Detection of electric arcs in an electrical circuit of an aeronautical system by a gaussian mixture model

Abstract

The invention relates to a method for detecting electric arcs in an electrical circuit of an aeronautical system, the method being implemented by computer and comprising: - a first phase (P1) of learning a model of the behaviour of an electric current on a line (3') of a learning electrical circuit, which phase comprises discovering (42) patterns in the behaviour of the current, and determining (45) the model on the basis of first values of descriptors; and - a second diagnosis phase (P2), which comprises calculating (44') second values of the descriptors for an electric current on a line (3) of the electrical circuit, calculating a distance (46) between the model and these second values, and detecting (47) an electric arc if the distance is greater than a predetermined threshold.

Description

DESCRIPTION TITLE: Detection of electrical arcs in an electrical circuit of an aeronautical system using a Gaussian mixture model TECHNICAL FIELD

[0001] The present invention relates to the detection of faulty electrical arcs on an electrical line and is particularly applicable to the field of aeronautics and embedded systems.

[0002] An electric arc is a self-sustaining discharge with a high current.

[0003] Two types of electrical arcs can occur in an aeronautical environment: breaking arcs, present in contactors when a circuit is opened or closed, and fault arcs, which can appear unexpectedly on any component of the electrical system. The latter can cause severe damage to equipment, systems, and even the aircraft structure. This is therefore a critical point of vigilance.

[0004] Furthermore, fault arcs can be of two types depending on their position on the electrical circuit: parallel arcs and series arcs.

[0005] In current aircraft systems, these problems are partly resolved, or mitigated, by several factors: The distributed voltage levels are generally at most 230 V to 400 V, which reduces the impact of electric arcs; The distribution of an alternating (AC) waveform also helps to promote the self-extinction of the arc at each half-period, when the voltage passes through 0; In continuous mode, voltage levels are generally lower, on the order of 28 V; Passive protections can be used to limit the consequences of potential fault arcs: choice of materials resistant to these phenomena, distancing of the different elements, etc.; Finally, active protection measures can also be implemented, such as arc detection and line opening mechanisms that activate when an arc is detected. Current active protection systems can detect most parallel arcs, but not series arcs, for which no active protection is currently deployed.

[0006] However, recent work on aircraft electrification suggests a distribution of direct current (DC) waveforms with high voltage levels, potentially reaching kilovolts. This paradigm shift obviously calls into question the passive protection strategy mentioned earlier.

[0007] Indeed, climate change is a major concern for many legislative and regulatory bodies worldwide. Various restrictions on carbon emissions have been, are being, or will be adopted by different countries. In particular, an ambitious standard applies to both new types of aircraft and those already in service, requiring the implementation of technological solutions to bring them into compliance with current regulations. Civil aviation has been actively working for several years now to contribute to the fight against climate change.

[0008] Technological research efforts have already led to significant improvements in the environmental performance of aircraft. The Applicant takes into account factors impacting all phases of design and development to obtain aeronautical components and products that are less energy-intensive, more environmentally friendly, and whose integration and use in civil aviation have moderate environmental impacts, with the aim of improving aircraft energy efficiency. Consequently, the Applicant is continuously working to reduce its climate impact by employing methods and operating virtuous development and manufacturing processes that minimize greenhouse gas emissions in order to reduce the environmental footprint of its business.

[0009] This research and development work therefore focuses on new generations of aircraft engines, the weight reduction of aircraft, particularly through the materials used and lighter onboard equipment, and biofuels. aeronautics and the development of the use of electrical technologies to provide propulsion.

[0010] Thus, in the context of increasing voltage and electrical power levels in aircraft networks, the series electrical arc must also be taken into account, just like the parallel arc, because the damage associated with the generation of higher power faults subjected to a continuous voltage risks damaging the aircraft and its on-board systems, and could even impact the safety of passengers and crew.

[0011] There are several proposals for detecting an electrical arc on a power line in order to isolate it (by cutting the circuit). However, these proposals must comply with certain constraints: Reliability: dangerous electrical phenomena must be detectable systematically and under all circumstances. In other words, a high true positive rate, close to 100%, is required. Robustness: the active protection mechanism must be immune to any event other than the one for which it was designed. In other words, the false positive rate must be as low as possible, i.e., close to 0%.

[0012] So far, these proposals show shortcomings either in terms of reliability or in terms of robustness.

[0013] For example, patent application EP3959525 proposes arc detection by combining two typical behaviors: a high scanning speed at the onset of the arc and a high-frequency behavior. This proposal can therefore detect electric arcs, but it can also mistake normal behaviors related to the connected load and the power line for electric arcs. Consequently, the false positive rate is high.

[0014] The same applies to patent application WO202143027, which describes a machine learning-based method. Application US20040156154 proposes another method but does not allow for the isolation of all nominal behavior, including all types of electrical faults. DESCRIPTION OF THE INVENTION

[0015] Therefore, there is a need to improve current state-of-the-art proposals.

[0016] The invention aims, in particular, to improve the performance of arc fault detection on a power line. Specifically, it allows these arc faults to be distinguished from transient phenomena related to the load, and thus significantly improves the false positive rate. In other words, the invention makes it possible to greatly increase the true positive rate and also greatly decrease the false positive rate.

[0017] According to a first aspect, the present invention can be implemented by a method for detecting electric arcs in an electrical circuit of an aeronautical system, the method being implemented by computer and comprising: a first phase of learning a model of the behavior of an electric current on a training electric line of a training electric circuit approximating said electric circuit, including the discovery of patterns in the behavior of said current, and the determination of said model from first values ​​of descriptors calculated on said patterns, and, a second diagnostic phase comprising a calculation of second values ​​of said descriptors for an electric current on an electric line of said electrical circuit, over a time window, a calculation of a distance between said model and said second values, and a detection of an electric arc if said distance is greater than a predetermined threshold.

[0018] According to preferred embodiments, the invention comprises one or more of the following features, which can be used separately, in partial combination, or in total combination: said model is determined by iterative steps of Project said patterns into the space of said descriptors, Determine a Gaussian mixture model delimiting the set of said patterns in said space, Estimate a relevance score for said descriptors for said model, Remove the descriptor corresponding to the lowest relevance score, Until a satisfactory model is obtained on a second set of patterns, said model being satisfactory if said relevance score is greater than a second predetermined threshold. said Gaussian mixture model is a proportion-weighted sum of Gaussian distributions, the number of which is determined by minimizing a Bayesian information criterion, each distribution being characterized by a mean value and a variance-covariance matrix, said mean values, said variance-covariance matrices, and proportions being preferably determined by an expectation-maximization algorithm. said descriptors include statistical moments, a frequency content, and an entropy of said patterns.said first phase includes a step of acquiring measurement data relating to said electric current, and of storing said measurement data to form a time series, as well as a step of recognizing patterns within said time series of measurements.

[0019] Another aspect of the invention relates to a computer program comprising instructions for implementing a process as previously described when executed on an information processing platform.

[0020] Another aspect of the invention relates to a device for detecting electric arcs in an electrical circuit of an aeronautical system, comprising a predetermined model of the behavior of the electric current on said power line and further comprising a functional module for calculating descriptor values ​​for an electric current on said power line over a time window, a module functional calculation of a distance between said model and said values, and a functional module for detecting an electric arc if said distance is greater than a threshold.

[0021] Another aspect of the invention relates to a device for learning a model of the behavior of an electric current for the detection of electric arcs in an electric line of an electrical circuit of an aeronautical system, comprising a functional model for discovering patterns in the behavior of said electric current on a training electric line of a training electrical circuit approximating said electrical circuit, a functional module for calculating descriptor values ​​on said patterns, and a functional module for determining said model from said descriptor values.

[0022] Another aspect of the invention relates to an aircraft comprising at least one detection device.

[0023] Another aspect of the invention relates to a system comprising a detection device and a learning device as previously described.

[0024] According to preferred embodiments, this device may include one or more of the previously mentioned features in relation to the process, which may be used separately or in partial or total combination with each other.

[0025] Other features and advantages of the invention will become apparent from the following description of a preferred embodiment of the invention, given by way of example and with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The attached drawings illustrate examples of the invention: Figures aa and lb schematically illustrate a functional architecture enabling the implementation of a detection device according to two embodiments of the invention. Figure 2 illustrates a high-level functional architecture enabling the implementation of a process according to an embodiment of the invention. Figures 3a and 3b represent two examples of electric current behavior in the supervised power line. Figure 4 represents a flowchart for a possible embodiment of a step in determining a model of current behavior. Figure 5 illustrates a pattern projection step in a descriptor space, according to one embodiment of the invention. DETAILED DESCRIPTION OF SPECIFIC METHODS OF IMPLEMENTATION

[0027] The proposed process is based on two distinct phases: a learning phase PI (or training, the two terms being equivalent) and an exploitation phase P2.

[0028] The PI learning phase aims to determine a model capable of representing the nominal behavior of the electric current. This nominal behavior excludes any possible fault, such as a fault arc. It therefore represents the desired, ideal behavior of the electric current flowing through the monitored electrical circuit.

[0029] The purpose of the P2 diagnostic phase is to determine any deviation in the behavior of the measured electrical current of this model.

[0030] In particular, it allows us to discriminate between normal electrical artifacts corresponding to normal variations in electrical charges (i.e., electrical noise) and artifacts corresponding to faulty electrical arcs that are problematic for the condition of the electrical circuit, the components connected to it, or even for the aircraft.

[0031] This allows us to improve the detection rate of fault arcs (true positive rate) but also to considerably reduce the false positive rate.

[0032] Furthermore, the proposed method, along with the associated detection device 4, learns the behavior of the power line without making any presuppositions. It consists, in effect, of determining all the recurring patterns occurring on the power line over time, so that the specific characteristics of the line (particularly its combination of electrical loads) can be taken into account. Therefore, it is not necessary to provide specific or parameterized identification mechanisms based on the type of line, or a type of load, etc. On the contrary, the process relies on a self-discovery mechanism.

[0033] These two phases, Pl, P2 can follow each other in time, the exploitation and diagnostic phase following the learning phase.

[0034] The PI learning phase is preferably carried out in a laboratory, with a data acquisition system as close as possible to the reality of the actual system being monitored. In other words, for the PI learning phase, we consider a power line from a training circuit that approximates the electrical circuit to be monitored. This training circuit must therefore have characteristics as close as possible to the circuit installed on the aircraft, particularly in terms of power supply, current waveform, electrical charge, etc.

[0035] The P2 diagnostic phase can be implemented by a device onboard an aircraft. This detection device can be integrated into the monitoring systems typically found in the aircraft's electrical core, such as solid-state power controllers (SSPCs). An SSPC consists of one or more solid-state switching devices and associated solid-state circuits for protection, control signal actuation, and status information provision.

[0036] Figures a and lb illustrate two embodiments among several possible ones.

[0037] In the embodiment of figure aa, the detection device 4 is positioned upstream of the power line 3, close to the current source 1. In the embodiment of figure lb, the detection device 4 is positioned downstream of the power line 3, near the load 2.

[0038] Figure 2 illustrates a high-level functional architecture enabling the implementation of the described process.

[0039] The described architecture comprises a set of functional modules, each module corresponding to a step in the process. This functional breakdown allows for the clearest possible explanation. However, those skilled in the art can certainly define other divisions to arrive at different implementations of the process. As these are functional elements, the various functional modules shown can, for example, be combined or subdivided during a technical implementation.

[0040] The architecture of the example in this figure 2 can be broken down into a detection device 4, corresponding to the diagnostic phase P2, and a learning device 4' corresponding to the learning phase PI.

[0041] As previously stated, the learning device 4' can be outside the aircraft, while the detection device 4 is on board the aircraft.

[0042] The learning device 4' is designed to implement a first PI phase of learning a model of the behavior of an electric current. This behavior is typically based on the intensity of the electric current.

[0043] The training device 4' has a first functional measurement module 41' designed to perform measurements on the electrical line 3', for example, measurements of the electrical current intensity. As explained previously, this electrical line 3' belongs to a training electrical circuit that approximates the electrical circuit 3 to be monitored in the aircraft. The training electrical line 3' is therefore distinct from the monitored electrical line 3 but shares characteristics that are as similar as possible.

[0044] The 41' measurement module can, for example, include one or more Hall effect type sensors, for example with a bandwidth of 500kHz.

[0045] The functional discovery module 42 can thus be designed to discover recurring patterns in the behavior of the electric current, as measured, on the power line. The discovered recurring patterns can then be stored in a pattern database 43.

[0046] More specifically, the proposed process may include a step of acquiring measurement data (from the functional measurement module 41'). This measurement data is stored in a memory, not shown.

[0047] These measurement data thus constitute a time series.

[0048] A time series, or chronological series, is a sequence of numerical values ​​representing the evolution of a specific quantity over time.

[0049] A subsequent step aims to recognize recurring patterns within this time series of measurements.

[0050] A pattern can be defined as a time series that repeats itself (with a possible error rate) within a larger time series.

[0051] The concept of pattern discovery in a time series was proposed in the article by P. Patel, E. Keogh, J. Lin and S. Lonardi, "Mining motifs in massive time series database" in 2002 IEEE International Conference on Data Mining, 2002 Proceedings, pages 370-377.

[0052] We can define a time series T=(ti, t2, .... t n ) of length n as an ordered sequence of n real values.

[0053] We can also define a subsequence of a time series T, with l < i < n and 1 < i + -^ < n, as a time series of length E consisting of the E successive real values ​​belonging to T and starting at index i:

[0054] Pattern discovery then becomes a matter of searching for longer subsequences that satisfy a minimum distance between them. The distance can be a Euclidean distance or, more specifically, a z-normalized Euclidean distance.

[0055] We can define a normalized z-Euclidean distance between two subsequences such that

[0056] We also define, for each time series, the average respectively and the standard deviation a^, respectively.

[0057] The normalized z-Euclidean distance ZED can then be written

[0058] However, other distances can also be used.

[0059] We can then define the notions of correspondence and trivial correspondences between two subsequences, based on a distance measure.

[0060] Two sub-sequences Sj (form a "matching" if and only if - ZED(S i l ,S j i)' < reR, and Sj ( do not form a trivial correspondence.

[0061] The radius r is a parameter that defines the proximity that two subsequences must have to be considered "matching". For this reason, the term "R-matching" is used in English to define this match.

[0062] Trivial correspondences are such that any subsequence forms a sequence slightly shifted in time. These correspondences are excluded in pattern searches.

[0063] A possible definition of trivial correspondence could be: two subsequences Sj (of the same length and of the same time series form a trivial match if and only if they share at least f / 2 common indices of the time series T:

[0064] The aforementioned article by P. Patel, E. Keogh, J. Lin and S. Lonardi proposes a first method called "K-motifs".

[0065] Given a time series T, a subsequence length n, and a radius R, the most significant pattern in T is the subsequence C1 that has the largest number of nontrivial matches. The K-pattern is the largest set of subsequences of length I in which every subsequence forms a match ("R-matching") with every other subsequence in the set.

[0066] Numerous other methods have been proposed to enable the discovery of patterns in time series depending on the nature or type of patterns to be discovered.

[0067] For example, a method described in the article by M. Linardi, Y. Zhu, T. Papanas and E. Keogh, “Valmod: A suite for easy and exact detection of cariable length motifs in data series”, in Proceedings of the 2018 International Conference on Management of Data, pages 1757-1760, 2018, consists of first determining a pair of subsequences forming a correspondence, then iteratively determining new subsequences forming a correspondence with members of a set that is thus gradually grown.

[0068] In one embodiment, a k-motiflet method is used. This process was described in the article by Patrick Schäfer and Ulf Leser, "Motiflets - Fast and Accurate Detection of Motifs in Time Series" in Woodstock '18: ACM Symposium on Neural Gaze Detection, June 3-5, 2018, Woodstock, New York, doi.org / 10.1145 / 1122445.1122456

[0069] The extent of a set S of motifs is defined as the maximum value of the set of Euclidean distances between each motif in the set, taken two at a time. In other words:

[0070] The best k-motiflet is defined as the set S, of cardinality k, of subsequences of length F for which

[0071] All subsequences of S form pairwise correspondences,

[0072] There is no set S' with extent(S') < extent(S) that also satisfies these constraints.

[0073] The previously cited article also describes algorithms for determining k-motiflets within a time series.

[0074] One advantage of an implementation based on a k-motiflet method is its independence from the radius r required for Valmod and k-motif methods. Current analysis can therefore be independent of the electrical monitoring system.

[0075] The article describes a method for automatically finding the values ​​of k and I. This method involves examining the value of each extent(Sk) over the entire acquisition. By doing so, the elbow points of the extent(Sk) indicate pattern changes throughout the acquisition. The number of different inclinations of the extent(Sk) thus provides an estimate of the parameter k. To determine the optimal value of the parameter I (pattern length), one can look for the value of f for which the area under the extent(Sk) is minimal.

[0076] Figures 3a and 3b represent two examples of electric current behavior in the supervised power line.

[0077] This behavior is captured by measurement data, for example, the current intensity expressed in Amperes (A in the figures). All of this measurement data thus represents a time series where each instant t corresponds to a current value A.

[0078] In this example, the discovery phase reveals a pattern at locations T1, T2, and T3. This recurring pattern corresponds to a transient current phenomenon caused by loads in the electrical network. For example, it could be the regular or irregular ignition of an engine or other aircraft component. In any case, it corresponds to the aircraft's normal operation.

[0079] Figure 3b shows another example, in which a T4 motif is discovered.

[0080] The patterns discovered by analyzing the stored time series are then stored in pattern database 43.

[0081] Thus, at the end of the discovery phase, this pattern database 43 contains a dictionary of patterns corresponding to the transient phases of the electric current during normal operation of the electrical circuit. The PI learning phase is adapted so that this dictionary contains the largest possible number of normal current transients during aircraft operation.

[0082] The training phase is designed to learn a model of normal current behavior, that is, without faults (specifically, without fault arcs). To achieve this, the current transmitted in the power line 3' is assumed to be fault-free. The patterns stored in the pattern database 43 therefore correspond to this normal current behavior.

[0083] On this basis, it is possible to determine a behavioral model of the stream corresponding to a class optimally delimiting features extracted from the pattern base (i.e., the training set).

[0084] Furthermore, a second database, known as the validation database, must also be created. This database must contain both nominal operating conditions and fault conditions (i.e., those exhibiting fault arcs). This database will be used later, once the model has been trained.

[0085] A functional calculation module 44' is planned to calculate initial descriptor values ​​on all or part of the patterns discovered and stored in the base 43.

[0086] These descriptors are metrics that can be calculated from measurement data on the physical phenomenon being studied, here the patterns stored in pattern database 43.

[0087] Examples of descriptors include statistical moments, frequency content, entropy...

[0088] For example, the entropy H of the time series of the intensity i(t) of the electric current can be explained:

[0089] pj represents the probability (or proportion) that the intensity i(t) has a value in an interval Ij, the set of values ​​of the intensity that can be taken for a pattern being subdivided into n intervals (or "bins" in English).

[0090] The statistical moments of a time series, such as that of the electric current intensity i(t), are quantities that provide information about the characteristics of the distribution of values ​​in the series. The moments commonly used are the first-order moment (mean), the second-order moment (variance), the third-order moment (skewness), and the fourth-order moment (kurtosis).

[0091] Other descriptors include autocorrelation values, statistical moments of the wavelet transform, statistical values ​​such as maximum, minimum, mean, root mean square (or "root mean square" in English), etc.

[0092] In a specific application case, one can, for example, use one or more dozen descriptors.

[0093] The process can be independent of the number of descriptors used and the different descriptors used.

[0094] From these initial descriptor values, the functional module 45 can determine a model of the behavior of the electric current in the normal case (or nominal, corresponding to the absence of faulty electric arc).

[0095] The model can be determined in different ways. One example is single-class learning based on a support vector model (or "Support Vector Model", SVM).

[0096] One usable method is the "OneClassSVM" method described in Sohrab, Fa had et al., "Subspace Support Vector Data Description", 2018 24th International Conference on Pattern Recognition (ICPR), 722-727.

[0097] Another usable method is a single-class learning method based on the article by A. Kowalczyk and B. Raskutti, "One class SVM for yeast regulation prediction", in ACM SIGKDD Explorations Newsletter, volume 4, pages 99-100, ACM 2022.

[0098] According to another embodiment, illustrated in Figure 4, it is determined by a succession of iterative steps: Projection, SI, of the patterns from training set 43 into the space of the N descriptors used, Determination, S2, of a Gaussian mixture model delimiting the set of these motifs in this space, Estimation, S3, of a relevance score for these descriptors for the current model, Withdrawal, S4, of the descriptor corresponding to the lowest relevance score.

[0099] This sequence is then iterated over a space of Nl descriptors. The iterations can stop when a satisfactory model is obtained. This satisfaction can be evaluated, S5, on a second basis of 43' patterns, called the "validation" basis, mentioned previously.

[0100] Figure 5 illustrates the first step of projecting the patterns, represented by disks, into the descriptor space {d1, d2}. Only two descriptors are used in this example for clarity of the figure, but in the general case, any number N of descriptors can be used.

[0101] At stage S2, this distribution (in N dimensions) can be modeled by a Gaussian mixture.

[0102] A Gaussian mixture model (commonly referred to by the English acronym GMM for "Gaussian Mixture Model") is a model used to parametrically estimate the distribution of random variables as the sum of several Gaussians, called kernels.

[0103] Determining the parameters of the Gaussian mixture modeling the projection of the patterns in the space of descriptors corresponds to determining the number of Gaussian distributions in the mixture and, for each distribution, its mean, its variance and its amplitude (or a "proportion", weighting the influence of this distribution in the mixture).

[0104] In other words, a Gaussian mixture model can be expressed by its density p(x), with:

[0105] N(x\p k , Z k) represents the k-th Gaussian distribution (or "cluster" according to English terminology). p k , k represent, respectively, the mean and variance-covariance matrix of this distribution. K is the number of Gaussian distributions in the mixture.

[0106] n k represents the proportion of this distribution k in the mixture (that is, its contribution or importance, which is equivalent to its relative magnitude). These proportions obey the following criterion:

[0107] In one embodiment, the parameters of the Gaussian mixture are optimized according to the maximum likelihood criterion in order to approximate the desired distribution as closely as possible. This optimization is often performed by applying the iterative procedure called expectation-maximization (EM) or "Expectation-Maximization algorithm" in English.

[0108] The EM algorithm is an iterative process that finds the parameters maximizing the likelihood of a probabilistic model when the model depends on unobservable latent variables. It was proposed by A.P. Dempster, N.M. Laird, and Donald Rubin, "Maximum Likelihood from Incomplete Data via the EM Algorithm," in Journal of the Royal Statistical Society, Series B (Methodological), vol. 39, no. 1, 1977, pp. 1–38 (JSTOR). 2984875). Numerous variants have subsequently been proposed, forming an entire class of algorithms.

[0109] In more detail, the EM algorithm consists of iterating two steps: A step in evaluating the expected value, where the expected likelihood is calculated taking into account the last observed variables, A maximization step, where the likelihood function is maximized by adjusting the model parameters to obtain new values.

[0110] In the next iteration, the parameters found in the maximization step serve as the starting point for the expectation evaluation step.

[0111] The number K of Gaussian distributions to be considered in the mixture can be estimated by minimizing a Bayesian information criterion.

[0112] The Bayesian information criterion (BIC), also known as the Schwarz information criterion, is an information criterion that can be expressed as: BIC = -2. Z (L) + ix ln(N)

[0113] "In" represents the natural logarithm function, L is the likelihood, N is the number of observations in the sample (i.e., the number of patterns in the training set 43), and i is the number of free parameters of the model. This is the total number of training points used.

[0114] The Gaussian mixture model p(x) defines a region of the descriptor space that delimits, or encompasses, the patterns of the training set. It divides the space between a class belonging to this region and a class outside this region.

[0115] However, this first model of Gaussian mixture p(x) is not optimal.

[0116] In particular, it is expressed in the space of available distributors, but these are not chosen according to the patterns to be classified. An additional mechanism allows the determination of the "good" descriptors among those available, that is to say, of minimize the number of descriptors while allowing the modeling of the pattern class of the training base 43.

[0117] To do this, in step S3, a relevance score is estimated for each descriptor.

[0118] The relevance score 1(d) of a descriptor d can be the sum of relevance subscores established for each distribution k.

[0119] These "sub-scores" can be established by performing a principal component analysis.

[0120] In particular, they can be determined based on their respective proportions n k of each distribution k, of eigenvalues ​​A of the variance-covariance matrix associated with principal components ] of the distribution k, and of components of the eigenvector v d of the variance-covariance matrix associated with the principal components ] and the descriptor d in the k distribution.

[0121] We can express this importance score 1(d) of the descriptor d as follows:

[0122] with JJ = 1 d = 1

[0123] J represents the number of main components.

[0124] In one embodiment, two main components are used. The importance 1(d) of the descriptor d can then be expressed in a simplified form:

[0125] With Eigenvalue of the matrix Zk associated with the first principal component in the distribution k Â2: Eigenvalue of the matrix Zk associated with the second principal component in the kv distribution d Component of the eigenvector of the matrix Zk associated with the first principal component and the descriptor d in the distribution k V2 id : Component of the eigenvector of the matrix Zk associated with the second principal component and the descriptor d in the distribution k

[0126] This score 1(d) is therefore calculated for all the descriptors used to establish the Gaussian mixture model.

[0127] In step S4, we select the descriptor d with the lowest relevance score 1(d), in order to remove it for the following iterations.

[0128] Step S5 involves testing an exit condition of the iterative loop. To do this, we check if the Gaussian mixture model is satisfactory on a second set of patterns.

[0129] As explained previously, this second set of patterns, contained in a validation base 43', is determined in the same way as the patterns in the training base 43, but instead of applying fault-free behavior to the current flowing through the power line 3', this second set includes patterns corresponding to fault-free behaviors and patterns corresponding to behaviors with failure (i.e., corresponding to a faulty electric arc).

[0130] For an example (pattern) of the validation basis, we can determine a distance from this pattern projected in the descriptor space to the region corresponding to the current Gaussian mixture model.

[0131] This distance DM(X) can be calculated as the minimum distance among the distances k (x) of the pattern (projected into the space of descriptors) x to each of the distributions k.

[0132] This distance k (x) can be a Mahalanobis distance which can be expressed as:

[0133] / z k and Z k are, respectively, the mean and variance-covariance matrix of the Gaussian distribution k.

[0134] The final distance D_M (x) can be expressed by D M

[0135] This distance can help determine whether an input data (pattern) x corresponds to a faulty electric arc or to normal electric current behavior (including despite the presence of electrical noise).

[0136] To do this, this distance DM(X) can be compared to a predetermined threshold s, for example stored in memory.

[0137] If the distance is greater than the threshold, D M x~) > s, then an electrical fault is detected (electric arc)

[0138] If the distance is less than or equal to the threshold, D M x~) < s, then the electric current has normal behavior.

[0139] This decision can be compared to "labels," that is, to the truth, which is known since the validation base is built from constructed examples. This validation base therefore associates patterns with a label that can have two values: normal behavior or presence of an electric arc.

[0140] By comparing the labels and predictions made by the Gaussian mixture model, we can obtain a relevance score for this Gaussian mixture. This score reflects the degree of agreement between the predictions and the labels.

[0141] This score can be compared to a second predetermined threshold, for example stored in memory.

[0142] If the relevance score is above this threshold, then the Gaussian mixture is satisfactory on this validation basis. If it is below this threshold, then it is not satisfactory.

[0143] If it is satisfactory, then this last mixture of Gaussians is the model of the current behavior, which can be used in the P2 diagnostic phase.

[0144] If it is not satisfactory, then the process loops back to the IF step for a new iteration.

[0145] A new SI projection of the patterns is made on the space of descriptors (this space being modified by the deletion of a descriptor in the previous iteration), a new S2 determination of a Gaussian mixture on the basis of this new space, a new estimation of the relevance scores for the remaining descriptors, and the removal S4 of a new descriptor, and so on.

[0146] Once the model has been learned in the laboratory, it can be incorporated into a detection device 4.

[0147] One advantage of the proposed method is that the model transferred to the detection device 4 is fixed. It can therefore be easily used within an embedded system designed to minimize resource requirements. It can also be used directly on the aircraft, barring any additional adaptation or learning phases, and can thus detect potential electrical faults from the very first minute of taxiing or flight.

[0148] This detection device 4 includes a second functional measurement module 41, which is designed to perform measurements on the power line 3, for example, measurements of the electric current intensity. This second functional module may be identical or similar to the first functional module of the learning device 4'. The power line belongs to an electrical circuit of an aeronautical system.

[0149] The proposed method may include a step of acquiring measurement data (from the second functional measurement module 41). This measurement data is stored in a memory, not shown, in order to allow the creation of a time series.

[0150] A functional calculation module 44 is planned to calculate second values ​​of descriptors over time windows of the time series extracted by the functional measurement module 41.

[0151] These time windows are designed to match the patterns stored in pattern base 43. In particular, they can be the same size as the patterns stored in pattern base 43 and in validation base 43' (i.e. include the same number of values).

[0152] The descriptors are the same as those used during the PI learning phase.

[0153] The distance calculation module 46 is designed to calculate a distance between the second values ​​of the descriptors, calculated for a time window, with the model of the behavior of the electric current.

[0154] As previously explained for the determination of the model (functional module 45), this distance can be a Mahalanobis distance between the descriptors (which correspond to the time window signal projected into the descriptor space) to the different Gaussian distributions of the mixture.

[0155] As before, the distance considered can be the minimum distance among the set of distances with each of the Gaussian distributions.

[0156] A detection module 47 is provided to detect the presence of an electrical fault on the monitored power line 3 based on the value of this minimum distance D M x~).

[0157] If this minimum distanceM (x) is greater than a predetermined (third) threshold, then the behavior of the measured current is too far from the current modeled, and we can detect the presence of an electrical fault such as a faulty electrical arc.

[0158] If the distance M (x) is less than this threshold, then the behavior of the measured current conforms to the model and no electrical fault is detected.

[0159] In the event that an electric arc is detected, a detection processing step may be triggered.

[0160] This step may include emergency responses such as shutting down and isolating the supervised power line: an electrical arc indicates abnormal behavior that can generate further electrical arcs in the future, each potentially damaging the system locally, including the aircraft, as previously discussed. It is therefore essential to prevent any potential damage by shutting down the power line as soon as the first electrical arc is detected.

[0161] Also, an alert can be triggered to notify a human operator who can compensate for this fault (activation of a possible redundant system following the shutdown of the faulty one, interventions to troubleshoot the fault, etc.)

[0162] Of course, the present invention is not limited to the examples and embodiments described and illustrated, but is defined by the claims. In particular, it is susceptible of numerous variations accessible to those skilled in the art.

Claims

DEMANDS 1. A method for detecting electric arcs in an electrical circuit of an aeronautical system, the method being implemented by computer and comprising: a first phase (P1) of learning a model of the behavior of an electric current on a training electric line (3') of a training electric circuit approximating said electric circuit, comprising a discovery (42) of patterns in the behavior of said current, and the determination (45) of said model from first values ​​of descriptors calculated (44) on said patterns, and, a second phase (P2) of diagnosis comprising a calculation (44') of second values ​​of said descriptors for an electric current on an electric line (3) of said electric circuit, over a time window, a calculation of a distance (46) between said model and said second values, and a detection (47) of an electric arc if said distance is greater than a predetermined threshold.

2. A method according to the preceding claim, wherein said model is determined by iterative steps of Projecting said patterns into the space of said descriptors, Determine a Gaussian mixture model that delimits the set of said patterns in said space, Estimate a relevance score for said descriptors for said model, Remove the descriptor corresponding to the lowest relevance score, until a satisfactory model is obtained on a second set of patterns, said model being satisfactory if said relevance score is greater than a second predetermined threshold.

3. A method according to the preceding claim, wherein said Gaussian mixture model is a proportion-weighted sum of Gaussian distributions, the number of which is determined by minimizing a Bayesian information criterion, each distribution being characterized by a mean value and a variance-covariance matrix, said mean values, said variance-covariance matrices and proportions being preferably determined by an expectation-maximization algorithm.

4. A method according to any one of the preceding claims, wherein said descriptors comprise statistical moments, a frequency content, an entropy of said patterns.

5. A method according to any one of the preceding claims, wherein said first phase (PI) comprises a step (SI) of acquiring measurement data relating to said electric current, and of storing said measurement data to form a time series, as well as a step (S3) of recognizing patterns within said time series of measurements.

6. Computer program comprising instructions for implementing a method according to one of the preceding claims when executed on an information processing platform.

7. Detection device (4) for detecting electric arcs in an electric line (3) of an electrical circuit of an aeronautical system, comprising a predetermined model of the behavior of the electric current on said electric line and further comprising a functional module for calculating (44') descriptor values ​​for an electric current on said electric line (3) over a time window, a functional module for calculating (46) a distance between said model and said values, and a functional module for detecting an electric arc if said distance is greater than a threshold.

8. A learning device (4') for a model of the behavior of an electric current for the detection of electric arcs in an electric line (3) of an electrical circuit of an aeronautical system, comprising a functional model for discovering patterns (42) in the behavior of said electric current on a training electric line (3') of a training electrical circuit approximating said electrical circuit, a functional module for calculating (44) descriptor values ​​on said patterns, and a functional module for determining said model from said descriptor values.

9. Aircraft comprising at least one detection device (4) according to claim 7.

10. System comprising a detection device (4) according to claim 7 and a learning device (4') according to claim 8. Device (20)

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