Automatic method for monitoring rotating parts of rotating machines by means of domain adaptation

Abstract

The invention relates to a method (100) for automatically monitoring a plurality of rotating parts of rotating machines on the basis of a target database comprising a plurality of time signals from a distribution generated from each rotating part and on the basis of a source database comprising a plurality of time signals from a distribution S different from the distribution T generated from a source rotating part of a source rotating machine and being associated with an operating class, the monitoring being carried out by means of an adaptive deep learning model making it possible to adapt the source distribution to the target distribution, the deep learning module being trained by minimisation of a cost function relating to Gaussian kernel functions having a parameter σ; σ being calculated in each period on the basis of the difference in distributions weighted by a constant static value estimated on the basis of a Pascal's triangle.

Description

DESCRIPTION TITLE: Automatic method for monitoring rotating parts of rotating machines by adapting domains. TECHNICAL FIELD OF THE INVENTION

[0001] The technical domain of the invention is that of domain adaptation of distributions and deep learning transfer.

[0002] The present invention relates to an automatic method for monitoring a rotating part of a rotating machine. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] In many industrial sectors, the diagnosis and monitoring of mechanical components, such as engines and their various rotating parts (bearings, gears, shafts, fans, etc.), are essential to understanding their operating condition and thus planning maintenance operations to minimize downtime. A reliable diagnostic and monitoring system or process enables the early detection and identification of damage, preventing its propagation to other mechanical parts, and allowing for the scheduling of appropriate maintenance based on the condition of the monitored component. Therefore, mechanical monitoring is of paramount importance for mechanical industries, and particularly for the aerospace industry.

[0004] Monitoring a rotating part of a rotating machine is typically performed by analyzing vibration signals generated by the rotating part and acquired by vibro-acoustic sensors, such as accelerometers. This method is commonly used to determine the operating condition of aircraft engines and their rotating components. During production or maintenance phases, high-frequency vibration signals are acquired while the rotating machine is running to detect weak signals characteristic of mechanical part damage, known as signatures, and thus prevent engine failure. Vibration signal analysis is one of the most widely used methods due to its non-intrusive nature and the wealth of diagnostic information provided by vibration signals.

[0005] The traditional approach to vibration diagnostics is based on signal processing techniques applied to vibration signals. These signals are the input to a processing task that includes various processing methods (source separation, filtering, denoising, etc.) aimed at extracting or enhancing a relevant "vibration signature" and associating it with a mechanical component. Vibration analysis thus involves inferring the health status of a rotating mechanical component from its vibration signature. This inference requires prior kinematic knowledge and expert monitoring. Subsequently, appropriate indicators can be developed to quantify damage and facilitate decision-making.

[0006] Artificial intelligence-based monitoring and diagnostic methods are increasingly being developed. The main goal of these methods is to replace the human knowledge required in traditional approaches with machine learning from vast amounts of data.

[0007] In this context, intelligent fault diagnosis (IDD) is emerging as an auxiliary or alternative solution to the previously mentioned "signal processing" approach. With the rapid development of deep learning, intelligent fault diagnosis has shown significant promise in recent years.

[0008] The success of a deep learning model depends on both the choice of the model's architecture and the representativeness and abundance of the training data. For example, when monitoring bearings, signals from healthy bearings and from each type of fault are required to train the model so that it can analyze new bearings and classify their condition. The success of DID approaches relies on a common assumption: that sufficient labeled data exists to train reliable diagnostic models. In aeronautics, however, collecting enough labeled data is difficult due to the rarity of faults. Consequently, unlabeled data from real machines cannot train diagnostic models to provide accurate results.Furthermore, the difference in acquisition context between the training signals from existing databases and the signals to be classified affects the performance of the learning models because two. Signals acquired in two different contexts come from two different probability distributions.

[0009] Domain adaptation is a tool that allows the reuse of knowledge learned from a set of signals acquired from a rotating machine in a first context—this dataset is called the source domain—by ​​transferring it to related signal analyses acquired for the same type of rotating machine but in a different context: this data set is called the target domain. The source domain represents a set of data that has already been acquired and labeled, i.e., whose operating class is known.

[0010] To reuse source databases for diagnostic tasks on a target database, deep transfer learning models are used, taking into account adjustable parameters, particularly for the model's cost function. These models are employed due to their efficiency and their ability to reduce the large distributional differences between the source and target domains. However, the health status of the monitored mechanical part is unknown. Therefore, the target domain data is inherently unlabeled. The main challenge, then, is to be able to adjust the parameters of the deep learning model without relying on the operating state labels of the rotating machine to determine whether the model has correctly predicted its current state. SUMMARY OF THE INVENTION

[0011] The invention offers a solution to the problems mentioned above, by enabling automatic monitoring of a rotating part, whose operating class is unknown, from a deep transfer learning model on a source and target database by setting parameters relating to the learning model independently of the labels of the target database.

[0012] A first aspect of the invention relates to a method for automatically monitoring at least one rotating part of a rotating machine, using an unlabeled database, referred to as the target database, comprising at least one time signal from a distribution T, the time signal being generated from the rotating part, and from a source database comprising a plurality of time signals from a distribution S different from the distribution T, each time signal in the source database being generated from a part rotating source of a rotating source machine and being associated with an operating class from a set of operating classes comprising at least one nominal operating class and one defective operating class, the process being characterized in that it comprises the following steps: Training of a first trained neural network capable of associating a non-stationary temporal signal from the S distribution with an operating class from the set of operating classes, the first neural network comprising a first part for feature extraction and a second part for classification, the artificial neural network being trained on the source database, Training of an artificial neural network called adaptive according to a number of epochs M of trainings, to obtain a trained artificial neural network capable of associating to a temporal signal from a union distribution of S and T a class among the set of operating classes, the adaptive neural network comprising a first part of feature extraction, corresponding to the first part of the first neural network, and a second part of adaptation of the distribution S to the distribution T and classification, the artificial neural network being trained simultaneously on the source and target databases, the training being carried out by minimization of a cost function comprising: a first term corresponding to the error between the class obtained by the neural network for each signal of the source database and the class associated with said signal of the source database;a second term calculated from at least one mean maximum deviation between a function in the source database and a function in the target database, the mean maximum deviation being calculated from at least one Gaussian kernel function of parameter o, the parameter o being estimated from a Pascal triangle, the parameter o being relative to a variance of the Gaussian kernel function and being dependent on each epoch; training, the Gaussian kernel function, of order being determined from the last line of a Pascal triangle of size Use on each signal from the target database of the trained adaptive artificial neural network, to associate a class of operation with said signal.

[0013] We define the target domain D Τ such as D Τ = { X, T= PT(X 7)} ; where X is a space of descriptors of the characteristics of a signal, T = P(X T ) is the marginal probability distribution and X Τ ∈ X.

[0014] We define the source domain Ds such that Ds = { X, S = Ps(X s )} ; where X is a space of descriptors of the characteristics of a signal, S = P(X S ) is the marginal probability distribution and Xs∈ X.

[0015] By "distribution S different from distribution T" we mean

[0016] In particular, adapting the S distribution to the T distribution is achieved by minimizing the second term of the cost function, which is calculated from the source database derived from the S distribution and the target database derived from the T distribution. The goal of domain adaptation is to reduce the difference between the distributions of the two source and target databases (during or after training) so that the classification in the target database is nearly identical to that of the source database. Both databases deal with the same subject (e.g., bearing defects in a rotating machine), but each concerns different operating conditions of the rotating machine (rotational speeds, load, torque, etc.).In particular, the maximum mean discrepancy (MMD) is, for example, one of the most efficient functions, based on minimizing the maximum discrepancy between distributions, to minimize the gap between distributions and thus achieve an adaptation between domains.

[0017] Thus, the first part of the adaptive artificial neural network is identical to the first part of the first neural network before the adaptive artificial neural network was trained. The architecture and parameters of the first part of the artificial neural network are identical to the architecture and parameters of the first part of the first neural network. The architecture of a neural network (or a part of the network) corresponds to the number of layers, neurons and their arrangement. In other words, the first part of the artificial neural network and the first part of the first neural network are identical.

[0018] The invention advantageously allows the classification of signals from an unlabeled target database, the state of the rotating machine being therefore unknown under the conditions of acquisition of the distribution signals T, into a class of a set of classes, from a labeled source database, the signals of the source database being of different distribution from the distribution of the signals of the target database, thanks to a parameter o depending on a pascal triangle, without requiring adjustment from missing labels of the target database.Indeed, since the minimization of the neural network's cost function is achieved in part using a Gaussian kernel function, the last row of a Pascal triangle advantageously represents a Gaussian kernel function of the same size as the last row of the triangle. The size is chosen according to the source and target databases, for example, allowing its parameters to be determined without any additional external adjustments. Thus, the invention enables automated monitoring of rotating parts of rotating machinery, using signals from a label-free T-distribution, without expert intervention, thereby saving time during rotating machinery maintenance.

[0019] The Gaussian kernel used to calculate the parameter θ (and therefore the cost function) is introduced to reduce the difference in distributions between the databases, both relative to each other and within each database. Using the same kernel to reduce this difference each time is not very efficient, as it changes every time the model adjusts its weights (i.e., at each training epoch). Consequently, the Gaussian kernel must be defined during each iteration to update the pattern of this reduction. Furthermore, since the parameter defining the Gaussian kernel is its variance, or equivalently its standard deviation, which is denoted θ in this case, θ depends on the difference in distributions, and therefore changes accordingly.

[0020] Thus, the parameter a varies according to each training period, during which the distributions are brought closer together, the estimation of this parameter is very robust to the variance relative to the difference of the distributions.

[0021] Advantageously, the second term of the cost function, and in particular the maximum mean deviation, is a dynamic value that varies at each training epoch.

[0022] Advantageously, no trial and error or adjustments are made by an operator to find the best variance (or equivalent standard deviation) of the Gaussian kernel.

[0023] In addition to the features mentioned in the preceding paragraph, the method according to a first aspect of the invention may have one or more of the following complementary features, considered individually or in all technically possible combinations: the first part of the adaptive neural network comprises a number of layers Ne, where Nd is a natural number greater than or equal to 1, and the second part of the adaptive neural network comprises a number of layers Nc2, where Nc2 is a natural number greater than or equal to 1, the second term of the cost function being calculated on one or more layers belonging to the second part of the neural network and located before a final layer of the second part. In particular, on each layer of a set of layers (located before the final layer) of the second part, a maximum mean deviation is calculated.The second term of the cost function thus includes the sum of each calculated mean maximum deviation. The last layer is a decision layer that classifies the input signal into an operating class, after a reconciliation of the distributions performed in the layer(s) preceding the last layer. Monitoring is performed for a plurality of n. Τ rotating parts of rotating machines and in that the target database comprises a plurality of denoted signals The plurality of signals in the source database is noted. and the second term of the cost function is calculated at each epoch at starting from the function the set of signals representing the output of the m-th layer of the adaptive artificial neural network for an input X s each signal f m (Xf) having a length Lms, and the set of signals representing the output of the m-th layer of the adaptive artificial neural network for an input X T each signal j having a length Lm Τ , m being an integer included in a set Ncc comprising each layer number of the second part from which a maximum average deviation is calculated, with: With: the variance of the Gaussian kernel function k p relating to the set f m (X s ) , p j is the variance of the Gaussian kernel function k p relating to the set f m (X r ) | a variance of the Gaussian kernel function k p relating to the set f m (X s ) and to the set f m (X r ), where P is a natural number greater than or equal to 1, each vector [Omss (p)] P >1 being denoted Omss, each vector being noted OmT Τ , each vector being noted and being denoted, the parameter o being equal to the set Advantageously, the number P of Gaussian kernel functions k p allows for increased calculation accuracy of the function pp and therefore of the training cost function of the adaptive artificial neural network. In particular, during each training epoch, the distributions of S and T vary. Thus, at each epoch, the parameter allowing the calculation of the second term of the cost function (and comprising three components) also varies to correspond to the new distributions. Thus, the three components vary at each epoch to adapt to the variations of the S and T distributions. The training step of the adaptive neural network is carried out over a number of epochs M, and for each epoch of the number of epochs M, the parameter is estimated according to the following sub-steps: For each layer : o Determination of Lmax, Lmax being the maximum length between the lengths of each signal in the set and each signal from the set o Resampling of each signal in one image in two dimensions of size and resampling each signal into an image in two dimensions of size o Determining the variance of a kernel function has Gaussian order according to the following substeps: ■ Construction of a matrix representing a Gaussian kernel of order the matrix equal to TP^Lmax representing the last row of a Pascal triangle of order And being the transposition of ■ Calculating the variance using the formula: , m being equal to the value maximum matrix Calculating a vector involves the following sub-steps: Calculation of s from Calculation of from Calculation of from Calculation of according to the following formula: Advantageously, the signals are resampled and converted into images to save computation time. Furthermore, the parameter θ is estimated using both the source and target databases and Pascal's triangle, without requiring labels for the target database to be classified. The components are calculated at each training period because they depend on the difference in distribution which changes during each training period. is a static reference value (in other words : this value does not vary according to the training periods) and allows us to evaluate the change after each training period and therefore each adjustment of the parameters (or weights) of the adaptive neural network. According to one embodiment: - each coefficient - each coefficient ' each coefficient P is equal to 5. The higher P is, the more accurate the parameter estimate is. precise. Increasing the order has a drawback in terms of the resources available to perform the calculations. Advantageously, P equal to 5 allows for a compromise between a correct estimation of and reduced calculation time.

[0024] A third aspect of the invention relates to a computer program product comprising instructions which, when the program is executed on a computer, cause the computer to carry out the steps of the process according to a first aspect of the invention and the process according to a second aspect of the invention.

[0025] The invention and its various applications will be better understood by reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0026] The figures are presented for illustrative purposes only and are in no way limiting to the invention. Figure 1 shows a block diagram of a method for monitoring a rotating part of a rotating machine according to the invention. Figure 2 represents the resampling of a time-domain signal into a two-dimensional image. Figure 3 represents a Gaussian kernel of size 28 x 28. DETAILED DESCRIPTION

[0027] The figures are presented for illustrative purposes only and are in no way limiting to the invention.

[0028] Figure 1 shows a schematic representation of a block diagram of a method 100 for the automatic monitoring of at least one rotating part of a rotating machine, from a so-called target database comprising at least one time signal from a distribution T and generated from the rotating part, and from a source database comprising a plurality of time signals from a distribution S different from the distribution T.

[0029] The rotating machine is, for example, an engine, preferably an aircraft turbojet engine.

[0030] For example, the rotating part of the rotating machine is one or more mechanical shafts, one or more bearings, one or more fans, one or more turbines or one or more compressors.

[0031] According to one embodiment, monitoring is carried out for a plurality of n Τrotating parts of rotating machines and in that the target database comprises a plurality of signals denoted X being a natural number greater than 1.

[0032] The n Τ rotating parts are of the same type, thus, the n Τ Rotating parts include bearings, for example.

[0033] Each time signal is generated from a rotating part among the n Τ rotating parts.

[0034] Every time-domain signal can be a non-stationary time-domain signal. By "non-stationary time-domain signal," we mean a physical time-domain signal whose frequency content varies over time.

[0035] In the following text, the terms "temporal signal" or "signal" will be used interchangeably.

[0036] In the following text, the terms "target database signal" or "target signal" will be used interchangeably.

[0037] Each target signal is preferably generated from vibrations of a rotating part called the target of a rotating machine called the target.

[0038] Each target signal is, for example, measured using a sensor, possibly mounted in a target rotating machine, for example a sensor Vibro-acoustic. The vibro-acoustic sensor is, for example, an accelerometer, a strain gauge, or a microphone.

[0039] Each target signal includes a number L Τ of points, the number LT may depend on the sampling frequency of the sensor.

[0040] According to a preferred embodiment, each target signal is a vibrational signal.

[0041] The plurality of target signals is denoted n Τ being an integer non-zero natural number representing the number of target signals in the target database.

[0042] Each non-stationary time signal from a distribution T is a signal generated from the vibrations of the rotating part of the rotating machine in a context T'.

[0043] We define the target domain D Τ such as D Τ = { X, T= PT(X 7 )} ; where X is a space of descriptors of the characteristics of a signal, T = P(X T ) is the marginal probability distribution and X Τ EX.

[0044] A context corresponds to the operating conditions of a rotating machine, for example, the values ​​of parameters relating to the rotating machine. A parameter relating to the rotating machine can be the rotational speed of the rotating machine, the load, the temperature of the rotating machine, the type of rotating machine, or the position of the vibro-acoustic sensor in the rotating machine.

[0045] The plurality of source signals is denoted ns, where ns is an integer. A non-zero natural number representing the number of source signals in the source database. The source database includes ns signals generated from ns rotating source parts of rotating source machines.

[0046] Each time-domain signal in the source database is generated from a rotating source part of a rotating source machine and is associated with an operating class from a set of operating classes. Preferably, each signal in the source database is generated from vibrations of the rotating source part.

[0047] A database in which each signal is associated with a class from a set of classes is said to be "labeled". Thus, the source database is labeled.

[0048] In the following text, the terms "source database signal" or "source signal" will be used interchangeably.

[0049] Each source signal is measured, for example, using a sensor, possibly integrated into a rotating source machine, such as a vibro-acoustic sensor. The vibro-acoustic sensor could be, for example, an accelerometer, a strain gauge, or a microphone.

[0050] Each source rotating part is of the same type as each other rotating part, that is to say, if each rotating part is a bearing, each source rotating part is a bearing.

[0051] Each source signal comprises a number Ls of points, the number Ls of which may depend on the sampling frequency of the sensor.

[0052] Each source rotating machine is of the same type as each target rotating machine, i.e., if each target rotating machine is an aircraft engine, each source rotating machine is also an aircraft engine.

[0053] The natural number ns can be equal to or different from the natural number HT.

[0054] Two signals are from the same distribution if, during their acquisition, the value of a single parameter relating to the rotating machine varies.

[0055] Each non-stationary time signal from the distribution S is a signal generated from the vibrations of the rotating part of the rotating machine in a context S'.

[0056] We define the source domain Ds such that Ds = { X, S= Ps(Xs)} ; where X is the space of descriptors of the characteristics of a signal, S = Ps(Xs) is the distribution of the marginal probability and Xs∈ X.

[0057] Contexts S' and T' are different.

[0058] If two signals are acquired in two different contexts, at least two parameters relating to the rotating machine have different values ​​and the two signals have different distributions.

[0059] When two signals are acquired in two different contexts, their domains are considered to have different distributions. Thus, the domains D are considered s and D Τ are of different distributions.

[0060] By "domains Ds and D Τ are of different distributions" we hear:

[0061] For example, a set of signals, comprising a first, second, and third signal, is measured by a sensor mounted on the same rotating machine. Each signal is measured on the same type of rotating machine, at the same temperature and position. The only variable parameter is the rotational speed of the rotating machine, denoted N2. The first signal is measured at N2 = 600 revolutions per minute, the second signal at N2 = 800 revolutions per minute, and the third signal at N2 = 1000 revolutions per minute. The first, second, and third signals are measured in the same context and belong to the same distribution.

[0062] For example, a first signal and a second signal are measured by a sensor attached to a rotating machine. The first signal is measured at a speed N2 = 600 rpm and a load of 1 HP, while the second signal is measured at a speed N2 = 800 rpm and a load of 3 HP. Since two parameters related to the rotating machine have different values ​​during the acquisition of the first and second signals, the first and second signals do not originate from the same distribution.

[0063] The set of operating classes is a set of operating classes of the rotating part.

[0064] For example, the set of operating classes of the rotating part includes at least the following classes: nominal operating class and defective operating class.

[0065] For example, the set of operating classes for the rotating part includes the following classes: nominal operating class, operating class with a first defect, operating class with a second defect, and operating class with a third defect. The first defect could be, for example, wear and tear. A second defect could be, for example, flaking.

[0066] According to a first embodiment, the process 100 can include a first step 101 of supervised training of a first artificial neural network to obtain a trained artificial neural network capable of providing, from a signal belonging to the distribution S, a class included in the set of operating classes.

[0067] Supervised training, also known as supervised learning, allows an artificial neural network to be trained for a predefined task, by updating its parameters in such a way as to minimize a cost function corresponding to the error between the output data provided by the artificial neural network and the true output data, that is to say what the artificial neural network should provide as output to fulfill the predefined task on a certain input data.

[0068] The artificial neural network preferably includes a first part for feature extraction, and a second part for classification.

[0069] The first part preferably comprises a set of convolutional artificial neuron layers and a set of pooling artificial neuron layers, each pooling artificial neuron layer being preceded and followed by a convolutional artificial neuron layer. For example, the first part performs the extraction of health indicators from the rotating machine and is trained to correctly extract (using a cost function) the characteristics of these health indicators.

[0070] The first part comprises a number of layers Nd, Nd being a natural number greater than or equal to 1 and preferably equal to 4.

[0071] Supervised training of the first artificial neural network consists of updating the parameters of the first artificial neural network in such a way as to minimize a cost function corresponding to the error between the prediction of the class provided by the artificial neural network from a source signal in the source database and the class associated with said source signal in the source database.

[0072] The cost function is, for example, a mean quadratic function or a cross-entropy function.

[0073] The minimization of the cost function is for example achieved by a stochastic gradient descent algorithm with backpropagation (“Back-Propagation Through Time” or BPTT).

[0074] The training of the first neural network is carried out over a number of epochs B, where B is a natural number greater than 1.

[0075] The process 100 includes a step 102 of training an adaptive artificial neural network to obtain a trained artificial neural network capable of associating a class from among the set of classes with a non-stationary time-domain signal from a union distribution of S and T. A non-stationary time-domain signal from a union distribution of S and T is a signal that can be derived from either the S distribution or the T distribution.

[0076] The adaptive artificial neural network is trained simultaneously on the source database and on the target database.

[0077] The adaptive neural network comprises a first part of feature extraction and a second part called domain adaptation and classification.

[0078] Preferably, the first part of the adaptive neural network is conflated with the first part of the first neural network before training the adaptive neural network begins. Thus, the first part of the adaptive neural network comprises a number of layers being a natural number greater than or equal to 1 and preferably equal to 4.

[0079] Preferably, the second part of the adaptive neural network comprises a set of layers called "fully-connected".

[0080] Preferably, the second part of the adaptive artificial neural network comprises a number of layers being a natural number greater than or equal to 1 and preferably equal to 4 or 5 for example.

[0081] In what follows, the notation f m X s) represents the output of the m-th layer of the adaptive artificial neural network for an input X s , and f m (X r ) represents the output of the m-th layer of the adaptive artificial neural network for an input X, m being a natural number within the interval

[0082] The set

[0083] Each element of the whole is a signal having a number of points Lms, Lms being a non-zero natural number.

[0084] The set

[0085] Each element is a signal having a number of points being a non-zero natural number.

[0086] The integers can be equal or different.

[0087] In the following, we will use the expressions "number of points of a signal" and "length of a signal" interchangeably.

[0088] The training of the adaptive neural network is carried out over a number of epochs M,M being an integer greater than or equal to 1, by minimizing a cost function relating to the adaptive artificial neural network at each epoch.

[0089] In the following, we will use the expressions "cost function relative to the adaptive artificial neural network" and "adaptive cost function" interchangeably.

[0090] The minimization of the adaptive cost function is for example achieved by a stochastic gradient descent algorithm with backpropagation (“Back-Propagation Through Time” or BPTT).

[0091] The cost function includes at least a first term and a second term.

[0092] The first term of the cost function is proportional to the error between the prediction of the class provided by the adaptive artificial neural network from a source signal in the source database and the class, among the set of function classes associated with said source signal in the source database.

[0093] The second term of the cost function is calculated from at least the sum of each maximum mean discrepancy (MMD) calculated at the output of at least one layer of the second part, for the source database and the target database as input to the adaptive neural network.

[0094] The second term is calculated using the following formula:

[0095]

[0096] The index m belongs to a set Ncc comprising each layer number of the second chosen part and from which a maximum average deviation is calculated. Ncc may comprise a single layer number or a number of layer numbers greater than 1 and strictly less than

[0097] The formula of is as follows:

[0098]

[0099] k P being a Gaussian kernel function.

[0100] A sum of Gaussian kernel functions is considered to be a Gaussian kernel function.

[0101] P is a natural number greater than or equal to 1 representing the number of Gaussian kernel functions considered for the calculation of the second term.

[0102] Note the term with )equal to: avec the variance of there Gaussian kernel function k p relating to the whole

[0103] Note MMDTT P the term with equal to: , with the variance of the function ion nucleus Gaussian k p relating to the set f m (X T ) .

[0104] Note MMDST P the term with equal to: e with the variance of the function Gaussian kernel k p relating to the whole and to the whole

[0105] So,

[0106] Each vector is noted each vector East noted and the whole is noted Thus, o is a parameter of the function

[0108] The function is a sum of Gaussian kernel functions.

[0109] At each epoch of the number M of epochs of the training of the adaptive neural network, the cost function is minimized, and therefore the first term and the second term of the function are minimized.

[0110] The parameter o is estimated at each epoch from the number of epochs M, before minimizing the second term of the cost function.

[0111] The determination of the parameter o comprises a plurality of sub-steps described below.

[0112] For each layer A first substep of determining the parameter o is a substep of determining a length Lmax, representing the maximum length between the length Lm Τ and the length Lms.

[0113] A second step in the estimation process is a resampling step of each signal into an image , in two dimensions on a grayscale and each signal in one image in two dimensions on a grey scale.

[0114] Each column of the image includes a number of pixels equal to and each line of includes a number of pixels equal to

[0115] Each column of the image vertical includes a number of pixels equal to and each line of the image comprises a number of pixels equal to

[0116] Figure 2 is a representation of the two-dimensional resampling step of a signal of length M.

[0117] A second substep for determining the parameter o is a substep for constructing a matrix representing a Gaussian kernel of size and variance from the last row of a Pascal triangle order

[0118] The construction of the matrix is created from a vector comprising columns and a row and representing the last row of the Pascal's triangle of order

[0119] The matrix is equal to being the transposition of

[0120] The matrix represents a reproduction of the Gaussian kernel of size, the central value of the matrix being the maximum value, the values of said matrix gradually decreasing as it moves away from the center, in order to reach the corners of the matrix presenting values ​​equal to 1.

[0121] For example, to the last row of a Pascal triangle of order 5 is the following vector: [1 4 6 4 1],

[0122] Thus, for

[0123] Thus N

[0124] The image of a matrix representing a Gaussian kernel of size 28*28 is represented in [Fig. 3].

[0125] A third substep for determining the parameter o is a substep for calculating the variance of the Gaussian kernel represented by the matrix The matrix represents the Gaussian kernel with the following formula: The function is maximal when the term exponential tends towards 1, thus and is equal to

[0126] Note the maximum value of the matrix Thus, this allows us to obtain: x

[0127]

[0128] ne does not depend on the training period, so, maybe calculated only at the first epoch and then reused for each epoch among the number of epochs M, or recalculated at each epoch.

[0129] A fourth substep for determining the parameter o is a substep for calculating the value of a matrix

[0130] is calculated from the formula

[0131] is calculated from the formula

[0132] is calculated from the formula

[0133] Preferably, Each coefficient of the oss matrix is ​​equal to

[0134] Preferably each coefficient of the matrix δ TΤ is equal to

[0135] Preferably, Each coefficient δST(P) of the matrix δS Τ is equal to

[0136] According to one embodiment, P is equal to 1. Thus, in this embodiment,

[0137] Preferably, P is equal to 5. A value of P equal to 5 provides a balance between the computation time of the adaptive cost function and a satisfactory accuracy in estimating the difference in distributions.

[0138] Thus, the matrix depends on each training period, the whole and the whole being modified at each time training the number M of epochs.

[0139] The matrix estimation process includes a step of calculating the matrix from the product of the variance and the matrix

[0140] Preferably

[0141] Thus, the parameter equals the set is estimated according to the sub- previous steps.

[0142] The process 100 includes a usage step 103 on each signal in the target database of the trained adaptive artificial neural network, to associate an operating class with said signal.

Claims

DEMANDS

1. A method (100) for automatically monitoring at least one rotating part of a rotating machine, from an unlabeled database called the target database comprising at least one time signal from a distribution T, the time signal being generated from the rotating part, and from a source database comprising a plurality of time signals from a distribution S different from the distribution T, each time signal from the source database being generated from a source rotating part of a source rotating machine and being associated with an operating class from a set of operating classes comprising at least one nominal operating class and one defective operating class, the method being characterized in that it comprises the following steps: - Training (101) of a first trained neural network capable of associating a non-stationary temporal signal from the distribution S with an operating class from the set of operating classes, the first neural network comprising a first part for feature extraction and a second part for classification, the artificial neural network being trained on the source database, - Training (102) of an artificial neural network, called adaptive, over a number of training epochs M, to obtain a trained artificial neural network capable of associating a class from the set of operating classes with a temporal signal from a union distribution of S and T. The adaptive neural network comprises a first part for feature extraction, corresponding to the first part of the first neural network, and a second part for adapting the distribution S to the distribution T and for classification. The artificial neural network is trained simultaneously on the source and target databases. The training is performed by minimizing a cost function comprising: o a first term corresponding to the error between the class obtained by the neural network for each signal in the source database and the class associated with said signal in the source database; o a second term calculated from at least one mean maximum deviation between a function in the source database and a function in the target database, the mean maximum deviation being calculated from at least one Gaussian kernel function of parameter o, the parameter o being estimated from a Pascal triangle, the parameter o being relative to a variance of the Gaussian kernel function and being dependent on each training epoch, the Gaussian kernel function, of order n, being determined from the last row of a Pascal's triangle of size - Use (103) on each signal in the target database of the trained adaptive artificial neural network, to associate a class of operation with said signal.

2. A method (100) according to any one of the preceding claims, characterized in that the first part of the adaptive neural network comprises a number of layers being a natural number greater than or equal to 1 and in that the second part of the adaptive neural network comprises a number of layers Nc2, Nc2 being a natural number greater than or equal to 1, the second term of the cost function being calculated on one or more layers belonging to the second part of the neural network, and located before a final layer of the second part. [Claims] A method (100) according to any one of the preceding claims, characterized in that the monitoring is carried out for a plurality of rotating parts of rotating machines and in that the target database comprises a plurality of denoted signals

4. A method according to claims 2 and 3 characterized in that the plurality of signals from the source database is noted and in that that the second term of the cost function is calculated at each epoch from the function the set of signals representing the output of the m-th layer of the neural network Artificial adaptive for an entry each signal having a length and the set of signals representing the output of the mth layer of the adaptive artificial neural network for an input X T each signal having a length being an integer contained in a set Ncc including each layer number of the second part from which a maximum average deviation is calculated, with: With : - avec the variance of the Gaussian kernel function k p relating to the whole - with variance of the Gaussian kernel function relative to the set - with the variance of the Gaussian kernel function k p relating to the whole and to the whole Given a natural number P greater than or equal to 1, each vector being denoted O, each vector being denoted , each vector being being noted , the parameter being equal to the whole

5. A method (100) according to the preceding claim, characterized in that the training step (102) of the adaptive neural network is carried out according to a number of epochs M, and in that for each epoch of the number of epochs M, the parameter is estimated according to the following sub-steps: - For each layer o Determination of max, where max is the maximum length between the lengths of each signal in the set and each signal from the set o Resampling of each signal in one image in two dimensions of size and resampling of each signal into an image in two dimensions of size o Determining the variance of a kernel function Gaussian order according to substages following: ■ Construction of a matrix representing a Gaussian kernel of order the matrix equal representing the last line of a Pascal triangle of order being the transpose of ■ Calculating the variance using the formula: being equal to the value maximum matrix o Calculating a vector according to the substeps following: Calculation from Calculation from Calculation from o Calculation of according to the following formula:

6. A method (100) according to the preceding claim, characterized in that: - each coefficient o - each coefficient being equal to - each coefficient (P) being equal to

7. Method (100) according to any one of claims 4 to 6 characterized in that P is equal to 5.

8. Computer program product comprising instructions which, when the program is executed on a computer, cause the computer to carry out the steps of the process (100) according to any one of claims 1 to 7.

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