domain: spi math

text:
Mahfoud Herraz

Jean-Max Redonnet

Mohammed Sbihi

Marcel Mongeau

Blackbox optimization and surrogate models for machining free-form surfaces

Keywords: blackbox optimization, clustering, surrogate model, free-form surfaces, principal component analysis, toolpath planning

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

Milling is an industrial manufacturing process where a rotating cutter is moved into a work piece and removes matter on its way. As a result, the envelope of all the successive positions of the cutter is removed from the initial part. When the tip of the cutter is the working area of the cutter, this process is called end-milling.

In the field of manufacturing, all non prismatic nor revolution surfaces are called free-form surfaces. To manufacture a part defined by free-form surfaces, a computerdriven machine, i.e. a CNC (Computer Numerical Control) machine, is needed. The CNC machines commonly encountered in industry are 3-or 5-axis machines, according to the number of degrees of freedom they provide. On a 3-axis machine, only pure translation of the cutter is allowed, while 5-axis machines permit some rotations of the cutter. In the context of free-form surfaces machining, socalled 3+2-axis machining (i.e. 3-axis machining plus two rotation axes for positioning the part between two milling phases) is often preferred to 5-axis machining. Indeed, rotation axes dynamics often bring out slowdowns when continuously used [START_REF] Suh | Five-axis part machining with three-axis CNC machine and indexing table[END_REF]. This paper is therefore dedicated to both 3-axis machining and 3+2-axis machining.

From a purely geometric point of view, the key point is: whatever the path the cutter is taking, it cannot hug perfectly the definition surface at each point. The remaining matter, called scallop, is removed later, often manually (see Figure 1). Actually, the scallop height is the quality criterion of the whole operation; while, for productivity reasons, the objective is to machine the surface as fast as possible. Yet, because of machinability considerations, the speed of the cutter must be fixed to an acceptable value. The only way to decrease machining time is therefore to improve the cutter trajectories. This is the toolpath planning phase, and it is a wide topic of research in the manufacturing field.

End-milling of free-form surfaces on multi-axis CNC machines is complex, and it involves expensive operations in the production of many high-value parts, such as molds and stamping dies. Currently, in the industry, these operations are still carried out using reliable and proven, but far from optimal, toolpath planning strategies. The parallel-plane strategy (Figure 1) is the most commonly adopted strategy for industrial manufacturing, as it ensures that the entire surface is covered and it is easy to implement.

Using this strategy, toolpaths are defined by the intersection of the surface to be machined with a set of parallel planes covering the whole surface. Practically, each toolpath is a sequence of interpolation points calculated using surface-surface intersection algorithms, such as those described in [START_REF] Barnhill | Surface/surface intersection[END_REF].

Ball-end mills, i.e. cutters whose tip is hemispherical, are the most widely used cutters in industry. Many sources ( [START_REF] Bedi | Toroidal versus ball nose and flat bottom end mills[END_REF] for instance) point out that toroidal cutters, i.e. cutters whose tip is rounded as a quarter torus, may however provide better results when machining along the steepest-slope direction. Unfortunately, they also can provide worse results when machining along a direction perpendicular to the steepest-slope direction. Figure 2 illustrates this point on a plane for the sake of clarity, but the same applies on a free-form surface (on this figure the same depth of cut is used for both ball-end and toroidal machinings along a given direction).

Since the steepest-slope direction may vary much across a free-form surface, partitioning this surface into zones (each of which will then be machined along an appropriate direction) is a good approach to improve efficiency of the toroidal cutter.

The present paper deals with optimization of toroidal cutter tool path planning in 3-axis and 3+2-axis machining contexts, using a parallel-plane strategy applied to dedicated zones on a free-form surface. It is structured as follows. Section 2 presents the required background on surface partitioning, toolpath planning optimization, and derivative-free and blackbox optimization. We propose an optimization formulation of the toolpath planning problem for miling free-form surfaces in Section 3.

Section 4 introduces and evaluates surrogate functions to improve the blackbox optimization process. Computational results are presented in Section 5, while Section 6 is devoted to comparison with previous work. Section 7 briefly illustrates the application of our methodology to a real-world industrial part. Finally, Section 8 draws conclusions and presents perspectives for future work.

Background

This section presents the required background on surface partitioning, toolpath planning optimization, and derivative-free and blackbox optimization. Only the most relevant papers in relation to our work are presented here.

For a broad review of the state of the art in CNC machining of free-form surfaces, see [START_REF] Lasemi | Recent development in CNC machining of freeform surfaces: A state-of-theart review[END_REF] or [START_REF] Mali | A comprehensive review of free-form surface milling-Advances over a decade[END_REF] and references therein.

Surface partitioning

Finding an optimal surface partitioning for 3-axis machining is discussed for instance in [START_REF] Herraz | Analysis of clustering algorithms for by-zone machining of free-form surfaces[END_REF]. The idea is to use a clustering approach to partition the surface based on a metric specifically dedicated to free-form surface clustering. Other works on surface partitioning include heuristic-based methods inspired by the Vehicle Routing Problem [START_REF] Djebali | Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling[END_REF], an approach based on Adaptive Multi-Agent Systems [START_REF] Djebali | Milling plan optimization with an emergent problem solving approach[END_REF], and an approach based on the concept of efficiency intervals (set of directions where toroidal cutter is better than ball-end one) is proposed by [START_REF] Duc | Automatic minimal partitioning method guaranteeing machining efficiency of free-form surfaces using a toroidal tool[END_REF]. In [START_REF] Makhanov | Optimization and correction of the tool path of the five-axis milling machine: Part 1. Spatial optimization[END_REF], surface zones are generated based on a vector field of locally-optimal machining directions. A similar approach is adopted in [START_REF] He | Quasi-Developable and Signed Multi-Strip Approximation of a Freeform Surface Mesh for Efficient Flank Milling[END_REF] for flank milling. The objective of surface partitioning approaches is to find zones with small variations of the steepest-slope direction. This increases the effective radius of the cutter leading to maximal step-over distances, and minimizes thereby the toolpath length, and as a consequence the machining time is expected to decrease.

Toopath planning optimization

Toolpath planning is a complex problem and few authors have approached it in its globality with an optimization approach. The authors of [START_REF] Bartoň | Geometry and tool motion planning for curvature adapted CNC machining[END_REF] are addressing this problem by building an objective function that attempts to ensure all requirements for obtaining acceptable milling trajectories. The objective function is in fact a weighted sum of conflicting criteria that neglects the real objective for practitioners, which is to minimize machining duration. Several authors nevertheless propose optimization formulations to improve some particular aspects of the overall toolpath planning problem. For instance [START_REF] Agrawal | Optimization of CNC isoscallop free form surface machining using a genetic algorithm[END_REF] uses a genetic algorithm to find a parametric cutter path curve of the form v = A 0 + A 1 u + A 2 u 2 + A 3 u 3 , that minimizes the toolpath length using isoscallop strategy in 3-axis machining, where the coefficients A 0 , . . . , A 3 are the optimization variables. A traveling salesman problem formulation involving precedence constraints is proposed in [START_REF] Castelino | Toolpath optimization for minimizing airtime during machining[END_REF] to minimize the non-productive time (so-called airtime) by optimally connecting different toolpath segments. Again, a traveling salesman problem formulation is used by [START_REF] Lazoglu | Tool path optimization for free form surface machining[END_REF] together with a minimum spanning tree in view of minimizing cutting forces, with imposed passing points. Two toolpath planning optimization procedures are presented in [START_REF] Makhanov | Optimization and correction of the tool path of the five-axis milling machine: Part 1. Spatial optimization[END_REF]. The first one defines a toolpath based on a curvilinear grid generation approach, defined by minimizing the kinematics error in 5-axis machining.

The second one relies on space filling curves algorithms to fill an isoparametric grid according to the machining strip calculated for a flat-end cutter. CNC machine-tool kinematics is also a field of interest: [START_REF] Dong | Feed-rate optimization with jerk constraints for generating minimum-time trajectories[END_REF] introduces permissible jerk (derivative of the acceleration) as a constraint in an optimization model of the feedrate under velocity and acceleration constraints to generate minimum-time trajectories.

Free-form surface machining-time cannot be expressed as a closed-form formula. It requires a complete milling simulation that includes an accurate evaluation of the elapsed time. This simulation relies on complex algorithms and produces a non-smooth objective function that is subject to noise, and that features numerous spurious local minima. That is why most of the proposed optimization algorithms are either heuristics, or address partially the machining-time minimization problem.

Derivative-free and blackbox optimization

Since the 1990's, due to strong demand from industry, optimization methods with proofs of convergence have been developped to address problems involving objective and constraint functions given by costly simulations and/or without any gradient information available. Introductions to blackbox and derivative-free optimization algorithms are given in [START_REF] Conn | Introduction to Derivative-Free Optimization[END_REF][START_REF] Audet | Derivative-Free and Blackbox Optimization[END_REF]. In this paper, we shall use the blackbox optimization software NOMAD [START_REF] Audet | NOMAD user guide[END_REF][START_REF] Digabel | Algorithm 909: NOMAD: Nonlinear Optimization with the MADS algorithm[END_REF] to solve the machining time minimization problem. NOMAD is considered as the best performer for the type of problem we consider here [START_REF] Ploskas | Review and comparison of algorithms and software for mixed-integer derivativefree optimization[END_REF]. It is a C++ implementation of the MADS algorithm, an iterative method that proposes a new point where to evaluate the objective function (and the constraints) at the next iteration. An iteration of MADS algorithm involves two steps: a search step and a poll step. The search step attempts to escape from local optima; any heuristic can be used in the search step in order to find a better point. This step is to be defined by the user. If the search step is not successful, then the poll step is performed. It selects a set of directions that rely on a mesh constructed from a positive spanning set of the search space. These directions are used to define new points. If a better point is found, the mesh is coarsened ; otherwise, it is refined. The convergence of MADS is mathematically guaranteed by the poll step. Details about the MADS algorithm can be found in [START_REF] Audet | Mesh Adaptive Direct Search Algorithms for Constrained Optimization[END_REF].

NOMAD allows the user to provide a so-called surrogate (cheaper-to-evaluate models) of the costly objective and constraints functions in order to improve the optimization computing time. It is either a simplified physical model of the blackbox functions, or an approximation model obtained by evaluating the blackbox function at a given number of points then by interpolating or smoothing the values. Two types of surrogates can be envisaged: static and dynamic. Static surrogates are provided by the user and are not updated during the optimization, but in return they allow introduction of business knowledge about the application into the surrogate. Dynamic surrogates are in contrast constructed gradually from the evaluations available made in previous iterations. A surrogate can also be used to re-order the poll points, before they are evaluated by the blackbox. The use of surrogates may reduce considerably the number of blackbox evaluations and, sometimes, may help to find a better solution (than the one found without surrogate). NOMAD provides a library of dynamic surrogates. For more details, see [START_REF] Booker | A rigorous framework for optimization of expensive functions by surrogates[END_REF] which presents a survey on surrogate optimization.

One contribution of this article is to propose (in Section 4) fast surrogates of the expensive machining-time blackbox.

Optimization formulation

We are given a free-form surface, S, parameterized by two coordinates, u and v. The objective is to machine S in minimal time under a given threshold constraint. The optimization approach proposed in this paper involves a black box that consists of two main steps: partitioning and machining. Partitioning the surface S into zones is done using unsupervised clustering algorithms applied on a set of N sample points, denoted S i , i = 1, 2, . . . , N , built from an isoparametric meshing (Figure 3). Some clustering algorithms, such as K-means, requires the user to specify the number of clusters, denoted K, which can thus be considered as a first optimization variable. An upper bound, K max , of K can easily be defined since beyond a certain number of clusters, machining time increases, due to the time loss each time the tool finishes a zone and moves to the next one. This time loss must be taken into account otherwise the problem becomes trivial: the solution is obtained by considering as many clusters as there are sample points. Furthermore, clustering algorithms require in general a feature vector and a measure of dissimilarity, hereafter called (by misuse of language) the metric.

Following in [START_REF] Herraz | Analysis of clustering algorithms for by-zone machining of free-form surfaces[END_REF], we choose the feature vector (u i , v i ,

S(u, v) u v sample point S i
Legend:

elementary mesh Figure 3: The sample points to be clustered.

S i = S(u i , v i ) n(u i , v i ) X Y Z θ i s i
Figure 4: One sample point S i of the surface and the four components (u i , v i , s i and θ i ) of its feature vector.

s i , θ i ), where (see Figure 4):

• (u i , v i ) is the parametric coordinates of the sample point S i ;
• s i is the steepest-slope angle, i.e. the angle between the vector n (ui,vi) , normal to the surface at S i , and the horizontal plane (X, Y);

• θ i is the steepest-slope orientation, i.e. the angle between the X axis and the projection of n (ui,vi) onto the horizontal plane (X, Y).

For the metric, we choose a weighted Euclidean distance, as proposed also in [START_REF] Herraz | Analysis of clustering algorithms for by-zone machining of free-form surfaces[END_REF]. More precisely, the distance between two given points S i and S j is given by:

w1(ui -uj) 2 + w2(vi -vj) 2 + w3(si -sj) 2 + w4(θi -θj)
where the values of the weights, 0 ⩽ w1, w2, w3, w4 ⩽ 1, can be considered as further optimization variables. In the sequel we shall denote by W the vector whose components are w 1 , w 2 , w 3 and w 4 .

This first step produces a partition of the surface into K zones. Let I k be the index set of the sample points that belong to zone k, k = 1, 2, . . . , K. The clustering step is interpreted as the following blackbox constraint:

I = c(K, W ), (1)
where c is a function that represents this clustering step procedure that outputs a partition, I, of the index set of the data points; I is a vector whose

k th component is I k , k = 1, 2, . . . , K.
The machining step addresses each zone separately according to the parallel-plane strategy. The distance between two adjacent planes (called step-over distance) is defined as the maximum distance such as the scallop height constraint is respected for the whole path. At a given plane, the position of the adjacent plane is easy to determine: it suffices to consider the worst point, in terms of scallop height, of the path defined by the given plane. This is enough to ensure that the quality constraint will be satisfied for the entire trajectory. From the optimization point of view, this strategy is very useful because the constraints are thereby satisfied by construction. The scallop height may be calculated from the surface swept by the cutter during milling [START_REF] Roth | Surface swept by a toroidal cutter during 5-axis machining[END_REF][START_REF] Machchhar | Precise algebraic-based swept volumes for arbitrary freeform shaped tools towards multi-axis CNC machining verification[END_REF], but using a fast scallop height calculation method, such as in [START_REF] Redonnet | Study of the effective cutter radius for end milling of free-form surfaces using a torus milling cutter[END_REF], the above-described toolpath planning process (including milling time calculation [START_REF] Pessoles | Kinematic modelling of a 3-axis NC machine tool in linear and circular interpolation[END_REF]) is rapid enough to be used as the objective function of an optimization procedure. In the case of 3-axis machining, for each cluster k, the toolpath planning depends only on the machining direction. The angle, noted γ k , between this direction and the X axis is an optimization variable.

When 3+2-axis machining is considered, two more orientation angles must be determined for each zone k. Firstly, we define the angle, φ k , between the tool axis and the Z axis. Secondly, we define the angle, ψ k , between the X axis and the projection of the tool axis on the XY plane. As for γ k , these orientation angles, illustrated on Figure 5, are optimization variables. In the sequel we shall use the following vector notation:

Γ K = (γ 1 , γ 2 , . . . , γ K ), Φ K = (φ 1 , φ 2 , . . . , φ K ) and Ψ K = (ψ 1 , ψ 2 , . . . , ψ K ) (each component corresponds to one zone).
All points of the zone should be accessible by the tool. More precisely, consider a zone k and a given point of that zone, of parametric coordinates (u, v). Let β (u,v) (φ k , ψ k ) be the angle between the Z axis and the vector, n (u,v) (φ k , ψ k ), normal to the zone k at (u, v). This given point is considered accessible by the tool if

|β (u,v) (φ k , ψ k )| ⩽ π 2 .
In practice, this constraint is evaluated only over the sample points to zone k). This will be ensured within the objectivefunction blackbox evaluation, f . To sum up, the resulting optimization problem involves a blackbox objective function (the machining time), and the blackbox clustering constraint [START_REF] Suh | Five-axis part machining with three-axis CNC machine and indexing table[END_REF]. A chart summarizing the working flow is shown on Figure 6, and the constrained mixed variable optimization problem considered is:

(u i , v i ) ∈ I k (belonging X Y Z γ k φ k ψ k cutter motion
min K,W,Γ K ,Φ K ,Ψ K F (K, W, Γ K , Φ K , Ψ K ) subject to I = c(K, W ) 0 ⩽ w i ⩽ 1, i = 1, 2, 3, 4 0 ⩽ γ k ⩽ π, k = 1, 2, . . . , K -π 2 ⩽ φ k ⩽ π 2 , k = 1, 2, . . . , K 0 ⩽ ψ k ⩽ π, k = 1, 2, . . . , K K ∈ {1, 2, . . . , K max }, (2)
where

F (K, W, Γ K , Φ K , Ψ K ) = K k=1 f (I k , γ k , φ k , ψ k ).
This problem is partially separable per zone, the only linking constraint being constraint I = c(K, W ) through the components, I k , k = 1, 2, . . . , K, of the sample-point index-set partition I.

Remark that the number of variables and constraints of our problem depends directly on the number of zones, K, which is itself a variable. Although it is integer valued, the optimization variable K plays a role of categorical variable: its continuous relaxation is meaningless.

4

Surrogates models and their numerical evaluation

This section proposes and evaluates surrogate functions to improve the blackbox optimization process.

In this section, we focus on static surrogates. The aim is to construct the cheaper surrogates to reduce the computational time, without losing too much precision. An efficient surrogate does not need to be a good approximation of the exact values of the blackbox, it may solely approximate its variations and the location of its optimal points.

In our context, the machining time is the result of a blackbox simulation based on numerical calculation of intersections of the part surface and parallel planes. The intersection curves (the machining toolpath) rely on an isoparametric meshing of the part surface. The precision of the curves and the time for their calculation increase with the mesh step size. Therefore, the mesh step size is a parameter that allows simplification of the physical model (cheapest evaluations but less precision) and can be used to create surrogates. This will be used to create our Surrogates 1 and 2. Note that the mesh step size cannot be directly defined on the actual surface, it has to be defined in the parametric variable space. Consequently, a reverse approximation procedure is implemented to set the step size, targeting a given value in the 3D space.

A second parameter that could be used to shorten the simulation time is the scallop height tolerance. In fact, increasing this value leads to larger step-over distances which reduces the number of parallel planes, and subsequently the number of intersections to be computed with the part surface. Of course, this will impact the objectivefunction values (reduced machining times). Nevertheless, it is reasonable if the variations and optimal points were preserved. This will be investigated further in this section and it motivate our Surrogate 4.

So far, simplifications of the model have concerned the machining step rather than the clustering step. One way of simplifying the clustering step is to increase the clustering mesh step size. This leads to the reduction of the computational time required for clustering, since the K-means algorithm (and any other clustering algorithm) needs less time to run for fewer data points. However, the precision of the part surface zones (the clusters) is then deteriorated; the borders of the zones are roughly approximated, which will affect the machining times values. The simulation time reduction is more or less efficient depending on the algorithm used. In our case, empirical tests show that the K-means algorithm is fast enough, and that this does not yield a sufficient benefit.

Yet another alternative to simplify the blackbox would be to approximate the part surface zones to be machined by rectangular planes, so that machining times could be calculated analytically, which is expected to reduce drastically the computational time of the blackbox evaluation. The approximation by planes should be accurate, even though some zones may not be adapted for such an approximation. Principal Component Analysis (PCA) is used to calculate the planes that best fit the surface zones. This procedure is the same one as that introduced in [START_REF] Herraz | A new method for choosing between ball-end cutter and toroidal cutter when machining free-form surfaces[END_REF], but we shall apply it here to zones instead of applying it to the whole surface. The machining time is thereafter calculated, via Surrogate 4, using the analytical approach detailed in A.

To summarize, we propose the four surrogate functions to approximate the blackbox function f :

• Surrogate 1 approximates coarsely the blackbox function, targeting a value of 5 mm for the mesh step size (instead of the original value 0.5 mm).

• Surrogate 2 is a finer approximation of the black-box function, targeting a value of 2 mm for the mesh step size.

• Surrogate 3 approximates the blackbox function using an analytical calculation based on the abovementionned PCA-based approach.

• Surrogate 4 approximates the blackbox function using a scallop height tolerance increased to 1 mm (instead of the original value 0.1 mm).

In order to investigate the efficiency of the four surrogates, we are content with the case of 3-axis machining (i.e. the components of the orientation variables Φ K and Ψ K are set to the constant value zero).

In this paper, we use two test surfaces: a 4 × 4 bicubic Bézier surface (named Surface 1) and a 3 × 3 quadratic Bézier surface (named Surface 2). The corresponding control points are given in B.

These surfaces are partitioned using the K-means algorithm (clustering step) and the Euclidean metric (i.e. w 1 = w 2 = w 3 = w 4 = 1), leading to a total of seven zones to be studied (Figure 7).

Figures 8 and9 display the variations of the four surrogates and those of the blackbox machining-time function, f , for each zone k of Surface 1 and of Surface 2, respectively. To compare the different surrogates and their correlations with the blackbox, we calculate a correlation coefficient for each zone as follows. Consider a particular zone k. Let (γ i ) i=1,2,...,m be a uniform sampling of the domain [0, π]. Let h denote one of the four surrogate functions. The correlation coefficient ρ between f (the blackbox) and the surrogate function h is computed from the sample values f (I k , γ i , 0, 0) i=1,2,...,m and h(I k , γ i , 0, 0) i=1,2,...,m .

Table 1 gives the percentages of the computation times of each surrogate compared to the blackbox function f for the different zones, while Table 2 provides the correlation coefficient of each surrogate with the blackbox.

All surrogates show a relatively good correlation with the blackbox to approximate. We shall therefore eliminate the two candidates (Surrogates 1 and 2) that are the slowest in terms of computational time. Surrogate 3 is particularly interesting with respect to its very low computational time. This is due to its PCA-based analytical computation, which renders Surrogate 3 especially relevent when dealing with zones whose shapes are almost rectangular (such as the zones of Surface 2). For zones whose shape is far from being rectangular, one should rely on Surrogate 4. But, somewhat unexpectedly, at least for surfaces tested in Section 5, Surrogate 3 also provides very good results.

Tests and results

In this section, we present computational results of our optimization methodology using Surrogates 3 and 4 on Surfaces 1 and 2.

Test protocol

Machining is performed with a toroidal cutter whose radii are R = 5 mm (outer radius) and r = 2 mm (torus radius). The parallel-plane strategy is used. The scallop height tolerance is set to sh = 0.01 mm, a value commonly used in industry. The kinematic parameters of the CNC machine tool are:

• jerk (constant): J = 40 m/s 3 ;

• maximum acceleration: A max = 6 m/s 2 ;

• nominal feedrate: V f = 0.083 m/s (5 m/min).

For the sake of simplicity, in this study we are content with using an enumerative strategy to determine the value of the decision variable K (the number of zones). More precisely, the optimization problem is solved successively for K = 2, 3, . . . , K max . This proves, in our tests, to be more efficient than introducing K as an optimization variable. Remark that the resulting K max optimization problems could then even be solved in parallel. The upper limit on the number of clusters is set to K max = 10.

Let us now consider one fixed value of K. The mesh used for clustering is a uniform 80×80 isoparametric grid.

The maximum number evaluations of the blackbox (Figure 6) is set empirically to 1,000. The mesh direc- tion type parameter of the MADS algorithm is set to ORTHO 2N (i.e., poll directions are generated using the maximum positive spanning set produced from an orthogonal basis of the search space and its opposite).

The initial point given to NOMAD is defined with ω i = 1, i = 1, 2, 3, 4, and φ k = ψ k = 0, , k = 1, 2, . . . , K and γ k , k = 1, 2, . . . , K, is set to the average steepest slope direction of zone k. This starting solution is considered by practitioners to be a good machining configuration.

For each optimization run, the gain η is defined in relation to this initial point:

η = F 0 -F * F 0 , (3)
where F 0 is the value of the objective function at the initial point, and F * , the best value of the objective function.

As it is common practice in blackbox optimization, the evaluation of surrogates is counted in the computation time in proportion to their relative cost in time with re-spect to that of the blackbox. For the sake of comparison, the optimization process is stopped after a computational time equivalent to 1,000 blackbox evaluations.

Optimization results for 3-axis machining

To simulate 3-axis machining, angles ϕ k and ψ k are fixed constant, to zero, throughout the optimization process.

For each test surface, three optimizations are run: one without surrogate, the other with Surrogate 3 and the last with Surrogate 4. Table 3 summarizes the optimization results for each of these three cases for Surface 1. This example illustrates how using an efficient surrogate may allow the optimization to explore a larger part of the search space. Indeed, the best objective-function value is found using Surrogate 3 (with K = 8). The optimization history graphs, presented in Figure 10, show that the surrogate functions, especially Surrogate 3, accelerate convergence, requiring 4 summarizes the optimization results for Surface 2. In this configuration, again, the best point is found using Surrogate 3 (for K = 4). In this case, however, using surrogates does not yield a better objective-function value. The optimization history graphs presented in Figure 11 show, again, that the surrogates functions, especially Surrogate 3, accelerate convergence, requiring fewer blackbox evaluations. This means that even if using surrogates does not improve the result, it still allows one to reach the best objective-function value faster.

Optimization results for 3+2-axis machining

Due to the high number of optimization variables involved in 3+2-axis machining, especially for high values of K, NOMAD's search step is skipped (constructing search models may be very time consuming for 3+2-axis machining). Moreover, here, we present only results using Surrogate 3, as it systematically yields results that are better than those of Surrogate 4. Tables 5 and6 summarize the optimization results for Surfaces 1 and 2, respectively. As for the results obtained in 3-axis-machining, the optimization history graphs (Figures 12 and13) here again reveal that Surrogate 3 accelerates convergence, requiring fewer blackbox evaluations.

For each value of K, both optimization runs took nearly the same CPU time, approximately 1 hour.

To sum up, for both 3-axis and 3+2-axis machinings, the optimization process allows improvements of machining times, both on Surfaces 1 and 2, of nearly 15% compared to the reference values. Recall that these reference values are obtained using solely a clustering step with a particular (non-optimized) choice of the weights w i 's that is fairly representative of recent, the-state-of-art results [START_REF] Herraz | Analysis of clustering algorithms for by-zone machining of free-form surfaces[END_REF].

As expected the machining times are generally better in 3+2-axis machining than in 3-axis machining (more degrees of freedom for optimizing). Some exceptions are due to the fact that the optimization algorithm cannot guarantee global optimality and the variable space is likely to be explored differently from one case to another. The main point to keep in mind here is that for the best values obtained, 3+2 axis machining does better than the 3-axis counterpart. Surrogate 3 is not only the fastest, because of its analytical formulation, but it is also the one that yields the best results. In addition, the optimization history plots show a faster decrease of machining times when Surrogate 3 is used. They also reveal that our methodology generally reaches best solutions within a number-of-evaluation budget that is much lower that the 1,000 iterations we used in our tests.

K

Comparison with other works

This section compares numerically our approach with other works from the literature. We test on the same test surfaces (Surface 1 and Surface 2) and on third surface from [START_REF] Roman | Three-half and halfaxis patch-by-patch NC machining of sculptured surfaces[END_REF]. We use for comparison previous works from the literature that provide sufficient information (machining time obtained, and when it is not given: the path length obtained) and we use the same machining parameters. Remark that, to our knowledge, these studies are the only ones providing sufficient data to make comparisons possible.

Surface 2 is studied in [START_REF] Djebali | Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling[END_REF] and [START_REF] Djebali | Milling plan optimization with an emergent problem solving approach[END_REF]. In [START_REF] Djebali | Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling[END_REF], Clarke and Wright algorithm is used, among others, for partitioning, while in [START_REF] Djebali | Milling plan optimization with an emergent problem solving approach[END_REF], an adaptive multi-agent system approach is adopted. Both papers use the parallel-plane strategy for 3-axis machining. Only the best results provided by these two papers are included into the present comparison.

In [START_REF] Djebali | Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling[END_REF], a toroidal cutter with radii R = 5 mm, r = 2 mm is used, and the maximum scallop height is set to sh = 0.01 mm. The shortest toolpath length, provided by this study is 4,988 mm. Our methodology provide a better result: 4,018 mm using 200 blackbox evaluations per value of k (k = 2, 3, . . . , 10).

In [START_REF] Djebali | Milling plan optimization with an emergent problem solving approach[END_REF], a toroidal cutter with radii R = 3.175 mm, r = 1 mm is used, and sh = 0.254 mm. The shortest toolpath length obtained is 1183 mm, but this is not taking into account the connections between adjacent paths. Our approach yields again a better toolpath length: 995 mm. Surface 1 is studied in a more recent work [START_REF] Duc | Automatic minimal partitioning method guaranteeing machining efficiency of free-form surfaces using a toroidal tool[END_REF] where a partitioning approach based on the concept of efficient machining intervals is proposed. The surface is machined in 3 axes using a toroidal tool with the same radii as in Section 5. Two feed rates are considered: a low feed rate of 1 m/min (for hard materials and/or large tools), and a (a) without surrogate (b) Surrogate 3 A fuzzy C-means algorithm is used in [START_REF] Roman | Three-half and halfaxis patch-by-patch NC machining of sculptured surfaces[END_REF] with a 5parameter feature vector, (u, v, n), to partition, for 3+2axis machining, a test surface defined in the same paper. Our approach is tested with the same toroidal cutter of radii R = 6.7 mm,r = 0.7 mm, using the maximum scallop height: sh = 0.0254 mm, the nominal feed rate V = 2 m/min, and K = 4 zones. The authors of [START_REF] Roman | Three-half and halfaxis patch-by-patch NC machining of sculptured surfaces[END_REF] report a machining time of 634 seconds, while our approach still leads to a better machining time: 601 seconds.

The computational time for all the algorithms in studies presented hereabove (including ours) are of the same order of magnitude, and their cost is negligeable with regards to the cost of industrial machining processes (hourly rate for exploiting of a machine tool is far above hourly rate for the use of a computer). Furthermore, toolpath planification is done only once while real world parts may be produced a very large number of times.

Real-world part application

The tests and results presented in subsections 5.2 et 5.3 focused on surfaces extracted from the literature and that provides enough data for comparison purposes (see Section 6). However, the methodology we introduced obviously also applies to surfaces with more complex geometries. As an example of such an application, below is provided the result of our optimization workflow to an industrial surface: the blade of a propeller (shown on Figure 14). On such a surface, optimal partitioning and optimal machining directions are far from being obvious.

Figure 15 displays the four zones resulting from clustering, and relative scallop height distribution. The relative scallop height is defined as the ratio: effective scallop height maximum allowed scallop height .

Recall that since the scallop height constraint is integrated in our toolpath planning algorithm, it is necessarily satisfied, by construction. Thus, the relative scallop The optimization results (machining time) is better when the relative scallop height ratio is close to one, since an effective scallop height near to the maximum allowed scallop height implies faster machining process. Indeed, as it is common when optimizing in presence of a constraint that is strongly conflicting with the objective, the scallop height constraint is active (or almost active) over most of the surface.

Conclusion and perspectives

The blackbox optimization approach for machining freeform surfaces introduced in this article involves an objective function that is composed of two blackboxes: a clustering step producing a partition of the surface into zones, followed by a machining-time computation for each zone. The clustering step is driven by the number of zones, and by the weighting coefficients for the metric used for clustering. The machining-time computation step addresses, for each zone, the choice of the machining direction (and also orientation angles in the case of 3+2-axis machining).

In order to improve the performance of the optimization process, we proposed and evaluated the efficiency of four surrogate functions, one of which is analytical and thereby cheap to evaluate. Numerical experiments on several benchmark test surfaces from the literature show that our methodology outperforms other approaches. Figures comparisons show that our algorithms always provide a better result than other approaches. These gains can go up to 40% in terms of machining time. However, numerical comparisons should be taken with caution because the performances of algorithms are strongly dependant on the topology of the test surfaces. In any case, the main benefit of our methodology is to allow a broader exploration of the search space, in particular thanks to the use of surrogates that takes advantage of specific business knowledge.

Future tracks of research may consider integrating more categorical decision variables such as: the cutter type to be used, the machining strategy (other than the parallel planes), the clustering algorithm used in the partitioning step or even the metric upon which it is based to define the zones. Finally, the partial-separability of the optimization formulation introduced in this paper could probably be advantageously exploited.

A

Analytical calculation of machining time for Surrogate 3

For a given zone, the coordinates of the points belonging to the zone are gathered and their covariance matrix is calculated. Let x I and x II be the first and second principal directions resulting from the eigen-decompostion of this covariance matrix . Let λ I and λ II be the corresponding eigenvalues (λ I ⩾ λ II ). The rectangular plane that best fits the zone is generated by x I and x II : its width is along x I , and is denoted w = √ 12λ I , while its height is along x II , and is denoted h = √ 12λ II . This plane is called Π and its normal is n = x I × x II . The coordinates of n are denoted n x , n y and n z .

Let F be the unit vector defining the machining direction in the XY plane of the machine tool, and γ the angle between X and F. Let F p be the feedrate vector; it belongs to the plane Π, and F is the projection of F p in the XY plane. The angle between F p and x I is called α (see Figure 16). The objective is to compute the machining time of the rectangular plane Π as a function of the machining direction γ. First, we need to express α as function of γ. The coordinates of F and F p are:

F =   cos(γ) sin(γ) 0   and F p =   cos(γ) sin(γ) z   ,
where z is to be determined. We know that F p • n = 0, which yields: z = -n x cos(γ) + n y sin(γ) n z .

Therefore, the angle α is given by:

cos(α) = x I • F p ∥x I ∥ ∥F p ∥ .
Now the machining time can be computed as a function of α. Let p be the step-over distance between two adjacent paths; p is constant for planar surfaces, and two cases are considered according to the value of α. Concerning the machine kinematics, we assume that the nominal feedrate, V f , is achieved on each path, and not achieved for the connections between adjacent paths. The maximum acceleration, A max , is never achieved.

-1 st case: tan(α) ⩾ h w . In this case, the toolpath is composed of constant-length paths in the center area (in gray on Figure 17), and remaining paths near the sides. The length, l, of all paths in the central area is given by l = h sin(α)

The number, n 1 , of these paths is the integer part of n which is defined by: n δ = w -a, where δ, the projection of p on the x I axis, is given by and the machining time associated to this area is

t 1 = n 1 l V f + 2 V f J + 4 3 δ 2J ,
where J is the constant jerk of the machine tool.

For the side areas, paths with different lenghts have to be taken into consideration. The number of these paths, denoted n 2 , is the integer part of a δ = h cos(α) p . The length of the i th path is i p cos(α) sin(α)

. Taking into account the connections, the machining time associated to each side area is

t 2 = n2 i=1 i p cos(α) sin(α) V f + 2 V f J + 2 3 δ 2J + 2 3 p 2J cos(α) .
Finally, in this case, the total machining time is t = t 1 + 2 t 2 .

-2 nd case: tan(α) < h w .

In this case the constantlength paths are ending on the narrower side of the rectangle. Apart from this difference the computation can be carried out analogously.

The length l of the central area is

l = w cos(α)
.

The number of these paths, denoted n 1 , is the integer part of n defined by

n δ = h -b,
where δ, the projection of p on the x II axis, is defined by

δ = p cos(α)
and b, the size of remaining side areas, is expressed as b = w tan(α).

As a result, we obtain

n = cos(α) p (h -w tan(α)) ,
and the machining time associated to this area is

t 1 = n 2 l V + 2 V J + 4 3 δ 2J
For the side areas, the number of paths, denoted n 2 , is the integer part of b δ = w sin(α) p . The length of the i th path is i p cos(α) sin(α)

. Taking into account the connections, the machining time associated to each side area is

t 2 = n2 i=1 i p cos(α) sin(α) V f + 2 V f J + 2 3 δ 2J + 2 3 p 2J sin(α) .
Finally, in this case, the total machining time is

surface plane i plane i + 1 path i path i + 1 scallopFigure 1 :

 11 Figure 1: The parallel-plane strategy.

Figure 2 :

 2 Figure 2: Ball-end cutter vs toroidal cutter.

Figure 5 :

 5 Figure 5: The three angle variables used for 3+2-axis optimization for a zone k.

Figure 6 :

 6 Figure 6: Working flow chart of the two-step optimization model.

Figure 7 :

 7 Figure 7: Clustering of the two surfaces (zones numbers are displayed in white).

Figure 8 :

 8 Figure 8: Evolution of machining times of the four surrogates compared to the real blackbox function for the zones of Surface 1 .

  (a) zone 0 of Surface 2 (b) zone 1 of Surface 2 (c) zone 2 of Surface 2

Figure 9 :

 9 Figure 9: Evolution of machining times of the four surrogates compared to the real blackbox function for the zones of Surface 2.

Figure 10 :

 10 Figure 10: Optimization history for 3-axis machining of Surface 1.

Figure 11 :

 11 Figure 11: Optimization history for 3-axis machining of Surface 2.

Figure 13 :

 13 Figure 13: Optimization history for 3+2-axis machining of Surface 2.

Figure 14 :Figure 15 :

 1415 Figure 14: An industrial application: a propeller blade extrado

Figure 16 :

 16 Figure 16: Analytical calculation of machining time for Surrogate 3.

Figure 17 :

 17 Figure 17: Computation of machining time in the 1 st case.

  and a, the size of remaining side areas, is expressed as tan(

  Surface partitioning . . . . . . . . . . . . . . . 3 2.2 Toopath planning optimization . . . . . . . . . 3 2.3 Derivative-free and blackbox optimization . . . 3

	Introduction	1
	Background 2.1 Optimization formulation	3 4	1	Introduction
	Surrogates models and their numerical evalua-
	tion	6
	Tests and results 5.1 Test protocol . . . . . . . . . . . . . . . . . . . 7 7 5.2 Optimization results for 3-axis machining . . . 8 5.3 Optimization results for 3+2-axis machining . . 9

Table 1 :

 1 Average CPU time ratios between each surrogate and the blackbox f , for each zone k.

	Surface zone Surrogate 1 Surrogate 2 Surrogate 3 Surrogate 4
		0	26.2%	62.5%	5.4%	14.9%
	1	1 2	25.2% 23.9%	66.7% 82.0%	3.1% 3.0%	17.4% 18.8%
		3	18.1%	59.4%	1.6%	14.0%
		0	18.8%	84.0%	3.0%	8.0%
	2	1 2	19.8% 13.6%	106% 103%	1.3% 1.2%	11.3% 9.4%

Table 2 :

 2 Correlation coefficient between each surrogate and the blackbox f , for each zone k.

	Surface zone Surrogate 1 Surrogate 2 Surrogate 3 Surrogate 4
		0	0.962	0.979	0.854	0.966
	1	1 2	0.925 0.973	0.915 0.982	0.824 0.850	0.925 0.980
		3	0.920	0.932	0.650	0.915
		0	0.813	0.992	0.931	0.820
	2	1 2	0.990 0.810	0.999 0.981	0.936 0.931	0.991 0.815

fewer blackbox evaluations, this is especially true when the number of variables is high (i.e., for large values of K).

Table

Table 3 :

 3 Optimization results for 3-axis machining of Surface 1 (machining times in seconds).

		initial value F 0	F * , no surrogate	F * , Surrogate 3	F * , Surrogate 4	η, no surrogate	η, Surrogate 3	η, Surrogate 4
	2	96.19	92.01	92.01	92.01	4.34%	4.34%	4.34%
	3	104.77	93.92	92.92	92.52	10.35% 11.31% 11.69%
	4	147,68	98.5	95.92	95.06	33.3% 35.04% 35.63%
	5	101.90	96.41	96.23	100.32	5.38%	5.56%	1.55%
	6	100.1	95.96	98.41	97.3	4.13%	1.68%	2.79%
	7	103.78 102.02	100.06	102.13	1.69%	3.58%	1.58%
	8	102.4	95.48	91.93	92.87	6.75% 10.22%	9.3%
	9	153,5	102.7	95.29	95.88	33.09% 37.92% 37.53%
	10	143,9	97.25	97.91	97.21	32.41% 31.96% 32.44%
	K	initial value F 0	F * , no surrogate	F * , Surrogate 3	F * , Surrogate 4	η, no surrogate	η, Surrogate 3	η, Surrogate 4
	2	91.54	90.91	90.82	91.01	0.68%	0.78%	0.57%
	3	91.62	86.83	90.77	90.63	5.22%	0.92%	1.08%
	4	103.53	78.86	78.86	87.55	23.82% 23.82% 15.43%
	5	96.75	90.06	87.26	89.49	6.91%	9.8%	7.5%
	6	102.8	88.49	90.03	87.28	13.92% 12.42% 14.52%
	7	106.1	89.05	86.89	87.87	16.06% 18.11% 17.18%
	8	108.55	93.61	86.52	90.32	13.76% 20.3% 16.79%
	9	108.23	88.39	86.75	87.94	18.33% 19.85% 18.75%
	10 116.11	88.11	90.97	87.38	24.11% 21.65% 24.74%

Table 4 :

 4 Optimization results for 3-axis machining of Surface 2 (machining times in seconds).

Table 5 :

 5 Optimization results for 3+2-axis machining of Surface 1 (machining times in seconds).

	K	initial value F 0	F * , no surrogate	F * , Surrogate 3	η, no surrogate	η, Surrogate 3
	2	96.19	85.46	85.68	11.15% 10.92%
	3	104.77	97.24	83.59	7.18% 20.21%
	4	147,68 100.11	100.14 32.21% 32.19%
	5	101.90	98.42	96.2	3.41%	5.59%
	6	100.1	97.19	97.41	2.9%	2.69%
	7	103.78	96.00	97.8	7.49%	5.76%
	8	102.4	93.48	94.36	8.71%	7.85%
	9	153,5	108.54	91.93	29.28% 40.11%
	10	143,9	99.70	96.09	30.71% 33.22%
	K	initial value F 0	F * , no surrogate	F * , Surrogate 3	η, no surrogate	η, Surrogate 3
	2	91.54	75.67	74.96	17.33% 18.11%
	3	91.62	77.23	73.84	15.70% 19.4%
	4	103.53	79.94	71.95	22.78% 30.5%
	5	96.75	83.67	82.01	13.51% 15.23%
	6	102.8	86.46	85.43	15.89% 16.89%
	7	106.1	91.29	82.23	13.95% 22.5%
	8	108.55	93.65	84.03	13.72% 22.58%
	9	108.23	91.28	93.91	15.66% 13.23%
	10 116.11	98.76	92.04	14.94% 20.73%

Figure 12: Optimization history for 3+2-axis machining of Surface 1 .

Table 6 :

 6 Optimization results for 3+2-axis machining of Surface 2 (machining times in seconds).high feed rate equal to 10 m/min (for light alloys and/or small tools). The low feed rate leads to a machining time equal to 311 seconds, and the high feed rate leads to 81 seconds. Our results are again better: 291 seconds for the low feed rate, and 48 seconds for the high speed rate.

Table 7 :

 7 t = t 1 + 2 t 2Surface 1 is a 4 × 4 bicubic Bézier surface whose P i,j control points are given in Table7. Surface 2 is a 3 × 3 quadratic Bézier surface whose P i,j control points are given in Table8. Cartesian coordinates the control points for Surface 1.

	B	Control points of Surfaces 1
		and 2

Table 8 :

 8 Cartesian coordinates the control points for Surface 2.


Frédéric Gazeau

Samir Alliouane

C Stolpe

Thierry Blasco

France Van Wambeke

Emilio Maranon

M Pérez-Lorenzo

Cécile Guieu

Impact of dust enrichment on the metabolism of Mediterranean plankton communities under present and future conditions of pH and temperature

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Impact of dust enrichment on the metabolism of Mediterranean plankton communities under present and future conditions of pH and temperature

Overall objective

The PEACETIME project aimed at extensively studying and parameterizing the chain of processes occurring in the Mediterranean Sea after dust deposition and to put them in perspective of on-going environmental changes.

During a cruise on board of the R/V "Pourquoi Pas ?" in May/June 2017 (oligotrophic season), three experiments in climate reactors were conducted with surface water collected in the Tyrrhenian Sea (TYR), Ionian Sea (ION) and Alboran Sea (FAST). Six experimental units (300 L) were used to follow simultaneously and with a high temporal resolution, the evolution of biological activity (oxygen and carbon community metabolism, heterotrophic bacterial production, 13 C net community production) among other parameters and processes, after dust addition (10 g m -2 ) both under present environmental conditions and following a realistic climate change scenario.

This study highlights the importance of initial community composition and metabolic requirements on the response of surface plankton communities to nutrient enrichment (dust addition) and to ongoing environmental changes.

• In the Tyrrhenian Sea (TYR), no clear impact of dust addition both under present and future environmental conditions was observed on community metabolism while the heterotrophic prokaryotic compartment significantly responded to both drivers. • In the Ionian Sea (ION), the productivity of photosynthetic microorganisms and heterotrophic bacteria was significantly enhanced by dust addition with higher rates observed at lower pH and higher temperature. • Interestingly, in the Alboran Sea (FAST), although dust addition led to much higher activities for both autotrophic and heterotrophic compartments, future environmental conditions only positively impacted heterotrophic bacterial metabolism with no detectable effects on the activity of photosynthetic microorganisms.

  d'Océanographie de Villefranche (CNRS/SU, UMR7093), France. Email: f.gazeau@obs-vlfr.fr 2 Mediterranean Institute of Oceanography, France 3 University of Vigo, Spain Watch out for the joint Special Issue in Biogeosciences/Atmospheric Chemistry and Physics

•

  13 C-HCO 3 -enrichment (+ 300 ‰) directly in each tank • Separated incubations for 14 C incorporation and O 2 metabolism (24 h, light-dark) at the corresponding irradiance and temperature levels • Dark incubations at the corresponding temperature levels for heterotrophic bacterial production ( 3 H-leucine,

Acknowledgements

We would like to thank the crew of the R/V « Pourquoi pas? », J.M. Grisoni, G. De Liège, F. Louis , D. Delhommeau and E. Tanguy for the development of the minicosms and D. Lefèvre for the seawater pumping system.


Carole Adam

Cédric Lauradoux

A serious game for debating about the use of Artificial Intelligence during the COVID-19 pandemic

Keywords: Serious game, Artificial Intelligence, COVID-19, education

Crises always impose a difficult compromise between safety and liberty, and the COVID-19 pandemic is no different. Governments have enforced various sanitary restrictions to reduce virus spread. With the help of Artificial Intelligence (AI), the scale of surveillance has risen to unprecedented levels. However, these technologies entail many risks, from potential errors or biases, to their extended enforcement beyond the duration of the initial crisis. Citizens should be aware that these technologies are not infallible, and measure the consequences of errors, so as to make informed decisions about what they want to accept, and for how long. To this aim, we have designed a serious game in the form of a municipal debate between citizens of a virtual town. Some first test sessions helped us improve the game design, and provided proof of the interest of this game to trigger debates and raise awareness.

INTRODUCTION

Crisis situations are often associated with restrictions of liberties and invasion of privacy, in the name of public safety. Many governments order mandatory evacuation or travel ban during floods, communication surveillance and control following terrorist attacks, or declare a "state of emergency" to provide their police forces with more powers to respond to the emergency situation. More recently during the COVID-19 pandemic, governments around the world have used the "state of health emergency" to justify lock-downs, curfews, contact tracing, sanitary passport, or mandatory vaccination. Surveillance has always existed, but new technologies enabled by Artificial Intelligence (AI), such as facial recognition or social networks, have changed its scale. We are now facing mass surveillance of billions of individuals. Besides, governments may be tempted to re-use technologies, initially adopted as emergency counter-measures against the pandemic, to serve other purposes1, or to extend the duration of new rules beyond the end of the original crisis. The drifts can have serious consequences, with China setting up a social credit system [START_REF] Liu | Multiple social credit systems in China[END_REF], or some countries imposing the need for a COVID-19 vaccinal pass despite the inequalities it creates [START_REF] Tanner | Vaccine Passports Done Equitably[END_REF][START_REF] Gostin | Digital Health Passes in the Age of COVID-19: Are "Vaccine Passports" Lawful and Ethical?[END_REF][START_REF] Kofler | Ten reasons why immunity passports are a bad idea[END_REF]. This pass has been required to enter most countries, to access leisure places, to travel, to work (e.g. healthcare workers in France, or any workplace in Italy), or even in some countries to use some more essential services 2.

AI technologies can offer many benefits, but we believe that it is essential for citizens to also understand their impact on surveillance, their potential biases and errors, in order to be able to make informed choices about what they accept and what they refuse. To this end, we have designed a serious game, where participants take on the roles of citizens with various profiles in a (not so) futuristic town, and debate about the new technologies that could be adopted in their town. This game is part of a wider series of debate games about different societal applications (health, transport) of AI technologies. This debate game is targeted at students in secondary school and high school, and is followed by a debriefing allowing participants to share experience and to learn about the real life implications of what they discussed in a simplified manner. This paper is structured as follows: we start by discussing the need for educating the general public about AI, and how serious games can help. One section is dedicated to the debate game, scenario, roles taken by the participants, and different AI solutions being discussed. Another section is dedicated to the debriefing session after the game, which is key to learning. Finally, one section discusses some first return of experience with groups of different ages. Finally, we conclude and discuss future prospects.

REQUIREMENT FOR EDUCATION

Education to AI

Educating the population is crucial at any time and even more during COVID-19, where the lack of information, or disinformation spreading on social networks, can have serious consequences. Indeed, conspiracy theories and other fake news spread fast, and can increase vaccine hesitancy or rejection [START_REF] Nieves-Cuervo | Infodemic: fake news and COVID-19 mortality trends in six Latin American countries[END_REF][START_REF] Lu | COVID-19 vaccine hesitancy: The effects of combining direct and indirect online opinion cues on psychological reactance to health campaigns[END_REF], with detrimental consequences on health. Besides, even though Artificial Intelligence can help fight COVID-19, there are also dangers to be avoided: [START_REF] Naudé | Artificial intelligence vs COVID-19: limitations, constraints and pitfalls[END_REF]) warns about the requirement for "a careful balance between data privacy and public health". Everybody needs to be aware of the potential benefits and dangers of Artificial Intelligence, whether in the context of the pandemic or in general. This requirement for educating people about AI is particularly highlighted in the latest UNESCO report (UNESCO 2021). This education should not concern only the underlying technologies, but also the value and usage of personal data, and the ethical implications of AI technologies.

"because living in digitalizing societies requires new educational practices, ethical reflection, critical thinking, responsible design practices and new skills, given the implications for the labour market, employability and civic participation" [p.18]. "Public awareness and understanding of AI technologies and the value of data should be promoted through open and accessible education, civic engagement, digital skills and AI ethics training [...] so that all members of society can take informed decisions about their use of AI systems and be protected from undue influence" [p.24]. "Member States should promote general awareness programmes about AI developments, including on data and the opportunities and challenges brought about by AI technologies, the impact of AI systems on human rights and their implications, [...] accessible to non-technical as well as technical groups. Member States should develop [...] AI ethics curricula for all levels, and promote cross-collaboration between AI technical skills education and humanistic, ethical and social aspects of AI education." [p.33]

Serious games

With the goal of involving the population as a whole in learning about AI and its use during the COVID-19 crisis, we believe that serious games [START_REF] Crookall | Serious games, debriefing, and simulation/gaming as a discipline[END_REF]) can be a powerful tool. Serious games have been successfully used in various fields: educating the population about appropriate behaviours in case of natural disasters, e.g. floods [START_REF] Rebolledo-Mendez | Societal impact of a serious game on raising public awareness: the case of FloodSim[END_REF][START_REF] Taillandier | Games ready to use: A serious game for teaching natural risk management[END_REF]; raising awareness about climate change and possible actions [START_REF] Wu | Climate change games as tools for education and engagement[END_REF]; training medical and surgical skills [START_REF] Graafland | Systematic review of serious games for medical education and surgical skills training[END_REF] or communicative skills of future doctors [START_REF] Jackson | Teaching communication skills using role-play: an experience-based guide for educators[END_REF]; or more recently explaining the pandemic and sanitary measures to improve their acceptability [START_REF] Cottineau | Understanding the current COVID-19 epidemic: one question, one model[END_REF].

Serious games do not need to be computerised, and we use this term to refer to any learning game, that uses playful elements to reach a pedagogical goal. There exists various forms of serious games, from computer simulations [START_REF] Taillandier | Games ready to use: A serious game for teaching natural risk management[END_REF], to board games or card games [START_REF] Wu | Climate change games as tools for education and engagement[END_REF], interactive narratives, role-playing games [START_REF] Jackson | Teaching communication skills using role-play: an experience-based guide for educators[END_REF], or debates [START_REF] Simonneaux | Role-play or debate to promote students' argumentation and justification on an issue in animal transgenesis[END_REF]. Given our stated goal of involving the general population, we designed a tabletop game that can be played by anybody regardless of their education, without a computer. Besides, our goal is to develop argumentation skills in future citizens, to enable them to make informed choices. We therefore propose a serious game in the form of a role-playing debate; the design of our game is explained in the following section.

OUR SERIOUS GAME: AI AGAINST EPIDEMIC IN WAFER CITY

Game design process

Our game is part of a larger series of debate games about AI in various fields, developed by Arbre des Connaissances (ADC)3, a scientific mediation association dedicated to opening science towards citizens. These games all take place in the same virtual (more or less futuristic) town, called Wafer city, an average size city with one million citizens. Half of the population is living in the town centre, the other half resides in suburban or rural areas. In each game of the series, a different issue is raised to the municipal council, played by the game participants. The first two episodes of the series were dedicated to AI in transport (Oct. 2018) and AI in health (Feb. 2019). The episode described here was developed by the two authors with the help of two members from the ADC, over about 1 year starting in February 2021, through to first experiments in October 2021, and until the official release in March 2022.

Game context

In our game, Wafer city is threatened by an epidemic. Each citizen of the city has a digital medical record (containing analysis results, current treatments...) managed by the city and available to its policy makers, who must take the best possible measures in order to limit the epidemics spread while addressing the following societal issues:

• Lockdown rules are considered too strict and prejudicial to mental health. It is critical to find measures that are not too restrictive for the population but still effective against the epidemic.

• The violation of rules by a few citizens could jeopardise the epidemic control strategy, thus threatening the entire population. It is therefore essential to effectively enforce sanitary restrictions, without overworking police officers by adding up to their usual missions. Besides, constraining rules might not always be well accepted and effort will be needed to prevent the deterioration of relationships between police and citizens.

• Asymptomatic people could unknowingly spread the epidemic, making it insufficient to test and quarantine only symptomatic people. However, it will be difficult to impose restrictions on healthy people who do not feel concerned. Sanitary restrictions should be adapted to the citizens' health status.

The context description purposely never mentions the name of the virus responsible for the epidemic in Wafer city, and avoids any allusion to COVID-19. Indeed, the game aims at discussing surveillance enabled by AI in a broader context, and should stay topical even after the end of the current pandemic. Besides, we also wanted to take some distance from a very sensitive context, as the COVID-19 epidemic is not over yet.

Sowana

The Sowana company is specialised in Artificial Intelligence and has previously worked with the town on other topics, such as public transportation or health. Sowana has answered the call for proposals of Wafer city regarding the epidemic with three solutions: Eye'Wana, Wana'Like and Wana'Pass, detailed below.

Eye'Wana

Eye'Wana is based on video-surveillance to ensure that sanitary rules are respected equally by all citizens at all times. It promises to unload police forces while avoiding human biases: everybody has the same risks of being controlled and fined when not respecting the r ules. This solution is based on three building b locks: (i) a network of CCTVs and a fleet of drones collect videos and images from public places, (ii) computer vision algorithms extract faces from these pictures, and (iii) facial recognition algorithms identify the individuals from their face. Eye'Wana can detect various violations of sanitary rules (failure to wear a mask or to respect physical distancing; violation of curfew or lockdown; etc), identify the author, and notify them of the subsequent fine they have to pay.

This solution therefore answers the need for equality in front of the law, but at the cost of great intrusion into people's privacy, since it is tracking their every move.

Wana'Like

Wana'Like is a free smartphone application to help citizens avoid crowded areas where the risk of contamination is higher. Sowana maintains a list of recommended places, checks if they respect the sanitary protocol, and can ban them if contaminations on their grounds are reported. The application analyses the user's interests from their online activity (social media posts, requests on the Sowana search engine...) to create a user profile. It also uses real-time localisation data to deduce current attendance. By combining this data, Wana'Like can make personalised but safe leisure suggestions, and offers discounts in partner places to further incentivise users to follow the recommendations.

This solution is much less restrictive, but potentially also less efficient. Besides, there are great risks related to commercial use of personal data, loss of privacy, or opinion manipulation. Finally, the question of accessibility to people who do not own a smartphone is also important.

Wana'Pass

Wana'Pass is a health points passport: it analyses the user's health record and data from their sensors (heart rate, temperature...) on a daily basis, to deduce the user's individual health status and risk. It then provides them with a number of points, with users in better health being granted more points, and infected individuals receiving zero. These points will be required to access public places (shops, restaurants, museums, etc), with the riskier places WiP Paper -Reimagining ethical, legal, and social issues in a COVID era Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022 requiring more access points. Each place will need to check and debit the necessary access points; once out of points (or as long as they are infectious), the user cannot enter these places anymore.

This solution aims to answer the problem of equitable rather than equal treatment: it protects people at risk and isolates contagious individuals, while letting healthy people live more normally in order to protect their mental health. However, it poses the question of discriminating and isolating elderly people even more on the pretext of protecting them.

Roles represented in the municipal council

As shown above, the different solutions all have pros and cons, and will be more or less acceptable to different user groups. In our debate game, participants do not play in their own name, but will assume a role as member of a specific group of citizens. The idea of having users play a role other than themselves is not new and is proven to favour perspective-taking [START_REF] Jarvis | Role-playing as a teaching strategy[END_REF][START_REF] Resnick | Diving into complexity: Developing probabilistic decentralized thinking through role-playing activities[END_REF]. We also wanted participants to take distance from their character to keep the debate more peaceful, all the more on a very sensitive topic while the COVID-19 epidemic is still not over. The participants in our game are randomly distributed in 5 small groups of citizens:

• City centre shopkeepers, focus on freedom of action and mobility, make a good living but have little free time;

• Ecologists and alter-globalists, rather young, focused on well-being of all and protection of nature, they favour walking and cycling to commute, and they ask for guarantees before adopting new technologies;

• Elderly people, over 60 years old, retired, focused on keeping their autonomy, can live in or out of town;

• Technology enthusiastic, mainly youngsters, very connected and active online, loving innovation, but with limited income;

• Remote citizens, living outside of town centre, in suburban and rural areas, either to search a better quality of life or lower property prices.

The members of each group will debate together to allocate a total of 5 points to the 3 solutions, keeping in mind the wishes of the role that they represent. Each group will therefore come up with different scores for each solution, which will be put in common and added up in the voting and debriefing phase.

GAME DEBRIEFING

Debriefing is an important part of a serious game and is essential to learning [START_REF] Crookall | Serious games, debriefing, and simulation/gaming as a discipline[END_REF][START_REF] Whalen | All they do is win': Lessons learned from use of a serious game for Circular Economy education[END_REF][START_REF] Dieleman | Games by which to learn and teach about sustainable development: exploring the relevance of games and experiential learning for sustainability[END_REF]. It pursues multiple goals: clarifying concepts manipulated during the game session to improve learning; link the simplified concepts with real-life complexity to ensure that learners can apply their knowledge; and share experiences and reflection between participants. It should be led by an informed moderator with a clear and predefined pedagogical objective in mind. The following paragraphs discuss the debriefing phases of our debate game.

Sharing and debating scores

At the end of the game, each group provides the scores they gave to each solution. The moderator reports the scores of all groups in a table drawn on the blackboard, along with their main arguments for their favourite solutions (see an example on the photo in Figure 3). The solution with the highest total score "wins" this first round of voting. The moderator then triggers a debate between supporters and opponents of the different solutions. For instance, members of one role group that supported a given solution, are asked to try and convince members of another role group that rejected that same solution, and vice versa. If they succeed, the scores on the board can be subsequently updated and the selected solution might even change as a result of this debate (see examples of such scenarios in the return of experience section below).

As recommended by [START_REF] Dieleman | Games by which to learn and teach about sustainable development: exploring the relevance of games and experiential learning for sustainability[END_REF], the debate is supervised by a moderator, who ensures a fair, peaceful and balanced debate between students. Playing a role that does not necessarily match their own opinions also helps students to take some distance with the argument and to speak more freely.

Evaluation scales

To further discuss and compare the different technological solutions offered by AI, the moderator then asks some specific questions in order to guide students to rate solutions on different scales. Some important scales to consider when evaluating AI solutions (inspired by (Castelluccia and Métayer 2020)) include:

• Their efficiency (here against the epidemic): the risk-benefit balance is one key indicator, used by privacy protection agencies to allow use of a technology, and by health institutions before allowing use of a drug;

• Their impact on individuals liberties: how constraining or restrictive are they? How much freedom is sacrificed? Is it worth it? Does it have negative side effects, e.g. on mental health?

WiP Paper -Reimagining ethical, legal, and social issues in a COVID era Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

• Their impact on privacy: what sort of personal data do they collect, and how sensitive is it? Who gets access to this data? What happens in case of a data leak?

• Their economical and ecological cost: how much will it cost and who will pay for deploying these technologies? What pollution is generated to create, maintain, use and recycle these technologies?

• Their accessibility to all, and the risks of discrimination. Do they ensure strict equality? (i.e. everybody is treated exactly the same) Are they equitable for everybody? (i.e. rules are adapted to everybody)

• Risks of errors and misuses: what risks that these technologies fail? What impact in case of errors? What risk of misuse? Can they be twisted to serve other purposes than their initial goal? With what consequences?

Contextualisation

To link back to reality, the moderators finally illustrate how the different virtual solutions discussed during the game actually relate to very real solutions that are already implemented in some countries.

• Technologies similar to Eye'Wana were used in China [START_REF] Chun | In a time of coronavirus, China's investment in AI is paying off in a big way[END_REF], where a large CCTV cameras network with drones and thermal cameras, complemented with facial recognition, was deployed to implement social control during the COVID-19 pandemic. But drones have also been experimented in France to monitor the beaches of Nice during the lockdown4.

• Wana'Like shares many similarities with social networks, that use recommendation algorithms to make personalised suggestions to the user. These already raise many problems of conflict of interest since they aim to maximise the time spent online by the user, even at the expense of their (mental) health [START_REF] Wells | Facebook knows Instagram is toxic for teen girls, company documents show[END_REF]).

• Wana'pass can be viewed as the result of the progress of medical AI (Petropoulos 2020) combined with China's Social credit system [START_REF] Shen | Social credit system in China[END_REF][START_REF] Liu | Multiple social credit systems in China[END_REF]. It can also be considered as an evolution of the health or vaccinal passport already deployed in many countries, raising discrimination problems due to unequal access to vaccines [START_REF] Tanner | Vaccine Passports Done Equitably[END_REF][START_REF] Gostin | Digital Health Passes in the Age of COVID-19: Are "Vaccine Passports" Lawful and Ethical?[END_REF][START_REF] Kofler | Ten reasons why immunity passports are a bad idea[END_REF].

These examples illustrate very concretely the potential dangers of a drift from useful to forceful use of AI, and help the students take out the intended message that they are all concerned by AI and its use.

RETURN OF EXPERIENCE

This game was first played with 6 groups from 3 high school classes during a national science fair (for a total of 103 students), as a first real-life test. It was later tested with around 80 students from an engineering school.

Game material

The game material5 comprises the following elements:

• Cards describing the roles, one different card to be distributed to each group;

• A sheet explaining the agenda of the municipal council, with the problems at hand;

• One sheet per solution, that provides the marketing argument by Sowana, some technical details about the AI beneath, and a testimony by a citizen that is designed to raise some first interrogations.

• A moderator guide aimed at the teachers who will supervise the game. This guide contains some more technical background, useful definitions, links to additional documentation, questions to feed the debate, and information about some similar but real-life solutions to present during the debriefing.

These elements are provided during the sessions we organise, but they can also be printed by any teacher willing to play the game with their students.

4https://news.trust.org/item/20200320105803-ztaq0 5The game material and booklet are freely available at https://jeudebat.com/jeux/lintelligence-artificielle/

Game setup

During the science fair, each session was played with a group of around 15-17 students, distributed in the 5 role groups, plus one of their professors present either as an observer or as a participant. The engineer school session was played with all 80 students together, distributed in 10 groups (2 per role). Each session lasted for 1.5 hours and was supervised by 2 moderators who facilitated discussions while staying neutral, i.e. without orienting them or making suggestions.

The pedagogical sequence is as follows:

1. The session starts with the moderators providing a brief introduction about AI, some definitions, and presenting the context of the game and the 5 roles represented in the municipal council.

2. The students debate the pros and cons of each solution in turn, within their role group.

3. Each group allocates a total of 5 points to the 3 solutions.

4. Each role group orally provides its scores and arguments that are reported on the board.

5. The winning solution is announced, and the results are discussed and debated, which might change the results.

6. The moderators provide some context about which similar solutions already exist in real life.

7. The high school teacher takes home some documentation and references to deepen the subject with their students in class later.

Example debate

With one group, we had a very interesting debate leading to multiple changes of the selected solution. After the first round (as shown in Table 2) Wana'Pass was shortly winning with 10 points, followed by Eye'Wana with 8 points, and Wana'Like with 7 points. We then guided a debate between students favouring the different solutions, and that Wana'Pass was inequitable, and convinced shopkeepers to move 1 point from Wana'Pass to Eye'Wana, and Techno-addicts to move 1 point from Wana'Pass to Wana'Like. After that second round, EyeWana was shortly ahead with 9 points, the other solutions scoring 8 points each.

Eye'Wana

Remote people were then asked to provide their arguments against Wana'Like, to which they had given 0 point. They argued that this application could manipulate its users. As a result, elderly people and central shopkeepers removed 1 point to Wana'Like and moved it to Eye'Wana, while ecologists moved 1 point from Wana'Like to Wana'Pass. Wana'Like now scored only 5 points, Wana'Pass 9 points, and Eye'Wana moved ahead with 11 points.

Finally, techno-addicts fiercely opposed to Eye'Wana (for its infringement of liberties, and because their lower income meant more sensitivity to fines) realised they could change the result: they moved 4 points from their favourite but losing solution (Wana'Like) towards their second option Wana'Pass, to prevent Eye'Wana from winning. Interestingly, it is a rare complete loss for Wana'Like (1 point), and the only win for Wana'Pass.

Quantitative results

We consider here only the sessions played during the October 2021 science fair with 6 high school groups (103 students), who are more representative of the target public for our debate game. The results (see Table 4) are:

• Wana'Like was selected three times, mostly because it provides financial advantages and is less constraining than the other solutions.

• In another session, Eye'Wana and Wana'Like received the same number of votes. Wana'Pass was rejected for discriminating the elderly.

• Eye'Wana was selected once because it was considered easier to deploy (no need for a smartphone) and because it enforces equality. In all other sessions, it was judged too intrusive and rejected fiercely.

• Wana'Pass won only once, after the interesting debate summarised above.

Wana'Like Wana'Pass Eye'Wana #Selections 4 1 2

Qualitative feedback

We got a general positive feedback from all the students and their professors. In this section, we discuss some specific comments made by the players after the different se ssions. This highlights the importance of the debriefing phase that allows such exchanges with participants, where they take some distance from the events debated in-game.

Link with COVID: despite our efforts to create a "virtual" town and epidemic, most students immediately referred to "COVID" in their discussions. One student mentioned they were against the COVID vaccine, which proved the importance of maintaining some distance from the current context in order to ensure a peaceful and targeted debate. However, this occurred only during debriefing, and did not influence debates since they had to stick to their roles. Besides, we believe this link will attenuate with time as the epidemics fades, while our game will stay topical.

Assumption of infallibility: students generally assumed that the proposed technologies were infallible, and as a result did not consider the harmful impacts of an error. This confirms the need to teach the basics of AI as well as its potential for biases and errors. Knowing how the algorithms work is required to understand how they could also fail.

Safety vs freedom: students focused much more on protecting their freedom than on efficiently fighting the virus. Even though the debates did mention the efficiency of the offered solutions, it came after arguments of loss of privacy or freedom of movement, and actually after any other argument. This might not be surprising in an age group that often does not feel directly concerned by the health risk. It also shows a lack of focus on efficiency in our game instructions. We have since then improved that point by asking participants explicitly to compare the solutions on the different scales listed above, including their e fficiency. This involves discussing whether they prefer to accept a very constraining (and efficient) solution for a short time, or a less constraining (but less efficient) solution that will probably need to be maintained for a longer period of time.

WiP Paper -Reimagining ethical, legal, and social issues in a COVID era Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

Soft and hard surveillance: while protecting their freedom and privacy, most students were either unaware of, or fatalist, regarding the surveillance already exerted on them by social networks algorithms. Most students considered that the most intrusive applications were Wana'Pass due to the use of medical data, or Eye'Wana because it films people permanently. They completely underestimate the risks associated with recommendation algorithms, since they already happily disclose large amounts of personal information on social networks. This shows that AI education should also insist on the value of personal data and what can be done with it.

Age target: having played the game with high school students (aged 15 to 18 years old) and engineering students (aged 22 to 24 years old), we got quite different feedback. Comments from participants tend to suggest that the game is better targeted at high school students, who have less technical background about Artificial Intelligence and feel happy to get an opportunity to discuss the current pandemic and its impact on their lives. On the contrary, engineering students felt more disappointed at the focus on ethical implications of AI when they expected to get more technical knowledge. Surprisingly, some also reported as a negative point that the solutions seemed too unrealistic because "none was good". Incidentally, this is precisely the intended take-home message: no AI technology is a perfect solution, and everybody should be aware of the pitfalls before accepting them.

CONCLUSION

In this paper, we presented a serious game in the form of a municipal debate between players distributed in 5 role groups, in order to choose AI solutions to fight an epidemic. Changing perspective and arguing to defend one's ideas is a good exercise for students, and they seem to have learned about Artificial Intelligence and its dangers in the process. This game therefore reaches its objective of educating the population, and the debriefing phase showed crucial in that process.

In the meantime, debriefing the debates with the participants also provided us with interesting insights about how the population thinks of Artificial Intelligence, its benefits and infallibility. This comforted our idea that we need to educate the next generation about these technologies. While AI can certainly help in fighting a crisis such as the COVID-19 pandemic, it is not infallible, and as it is becoming more and more pervasive in our lives, the potential impact of errors is also becoming more serious. It is therefore necessary that everybody knows the basics behind AI algorithms UNESCO 2021 and can make informed choices about their use.

  3Arbre des Connaissances website: https://arbre-des-connaissances-apsr.org/ WiP Paper -Reimagining ethical, legal, and social issues in a COVID era Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

Figure 1 .

 1 Figure 1. Extract of game card distributed to the players to describe Wana'Like -illustration © Marie Jamon

Figure 2 .

 2 Figure 2. Extract of game cards describing two of the roles. Illustration © Marie Jamon

Figure 3. Game board

	Solution	S1 Eye'Wana	S2 Wana'Like	S3 Wana'Pass
	Alter-glob	0	3 (+) discounts	2 (-) unfair
			(+) normal life
		(-) privacy	(+) control over data (-) mental health
	Shops	4 (+) stay open	0 (-) lose clients	1 (-) lose clients
	Remote	1	3 (-) privacy	1
			(+) discounts	(-) unfair
	Techno	2 (+) fair, jobs	2 (+) freedom	1
			(+) discounts
	Elderly	3 (+) health	2 (-) no smartphone	0 (-) autonomy
		(+) live on		(-) privacy
	TOTAL	10	10	5

Table 1 . Transcription of the game board

 1

Table 2 . Example of blackboard after one round of discussion in one game session: scores (S), positive (blue) and negative (red) arguments.

 2

	Wana'like	Wana'Pass

  Table 3 illustrates the evolution of total scores over the four subsequent rounds of debate.

	Round Eye'Wana Wana'like Wana'Pass
	1	8	7	10
	2	9	8	8
	3	11	5	9
	4	11	1	13

Table 3 . Evolution of the results of the game after four rounds.

 3 Since the elderly people group was completely opposed to Wana'Pass (that would most probably grant them very few points to go out), they were asked to try and convince other groups to not choose this solution. They argued

WiP Paper -Reimagining ethical, legal, and social issues in a COVID era Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

Table 4 . Number of wins per solution over 6 sessions (the total is 7 since there was a draw in one session)

 4

1For instance, Singapore police forces can now exploit the data of the contact-tracing application originally designed to fight the pandemic: https://www.cnbc.com/2021/01/05/singapore-covid-19-contact-tracing-data-accessible-to-police.html 2https://www.capital.fr/economie-politique/pakistan-menace-de-carte-sim-bloquee-pour-ceux-refusant-la-vaccination-1406536

WiP Paper -Reimagining ethical, legal, and social issues in a COVID era Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

Proceedings of the 19th ISCRAM Conference -Tarbes, France 2022

ACKNOWLEDGEMENTS

The authors would like to thank the Arbre des Connaissances association, in particular Clara Fruchon and Camille Volovich, for their support along the entire game design process and with its distribution6; as well as Marie Jamon for illustrating the game material and booklet. The authors would also like to thank the scientific mediation team of Inria Rhône-Alpes, in particular Florence Polge-Cohen, for financial support and their help with organising the play sessions at Fête de la Science. Finally, we thank all students and teachers who participated in the game sessions.


Lucas Lachérade

Antoine Marache

Alain Denis

Isabelle Halfon

Luc Closset

Jérémy Rohmer

Florence Quesnel

Geostatisical modelling of geotechnical properties in the context of a tunneling project : application to the Grand Paris Express project (France) Topic of interest : Geological, Geotechnical Site Investigation and Ground Characterization

Keywords: Geostatistics, 3D modelling, Tunnels, Uncertainty, Geotechnics, Geology

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Abstract WTC 2023 : Athens

Title : Geostatisical modelling of geotechnical properties in the context of a tunneling project : application to the Grand Paris Express project (France) Topic of interest : Geological, Geotechnical Site Investigation and Ground Characterization Lucas Lachérade *1,2 , Antoine Marache 1 , Alain Denis In recent years, geostatistical methods have proven to be very useful for the spatial analysis of subsurface properties, in particular through the production of 2D or 3D geological and/or geotechnical models. Despite the existence of examples of geostatistical modelling applications in the context of tunneling projects, their use is still underdeveloped in this field.

The study presented in this paper aims to show that large linear projects such as tunnels constitute an ideal framework for the construction of efficient geostatistical models and that there is a real interest for decision-makers to increase their use. This is shown through the application of 3D geological-geotechnical modelling to certain sections of the Grand Paris Express (France).

From the panel of geotechnical data collected, the pressuremeter tests were chosen to build the model in terms of pressuremeter modulus and limit pressure. Their regular and dense distribution along the project (on average one pressuremeter test every hundred linear metres) allows for a correct appreciation of the spatial variability of the geotechnical behaviour of the geological units present on the tunnel alignment.

After introducing the methodological process used to design the 3D model, a comparative study between deterministic geostatistical methods and sequential simulation algorithms is conducted on one of the geological unit of interest. The performance and relevance of both methods are evaluated through statistical analysis of their respective results and quantification of uncertainties.

This comparison exhibits the benefits of simulation technics over deterministic technics in this context. On the one hand, they better represent the variability of geotechnical characteristics, specially for extreme values. On the other hand, they provide a better evaluation and localisation of uncertainties and can therefore constitute a tool for optimisation and risk management during the construction phase.


Chloé Cerutti

Sophie Leroux

Paul Terzian

Joanna Lledo

David Gourichon

Rémy-Félix Serre

Céline Vandecasteele

Christophe Klopp

Carole Iampietro

Christine Gaspin

Transgenerational epigenetics in quail

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

Transgenerational epigenetics in quail : whole genome DNA methylation analysis

Chloé Cerutti 1 , Sophie Leroux 1 , Paul Terzian 2 , Joanna Lledo 3 , David Gourichon 4 , Rémy-Félix Serre 3 , Céline Vandecasteele 3 , Christophe Klopp 2 , Carole Iampietro 3 , Christine Gaspin 2 , Denis Milan 1 , Cécile Donnadieu 3 , Frédérique Pitel 1 and Guillaume Devailly

Abstract

Prenatal environment influence on adult phenotype is partially mediated by epigenetics phenomena. One study highlighted significant effects of the in-ovo injection of endocrine disruptors or DNA methyltransferase inhibitor on quail development, significantly reducing their weight [START_REF] Cerutti | Short communication: Effects of in-ovo injection of endocrine disruptors and methylstransferase unhibitor on quail growth and egg-laying performances[END_REF]. Recently, an increasing number of studies highlighted the transmission of epigenetics marks between generations following an environmental exposure. However, there is much debate about their transmission beyond the exposed individuals. Recent studies revealed that non-genetics inheritance was probably present in avian species. In one of them [START_REF] Leroux | Embryonic environment and transgenerational effects in quail[END_REF], fertilized eggs were divided into two groups: one group injected with an endocrine disruptor, Genistein, and a non-injected control group. After three generations without any other injection, several traits were impacted by the ancestor treatment including reproduction and behavior. This pilot study highlighted the potential existence of transgenerational transmission of environmental effects in quails. To better understand the transgenerational transmission of these environmental effects, we generated DNA methylation data from blood samples of the third generation using WGBS (Whole Genome Bisulfite Sequencing) and ONT (Oxford Nanopore Technologies). To analyse the DNA methylation states, we developed a bioinformatics pipeline in order to detect differentially methylated cytosines (DMCs) due to transgenerational phenomena. We detected thousands of DMCs between both groups (Table 1). In addition to these analyses, these data allowed us to perform a comparative analysis between the WGBS and ONT sequencing technologies (Fig. 1). Heatmap of methylation rate of 10,000 common epilines DMCs detected from WGBS and ONT. The red and blue colors refer to the epi-and epi+ groups, respectively. The violet and green colors refer to the female (F) and male (M) quails, respectively. The diverging color gradient refers to a low (blue) or a high (red) methylation rate.

Figure 1 .

 1 Figure 1.

Table 1 .

 1 Number of measured CpGs sites and epiline DMCs detected from WGBS and ONT methylation data. A CpG site refers to a dinucleotide CG.

		measured CpGs sites epiline DMCs detected
	WGBS	5 881 815	12 872
	ONT	7 537 007	22 325

Acknowledgements

This work was supported by FEDER (European Funding for Regional Economic Development), the PhD scholarship to CC from Région Occitanie and INRAE Animal Genetics Division. We are grateful to the genotoul bioinformatics platform Toulouse Occitanie (Bioinfo Genotoul, https://doi.org/10.15454/1.5572369328961167E12) for providing computing and storage resources.