Method and weighing device, particularly for weighing wheeled vehicles

Abstract

The invention relates to a method for weighing a wheeled vehicle, comprising the steps of moving the vehicle over a weighbridge (1), with a first set of wheels of the vehicle simultaneously triggering input sensors (C1, C2) of the weighbridge, and then simultaneously triggering output sensors (C3, C4) of the weighbridge; acquiring and sampling, by a processing unit (PU), weighing signals (xi,1-xi,p) from the input and output sensors while the vehicle crosses the weighbridge; and executing a plurality of iterations of an expectation-maximization algorithm, each iteration comprising the calculation of parameters of a model based on the approximation of each of the weighing signals by a linear combination of square-integrable eigenfunctions, the calculated parameters comprising, for each weighing signal, a probability that the signal belongs to a given homogeneous group, and a probability that the signal exhibits an anomaly. Figure 1

Description

Title of the invention: Weighing method and device, in particular for weighing vehicles mounted on wheels Technical field

[0001] The present invention relates to the weighing of motor vehicles or towed vehicles, mounted on wheels, such as heavy goods vehicles or wagons. State of the art

[0002] Generally, the weighing of wheeled vehicles is carried out using a weighbridge comprising a platform arranged on a support, with weighing sensors being fixed between the platform and the support to measure the weight exerted by the platform on the support. The sensors can be arranged on the edges of the platform. The analog signals from the sensors can then be digitized and stored for analysis. A measurement is therefore made up of a set of curves, each curve being representative of the variations in the signal from one of the sensors.

[0003] Many statistical approaches have been developed to analyze such data. Among these approaches, functional analysis appears appropriate for analyzing data relating to the variations over time of one or more signals from one or more sensors, in particular when these data are acquired at a high frequency, for example one or several hundred Hertz. In this context, the detection of erroneous measurements is a crucial problem.

[0004] Functional analysis consists of modeling the signal from a sensor by a linear combination of functions belonging to the L2 set of square-integrable functions. Some models propose to classify the measured signals into homogeneous groups (called "clusters"), which would facilitate the detection of erroneous signals. Indeed, the differences between the groups are mainly due to differences between the entities, here the vehicles that are measured, independently of the possible presence of anomalies. Thus, document [1] describes a model in which normal and abnormal data are modeled in a functional subspace, by implementing a multivariate functional principal component analysis.

[0005] This model makes it possible to detect anomalies in measurements, with very low false positive and false negative rates. In addition, it has the advantage of being able to be refined as it is executed, and does not require fixing a proportion of anomalies, nor fixing a number of groups. On the other hand, this model requires the implementation of a significant storage capacity and / or execution times which can be excessive, particularly in an industrial environment. Thus, a standard computer running this model provides a result in several minutes, knowing that a vehicle crosses the weighbridge in a few dozen seconds.

[0006] It is therefore desirable to be able to propose a method for processing weights which is robust, and whose processing speed is compatible with the weighing of a vehicle using a weighbridge. Summary of the invention

[0007] Embodiments relate to a method for weighing a wheeled vehicle, comprising the steps of: moving the vehicle onto a weighbridge such that a first set of wheels of the vehicle simultaneously loads input sensors of the weighbridge, and then simultaneously loads output sensors of the weighbridge; acquiring and sampling, by a processing unit, weighing signals from the input and output sensors, while the vehicle is traveling across the weighbridge;and executing by the processing unit a plurality of iterations of an expectation-maximization algorithm, each iteration comprising the calculation of parameters of a model based on the approximation of each of the weighing signals by a linear combination of square-integrable type basis functions weighted by coefficients, the calculated parameters comprising for each weighing signal a probability that the weighing signal belongs to a given homogeneous group of weighing signals, and a probability that the weighing signal presents an anomaly. ;

[0008] Thanks to these arrangements, the signals from the pairs of input or output sensors are highly correlated. The signals from the sensors on the same side of the weighbridge are also highly correlated with a time lag corresponding to the time taken by the vehicle to cover the distance between these sensors. As a result, the number of basic functions of the model and the number of groups are significantly reduced than if the weighing signals were not correlated with each other. The anomaly detection calculations are therefore significantly reduced.

[0009] According to one embodiment, each iteration of the plurality of iterations is based on the execution of an expectation-maximization algorithm comprising: an expectation step comprising the calculation of probabilities, a first maximization step comprising the calculation of estimates of the parameters of the model using a multivariate functional principal component analysis, making it possible to define a functional subspace of the functional space defined by the basic functions, each homogeneous group having a matrix variance in the functional space defined by the eigenfunctions, modeled in a parsimonious manner by elements formed from the largest eigenvalues ​​and elements considered as noise and all equal to one of the parameters of the model, and a second maximization step comprising the calculation of an inflation factor.

[0010] According to one embodiment, the probabilities are estimated by considering only the coefficients of the basis functions having an impact greater than a threshold value on the results and using a projection operator,

[0011] each probability that one of the weighing signals belongs to one of the homogeneous groups being obtained by calculating the ratio between a contaminated Gaussian density of the homogeneous group and a sum of the contaminated Gaussian densities of all the homogeneous groups, taking into account the coefficients, the contaminated Gaussian density of each of the homogeneous groups being calculated by the weighted sum of a first Gaussian density of each of the normal signals and a second Gaussian density of each of the abnormal signals in each homogeneous group, a covariance matrix of the Gaussian density of the abnormal signals being equal to a covariance matrix of the Gaussian density of the normal signals multiplied by an inflation factor, each of the first and second Gaussian densities being calculated by the sum of a projection norm of the coefficients of the model in a functional subspace defined for the homogeneous group,of a norm of a difference between the coefficients and the projection of the coefficients in the functional subspace defined for the homogeneous group and a term depending on the eigenvalues ​​of the covariance matrix, and, ,

[0012] each probability that one of the weighing signals of one of the homogeneous groups presents an anomaly being equal to the ratio between the Gaussian density of the normal signals of the homogeneous group and the contaminated Gaussian density of the homogeneous group, both being calculated with the coefficients.

[0013] This arrangement makes it possible to significantly simplify the calculations of the parameters of membership of a weighing signal to a given homogeneous group, and of anomaly of a weighing signal.

[0014] According to one embodiment, the method comprises a step of initializing the parameters of the model, randomly or using algorithms based on a minimization of a sum calculated for each homogeneous group of distances between each coefficient and a centroid of the homogeneous group.

[0015] According to one embodiment, a new iteration is executed if an error variable relating to the calculated parameters is greater than a threshold value and if a maximum number of iterations is not reached.

[0016] According to one embodiment, the calculated parameters of the model comprise for each homogeneous group of weighing signals: a parameter representing a proportion of weighing signals belonging to the homogeneous group, a parameter representing a proportion of normal weighing signals in the homogeneous group, a parameter representing an average of a Gaussian distribution of the homogeneous group, a matrix gathering coefficients of a set of eigenfunctions of the homogeneous group, the coefficients of the eigenfunctions being obtained from from multivariate functional principal component analysis, and a matrix variance having the form of a diagonal matrix gathering eigenvalues ​​of the homogeneous group, obtained from multivariate functional principal component analysis, the matrix variance comprising the first largest eigenvalues ​​and elements equal to an average value of the smallest eigenvalues, and a parameter representing an inflation factor of the covariance matrix of the homogeneous group, calculated using projection operators.

[0017] According to one embodiment, the method comprises steps of acquiring new weighing signals, calculating new coefficients obtained by approximating each of the new weighing signals by a linear combination of the basic functions weighted by new coefficients, and updating the parameters of the model in one iteration, the probability that one of the new weighing signals belongs to a homogeneous group of weighing signals and the probability that one of the new weighing signals has an anomaly, being estimated by using the projection operators to project the new coefficients into the functional subspaces defined from the previously calculated parameters of the model.

[0018] In this way, it can be determined whether new measurements have anomalies from the previously calculated model parameters. The model parameters can thus be refined and evolve as new measurements are acquired. Furthermore, thanks to this updating method, it is not necessary to store all the measurements that were previously used to determine the model parameters.

[0019] According to one embodiment, the updated parameters of the model comprise for each homogeneous group: a parameter representing a proportion of previous and new weighing signals belonging to the homogeneous group, and calculated by a weighted average of the corresponding previous parameter and a number of new signals belonging to the homogeneous group, a parameter representing a proportion of previous and new normal weighing signals in the homogeneous group, and calculated by a weighted average of the corresponding previous parameter and the number of new normal signals belonging to the homogeneous group, a parameter representing an average of the previous and new weighing signals of a Gaussian distribution of the homogeneous group, and calculated by a weighted average of the corresponding previous parameter and an average of the new signals belonging to the homogeneous group, a matrix of vectors formed by coefficients of eigenfunctions,the matrix being estimated by a multiplication of a rotation matrix by the previous matrix if the new weighing signals are well represented in the functional subspace, or otherwise estimated by a multiplication of the matrix of, rotation by a matrix consisting of a concatenation of the corresponding previous matrix and a matrix consisting of projection errors of the new coefficients in the functional subspace, a matrix variance having the form of a diagonal matrix gathering new eigenvalues ​​of the homogeneous group, obtained from the previous matrix variance, the previous vector matrix, the new coefficients and the average of the normal weighing signals, and elements obtained from an average value of the difference between the sum of the elements of the previous matrix variance and the sum of the new eigenvalues, and a parameter representing an inflation factor of the covariance matrix of the homogeneous group, calculated by a weighted average of the corresponding previous parameter and an inflation factor of the new weighing signals calculated from projection operators.

[0020] According to one embodiment, the method comprises steps of acquisition and sampling, by the processing unit, of weighing signals from intermediate sensors installed on the weighbridge between the input and output sensors.

[0021] Embodiments may also relate to a system for weighing a wheeled vehicle, comprising: a weighbridge comprising input sensors arranged to be acted upon simultaneously by a first set of wheels of the vehicle, and output sensors arranged to be acted upon simultaneously by the first set of wheels of the vehicle, when the vehicle crosses the weighbridge, a processing unit configured to acquire and sample weighing signals from the input and output sensors and execute a plurality of iterations of calculating parameters of a model, in accordance with the method previously defined.

[0022] According to one embodiment, the sensors are aligned along side edges of the weighbridge.

[0023] This arrangement makes it possible to obtain redundant measurements, and therefore to facilitate the detection of anomalies by the method defined previously.

[0024] According to one embodiment, the system comprises at least three sensors aligned along a side edge of the weighbridge.

[0025] This arrangement makes it possible to obtain more redundant measurements, and therefore to facilitate the detection of anomalies by the method defined previously.

[0026] According to one embodiment, the sensors are arranged so as to be aligned along axes perpendicular to a longitudinal direction of the weighbridge.

[0027] This arrangement makes it possible to obtain several correlated measurements simultaneously, and therefore to limit the calculations for detecting anomalies by the method defined previously. Brief description of the figures

[0028] The present invention will be better understood with the aid of the following description of exemplary embodiments with reference to the appended figures, in which identical reference signs correspond to structurally and / or functionally identical or similar elements.

[0029] [Fig-1] Figure No. 1 is a schematic top view of a weighbridge, according to a embodiment,

[0030] [Fig.2] Figure No. 2 is a schematic profile view of the weighbridge, according to one embodiment,

[0031] [Fig.3] Figure No. 3 schematically represents a system for processing measurements from sensors installed in the weighbridge, according to one embodiment,

[0032] [Fig.4] Figure No. 4 schematically represents functions of the processing system, according to one embodiment,

[0033] [Fig.5] Figure No. 5 represents steps of a method for determining measurements presenting anomalies, implemented by the processing unit, according to one embodiment,

[0034] [Fig.6] Figure No. 6 represents steps of an incremental method for determining measurements presenting anomalies, implemented by the processing unit, according to one embodiment,

[0035] [Fig.7] Figure No. 7 is a schematic top view of a weighbridge, according to another embodiment,

[0036] [Fig.8] Figure No. 8 is a schematic side view of the weighbridge of Figure No. 7. Detailed description

[0037] Figures 1 and 2 show a weighbridge 1 for weighing a wheeled vehicle. The bridge 1 comprises an upper platform 2 designed to receive a vehicle. The bridge 1 may comprise a base 3 on which the platform 2 is fixed. The platform 2 is fixed to the base 3 by means of sensors C1, C2, C3, C4, so that the entire weight of the platform rests on the sensors C1-C4. The base 3 may simply be placed on the ground.

[0038] The bridge 1 may also comprise an access ramp 4 arranged at an entry end of the bridge 1 to allow vehicles to climb onto it (and possibly descend in reverse). If the bridge 1 is intended to be crossed by the vehicles to be weighed, the bridge 1 may also comprise an exit ramp at an exit end opposite the entry end, in a longitudinal direction X of the bridge. The vehicle can move on the bridge 1 while the signals from the sensors C1-C4 are acquired and sampled by a processing unit CU.

[0039] Figure No. 3 represents a system for processing measurements from sensors Cl-Cp, according to one embodiment. The system comprises the processing unit CU connected to the sensors Cl, C2, .... Cp (with p for example equal to 4) arranged between the plate 3 and the base of the bridge 1. The processing unit CU may comprise a processor PRC, a memory MEM and an address and data system bus SBS. The bus SBS makes it possible to interconnect the processor PRC, the memory MEM. The processor PRC may comprise hardware components for performing data and signal processing and for executing program instructions stored in the memory MEM.

[0040] The processing unit CU may be adapted to execute instructions stored on a recording medium. The processing unit CU may be connected to other systems via a network such as an intranet or the Internet. The processing unit CU may comprise one or more devices that individually or cooperatively execute instructions stored on a recording medium.

[0041] The memory MEM may comprise a volatile memory VM, for example of the RAM (Random-Access Memory) type, and a non-volatile memory NVM, for example of the ROM (“Read-Only Memory”) type, EPROM (“Erasable Programmable Read-Only Memory”), EEPROM (“Electrically Erasable Programmable Read-Only Memory”), Flash memory, etc. The memory may also comprise any medium that can be used to store programs or data and that can be accessed by the processor PRC. The processing unit CU may further comprise or be connected to a recording medium STD which may comprise one or more memory units, such as a local or external hard disk, and a Flash memory. The storage unit STD may be used as a non-volatile storage unit for storing programs and / or data.

[0042] The processing unit CU may also comprise a user interface circuit UI configured to receive commands from a user when the control unit executes a program, via control members such as a keyboard, a mouse, and a sensitive surface. The interface circuit UI may also be configured to be connected to an output device such as a display screen DSU. The interface circuit UI may be connected to the processor PRC, via the SBS bus, or any other interface.

[0043] The processing unit CU may also comprise an input / output circuit IOI connected to the processor PRC via the bus SBS. The input / output circuit IOI may be configured to receive analog or digital signals, and in particular, to connect to the sensors Cl-Cp.

[0044] The processing unit CU may also comprise a communication circuit COM configured to connect the processing unit CU to a transmission network. data.

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] The processing unit CU is configured to provide weighing values ​​Mi>rMi>n per sensor, each associated with a validity indicator IVii-IVijn, and possibly a resulting weighing value, following the passage of a vehicle over the bridge 1, and to signal the presence of anomalies with regard to the weighings and the digitized measurement signals x;(t) = (xki(t), xi>2(t), ..., xi>p(t)) provided by the sensors Cl-Cp during a measurement interval [ti>0, tu], the index i representing a weighing number, and t representing the time belonging to the measurement interval [ti>0, tu]. Each of the measurement signals x ij(t), once digitized, comprises a sequence of discrete points which can be modeled by a functional form of the following form: with 1 < i < n, 1 < j 0 < t < tu, fj,b(t), 1 < b < Bj, is one of the basis functions used to model the signal from sensor j, Bj represents the number of basis functions used and {cl|b (represents a set of coefficients. The choice of the type of basis functions fj b and their number depends on the nature of the data. For example, Fourier functions can be used when the data have periodic patterns, spline-type functions can be used when the data form a smooth curve, and wavelet-type functions can be used when the data form a very irregular curve. The number Bj of basis functions fj>b chosen depends on the complexity of the curve. According to document [1], to classify the observed multivariate measurements xb x2, ..., xm into K groups and to detect the presence of erroneous measurements, we associate with the measurement signals x; the latent variables z; = (z; i, ..., ziK) and y; = (yi i, ..., yiK), such that zijk = 1 if the measurement signal x; belongs to group k, and otherwise zijk = 0, and yik = 0 if the measurement signal x; presents an anomaly and otherwise yik = 1. Knowing that each measurement signal x; can be identified by its basic coefficients Ci, document [1] shows that the set of measurement signals can be represented by the following model: in which u = {pk, ak, qk, hk, ek / k = 1, ..., K] represents all the parameters of the model to be estimated, g represents the density of the mixture of Gaussian distributions mul contaminated tivariates, Fk(pk,ak,qk,hk,ek) = [ak-fg(ci,qk,l,hk)+(l-ak)-fg(ci,qk,ek,hk)], pk e ]0,l] is the proportion of measurement signals belonging to group k, yK p = 1' ak e [0,1] is the proportion of normal measurement signals belonging to group k, fg(c i,qk,ek,hk) is the density of a Gaussian distribution with mean qk and covariance matrix hk, and represents the marginal density of the coefficients c;, and ek > 1 is a covariance inflation factor. The function fg can be expressed by the following equation:

[0051] , 1 T 1 / \TZ u \ 1 (3) fg(c.„qe t ,h k ) = —W qq {^71) |eknkl

[0052] in which g _yp g represents the number of basis functions used for model the measured signals.

[0053] Figure No. 5 represents steps S1 to S14 executed by the processing unit CU to detect the presence of anomalies among the measured signals x;. Steps S1 to S9 are executed successively. In step S1, a set of measurement signals xi is received from the sensors C1-Cp, and digitized. In step S2, the processing unit CU determines the basic coefficients c; for the measurement signals x; acquired, taking into account the chosen basic functions fj>b. In step S3, the processing unit CU initializes parameters, namely a number of groups K, numbers of intrinsic dimensions dk to be considered in a functional subspace SEk having a reduced number of dimensions, for each group k, a maximum error value e for example set at 0.0001, and a maximum number of iterations MX. The numbers of dimensions dk can be determined by a positive integer grid search method or the Catell test, both implementing the BIC (Bayesian Information Criterion) method.

[0054] In step S4, the respective estimates f and s; of the parameters z; and yi5 and the parameters ek are initialized. The estimate f can be initialized randomly or by using algorithms that rely on minimizing the sum of the distances between each data item and the centroid of the group k. The estimate s; is initialized to 1. The parameters ek are initialized to 1.

[0055] In step S5, an index m is initialized to 1. In step S6, the parameters pk(i), ak(ij, qk(ij, Qk(i), «k(i)j, Pk(i) of the set u(i) of the model are estimated for a first iteration (1).

[0056] Generally speaking, the parameters u of the model can be estimated in several iterations of the expectation-maximization algorithm EM ("Expectation-Maxhnization"), or ECM ("Expectation Conditional Maxhnization") which is a generalization of the EM algorithm. At each iteration m of the algorithm, estimates tijk(m) and si>k(m) are calculated (in step S7) using the following expressions:

[0057]

[0058] ak(m)%¾(5) fk(m)

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] with Fk(m)(ci,qk(m),ek(m)hk(m)) ak^myfg(Ci,qk^m^,lik^m^)+(l ak^m0*fg(Ci,qk^m^,ek^m^hk^m^). The estimate tijk(m) represents the posterior probability evaluated at iteration m that measurement i belongs to group k, and the estimate sijk(i) represents the probability evaluated at iteration m that measurement i is normal, in group k. In the space generated by the eigenfunctions, the first dk variance components of group k can be modeled precisely by the first dk eigenvalues. Thus, the first dk eigenvalues ​​correspond to the main part of the variability of the data. The last B-dk components are considered as noise components and modeled in a parsimonious way by a single parameter [3k. In this way, the covariance matrix of group k in the eigenspace can be represented by the following matrix: Ak= / «kï V «k2 0 «kdk 0 i (6) 0 in which W is the matrix containing the scalar products between the functions f(-) and Qk (= lqk,i, l <r et 1<B) est une matrice orthogonale de dimension B x B rassemblant les coefficients des fonctions propres du groupe homogène, ces coefficients étant obtenus à partir de l’analyse en composantes principales fonctionnelles multivariée, Iq ki représente la colonne 1 de la matrice Qk et QT représente la matrice transposée de Qk. ^k The estimation of the parameter ek depends on that of the parameters qk and hk and vice versa. All the parameters u of the model are estimated by the ECM algorithm, the parameter ek being estimated following the estimation of the other parameters of the model. Thus, at the step S6 of conditional maximization, the parameters pk, ak> qk, Qk , ak, [3k can be estimated for the iteration m (m=l) using a multivariate functional principal component analysis, allowing to define a functional subspace (SEk) of the functional space defined by the basic functions. For this purpose, the following equations are used: X1- œ Pk(m“ n (8)

[0067] £ CïhkimA.k(m)Xl-W^ (9) q ——uj------------------ jti.ktmi ( 1 ■Si.ktmiyeklmj )

[0068] in which the estimates tijk(m) and si>k(m) are those initialized in step S4. To estimate the variance parameters Qk, ak, pk, we consider the covariance matrix for group k, as follows:

[0069] _ i / y11 f , / 1 td „ \Tf„ \ \ (10)

[0070] with Vn t ®k(m) “i=j 'klm)

[0071] The first dk columns of the covariance matrix Qk(m) are estimated using the coefficients of the eigenfunctions associated with the largest eigenvalues ​​of W1 / 2HlkW1 / 2-

[0072] The parameters ak(m) are estimated by the dk largest eigenvalues ​​Ip lk,i(m) of the matrix W1 / 2HlkW1 / 2, with lplkj(m) = Iq^ p»Vi / 2HlkWl / 2lqk} and i represents column 1 of the matrix Qk.

[0073] The parameter [3k(m) is estimated using the following equation:

[0074] Pu) = bV [tr(W1 / 2HlkWi / 2)-ydk Ip L] (1 rk(m) B-dk vk ' * M(m)

[0075] in which tr(X) represents the trace of the matrix X.

[0076] Each homogeneous group k is thus associated with a matrix variance in the functional space defined by the eigenfunctions. The variance of the model is modeled parsimoniously by elements formed from the largest eigenvalues ​​ak>j and elements considered as noise and all equal to the parameter [3k of the model.

[0077] In step S7, the estimates tijk(m+i) and sijk(m+i) are calculated using equations (4) and (5), for the next iteration, using the values ​​of the parameters pk(m), ak(m), qk(m), Qk(m), otk(m), Pk(m) determined previously (step S6 or S8). In step S8, the parameters pk(m+i), ak(m+1), qk(m+i), Qk(m+i), ak(m+1), |3k(m+i) of the next iteration are determined using the estimates tijk(m+i) and sijk(m+i) calculated in step S7 by performing the same calculations as in step S6.

[0078] In step S9 of the second conditional maximization, the parameter ek(m+i) representing the inflation factor is estimated by the following equation:

[0079] ek(m+l) = MAX {1, Ek(m+i)} (12)

[0080] in which:

[0081] Ek(m) = ' (13) B(nlk <mrn2klm>)

[0082] n )~J^n 7: k( ) is the number of measurement signals xijk belonging to the group k and n2k z- k( 'Y- is the number of measurement signals xi>k not presenting of anomaly in group k.

[0083] Step S11 is executed only if in step S10, the index m is greater than 1, then steps S12 and S13 are executed. In step S11, an error variable ERR is calculated using the following equation:

[0084] ERR = lc(m+l) - lc(m) (14)

[0085]

[0086]

[0087]

[0088]

[0089] in which: lc« 4LLh(nkimrnk",mk)loë <ek^ (15) -^log^rc) lp2k,i(m) = ]qT WI / 2H2. W1 / 21q ' with lQk.1 representing column 1 of the matrix Qk 'kl *c ^k,l , And

[0090] i / v*n / \ T / \ \ (16)

[0091] represents the empirical covariance matrix of group k.

[0092] In step S12, the index m is incremented by one. In step S13, if the index m is less than the maximum number of iterations Mx and the variable ERR is greater than the maximum error value e, then the processing unit CU executes an additional iteration from step S7. Otherwise, the processing unit CU provides as results of the algorithm the estimates tijk(m+i) and sijk(m+i), k = 1, ..., K, calculated during the last execution of step S6 and which designate the correct measurements xi>k and the erroneous measurements (step S14).

[0093] The use of the algorithm described above can be extremely costly in terms of computing time and memory required, particularly when the number of data from the measurements increases. However, in an industrial context, it is desirable to limit the computing power and memory required.

[0094] According to one embodiment, the calculation of the tijk and sijk estimates is simplified by considering only the coefficients of the eigenfunctions having a non-negligible impact on the results and by using a projection operator.

[0095] Each probability tijk(m+i) is obtained by calculating the ratio between a contaminated Gaussian density of the homogeneous group and a sum of the contaminated Gaussian densities of all the homogeneous groups, taking into account the coefficients c;. The contaminated Gaussian density of each of the homogeneous groups k can be calculated by the weighted sum of a first Gaussian density of each of the normal signals and a second Gaussian density of each of the abnormal signals in each homogeneous group k. A covariance matrix of the Gaussian density of the abnormal signals is equal to a covariance matrix of the Gaussian density of the normal signals multiplied by the inflation factor ek. Each of the first and second Gaussian densities can be calculated by the sum of a norm of projection of the coefficients of the model in a functional subspace SEk defined for the homogeneous group k, a norm of a difference between the coefficients and the projection of the coefficients in the functional subspace defined for the homogeneous group k and a term depending on the eigenvalues ​​of the covariance matrix.

[0096] Each probability si>k is equal to the ratio between the Gaussian density of the normal signals of the homogeneous group and the contaminated Gaussian density of the homogeneous group, both being calculated with the coefficients (cO.

[0097] Indeed, it can be demonstrated that the calculation of the function fg(c;,qk,ekjhk)] implemented to calculate the estimates ti>k and si>k (equations (4) and (5)), can be simplified as follows: 100981 fg(c i ,c] k ,e t ,h k ) = exp(J [BJog(2n) a u )+(Bd k )log(p k )

[0099]

[0100] + ^||wl / 2(c._qk).p(Wl / 2(c..qJ^

[0101] in which P represents the projection operator on the subspace SEk which is generated by the first dk columns of the matrix Qk: P(x) = q qtx, || x || 2 =xT.Dk .x, Dk = q Q is the matrix B x B containing the first dk components of k. kk Qk completed by zeros, Q — Q -Q , Ak is the diagonal matrix containing the eigenvalues ​​akb ak2, ..., akdk,bk, presented by equation (6), and det(W) is the determinant of the matrix W. The expression of Ekindicated by equation (13) can also be rewritten as follows:

[0102] Ek = u J | ||p(W^(Ci-qt)) ||^ llW'^q-qj-Pjw'^-qj ) ||2] (18> B(nlk-n2k)

[0103] According to one embodiment, illustrated by steps S21 to S27 of figure 6, the parameters of the model {u(n), tijk(n), sijk(n)} calculated for example using the algorithm of figure 5, can be updated at each new acquisition of a set of measurements x*. For this purpose, a set of thresholds thk, k = 1, ..., K, comprising a threshold thk per group k, is defined. The thresholds thk make it possible to determine whether or not the modeling of the new measurements requires the addition of new basic functions and therefore new dimensions to the functional subspaces SEk. The parameters pk(n+n*), ak(n+n*), qk(n+n*), Qk(n+n*), (A(n+n*), J3k(n+n*),^k(n+n*),ti,k(n+n*), Lkui+rrj of the pCUVCUt CtTC model updated in an iteration, the probability t*i>k that one of the new weighing signals x*; belongs to a homogeneous group of weighing signals and the probability s*i>k that one of the new weighing signals has an anomaly, being estimated using the projection operators to project the new coefficients into the functional subspaces SEk defined from the previously calculated model parameters pk(m+l), ^k(m+l), Qk(m+1 )» Qk(m+1), ^k(m+l),j, [>k(m+l ).tk(m+l ), A .k< m+1).

[0104] Thus, in step S21, the processing unit CU acquires a set of n* measurements x* , i=1, ..., n*. In step S22, the processing unit CU determines the basic coefficients C? for the measurement signals xj" acquired, taking into account the chosen basic functions fj>b. During step S23 of conditional maximization carried out for each group k = 1, ..., K, the estimates ti>k* and si>k* are evaluated using equations (4) and (5) applied to the parameters of the model u(n) determined previously. During step S23, the processing unit CU also calculates an accumulation ratio ac using the following equation:

[0105] <w> ac =-—--— --:-— --S—:--------

[0106] with: [°107] wt- k ( S k+( 1 -¾ k ) / ek( )) representing a weight associated with the previous model (before step S23), associated with group k,

[0108] n* / „* * j / e ) representing a weight associated with group k, calculated in k । hk \ •'i.Vk •Vk / - kz taking into account the new measures x*, and

[0109] c't*kissj +( ! -s\) / ek) representing the average of the measurements of group k, including ....-..1.:.2:...2:2.,.......2..— k E^CkKkHHkM) the new measures.

[0110] In step S24, the processing unit CU compares the accumulation ratio ac with the thresholds thk. For each group k, if the accumulation ratio ac is greater than the threshold thk, the parameters of the model u(m+n*) are calculated in step S25, otherwise they are calculated in step S26.

[0111] The parameterized pk(n+n*k ^k(n+n*), qkui+rr ^ Qk(n+n*k C[k(n+n*), f^k(n+n*),^k(n+n*),ti,k(n+n*)î Akui+irj updated from the model include for each homogeneous group (k):

[0112] a parameter pk(n+n*) representing a proportion of previous and new weighing signals xi>i-xi>px*i>ix*i>p belonging to the homogeneous group, and calculated by a weighted average of the corresponding previous parameter (pk(m)) and a number of new signals belonging to the homogeneous group,

[0113] a parameter ak(n+n*) representing a proportion of previous and new normal weighing signals in the homogeneous group, and calculated by a weighted average of the corresponding previous parameter ak(n) and the number of new normal signals belonging to the homogeneous group,

[0114] a parameter qk(n+n*) representing an average of the previous and new weighing signals of a Gaussian distribution of the homogeneous group, and calculated by a weighted average of the corresponding previous parameter (qk(n)) and an average of the new signals belonging to the homogeneous group,

[0115] a matrix Qk(n+n*) of vectors formed by coefficients of eigenfunctions, the matrix being estimated by a multiplication of a rotation matrix by the previous matrix Qk(n) if the new weighing signals are well represented in the functional subspace, or otherwise estimated by a multiplication of the rotation matrix by a matrix consisting of a concatenation of the corresponding previous matrix and a matrix consisting of projection errors of the new coefficients in the functional subspace,

[0116] a matrix variance [akj(n+n*), [3k(n+n*)] having the form of a diagonal matrix gathering new eigenvalues ​​akj(n+n*) of the homogeneous group, obtained from the previous matrix variance, the previous vector matrix Qk(n), the new coefficients Ci* and the average of the normal weighing signals, and the elements [3k(n+n*) obtained from an average value of the difference between the sum of the elements of the previous matrix variance [akjj(n), [3k(n)] and the sum of the new eigenvalues ​​akj(n+n*), and

[0117] a parameter ek representing an inflation factor of the covariance matrix of the homogeneous group, calculated by a weighted average of the corresponding previous parameter ek(n) and an inflation factor of the new weighing signals calculated from projection operators.

[0118] Thus, in steps S25 and S26, the parameters pk(n+n*), ak(n+n*), qk(n+n*) of the set of parameters Ukn+n*j {Pk(n+n*)? ^Hn+rrj, qkui+rr ^ Ctk(n+n*)? f^kui+rr ^ Qk(n+n*) / k 1, ..., K] SOttt estimated using the following equations: [0H9] Pk(n+n*) n+n*

[0120] (21) ak(n+n*)— ,k4n;

[0121] (22) ^k(n+n*) wk(n)+w^

[0122] with n _yn t representing the number of previous measurements belonging to the Uk-Li=ilhk group k, * _ vn* representing the number of new measures added to the nk " Li=1l>4 group k.

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140] The covariance matrix Qk(n+n*) can be estimated by considering that it results from a rotation Rk of a matrix consisting of a concatenation of the covariance matrix previous variance Qk(n) and a matrix Hk, according to the following equation: Qk(n+n*) = [Qk(n), H3k]Rk (23) in which H3k = ​​[hk k hk hk,ikL with 1 k nk, lk being the number of dimensions added to group k, nk being the number of measures of the n* new measures added to group k, and H. .—_22_» with 1 < j < lk, and hk r* r. j (Qk(n))(Qk(n)yL." _ n Y Ilk J~ iimi lmh qk(nj ) k,k^i qk(n); If the accumulation ratio ac is less than the threshold thk (step S25), then the parameters ak(n+n*), |3k(n+n*), Qk(n+n*) of the parameter set u(n+n*) are estimated as follows: «kj(n+n*) ~ ^k,j(n+n*), j = 1, dk (24) Ln-Hr. = [tr(Ak(n))+(p- <lk) Pk(n) ’ tr(Ak(n+n^)] <25> in which akj(n+n*) is the jth eigenvalue of the matrix Ak(n+n*) (cf. equation (6)), and lk is the number of p-dimensional vectors that are added to the previous dk vectors of group k to avoid loss of information, and lk also represents the number of eigenfunctions added to group k. The RK rotation is defined by the matrix of eigenvectors obtained by decomposing the following matrix into eigenvalues: n k(n) / Ak(n ) d A°\ / glgl T glg2 T \ dk,dk0 / g2g2Tj ïi' "z Th "ào En' v3^4t i , (nw«M+wt( / L T1 H Ira 4^ ___ wk2+2w, ,wï £n g5.g6T^ (26) V* n* in which: gl=(W'% n / (q--q k(n ,)' g2=(W 1 / 2 H3 k ) T (q*-q k(ii) )-g3.=<(ï4(î<^ g5.=jt' k ( Skk +(l-s' k ) / e k ) (W lp -Q k(n / ( c'-q* ) 101411 (W' / 2 H3 t ) T ( <-q* )

[0142] If the accumulation ratio ac is greater than or equal to the threshold thk (step S26), then no new dimension is added, and the parameters ak(n+n*), [3k(n+n*h Qk(n+n*) of the parameter set u(n+n*) are estimated as follows:

[0143] «k,j(n+n*) ~ ^k,j(n+n*), j = 1, ..., dk (27)

[0144] = FA [tr(Ak(n))+(pA)^ (28)

[0145] The RK rotation is then defined by the matrix of eigenvectors obtained by decomposing the following matrix into eigenvalues:

[0146] UklD) ।__A Ainï < i T nW+nk k(n) (üktn^X^+W^^ 101471 H_____ïL____y”' S 3 g3T + .......ÎAj........y"' g5 “5t (29)

[0148] The second conditional maximization step S27 is executed following one or other of the steps S25 and S26. During the step S27 performed for each group k = 1, ..K, the parameter ek(n+n*) is calculated using the following equation: 101491

[0150] with:

[0151] ~ Am n -r . L ■ rw* ... ... \ (31)

[0152] tfk and stfk being those calculated in step S23, and tj,k(n) and S1'kW being the values estimated before executing the procedure in Figure 6.

[0153] In the application to the weighing of a vehicle, the vehicle moving forward on the weighbridge 1, each axle of the vehicle simultaneously requests the pair of input sensors (Cl, C2), then the pair of output sensors (C3, C4). The signals from the sensors of each pair Cl, C2), (C3, C4), are therefore strongly correlated. Similarly, each wheel of the vehicle moving forward on the bridge 1 will successively request the sensors Cl and C3 or C2 and C4, on the same side of the bridge 1, with a time lag Dt = D / V, D being the distance between the sensors Cl and C3 or C2 and C4, and V being the speed of movement of the vehicle on the bridge 1. The signals from the pairs of sensors (Cl, C3) and (C2, C4) are also strongly correlated, to within time Dt. As a result, compared to an application where the signals to be processed are completely uncorrelated with each other, the number of basis functions f for modeling the signals from sensors C1-C4 are necessarily smaller.The same is true for the number K of groups, which implies a reduction in the number of iterations in the calculations described previously.

[0154] It will be clear to those skilled in the art that the present invention is susceptible to various variant embodiments and various applications. In particular, the invention is not limited to a weighbridge comprising only one pair of input sensors C1, C2 and one pair of output sensors C3, C4. Indeed, a bridge may comprise more than 4 sensors. In the example of figures 7 and 8, the weighbridge comprises eight sensors C1-C8. Sensors C5 and C7 are aligned with sensors C1 and C3 along one transverse edge of the bridge 1, and sensors C6 and C8 are aligned with sensors C2 and C4 along the other transverse edge of the bridge. Sensors C5, C6, C7, C8 are called intermediate sensors. Note that the number of sensors on a weighbridge is not theoretically limited and it is not necessary for the number of sensors on each side of the bridge to be identical.It is also not necessary for the sensors to be aligned exclusively on the transverse sides. It can therefore be planned to align sensors along the longitudinal axis X of the weighbridge.

[0155] According to one embodiment, the input sensors C1, C2 are aligned along a transverse axis Y1 perpendicular to the longitudinal direction X of crossing of the bridge 1. Similarly, the output sensors C3, C4 are aligned along a transverse axis Y2 perpendicular to the longitudinal direction X.

[0156] In the embodiment illustrated by figures 7 and 8, the sensors C5 and C6 on the one hand and on the other hand, the sensors C7 and C8 can be aligned in directions parallel to the axes Y1 and Y2.

[0157] Furthermore, the invention is not limited to a particular method of calculating the weight of the vehicle from the signals xi(t) provided by the sensors Ci. For safety reasons, for example, the weight of each axle of the vehicle can also be estimated and controlled separately by identifying the passage of each wheel of the vehicle in the signals xi(t) from the sensors Ci, by calculating an average value of the maximum values ​​of the signals xi from the sensors Ci for each wheel, and by adding the average values ​​for each wheel.

[0158] In the case of a railway vehicle, the lateral position of which is determined by the guidance of the rails, the right / left balancing values ​​of the vehicle can also be measured by this same method.

[0159] Documents cited

[0160] 1. “Outlier Detection in Multivariate Functional Data Through a Contaminated Mixture Model", M. Amovin-Assagba, I. Gannaz, J. Jacques, Computational Statistics and Data Analysis, 174:107496 (2022),< / w>

Claims

Claims

1. 1. A method of weighing a wheeled vehicle, comprising steps consisting of: moving the vehicle onto a weighbridge (1) so that a first set of wheels of the vehicle simultaneously requests input sensors (C1, C2) of the weighbridge, then simultaneously output sensors (C3, C4) of the weighbridge; acquiring and sampling, by a processing unit (CU), weighing signals (Xi,i-Xi,p) from the input and output sensors, while the vehicle crosses the weighbridge; and executing by the processing unit a plurality of iterations (m) of an expectation-maximization algorithm, each iteration comprising the calculation of parameters (pk(m+i), ak(m+i), qk(m+i)» Qk(m+i)» ^k(m+i),j, [>k <m+1),ek(m+1)) d’un modèle à l’aide d’une analyse en composantes principales fonctionnelles multivariée, et le calcul d’estimations de probabilités (tijk(m+i), sijk(m+i)), le modèle étant basé sur une approximation de chacun des signaux de pesée par une combinaison linéaire de fonctions de base de type carré intégrable pondérées par des coefficients (Cj), les estimations de probabilités calculées du modèle comprenant pour chaque signal de pesée une probabilité (tijk(m+i)) que le signal de pesée appartienne à un groupe homogène (k) de signaux de pesée donné parmi plusieurs groupes homogènes, et une probabilité (si> k(m+i)) that the weighing signal has an anomaly, in which the probability estimates (tijk,sijk) are estimated by considering only coefficients of eigenfunctions having an impact greater than a threshold value on the results and by using an operator for projection of the model coefficients into functional subspaces (SEk), each functional subspace being defined for a respective homogeneous group of the homogeneous groups.

2. 2. The method of claim 1, wherein each iteration (m) of the plurality of iterations is based on the execution of an expectation-maximization algorithm comprising: an expectation step comprising the calculation of probability estimates (ti>k, si>k,), a first maximization step comprising the calculation of parameter estimates (pk(m), ak(m), qk(m), Qk(m), «kj, fk) of the model using a multivariate functional principal component analysis, allowing to define for each homogeneous group (k) a matrix variance in a functional subspace (SEk) defined by eigenfunctions, the matrix variance being modeled in a parsimonious manner by elements formed of larger eigenvalues ​​(akj) of the homogeneous group and elements considered as noise and all equal to one of the parameters (|3k) of the model, and a second maximization step including the calculation of an inflation factor (ek).

3. 3. Method according to one of claims 1 to 2, in which: each probability (tijk(m+i)) that one of the weighing signals belongs to one of the homogeneous groups (k) is obtained by calculating the ratio between a contaminated Gaussian density of the homogeneous group and a sum of the contaminated Gaussian densities of all the homogeneous groups, taking into account the coefficients (c;), the contaminated Gaussian density of each of the homogeneous groups being calculated by the weighted sum of a first Gaussian density of each of the normal signals and a second Gaussian density of each of the abnormal signals in each homogeneous group, a covariance matrix of the Gaussian density of the abnormal signals being equal to a covariance matrix of the Gaussian density of the normal signals multiplied by an inflation factor (ek), each of the first and second Gaussian densities being calculated by the sum of a projection norm of the coefficients of the model in a functional subspace (SEk) defined for the homogeneous group,of a norm of a difference between the coefficients and the projection of the coefficients in the functional subspace defined for the homogeneous group and a term depending on eigenvalues ​​of the covariance matrix, and, each probability (si>k) that one of the weighing signals of one of the homogeneous groups (k) presents an anomaly is equal to the ratio between the Gaussian density of the normal signals of the homogeneous group and the contaminated Gaussian density of the homogeneous group, both being calculated with the coefficients (Cj).,

4. 4. Method according to one of claims 1 to 3, comprising a step initialization of the parameters (pk(m), ak(m), qk(m), Qk(m), ak(m)>j, [3k(m)»ek(m)) and probability estimates (tijk(m), sijk(m)) of the model, randomly or using algorithms based on minimization of a sum calculated for each homogeneous group (k) of distances between each coefficient (c;) and a centroid of the group homogeneous.

5. 5. Method according to one of claims 1 to 4, in which a new iteration is executed if an error variable (ERR) relating to the calculated parameters (pk(m+i), ak(m+i), qk(m+i)» Qk(m+i), ^k(m+i), [Ktm+i^c^m+i J and the probability estimates (ti>k(m+i), sijk(m+i)) is greater than a threshold value (e) and if a maximum number of iterations (MX) is not reached.

6. 6. Method according to one of claims 1 to 5, in which the calculations of the model comprise for each homogeneous group (k) of weighing signals: a parameter (pk) representing a proportion of weighing signals (xi rx ijP) belonging to the homogeneous group, a parameter (ak) representing a proportion of normal weighing signals in the homogeneous group, a parameter (qk) representing a mean of a Gaussian distribution of the homogeneous group, a matrix (Qk) gathering coefficients of a set of eigenfunctions of the homogeneous group, the coefficients of the eigenfunctions being obtained from the multivariate functional principal component analysis, and a matrix variance (akj, Pk) having the form of a diagonal matrix gathering eigenvalues ​​of the homogeneous group, obtained from a multivariate functional principal component analysis,the matrix variance comprising first largest values ​​(akjj ) of the eigenvalues ​​and elements equal to an average value (|3k) of the smallest values ​​of the eigenvalues, and a parameter (ek) representing an inflation factor of the covariance matrix of the homogeneous group, calculated using projection operators.,

7. 7. Method according to one of claims 1 to 6, comprising steps of acquiring new weighing signals (xi*), calculating new coefficients (c*;) obtained by approximating each of the new weighing signals by a linear combination of the basic functions weighted by new coefficients (c*;), and updating parameterized S (pkni+rrh ^k(n+n*), qk(n+n*), Qk(n+n*), ^kui+rr:b J)k(n+n*),^k(n+n*)) Ct of the probability estimates (tijk(n+n*), Sijk(n+n*)) of the model in one iteration, the probability (t*ijk) that one of the new weighing signals (x*j) belongs to a homogeneous group of weighing signals and the probability (s*i>k) that one of the new weighing signals has an anomaly, being estimated using projection operators to project the new coefficients into the functional subspaces (SEk) defined from previously calculated model parameters (Pk(m+1), ^k(m+l), qk(m+l), Qk(m+1), ^k(m+l),j, ^k(m+l),^k(m+l))*

8. The method of claim 7, wherein the updated parameters (pk(n+n*), ak(n+n*), qk(n+n*), Qk(n+n*), ^k(n+n*), ^k(n+n*),^k(n+n*),ti,k(n+n*)î ^i.kui+rrj) of the model comprise for each homogeneous group (k): a parameter (pk(n+n*)) representing a proportion of previous and new weighing signals (xi>i-xi>px*i>ix*i>p) belonging to the homogeneous group, and calculated by a weighted average of a corresponding previous parameter (pk(n)) and a number of new signals belonging to the homogeneous group, a parameter (ak(n+n*)) representing a proportion of previous and new normal weighing signals in the homogeneous group, and calculated by a weighted average of a corresponding previous parameter (ak(n)) and the number of new normal signals belonging to the homogeneous group, a parameter (qk(n+n*)) representing an average of the previous and new weighing signals of a Gaussian distribution of the homogeneous group,and calculated by a weighted average of a corresponding previous parameter (qk(n)) and an average of the new signals belonging to the homogeneous group, a matrix (Qk(n+n*)) of vectors formed by coefficients of eigenfunctions, the matrix being estimated by a multiplication of a rotation matrix by a corresponding previous matrix (Qk(n)) if the new weighing signals are represented in the functional subspace (SEk), or otherwise estimated by a multiplication of the rotation matrix by a matrix consisting of a concatenation of the corresponding previous matrix and a matrix consisting of projection errors of the new coefficients in the functional subspace, a matrix variance (akj(n+n*), |3k(n+n*)) having the form of a diagonal matrix gathering new eigenvalues ​​(akj(n+n*)) of the homogeneous group, obtained from a previous matrix variance, of the previous vector matrix (Qk(n)),new coefficients (c;*) and the average of the normal weighing signals, and elements (|3k(n+n*)) obtained from an average value of the difference between the sum, elements of the previous matrix variance (akj(n), |3k(n)) and the sum of the new eigenvalues ​​(akj(n+n*)), and a parameter (ek) representing an inflation factor of the covariance matrix of the homogeneous group, calculated by a weighted average of a corresponding previous parameter (ek(n)) and an inflation factor of the new weighing signals calculated from projection operators.

9. 9. Method according to one of claims 1 to 8, comprising steps of acquisition and sampling, by the processing unit (CU) of weighing signals (x^-x^) from intermediate sensors (C5-C8) installed on the weighbridge (1) between the input and output sensors (C1-C4).

10. 10. A system for weighing a wheeled vehicle, comprising: a weighbridge (1) comprising input sensors arranged to be acted upon simultaneously by a first set of wheels of the vehicle, and output sensors arranged to be acted upon simultaneously by the first set of wheels of the vehicle, when the vehicle crosses the weighbridge, a processing unit (CU) configured to acquire and sample weighing signals (Xi,i-Xi,p) from the input and output sensors and execute a plurality of iterations (m) for calculating parameters (pk(m+i), ak(m+i), Qk(m+i)» Qk(m+i)» c^k(m+i)» ^k(m+i)^k(m+ij) and probability estimates (tijk(m+i), sijk(m+i)) of a model, in accordance with the method according to one of claims 1 to 10.

9.

11. 11. System according to claim 10, wherein the sensors (Cl, C3 - C2, C4) are aligned along lateral edges of the weighbridge (1).

12. 12. System according to claim 10 or 11, comprising at least three sensors (C1, C3, C5, C7) aligned along a lateral edge of the weighbridge (1).

13. 13. System according to one of claims 10 to 12, in which the sensors (C1-C4, C1-C8) are arranged so as to be aligned along axes (Yl, Y2) perpendicular to a longitudinal direction (X) of the weighbridge (1).

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