Low-quality and Few-sample Diagnosis Method for Transmission Systems Based on Second-order Moment Metrics of Diffusion Processes

Abstract

The present invention relates to the technical field of intelligent operation and maintenance of machine equipment, and particularly relates to a low-quality and few-sample diagnosis method for a transmission system based on the second-moment metric of the diffusion process, including: obtaining a fault diagnosis data set of an electromechanical composite transmission system with incorrect labels, randomly extracting samples therefrom to obtain a kernel sample construction set and a network parameter update set; calculating the second-moment metric matrix of the diffusion process; calculating the kernel samples of each healthy category in the kernel sample construction set; calculating the similarity between the second-moment metric matrix of the sample feature vectors in the network parameter update set and the representations of the kernel samples of various healthy categories based on a classifier, and calculating the probability of the healthy category to which the samples in the network parameter update set belong according to the similarity; constructing a loss function that can attenuate the influence of outliers, and iteratively training the feature extractor and the classifier. The present invention can effectively learn in a small-sample training data set with incorrect labels and obtain good diagnostic performance.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent operation and maintenance of machine equipment, and more specifically, to a low-quality and few-sample diagnosis method for a transmission system based on the second-moment metric of the diffusion process. Background Art

[0002] With the increasing close combination of industry and information technology, modern mechanical equipment is developing towards automation, intelligence, and precision. Among them, the mechanical transmission system, as an important subsystem of mechanical equipment, is widely used in fields such as transportation facilities, electric power energy, and mechanical manufacturing. Its health status directly affects the safety and reliability of mechanical equipment. Once a failure occurs, it may lead to economic losses and even casualties. In recent years, accidents caused by failures of mechanical transmission systems have occurred frequently. In order to prevent failures and take appropriate maintenance measures, it is necessary to comprehensively monitor and diagnose the transmission system.

[0003] Intelligent diagnosis methods based on deep learning networks have been widely studied due to their excellent end-to-end recognition capabilities, promoting the transformation of mechanical transmission systems from "regular maintenance" to "predictive maintenance". However, intelligent diagnosis methods based on deep learning usually rely on a large number of training samples. The lack of training samples will lead to serious overfitting, thereby affecting the diagnostic performance. In the operation and maintenance of mechanical transmission systems, it is difficult to obtain sufficient labeled fault samples. In addition, the lack of professional knowledge of staff, misinformation transmission, and human negligence inevitably lead to the appearance of wrong labels, which brings great challenges to the engineering application of fault diagnosis models. In the problem of intelligent fault diagnosis of transmission systems under small-sample constraints, existing methods only consider the marginal distribution of features to evaluate sample similarity when training the network, ignoring the correlation between different features, and wrong labels will cause a significant decline in the diagnostic performance of the network.

[0004] Therefore, how to improve the diagnostic accuracy of intelligent fault diagnosis algorithms has become a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a low-quality and few-sample diagnosis method for a transmission system based on the second-moment metric of the diffusion process, which can effectively learn in a small-sample training dataset containing wrong labels and obtain good diagnostic performance, thereby solving the problem of the decline in diagnostic effect caused by scarce fault samples and wrong labels in actual engineering.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A low-quality and few-sample diagnosis method for a transmission system based on the second-moment metric of the diffusion process, comprising the following steps:

[0008] Obtain the fault diagnosis dataset D of the electromechanical composite transmission system with error labels, and randomly extract samples from it to obtain the kernel sample construction set S and the network parameter update set Q;

[0009] Based on the feature extractor, perform multi-dimensional feature extraction on each sample in the kernel sample construction set S and the network parameter update set Q, and calculate the weight of the sample feature vector and the second-order moment metric matrix of the diffusion process;

[0010] Calculate the kernel samples P of each healthy category in the kernel sample construction set S based on the weight of the sample feature vector and the second-order moment metric matrix of the diffusion process;

[0011] Based on the classifier, calculate the similarity between the second-order moment metric matrix of the diffusion process of the sample feature vector in the network parameter update set Q and the kernel samples P of various healthy categories, and calculate the probability of the healthy category to which the samples in the network parameter update set Q belong according to the similarity;

[0012] Construct a loss function that can attenuate the influence of outliers, and under the guidance of this loss function, perform iterative training on the feature extractor and the classifier.

[0013] Furthermore, the sample representation form inside the dataset D is {(X 0 ,Y 0 ),(X 1 ,Y 1 )…(X n ,Y n )}, where any sample represents the multi-source sensor data of the sample, L represents the time dimension, C represents the channel dimension, and Y a represents the corresponding label; X a is a time series, expressed as {x 1 ,x 2 ,…,x L}, where any value in the time series is expressed as x b,C represents the data of the b-th moment of the C-th channel of the signal.

[0014] Furthermore, randomly select N healthy categories from the dataset D, and randomly select K samples from each healthy category to form the kernel sample construction set S; select several additional samples with the same healthy categories as the kernel sample construction set S from the dataset D to form the network parameter update set Q, and the samples in the network parameter update set Q do not overlap with the samples in the kernel sample construction set S.

[0015] Furthermore, the feature extractor is composed of multiple one-dimensional convolutional layers. For any sample X a , its one-dimensional convolution calculation is as follows:

[0016]

[0017] Among them, d is the size of the convolution kernel; C is the channel dimension; i and j are variables in the summation process; w is the weight of the convolution kernel; b is the bias.

[0018] Input sample X a The multi-dimensional feature captured by the feature extractor F is represented as Among them, represents the non-linear mapping of the feature extractor, represents the learnable parameters in the feature extractor.

[0019] Furthermore, the extracted multi-dimensional feature t a is input to the multi-dimensional correlation distribution feature extraction layer, which is used to calculate the second-order moment metric matrix of the diffusion process based on the correlation distribution feature; among them, the calculation method of the second-order moment metric matrix of the diffusion process is as follows:

[0020] t a has the dimension of L×C, where L represents the time dimension and C represents the channel dimension, and the Euclidean space distance matrix of the multi-dimensional feature t a is calculated:

[0021]

[0022] Among them, represents the Euclidean space distance between the i-th feature vector and the j-th feature vector in the multi-dimensional feature t a ;

[0023] The second-order moment metric matrix of the diffusion process of the multi-dimensional feature t a is calculated:

[0024]

[0025] Furthermore, for the healthy category c in the kernel sample construction set S, the calculation formula of its kernel sample is:

[0026]

[0027] Among them, P c is the kernel sample of the healthy category c in the kernel sample construction set S; represents the second-order moment metric matrix of the sample X a with the healthy category c; is the weight of the sample X a in the kernel sample construction set S.

[0028] Furthermore, the weight a of the sample X in the kernel sample construction set S

[0029]

[0030] in, represents the sample X in the healthy category c in the core sample construction set S a The sum of the similarity of the second-order moment measurement matrix of the diffusion process is calculated as follows:

[0031]

[0032] in, represents the sample X in the healthy category c in the core sample construction set S a and X b The second-order moment of the diffusion process measures the matrix similarity.

[0033] Furthermore, two different samples X in the healthy category c in the core sample construction set S a and X b The calculation process of the second-order moment measurement matrix similarity of the diffusion process is:

[0034] Through the feature extractor, samples X are extracted respectively a and sample X b The multidimensional features of a and t b , and calculate the multidimensional features t a and t b The second-order moment measurement matrix M of the diffusion process a and M b ;

[0035] Calculate two samples X a and X b The second-order moment measurement matrix similarity of the diffusion process is:

[0036] ρ(t a ,t b )=tr(M a T M b )

[0037] Here, tr(·) represents the trace of the matrix.

[0038] Furthermore, the calculation formula for the probability of the healthy category to which the sample in the network parameter update set Q belongs is:

[0039]

[0040] Among them, P(Y i =c) represents sample X i The probability of belonging to health category c; Represents sample X i The core sample P of the healthy category c in the core sample construction set S cThe similarity between; k is one of the healthy categories k in N; N is the set of all healthy categories in the nuclear sample construction set S; is the sample X i and the nuclear sample P of the healthy category k k The similarity between;

[0041]

[0042] Among them, M i T is the second-order moment metric matrix of the diffusion process of the sample X in the network parameter update set Q i .

[0043] Furthermore, the expression of the loss function is:

[0044]

[0045] Among them, is the feature extracted from the data X i by the feature extractor; N is the set of all healthy categories; k is one of the healthy categories in the N healthy set; is the nuclear sample corresponding to the label healthy category Y i of the sample X i ; P k is the nuclear sample of the healthy category k.

[0046] θ i is the weight of the loss function, used to attenuate the influence of outliers; using the outlier attribute of the wrong label, attenuate the weight of the wrong label, and the weight calculation method is as follows:

[0047]

[0048] Among them, the sample X i is any sample in the network parameter update set; Y i is the healthy category label of the sample X i ; Y j is the healthy category label of the sample X j ; Y i =Y j means that the healthy category labels of the sample X i and the sample X j are the same, that is, X j is any sample in the network parameter update set with the same healthy category label Y j and Y i ; is the similarity between the sample X i and its healthy category Y i of the nuclear sample ; is the sample Xj with its health category Y j of the nuclear sample similarity.

[0049] As can be seen from the above technical solutions, compared with the prior art, the present invention has the following beneficial effects:

[0050] 1) The present invention captures multi-dimensional features of samples through a feature extractor, and calculates the second-order moment metric matrix of the diffusion process, making full use of multi-source sensor time series data and enhancing the feature extraction ability. By calculating the nuclear samples of the health category and performing prediction classification through similarity in the network parameter update set, the design and training process of the traditional classifier is simplified, and the accuracy and efficiency of fault diagnosis are improved.

[0051] 2) The present invention introduces an error label suppression learning strategy, uses the nuclear samples generated by similarity-weighted aggregation to reduce the negative impact of mislabeled samples in the nuclear sample construction set, and constructs a loss function by attenuating the weights of mislabeled samples in the nuclear sample construction set for the category nuclear samples and the classification loss weights of mislabeled samples in the network parameter update set, effectively avoiding the reduction of diagnostic accuracy caused by label errors. Generally speaking, the present invention can achieve accurate fault diagnosis in a mechanical transmission system with mislabeled data sets under small sample constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings according to the provided drawings without creative efforts.

[0053] Figure 1 is a flowchart of a low-quality and few-sample diagnosis method for a transmission system based on the second-order moment metric of the diffusion process provided by the present invention;

[0054] Figure 2 is a schematic diagram of the principle of the nuclear sample network learning framework provided by the present invention;

[0055] Figure 3 is a schematic diagram of the principle of the error label suppression learning strategy in the weighted aggregation of nuclear samples provided by the present invention;

[0056] Figure 4 is a schematic diagram of the principle of the error label suppression learning strategy in the optimization process of the loss function provided by the present invention;

[0057] Figure 5 is a schematic diagram of the accuracy comparison between the method of the present invention and the prior small-sample learning method in motor diagnosis;

[0058] Figure 6 Schematic diagram of the accuracy comparison between the method of the present invention and the existing small-sample learning method in gearbox diagnosis;

[0059] Figure 7 Schematic diagram of the accuracy comparison between the method of the present invention and the existing small-sample learning method in axle box diagnosis. Specific embodiments

[0060] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0061] As Figure 1 - Figure 2 shown, the embodiments of the present invention disclose a low-quality and few-sample diagnosis method for a transmission system based on the second-order moment metric of the diffusion process, including the following steps:

[0062] S1. Obtain a fault diagnosis data set D of an electromechanical composite transmission system with incorrect labels, and randomly extract samples from it to obtain a kernel sample construction set S and a network parameter update set Q;

[0063] S2. Based on the feature extractor, perform multi-dimensional feature extraction on each sample in the kernel sample construction set S and the network parameter update set Q, and calculate the weight of the sample feature vector and the second-order moment metric matrix of the diffusion process;

[0064] S3. Calculate the kernel samples P of each healthy category in the kernel sample construction set S based on the weight of the sample feature vector and the second-order moment metric matrix of the diffusion process;

[0065] S4. Based on the classifier, calculate the similarity between the second-order moment metric matrix of the sample feature vector in the network parameter update set Q and the kernel samples P of various healthy categories, and calculate the probability of the healthy category to which the samples in the network parameter update set Q belong according to the similarity;

[0066] S5. Construct a loss function that can attenuate the influence of outliers, and under the guidance of this loss function, perform iterative training on the feature extractor and the classifier.

[0067] The above steps will be further described below.

[0068] S1. Obtain a fault diagnosis data set D of an electromechanical composite transmission system with incorrect labels, and adopt an incorrect label suppression learning strategy to carry out kernel sample network training. The network mainly includes a feature extractor and a classifier.

[0069] The sample representation form inside the data set D is {(X0 , Y 0 ), (X 1 , Y 1 )…(X n , Y n )}, where any sample represents the multi-source sensor data of the sample, L represents the time dimension, C represents the channel dimension, and Y a represents the corresponding label; X a is a time series, expressed as {x 1 , x 2 , …, x L}, where any value in the time series is expressed as x b,C represents the b-th data point of the C-th channel of the signal. Different from general small-sample learning tasks, there are some mislabeled samples in the dataset D.

[0070] To carry out the training of the fault diagnosis network, randomly select N healthy categories from the dataset D, and randomly select K samples from each healthy category to form the core sample construction set S; select several additional samples from the dataset D that are of the same healthy category as the core sample construction set S to form the network parameter update set Q. The samples in the network parameter update set Q do not overlap with the samples in the core sample construction set S.

[0071] S2. Use the core sample construction set S and the network parameter update set Q as the training samples for this round, and input them into the constructed feature extractor F for multi-dimensional feature extraction, and calculate the weight of the sample feature vector and the second-order moment metric matrix of the diffusion process.

[0072] S21. The feature extractor consists of multiple one-dimensional convolutional layers. For any sample X a , its one-dimensional convolution calculation is as follows:

[0073]

[0074] where d is the size of the convolution kernel; C is the channel dimension; i and j are variables in the summation process; w is the weight of the convolution kernel; b is the bias.

[0075] The multi-dimensional features captured by inputting the sample X a through the feature extractor F are expressed as where represents the non-linear mapping of the feature extractor, represents the learnable parameters in the feature extractor.

[0076] S22. The extracted multi-dimensional features t aInput to the multi-dimensional correlation distribution feature extraction layer, which is used to calculate the correlation distribution feature matrix based on the second moment of the diffusion process; among them, the calculation method of the second moment metric matrix of the diffusion process is as follows:

[0077] Define t a With the dimension of L×C, where L represents the time dimension and C represents the channel dimension, calculate the multi-dimensional feature t a Euclidean space distance matrix of:

[0078]

[0079] Among them, Represents the Euclidean space distance between the i-th feature vector and the j-th feature vector in the multi-dimensional feature t a ;

[0080] Calculate the second moment metric matrix of the diffusion process of the multi-dimensional feature t a :

[0081]

[0082] S3. Calculate the kernel sample P for each healthy category in the kernel sample construction set S, specifically including:

[0083] Calculate the kernel sample P for each healthy category in the kernel sample construction set S. For the healthy category c, the calculation formula of its kernel sample is:

[0084]

[0085] Among them, P c Is the kernel sample of the healthy category c in the kernel sample construction set S, Represents the second moment metric matrix of the sample X a In the kernel sample construction set S with the healthy category c, Is the sample X in the kernel sample construction set S a Weight of.

[0086] Is related to determining and improving the robustness of mislabeled samples. Using the outlier attribute of mislabeled tags, attenuate the weight of mislabeled tags, and its principle is as Figure 3 Shown, the weight of the sample X a In the kernel sample construction set S Calculation formula of is:

[0087]

[0088] Among them, Represents the sum of the similarities of the second moment metric matrices of the samples X a In the healthy category c in the kernel sample construction set S, and its calculation method is as follows:

[0089]

[0090] Among them, represents the similarity of the second-order moment metric matrix of the diffusion process of sample X in the healthy class c in the nuclear sample construction set S a and X b .

[0091] For two different samples X a and X b in the healthy class c of the nuclear sample construction set S, the calculation process of the similarity of the second-order moment metric matrix of their diffusion process is as follows:

[0092] Extract the multi-dimensional features t a and sample X b of sample X and sample X respectively through the feature extractor according to the method of S2 a and t b , and calculate the second-order moment metric matrix M a and t b of the diffusion process of the multi-dimensional features t a and M b ;

[0093] Calculate the similarity of the second-order moment metric matrix of the two samples X a and X b :

[0094] ρ(t a , t b ) = tr(M a T M b )

[0095] Among them, tr(·) represents the trace of the matrix. Without loss of generality, for an m-order square matrix G, its trace is calculated as follows:

[0096] g ii represents the value of the i-th row and i-th column of the square matrix G.

[0097] S4. Classify the samples in the network parameter update set Q into the healthy class with the highest similarity index:

[0098] Calculate the similarity between the sample feature vectors in the network parameter update set Q and various healthy class nuclear samples P c , and classify the samples in the network parameter update set into the most similar class according to the similarity. The class probability is calculated as follows:

[0099]

[0100] Among them, P(Y i= c) represents the probability that the sample X i belongs to the healthy category c; represents the sample X i and the core sample P of the healthy category c in the core sample construction set S c The similarity between them; k is the healthy category k, and N is the set of all healthy categories in the core sample construction set S. For the sample X i and the core sample P of the healthy category k k The similarity between them.

[0101]

[0102] Among them, M i T is the second-order moment metric matrix of the diffusion process of the sample X in the network parameter update set Q i .

[0103] S5. To avoid incorrect network updates caused by mislabeled query samples, a loss function with outlier decay is adopted. The expression of the loss function is:

[0104]

[0105] Among them, is the core sample corresponding to the healthy category label Y i of the sample X i ; is the feature extracted from the data X i by the feature extractor; N is the set of all healthy categories; k is one of the healthy categories in the N healthy set; P k is the core sample of the healthy category k.

[0106] θ i is the weight of the loss function, used to attenuate the influence of outliers, which is calculated based on the outlier decay strategy. Its principle is as Figure 4 shown, specifically: using the outlier attribute of the wrong label to attenuate the weight of the wrong label, and the calculation method is as follows:

[0107]

[0108] Among them, the sample X i is any sample in the network parameter update set; Y i is the healthy category label of the sample X i ; Y j is the healthy category label of the sample X j ; Y i = Y j represents the sample X i and the sample X jThe health category labels are the same, i.e., X j is the health category label Y in the network parameter update set j and Y i any sample that is the same; is the sample X i and its health category Y i of the core sample similarity; is the sample X j and its health category Y j of the core sample similarity.

[0109] When the health category Y of the sample X i is incorrect, its similarity i is lower than that of the correct sample, the corresponding numerator of the fraction is smaller, so the weight is smaller. According to the above formula, the sample with the incorrect label has a small weight, and the sample with the correct label has a large weight. When optimizing the parameters by backpropagation, the influence of the sample with the incorrect label can be attenuated.

[0110] Through the above loss function, calculate the classification loss, and use the gradient descent algorithm to update the model parameters. The feature extractor and classifier are updated iteratively in multiple few-shot learning tasks. In each iteration, train with new task data, and continuously adjust the parameters of the feature extractor and classifier to improve the diagnostic performance and robustness of the model.

[0111] Next, further verify the performance of the method of the present invention.

[0112] Taking the fault diagnosis of the electromechanical composite drive system of urban rail trains as an example, the effectiveness of the method of the present invention is verified through the fault simulation data of the test bench. The test bench is designed according to the subway train bogie, and the ratio of the test bench to the real bogie is 1:2. The signals collected in the experiment include 18 channels, and the sampling frequency is 64 kHz, including the three-axis acceleration of the motor, gearbox and axle box and the three-phase current of the motor. Nine working conditions are considered in the experiment, and different motor speeds are controlled by the frequency converter to simulate different train speeds, and different lateral loads are applied by the electro-hydraulic load device to simulate the running state of going straight or turning. The experiment simulates 19 different health states of the train drive system, including motor faults, gearbox faults, axle box faults, etc. Each health state in the training data set stores 10 samples, and each sample is 0.05 s. Among them, 5 samples of each state are randomly selected as the core sample construction set, and the other 5 samples are used as the network parameter update set. Test them with samples outside the training data set.

[0113] The experiment uses the method proposed by the present invention to diagnose the faults of the motor, gearbox and axle box in the drive system, and compares the diagnostic accuracy with 4 existing methods.

[0114] Method A: A baseline method that uses a typical kernel sample network and does not take special measures to handle mislabeled data.

[0115] Method B: Combines a kernel sample network and a transfer matrix learning method to achieve few-shot learning and improve robustness to mislabeled data.

[0116] Method C: Trains a kernel sample network using the generalized cross-entropy loss to mitigate the impact of mislabeled data.

[0117] Method D: Trains a kernel sample network based on a joint teaching strategy to mitigate the impact of label errors.

[0118] The basic structure of the kernel sample network is shown in Table 1:

[0119] Table 1. Summary of the basic network structure

[0120]

[0121]

[0122] The training-related parameters are shown in Table 2.

[0123] Table 2. Summary of the training-related parameters

[0124] Parameter Name Setting Number of Training Iterations 500 Learning Rate 0.001 Optimizer Adam

[0125] The experimental results are summarized in Tables 3 - 5 and Figure 5 - Figure 7 .

[0126] Table 3. Summary of the accuracy of datasets with different proportions of mislabeled data in motor diagnosis

[0127]

[0128] Table 4. Summary of the accuracy of datasets with different proportions of mislabeled data in gearbox diagnosis

[0129]

[0130]

[0131] Table 5. Summary of the accuracy of datasets with different proportions of mislabeled data in axle box diagnosis

[0132]

[0133] It can be seen from the experimental results that the present invention's suppression of mislabeled samples does not rely on a large-scale training dataset, but rather designs specific mechanisms for different mislabeled data scenarios, thereby obtaining excellent diagnostic performance and having obvious superiority over existing methods.

[0134] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For related parts, reference can be made to the description in the method section.

[0135] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A low-quality and small sample diagnosis method for transmission systems based on the second-order moment measurement of the diffusion process, characterized in that: The following steps are involved: Obtain a mechatronic transmission system fault diagnosis dataset D containing wrong labels, randomly extract samples from it to obtain a core sample construction set S and a network parameter update set Q; Based on the feature extractor, multi-dimensional features are extracted for each sample in the core sample construction set S and the network parameter update set Q, and the weight of the sample feature vector and the second-order moment measurement matrix of the diffusion process are calculated; Calculate the core sample P of each healthy category in the core sample construction set S based on the weight of the sample feature vector and the second-order moment measurement matrix of the diffusion process; Based on the classifier, the second-order moment measurement matrix of the diffusion process of the sample feature vector in the network parameter update set Q is calculated, and the similarity between the kernel samples P of various health categories is calculated. According to the similarity, the probability of the healthy category to which the sample in the network parameter update set Q belongs is calculated; Construct a loss function that can attenuate the impact of outliers, and iteratively train the feature extractor and classifier under the guidance of this loss function; The extracted multidimensional features t a Input to the multidimensional correlation distribution feature extraction layer, which is used to calculate the second-order moment measurement matrix of the diffusion process based on the correlation distribution features; the calculation method of the second-order moment measurement matrix of the diffusion process is as follows: t a With L×C dimensions, L represents the time dimension and C represents the channel dimension. The multidimensional feature t is calculated. a The Euclidean space distance matrix of : in, Represents multidimensional features t a The Euclidean space distance between the i-th eigenvector and the j-th eigenvector in ; Calculate multidimensional features t a The second-order moment measurement matrix of the diffusion process is:

2. The low-quality and small sample diagnosis method for transmission system based on the second-order moment measurement of diffusion process according to claim 1 is characterized in that: The sample representation of the dataset D is {(X0,Y0),(X1,Y1)…(X n ,Y n )}, where any sample Represents the multi-source sensor data of the sample, L represents the time dimension, C represents the channel dimension, and Y a Indicates the corresponding label; X a is a time series, represented by {x1,x2,…,x L }, where any value in the time series is represented by (b=1,2,…,L),x b,C Represents the data of the Cth channel of the signal at time b.

3. The low-quality and small sample diagnosis method for transmission system based on the second-order moment measurement of diffusion process according to claim 1 is characterized in that: N health categories are randomly selected from the data set D, and K samples are randomly selected from each health category to form a core sample construction set S; several additional samples of the same health category as the core sample construction set S are selected from the data set D to form a network parameter update set Q, and the samples in the network parameter update set Q do not overlap with the samples in the core sample construction set S.

4. The low-quality and small sample diagnosis method for transmission system based on the second-order moment measurement of diffusion process according to claim 1 is characterized in that: The feature extractor consists of multiple one-dimensional convolutional layers. For any sample X a , its one-dimensional convolution is calculated as follows: Among them, d is the size of the convolution kernel; C is the channel dimension; i and j are variables in the summation process; w is the weight of the convolution kernel; b is the bias; Input sample X a The multidimensional features captured by the feature extractor F are expressed as in, represents the nonlinear mapping of the feature extractor, represents the learnable parameters in the feature extractor.

5. The low-quality and small sample diagnosis method for transmission system based on second-order moment measurement of diffusion process according to claim 1 is characterized in that: For the healthy category c in the core sample construction set S, the calculation formula of its core sample is: Among them, P c Construct the core samples of healthy category c in the core sample set S; represents the sample X of healthy category c in the core sample construction set S a The second-order moment measurement matrix of the diffusion process; Construct sample X in set S for the core sample a The weight of .

6. The low-quality and small sample diagnosis method for transmission system based on the second-order moment measurement of diffusion process according to claim 5 is characterized in that: Sample X in the core sample construction set S a Weight The calculation formula is: in, represents the sample X in the healthy category c in the core sample construction set S b The sum of the similarity of the second-order moment measurement matrix of the diffusion process; represents the sample X in the healthy category c in the core sample construction set S a The sum of the similarity of the second-order moment measurement matrix of the diffusion process is calculated as follows: in, represents the sample X belonging to the healthy category c in the core sample construction set S a and X b The second-order moment of the diffusion process measures the matrix similarity.

7. The low-quality and small sample diagnosis method for transmission system based on second-order moment measurement of diffusion process according to claim 6 is characterized in that: Two different samples X in the healthy category c in the core sample construction set S a and X b The calculation process of the second-order moment measurement matrix similarity of the diffusion process is: Through the feature extractor, samples X are extracted respectively a and sample X b The multidimensional features of a and t b , and calculate the multidimensional features t a and t b The second-order moment measurement matrix M of the diffusion process a and M b ; Calculate two samples X a and X b The second-order moment measurement matrix similarity of the diffusion process is: ρ(t a ,t b )=tr(M a T M b ) Here, tr(·) represents the trace of the matrix.

8. The low-quality and small sample diagnosis method for transmission system based on the second-order moment measurement of diffusion process according to claim 5 is characterized in that: The calculation formula for the probability of the healthy category to which the sample in the network parameter update set Q belongs is: Among them, P(Y i =c) represents the sample X i The probability of belonging to health category c; For sample X i The core sample P of the healthy category c in the core sample construction set S c The similarity between them; k is one of the health categories k in N; N is the set of all health categories in the core sample construction set S; For sample X i and the kernel sample P of healthy category k k The similarity between Among them, M i T Update the network parameters with sample X in set Q i The second-order moment metric matrix of the diffusion process.

9. The low-quality and small sample diagnosis method for transmission system based on second-order moment measurement of diffusion process according to claim 1 is characterized in that: The expression of the loss function is: in, For data X i Features extracted by the feature extractor; N is the set of all health categories; k is one of the health categories in the health set N; For sample X i Corresponding label health category Y i Nuclear samples; P k is the core sample of healthy category k; θ i is the weight of the loss function, which is used to attenuate the impact of outliers. The weight of the wrong label is attenuated by using the outlier attribute of the wrong label. The weight is calculated as follows: Among them, sample X i is any sample in the network parameter update set; Y i For sample X i Health category label; Y j For sample X j Health category label; Y i =Y j Represents sample X i and sample X j The health categories are the same; For sample X i With its health category Y i Nuclear samples similarity; For sample X j With its health category Y j Nuclear samples The similarity.

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