IMPROVED DETERMINATION OF FUEL ASSEMBLY COMPONENT POSITIONS

Abstract

The invention relates to a method for determining the positions of elements of fuel assemblies arranged in a tank, each fuel assembly comprising at least one element, at least one geometric constraint of the fuel assembly or of the tank being predefined, the method comprising the following steps: - obtaining a first set of positions estimated beforehand of the elements; - determining a criterion representative of the distances between the positions of the first set and the parameters to be optimized, the parameters identifying possible positions of the elements, the possible positions respecting the predefined geometric constraint; - determining a second set of estimated positions optimized from the parameters for which the criterion is minimized in the sense of a predetermined standard.

Description

Improved determination of the positions of fuel assembly elements The present invention relates to a determination of the positions of objects, such as fuel assemblies of a vessel of a nuclear reactor, with an optimized position estimation method. It relates in particular, but not exclusively, to safety applications for the fuel assemblies of a nuclear reactor. In a nuclear reactor vessel of an electricity production plant, fuel assemblies forming a fuel core are periodically inspected and renewed. To this end, it is necessary to unload and reload the fuel core with new fuel assemblies. Once the new fuel assemblies have been loaded, it is necessary to check that they are correctly positioned before folding down a cover of the vessel, the cover comprising Upper Internal Elements (EIS). The EIS comprise studs which protrude and are intended to be introduced into corresponding housings of the fuel assemblies, called "S-holes". A set of nominal positions is ideally defined for the fuel assemblies. However, it may happen that a fuel assembly is offset from its nominal position beyond a certain recentering capacity, which generates a risk of the assembly snagging when refitting the EIS. Indeed, such an offset can cause the EIS pawns to force their way into the holes S of the fuel assemblies. Although this is not a problem for the operation of the nuclear reactor, the fuel assemblies can remain attached to the EIS during the next opening of the vessel, which leads to long and costly maneuvers to unjam them and which generates a potential risk. for the safety of the installation. What is more, the fuel assemblies are immersed in water, which makes the activities of securing and unjamming the assemblies even more difficult. It is therefore necessary to precisely determine a position for each hole S of the fuel assemblies before refitting the EIS, in order to be able to intervene in the event that one of the assemblies is too offset with respect to a nominal position (and is consequently likely to to be subsequently stuck in an EIS). Given various constraints, and in particular the fact that the fuel assemblies are submerged under water, it is complicated to accurately estimate the position of the holes S. Turbulence due to inhomogeneities in the liquid medium (local temperature differences ) complicate such estimates. The position of a hole S is only estimated with a certain uncertainty, which is the maximum difference that the detection process causes between a position "estimated" by the process and a "real" position of the hole S. The position of each hole S is not known: it is located inside a circle A whose center is the "estimated" position and whose radius is equal to the maximum error of the detection method. In order to prevent a fuel assembly from remaining jammed when the lid is opened, a deviation tolerance that can be retained between the "nominal" position of the fuel assembly and the actual position is 8.3 millimeters (mm). This translates into the fact that the “real” position of the fuel assembly must lie within a circle B having the “nominal” position of the fuel assembly as its center and a radius of 8.3 mm. By integrating the uncertainty linked to the process, this means that the difference between the position estimated by the process, to within the uncertainty, and the nominal position is less than 8.3 mm. This condition will be better understood in view of FIG. 1. A nominal position 10 of a hole S is known. Circle B is referenced 11 and the radius of circle 11 corresponds to the aforementioned tolerance (for example 8.3 mm). The position estimated by the method is referenced 12. The circle A referenced 13 is centered around the estimated position 12 and has a radius corresponding to the maximum error of the detection method. To prevent the fuel assembly from being jammed when the cover is opened, it is therefore necessary for the circle 13 to be entirely contained within the circle 11. Each time that there is a circle 13 at least partially outside a circle 11, the corresponding fuel assembly must be declared incorrectly positioned in order to initiate repositioning operations prior to refitting the EIS. These repositioning operations significantly increase the duration of the shutdown of the plant and therefore reduce the availability of the plant. Thus, if the maximum error of the detection method is large and in particular if it approaches the value of the tolerance (for example 8.3 mm), the detection becomes inoperative insofar as many assemblies will be considered as badly positioned due to uncertainty, although their actual position is close to the nominal position. A major challenge is then to reduce as much as possible the maximum error that the detection method causes between the position estimated by the method and the real position of a hole S. In any event, the maximum error must be small before the deviation tolerance between the actual position and the nominal position. Several methods for estimating the positions of the holes S are known. They generally consist in acquiring many photos according to different shots of the tank. On these shots, the various holes S are located by image processing methods making it possible to identify circles or ellipses. Then, the different shots are readjusted in relation to each other in order to build a complete cartography of the tank. However, many sources of error are likely to degrade the accuracy of these estimates, for example: - poor image quality (turbulence due to heat release, insufficient contrast, etc.); - the instability of the cameras (variation of angle and altitude). Model tests, in which the real positions of the S holes are known, show that the maximum error between the estimated positions of the S holes and the real positions can reach 7 mm, which is too close to 8.3 mm for make these detection methods usable. Thus, there is a need to significantly reduce the maximum error linked to the detection methods of the prior art, between the position estimated by these methods and the real position of the holes S. The present invention improves the situation. A first aspect of the invention relates for this purpose to a method for determining (typically by optimizing estimates) positions of fuel assembly elements arranged in a vessel, each fuel assembly comprising at least one element, at least one constraint geometry of the fuel assembly or of the vessel being predefined, the method comprising the following steps: - obtaining a first set of positions estimated beforehand for the elements; - determining a criterion representative of the distances between the positions of the first set and of the parameters to be optimized, the parameters identifying possible positions of the elements, the possible positions respecting the predefined geometric constraint; - determining a second set of estimated positions optimized from the parameters for which the criterion is minimized within the meaning of a predetermined standard. Thus, the present invention makes it possible to take into account a predefined geometric constraint when determining the second set of optimized estimated positions. No restriction is attached to the geometric constraint considered. It may for example be a constraint on the fuel assemblies (width of the assemblies, distance between elements of the same assembly) or a constraint on the vessel (dimensions and shape of the vessel). Thus, optimized estimated positions are determined which are close to the positions estimated beforehand and which also comply with the geometric constraint. Indeed, the parameters varying among the possible positions determined by the geometric constraint, the positions of the second set obtained respect a fortiori the geometric constraint. No restriction is attached to the method making it possible to obtain the first set of positions estimated beforehand. For this purpose, a camera or a camera can fly over in a plane of constant z altitude the top of the tank in order to acquire a video or a set of photos from which the first set of positions estimated beforehand can be determined. . Moreover, no restriction is attached to the method used to minimize a criterion as a function of parameters. Known methods such as the fmincon function of MatlabTM can for example be used. By element is meant any part of a fuel assembly that it may be appropriate to locate. For example, it can be the S-holes, as discussed in the introductory part. By improving the precision on the location of the holes S, it is ensured to detect a possible blocking of the EIS in the holes S with increased reliability. Several examples of criteria will be given below, and the invention is in no way restricted to the determination of one of these criteria. According to one embodiment of the invention, each fuel assembly can comprise at least two elements located on one face of the fuel assembly, and a predefined geometric constraint can be, for each fuel assembly, a relative position of each element with respect to at a center of the face of the fuel assembly. Thus, this embodiment makes it possible to ensure that the relative position between the elements of the same fuel assembly conforms to reality. Indeed, the geometry of a fuel assembly is generally known in advance. By integrating this constraint in the minimization of the criterion, compliance with the geometry of the fuel assemblies is thus ensured. In addition, for each fuel assembly, the parameters can be three coordinates making it possible to locate the face of the fuel assembly in a plane of space, the three coordinates comprising two coordinates of the center of the face and an angle of rotation of the face relative to an axis of the plane of space, and the second set of optimized estimated positions can be determined, for each fuel assembly, from the parameters representative of the position of the center of the face and the predefined relative positions of each element relative to the center of the face. Thus, the criterion minimization problem is solved for the coordinates of the centers of the fuel assemblies. From these coordinates, it is possible to directly deduce the estimated optimized positions of the elements, the geometry of the face of each fuel assembly being known. In addition or as a variant, a predefined geometric constraint can comprise a minimum distance between the centers of two distinct fuel assemblies and / or between the center of an assembly and an end of another fuel assembly. Such an embodiment also makes it possible to take into account the impossibility for two fuel assemblies to overlap. Indeed, due to the detection errors having led to the first set of positions estimated beforehand, it is possible that these positions estimated beforehand reflect an intersection of fuel assemblies. Taking this geometric constraint into account in the minimization of the criterion makes it possible to correct this anomaly. In addition, the minimum distance can be a function of the respective widths of the fuel assemblies. By width is meant a minimum dimension of the face of a fuel assembly in the plane of the space considered. In one embodiment of the invention, the geometric constraint can be a maximum distance between elements of two fuel assemblies, the maximum distance being determined as a function of the geometry of the vessel. Thus, the invention also provides for taking into account the geometry of the vessel. Indeed, it is not conceivable that fuel assembly elements can be located beyond the walls of the vessel. Since this problem is not dealt with when obtaining the first set of positions estimated beforehand, the invention allows this geometric constraint to be taken into account when minimizing the criterion. In addition, the elements of the fuel assemblies can be included in a plane identified by an abscissa axis and an ordinate axis, nominal positions of the fuel assemblies in the vessel can be predefined, the fuel assemblies being arranged in columns and in rows in the vessel, the fuel assemblies may comprise a first subset of fuel assemblies having elements of maximum respective ordinates and a second subset of fuel assemblies having elements of minimum respective ordinates, and the distance between the ordinate of the possible position of an element of a first fuel assembly of the first assembly and the ordinate of the possible position of an element of a second fuel assembly of the second assembly can be less than a maximum distance between the first and second assemblies combustibles, the maximum distance being defined from the geometry of the tank.Thus, the minimization of the criterion is constrained by a plurality of geometric constraints linked to the vessel, taking into account the positions of the fuel assemblies with respect to each other. The precision associated with the determination of the second set of optimized estimated positions is then increased. According to one embodiment of the invention, the criterion is minimized at least twice for at least two distinct initializations of the parameters to be optimized, and the second set of estimated optimized positions can be determined from the parameters associated with the smallest value of the criterion obtained after minimization. Indeed, a single initialization of the parameters makes it possible to obtain a minimized criterion which is not necessarily minimum in absolute terms, which is due to the non-convexity of the set of solutions respecting the constraint(s). By iterating the minimization of the criterion for several initializations, the precision in determining the second set of optimized estimated positions is improved. The invention also provides for a number of initializations greater than two. According to one embodiment of the invention, the criterion representative of the distances between the positions estimated beforehand of the first set and of the parameters to be optimized can be a least squares criterion. In one embodiment, the method further comprises the following steps: comparing the estimated optimized positions of the second set with nominal positions of the elements of the fuel assemblies; and - if the difference between an estimated optimized position of an element of a fuel assembly and the nominal position of the element is greater than a predetermined threshold, triggering an alert with a view to modifying the position of the fuel assembly. A second aspect of the invention relates to a computer program product comprising program code instructions recorded on a medium readable by a computer, for the execution of the steps of the method according to the first aspect of the invention. A third aspect of the invention relates to a device for determining the positions of fuel assembly elements in a vessel, each fuel assembly comprising at least one element, at least one geometric constraint of the fuel assembly or of the vessel being predefined, the device comprising: - a unit for obtaining a first set of previously estimated positions of the elements; - a first unit for determining a criterion representative of the distances between the positions of the first set and the parameters to be optimized, the parameters identifying possible positions of the elements, the possible positions respecting the predefined geometric constraint; - a second unit for determining a second set of estimated positions optimized from the parameters for which the criterion is minimized within the meaning of a predetermined standard. According to one embodiment, the device further comprises: - a unit for comparing the estimated optimized positions of the second set with the nominal positions of the elements of the fuel assemblies; and - an alert triggering unit for, if the difference between an estimated optimized position of an element of a fuel assembly and the nominal position of the element is greater than a predetermined threshold, triggering a 2 9 9 901 1 9 alert to modify the current position of the fuel assembly. Other characteristics and advantages of the invention will appear on examination of the detailed description below, and of the appended drawings in which: - figure 1 illustrates the tolerance allowed in the difference between the nominal position and the position estimate of a hole S as a function of the uncertainty associated with the method for determining current positions of the hole S; - Figure 2 illustrates a section in a vertical plane (x, z) of a nuclear reactor vessel 10 comprising a plurality of fuel assemblies; - Figure 3 is a diagram representing the steps of a method according to certain embodiments; - Figure 4 illustrates a section in a horizontal plane (x, y) of a fuel assembly; FIG. 5 illustrates a section in a horizontal plane (x,y) of two fuel assemblies located according to a method of the prior art in a case where there is overlap according to the positions estimated beforehand; - Figure 6 illustrates a section in a horizontal plane (x, y) of two fuel assemblies; FIG. 7 illustrates a section in a horizontal plane (x,y) of a nuclear reactor vessel comprising a plurality of fuel assemblies; - Figure 8 illustrates a device according to certain embodiments of the invention. FIG. 2 illustrates a nuclear reactor vessel 20 comprising a plurality of fuel assemblies 21, each assembly 21 being indexed by an index, i for example, between 1 and nA, nA designating the total number of fuel assemblies of the vessel 20. The number nA of fuel assemblies 21.i as well as their nominal positions are preferably predefined. As shown in Figure 2, the fuel assemblies 21 are separated by an inter-assembly clearance. A coordinate system of space (x,y,z) is defined and figure 2 illustrates a section in a plane (x,z). A lid of the vessel 20, not shown in Figure 2, is able to cover the vessel 20 and EIS are able to cooperate with holes S of the fuel assemblies 21. In what follows, it is considered that each fuel assembly comprises two S holes. However, no restriction is attached to the number of S holes that each fuel assembly 21 comprises.As a variant, it is possible to identify elements of the fuel assembly other than the holes S. The holes S are however considered in what follows by way of example. The dimensions of the tank can also be known (possibly with an uncertainty, for example equal to 1 mm) and a tank structure will be illustrated later (with reference to FIG. 6). Figure 3 is a diagram illustrating the steps of a method according to certain embodiments of the invention. At a step 301, a first set of positions estimated beforehand of the holes S of the fuel assemblies 21.i is obtained. No restriction is attached to the method for obtaining the first set of positions estimated beforehand. For example, any known method may be employed. For this purpose, a camera or a camera can fly over in a plane of constant z altitude the top of the tank in order to acquire a video or a set of photos from which the first set of positions estimated beforehand can be determined. . In addition, the method described in the patent application FR1150655 can for example be implemented to restore the acquired photos. The present invention provides for obtaining one or more estimates of positions estimated beforehand for each hole S. The acquisition of a single video or a single set of photos of the vessel can make it possible to deduce several different estimates as to the estimated position of a same hole S. These estimates are added to the first set. Each position estimated beforehand for hole S comprises an abscissa, an ordinate, and possibly an altitude, indexed by the index of the assembly comprising the hole S. It is also necessary to differentiate between the two holes S of the same fuel assembly . To this end, with reference to FIG. 4, a fuel assembly 21.i comprises a first hole 41.1 located "at the bottom right" and a second hole S 41.2 located "at the top left". The number of holes S per fuel assembly 21.i as well as their relative positions on the fuel assembly are given solely by way of illustration in FIG. 4. It is of course possible to change the relative positions of the holes S, or to add or subtract holes S. The positions estimated beforehand of the first set are, according to the techniques of the prior art, imprecise in that they do not take into account the predefined geometric constraints of the vessel and / or of the fuel assemblies. The center distance is the distance between the centers of the two holes S of the same fuel assembly. Due to the low quality of the images acquired, the positions estimated beforehand of two holes S of the same fuel assembly 21.i can be separated by a distance which is different from the center distance of the fuel assembly 21.i , which is nevertheless non-deformable (at least in view of the low mechanical stresses it undergoes). In addition, it happens that according to the positions estimated beforehand, fuel assemblies 21.i overlap, which is not possible from a practical point of view, or that fuel assemblies 21.i occupy a larger space than that delimited by the internal structure of the tank. The present invention proposes to optimize the first set of positions estimated beforehand in order to obtain a second set of optimized estimated positions which respect at least one of the geometric constraints defined above. At a step 302, a criterion representative of the distances between the positions estimated beforehand of the first set and the possible positions of the elements is determined, the possible positions respecting the predefined geometric constraint(s). For example, as detailed below, the criterion in question may be a least squares criterion. In order to integrate the geometric constraint according to which the spacing is constant, the positions of two holes S of the same fuel assembly 21.i are expressed with respect to the center of this assembly. Referring again to FIG. 4, the fuel assembly 21.i is square, with side L, and comprises a center 40. The inclination of the fuel assembly relative to the abscissa axis x is parameterized by the angle O. . The position of the hole S 41.1 is identified by the coordinates of the center 42.1 of the hole S 41.1 and the position of the hole S 41.2 is identified by the coordinates of the center 42.2 of the hole S 41.2. The center distance is denoted D thereafter. We note x, the abscissa of the center 40 of the fuel assembly 21.i and y its ordinate. For a triplet (x, c, , 0, ), the coordinates of the center 42.2 of the hole S 41.2, defining its position, are given by: D xLJ,-=x9 --cos(-71+0); (1) 2 4 D TC (2) y" c =y, --sin(--+O). Similarly, the coordinates of the center 42.1 of the hole S 41.1, defining its position, are given by: g c x = + -D , 2cos(-71+0,); (3) 4 D TC y'3 c = y, + -2sin(--4+ 0i) (4) By locating the position of holes S 41.1 and 41.2 in function of the center 40 of the fuel assembly 21.i which includes them, the geometric constraint on the center distance of the assemblies 21.i is taken into account. 301 are designated by the following notations: - n," (respectively n,B) is the number of positions estimated beforehand for the center 42.2 (respectively 42.1) of the hole S 41.2 (respectively 41.1) located at the top left (respectively in bottom right) of the fuel assembly 21.i of index i. n," and n,B are greater than or equal to 1, - for the jth position estimated beforehand for the hole S 41.2 of the fuel assembly 21.i, j varying between 1 and n", (x",y" ) are the coordinates defining the previously estimated position; - for the jè" position estimated beforehand for the fuel assembly 21.i, j varying between 1 and ri,13, coordinates defining the position estimated beforehand. From these data, a criterion C in the sense can be defined at step 302 as follows: ( 2 nA niH X'. -2 cos(-71 + O.) - rliB X.c -D cos(-71+ Oi) - c D H C y 2 4 i=1 j=1 C D - :il" H Oi) - j=1 YiC +- 12 2 4 No restriction is attached to standard 11 considered above. As detailed later, no restriction is attached to the criterion considered, criterion C being given for illustrative purposes. From the criterion C, it is possible to vary the parameters x, e and 0, in order to minimize the criterion. At a step 303, the parameters e and 0 are obtained, minimizing the criterion C. For example, in order to solve the problem of minimizing the criterion C, an approximation consists in considering that the values ​​of 0, sought are very close to 0 The expression of the criterion C can then be linearized and written in matrix form: C = with: i=1 nA j=1 Xi - ;MB 2 ri'3 D X, x, _ IMNAH D + IOMBX, MH = _ 0 0 j=1 1 1 1 0 0 0 1 2-e 2e D D 2-e_ the hole S 41.1 of are the least squares + D and yB, 2V2 D In order to accelerate the convergence of the algorithm towards a minimizer of x, criterion, the different parameters X of the criterion are optimized 0, jointly. For this purpose, all the parameters, for i varying between 1 and nA, can be grouped together in the same vector X of size 3nA. Without taking into account the constant terms, the expression of the criterion is then written in a form: C--1XTHX+fTX. 2 It is possible to take other geometric constraints into account in order to constrain the problem of minimizing criterion C. A second geometric constraint to be taken into account relates to the non-overlapping of the fuel assemblies 21.i. Indeed, FIG. 5 represents a top view (section in the horizontal plane (x,y)) of two fuel assemblies 21.i and 21.k located according to a method of the prior art in a case where there is overlap according to the positions estimated beforehand. The methods for estimating the positions of the holes S according to the prior art take no account of the geometry of the fuel assemblies, the centers 42.1.i and 42.2.i of the holes S of the first fuel assembly 21.i and the centers 42.1. k and 42.2.k of holes S of the second fuel assembly 21.h can be located as shown in Figure 5. Such estimates are inconsistent in that the assemblies 21.i and 21.k overlap. The present invention then proposes to take into account the geometry of the fuel assemblies 21.i and 21.k. By considering the two neighboring fuel assemblies 21.i and 21.k in the vessel 20, the following five inequality constraints can be formulated: i) the distance, according to the L1 standard (sum in absolute value of the differences between respective abscissas and respective ordinates), between the center 40 of the fuel assembly 21.i and the two closest corners of the fuel assembly 21.k must be , L greater than a , L designating the width of a fuel assembly 21.i (it is considered that all the fuel assemblies have the same width). FIG. 6 presents a top view (section in the horizontal plane (x,y)) of the two fuel assemblies 21.i and 21.k. An orthonormal reference whose origin is the center 40.i of the fuel assembly 21.i and whose axes are denoted Xi and Yi (such that the axis Xi passes through the centers 42.1.i and 42.2.i of the holes S of the fuel assembly 21.i) is defined. A corner 50.k of the fuel assembly 21.k is located by the coordinates (Xk ,ylk ) in this orthonormal reference. In this reference, the first of the three geometric constraints of non-overlapping is written: )(' + > i,k i k - 2 In order to return to the initial reference (axes x, y and z), it is advisable to apply a translation and a rotation: ( k - x9)cos(- -7C Oi -y)sin ----FO i, 4' \ ( - ()('k +0;)+(yil,k -yc)cos , 4 4 where x,1 and y,1 denote respectively the abscissa and the ordinate of the corner 50.k in the initial frame, comprising the axes x, y and z. In the same way, an additional inequality is obtained for a second corner 51.k of the fuel assembly 21.k. ii) the same approach as for i) can be applied by swapping the indices i and k: the distance in standard L1 between the center 40.k of the fuel assembly 21.k and the two corners closest to , L l fuel assembly 21.i must be greater than a , which makes it possible to obtain two additional inequalities. iii) In addition, the Euclidean distance between the centers of the fuel assemblies 21.i and 21.k must be greater than L: A third geometric constraint to be taken into account relates to the dimensions of the vessel 20 and to the space occupied by all of the fuel assemblies 21. In order to take this geometric constraint into account, it is possible to take into account only the fuel assemblies 21 located on the periphery of the vessel 20. In what follows, we distinguish the geometric constraints according to the ordinate axis (y axis) and the geometric constraints along the abscissa axis (x axis). FIG. 7 illustrates the geometric constraints along the ordinate axis. FIG. 7 presents a geometry of the vessel 20, comprising a plurality of fuel assemblies 21 arranged in rows and in columns. Among the fuel assemblies 21, fuel assemblies 60 which, for each column, occupy extreme positions along the y axis, have been grayed out. It is noted that the set of fuel assemblies 60 can be separated into a first subset having vertices (and therefore holes S) of maximum respective ordinates and a second subset having vertices (and therefore holes S) d minimum respective ordinates. Thus, it is possible to define a geometric constraint between each pair of fuel assemblies comprising a fuel assembly of the first subassembly and a fuel assembly of the second subassembly. For example, the fuel assemblies referenced 21.m (first sub-assembly) and 21.n (second sub-assembly) are considered. The fuel assembly 21.m comprises two vertices 61.m whose ordinates (denoted yHmi and yHm2 ) are maximum for the column of fuel assemblies comprising the fuel assembly 21.m. The fuel assembly 21.n comprises two vertices 61.n whose ordinates (denoted ynBi and ynB2) are minimum for the column of fuel assemblies comprising the fuel assembly 21.n. The geometry of the tank makes it possible to know the maximum distance 62 between the two ends of the tank corresponding to the positions of the vertices 61.m and 61.n. By projecting the distance 62 onto the y-axis of the ordinates, a distance Dm,n is obtained. The distance Dm,n, representing the maximum difference between the ordinates of the vertices 61.m and 61.n, makes it possible to obtain four new constraints: yHm,_yBn2<Dm,n; yHm2 _ ynB, < Dm,n; YHml - YnI31 Dm,n; yHm2 _ yBn2 < Dm,n. As mentioned previously, the geometry of the tank can be known with an uncertainty, for example of 1 mm, in which case this uncertainty is added to the distance Dm,n. Four inequalities, such as those presented above, are obtained for each pair of fuel assemblies comprising a fuel assembly from the first subassembly and a fuel assembly from the second subassembly. Similar geometric constraints are obtained along the horizontal axis: the fuel assemblies 21 considered are the fuel assemblies located at the left and right ends (along the x axis of the abscissa). All of the inequalities defined above, based on the geometric constraints linked to the space occupied by the fuel assemblies relative to the vessel and on the geometric constraints of non-overlapping of the fuel assemblies, can be put in the following form: Rk(X). Thus, from the criterion C and the set of inequalities Rk (X) 0 defined above, the problem of optimization under constraints can be solved by means of an algorithm of interior points. Such an algorithm is cited solely by way of illustration and the present invention cannot be restricted to the use of this single algorithm. In particular, it is possible to use the fmincon function of MatlabTM by indicating the calculation function of the criterion (C) and its gradient as well as the functions associated with the geometric constraints ( Rk (X) ). The aforementioned algorithm is a local optimization method. However, the set of feasible solutions is non-convex. Thus, for a given initialization of the parameters corresponding to the possible positions of the holes S, it is possible not to converge towards a solution which globally minimizes the criterion C. Thus, the invention proposes to launch the optimization procedure for different initializations. Among the different solutions obtained, the one corresponding to the smallest value of C after convergence is retained. In practice, it is possible to generate the different initializations by bringing slight disturbances with respect to the nominal position of the fuel assemblies 21 (shift of the centers 40 of the fuel assemblies 21, change of the orientation angle 0, of the fuel assemblies 21 , reduction of inter-assembly play), so that the geometric constraints are respected when initializing the parameters. An alternative solution for initializing the algorithm consists in solving the optimization problem by fixing the angles 0, to zero and by only varying the position of the centers 40 of the fuel assemblies 21. It should be noted that, in practice, the angle of orientation 0, of the fuel assemblies is very close to zero, and thus, by fixing 0, to zero, the convergence towards the sought solution is considerably accelerated while preserving a significant precision. From the parameters x, y and [deg.] minimizing the criterion C and respecting the geometric constraints Rk (X), a step 304 gives a second set of optimized estimated positions of the holes S 41 (entirely defined by the parameters x , y and 0, and by relations (1), (2), (3) and (4), for i varying between 1 and nA). The estimated optimized positions of the second set respect the geometric criterion of the center distance since the estimated optimized positions of the holes S are obtained directly from the result parameters x, y and 0, resulting from the minimization of the criterion C and from the geometry of the fuel assemblies 21. Compliance with the non-overlapping constraints and the space occupied by the fuel assemblies 21.i is also ensured by constraining the optimization of the criterion by the set of inequalities Rk(X). The invention is in no way restricted to the simultaneous taking into account of the three geometric constraints set out above. Indeed, the invention may provide for taking into account other geometric constraints, or for taking into account only one or any two of the three constraints presented previously. At a step 305, the estimated optimized positions of the holes S 41 in the second set are compared with the respective nominal positions of the holes S 41. In the case where, for a hole S 41, and using the notations of FIG. 1, the circle 13 centered on the optimized estimated position and whose radius is equal to the uncertainty of the method comes out of the circle 11 centered on the nominal position and whose radius is equal to the tolerance (for example 8.3 mm), a alert is generated at a step 307 so that the fuel assembly(ies) comprising the hole(s) S 41 concerned can be replaced. Otherwise, the lid of the tank can be closed in a step 306. Figure 8 illustrates a device 70 according to some embodiments of the invention. The device comprises a unit 71 for obtaining a first set of positions estimated beforehand for elements (holes S for example) of the fuel assemblies. As described above, no restriction is attached to the way of acquiring the first set, a known method being able to be implemented. The device 70 further comprises a first determination unit 72 capable of determining a criterion representative of the distances between the positions of the first set and of the parameters to be optimized, the parameters identifying possible positions of the elements, the possible positions complying with a predefined geometric constraint. The criterion may be a criterion in the sense of least squares, or any other criterion, as described below. As described previously, the parameters to be optimized can be the parameters x, and 0, of the fuel assemblies 21.i. The device 70 can further comprise an optimization unit 73 making it possible to minimize the criterion determined by the first determination unit 72, within the meaning of a predetermined standard, while respecting the geometric constraint(s). As described previously, the criterion can be minimized for different initializations of the parameters, and the smallest value of the criterion obtained after minimization can then be chosen to deduce the parameters corresponding to optimized estimated positions of a second set. For this purpose, a second determination unit 74 is able to determine a second set of estimated positions optimized from the parameters for which the criterion is minimized. In addition, the device 70 may comprise a unit 75 for comparing the estimated optimized positions of the second set with the nominal positions of the elements of the fuel assemblies and a unit 76 for triggering an alert for, if the difference between an estimated optimized position d an element of a fuel assembly and the nominal position of the element is greater than a predetermined threshold, triggering an alert in order to modify the actual position of the fuel assembly in question. The invention is not restricted to the embodiments described above. It extends to other variants. For example, steps 302 and 303 have been described so as to determine the parameters x, y and 0, of the various fuel assemblies 21.i which minimize a least squares criterion C under constraints. However, this assumes that the error in the position of each hole S follows a Gaussian law. However, the Gaussian model can be improved in the case of a modeling of the errors on the position of each hole S. Indeed, the error on the position is generally of low amplitude except for a small number of holes S for which it is significantly more important. In order to take into account the isolated nature of certain errors, the invention may provide for the use of a different standard, in order to define the following criterion C′ at step 302: ( , \2 ( \ 2 n, ( ,C D', n da\ _i_ ,,C D y--sin(-+e)-y.ic _,_ " \ ' 1 A, - -,.....,s - - + uo, ) - x :1 1 y i - -uni 8' -- 1 %Ji j - y 1E11 A 2 4 2 4 n J=1 ) ) 1 \ 2 \ 1=1 D .\ii \2 ( D nP ( +- / Xic +- -cos( - -ic +- ei)- X1131 +- y, +-sin(--+0,)-y,B1 c ic 2 4 2 4 0 ) ) ) The disadvantage of this expression is that 'it is not differentiable (because of the non-differentiability of the square root at zero). The following approximation can then be used: D ii \ 2 C ic \2 ( c D ic 1 x, --cos(- -+e,)-x," + y, --sin(--+ei) y.j _Fe nA J=1i 2 4 d) 2 4 ) C'= ( D \2 + \ 2 C ( D +1.12 x , +-cos(-+0,)-x,31 c n \ 2 4 ) y, +-sin(--+0,)-y,B1 2 4 ) C'= The value of p. is chosen very small compared to the desired precision in order to minimize the impact of this approximation. For example p. = 0.05mm can be chosen for a desired precision of 1 mm. The invention extends to the consideration of other criteria.

Claims

CLAIMS 1. Method for determining positions of fuel assembly elements (21) arranged in a vessel (20) of a nuclear reactor, each fuel assembly comprising at least one element (41.1; 41.2), at least one geometric constraint of the fuel assembly or the vessel being predefined, the method comprising the following steps: - acquire a plurality of images of the nuclear reactor, - use the plurality of images to estimate a first set of positions of the elements, - determine a criterion representative of the distances between the positions of the first set and the parameters to be optimized, said parameters identifying possible positions of the elements, said possible positions respecting said predefined geometric constraint; - determine a second set of estimated positions optimized from the parameters for which said criterion is minimized within the meaning of a predetermined standard.

2. Method according to claim 1, wherein each fuel assembly (21) comprises at least two elements (41.1; 41.2) located on a face of said fuel assembly, and wherein a predefined geometric constraint is, for each fuel assembly, a relative position of each element with respect to a center (40) of the face of the fuel assembly.

3. Method according to claim 2, in which, for each fuel assembly (21), the parameters are three coordinates making it possible to locate the face of said fuel assembly in a plane (x,y) of space, the three coordinates comprising two coordinates of the center (40) of the face and an angle of rotation of the face relative to an axis of the plane of space, and in which the second set of optimized estimated positions is determined, for each fuel assembly, from the parameters representative of the position of the center of the face and the predefined relative positions of each element relative to said center of the face.

4. Method according to claim 2 or 3, in which a predefined geometric constraint comprises a minimum distance between the centers (40) of two distinct fuel assemblies (21) and / or between the center of one assembly and one end (50.k; 51.k) of another fuel assembly.

5. Method according to claim 4, in which the minimum distance is a function of respective widths of the fuel assemblies.

6. Method according to one of the preceding claims, in which the geometric constraint is a maximum distance between elements (41.1; 41.2) of two fuel assemblies (21), the maximum distance being determined as a function of the geometry of the tank (20).

7. Method according to claim 6, in which the elements (41.1; 41.2) of the fuel assemblies (21) are included in a plane (x,y) identified by an abscissa axis and an ordinate axis, in which nominal positions of the fuel assemblies in the tank (20) are predefined, the fuel assemblies being arranged in columns and rows in the tank, in which the fuel assemblies comprise a first subset of fuel assemblies (21.m) having elements of maximum respective ordinates and a second subset of fuel assemblies (21.n) having elements of respective minimum ordinates, and in which the distance between the ordinate of the possible position of an element of a first fuel assembly of the first set and the ordinate of the possible position of an element of a second fuel assembly of the second set is less than a maximum distance between the first and second fuel assemblies, said maximum distance being defined from the geometry of the tank.

8. Method according to one of the preceding claims, in which the criterion is minimized at least twice for at least two initializations of the distinct parameters to be optimized, and in which the second set of optimized estimated positions is determined from the parameters associated with the smallest value of the criterion obtained after minimization.

9. Method according to one of the preceding claims, in which the criterion representing the distances between the previously estimated positions of the first set and the possible positions defined from the parameters to be optimized is a least squares criterion.

10. Method according to one of the preceding claims, said method further comprising the following steps: - comparing the optimized estimated positions of the second set with nominal positions of the elements (41.1; 41.2) of the fuel assemblies (21); and - if the difference between an optimized estimated position of an element of a fuel assembly and the nominal position of said element is greater than a predetermined threshold, trigger an alert with a view to modifying the position of said fuel assembly.

11. Computer program product comprising program code instructions recorded on a computer-readable medium, for carrying out the steps of the method according to any one of claims 1 to 10.

12. Device for determining positions of elements (41.1; 41.2) of fuel assemblies (21) in a vessel (20) of a nuclear reactor, each fuel assembly comprising at least one element, at least one geometric constraint of the fuel assembly or of the vessel being predefined, the device comprising: - a unit (71) for obtaining a first set of positions of the elements, estimated from a plurality of images acquired from the nuclear reactor, - a first determination unit (72) of a criterion representative of the distances between the positions of the first set and the parameters to be optimized, said parameters identifying possible positions of the elements, said possible positions respecting said predefined geometric constraint; 5 - a second unit for determining (74) a second set of estimated positions optimized from the parameters for which said criterion is minimized within the meaning of a predetermined standard.

13. Device according to claim 12, said device further comprising: 10 - a comparison unit (75) of the optimized estimated positions of the second set with nominal positions of the elements of the fuel assemblies; and - an alert triggering unit (76) for, if the difference between an optimized estimated position of an element of a fuel assembly and the nominal position of said element is greater than a predetermined threshold, triggering an alert with a view to modifying the position of said fuel assembly.

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