 offres, et pour un temps de réponse de notre système réduit à quelques secondes. Ce travail ouvre la voie d'une offre multimodale dynamique intégrant le véhicule individuel. Références

FIGURE 1 -

 1 FIGURE 1 -Covoiturage 3-intra-modal avec report de charges changement de rôles (chauffeur vers passager à l'aller puis passager vers chauffeur au retour) pour des itinéraires A-R avec Vias et fenêtres de temps dynamiques et sa mise en oeuvre, tient compte des fenêtres de temps dynamiques, des chargements partiels et des livraisons partielles des covoiturés et covoitureurs. La flotte de véhicules est hétérogène et les itinéraires considérés sont composés de vias. Il est important de noter ici que cette formulation, associant les vias et les fenêtres de temps, permet la modélisation généralisée d'une organisation d'un transport où toutes les étapes d'un voyage se spécifient (aller-retour, vias), pour un déroulement sur une même journée ou sur plusieurs jours.


Dermas Moffo
email: dermas.moffo@femto-st.fr

Philippe Canalda
email: philipe.canalda@femto-st.fr

François Spies
email: francois.spies@femto-st.fr

FUTURMOB'17 Le positionnement et les enjeux de la mobilité pour les microsystèmes et les systèmes de micro-robots

Keywords: Micro-robots, microsystèmes, positionnement, mobilité, distribué, absolu, relatif Micro-robots, microsystems, positioning, mobility, distributed, absolute, relative

Résumé.

Les avancées réalisées dans le processus de fabrication de micros éléments, de circuits intégrés ont permis l'émergence de micro systèmes. De nombreux projets sont conduit afin d'intégrer de l'intelligence, de la coordination, de la communication aux micros systèmes permettent d'obtenir des systèmes distribués de micro-robots, comprenant des centaines voir des milliers de micros éléments. Ces microéléments disposent de ressources limités individuelles, mais leur utilisation collective permet d'avoir des systèmes capables de résoudre des problèmes de grande complexité. Leur utilisation repose également sur leur mobilité, qui elle nécessite une détermination de leur position. Dans nos travaux nous proposons des solutions de positionnement pour les microsystèmes et les systèmes de micro-robots, et nous montrons ici son intérêt pour la mobilité.

Enjeux de la mobilité pour les micros systèmes et micro-robots

Les systèmes de robots modulaires auto-reconfigurables sont composés de modules indépendants interconnectés, capables de collaborer et de se coordonner pour atteindre un objectif commun. Ils sont dotés de capacité de traitement internes, et grâce aux communications, à la coordination et à leur mobilité, ils peuvent changer de forme [Naz et All.]. Cette mobilité demande une connaissance continue de la position de chaque robot modulaire. L'usage de systèmes de micro-robots massivement distribués, auto-reconfigurables, est une partie d'un problème plus grand : la matière programmable. La matière programmable c'est de la matière qui peut changer ses propriétés physiques (forme, densité, la couleur, les propriétés chimiques) en fonction d'un programme, d'une commande externe, ou des données obtenues de ses capteurs. Une fois de plus ces changements de propriétés et de forme sont localisés et dépendent des positions des différents modules qui compose le système. [Golstein et All.] La mobilité de microsystèmes peut aussi avoir une utilité dans la découverte d'un territoire. Un ou plusieurs groupes de micro robots, dotés de capteurs environnementaux sont dispersés sur un territoire qu'ils vont explorer, et en construire la carte en fonction des observations faite. La mobilité permet à ces robots de parcourir le territoire d'exploration, la coordination leur permet d'éviter d'explorer plusieurs fois la même zone, ou d'explorer une zone déjà parcouru par un autre groupe. Cette construction de carte est une fois de plus liée à la mobilité des éléments mais aussi et surtout de leur position.

Le positionnement au sein d'un système de micro-robots

Le positionnement pour les microsystèmes et les micro-robots est un préalable pour leur usage dans différentes applications. Cette question complexe (en raison des traitements à effectuer et du peu de ressources dont disposent ces micros éléments) et centrale (car préalable a toute mobilité) n'est que très peu traitée jusqu'à présent.

Nos travaux de thèse ont abordé ce problème de positionnement au sein de microsystèmes à forte densité.

  Nous proposons une modélisation d'un microélément qui prend en compte sa forme géométrique, ses composants, et ses fonctionnalités. Nous modélisons également les reliaisons possibles entre éléments voisins, et nous basant sur cette modélisation, nous proposons deux algorithme de positionnement a à la fois absolu et relatif. Dans [MoffoIpin16 et All] nous proposons un algorithme séquentiel de positionnement, qui est approfondi et évalué dans [MoffoCit16] sur un système dont la taille atteint 700000 éléments pour un temps de traitement inférieur à 80s. Dans [MoffoIpin17] nous proposons un algorithme distribué, multi-initiateurs tenant compte du voisinage qui qui réduit le temps de positionnement de 700000 éléments à moins de 20s.

Figure 2 Figure 2

 22 Figure 2 Position relative d'un Mems dans le repère relatif d'un Mems voisin Figure 2 Position relative

Figure 1

 1 Figure 1 Modélisation d'un Mems de son repère relatif, du repère absolu et de ses composants.

Figure 3

 3 Figure 3 Exemple de forme obtenue par un agencement de Mems circulaires en contact

Remerciements

Ce projet a été réalisé en coopération avec le programme Labex ACTION (contrat ANR-11-LABX-0001-01). Il a également été soutenu par le Ministère de l'Enseignement Supérieur et de la Recherche et de l'Innovation.


Elodie Bernard ⇤ †

Fabrice Ambert ⇤

Bruno Legeard

A Lightweight MBT approach for Visual Acceptance-Test Driven Development -Experience Report

Keywords: Model-based-testing, Lightweight MBT, Agile Software Development Lifecycle, ATDD

In this presentation, we give the results of an experiment using a lightweight MBT approach to implement Acceptance Test driven Development in a large Agile IT project.

I. INTRODUCTION

The practice of Acceptance Test Driven Development (ATDD) was born as an extension of Test Driven Development [START_REF] North | Behavior modification: The evolution of behavior-driven development[END_REF] [2] [START_REF] Pugh | Lean-agile acceptance test-driven development: better software through collaboration[END_REF]. In ATDD, acceptance tests are produced collaboratively during requirements analysis by business analysts, product owners, testers and developers. To write readable test cases that support test automation, ATDD often use a domainspecific scripting language, called the Gherkin language [START_REF] Santos | Automated acceptance tests as software requirements: An experiment to compare the applicability of fit tables and gherkin language[END_REF], in a Given-When-Then format. Gherkin's language test cases written in Gherkin language are often quite atomic, covering one aspect of a User Story for example. [START_REF] Santos | Automated acceptance tests as software requirements: An experiment to compare the applicability of fit tables and gherkin language[END_REF]. To define more global acceptance tests, for example end-to-end test cases, an approach using a graphical representation of workflows and a lightweight MBT approach [START_REF] Bernard | Lightweight Model-Based Testing for Enterprise IT[END_REF] can be appropriate. This is what we present in this experience report of using Lightweight MBT to implement a visual ATDD approach in the context of a large-scale IT project.

II. EXPERIMENTATION AND LESSON LEARNED

The research questions we aimed to verify were as follows:

• RQ1: To what extent is the Lightweight MBT approach adapted to short agile iterations? • RQ2: To what extent is the Lightweight MBT approach efficient at creating and maintaining automated scripts? We will present our experiments on two projects with two distinct contexts with our Lightweight MBT tool: Yest. Now we will present the two contexts of the projects on which we conducted our experiments a) Context 1: The first project, which we will call Project A, dealt with the testing of a web application on a large quality management application in a French railway company. It was developed in an Agile context with 4-week sprints and a test approach to verify the features implemented at the end of each sprint. Test automation started 1.5 years after the beginning of the application development and used the Lightweight MBT approach (with the Yest tool) and the Selenium framework. The test cases to be automated were built by the test automation specialist via Yest then he completed the adaptation layer and built the automation code. Only test cases for automation were built with Yest, existing test cases were created in a standard test management tool (here Squash) for 1,5 years, manual test cases had been developed without any information about a future test automation plan.

b) Context 2:

The 2nd project, which we will call Project B, dealt with the testing of a web application to manage employees skillset of a French railway company. It was developed in an Agile context with 4-week sprints and an ATDD approach. As early as sprint 1, the test teams were made aware of automation and the tests were built according to a set of methodologies and best practices. Automation was initiated after 6 months of the project (as soon as stable processes were identified) using an MBT approach (with the Yest tool) and the Selenium framework. The tests to be automated were built by the test team via Yest and then an automation engineer completed the adaptation layer in Yest and built the automation code. The objective of these two approaches was to evaluate how the use of Lightweight MBT could facilitate test design in an agile context and the implementation of test automation on a large IT project. The metrics collected to evaluate the efficiency of the approach were the time dedicated to test design and implementation [START_REF]ISTQB Certified Tester Foundation Level Syllabus, 2018 Version[END_REF], the number of test cases produced and the number of steps per test, as well as the number of US processed.

The following section will discuss the study of manual test design and implementation compared to an approach with Lightweight MBT.

A. Manual test design and implementation vs. Lightweight MBT approach

In order to compare the two approaches we confronted the test design and implementation between projects A and B over a 3-month period. For both projects, the basis for designing the tests was the US. These US had exactly the same model for both projects: i.e. a presentation of the context, followed by a description of a set of management rules. These rules must be processed in test cases.

In Project B we ensured that the Lightweight MBT approach was applied throughout the project. As part of the experiment we analyzed the US and defined the scope that would be covered during the next sprint. We therefore had visibility into the US that were new and the features that would need to be updated. So we started each sprint by quickly updating the highest priority test cases to be run.

We will now present the results obtained following these test design and implementation phases on each of the projects. For a 4-week sprint, the time dedicated to design was about 1740 minutes for Project A and 1770 for Project B (an average of four days). We will use hours and minutes as the unit of measurement, as we will report design times by test case and US. Team A processed an average of 13 US per sprint compared to 32 US for team B. Now let's take a more detailed look, i.e. at the number of test cases produced and taking into consideration the number of steps per test case. Team A produces an average of 102 test cases per sprint with an average of 10 steps per test case, and team B produces an average of 131 test cases with an average of 15 steps per test case. If we take into account the number of steps per test case, i. e. an average of 1020 steps for project A and 1965 steps for project B, we arrive at a conception time of 1 min 42 s per step for team A against 54 s for team B, i. e. a decrease by almost 50%. (47%)

For rather similar project perimeters, with a similar test case design and implementation source, the results of our experiments indicate that test design with Lightweight MBT approach is 47% more efficient than a traditional manual design approach. (shown in the figure 1) In order to explain these results, here is a summary of the points that made it possible to be more efficient with a Lightweight MBT approach. To begin the manual design of tests is traditionally done in a test management and execution tool such as hp ALM, Squash TM or Excel. (Here Squash TM is used) In these tools, in case of a change affecting a set of test cases it is necessary to take each of these test cases individually. With a Lightweight MBT tool it is easy to identify the model impacted by a change, update the model as required and then generate all the updated test cases, without having to modify them individually. This generation of test cases saves a lot of time, and this is possible through the easy use of the tool, hence the Lightweight aspect which allows easy and fast updates in a workflow and then regenerating test cases. This tendency is confirmed by the study of update times. In the context of project B, time spent updating test cases was distinguished from time spent creating new test cases. On the design study of 268 test cases with 110 new test cases and 156 in update, we observed an average gain of 60% on the update time of test cases, so it is twice faster than the design phase. Compared to a manual approach, design with Lightweight MBT gives good results and is more efficient for test case design and implementation and very efficient for updating test cases.

B. Automation

As part of our evaluation of the Lightweight MBT, we sought to evaluate how effective this approach was in creating and maintaining automated test cases. To this end, we conducted two experiments, one on project A and the other on project B, which we presented in the previous section. On project A no tests were produced by the test team with the MBT tool, it was the test automation engineer who created the test workflows and generated the test cases and then the scripts. The objective was to reproduce in the MBT tool the test cases already existing on the project. The choice of this approach was guided by the desire to compare two approaches: build test cases in a Lightweight MBT tool with visibility on automation (project B) and take existing test cases and adapt them in a Lightweight MBT tool, but without considering future automation (project A). Thus on project B, the test cases were already existing and the automation engineer only completed the adaptation layer to produce the scripts. Still with a view to experimenting with the Lightweight MBT approach, on project B, we completed the adaptation layer during the sprint on a 1st perimeter and then on another perimeter during a subsequent sprint. Including maintenance phases to update Keywords. These phases are perfectly integrated during the sprint. A total of 26 days were dedicated to automation on project A compared to 8 days on project B. The objective on project A was to automate 5 test cases, representing a total of 48 steps to automate and on project B 12 test cases composed of 58 steps to automate, i.e. a fairly similar scope to automate (20% step more on project B) in terms of number of steps to work on, therefore comparable.

For project A, 6 days were dedicated to the modeling of the workflow and 2 days to the completion of the adaptation layer, i.e. 30% of the total effort for automation against 1.5 days for project B, i.e. 18.75% of the total effort for automation. If we compare these two global percentages 30% and 18.75% we obtain a difference of 40%: this is explained by the fact that the workflows and test cases did not exist on the project A which required a lot of work by the automation engineer to identify the existing test cases and introduce them in Yest. The 1st results show that when the test cases are already present the effort to complete the adaptation layer in Yest is reduced. After the test design phase and the completion of the adaptation layer in Yest, we studied the design phase of Keywords. Their coding accounted for 42% of the time dedicated to automation on project A compared to 62% on project B, a difference of 20%. If we compare the coding time between the two projects (11 days on project A, 5 on project B) we observe a difference of 55%. The writing of Keywords was twice as fast on project B as on project A. This can be explained by the fact that on project B the testers who designed the tests had conceived the test workflow with a view to automation, ensuring that there were uniform and consistent test cases that could be easily adapted to a Keywords system. On the 1st project, the test cases had been developed without any real reflection on the automation phase that would follow.

An example of good practice applied is to limit the number of steps (and their content) in test cases to be automated, this facilitates the completion of the adaptation layer. This limits the writing of keywords and their sequencing. As a test case becomes longer, it can be assumed that it will be more complex and therefore involve a certain level of complexity to automate. If we review the experiments and compare the length of the test cases, i.e. the number of steps they contain between projects A and B, we can see that the distribution of the number of steps in the test cases was rather different. Indeed, on project A on 10 test cases to be automated, only one test case had less than 10 steps (10 steps exactly) that is 10% of the referential. On project B, on 13 test cases, 6 test cases had less than 10 steps, almost half of the referential (46%). A majority of short tests therefore contribute to facilitate and save time in the completion of the adaptation layer.

This was to assess how the use of good practice on the Lightweight MBT reduced the design effort of Keywords. The application of good practices facilitates automation even if the writing of Keywords remains a major part of the automation phase. Script generation on both projects is automatic in the Lightweight MBT tool: once the adaptation layer is completed and the Keywords implemented, it is possible to generate the scripts and integrate them into an automated test execution tool. We did not discuss this part in our study because it was independent of the use of Yest. Finally, we studied the maintenance phase: we measured the time dedicated to maintenance on each of these projects, 7 days on project A, 1.5 days on project B. The perimeter of Keywords was similar, but there was more complexity in maintaining the Keywords of project A than on project B. This is the direct consequence that on project A, the tests were not completely adapted to be automated so a certain gymnastics had to be set up to create adapted Keywords and therefore led quite naturally to maintenance difficulties, because the Keywords were complex. On the B project the Keywords were simpler, configurable and reusable on different test steps, thus limiting the updates to be performed to maintain the scripts. This explains why Project B has a maintenance time 78% shorter than Project A and represents 18.75% of the overall effort for automation compared to 27% for Project A.

III. CONCLUSION

Our approach sought to deal with two challenges : the optimization of test case design and test automation in Agile contexts. These results and our experience allow us to affirm that the tst case designe and implementation with Lightweight MBT is very well adapted to Agile cycles with short iterations, because this approach allows us to quickly generate new test cases, update it and thus allow the earliest possible test execution. On the B project, applying the Lightweight MBT approach, nearly 700 test cases were generated via Lightweight MBT in Agile and ATDD context over 8 months of project without the test design time delaying the different phases of the cycle, on the contrary.

With regard to test automation, an early account that test cases will be automated as part of the project is a key success factor and a major facilitator of automated test development and maintenance in the context of large IT projects. On the project A automation was initiated after more than a year of development without automation being planned and the subject was treated without implementation of good practices both in test design and keywords. As a result, the automation framework was too complex and its maintenance was very difficult. On project B, from the beginning of the project, the tests were designed in a uniform way, trying to use existing elements as often as possible instead of creating new ones in order to have the most "coherent" test cases as we can.

Introduction

Verified solution

MBT

Fig. 1 .

 1 Fig. 1. Summary of results on the study of design times between manual design and implementation vs. Lightweight MBT

•

  Test analyst : built test (only for manual execution)Do not use ATDD approachOnly test cases for automation have been created with Yest • Testing of a web application • Agile context with 4-week sprints Context presentation (Reminder) Using the Lightweight MBT approach (with Yest) • Using Selenium and Junit QRS 2019 | Tuesday, July 23, 2019 Lightweight MBT for automation Overview • Keyword-driven-testing • Java Selenium add-on • Data set management Lightweight MBT for automation Test automation process The visual representation of the test The abstract scenario and the corresponding automated test script The test script in java/Selenium with the use of dataset QRS 2019 | Tuesday, July 23, 2019 Lightweight MBT for automation Test automation process the scope of the version Functional testers actively participate in automation Clarify the business needs Improve the validation of the US

On project B an average gain of 60% on the update time of test cases QRS

  • built test to automate (Based on the current one) • completed the adaptation layer • built the automation code.

	Context presentation Manual test design vs. Lightweight MBT approach
	Lightweight MBT approach
	Project A	Project B
	Product owners Only test cases for automation have been created with Yest • Testing of a web application • Agile context with 4-week sprints Manual test design and implementation vs. Lightweight MBT approach Product owners	All test cases have been created with Yest • Using the Lightweight MBT approach (with Yest) • Using Selenium and Junit Increase Clarify the visibility of business the scope of the needs All test cases have been created with Yest
	business analysts business analysts Do not use ATDD approach ATDD	version Use ATDD approach Use ATDD approach
	(Acceptance Test Driven Development)	Improve
	Testers Test automation specialist : Developers • completed the adaptation layer • built the automation code. Testers • built test to automate (Based on the current one) Test analyst : built test (only for manual execution) Developers Test automation specialist :	Test automation specialist : • completed the adaptation layer • built the automation code. Test analyst : built test (including those that will be automated) • built the automation code. • completed the adaptation layer the validation Test analyst : Make built test (including those that will be automated) testing of the US easier Test automation specialist :
		• Initialization of automation : from the beginning of
	Initialization an implementation of automation : Initialization an implementation of automation :	the project
	after one and a half years after one and a half years	• Implementation of automation : after 6 month (as
		soon as stable processes were identified)

QRS 2019 | Tuesday, July 23, 2019 Manual test design vs. Lightweight MBT approach Overview QRS 2019 | Tuesday, July 23, 2019 Manual test design vs. Lightweight MBT approach Lightweight MBT approach QRS 2019 | Tuesday, July 23, 2019 QRS 2019 | Tuesday, July 23, 2019 Manual test design vs. Lightweight MBT approach Results 2019 | Tuesday, July 23, 2019 Manual test design vs. Lightweight MBT approach Conclusion • Design and update time are almost halved • Communication between stakeholders is facilitated • The expression and dissemination of customer needs is improved • Overall test management is straightforward Automation • Initialization of automation : from the beginning of the project • Implementation of automation : after 6 month (as soon as stable processes were identified)


Kevin Laurent
email: kevin.laurent@femto-st.fr

Valérie Lepiller

Philippe Nika

Yannick Bailly

Modélisation numérique d'échangeur de chaleur par méthode nodale et CFD

Keywords: Echangeur de chaleur, Nodale, Modélisation Thermique

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

INTRODUCTION

Le transport est un domaine en perpétuelle croissance depuis la révolution industrielle et même bien avant avec entre autres les véhicules propulsés par la force animale. L'automobile a été inventée au XIXème siècle en utilisant d'abord comme source d'énergie la vapeur. Mais il faut attendre l'arrivée du moteur à combustion interne et son utilisation avec le pétrole comme carburant pour obtenir une évolution des productions sans précédent. Au début du XXème siècle, la France est très présente dans le domaine de la production automobile avec une trentaine de constructeurs différents. Mais récemment de nouvelles problématiques apparaissent, en parallèle avec les différentes crises écologiques. Malgré que différentes alternatives au moteur thermique aient été soulevées et testées, aucune ne semble trouver ses intérêts sociétal et économique. Le [START_REF] Kakaç | Heat Exchangers : semection, rating and thermal desing[END_REF]. Un tel échangeur aura un régime de fonctionnement fortement instationnaire rythmé par les ouvertures des soupapes d'admission. Or le dimensionnement des échangeurs de chaleur est un problème actuel étudié par la communauté scientifique. Des méthodes de calcul existent comme la méthode de l'efficacité et du nombre d'unité de transfert [START_REF] Stone | Review of literature on heat transfer enhancement in compact heat exchangers[END_REF][START_REF] Incropera | Fundamentals of Heat and Mass Transfer[END_REF]. Mais la majorité des études et des modèles génériques [START_REF] Liu | A general steady state mathematical model for fin-and-tube heat exchanger based on graph theory[END_REF][START_REF] Kays | Compact Heat Exchanger[END_REF][START_REF] Weimer | A general steady state mathematical model for fin-and-tube heat exchanger based on graph theory[END_REF][START_REF] Pingaud | Steady-state and dynamic simulation of plate fin heat exchangers[END_REF] sont seulement en régime stationnaire, les résultats ne sont pas utilisables dans le cas d'une modélisation en régime instationnaire. Cependant, quelques modèles numérique et analytique en transitoire ont fait leur apparition dès les années 70-80 [START_REF] Gvozdenac | Analytical solution of transient response of gas-togas parallel and counterflow heat exchangers[END_REF][START_REF] Romie | Transient response of gas-to-gas crossflow heat exchangers with neither gas mixed[END_REF][START_REF] Romie | Transient response of the counterflow heat exchangers[END_REF].

Dans l'industrie automobile, les échangeurs de chaleur sont majoritairement utilisés pour le refroidissement du moteur thermique. Existant pour plusieurs géométries (échangeur à tubes, à ailettes, mousse…), l'échangeur sur lequel porte cette étude est un échangeur air/eau dit WCAC pour Water cooled Charge Air Cooler, qui est utilisé sur un véhicule muni d'un turbocompresseur. Son rôle est de refroidir l'air pour augmenter son débit massique. L'échangeur utilise le liquide de refroidissement déjà présent dans le véhicule. Celui-ci permet une perte de charge moins importante, une température de l'air plus stable et donc une meilleure combustion. Ainsi, cela entraine une réduction de la consommation, et donc une meilleure réponse du moteur.

Notre étude consiste à modéliser un échangeur de ce type en trois dimensions avec un modèle simple pour gagner en temps de calcul tout en gardant un écart acceptable (vers 5%). En effet, les codes de calcul les plus utilisés dit CFD pour Computation Fluid Dynamique sont des outils efficaces mais le temps de calcul peut être très long. Notre étude propose une méthode nodale.

MODELISATION NODALE

La modélisation nodale consiste à discrétiser un système étudié en noeuds. Chaque noeud fait référence à un volume du système. L'interaction entre chaque noeud est visualisée comme une résistance qui modélise un phénomène thermique. La modélisation finale est un maillage correspondant à l'assemblage des noeuds et des résistances internodales. Une analogie existe avec la schématisation d'un circuit électrique (Fig. 1).

Programmation

Dans le but de résoudre les équations présentées précédemment, nous avons créé un programme utilisant le langage Python™, nommée NACS pour Nodal Analysis Computation Software, qui suit l'algorithme suivant : Pour permettre la résolution, nous avons besoin de renseigner le temps initial, les températures initiales de chaque noeud ainsi que la dérivée par rapport au temps de la température donnée par l'équation [START_REF] Kakaç | Heat Exchangers : semection, rating and thermal desing[END_REF]. Nous obtenons au final un tenseur d'ordre 5, qui regroupe les températures de chaque noeud selon leur position en 3 dimensions et le temps.

COMPARAISON NODALE / CFD

Afin de valider notre programme de calcul par méthode nodale, nous avons décidé de faire des comparaisons avec le logiciel de CFD.

Cas conductif simple

Pour pouvoir faire des comparaisons, nous nous sommes intéressés à un transfert de chaleur par conduction simple. Un solide est à une température fixe au temps initial (t=0) ; nous appliquons à ce solide une condition limite du troisième type dite condition aux limites de Robin, sur toutes ses faces. Nous utilisons le même maillage avec les deux logiciels. La figure 3 représente l'évolution de la température du solide suivant le temps. Notre étude a également porté sur les écarts relatifs entre les méthodes obtenus dans les cas où nous n'aurions pas le même maillage (Fig. 4). L'objectif est de déterminer à partir de quel maillage nous avons un écart acceptable en comparaison de la CFD.

T1 T0

Rth

Modélisation d'échangeur thermique

Notre étude s'est portée sur le cas de l'échangeur thermique à plaques centimétriques. Deux fluides, air et eau, échangent de la chaleur à travers une plaque sans transfert de fluide. Ces fluides s'écoulent dans des canaux rectangulaires. Cet échangeur est nommé échangeur à contre-courant. Le fluide chaud (air) s'écoule dans le sens inverse du fluide froid (eau). A l'aide du modèle nodal décrit sur la figure 6, nous étudions les deux types de transfert thermique qui interviennent dans l'échangeur : la convection s'exerçant entre le fluide et la paroi et la conduction à l'intérieur de la paroi. Le transfert par advection est aussi à intégrer dans notre modèle car les fluides sont à un débit fixe. Pour décrire les échangeurs WCAC, nous imposons un saut de température de l'air à l'entrée de l'échangeur. La température de l'air est préalablement imposée à 80°C pendant 2 secondes puis elle passe à 175°C. Les entrées d'eau ont une température fixée à 45°C. Les débits fixés pour la simulation sont de 0,25 g.s -1 pour l'air et de 7,5 g.s -1 pour l'eau. La température initiale de l'échangeur est fixée à 80°C. La figure 7 représente l'évolution de la température de sortie de la veine d'air en fonction du temps. Les résultats mettent en évidence la difficulté de la méthode nodale pour suivre des changements brutaux de condition limite.

MONTAGE DE NOEUDS EN SERIE

Notre étude s'est portée également sur l'influence du nombre de noeuds (Fig. 8).

Fig. 1

 1 Fig.1 Principe de la méthode nodale thermique En effet, en s'intéressant à la modélisation thermique nodale, nous pouvons faire les liens suivants : • le courant électrique et le flux thermique (i ⟺ Φ) • la tension électrique et la température (U ⟺ T) • la résistance électrique et thermique (Relec ⟺ Rth)Ensuite, pour la résolution de ce circuit, nous passons par des lois issues de l'électricité. Nous pouvons ici mettre en évidence les lois de KIRCHHOFF. Celles-ci regroupent la loi des mailles et la loi des noeuds. En appliquant ces lois au maillage précédemment obtenu, nous obtenons un système d'équation d'ODE.

Fig. 2

 2 Fig.2 Algorithme de résolution Nous pouvons voir sur la figure 2 que le programme a été construit suivant deux grandes étapes. La première consiste à générer des matrices, celle des conductances   G , des

Fig. 3

 3 Fig.3 Réponse thermique transitoire d'un cube solide et son écart relatif par rapport à la CFD Nous remarquons que l'échauffement du solide donné par la méthode nodale est similaire à celui donné par la CFD. En effet, nous pouvons voir que l'écart entre les résultats donnés par le programme NACS et la CFD sont inférieurs à 0,5%.

Fig. 4

 4 Fig.4 Ecart relatif entre NACS et la CFD pour des maillages différents Avec le modèle NACS et un maillage 12 fois moins défini, nous obtenons un écart maximal de 0,5% par rapport à la solution CFD. La figure 5 représente la durée des calculs en fonction des méthodes pour des maillages différents.

Fig. 5

 5 Fig.5 Temps d'exécution entre NACS et la CFD pour différents maillages La durée d'un calcul avec la méthode nodale est 17 fois plus réduite que les calculs itératifs de la CFD pour le même maillage et le même nombre de points temporels.

Fig. 6

 6 Fig.6 Modèle nodal pour un échangeur contre-courant à plaque

Fig. 7

 7 Fig.7 Réponse en température de la sortie de la veine d'air de l'échangeur

Fig. 8

 8 Fig.8 Modélisation nodale en série Nos résultats ont mis en évidence que plus le nombre de noeuds augmente, plus le modèle semble contenir une inertie artificielle qui semble être présente dans la résolution d'advection par la méthode nodale 5. CONCLUSIONS ET PERSPECTIVES La modélisation d'échangeur de chaleur est un domaine toujours en perpétuelle évolution. La géométrie de plus en plus complexe des échangeurs de chaleur dans l'habitacle moteur les rend plus difficile à traiter. Le temps de calcul des logiciels de CFD est très long. En effet, pour obtenir une solution fiable, il faut avoir un maillage très dense. La méthode nodale par son analogie avec un circuit électrique est plus simple à mettre en place et à résoudre. Les avantages sont multiples sur des cas simples de transfert conductif. La méthode se révèle aussi précise avec un écart inférieur à 0,5% et 17 fois plus rapide à l'exécution. De plus, avec un maillage 12 fois moins dense, nous obtenons un écart acceptable. Néanmoins, l'application de cette méthode à un échangeur de chaleur se montre difficile. En effet, dans ce cas, le transfert de chaleur est associé à des phénomènes de convection et d'advection. Nous avons montré que la méthode nodale ne peut pas actuellement répondre à un cas d'échangeur thermique. L'ajout de noeuds en série crée une inertie de plus en plus grande.

  moteur thermique va probablement prospérer pendant encore plusieurs années. Ce n'est pas pour autant que les enjeux environnementaux et économiques ne sont pas pris en compte. Alors il vient naturellement la nécessité d'améliorer les systèmes existants. Deux voies d'améliorations sont en vue, le traitement des effluents gazeux, et également la réduction de la consommation induisant une réduction des émissions de polluants. L'objectif est d'améliorer le moteur thermique en vue d'un meilleur rendement. Pour cela, le moteur doit Mais cela induit une augmentation de la température de l'air d'admission. Afin d'éviter les phénomènes de cliquetis, où le mélange comburant et carburant s'auto enflamme avant que le piston soit au point mort dû à une trop grande compression d'air. Afin d'accroitre la masse de gaz qui pénètre dans le cylindre, nous devons réduire la température

	fonctionner	dans	des	conditions	optimales.	Le
	turbocompresseur est une des principales avancées
	technologiques. d'admission d'air. C'est pour cela que les constructeurs
	automobiles installent un échangeur de chaleur sur le circuit
	d'alimentation d'air. En effet, un échangeur est un dispositif
	permettant le transfert de chaleur entre au moins deux fluides
	ayant une différence de température, sans qu'il y ait pour autant
	transfert de masse


est destinée au dépôt

Procédure expérimentale appliquée à l'identification des propriétés hygrothermiques des matériaux de construction par méthode non destructive

Fatima El Mankibi, Yacine Ait Oumeziane, Valérie Lepiller, Marina Gasnier,

Philippe Désévaux

To cite this version:

Fatima El Mankibi, Yacine Ait Oumeziane, Valérie Lepiller, Marina Gasnier, Philippe Désévaux. Procédure expérimentale appliquée à l'identification des propriétés hygrothermiques des matériaux de construction par méthode non destructive. Congrès Français de Thermique, Jun 2019, Nantes, France. hal-02472657

Congrès français de thermique

Thermique et Industrie du futur (*) f.elmanki@femto-st.fr [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois aux bétons de chanvre[END_REF] Institut FEMTO-ST, Univ. Bourgogne Franche-Comte, CNRS, 2 avenue Jean Moulin, 90000 Belfort [START_REF] Rouchier | Solving inverse problems in building physics: An overview of guidelines for a careful and optimal use of data[END_REF] Institut FEMTO-ST/RECITS, Univ. Bourgogne Franche-Comte, CNRS, 2 avenue Jean Moulin, 90000 Belfort, France Procédure expérimentale appliquée à l'identification des propriétés hygrothermiques des matériaux de construction par méthode non destructive Fatima EL MANKIBI (1 * ) , Yacine AIT OUMEZIANE [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois aux bétons de chanvre[END_REF] , Valérie LEPILLER [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois aux bétons de chanvre[END_REF] , Marina GASNIER [START_REF] Rouchier | Solving inverse problems in building physics: An overview of guidelines for a careful and optimal use of data[END_REF] , Philippe DESEVAUX [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois aux bétons de chanvre[END_REF]  L'isotherme de sorption est fortement influencée par les conditions climatiques imposées.

 Pour la conductivité thermique, les évolutions obtenues pour les trois séquences présentent des différences très faibles.

 Le résultat obtenu à partir de la résolution du problème inverse a la même allure que les mesures de température et d'humidité relative.  Modélisation 1D des transferts hygrothermiques [START_REF] Oumeziane | Evaluation des performances hygrothermiques d'une paroi par simulation numérique : application aux parois aux bétons de chanvre[END_REF]  Méthodologie de caractérisation: validation croisée [START_REF] Rouchier | Solving inverse problems in building physics: An overview of guidelines for a careful and optimal use of data[END_REF]  Modèle d'optimisation : ALEMBERT, basé sur l'algorithme de Levenberg-Marquardt avec la mise à jour de la matrice jacobienne par la méthode de Broyden [START_REF] Jamal | Méthodologie pour une meilleure connaissance des matériaux du patrimoine industriel[END_REF]  Transition énergétique : le secteur du bâtiment représente un fort potentiel d'économie d'énergie.

 Patrimoine industriel : la reconversion des édifices industriels nécessite une meilleure connaissance de leurs matériaux de construction.

 Evaluation d'une méthode de caractérisation non destructive par validation croisée des propriétés hygrothermiques des matériaux de construction.





  La variabilité des paramètres hygriques obtenus montre que la modélisation choisie du problème direct nécessite d'être enrichie.  Paroi étudiée : fibre de bois  Capteurs : thermo-hygromètres enregistreurs  Précision :  0,2°C température  2,5% humidité relative  Temps d'acquisition : 15 min  Durée des essais : 7 jours  Consignes imposées :  Séquence 1 : ΔT ≠ 0 et ΔP v ≠ 0 Séquence 2 : ΔT ≠ 0 et ΔP v = 0 Séquence 3 : ΔT ≠ 0 et ΔP v ≠ 0 Enceinte biclimatique Paramètres à identifier : [ 𝝆 𝟎 , 𝒄 𝟎 , 𝒖 𝒔𝒂𝒕 , 𝝀 𝟎 , A , 𝝁 𝟎 , α , η ]



  Utiliser une méthode stochastique pour résoudre le problème d'optimisation  Enrichir le modèle physique utilisé en prenant en compte les phénomènes négligés tels que la diffusion liquide et le phénomène d'hystérésis  Confronter les résultats obtenus par la méthode non destructive à ceux de la méthode destructive Appliquer la méthode de caractérisation in situ sur un ancien atelier industriel de valeur patrimoniale Isotherme de sorption Evolution de la conductivité thermique Evolution de la température et de l'humidité relative de la surface extérieure de Evolution de la température et de l'humidité relative des surfaces intérieure et extérieure de la paroi.


Taib Arif

Shwetank Yadav

Guillaume Colas

Chandra Veer Singh
email: chandraveer.singh@utoronto.ca

Tobin Filleter
email: filleter@mie.utoronto.ca

Understanding the independent

Keywords: Nanotribology, MoS2, Oxidized-MoS2, Friction, DFT

Introduction

Billions of dollars are wasted annually due to energy loss caused by friction [1] , where energy is dissipated primarily as heat. [2,3] To decrease friction on sliding contacts, microscale-MoS2 and graphite are widely used solid lubricants for space [START_REF] Lince | Proc. 43rd Aerosp. Mech. Symp[END_REF][START_REF] Gibson | Conf. Proc. 15th Eur. Sp. Mech. Tribol. Symp[END_REF] (joints, bearings etc.) and aerospace [START_REF] Voevodin | [END_REF] (gears, reaction wheels etc.) applications. Though both of the materials consist of weakly interacting layered structures (2D-MoS2 and graphene), they display a contrary dependence on the humidity at the microscale, where the coefficient of friction (COF) is reported to drop for graphite in the presence of water, yet increases for microscale-MoS2 coatings. [7][8][9][10] In the case of MoS2, the widely accepted mechanism for the increase in COF is the oxidation of microscale-MoS2 to the less lubricious MoO3 from exposure to humidity [11] .

However, separating the effect of the unreacted water molecules present and oxidation is difficult in microscale studies. Furthermore, the sensitivity of microscale-MoS2 to water can be influenced by the structure (amorphous/crystalline) of MoS2 [12] and alloying elements. [13,14] Oxidation thickness of microscale-MoS2 is reported to be thinner and on the surface with less oxygen penetration within the coating when MoS2 layers are highly ordered as compared to amorphous. [11] While there is some understanding of mechanisms (localized interlayer shearing, puckering effect, electron phonon coupling etc.) at the nanoscale associated with water influencing friction for graphene, graphene oxide (GO) and graphite edges [15][16][17][18][19][20][21][22][23][24] , there is only limited understanding for MoS2 and oxidized-MoS2 at the nano/molecular scale. Advancement of technological tools such as the atomic force microscope (AFM) has allowed studying the fundamental mechanisms governing friction at atomic/molecular scale. [17,18,25,26] In particular, recent advancements for controlling the environment locally around the single AFM contact have expanded our understanding, by moving away from studying friction as a function of normal load only to consider the role of other variables such as relative humidity [15] and temperature. [27,28] At the atomic scale, MoS2 is categorized as a 2D transition metal dichalcogenide (TMD), consisting of a covalently bonded tri-layer structure, with molybdenum atoms sandwiched between sulfur atoms. [29] In vacuum, a friction study between 2D-MoS2/2D-MoS2 has demonstrated superlubricity, with a COF on the order of 10 -4 due to incommensurability. [30] Humidity has been shown to increase the coefficient of friction and interlayer shear strength of MoS2 in contact with a sharp Si3N4 AFM tip, however the study neglected to separate the influence of water and oxidation, did not account for the change in geometry of the sharp tip or the substrate effect, and did not identify the underlying mechanisms (specifically, the effect of water molecules vs. oxidation). [31,32] 2D-MoS2 deposited on few layers of water was found to exhibit elevated vibrational energy resulting in an increase of friction. [33] A similar mechanism of phonon excitation has been reported to increase friction for graphene by similarly suspending graphene on water. [34] The interaction of water molecules is relatively weak with the basal plane of 2D-MoS2 but they can interact strongly at defects and edges, where oxidation is understood to initiate. [35,36] Though the literature generally agrees that the oxidized state of MoS2 as MoO3 at the microscale is detrimental to its lubricious behavior, recent studies have questioned this frictional behavior of oxidized 2D-MoS2. [37,38] For instance, theoretical DFT simulations have reported easier shearing between 2D-MoS2/2D-MoO3 than 2D-MoS2/2D-MoS2. Additionally, Chow et al. reported that the substitution of sulfur atoms with oxygen atoms can change the wettability of monolayer 2D-MoS2. [39] While wettability has been shown to influence the friction behavior on other 2D materials, it has not been studied for 2D-MoS2. [15] Therefore, there is a need for studying the influence of water and oxidation on MoS2 to better understand how they can improve or degrade frictional behavior, while also conducting complementary atomistic simulations for further insights on the mechanisms. Such fundamental understanding will be of great importance in particular for space applications where MoS2 coating already undergo extensive testing ensuring its durability.

In this work, we study the independent and inter-dependent role of water and oxidation on the tribological behavior of ultrathin-MoS2 (few layers of 2D-MoS2). In particular, the behavior of pristine ultrathin-MoS2 is compared with our previous studies on ultrathin-graphene [15] to provide insight into the role of water. Furthermore, the influence of oxidation on ultrathin-MoS2 was studied using a combined experimental and computational approach by comparing the tribological behaviour of pristine ultrathin-MoS2 and oxidized ultrathin-MoS2 at varying humidity to deconvolute the role of water before and after oxidation. Density functional theory (DFT) simulations were used to gain further insight into the electron charge interactions for both pristine and oxidized MoS2 on basal planes and step edges for deconvoluting the role of water and oxidation.

Results and Discussion

Water adsorption and oxidation of ultrathin-MoS 2

Figure 1a shows the change in thickness by tapping mode AFM imaging of pristine ultrathin-MoS2 while varying the humidity and comparing the behavior to that of ultrathin-graphene. The thickness was normalized (Figure 1 -yaxis) by dividing the current thickness (Hi) at a given humidity with the thickness at RH5% (HRH5%) for pristine-MoS2. Pristine-MoS2 of approximately 5 layers (~3.3nm) was exposed to varying humidity from RH5% to RH75%. It was observed that the increase in humidity had no influence on topography and minimal effect on the change in thickness of ~0.4nm (~12% increase in thickness) for MoS2 (Figure 1b). This behavior of pristine-MoS2 was observed to be similar to graphene, and contrary to the large increase in thickness previously reported for graphene oxide. [15] This is consistent with previous reports that water intercalating between the MoS2/substrate requires very long exposure time (weeks) at extremely high humidity (+RH95%). [33,34] Furthermore, the atomic structure of pristine-MoS2 also prevents water from intercalating between the layers due to the small interlayer distance, the lack of strong interlayer bonding sites for the water molecules and native oxides at the edges. [15,40] Both pristine-MoS2 and graphene physically interact with water at the basal plane [35] and recent studies have suggested the formation of ice like water on the basal plane of other 2D materials. [41] Therefore the small increase in thickness of pristine-MoS2 by ~0.4nm is attributed to a single layer of water adsorbing on the pristine-MoS2 surface. [33] X-ray photoelectron spectroscopy (XPS) reveals the presence of 3.9at% of oxygen in the unannealed pristine-MoS2 sample (Figure 1c). The oxygen measured is expected as the highly reactive edges/defects can substitute sulfur atoms with environmental oxygen atoms to form native edge oxides.

This behavior was further supported by our DFT results, which showed that oxidation of pristine-MoS2 edges through substitution of sulfur atoms is highly energetically favorable (Figure 1d). To further oxidize MoS2, samples were annealed in air at 290°C for 3hrs. XPS confirmed the increase in oxygen from 3.9at% to 9.6at% (Figure 1c). High-resolution XPS shows an increase in the intensity of the O1s peak (Figure 1c) as well as some broadening of the Mo3d3 peak at 232.2eV and the initiation of a new Mo3d3/2 peak at 235.4eV, indicating the formation of MoO3 structure post-annealing (Supporting information; Figure S1). Annealing is also expected to increase the coverage of oxygen along the basal plane of MoS2 in addition to at the edges/defect sites. [11]

Role of water on friction of pristine ultrathin MoS 2

The friction and adhesion behavior of pristine ultrathin-MoS2 was investigated as a function of humidity and compared to that of ultrathin-graphene (Figure 2) using a custom SiO2 beaded AFM cantilever. It was observed that the increase in humidity increased the overall friction force for the SiO2/ pristine-MoS2 interface from ~1.7±0.1nN (RH3%) to ~8.9±0.2nN (RH65%). Comparing the behavior of pristine-MoS2 with graphene, both the materials experienced an overall increase in friction force with the presence of water. Though the general increasing friction trends are similar for both the 2D materials, it is interesting to highlight that the friction transitions at lower humidity for pristine-MoS2 as compared to graphene. For pristine-MoS2, increase in friction occurs at humidity as low as RH20% while for graphene at RH50% (Figure 2a grey and black arrows). This behavior was repeatable for two different sample datasets and for varying normal loads (Supporting information; Figure S2). Adhesion between the SiO2/pristine-MoS2 interface was determined by measuring the pull off force and was found to increase from ~943±8nN (RH10%) to ~1495±143nN (RH45%) for the first data set and from ~530±14nN (RH10%) to ~1180±14nN (RH60%) for the subsequent dataset. The overall adhesion between the SiO2/pristine-MoS2 interface was observed to be higher than SiO2/graphene. The adhesion and friction trends overlapped for pristine-MoS2 and are observed to increase at RH20%, indicating that adhesion plays a significant role in defining the friction behavior for pristine-MoS2. From the previous section (Figure 1), it was concluded that both pristine-MoS2 and graphene have similar water adsorption behavior, where both the materials physisorb a single layer of water on the top surface. Herein, both the materials show overlapping friction-adhesion trends (Figure 2) indicating water adsorption as the primary mechanism dictating their tribological behavior at the atomic scale. This was further supported as a similar behavior of pristine-MoS2 was also observed for sliding against a sharp diamond tip (Supporting information; Figure S3). To understand the difference in sensitivity to water between pristine-MoS2 and graphene, it is important to highlight their differences in interaction with water.

MoS2 has a tri-layer atomic structure, where the Mo/S atoms can polarize more strongly than the monolayer carbon structure of graphene to physisorb water on to the surface. [35] The absorption energy of a water molecule on defect free monolayer MoS2 is reported to be -0.18eV compared to -0.15eV on graphene. [35] The adsorption energy is reported to further increase for thicker and defective MoS2. [35] Water contact angle (WCA) measurements show a lower contact angle of ~80 on pristine-MoS2 as compared to ~91°on graphene (Supporting information; Figure S4). In addition, the water slip length on respective surfaces has been reported to be lower on MoS2 (~1.8nm) compared to that on graphene (~12nm). [42][43][44][45] The slip length is the distance between solid (2D material)/liquid(water) interface and the velocity profile extrapolated to zero. [45] It is used as an indicator to give an insight on the relative ease of water mobility and energy dissipation on a solid surfaces. The lower slip length on MoS2 basal plane suggests more difficult water slippage resulting in higher viscous interfacial force experienced by the sliding counter surface. This is also consistent with the recent atomistic simulations and theoretical calculations which predict that the COF between water/MoS2 to be higher than between water/graphene [44,46] , hence influencing the energy dissipation mechanism of interlayer shearing as a result of the newly evolved interface from water adsorption. Therefore, it is the atomic structure of MoS2 which makes it more sensitive to water at lower humidity of RH20%.

Role of oxidation on friction of ultrathin MoS 2

This section compares the tribological behavior of pristine ultrathin-MoS2 and oxidized ultrathin-MoS2 as a function of humidity using the same SiO2 beaded tip. The average friction force on oxidized-MoS2 (Figure 3) was observed to be significantly higher as compared to that of pristine-MoS2 at any given humidity, with friction increasing from 27±1.3nN (RH3%) to 145nN±8nN (RH70%). This behavior was repeatable for two different sample datasets and for varying normal loads (Supporting information; Figure S5). The less lubricious behavior of oxidized-MoS2 is consistent with oxidized microscale-MoS2 behavior. [11] Adhesion measurements between SiO2/oxidized-MoS2 show some increase between RH3% (679nN) and RH11% (842nN) and plateaus with further increase in humidity. Unlike the behavior of SiO2/pristine-MoS2 observed earlier (Figure2), friction and adhesion trends do not correlate well for SiO2/oxidized-MoS2. A large increase in friction initiates around 30% humidity, however, minimal change in adhesion between 11-70% suggests that adhesion does not play as important a role in the oxidized-MoS2 case. Interestingly, oxidized-MoS2 was found to be more sensitive to water, with friction increasing at even lower humidity of RH11%, compared to the RH20% for pristine-MoS2. Chow et al reported MoS2 to be more hydrophilic once sulfur atoms are substituted with oxygen atoms. [47] Therefore water is seen to play a much more detrimental role on the tribology of MoS2 contacts once some oxidation has initiated, particularly along the basal plane.

To further investigate the effect of oxidization on friction for MoS2, DFT simulations were conducted to characterize the surface interaction of a diamond tip as it moved across pristine and oxidized MoS2 basal planes and step edges. The change in the potential energy surface shape, specifically its corrugation, with changes in relative position of interacting surfaces as they slide past one another is directly correlated with the resistance to sliding and hence the friction force. [48,49] The larger the energy change with position, in effect an energy barrier, the greater will be the friction force. Hence, we tracked system energy as the diamond tip was translated across a particular surface in fixed distance increments and plotted the changes in system energy with regards to distance travelled to identify which surfaces produced higher friction force (Figure 4).

For the basal planes, random surface layer sulfur atoms were substituted with oxygen in increasing proportions of 30%, 45% and 60% oxygen coverage corresponding to 9.7, 15.3 and 19.4 at% of total oxygen for the MoS2 material system. The XPS result earlier (Figure 1c) showed similar range of oxidation after annealing with 9.6 at% oxygen corresponding to the 30% oxygen coverage DFT case.

Figure 4a shows the absolute energy change of the system with regards to the energy of the initial configuration. The overall trend was that higher oxygen content produced higher relative energy changes, especially in terms of the maximum change (Table 1). The random distribution of oxygen, different for each surface, would account for why the trend isn't always present at every point along the path (Figure 4b-c).

The step edge displayed the same trend with the native oxidized edge (where the maximum possible oxygen substitution leads to MoO3 units at the edge [50] and is very energetically favorable) showing greater change in interaction energy than the pristine step edge (Figure 4d-f). Figure 4d shows the system energy relative to the starting position, whether higher or lower, in order to capture the effect of going over the edge. The barrier that is visible in the energy profile as a sharp peak and drop-off, when the tip approaches the step edge at around 33 Å, is often referred to as the Schwoebel barrier/effect and is also observed for graphene. [51] For the native oxidized edge, this barrier was found to be ~ 25% higher than for the pristine edge which further confirms that oxidation increases friction. The maximum energy change for either case is also significantly higher than for any basal plane case. Experiments also show the overall trend of increasing friction when going over an edge versus a basal plane. High resolution FFM was performed using a sharp diamond tip on a native oxidized MoS2 edge, exhibiting 3 times the increase in friction from 0.4±0.2nN at the basal plane to 1.1±0.1nN over the expose edge (Supporting information; Figure S7). Note that, while the experimental results show the same overall trend as the simulations, it can be difficult to quantitatively compare values. The tip utilized for the DFT simulations was cut to form a 5 nm radius hemisphere, while the actual contact between the two surfaces was localized to the scale of angstroms due to system size constraints and essentially led to a flat tip surface. On the other hand, for experiments, the diamond tip radius was much larger (indirectly measured to be ~ 40 nm using the lateral peak width technique [52] ). Hence, the contact area was much larger and was affected by tip shape. The tip also moved across a non-perfect surface where the interaction could be affected by variation in topography, defects, substrate effects and environmental effects (especially humidity which could not be completely removed experimentally). The DFT simulations mainly capture electronic interaction effects and are generally only useful for comparative trends within the same simulation conditions. They looked at the specific case of laterally moving a tip surface while only oxygen content was varied (this isolation of a specific variable is not easily achieved in experiments, for example a pristine unoxidized edge was not available to be measured).

Figure 5a shows the charge (electron) density for a cross-section of the pristine MoS2 basal plane with the diamond tip over it, where the structure of the MoS2 with Mo atoms in center (and with the highest charge concentration) sandwiched by S atoms is clearly visible. The scale Δn(r) represents change in charge density compared to a region of no charge (shown by red). A continuous region of similar charge density extends between surface S atoms in contact with diamond tip C atoms within the same contour of charge. In contrast, for the oxidized basal plane in Figure 5b, there is a lower region of charge density present between the surface O atoms and tip atoms. The O atoms can be seen to be more electronegative than S; i.e. they have a greater concentration of charge and have pulled more charge from the nearest Mo atom than S atoms do. The region of relatively greater charge density between the tip and pristine surface S atoms likely leads to a more stable system and also allows for easier sliding of the tip as there is relatively less variation in charge as the tip travels. On the other hand, for the oxidized plane, the lowered interfacial charge density between the tip and surface O atoms likely leads to a less favorable system and the increased localization of charge also causes more drastic variations in charge as the tip travels; this would lead to greater energy variations and more resistance to sliding. A decrease in the uniformity of charge density at the surface has also been previously suggested to increase friction. [53][54][55]

Summary & Conclusions

In this work, the separate role of water and oxidation on the tribological behavior of ultrathin-MoS2 (few layers of 2D-MoS2) was investigated and compared to ultrathin-graphene. Water adsorption studies illustrated a similar behavior for pristine-MoS2 and graphene, where a single layer of water adsorbs on the top MoS2 surface without intercalating between the layers. The similar adsorption behavior herein was attributed to the atomic structure of these ultrathin 2D materials. XPS confirmed the presence of some oxygen on MoS2, where exposure to the environment oxidized the reactive edges/defects site. This behavior was further supported by our DFT results, which showed that oxidation of MoS2 edge through substitution of sulfur atoms is highly energetically favorable. Annealing MoS2 in air at 290°C enhanced oxygen substitution on MoS2, increasing the oxygen content from 3.9at% to 9.6at% along the basal plane.

The role of water was studied by comparing the friction and adhesion behavior of SiO2/MoS2 with SiO2/graphene, the study demonstrates that pristine-MoS2 (few layers) is more sensitive to the presence of water. MoS2 was observed to retain its low friction and adhesion behavior only within a low humidity regime and for a shorter humidity range (RH5-20%) as compared to graphene (RH5-50%).

Water adsorption was identified as the primary mechanism dictating the tribological behavior for pristine-MoS2 and graphene against the SiO2 counter surfaces (SiO2/MoS2 and SiO2/graphene). This also highlights that even though the same mechanism of water adsorption is the dominant factor on MoS2 and graphene, small changes in 2D material-water interaction can significantly influence the tribological behavior and their sensitivity to water.

The role of oxidation was studied by comparing ultrathin-MoS2 and oxidized ultrathin-MoS2 at varying humidity to deconvolute the role of water before and after oxidation. It was found that oxidation of MoS2 along the basal plane significantly increases the average friction as well as increases the sensitivity to water. Pristine-MoS2 itself remains in a relatively lubricious state regardless of the humidity, and only upon increased oxidation does the observed behavior change drastically where water begins to play a more detrimental role. This was confirmed via DFT simulations which predicted an increase in friction for surface and edge oxidation. The DFT studies showed that the substitution of sulfur atoms with oxygen atoms can increase the resistance to sliding along the basal plane and over the edge.

The maximum relative energy change as the tip moved across the surface increased by ~66% upon oxidation for the basal plane and the barrier for moving over the edge increased by 25% at the native oxidized edges. Charge density simulations suggest this occurs because of oxygen's more electronegative nature which causes stronger localization of charge at the surface and hence more uneven electron and energy interactions at the surface as the tip moves across it. Both DFT and experimental results suggest that oxidation on the basal plane is more detrimental to the lubriciousness of MoS2 than oxidation at the edges alone. This work suggests there is a threshold limit in terms of controlling humidity to be lower than RH20% around contacts/interfaces composed of MoS2 to maintain a low friction regime. Sliding contacts/interfaces should be designed such that the oxidation on the basal plane surface be minimized as it is proven to be more detrimental to the behavior of MoS2 than native oxidized edge alone. Lastly, the oxidation findings on ultrathin MoS2 can provide insights into the behavior of microscopic MoS2 coatings which are known to undergo re-crystallization towards well oriented planer layers.

Materials and Methods

Experimental

Sample preparation and material characterization. An extra large MoS2 crystal (Graphene Supermarket) of >99% purity was used to fabricate the samples. Ultrathin-MoS2 (5-8 layers of 2D MoS2) samples were prepared by mechanical exfoliation using scotch tape onto a silicon wafer. An n-doped silicon wafer was used as a substrate which was cleaned using ethanol and methanol in an ultrasonic bath for 10 min. XPS characterization was performed on thick MoS2 using the ESCALAB 250Xi to track the oxygen state, which uses an Al K alpha gun source (Supporting information; Figure S1). To oxidize MoS2, Samples were annealed at 290C for 3hrs while exposed to air in a Cole Parmer Sabletemp vacuum oven (model 281A). Raman spectroscopy was performed on a Bruker Senterra dispersive microscope using a 532nm laser. (Supporting information; Figure S8).

AFM calibration and measurements.

All AFM experiments were performed on the Asylum Research MFP 3D AFM. Custom built AFM cantilevers were used for friction and adhesion experiments. Silica spherical beads (Polyscience Inc.) were cleaned in an ultrasonic bath using ethanol and methanol for 10 mins. The clean beads were then attached to tipless silicon cantilevers (APPNano) with epoxy using a micromanipulator-microscope setup. Using SEM (Hitachi SU3500), the bead diameter was measured (∼14 μm). The cantilever was calibrated normally and laterally, where the normal deflection sensitivity was obtained by deflecting the tip against a clean silicon wafer to obtain the slope of the normal voltagedisplacement curve. The lateral deflection sensitivity was acquired by laterally deflecting against a cleaved potassium bromide (KBr) surface using the test probe method [56] . The normal and torsional stiffness of the cantilever was calibrated using Saders methods [57,58] , giving a normal stiffness of 6.42 N/m. FFM was performed by scanning the probe at 90° scan angle against the sample surface, line by line at the scan rate of ∼5μm/s. The AFM tip scanned forward (trace) and backward (retrace) for each scan line, where the friction force is calculated as half the difference between trace and retrace. To convert the lateral voltage to lateral force, trace and retrace voltage signals were multiplied by lateral sensitivity, torsional stiffness, and 1/h 2 , where h is the height of the AFM tip. Adhesion experiments were performed with a maximum normal load of 800nN with the dwell time of 1s. Thickness measurements were performed using tapping mode AFM imaging of MoS2 using sharp silicon cantilever (Nanoworld) of 42 N/m stiffness and 320 kHz resonance frequency. The thickness of MoS2 in Figure 1 were measured relative to the silicon substrate using a similar protocol reported in the literature [15,40] . The topography data points for MoS2 and the silicon substrate were fit using a Gaussian distribution, where the difference in the mean represented the thickness. Humidity Control. To conduct humidity dependent experiments, a custom built humidity box was used, which allowed for the control of humidity around the contact while continuously monitoring using an embedded humidity sensor (Honeywell HIH 4000). The desired humidity was maintained by controlling the ratio of wet and dry nitrogen gas of 99.9% purity into the humidity box. Wet nitrogen gas was obtained by passing the gas into a water bubbler. Experiments were initiated using new samples placed within the humidity box and purging of N2 gas. The desired environment was allowed to stabilize before conducting experiments to ensure there was minimal drift.

Density Functional Theory. The simulations were performed using plane wave based DFT as implemented in the Quantum Espresso software package. [59] Interactions between the valence electrons and the ionic core were represented by the projector augmented wave (PAW) [60] method with Perdew-Burke-Ernzerhof (PBE) formulation. [61] Kinetic energy cutoffs of 680 eV (50 Ry) and 5578 eV (410 Ry) were used for the wave functions and the charge density, respectively. Brillouin zone integrations were performed over the Γ point and all calculations were non spin polarized. A vacuum layer of 15 Å, based on iterative testing, was added to avoid interaction between periodic surface images. Details of the system geometries are given in supporting information (Supporting information; Figure S6). work to help compare the behavior [15] ). b) pristine-MoS2 thickness at RH5% (green) and RH75% (red) relative to the silicon wafer (blue). c) High-resolution XPS of O1s oxygen peak for MoS2 and annealed published work [15] )

Associated Content:

  Complementary experimental and DFT studies are reported in the supporting information.

Figure 1 :

 1 Figure 1: a) Normalized thickness of pristine ultrathin-MoS2 as a function of humidity. Inset: Tapping

Figure 2 :

 2 Figure 2: a) Comparison of average friction force between a beaded SiO2 tip against pristine-MoS2 and

Figure 3 :

 3 Figure 3: Comparison of average friction force between beaded SiO2 tip against pristine-MoS2 and

Figure 4 :

 4 Figure 4: a) DFT based comparison of diamond tip interaction tracking the relative energy change as tip

Table 1 :

 1 Experimental-computational comparison of friction for oxidized MoS2. Left: Sample configurations. Middle: The maximum energy changes for different MoS2 surfaces as a diamond tip was translated using DFT. Higher energy changes correspond to greater friction force. Right: AFM friction measurements on MoS2 and oxidized MoS2 along the basal plane and edge using SiO2 and diamond tips.

	Surface	DFT maximum energy	Experimental friction [nN]
		change [eV]	-at RH3-5%
		Basal Planes
	Pristine	0.035	1.7±0.1nN [SiO2 sphere tip]
			0.4±0.2nN [Diamond sharp
			tip]
	30% oxygen coverage (9.7at%)	0.042	27±1.3 nN [SiO2 sphere tip]
	45% oxygen coverage (15.3at%)	0.052	-
	60% oxygen coverage (19.4at%)	0.058	-
		Step Edges
	Pristine	1.952	-
	Oxidized	2.432	1.1nN ± 0.1nN [Diamond
			sharp tip]

Acknowledgments: The authors acknowledge financial support from the Ontario Ministry of Research and Innovation Early Researcher Award; the Erwin Edward Hart Endowed Professorship; the Natural Sciences and Engineering Research Council of Canada (NSERC); and the Canada Foundation for Innovation (CFI). SEM analysis was carried out at Ontario Center for the Characterization of Advanced Materials (OCCAM). The authors would also like to acknowledge B. Hatton, R. Sodhi and P. M. Sudeep for assistance with WCA measurements, XPS measurements, and Raman measurements respectively.

Author Information

Corresponding Authors: *E-mail: filleter@mie.utoronto.ca., *E-mail: chandraveer.singh@utoronto.ca.

Author Contributions: § T.A, and S.Y. contributed equally