G Dusserre
email: gilles.dusserre@enstimac.fr

F Schmidt

G Dour

G Bernhart

Thermo-mechanical stresses in cast steel dies during glass pressing process

Keywords: Glass pressing process, Numerical simulation, Thermo-mechanical stresses, Cast steel dies

Cast steel dies used in glass pressing process present an important dispersion in their lifetime in spite of apparently similar pressing parameters. In order to know if undetectable variations of any process parameter could produce such lifetime dispersal, a finite element simulation of glass pressing process is proposed. In this paper, glass is supposed to be a Newtonian fluid, the mould is considered as a thermo-elastic material, thermal transfer between glass and mould depends only on time and radiative heat transfer in glass is not taken into account. The validation of the results of this simulation is performed by comparison of the calculated pressing force and of the experimental one. Although the data introduced in the simulation are taken from the literature on the subject, the order of magnitude of the calculated pressing force is similar to the industrial one.

Introduction

Glass pressing is a forming process used to make hollow parts in only one stage (Fig. 1). The glass is heated up to 1500 • C in a furnace and then cooled around 1250 • C in the feeder. A gob is formed and it falls into the preheated lower mould. The glass flows then between the lower and the upper mould, activated by a hydraulic press. These tools are made of cast martensitic stainless steel GX30Cr13 (norm NF EN 10027-1 and Table 1). This process involves high temperature, high strain rate, thermal and mechanical stresses, fatigue phenomena, oxidation and complex shapes. They all lead to the formation of cracks on the lower mould surface. These cracks are mostly initiated on casting defects (shrinkage).

The lifetime of the mould is determined by the dimensions of these cracks: no defect must be visible on the finished part. It has been observed that the so defined lifetime could be very different (factor 2) between two moulds of the same batch, whereas the process parameters do not seem to have changed.

This paper presents a finite element simulation of the glass pressing process to calculate the thermo-mechanical stresses in the dies. This simulation aims at identifying the process parameters for which small variation would involve significant stresses variation. The software FORGE2 ® was used because it authorizes a precise description of the kinematic of the process and possesses an automatic remeshing module. FORGE2 ® software is based on the finite element method. P1 + P1 linear triangular elements and an updated Lagrangian formulation are used. In order to minimize time calculation, a axisymmetrical simulation will be realized. The parameters that are meant to have the most important influence on the stresses in the mould are: the rheological behavior of glass, the mechanical behavior of the steel, the radiative and conductive heat fluxes in the glass, the heat flux density at gob/mould interface and the friction between glass and steel. It has been chosen to investigate this five parameters.

Input data of the simulation

Rheological behavior of glass

The glass under study is Pyrex ® (Table 2). It is a borosilicate glass with a low expansion coefficient in order to resist thermal shocks up to 300 • C. The rheological behavior of glasses is very temperature dependant [START_REF] Zarzycki | Glasses and the Vitreous State[END_REF]. At low temperature, glass behaves like a brittle elastic solid; around the glass transition temperature, it behaves like a thermo-rheological simple visco-elastic material [START_REF] Wiertel | Optimization techniques for flat glass tempering[END_REF][START_REF] Hessenkemper | Elastic constants of glass melts above the glass transition temperature from ultrasonic and axial compression measurements[END_REF][START_REF] Van Iseghem | Residual stress simulation in a glass/metal contact[END_REF]; and at high temperature it behaves like a thermodependent viscous fluid [START_REF] Lochegnies | Finite element contributions to glass manufacturing control and optimization. Part 2. Blowing, pressing and centrifuging of hollow items[END_REF][START_REF] Milutinović-Nikolić | Mathematical modelling and simulation of drawing thin glass sheet from a rectangular perform[END_REF][START_REF] Hyre | Effect of feeder design and operation on gob shape[END_REF].

Non-Newtonian behavior is observed [START_REF] Yue | On the different descriptions of the non-Newtonian viscosity (shear-thinning effect) of glass melts with respect to heat dissipation[END_REF] as the viscosity of the glass melt decreases with an increase of strain rate. Nevertheless in this paper, glass will be assumed to be a Newtonian fluid (Eq. ( 1)), that means that the viscosity varies only with the temperature as described by the Vogel-Tammann-Fulcher (VTF) equation (cf. Eq. ( 2) and Fig. 2) [START_REF] Sipp | Viscosity, configurational entropy and relaxation kinetics of borosilicate melts[END_REF]. This equation is only valid at temperatures over 900 • C, but it will be assumed that below this temperature the glass is almost rigidified and does not flow anymore 3). where s --is the deviatoric part of the Cauchy stress tensor, η is the glass viscosity, ε --is the strain rate tensor, T is the temperature and A, B, T 0 are constants given in Table 3.

s -- = 2η(T )ε -- (1)
log η = A + B T -T 0 (2)

Mechanical behavior of GX30Cr13 steel

It will be assumed that the steel of the mould behaves as a thermo-elastic solid. Young's modulus is introduced in the software FORGE2 ® as a function of temperature (Fig. 3) and the Poisson ratio is set to the usual 0.3.

C 1 (W m -1 • C -1 ) 0.7222 C 2 (W m -1 • C -2 )
0.001583

Conductive and radiative heat transfer in glass

The high temperature dependency of the glass rheological behavior involves the necessity of a precise thermal computation. Glass being a semi-transparent media, heat transfer occurs not only by conduction but also by radiation. The thermal conductivity of glass is supposed to vary linearly with temperature as described by Loulou et al. (cf. [START_REF] Loulou | Estimation de la résistance thermique de contact durant la solidification du verre[END_REF] and Eq. ( 3)). Experimental data missing, the values of the constants C 1 and C 2 are taken to be the same as in [START_REF] Loulou | Estimation de la résistance thermique de contact durant la solidification du verre[END_REF] (see Table 4)

k cond = C 1 + C 2 T (3)
Radiative heat transfer is a phenomena hard to model because heat flux in one point of the gob is influenced by every other points of the glass part. The easiest way to take the radiative heat transfer into account is to use a diffusion approximation: a radiative conductivity is defined as a function of the temperature, radiative and conductive heat fluxes are then calculated by Fourier's law. An expression of this radiative conductivity k rad was proposed by Rosseland [START_REF] Rosseland | Note on the absorption of radiation within a star[END_REF] (Eq. ( 4) and Fig. 4)

k rad (T ) = 16n 2 σ 3κ Ross (T ) T 3 (4) 1 κRoss (T ) = ∞ 0 1 κ(ν) ∂B(ν,T ) ∂T dν ∞ 0 ∂B(ν,T ) ∂T dν ( 5
)
where n is the refractive index of the semi-transparent media, σ is the Stefan-Boltzmann constant, T is the temperature in K and κRoss is the Rosseland mean extinction coefficient defined by Eq. ( 5). ν is the frequency of the radiation, κ(ν) is the extinction coefficient and B(ν, T) is the blackbody intensity as described by the Planck's law. This method is easy to compute, but it is based on the assumption that the glass is optically thick. This means that most of the radiation is absorbed in the neighborhood of the particle that emitted it. This assumption is not valid for a glass domain with small dimensions, as in the present case.

An analytical solution of the Radiative Transfer Equation is available in a one-dimensional case, but it requires to know the optical properties of the glass and the surface of the mould, and strong assumptions are made on the geometry of the problem [START_REF] Loulou | Estimation de la résistance thermique de contact durant la solidification du verre[END_REF][START_REF] André | A reduced analytical model for solving heat transfer in glasses[END_REF].

Numerical methods could be used such as discrete ordinate method, improved diffusion approximation, ray tracing, Monte Carlo [START_REF] Van Der Linden | Radiative heat transfer in hot glass melts[END_REF], but they require long calculation time, incompatible with our objectives.

Fig. 5 presents the profile of heat flux divergence in the glass supposed to be an infinite plate with a thickness of 9 mm (intermediate thickness of the dish during pressing), for a computed temperature profile with a high temperature gradient around the boundaries, as calculated with the Rosseland diffusion approximation, the analytical method [START_REF] Loulou | Estimation de la résistance thermique de contact durant la solidification du verre[END_REF][START_REF] Van Der Linden | Radiative heat transfer in hot glass melts[END_REF] and without any radiation effects. One can observe that the Rosseland method over evaluates the heat flux divergence compared to the analytical method. This figure shows that radiative heat flux divergence is important, especially in the middle of the glass where conductive heat flux divergence is negative whereas radiative heat flux divergence is positive. In a first step, it will be chosen to assume that radiative heat transfer could be neglected compared to conductive heat transfer because analytical and numerical methods are not easy to introduce in FORGE2 ® software, and Rosseland diffusion approximation is not valid.

Heat flux density at gob/mould interface

The second function of a mould being to cool the glass, the thermal computation requires to know the heat flux den-Fig. 5. Comparison of profile of heat fluxes divergence in the onedimensional case for Rosseland diffusion approximation, analytical method and without radiation. Fig. 6. Heat transfer coefficient at glass/mould interface as a function of time [START_REF] Moreau | Experimental methodology for the determination of the heat transfer coefficient at the glass/mould interface[END_REF]. sity exchanged between the gob and the mould. Experiments have been reported in literature [START_REF] Loulou | Estimation de la résistance thermique de contact durant la solidification du verre[END_REF][START_REF] Lochegnies | Computation procedure for the temperature in hot glass. Application to the finite element simulation of hollow glass forming[END_REF][START_REF] Moreau | Experimental methodology for the determination of the heat transfer coefficient at the glass/mould interface[END_REF] to measure heat flux at the glass/mould interface as a function of time. Semiempirical models have been developed by decoupling radiative and convective parts of the flux. For example, Pchelyakov [START_REF] Loulou | Estimation de la résistance thermique de contact durant la solidification du verre[END_REF][START_REF] Viskanta | Analysis of heat transfer during glass forming[END_REF][START_REF] Storck | Heat transfer modeling of the parison forming in glass manufacturing[END_REF][START_REF] Brauns | Finite element calculation of thermomechanical stresses in candidate ceramic components for press and blow moulds[END_REF] proposed a heat transfer coefficient equal to the conductivity divided by the thickness of a gap between gob and mould. In this paper we prefer to use the experimental results of Moreau et al. [START_REF] Moreau | Experimental methodology for the determination of the heat transfer coefficient at the glass/mould interface[END_REF] as depicted in Fig. 6.

Friction between glass and mould

Friction between glass and steel is greatly influenced by the temperature of the glass at the interface. Studies were led on friction between glass and steel in the condition of delivery gobs into moulds [START_REF] Falipou | New method for measuring the friction between hot viscous glass and metals[END_REF]. Li et al. [START_REF] Li | An experimental study of the lubrication behavior of A5 glass lubricant by means of the ring compression test[END_REF] investigated the influence of temperature and strain rate on the friction at the interface during compression test of titanium rings lubricated with glass. Below 950 • C, strain rate does not seem to play a significant role on the friction behavior. These results will be used in this paper: it is supposed that glass temperature at the interface is 750 • C, and that friction behavior follows the Tresca model with a fiction factor m equal to 0.28 (cf. [START_REF] Li | An experimental study of the lubrication behavior of A5 glass lubricant by means of the ring compression test[END_REF]). In the present case, FORGE2 ® software describes the Tresca model as in Eq. ( 6), τ is the shear stress and ∆ ⃗ V is the difference between the velocity of the glass and the velocity of the mould

τ = -mη(T ) ∆ ⃗ V ∥∆ ⃗ V ∥ (6)

Heat capacity of Pyrex ®

The heat capacity of Pyrex ® is introduced in FORGE2 ® software as a function of the temperature as described by Richet et al. [START_REF] Richet | Configurational heat capacity and entropy of borosilicate melts[END_REF].

Simulation of the gob loading into the mould

Initial conditions

The first stage of the glass pressing process that has been chosen for simulation is loading step of the gob into the mould. The initial gob shape and temperature distribution are presented in Fig. 7. It represents the cooling due to the short contact of the gob with the sliding channel (heat transfer coefficient set to classical value 2000 W m -2 K -1 ) during the transfer from the feeder to the mould and air at 25 • C (heat transfer coefficient 150 W m -2 K -1 [START_REF] Lochegnies | Inverse determination of glass viscosity and heat transfer coefficient by industrial testing[END_REF]). The gob has been placed at a distance of 50 mm from the mould and falls freely. To perform such simulation, the initial mesh contains 728 triangular nodes. The initial shape and temperature distribution of the mould are shown in Fig. 8. The initial temperature distribution is the result of a 30 s cooling by convection in free air (heat transfer coefficient 10 W m -2 K -1 ) corresponding to the time between loading the mould on the press and first pressing. The initial mesh contains 2518 nodes.

Boundary and interfacial conditions

Thermal exchanges considered are convection with air during gob loading, convection between the mould and air, and thermal exchanges between mould and glass. The heat transfer coefficient between the gob and air is equal to 150 W m -2 K -1 , as it could be interpolated at 1100 • C from the results of the inverse method proposed by Lochegnies and Marechal [START_REF] Lochegnies | Inverse determination of glass viscosity and heat transfer coefficient by industrial testing[END_REF]. Convection coefficient between air and steel as been set to 10 W m -2 K -1 (a classical value for natural convection between steel and calm air) eat transfer coefficient as been defined as a function of time (Section 2.4 and Fig. 6).

Friction between glass and steel is defined in Section 2.5.

Results

The total time of the simulation is 2 s corresponding to the actual waiting time before pressing starts. CPU time calculation is 6 min 4 s. The final configuration of this simulation will be defined as initial configuration of the next pressing stage (Fig. 9). Fig. 10 presents the variation of the Von Mises equivalent stress at the surface of the mould on the axis (Fig. 9, point A) during gob loading simulation and Fig. 11 shows the temperature at the same point. The maximum Von Mises equivalent stress reaches 430 MPa at 515 • C (the maximum temperature reached is 520 • C). Mechanical behavior of GX30Cr13 cast steel should be studied in details, but it could be supposed, that this stress could at least induce local plastic deformation in the shrinkage zones where stress concentration may occur, and lead to cracks appearance.

Simulation of the pressing stage

Initial conditions

The second stage of the process to be simulated is pressing. The initial configuration corresponds to the final one of the gob loading stage. Fig. 9 shows the initial temperature distribution in the gob and in the lower mould. Initial temperature of the upper mould has been set to an uniform value (250 • C).

Boundary conditions

The boundary conditions for this simulation are the same as for gob loading, except the heat transfer coefficient between gob and moulds is now set to a constant value (2000 W m -2 K -1 ). It has indeed been supposed that pressure has little effect on heat transfer coefficient and that its value is the final one of the gob loading stage (Fig. 6). The inner surface of the upper mould is cooled by a 20 • C water flow (with a heat transfer coefficient set to 20,000 W m -2 K -1 ).

Press piloting

The lower mould is fixed and the upper one is moved according to the height-time curve (Fig. 12). This curve has been interpolated from initial height, final height and initial velocity with an exponential function.

Validation of the computation

In order to validate this numerical computation with experimental data, computed pressing force has been com- pared with the real one (the maximal force of the industrial hydraulic press). The calculated force has been plotted in Fig. 13. Some numerical accident due to calculation restarts may explain the five instants where the force is null. Although the models that have been introduced in the software are not very accurate (radiative heat transfers neglected) or correspond to conditions that are not exactly similar to the ones of our case (values from the literature), the order of magnitude of the computed pressing force does not reach the maximum value of the real press and seems to be coherent. It could be expected that the force increase up to a maximum value before to stabilize at this value. The difference between the calculated and the expected pressing force could be explained by the piloting of the press in the pressing simulation which does not correspond to measurement (the velocity is not described on a realistic way).

Results

CPU time calculation is 24 h and 15 min 8 s for a 1 s simulation. The final temperature distribution in gob and moulds is shown Fig. 14. The Von Mises equivalent stress at the surface of the mould on the axis (Fig. 9, point A) has been plotted as a function of time in Fig. 15a and temperature at the same point in Fig. 16. The maximum Von Mises equivalent stress is 162 MPa at 502 • C. As it could be seen in Fig. 17, there is other zone where stresses are important (in the edge of the plane surface of the mould: Fig. 9, point B). At this location, maximum Von Mises equivalent stress is not so important as on the axis but a high stress level exists (106 MPa at 494 • C). The evolution of the stress at this point during pressing is plotted Fig. 15b. One can observe in Fig. 17 that between the two zones previously mentioned, the stress level is not so high. It could be concluded that as for loading stage, plastic deformation could occur around the shrinkages during pressing but stress level is not so elevated as during gob loading.

Conclusion

In agreement with the computed Mises equivalent stress distribution, it could have been observed that cracks appearance could occur at two locations in the mould: at the center or at the edge of the plane surface. The first zone is solicited both thermally and mechanically, whereas the second one is solicited mostly mechanically. Industrial moulds present cracks in one or the other of these two zones depending on the shape of the mould: few proof and axisymmetrical moulds are damaged at the center whereas proof and elliptical moulds are damaged at the edge of the plane surface.

More investigations could be led to valid the calculated stress distribution in the mould more accurately as with the pressing force of the industrial process. For example, laboratory pressing tests could be led on a compression test machine to measure accurately the pressing force and the displacement of the upper mould with time. A simplest mould shape and temperature measurements with thermocouples could allow to evaluate heat fluxes at glass mould interface and to valid the thermal computation in the mould. Instrumentation of an industrial mould with thermocouples is also forecasted. This simulation could be improved by taking experimental data into account (glass rheology, mechanical behavior of GX30Cr13 steel, heat flux density at the gob/mould interface, piloting of the press, etc.) and by taking radiative heat fluxes into account, and then be used to study the influence of process parameters on moulds lifetime (initial glass and mould temperature, pressing velocity, etc.). Others mould materials could also be tested.

Fig. 1 .

 1 Fig. 1. Main stages of the glass pressing process: (a) delivery, (b) pressing, (c) pressure maintenance and (d) takeout.

Fig. 2 .

 2 Fig. 2. Temperature dependency of the viscosity of Pyrex ® : experimental points and VTF equation (with A, B and T 0 given in Table3).

Fig. 3 .

 3 Fig. 3. Young's modulus of GX30Cr13 steel as a function of temperature.

Fig. 4 .

 4 Fig. 4. Rosseland radiative conductivity of Pyrex ® as a function of temperature, computed with n = 1.47, κ(ν) = 654.7 m -1 ∀ν ∈ [5.52 × 10 4 Hz, 7.72 × 10 4 Hz, κ(ν) = 9.16 m -1 ∀ν ∈ [7.72 × 10 4 Hz, 9.44 × 10 4 Hz and κ(ν) = 52.68 m -1 ∀ν ∈ [9.44 × 10 4 Hz, 7.91 × 10 8 Hz.

Fig. 7 .

 7 Fig. 7. Initial condition of the gob for the loading stage.

Fig. 8 .

 8 Fig. 8. Initial condition of the mould for the loading stage.

Fig. 9 .

 9 Fig. 9. Initial temperature distribution for the pressing stage.

Fig. 10 .

 10 Fig. 10. Evolution of Mises equivalent stress at the surface of the mould with time during gob loading.

Fig. 11 .

 11 Fig. 11. Evolution of temperature at the surface of the mould with time during gob loading.

Fig. 12 .

 12 Fig. 12. Piloting height as a function of time.

Fig. 13 .

 13 Fig. 13. Computed pressing force as a function of time.

Fig. 14 .

 14 Fig. 14. Temperature distribution in gob and moulds at the end of pressing.

Fig. 15 .

 15 Fig. 15. Evolution of Mises equivalent stress at (a) point A and (b) point B with time during pressing.

Fig. 16 .

 16 Fig. 16. Evolution of temperature at the surface of the mould with time during pressing.

Fig. 17 .

 17 Fig. 17. Mises equivalent stress distribution in lower mould during pressing.

Table 1 Chemical

 1

	composition (wt.%) of GX30Cr13 steel
	C	0 .3
	Cr	13
	Si	0.6
	Mn	0.9
	Ni	<0.5

Table 2

 2

	Chemical composition (wt.%) of Pyrex ® glass [21]
	SiO 2	82.57
	B 2 O 3	10.81
	Na 2 O	5 .13
	Al 2 O 3	1.23
	K 2 O	0 .13
	CaO	0.05
	MgO	0.05
	TiO 2	0.02
	FeO	0.01

Table 3

 3 Values of coefficients of Pyrex ® glass TVF equation (viscosity in poise and temperature in • C)

	A

Table 4

 4 Values of coefficients of glass conductivity (temperature in • C)[START_REF] Loulou | Estimation de la résistance thermique de contact durant la solidification du verre[END_REF]

Acknowledgements

The present investigation has been carried out with the financial support of Aubert et Duval, Newell S.A and Saint-Gobain SEVA.


Ben Ramzi

Stéphane Ayed

Brisset

n-LEVEL OUTPUT SPACE MAPPING FOR ELECTROMAGNETIC DESIGN OPTIMIZATION

Keywords: Finite element model, Optimization, Output Space Mapping, Superconducting Magnetic Energy Storage

Purpose -The aim of this paper is to reduce the evaluation number of the fine model within the output space mapping technique in order to reduce their computing time.

Design/methodology/approach -In this paper, n-level output space mapping is proposed and expected to be even faster than the conventional output space mapping. The proposed algorithm takes advantages of the availability of n models of the device to optimize, each of them representing an optimal trade-off between the model error and its computation time. Models with intermediate characteristics between the coarse and fine models are inserted within the proposed algorithm to reduce the number of evaluations of the consuming time model and, then the computing time. The advantages of the algorithm are highlighted on the optimization problem of superconducting magnetic energy storage.

Findings -A major computing time gain equals to 3 is achieved using the n-level output space mapping algorithm instead of the conventional output space mapping technique on the optimization problem of superconducting magnetic energy storage.

Originality/value -The originality of this paper is to investigate several models with different granularities within output space mapping algorithm in order to reduce its computing time without decreasing the performance of the conventional strategy.

I-INTRODUCTION

In electrical engineering field, space mapping (SM) techniques [START_REF] Echeverria | Optimization in electromagnetic with the space mapping technique[END_REF] and (Bandler et al., 1194) are recognized as iterative optimization strategies that avoid the use of a computationally expensive (fine) model in the optimization process by shifting the optimization burden from the fine model to a cheap (coarse) one. Generally speaking, the coarse model means a low fidelity model which can be evaluated in a very short time and the fine model is an accurate model which consumes computing time.

In each iteration of SM a surrogate model is constructed from the coarse model in such a way that each constructed one is a suitable distortion of the cheap model, such that given matching conditions are satisfied. The quality of the coarse/surrogate model strongly affects the convergence of the SM optimization algorithm. Indeed, a poor coarse/surrogate model may result in a lack of convergence. To avoid this problem a method for assessing the quality of coarse/surrogate model is proposed in [START_REF] Koziel | Quality assessment of coarse models and surrogates for space mapping optimization[END_REF].

To avoid the evaluation of the fine model several times and hence reduce computing time of SM technique a Space-Mapping-Based interpolation is proposed in [START_REF] Koziel | Space-Mapping-Based interpolation for engineering optimization[END_REF]). The proposed interpolation scheme uses already available fine model data, so no additional fine model evaluations are necessary to perform this interpolation. The method sounds interesting but can't be used if there aren't fine model data as in case of new device design.

Manifold Mapping (MM) is a common SM technique that recently investigated in optimization of electromagnetic devices (Echeverrίa et al. 2006). An improvement of MM in terms of computing time and quality of optimal solution is studied in (Echeverrίa et al. 2007) by using a multilevel approach within the MM algorithm. Results show that three-level approach improved the quality of solution enclosed by MM but the gain on computing time is not significant. These results are found using two mathematical examples: Poisson-based optimization and a parameterized ellipse. In both examples coarse, medium and fine model are analytic and the optimization problem is without constraints. The three-level MM (3L-MM) algorithm is also applied in the optimization of an octangular double-layered shield in [START_REF] Crevecoeur | Optimization of an octangular double-layered shield using multiple forward models[END_REF]). An analytic model, a 2D and a 3D finite element models are used. 3L-MM converges towards satisfactory solution after 13 evaluations of the computationally expensive model.

Output Space Mapping (OSM) [START_REF] Ben Ayed | Multidisciplinary optimization formulations benefits on space mapping techniques[END_REF] and (Encica et al., 2008a) strategy is also an interesting variant of Space Mapping techniques. It aligns iteratively the fine model with the coarse model using correctors. This strategy is named two-level OSM (2L-OSM) because two models with different accuracy levels are used. The purpose of 2L-OSM is to achieve the optimization in a minimum evaluation number of the expensive model, and then it allows obtaining accurate results in a short computing time. However, the computing time of 2L-OSM can be significant because the fine model is evaluated one time at each iteration and one fine model evaluation can takes hours as in the case of 3D finite element model (3D FEM) [START_REF] Tran | Adapted Output Space-Mapping Technique for a Bi-Obejtive Optimization[END_REF].

To overcome this problem, a generalized version of OSM strategy is proposed. The generalized algorithm is named n-Level Output Space Mapping (nL-OSM) technique and is able to take profit of n models of the device to optimize. The n models represent tradeoffs between accuracy of results and computation time.

This paper is structured in three main parts. Firstly, the conventional OSM algorithm is reminded. In the second part, the adapted nL-OSM technique is explained and detailed. The optimization benchmark problem of the Superconducting Magnetic Energy Storage (SMES) [START_REF] Alotto | Multiobjective optimization in magnetostatics: a proposal for benchmark problems[END_REF] is presented in the third part, as well as the models with different accuracy levels. Finally, the solutions and computation time of the 2L-OSM are compared to nL-OSM ones and some remarks on the use of the proposed algorithm are given in the conclusion.

II-OUTPUT SPACE MAPPING

Output Space Mapping (OSM) technique is a common approach for the optimization of devices represented by accurate, but time consuming, models. It has been recently used for solving optimization problems of electromagnetic converters (Encica et al., 2008b) and [START_REF] Tran | A New efficient method for global discrete multilevel optimization combining branch-andbound and space mapping[END_REF]. This technique requires a second model, faster but less accurate, of the device to be optimally sized. This coarse model could be an empirical model, a FEM with a coarse mesh or an analytical model. The optimization is carried out with the coarse model and the results are validated with the fine one which is, in general, a high fidelity FEM.

The advantage of the OSM is its easier implementation. Indeed, by aligning the coarse model with the fine one, the precision is assured and the design space exploration is done by the optimization with the coarse model, avoiding though the possible numerical noise and mesh problems [START_REF] Neittaamäki | Inverse problems and optimal design in electricity and magnetism[END_REF]. The accuracy of optimization results are guaranteed by the FEM evaluations. Within the OSM technique, the role of the FEM is to adjust the analytical model outputs in order to better meet the constraints of the transformer optimization problem.

In a word, OSM is investigated in order to obtain satisfactory results with a minimum number of computationally expensive fine model evaluations. It aims to use both the coarse and fine models to reduce the computation time and increase the accuracy of the obtained solution.

III-n-LEVEL OUTPUT SPACE MAPPING TECHNIQUE

The proposed nL-OSM is expected to reduce even more the computational time compared to the conventional 2L-OSM. It takes advantages of the availability of n models of the device to optimize, each of them representing an optimal trade-off between the model error and its computation time. In Fig. 1, all the models are drawn as points which coordinates are the model error and the model computation time. The points belong to the Pareto optimal set and the curve joining those points is a Pareto front. The ideal model is the one that has the smallest error and time. Unfortunately, this model does not exist in reality. Fig. 1 shows that for an electromagnetic device it exist several models with different granularities. Each model presents an optimal tradeoff between the model error and its computing time. The 1 st model is the fastest while the n th model is the most accurate.

Ideal model

The idea of the proposed algorithm is to use the 1 st model during the optimization process to find an approximate solution. At iteration i, the i th model is evaluated with this solution to update the correctors until the discrepancy between the corrected 1 st model and the i th model is small enough. The algorithm stops at iteration n when the corrected 1 st model's outputs are equal to the n th model's ones. Contrary to the classical 2L-OSM that use only the 1 st and n th models, the nL-OSM uses all the n models to reduce the number of evaluations of the n th model and thus the computation time.

In this paper, the coarse computationally cheaper model is denoted by m 1 (x) ∈ R p with x ∈ R q , the fine computationally expensive model is denoted by m n (x) ∈ R p , and the (n-2) models with k accuracy levels are denoted by m k (x) ∈ R p , k = 2. . n-1. The inputs of all models are the same. The nonlinear constraints of the coarse, k th level accuracy, and fine models are g 1 (x), g k (x) and g n (x), respectively. Generally, the coarse model is denoted by c(x) and the fine one is denoted by f(x). In this paper m 1 (x) refers to c(x) and m n (x) refers to f(x). The optimization problem is expressed as:

(1)

𝑥 * = 𝑎𝑟𝑔 min 𝑥∈𝑋 ‖𝑚 𝑛 (𝑥) -𝑦‖ 𝑠. 𝑡. 𝑔 𝑛 (𝑥) ≤ 0
where y ∈ R p denotes a vector of design specifications and can be zeros in the case of minimization. This problem is hard to solve and is decomposed into series of problems. The key point of OSM is to avoid the use of the fine model within the optimization process. So, as in the conventional OSM, the use of the fine model m n (x) within the optimization is avoided by using the coarse corrected model m 1 (x, θ), where θ ∈ R p is the vector of correctors. The optimization problem at iteration j is:

(2)

𝑥 𝑗 * = 𝑎𝑟𝑔 min 𝑥∈𝑋 ‖𝑚 1 (𝑥, 𝜃 1 𝑗 ) -𝑦‖ 𝑠. 𝑡. 𝑔 1 (𝑥, 𝜃 1 𝑗 ) ≤ 0 (3) [ 𝑚 1 (𝑥, 𝜃 1 𝑗 ) 𝑔 1 (𝑥, 𝜃 1 𝑗 ) ] = 𝑑𝑖𝑎𝑔(𝜃 1 𝑗 ). [ 𝑚 1 (𝑥) 𝑔 1 (𝑥) ]
The other problems consist of correcting the coarse model with a minimum evaluation number of the most accurate model. Then, to reach this goal, the strategy of the nL-OSM is proposed. This strategy can be considered as a series of process that are launched iteratively. In the first process, the coarse model is corrected by the model with the next accuracy level (m 2 ) using the 2L-OSM algorithm. The others processes consist of aligning each model with the model that has the next level of accuracy. For example, during the k th process, the k th model is corrected by the (k+1) th model using corrective coefficients θ k ∈ R p . These coefficients are initialized to one and computed in order to have the same value for the outputs of the k th and (k+1) th The space-mapping between the corrected coarse and 2 nd models stops when ( 7) is checked, The nL-OSM algorithm stops when ( 8) is checked and k=n. In (8), ε refers to the required accuracy of results. This stopping criterion affects strongly the number of loops within the SM algorithm as well as the evaluation number of the most consuming time model. In general, results are acceptable when the discrepancy between the fine and the coarse corrected model is equal or less than 10 -4 .

(7) ‖[ 𝑚 1 (𝑥 𝑗 * , 𝜃 1 𝑗 ) 𝑔 1 (𝑥 𝑗 * , 𝜃 1 𝑗 ) ] -[ 𝑚 2 (
To summarize, the nL-OSM algorithm carries out the following main steps: 0-initialization: j = 0, k = 2, θ 1 0 = I, β 2..n = I 1-solve (2) in order to find x j * by using m 1 (x, θ 1 j ) as surrogate model 2-compute m 2 (x j * , β 2 ), g 2 (x j * , β 2 ) and θ 1 j+1 by using (4)

3-𝑗 = 𝑗 + 1 4-go to step 1 until ( 7) is true 5-compute m k+1 (x j * , β k+1 ) and g k+1 (x j * , β k+1 )

6-compute β 2 ⋯ β k by using (5) 7-go to step 1 until ( 8) is true 8-k = k + 1 9-go to step 5 while 𝑘 < 𝑛 10-stop

IV-APPLICATION CASES

The application case is the optimization problem of a Superconducting Magnetic Energy Storage system (SMES) that is known as the team workshop problem #22.

The SMES device consists of two concentric superconducting coils fed with currents that flow in opposite directions. The system is used for storing magnetic energy with a minimum magnetic stray field over a square perimeter of 10 meters from coil axis (Team workshop, 1996) as shown in Fig. 3.

The optimal sizing problem consists of 3 design variables that are the radius (R2), the width (d2) and the height of the outer coils. The objectives of optimization are:

-The stored energy in the device should be 180 MJ.

-The magnetic field must not violate a physical condition (quench condition) which guarantees superconductivity.

-The stray field measured at 10 meters from the device should be as small as possible.

 1 R   1 d   21 h   1 J   2 J 1-1 st model
This model refers the coarsest model (m 1 ) within it, each coil of the device is considered as a single filamentary loop of radius a i located at axis center [START_REF] Rezzoug | Analytical calculations of flux induction and forces of thick coils with finite length[END_REF]. This approximation simplifies greatly the calculation of magnetic parameters and allows achieving acceptable results if the measurement point is far from the device (i.e. located at a distance a i ≪ 𝑑), else the discrepancy is great as well as the measurement point is near the device.

The mathematical expression of the vector potential A i and both radial and axial components of the magnetic stray field B ρi , B zi at the point P (x, y, z) are defined as follows [START_REF] Wilson | Superconducting Magnets[END_REF]:

(9) Lets { ρ = √x² + y² k i = √ 4a i ρ (a i +ρ) 2 +z i ² { A i (ρ, z i , I) = µ 0 I kπ √ a i ρ [(1- k i 2 2 ) K(k i )-E(k i )] B ρi (ρ, z i , I) = - ∂A ∂z = µ 0 Ik i z i 4πρ√a i ρ [-K(k i ) + a i 2 +ρ 2 +z i 2 (a i -ρ) 2 +z 2 E(k i )] B zi (ρ, z i , I) = 1 ρ ∂ ∂ρ (ρA) = µ 0 Ik i z i 4π√a i ρ [K(k i ) + a i 2 -ρ 2 -z i 2 (a i -ρ) 2 +z i 2 E(k i )]
where K and E are the complete elliptic integrals of the first and the second kinds, respectively. Then, the vector potential of the system can be deduced easily by adding A 1 and A 2 A 1 and A 2 .

The stored energy by the two filamentary loops can be deduced from the mutual flux as follows:

(10)

{ W e12 = 1 2 I 2 Φ 12 Φ 12 = 2πa 2 A 1 (ρ, (z 2 -z 1 ), I 1 ) → W e12 = πa 2 I 2 µ 0 I 1 kπ √ a 1 a 2 [(1- k 2 2 ) K(k)-E(k)]
where k = √ 4a 1 a 2 (a 1 +a 2 )²+(z 2 -z 1 )²

2-k th model

This model considers that each coil is made of N k wires, carrying current I = J. dS as shown in Fig. 4. This approximation allows the calculation of different magnetic parameters at each point of the space with a small discrepancy [START_REF] Rezzoug | Analytical calculations of flux induction and forces of thick coils with finite length[END_REF].

Figure. 4. Subdividing coil to filamentary loops

So, the vector potential A c at P (x, y, z) generated by one coil and the stored energy W c by the system can be written:

(11)

𝐴 𝑐 (𝜌, 𝑧 𝑖 , 𝐼) = ∑ 𝐴 𝑖 (𝜌, 𝑧 𝑖 , 𝐼) = 𝑁 𝑘 𝑖=1 ∑ µ 0 𝐼 𝑘𝜋 √ 𝑎 𝑖 𝜌 [(1 - 𝑘 𝑖 2 2 ) 𝐾(𝑘 𝑖 ) -𝐸(𝑘 𝑖 )] 𝑁 𝑘 𝑖=1 (12) 𝑊 𝑏 = ∑ 𝑊 𝑒𝑖𝑗 𝑖≠𝑗 𝑖,𝑗 = ∑ 1 2 𝑖≠𝑗 𝑖,𝑗 I i Φ ji
With the same approach the magnetic stray field can be obtained easily.

3-n th model

The n th model has the highest accuracy. In our case it is a 2D FEM with fine mesh. It includes 552,202 nodes and 275,219 elements. One evaluation of this model takes 784 seconds.

4-Accuracy and computing time

The accuracy and computing time of the models increase with the number of filamentary loops used to model one coil. Therefore, many models with different levels of accuracy can be obtained easily by changing the number of loops as shown in Table 3. In this table, error refers the discrepancy between analytical models and 2D FEM outputs. Fig. 5 shows trade-offs between these models error and its computing time. 5 shows a Pareto front consisting trade-offs between models error and its computing time confirming that each model present an optimal compromise between error and time.

To justify the coherence of the analytical models, Fig 6 shows a comparison on calculated magnetic field within outer coil between an analytical model using 400 filamentary loops and the 2D FEM. Fig. 6 shows through magnetic maps of the outer coil that the discrepancy between magnetic field values calculated by the medium model and the 2D FEM is less than 1%. This confirms the coherence of the analytical models built. Color code refers the flux density in Tesla. Axes refers to coils radial and central axis

5-Optimization problem

The goal of the optimization problem is to find the design configurations that give a specified value of stored magnetic energy and minimal magnetic stray field. Mathematically, this is formulated as: ; E ref = 180 MJ and B norm = 3 mT with B stray i is the magnetic field measured in one point (i) located at 10 meters from the device.

6-Optimization results

In order to minimize the risk to enclose local optimum, optimization with the surrogate analytical model is launched with 10 starts points. The optimization uses Sequential Quadratic Programming (SQP) method that allows obtaining an optimum in a very short time.

Table 4 and 5 shows the results obtained with different number of models. Table 4 shows the computation time and the number of evaluations of each SMES model. Table 5 shows a comparison between optimal solutions found by the nL-OSM algorithm and an optimum solution found in literature (Team workshop, 1996). n-level OSM algorithm and the global optimization algorithm used in (Team workshop, 1996) converge to the same solution. This confirms that multi-starts optimization is an efficient method to reduce the risk of local optimum when using a local optimization algorithm such as SQP.

The 2-level OSM and the n-level OSM algorithms converge to the same solution. However, the computation time has decrease up to 3 times, thanks to the addition of models with intermediate accuracy and computation time. The computation time of nL-OSM stop to decrease when the number of intermediate models is greater than 2 in the case of the SMES. Indeed, computing time of the 5L-OSM and 4L-OSM are equal.

In the case of the SMES, the 4L-OSM is the best algorithm in terms of computing time. This result can't be generalized to other cases because the efficiency in terms of computing time of the nL-OSM is forcefully related to the accuracy and the computing time of built coarse and medium models. It's very important to highlight that it is possible that the computing time of the nL-OSM algorithm can be greater than the (n-1)L-OSM if medium models are chosen incorrectly: first feelings through the SMES case show that to have an additional gain on computing time, the introduced medium model (k) must satisfy two conditions. The first one is the medium model (k) must be at least three-times more accurate and ten-times less rapid than the coarse model. The second condition is that the medium model k must be at least seven-times more rapid and three-times less accurate than the medium model (k+1).

V-CONCLUSION

The n-level OSM algorithm allows reducing computing time in comparison with the traditional OSM algorithm thanks to n-2 models inserted between the coarse and the fine model. Inserted models can be obtained easily by changing the mesh size in FEM, the number of elements in lumped-mass models, and the number of assumptions in analytical models.

Using the different models with different granularities, the n-level OSM algorithm converge to the same optimum found by the conventional OSM algorithm with a major reduction of computing time equals to 3 and without decreasing the performance of the space mapping technique.

The gain in computing time with the adapted space mapping algorithm stops increasing when number of medium models is important. To avoid meeting this case, the authors propose to search for an automatic diagnostic of models to find the optimal number of medium models to introduce between coarse and fine ones.

VI-

Figure 1 .

 1 Figure 1. Models of the same electromagnetic device

Figure

  Figure 3. SMES design variables

Figure. 5 .

 5 Figure. 5. Trade-offs between models error and computing timeFig.5shows a Pareto front consisting trade-offs between models error and its computing time confirming that each model present an optimal compromise between error and time.

Figure. 6 .

 6 Figure. 6. Comparison between the analytical model using 400 filamentary loops (right) and a 2D FEM (left).Color code refers the flux density in Tesla. Axes refers to coils radial and central axis

  models.

	(4)	𝜃 1 𝑗+1 = [	𝑚 2 (𝑥 𝑗 * , 𝛽 2 )/𝑚 1 (𝑥 𝑗 * ) 𝑔 2 (𝑥 𝑗 * , 𝛽 2 )/𝑔 1 (𝑥 𝑗 * ) ]
	(5)	𝛽 𝑘 = [	𝑚 𝑘+1 (𝑥 𝑗 * , 𝛽 𝑘+1 )/𝑚 𝑘 (𝑥 𝑗 * ) 𝑔 𝑘+1 (𝑥 𝑗 * , 𝛽 𝑘+1 )/𝑔 𝑘 (𝑥 𝑗 * ) ] 𝑘 = 2. . (𝑛 -1)
	(6)	[	𝑚 𝑘 (𝑥 𝑗 * , 𝛽 𝑘 ) 𝑔 𝑘 (𝑥 𝑗 * , 𝛽 𝑘 )	] = 𝑑𝑖𝑎𝑔(𝛽 𝑘 ). [	𝑚 𝑘 (𝑥 𝑗 * ) 𝑔 𝑘 (𝑥 𝑗 * )	] 𝑘 = 2. . (𝑛 -1)

Table 3 . Models accuracy and computation time

 3

	Type Number of loops Error (%) Time (s)
	𝑚 1	1	254	0.016
	𝑚 2	100	7.2	1.61
	𝑚 3	400	0.3	24.8
	𝑚 4	900	0.14	127.53

Table 4 . Computation time and evaluation number of each SMES model

 4

	Evaluation number of each model	𝑚 5	𝑚 4	𝑚 3	𝑚 2	𝑚 1	Time (s)
	5L-OSM	2	2	2	10	1225	1849
	4L-OSM	2	2	3	-	1230	1849
	3L-OSM	2	4	-	-	1452	2101
	2L-OSM	7	-	-	-	2476	5527
		Table 5. Optimum found by different algorithms
		R 2 (m)	h 2 /2 (m)	d 2 (m)	OF	B stray ²(T²)	Energy (MJ)
	(Team workshop, 1996)	3.08	0.2390	0.3940	0.08808	7.9138e-7	180.0277
	2L-OSM	3.08	0.2405	0.3937	0.08910	7.9382e-7	180.1622
	3L-OSM	3.08	0.2405	0.3937	0.08920	7.9530e-7	180.1572
	4L-OSM	3.08	0.2405	0.3936	0.08960	7.9503e-7	180.2215
	5L-OSM	3.08	0.2405	0.3936	0.08963	7.9501e-7	180.2535


Adrien Van Den Bossche

Nicolas Fourty
email: nicolas.fourty@lcis.grenoble-inp.fr

Jean-Paul Jamont
email: jean-paul.jamont@lcis.grenoble-inp.fr

A Trusted Lightweight Synchronisation Protocol for Wireless Ad-hoc Networks

Keywords: Synchronisation, Trusted protocols, Medium Access Control, Wireless Ad Hoc Networks, Wireless sensor networks

This paper describes a trusted lightweight synchronisation protocol for wireless ad-hoc networks. The wireless ad-hoc network and wireless sensor networks is a large field of research. Their dynamic topologies make them difficult to synchronise (power consumption, slow convergence, accuracy). Moreover, these open networks are vulnerable to faulty nodes and attacks from malicious nodes. In this paper we propose to use the Simple Synchronisation Protocol (SiSP) enhanced with trust aspects making it more robust to attacks. We describe how to observe deviant behaviour and assign a confidence level to each node. Countermeasures are then adapted to the neighbourhood confidence level. The last part present simulation and results on the MASH simulator.

I. INTRODUCTION

Wireless Ad Hoc Networks promise a simple and decentralised way of connecting nodes, without need of coordination or hierarchy. Because the wireless nodes are generally mobile, they usually embed a limited quantity of energy and are considered as energy constrained. Thus, Medium Access Control (MAC) protocols have to minimize activities on medium, i.e. limit not only transmission but also reception activities, because of the complexity of the receiver: on these transceivers, the energy consumption is generally more important in the receive state than in transmit state. Nodes must enter sleep mode regularly, but also being available during common periods negotiated with their 1-hop neighbours. The nodes use the principle of rendez-vous to get this common period.

To achieve such a negotiation, the synchronisation is an important task in the whole MAC process. Many synchronisation protocols and algorithms have been proposed [START_REF] Akyildiz | Wireless mesh networks: a survey[END_REF], in order to share a common view of the time organization. To rely on the non-hierarchical characteristic of the Wireless Ad Hoc Networks, a decentralized synchronisation process is targeted, i.e. obtained a global synchronisation in a distributed fashion. Because of the collaborative nature of these protocols, their trust aspects must be studied, since they may be sensitive to attacks and malice operations. This paper presents SiSP, a simple and collaborativeoriented synchronisation protocol and studies the trusted aspects of the protocol. A trusted version of SiSP is proposed and studied by the use of the MASH simulator.

The reminder of this paper is following: in the next section, we remind the main challenges on synchronisation and trust aspects. Then, the SiSP protocol and its weaknesses and deviant behaviour are presented. A trusted version of SiSP is then being proposed, with some results obtained with this reinforced version of the protocol.

II. MAIN CHALLENGES

Wireless Ad-hoc networks refer to a lot of specific areas of wireless networks. Since there isn't any infrastructure, all nodes must sense the environment to construct their own neighbourhood image. This characteristic has a significant impact on node lifetime, reliability or even security. In order to save energy, Wireless Ad Hoc Networks often use rendezvous-based protocols or synchronisation protocols at MAClevel.

A. Synchronisation protocols

Time synchronisation over Wireless Networks is a wide research subject for a very long time [START_REF] Akyildiz | Wireless mesh networks: a survey[END_REF], and is still an active field of research [START_REF] Seongwook | A Comparison of Clock Synchronization in Wireless Sensor Networks[END_REF], since it impacts on several aspects such as MAC, Quality of Service, energy saving, data timestamping, etc. In the literature, the synchronisation protocols are evaluated by several metrics: synchronisation accuracy, energy consumption, overhead, convergence speed. They can use various approaches which can be classified in two categories.

A first category of synchronisation protocols is built on a hierarchical architecture, based on a hierarchical topology such as a star or a tree topology. Timing-sync Protocol for Sensor Networks (TPSN) [START_REF] Ganeriwal | Timing-sync Protocol for Sensor Networks[END_REF] is an example of synchronisation protocol based on a hierarchy, where each node is assigned a hierarchical level. The root node, on zero level, is unique, and must be re-elected each time the topology changes. A time synchronisation accuracy analysis, based on a real implementation with MICA motes with TinyOS has been conducted in [START_REF] Ganeriwal | Timing-sync Protocol for Sensor Networks[END_REF]; show an average accuracy of less than 20µs. Flooding Time Synchronisation Protocol (FTSP) [START_REF] Maroti | The Flooding Synchronization Protocol[END_REF] is an improvement of TPSN. With TPSN, topology changes due to node failure or link instability are heavy to report. The flooding nature of FTSP reinforces the quality of the synchronisation when the topology changes. The authors of [START_REF] Maroti | The Flooding Synchronization Protocol[END_REF] have studied the performances of FTSP and report an average synchronisation error of 10µs. Time Synchronised Mesh Protocol (TSMP) [START_REF] Pister | TSMP: Time Synchronized Mesh Protocol[END_REF] is the synchronisation protocol used on WirelessHART. It proposes a synchronisation service used for scheduling the medium accesses, allowing collision free schemes on a multichannel TDMA approach. TSMP synchronisation also provides a data time-stamping service used by sensors or actuators. TSMP provides a synchronisation precision of hundreds µs and supports scaling thanks to the centralized structure of the synchronisation. Wireless Deterministic Clock Synchronisation (WiDeCS) [START_REF] Beluch | Cross-Layered Synchronization Protocol for Wireless Sensor Networks[END_REF] is another example of synchronisation protocol based on a hierarchical architecture, coupled with a MB-OFDM PHY layer and a TDMA-based MAC-layer. An impressive precision of 100ns is achieved with a VHDL implementation on a simulator.

Another synchronisation protocol category is based on a shared clock obtained via a succession of consensuses [START_REF] Maggs | Consensus Clock Synchronization for Wireless Sensor Networks[END_REF]. This category is interesting since these protocols do not require a centralised organisation to synchronise the nodes. One of the first synchronisation protocols in this category is Reference Broadcast Synchronisation (RBS) [START_REF] Elson | Fine-Grained Network Time Synchronization using Reference Broadcast[END_REF]. RBS is based on a "clap" broadcasted by one of the node. This "clap" is considered as a reference by the other nodes of the network: just after the reception of the clap, the receiver nodes broadcast the timestamp corresponding to the instant of the clap reception, using their own clock. The timestamp exchanges enable the nodes to compute an image of their clock offset. This mode of synchronisation is often reported as "Receiverto-receiver" synchronisation [START_REF] Roche | Time Synchronization in Wireless Networks[END_REF]. After several cycles, the nodes converge on a shared clock, based on the consensus. Simple Synchronisation Protocol (SiSP) [START_REF] Van Den Bossche | SiSP: A lightweight synchronization protocol for Wireless Sensor Networks[END_REF] is also based on a consensual process: like RBS, SiSP regularly broadcasts SYNC messages containing the consensual clock, noted "Shared Clock" (SCLK). Every node receiving a SYNC message must average the received value with its local SCLK value. After several SYNC message exchanges, the nodes share a common synchronisation. As our study is based on SiSP, this protocol will be presented in the next section of this paper.

The table 1 resume the main characteristics of the protocols cited before.

B. Trust aspects

One of the most important aspects of WSN is that the network topology is very dynamic and must be self-configured and quickly reconfigured. The changes in topology, the data burst for reconfigurations, the low data rates for power saving make synchronisation in WSN a difficult challenge. SiSP protocol presented in the next chapter seems really interesting for a lightweight, accurate, energy saving, synchronisation protocol. However, in mobile ad-hoc networks (MANET), the decentralized nature of the network makes it vulnerable to deviant node behaviours. Deviant nodes can be faulty or malicious nodes.

While faulty nodes are transmitting erroneous data, malicious node tries to corrupt the synchronisation for its own interest. These interests are various (security hack, countermeasures, misused identity…) and results in a slow synchronization convergence, a traffic increase and a network life time reduced.

Security and reliability are key parameters of WSN. Our approach is to use trust aspects to improve every aspects and deal with this problem.

The trust management is social control mechanism which enable deviant behaviour detection. The general idea is to observe neighbour node behaviours in order to compare to a "normal" behaviour. In order to process this comparison they must affect to neighbour nodes a confidence level. This confidence level being is computed by the difference between observed and normal behaviour. This confidence level can then be used to adapt or prevent interactions with untrusted nodes. These last stage consequences are entities exclusion of all "social" interactions. This exclusion called social control mechanism is often associated with the reputation notion. A node reputation is built on the long term confidence level from all trusted neighbour nodes.

Node mobility and quick network reconfigurations from WSN make it difficult to model since it is an open system. A trust in the WSN state of the art can be found in [START_REF] Vercouter | Lightweight trusted routing for wireless sensor networks[END_REF] [START_REF] Han | Management and applications of trust in Wireless Sensor Networks: A survey[END_REF]. However most of the approaches using trust aspects have been focused on routing protocols [START_REF] Van Den Bossche | SiSP: A lightweight synchronization protocol for Wireless Sensor Networks[END_REF], data aggregation [START_REF] Van Den Bossche | SiSP: A lightweight synchronization protocol for Wireless Sensor Networks[END_REF] or intrusion detection [START_REF] Van Den Bossche | SiSP: A lightweight synchronization protocol for Wireless Sensor Networks[END_REF]. Very few recent works try to apply these technics into the MAC layers. For example in [START_REF] Diwanji | Effect of MAC layer protocol in building trust and reputation scheme in mobile ad hoc network[END_REF] an evaluation of MAC layer misbehaviours in the IEEE 802.11 protocol is achieved.

III. SIMPLE SYNCHRONISATION PROTOCOL

To achieve global synchronisation over the wireless network, we have proposed in [START_REF] Van Den Bossche | SiSP: A lightweight synchronization protocol for Wireless Sensor Networks[END_REF] a lightweight protocol called SiSP, for "Simple Synchronisation Protocol".

A. SiSP description

SiSP enables the nodes to establish a Shared Clock (SCLK) among all the nodes of the wireless network. The SCLK enables the nodes to share a common time base to coordinate medium accesses, generate timestamps for application events or synchronise sleeping periods to maximise the autonomy of a battery-powered node. The SCLK is a relative clock and is subject to deviation. It can be converted into absolute time/date by a gateway node which runs a global synchronisation protocol such as Network Time Protocol (NTP). SCLK is based on a local counter which update frequency is assumed to be the same on all nodes. SiSP aims to have these counters converge via a series of successive consensus, until the instantaneous values are the same for all nodes of the network. The main advantage of SiSP over well-known synchronisation protocols such as RBS or TPSN [START_REF] Roche | Time Synchronization in Wireless Networks[END_REF] is that it does not rely on a particular topology or even a hierarchy. SiSP is totally ad-hoc and does not require any particular MAC precaution: SiSP messages may be included in the payload of broadcasted frames such as beacons.

In the basic version, SiSP defines only one message: SYNC. SYNC contains the SCLK value of the node at the supposed instant of the SYNC message transmission. SYNC message is broadcasted as soon as possible but does not require a constant sending interval. The smaller the interval between SYNC messages, the faster is the convergence. Upon SYNC frame reception, the SiSP algorithm described below is executed. Let's consider a sispSyncIndication subroutine (Algorithm 1) called on message reception, beacon or SYNC message: The received clock (RCLK) is extracted from the incoming message payload and compared to the receiver's SCLK. If the two values are equal, the SCLK of the two nodes have converged: the two nodes are synchronised. If the values are different, the mean is calculated, rounded and applied by the receiver node as its new value of SCLK. In a few cycles, depending on the number of nodes and the topology, a consensus is reached. SCLK consensus is obtained in a decentralized way, without any hierarchical prerogative. Moreover, SiSP algorithm is simple (integer sums and division by 2) and perfectly fits on tiniest microprocessors.

B. Protocol Weaknesses and deviant behaviours

However the simplicity of SiSP makes it vulnerable to deviant behaviours. In order to deal with these weaknesses, we are going to make a survey of these behaviours. This section tries to list both faulty and malicious behaviours. We will take in consideration transmissions them-selves and consequences of these transmissions in order to define symptoms which can be observed at a network level.

Attack Name Description

Random clock (RC)

The node transmit random shared clock. This attack only tries to modify the shared clock value.

Fixed clock (FC)

The node doesn't modify its own shared clock. This attack only tries to modify the shared clock value.

Misused identity (MI)

The node transmits a faulty or misused source address. This attack tries to fake a node identity.

Quick clock (QC)

The node transmits its shared clock more often than planned. The shared clock value isn't targeted. This attack doesn't respect the normal behaviour rules.

A node using SiSP assumes that all its neighbours have a normal behaviour. It is then vulnerable to bad data or commands from these neighbours. The deviant behaviour observed can be the consequences from faulty hardware, bugs or even malicious nodes trying to break or disturb the synchronisation. Since WSN are open systems, they are particularly vulnerable to malicious node intrusion.

In this work we will focus on malicious behaviours where the node manufacturer intention is to disturb the WSN. We are going to address the malicious behaviours listed in table 2.

IV. TRUSTED SISP

In order to deal with these attacks we propose to enhance SiSP with trust aspects. However as mentioned above a confidence policy is quite complex to develop because a WSN node has constraints:

-Low computational power often not compatible with a transmission history management used to detect malicious behaviours, -Distributed trust management because it is not possible to use a global network model, -No authentication is used which is a crucial problem since in all approaches using trust aspects, a confidence level is associated to an identity.

The last point is really important and in this paper we propose to use trust as it is done in [START_REF] Pister | TSMP: Time Synchronized Mesh Protocol[END_REF] [START_REF] Pister | TSMP: Time Synchronized Mesh Protocol[END_REF] for WSN routing. However, in our case we use the confidence level to estimate neighbourhood reliability instead of an independent neighbour level. An untrusty neighbourhood is a node set where at least one malicious or faulty node is detected. As soon as a node supposes its neighbourhood untrusty, it enters a degraded mode. The degraded mode is a minimal function mode where the node only does what the network is expecting from it. This mode must prevent any neighbourhood interactions for shared clock synchronisation. The whole neighbourhood will be in quarantine when all the nodes of a zone will adopt the degraded mode.

In the next subsections we are going to address attacks listed in table 2 using trust aspects. For each attack we present observed symptoms and countermeasures envisaged.

A. Attack symptoms and countermeasures

For the "Random Clock" (RC) and "Fixed Clock" (FC) attacks, it is the shared clock value that is targeted. In these cases a history of neighbour last values should detect these attacks. The standard deviation of the value will tell us if the value is fixed or converging.

In the case of "Misused Identity" (MI) attacks, the lie can only be detected if the node identity is misused in its neighbourhood (confidence level will be drastically decreased). If a lie is suspected, the confidence level will be decreased proportionally to the probability of the deviance behaviour. For instance, a neighbourhood where new identities abnormally increase should be penalized.

For the "Quick Clock" (QC) attack, if a node does not lie on its identity, this behaviour is easily detected. If it is not the case the attack will be a particular case of the "Misused Identity" attack.

B. Penalization

When the attacks are detected the node confidence level should be penalized. This level will be decreased accordingly to malicious level. These levels are presented in table 3 where n is the identity of the node and id the identity of a neighbour node. On the other hand it is necessary to restore the confidence level over time for both node and neighborhood. Indeed, even a low mobility makes malicious nodes able to quit a neighborhood for another one. Moreover the malicious nodes can be suppressed from the network by moving to a bad location or even depleted batteries. In some cases a mistrust neighborhood case could result from several exceptional events coincidence. In this case the confidence should be restored over the time by slowly increasing the confidence level. This mechanism is described by Algorithm 2, where e in [0,1] is generally called forgetfulness constant.

C. Countermeasures

Trust in identifiers is used to estimate trust in an entire neighbourhood. A neighbourhood is considered untrusty when one of its neighbours has a low confidence level.

The only countermeasure envisaged in this paper is to enter in a degraded mode. In this mode the node still listen to SYNC messages but do not send its own SYNC message until the confidence level is over the threshold. The goal of this mode is the progressive isolation of the presumed attacker node. This should resume quarantining the zone around the attacker.

V. SIMULATIONS RESULTS

A. Simulation parameters

We have used a tool called MASH (Multi-agent Software/Hardware) simulator [START_REF] Pister | TSMP: Time Synchronized Mesh Protocol[END_REF] [START_REF] Pister | TSMP: Time Synchronized Mesh Protocol[END_REF]. It enables both the simulation and the execution of embedded distributed and decentralized systems:

-using real world agent behaviours by injecting them in the simulated system (an interaction protocol can be seen as a pattern of behaviour, the behaviour is inferred from transmitted messages); -using realistic physical models at the global level (environment models, wave propagation models, etc.) or at node level (energy consumption model, etc.). These models are computed with external tools (Matlab/Simulink, Labview).

The figure 1 presents on the left side a sensor network For all the simulation presented hereafter, the goal is to synchronise 300 nodes. The penalization parameters are a=0.8, b=0.05, c=0.2. These parameters have been chosen because results presented in this paper focus on FC attacks; a better value for b should be used to prevent RC attacks in future works. The threshold used for going into degraded mode is fixed to 0.5.

The test field is 750m x 500m and node communication range is fixed to 50m. The attackers are clustered in the centre of topology and all attackers perform a FC attack. All nodes start with a local clock value of 0 or 40M randomly chosen. The figure 2 presents a running simulation. The pink colour represents the attackers, the green colour represents nodes entered in degraded mode and a more or less shaded yellow colour represents the value of the local clock.

Each simulation lasts 5 minutes. For each simulation we present the convergence time between the ideal convergence clock value (without any attacks) and convergence clock value with attackers. In parameters we have represented in blue the ideal convergence clock value. Respectively in red, green and purple the convergence clock with 1%, 5% and 10 % of malicious node performing a fixed clock to 0.

B. Results

The results are presented in figure 3. In the right of this figure, we see the local clock chosen randomly. After this sequence the simulation starts and then, for the ideal case curve, the clock starts converging to the average clock value. The simulation average should be 20M but it is simulation dependant since the starting clock value is randomly chosen.

Figure 3. SiSP clock value convergence

The most interesting point is that as soon as we introduce malicious node the clock value starts decreasing towards 0. The more we introduce malicious nodes, the faster the convergence towards 0 is. This does not mean that nodes are synchronised since the clock is forced to 0. This phenomenon, describes that the attack succeeded in desynchronising the whole system. SiSP protocol is a very simple protocol not implementing safety or security countermeasures and as consequences is very sensitive to malicious nodes. These points will be treated by the trusted SiSP protocol proposed.

The figure 4 describes the trusted SiSP results. It describes the clock value difference between the ideal case with no malicious nodes and scenarios with malicious nodes introduced. The first interesting point is that the nodes are synchronised. Even if it is not the ideal clock value the nodes are synchronised. The more we introduce malicious nodes, the more the difference increases. This is due to our computation of the average clock value. Indeed this value is computed including attackers which have a fixed clock to 0. On this figure we can see that difference quickly increases at the simulation beginning and then stop and decreases. This is particularly visible on the 10% malicious curve. The starting of the decrease is due to attack detection and isolation of malicious nodes.

These first experiments show that FC attacks are very effective on the SiSP protocol since a malicious node can succeed to desynchronize the whole system. These attacks are detected by the trusted SiSP protocol presented in this paper. The degraded mode enables to isolate the attackers and to keep synchronisation active.

VI. CONCLUSIONS AND PERSPECTIVES

In this paper we have presented a trusted lightweight synchronisation protocol based on the SiSP protocol. We have proposed a very flexible solution able to detect several kinds of attacks such as Fixed Clock, Random Clock, Misused Identity… The only countermeasure presented is that when the attack is detected, the node enters a degraded mode. This countermeasure has demonstrated that it can help keeping the synchronisation while SiSP protocol cannot.

We are currently working on other kind of countermeasures by adapting the degraded mode enabling a better clock value difference. Other attacks are going to be deeply investigated in order to find the good a, b, c, to detect and prevent all kinds of attack type. Since the MASH simulator enables hardware emulation, our next simulation should then quickly implement hardware in the loop parameters.

Algorithm 1 :

 1 SiSP SYNC indication subroutine rclk = extracted received clock from sispPayload if rclk sclk: sclk = ( sclk + rclk ) / 2 synchroFlag ß false else: synchroFlag ß true endif

Algorithm 2 :

 2 Confidence level restorationfor each id in neigboorList do: trust(id) = (1 -e) trust(id) + e done

Figure 1 .

 1 Figure 1. MASH simulator

Figure 2 .

 2 Figure 2. Test topology of trusted SiSP

Figure 4 .

 4 Figure 4. Trusted SiSP Clock value convergence

TABLE 1 :

 1 MAIN CHARACTERISTICS OF CITED PROTOCOLS

	Protocol	Category	Physical Layer	Accuracy
	TPSN	Hierarchical	IEEE 802.15.	17µs
	FTSP	Hierarchical	38.4kbps, 433MHz (Mica2)	10µs
	TSMP	Hierarchical	IEEE 802.15.4	100µs
	WiDeCS	Hierarchical	MB-OFDM	100ns
	RBS	Consensual	IEEE 802.11b	30µs
	SiSP	Consensual	IEEE 802.15.4	50µs

TABLE 2 :

 2 ATTACKS DESCRIPTION

TABLE 3 :

 3 ATTACKS PENALIZATION

	Attacks	Detection	Penalization
	MI	id = n	trust(id)=0
	MI	New neighbours abnormally increase	trust(id)new neighbours== 0
		Too small shared clock
	FC	deviation estimated compared	trust(id)t+1== trust(id)t -at
		to SCLK(n)
	RC	Not correlated shared clock compared to SCLK(n)	trust(id)t+1== trust(id)t -b
	QC	Too many SYNC(id) messages	trust(id)t+1== trust(id)t -c


Imen Akermi
email: imen.akermi@irit.fr

Rim Faiz
email: rim.faiz@ihec.rnu.tn

A Mobile Context-Aware Proactive Recommendation Approach

Keywords: Context modeling, Context-aware recommendation, User modeling, Proactive recommendation

The Proactive Context Aware Recommender Systems aim at combining a set of technologies and knowledge about the user context not only in order to deliver the most appropriate information to the user need at the right time but also to recommend it without a user query. In this paper, we propose a contextualized proactive multi-domain recommendation approach for mobile devices. Its objective is to efficiently recommend relevant items that match users' personal interests at the right time without waiting for users to initiate any interaction. Our contribution is divided into two main areas: The modeling of a situational user profile and the definition of an aggregation frame for contextual dimensions combination.

Introduction

The development of mobile devices equipped with persistent data connections, geolocation, cameras and wireless capabilities allows current context-aware recommender systems (CARS) to be highly contextualized and proactive. They provide users with relevant information when it is most needed at the right time without waiting for the user to initiate any query. There are several context aware systems that attempted to meet the challenge of providing the right information at the right time without the interference of the user in a mobile environment. However,this requires good modeling of the dimensions of the context and especially the modeling of the user profile. Indeed, as mentioned by [START_REF] Mizzaro | A social approach to context-aware retrieval[END_REF], several dimensions of context, such as location, time, users activities, needs, resources in the nearbies, light, noise, movement, etc., have to be managed and represented which requires a big amount of information and are time consuming. Besides, the incorporation of too many context dimensions generate complex context models. On the other hand, context models integrating few dimensions are unable to figure out the whole user context.

We propose, in this paper, a proactive context-aware recommendation approach that integrates the modeling of a situational user profile and the definition of an aggregation frame for contextual dimensions combination. DOI: 10.1007/978-3-319-24069-5 38

The paper is organised as follows. We provide in section 2 an overview about the related work. Section 3 presents the proposed approach. We describe in section [START_REF] Pu | Location based recommendation for mobile users using language model and skyline query[END_REF] the experiments done within the TREC 2014 Contextual Suggestion Track. We finish in section 5 with our conclusions and thoughts for future work.

Related Work

The user profile modeling covers broad aspects such as the cognitive, social and professional environment to determine the user intentions during a search session [START_REF] Mizzaro | A social approach to context-aware retrieval[END_REF]. The user profile is an important dimension considered within context modeling. Indeed, context is defined as a set of dimensions that describe and/or infer user intentions and perception of relevance. Those dimensions cover situations related to factors such as location, time and the current application. Work in context-aware recommendation makes use of one or all of these dimensions to describe the user and integrate him forward in the various phases of the recommendation process. Proactive recommendation systems (PRSs) as described in [START_REF] Melguizo | What a proactive recommendation system needs -relevance, non-intrusiveness, and a new long-term memory[END_REF], intend to sort among a large quantity of documents, the information that is most likely to be relevant to the user needs, and recommend that information without user requests. Several systems have been developed to support proactive recommendation. Various approaches relied on the user's past or actual behavior history to determine the user interests. Behavior history includes Web browsing history/clicks ( [START_REF] Melguizo | What a proactive recommendation system needs -relevance, non-intrusiveness, and a new long-term memory[END_REF]); previous visiting behaviors for location based systems ( [START_REF] Pu | Location based recommendation for mobile users using language model and skyline query[END_REF][START_REF] Ijntema | Ontology-based news recommendation[END_REF]) and previous reading patters for news recommendation systems ([6,7,8,9]). Other approaches dealt with user profiling from an activity centric angle. The common activities used to build the user profile in these systems might take the form of: Opened web pages or documents ([10,11,12]); Ongoing conversation or activity such as phone calls [START_REF] Phelan | On using the real-time web for news recommendation & #38; discovery[END_REF]; The social media activity of the user such as the user's tweet stream on Twitter ( [START_REF] De Francisci Morales | From chatter to headlines: Harnessing the real-time web for personalized news recommendation[END_REF][START_REF] O'banion | Social media-driven news personalization[END_REF][START_REF] Dobson | Leveraging the subtleties of location[END_REF]). However, some approaches require that users express their interests and input keywords or tags which is, most of the time, inconvenient in a mobile environment since it entails extra efforts from the user such as tagging, searching, or clicking. Mobile systems can help keep track of user's activities, preference and location. Besides, many context aware systems dealt with user profiling from an activity centric angle. Nevertheless, we cannot reduce the user profile to some activities. One can simply open a document to work on without being related to it in any way or have a conversation about an issue that he/she is not concerned to know any recommendation about it. There are also the domain dependency issue. In fact, many of the actual contextualized systems are domain dependent (tourism, movie, news ...) and have specific context dimensions to apply according to the domain. However, most of them rely almost on the same context combination which includes location, time and user preferences with a slight difference on how to approach this information. Our approach tries to deals with these issues by integrating the modeling of a situational user profile and the definition of an aggregation frame for contextual dimensions combination.

We propose a multi-domain proactive context-aware recommendation approach that recommends the right item that match users personal interests at the right time without waiting for users to initiate any interaction or activity.

Context Modeling

We consider the context as a two-dimension representation context=(profile,location). These dimensions' instantiations form a situation S where recommendation is needed. We define in the following sections the different component of the context modeling process.

The User Profile. The user profile (U P ) model is defined by two features, Demographic data; the user related information such as name,age,etc, C ;the user's interests related to specific weighted categories : prof ile = {C i , w i }; i = 1..n A category is a set of weighted terms that are associated to the user preferences and to the interest that he expresses towards this particular category :

C i = {t (i) j , w (i) j }; j = 1..m
The categories are predefined using the Open Directory Project Dmoz1 .

Location. The location is inferred according to GPS coordinates (latitude and longitude). Those GPS coordinates are not the only features that we can consider when defining a location. Indeed, as discussed by [START_REF] Dobson | Leveraging the subtleties of location[END_REF], there are different ways to characterize the location of the mobile user, Absolute position; Relative (next to, ... ); A Place name; A named class that represents the type of the place, eg. museum, school, ... . We consider the absolute position and the named class representation to characterize the spatial dimension of the user. We define two levels of the location dimension: The actual location, that refers to the user's actual location at a given time; The user's related locations, the places related to the daily life of the user (work, home, ...). The actual location can be recovered using several tools such as Geonames2 or the Social Network Foursquare3 which assign a location category to a given GPS coordinates.

The Recommendation Process

Type of Information to Recommend. We consider that the recommendation process entails a pack of situations which reflect a specific area of interest characterized by the instantiations of the context dimensions. The possible situations are organized within a knowledge database. A situation is then represented by two specific dimensions: the actual location (D l ) and the user's category of interests related to that location.

These values are used to assess the current situation need in information and the category type of the information to recommend. Our key idea is that the user's need in information changes according to the user's actual location. For instance, a user might want to check the news once he is at work or he might want to visit a specific shop if he's found to be near a mall.

The category of interest of the information to recommend is inferred from the current situation.

Information Extraction. In order to retrieve the information to recommend, a query q is formulated as : q=(latitude, longitude, category of interest) The query is sent to a geo-based service. The query result is represented by a set of items I : I = {i 1 , ?, i n }. An item is defined as a weighted terms vector i j = {t j k , w j k }; j = 1..n, k = 1..p We filter out from the set I, the items suiting best the user's preferences by calculating a relevance score. The relevance of an item with respect to the category of interest entails two components: the topic and the location relevance. The topic relevance assess to which degree the user preferences related to the given category are related to an item and is calculated as :

T opic rel (V C i , It) = n j=1 V C j i * It j n j=1 (V C j i ) 2 * n j=1 (It j ) 2 (1)
Where:

V C i : the preferences keywords vector related to category C i It: the item keywords vector The location relevance is only used in case where the user has to move to get to the suggested item. It is expressed by a score measuring the accessibility to the actual place's location and is calculated as the distance between 2 GPS coordinates corresponding to the user's current location and the suggested item location: (P 1(lat1, long1) et P 2(lat2, long2)):

accessibility = R * c (2)
Where: R: The earth radius=6,371Km

c = 2 * atan2( √ a, (1 -a)) a = sin 2 ((lat2 -lat1)/2) + cos(lat1) * cos(lat2) * sin 2 ((long2 -long1)/2)
The overall relevance for a result is calculated as :

Rel = α * T opic rel (C i , It) + (1 -α) * accessibility (3)
The results are ranked according to their overall relevance scores. The recommendation process is summarized as follows :

Input: Profile{{C i , w i } i=1..n } C i = {(t i

Experiments

We evaluated our approach using the TREC 2014 Contexual Suggestion Track task. We present in this section, a general description of the task, then we expose the obtained results.

The TREC 2014 Contexual Suggestion Track

This task offers an evaluation platform for search techniques that depend highly on the context and the user interests. The input to this task consist of a set of profiles, a set of sample suggestions (a set of venues evaluated by the profiles) and a set of contexts. Each profile corresponds to a single user, and indicates the preference of the user with respect to the set of suggestions. For example, one suggestion could be a recommendation to have a beer at the Dogfish Head Alehouse. The profile describes the negative or the positive preference of the user regarding the set of suggested venues.

Profiles Processing. The profiles are constructed using the list of the suggested venues evaluated by the user. Each suggestion is evaluated according to two ratings: a rating for the venue's title and description and a rating for the venue's website. The profile should indicate which venues a user likes or does not like. The ratings are fixed on a five-point scale based on how interesting a venue would be for the user if he was visiting the city the venue was in: 4, Strongly interested; 3, Interested; 2, Neutral; 1, Disinterested; 0, Strongly disinterested; -1, Website didn't load or no rating given The suggestions (venues) representation : id,title,description,url 1,Fresh on Bloor,"Our vegan menu ...",www.freshrestaurants.ca The user's ratings : id,attraction id,description,website 1,1,1,0

In order to define the user's thematic profile, we identify for each suggested venue its category using Google Places API 4 . A profile is then expressed as a set of weighted categories under which there are terms set related to the liked suggestions :prof ile = {C i , w i }; i = 1..n The categories are represented by a set of weighted terms extracted from the suggestions' descriptions. For each profile, the weight assigned to a particular category takes into account the two ratings of the suggested venues that were rated by users. One rating for the venue's title and description and the other one is for the venue's website.

weight(category) = ∀s∈C R td + R w N p (4)
Where: ∀s ∈ C: for each suggestion s belonging to this category C R td : The venue's title and description rating R w : The venue's website rating N p : the number of suggestions belonging to this category Contexts Processing. The TREC task defines context according to GPS coordinates context=(latitude,longitude). For each context, we gather possible venues by querying two geo-based services: Google Places and Foursquare. The query is modeled as: Query={(latitude,longitude),category}

A venue (query result) is modeled as an object having specific attributes and belongs to a specific category:

venue={name,url,description,accessibility,category } accessibility: Represents the distance separating the venue from the specified location. The venue accessibility is measured as the distance between 2 GPS coordinates(see formula number 2).

(Profiles, Suggestions) Matching. The selection process of interesting places for each context-profile pair is summarized as follows:

For each p i ∈ P For each c j ∈ Cx -Calculate, for each suggestion s ∈ Cx j suggestions the relevance(Formula 3) -Normalize the relevance scores of the suggestions between 0 and 1 -Extract the suggestions which relevance score is ≥ 0, 5 and that belongs to the categories of interest that are appreciated by the profile category weight normalised ≥ 0.5

Where: P : The Profiles set Cx: The Contexts set Cx j suggestions : The set of suggestions related to context C j s: suggestion ∈ Cx j suggestions

Results

To measure the geographic relevance of the venues that we suggested for each context, we extracted a venues' sample V g which involves the intersection of our venues collection with the venues that have been evaluated geographically in the TREC task for each context. We obtained |V g | = 4802 venues across all contexts. Among these places, 4644 were evaluated geographically relevant which implies a total geographical precision equal to 0.97 and is calculated as:

geo relevance = N b Geo Relevant V enues |V g | (5)
To measure the profile relevance, there were two alternatives to note. A first alternative is to consider for each context, the intersection of our venues' collection with the venues provided by each run5 , however, this intersection almost gave the empty set. We opted for an intermediate solution of considering the intersection of our venues' collection with the union of the venues that each run has proposed across all profiles in order to get the suggested venues ratings. The cardinality of this intersection is |V p | = 889 venues. Then we measured for each venue the level of interest that it has requested from the profiles based on the number of profiles that have evaluated this venue as relevant compared to the total number of evaluations of the same venue. We obtained an average precision of 0,56 that is calculated as :

prof ile relevance = |V p | v=1 (nb prof iles v /tot nb prof iles v ) |V p | (6)
where: nb prof iles v : is the number of profiles that evaluated the venue v as interesting. tot nb prof iles v : is the total number of profiles that evaluated the venue v.

In order to compare approximately the result that we obtained with the other participants'results, we also applied this method to the other runs in order to measure the profile relevance. Indeed, for each run we calculated the number of the venues that were rated interesting by the profiles compared to the total rated venues that were suggested by the run (see table 1).

As we can notice from Table 1, the profile relevance for each run does not exceed 0.25. This is explained by the fact that for each run, there is a large gap between the number of profiles that have judged a venue (belonging to a given context) as relevant and the number of the total judgments for the given venue.

The results that we obtained using our approach are promising and show that the use of the categories classification of a profile's preferences implies better thematic relevance compared to the profile interests. These results also indicate that the choice of the parameters that we have set such as the radius used for the definition of the premises of the venues for a given context, are effective. However, this evaluation has only indicted a part of our approach. Indeed, the time notion and the current activity of the user are not incorporated in the TREC task whereas these dimensions are considered in our approach.

The fundamental purpose of Context-Aware Recommender Systems consists in combining the user's context and environment in a same infrastructure to better characterize the user information needs in order to improve the recommendation process.We proposed a proactive context-aware recommendation approach that can help users deal with information overload problem efficiently by recommending relevant items that match users? personal interests at the right time without waiting for users to initiate any interaction or activity. More specifically, our contribution is divided into two main areas: The modeling of a situational user profile and the definition of an aggregation frame for social contextual dimensions combination. Actually, we are planning to participate in the RecSys 2015 Challenge YOUCHOOSE in order to validate our approach by incorporating, this time, the user's current activity and the time notions within the experiments.

Table 1 .

 1 Profile relevance (NBInV is the number of venues that were rated as interesting by the profiles; NbTotV is the total rated venues that were suggested by the run; Prec. stands for the precision)

	id run	NbInVNbTotV Prec. id run	NbInVNbTotV Prec.
	1 BJUTa	352	1495	0,24	20 SScore	244	1496	0,16
	2 BJUTb	327	1495	0,22	21 SScoreImp 254	1496	0,17
	3 BUPT 01 81	671	0,12	22 tueNet	129	1497	0,09
	4 BUPT 02 78	704	0,11	23 tueRforest 138	1497	0,09
	5 cat	318	1496	0,21	24 UDInfo 1 201	1495	0,13
	6 choqrun 196	1465	0,13	25 UDInfo 2 360	1495	0,24
	9 dixlticmu 367	1496	0,25	26 uogTrBun 272	1495	0,18
	10 gw1	58	1466	0,04	27 uogTrCsL 199	1496	0,13
	11 lda	163	1496	0,11	28 waterlooA 260	1497	0,17
	14 RAMAR2 260	1497	0,17	29 waterlooB 286	1497	0,19
	15 RUN1	229	1494	0,15	30 webis 1	269	1477	0,18
	16 run DwD 181	1496	0,12	31 webis 2	230	1474	0,16
	17 run FDwD 262	1496	0,18

http://www.dmoz.org/docs/en/about.html

http://www.geonames.org/

https://fr.foursquare.com/

A run represents the set of venues proposed by a team participating in the TREC 2014 Contextual Suggestion Track.