Metamigration learning-driven small sample variable working condition rotating machine fault diagnosis method

Abstract

The invention discloses a meta transfer learning-driven small sample variable working condition rotating machine fault diagnosis method, which comprises the following steps of: dividing an original fault vibration signal into a source domain working condition data set and a target domain working condition data set, and extracting samples to form a training, verification and test task set; constructing a feature extractor to perform feature extraction of the training task set; building a meta transfer learning fault diagnosis model; the training tasks are input into the meta-migration model for multi-step optimized internal loop training, the model updating gradient of each training round is obtained, and the optimal parameters of each step of training of each task are found; performing outer loop training by using the verification task set, and updating randomly initialized model parameters and an inner loop learning rate; and inputting the test task into the optimal meta transfer learning fault diagnosis model to obtain the health state of the target domain rotating machinery. According to the method, the problems that overfitting is generated by using small sample task training and the model precision and generalization performance are reduced due to unstable training gradient are effectively solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of rotating machinery fault diagnosis, and in particular relates to a small sample variable operating condition rotating machinery fault diagnosis method driven by meta-transfer learning. Background Art

[0002] Large-scale mechanical equipment such as helicopters, combine harvesters, and wind turbines work in harsh and complex environments for a long time. High-intensity loads often cause equipment failures, disrupting normal operation, causing casualties and economic losses. In order to ensure the normal operation of large-scale mechanical equipment, intelligent fault diagnosis is of great research value.

[0003] Due to the complex internal structure of large-scale mechanical equipment, the vibration signals collected in complex environments are subject to various noise interferences, which easily lose important fault feature information, and it is very difficult to collect enough fault samples. Due to the continuous changes in operating conditions, the frequent occurrence of variable speed and variable load will cause significant changes in the frequency and amplitude of the signal and the data distribution, making the fault diagnosis model trained under a single working condition show poor robustness and low diagnostic accuracy in variable working condition scenarios.

[0004] Traditional fault diagnosis methods rely on a lot of expert experience and manually extracted features, which increases the difficulty of fault diagnosis of large mechanical equipment in actual operation. Deep learning obtains deep fault diagnosis through nonlinear fitting of multi-layer neural networks, which greatly improves the accuracy of fault diagnosis. When fault samples are scarce and the data distribution of the test samples is very different from that of the training samples, the fault diagnosis model based on deep learning is prone to overfitting problems, resulting in reduced diagnostic accuracy and generalization performance. Transfer learning can use the similarity between data to apply the models and knowledge learned in the source field to the target field. Meta-learning has low requirements on the amount of training data for the target task. Its goal is to master the ability to quickly learn new tasks through many small sample learning tasks.

[0005] Existing meta-transfer diagnosis methods have the following shortcomings: traditional meta-learning models are very sensitive to the choice of hyperparameters (such as learning rate) and network architecture, and are trained on small sample tasks, which poses a risk of overfitting. The unstable training gradient leads to reduced model accuracy and generalization performance. Summary of the invention

[0006] In view of the shortcomings in the prior art, the present invention provides a small-sample variable-condition rotating machinery diagnosis method driven by meta-transfer learning, which can effectively solve the problems of overfitting caused by small-sample task training and unstable training gradients leading to reduced model accuracy and generalization performance.

[0007] The present invention achieves the above technical objectives through the following technical means.

[0008] Meta-transfer learning driven small sample variable condition rotating machinery fault diagnosis method:

[0009] Collect the original vibration signal of rotating machinery;

[0010] The original vibration signal is divided into a source domain working condition data set and a target domain working condition data set according to different working conditions, and further divided into a training task set, a verification task set and a test task set of the meta-transfer learning fault diagnosis model;

[0011] Build a meta-transfer learning fault diagnosis model, including a feature screening module, a transfer feature domain adaptation module, and a classification module;

[0012] Use random values ​​to initialize the meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α, extract the features of the training task set through the feature extractor, input the features into the feature screening module, the migration feature domain adaptation module and the classification module for multi-step optimized inner loop training, obtain the model update gradient of each training round, and find each task T i The optimal parameter θ for each step of training i ′ ,k ;

[0013] Extract task T' from the verification task set i , according to each task T obtained in the inner loop training i The optimal parameter θ for each step of training i ′ ,k Calculate the outer loop training loss of each step, assign different weights to the outer loop training loss of each step according to the weight distribution principle, and use the total outer loop training loss after weight distribution to update the randomly initialized meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α;

[0014] The model parameters with the highest accuracy of the meta-transfer learning fault diagnosis model in the outer loop training are saved, and the model parameters are set as the optimal parameters; the tasks in the test task set are input into the meta-transfer learning fault diagnosis model using the optimal parameters to obtain the health status of the rotating machinery in the target domain.

[0015] Furthermore, the original vibration signal of the rotating machinery includes original vibration signals of five states of the rotating machinery under three working conditions.

[0016] Furthermore, the three working conditions are specifically as follows: working condition 1: 900r / min, load is 20% of full load; working condition 2: 900r / min, load is 50% of full load; working condition 3: 1500r / min, load is 20% of full load; the five states include combined fault sun gear and ring gear tooth breakage, normal gear, single fault planetary gear tooth missing, single fault ring gear pitting and single fault sun gear pitting.

[0017] Furthermore, the tasks of the training task set are composed of the support set of the source domain working conditions and the support set of the target domain conditions The verification task set consists of a query set of source domain conditions. and the query set of the target domain conditions Sampling composition: the test task set consists of data samples that have not been used in the target domain working condition data set.

[0018] Furthermore, the support set From the source domain working condition data set K samples are extracted from N categories, and the support set The target domain working condition dataset K samples are extracted from N categories, and the query set From the source domain working condition data set The query set consists of J samples extracted from N categories. From the source domain working condition data set J samples are drawn from N categories; among them, represents the i'th source domain condition sample, represents the sample label of the i'th source domain condition, represents the j-th target domain working condition sample, represents the label of the j-th target domain working condition sample, n represents the total number of categories of source domain working condition samples, m represents the total number of categories of target domain working condition samples, and N is less than both n and m.

[0019] Furthermore, the loss function of the inner loop is Among them, k is the number of steps of multi-step optimization in the inner loop training, λ 1 and λ 2 is the hyperparameter for weight balancing, L b represents the loss function of the inner loop feature screening module, L m represents the loss function of the inner loop migration feature domain adaptation module, L c represents the classification loss function of the inner loop classification module, x s Indicates the source domain condition to extract the support set The characteristic of-i is x s The smallest singular value of the i″th feature matrix, p is the number of singular values ​​that need to be suppressed, E P (·) and E q (·) represents the expected value, φ(·) represents the mapping function that maps the sample to the high-dimensional space, and x t Indicates the target domain condition to extract the support set Features, represents the feature space, |D S | is the cardinality of the source domain working condition data set, y represents the s The corresponding true label, y I Represents x s The corresponding predicted label, O represents the number of samples of the task.

[0020] Furthermore, each task T i The optimal parameters for each step of training Where θ represents the randomly initialized meta-transfer learning fault diagnosis model parameters, represents the updated gradient, Represents task T i The inner cycle loss, f θ represents a parameterized function of θ.

[0021] Furthermore, the outer loop training loss function

[0022] Furthermore, the total loss of the outer loop training is And γ 1 +γ 2 +…+γ k =1, where is the total loss of the outer loop training, γ k is the weight balancing parameter.

[0023] Furthermore, the total loss of the outer loop training after weight allocation is used to update the randomly initialized meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α:

[0024]

[0025] Among them, β is the outer loop learning rate, T′ i ~p(T), p(T) is a batch of tasks extracted from the verification task set, is each task T′ i Relative to the parameters θ obtained by each step of inner loop training i ′ ,k The gradient of represents the updated gradient of α.

[0026] The effective rights and interests of the present invention are:

[0027] (1) The present invention adopts a learnable inner loop learning rate α, which improves the model's ability to learn different tasks, reduces the time and labor costs associated with parameter selection, and can effectively solve the problem of overfitting of the meta-transfer model after training with small sample tasks, thereby improving the fault recognition rate of the target working condition;

[0028] (2) The present invention adopts a multi-step optimized inner loop training method, which can obtain stable model training gradients, reduce the risk of gradient explosion or gradient decay during inner loop training, and effectively solve the problem of unstable training gradients leading to reduced model accuracy and generalization performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is a flow chart of the fault diagnosis of rotating machinery with small sample and variable working condition driven by meta-transfer learning according to the present invention;

[0030] FIG2( a ) is a diagram of the original vibration signal collected when a composite fault occurs in the planetary gearbox test bench of working condition 1 of the present invention, and the sun gear and the ring gear are broken;

[0031] FIG2( b ) is a diagram of the original vibration signal collected when the planetary gearbox test bench of working condition 1 of the present invention is working normally;

[0032] FIG2( c ) is a diagram of the original vibration signal collected when a single fault occurs in the planetary gearbox test bench of working condition 1 of the present invention, and a planetary gear tooth is missing;

[0033] FIG2( d ) is a diagram of the original vibration signal collected when a single fault gear ring pitting occurs on the planetary gearbox test bench of working condition 1 of the present invention;

[0034] FIG2( e ) is a diagram of the original vibration signal collected when a single fault sun gear pitting occurs on the planetary gearbox test bench of working condition 1 of the present invention;

[0035] FIG3( a ) is a diagram showing the change of the feature screening loss function during the training process of the present invention;

[0036] FIG3( b ) is a diagram showing the change of the classification loss function during the training process of the present invention;

[0037] FIG3( c ) is a diagram showing the change of the total loss function of the outer loop during the training process of the present invention;

[0038] Figure 4 This is a rendering of the health status of mechanical equipment obtained in an embodiment of the present invention;

[0039] Figure 5This is a confusion matrix diagram corresponding to the health status of mechanical equipment obtained in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention will be described clearly and completely in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention. The present invention will be further described in conjunction with the drawings and the embodiments taking rolling bearings as examples.

[0041] Taking the gearbox as a key component of the rotating machinery, the method for diagnosing the fault of the rotating machinery with small sample and variable working condition driven by meta-transfer learning of the present invention is specifically described. The specific details are as follows: Figure 1 As shown, the following steps are included:

[0042] Step (1), gearbox vibration signal acquisition: This example conducts a fault diagnosis experiment on a planetary gearbox test bench (HD-CL-012X) at the University of Connecticut. This experiment uses five states of gears to be tested on the test bench, including four faulty gears and one normal gear. The five states are set as composite fault sun gear and ring gear tooth fracture (asr), normal gear (n), single fault planetary gear tooth missing (sptm), single fault ring gear pitting (srp) and single fault sun gear pitting (ssp). The above faults are all generated by manual processing. The speed of the motor (used to drive the planetary gearbox) is controlled by a frequency converter to simulate the operating state of the gearbox as a transmission system under different speeds and working conditions. The gearbox fault vibration signal data under variable working conditions is collected by a three-axis acceleration sensor installed on the surface of the gearbox housing. The data acquisition channels are 8 and the sampling frequency is 12.8kHz. In order to increase the types of test conditions, three tests under different speeds and loads were designed, namely condition one: 900r / min, load is 20% of the full load; condition two: 900r / min, load is 50% of the full load; condition three: 1500r / min, load is 20% of the full load; conditions one, two and three can be used as both source domain conditions and target domain conditions. Under the three conditions, the original vibration signals of the planetary gearbox in five states are collected. The original vibration signals of the planetary gearbox in five states of condition one are shown in Figures 2(a), (b), 2(c), 2(d) and 2(e). The specific division of the three conditions is shown in Table 1:

[0043] Table 1 Meta-transfer learning under different working conditions

[0044]

[0045] Step (2): Divide the task set

[0046] The original vibration signal data collected in the source domain working condition and the target domain working condition are cut and sampled according to a fixed sample length of 1024, and the original vibration signal is divided into source domain working condition data sets according to different working conditions and target domain condition dataset From D S K samples are extracted from N (N<n) categories to form a support set From D T K samples are extracted from N (N<m) categories to form a support set From D S Extract J samples from N (N<n) categories to form a query set From D T Extract J samples from N (N<m) categories to form a query set in, represents the i'th source domain condition sample, represents the sample label of the i'th source domain condition, represents the j-th target domain working condition sample, represents the label of the j-th target domain working condition sample, n represents the total number of categories of source domain working condition samples, and m represents the total number of categories of target domain working condition samples.

[0047] The dataset of the meta-transfer learning fault diagnosis model contains three task sets: training task set, verification task set and test task set. The minimum training unit of the input meta-transfer learning fault diagnosis model is a task, and each task consists of multiple groups of input samples. The tasks of the training task set are and Sampling composition, the tasks of the verification task set are composed of and Sampling composition, the test task set consists of data samples that have not been used in the target domain working condition data set. The specific division is shown in Table 2:

[0048] Table 2 Division of different task sets for meta-transfer learning

[0049]

[0050] In the migration scenarios in Table 2, → the left side is the source domain, → the right side is the target domain.

[0051] Step (3): Build a feature extractor

[0052] The feature extractor of the meta-transfer learning fault diagnosis model is composed of a one-dimensional deep convolutional neural network, which contains four modules: the first three modules are convolution modules, each of which contains a one-dimensional convolution layer, a batch normalization layer, a nonlinear activation layer, and a maximum pooling layer, where the one-dimensional convolution kernel length is 101, the kernel channels are 12, 18, and 24, the sliding step is 1, the padding step is 1, the maximum pooling layer filter size is 2, and the sliding step is 2; the last module is a linear output layer. When training the meta-transfer learning fault diagnosis model, the tasks in the three task sets under different working conditions are input into the one-dimensional deep convolutional neural network as training samples.

[0053] Step (4) combines the improved meta-learning method with the transfer learning method to build a meta-transfer learning fault diagnosis model, which includes three modules: feature screening module, transfer feature domain adaptation module and classification module. The feature screening module is used to screen features with strong transferability between source domain conditions and target domain conditions, the transfer feature domain adaptation module is used to align the feature distribution of source domain conditions and target domain conditions, and the classification module is used to train the model to correctly identify rotating machinery faults. The functional implementations of the feature screening module, the transfer feature domain adaptation module and the classification module are all prior art.

[0054] Step (5) uses random values ​​to initialize the meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α, extracts the features of the training task set through the feature extractor, inputs the features into the feature screening module, the migration feature domain adaptation module and the classification module for multi-step optimized inner loop training, obtains the model update gradient of each training round, and finds the optimal solution for each task T. i The optimal parameter θ for each step of training i ′ ,k .

[0055] Step (51), calculate the loss function L of the inner loop feature screening module b :

[0056]

[0057] Among them, x s Indicates the source domain condition to extract the support set The characteristic of -i is x s The smallest singular value in the i″th feature matrix, p is the number of singular values ​​that need to be suppressed.

[0058] Step (52), calculate the loss function L of the inner loop migration feature domain adaptation module m :

[0059]

[0060] Among them, E P (·) and E q (·) represents the expected value, φ(·) represents the mapping function that maps the sample to the high-dimensional space, and x t Indicates the target domain condition to extract the support set Features, Represents the feature space.

[0061] Step (53), calculate the classification loss function L of the inner loop classification module c

[0062] After extracting features through the feature extractor, the support set is extracted from the source domain conditions. Features of x s Mapped to class prediction label y I ; For supervised learning on source domain conditions, the classification loss function L c for:

[0063]

[0064] Among them, |D S | is the cardinality of the source domain working condition data set, y represents the s The corresponding true label, y I Represents x s The corresponding predicted label, O represents the number of samples of the task.

[0065] Step (54), calculate the inner loop loss function L i,k :

[0066]

[0067] Among them, k is the number of steps of multi-step optimization in the inner loop training, λ 1 and λ 2 is a hyperparameter for weight balancing.

[0068] Step (55), perform multi-step optimization inner loop training, obtain the model update gradient of each training round, and find each task T i The optimal parameter θ for each step of training i ′ ,k :

[0069]

[0070] Where θ represents the randomly initialized meta-transfer learning fault diagnosis model parameters, α represents the randomly initialized inner loop learning rate, represents the updated gradient, Represents task T i The inner cycle loss, fθ represents a parameterized function of θ.

[0071] Meta-transfer learning fault diagnosis model in Update the parameters in the direction, and the update length is the value of the learning rate α.

[0072] Step (6), extract task T′ from the verification task set i , according to each task T obtained in the inner loop training i The optimal parameter θ at each step i ′ ,k Perform feature extraction, input the features into the feature screening module, the migration feature domain adaptation module and the classification module for outer loop training (i.e., calculate the outer loop training loss), and assign different weights to the outer loop training loss of each step according to the weight distribution principle. Use the total outer loop training loss after weight distribution to update the randomly initialized meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α.

[0073] Step (61), calculate the outer loop loss function:

[0074]

[0075] Among them, L o,k represents the outer loop training loss at each step.

[0076] Step (62), assign different weights to the outer loop training loss of each step according to the weight distribution principle, and reconstruct the total outer loop training loss:

[0077]

[0078] in, is the total loss of the outer loop training, γ k is the weight balancing parameter, and γ 1 +γ 2 +…+γ k =1.

[0079] Step (63), use the total loss of the outer loop training after weight allocation to update the randomly initialized meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α:

[0080]

[0081] Among them, β is the outer loop learning rate, T′ i ~p(T), p(T) is a batch of tasks extracted from the verification task set, is each new task T′ i Relative to the parameters θ obtained by each step of inner loop training i′ ,k The gradient of represents the updated gradient of α.

[0082] Step (7), save the model parameters with the highest fault category classification accuracy (i.e., accuracy) of the meta-transfer learning fault diagnosis model in the outer loop training, and set the model parameters as the optimal parameters; input the tasks in the test task set into the meta-transfer learning fault diagnosis model using the optimal parameters to obtain the health status of the target domain mechanical equipment.

[0083] In this embodiment, the inner loop learning rate α is set to a learnable adaptive learning rate, the outer loop learning rate β is set to 0.001, and λ 1 and λ 2 They are set to 0.003 and 0.7 respectively. The number of inner loop training steps is 3, and γ 1 , γ 2 and γ 3 They are set to 0.1, 0.2 and 0.7 respectively. Taking the migration task condition 2 → condition 3 as an example, during the entire outer loop, the changes in the loss function, classification loss function and total loss function of the feature screening module are as follows: Figure 3(a) , 3(b) As shown in Figure 3(c), it can be seen that the decrease in total loss only requires a few iterations to achieve good stability, and the process is smooth and without oscillation. The deep features extracted from the test task set in the high-dimensional space are reduced to the two-dimensional space to obtain the health status of the mechanical equipment in the target domain. The visualization effect is as follows: Figure 4 The corresponding confusion matrix is ​​shown as Figure 5 .

[0084] In order to further verify the effectiveness of the present invention, another four methods were used for comparison. Method 1 is to align the features of the source domain and the target domain by adding an adaptive layer to the network, thereby achieving domain adaptation, and using the Maximum Mean Discrepancy (MMD) method to measure the distance between distributions. Method 2 is Domain-Adversarial Neural Networks (DANN), which introduces the idea of ​​adversarial learning into transfer learning, and selects features with stronger migration between different domains through domain discrimination loss and training loss. Method 3 is Meta Relation Net (MRN), which obtains the relationship score by calculating the similarity between the support set sample features and the query set sample features, thereby analyzing the degree of matching. Method 4 is Model-Agnostic Meta-Learning (MAML), which constructs multiple tasks through a small number of samples and generates a fast learner through training. As can be seen from Table 3, the average test accuracy of the method proposed in the present invention is improved by 26.31%, 31.32%, 5.37% and 20.12% respectively compared with the comparison method.

[0085] Table 3 Comparison of different fault diagnosis methods

[0086]

[0087] In summary, the small-sample variable-operating-condition rotating machinery fault diagnosis method driven by meta-transfer learning of the present invention quickly learns the fault information knowledge between different operating conditions through tasks containing a small number of samples, selects features with good transferability in the source domain, improves the model generalization performance and health status recognition accuracy, and completes the rotating machinery fault diagnosis under small-sample variable operating conditions.

[0088] Reference terms such as "one embodiment", "example", "specific example" and the like described in this specification are intended to mean that the specific features, materials, structures or characteristics in combination with the embodiment are included in at least one embodiment or example of the present invention. In this specification, the illustrative use of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0089] The embodiments are preferred implementations of the present invention, but the present invention is not limited to the above-mentioned implementations. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essential content of the present invention belong to the protection scope of the present invention.

Claims

1. A small sample variable working condition rotating machinery fault diagnosis method driven by meta-transfer learning, characterized by: Collect the original vibration signal of rotating machinery; The original vibration signal is divided into a source domain working condition data set and a target domain working condition data set according to different working conditions, and further divided into a training task set, a verification task set and a test task set of the meta-transfer learning fault diagnosis model; Build a meta-transfer learning fault diagnosis model, It includes feature screening module, migration feature domain adaptation module and classification module; Use random values ​​to initialize the meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α, extract the features of the training task set through the feature extractor, input the features into the feature screening module, the migration feature domain adaptation module and the classification module for multi-step optimized inner loop training, obtain the model update gradient of each training round, and find each task T i The optimal parameter θ for each step of training i ′ ,k ; Extract task T' from the verification task set i , according to each task T obtained in the inner loop training i The optimal parameter θ for each step of training i ′ ,k Calculate the outer loop training loss of each step, assign different weights to the outer loop training loss of each step according to the weight distribution principle, and use the total outer loop training loss after weight distribution to update the randomly initialized meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α; The model parameters with the highest accuracy of the meta-transfer learning fault diagnosis model in the outer loop training are saved, and the model parameters are set as the optimal parameters; the tasks in the test task set are input into the meta-transfer learning fault diagnosis model using the optimal parameters to obtain the health status of the rotating machinery in the target domain.

2. The method for diagnosing rotating machinery faults with a small sample size and variable operating conditions according to claim 1 is characterized in that: The original vibration signals of the rotating machinery include original vibration signals of five states of the rotating machinery under three working conditions.

3. The small sample variable operating condition rotating machinery fault diagnosis method according to claim 2 is characterized in that: The three working conditions are specifically: working condition one: 900r / min, load is 20% of the full load; working condition two: 900r / min, load is 50% of the full load; working condition three: 1500r / min, load is 20% of the full load; the five states include combined fault sun gear and ring gear tooth breakage, normal gear, single fault planetary gear tooth missing, single fault ring gear pitting and single fault sun gear pitting.

4. The method for diagnosing rotating machinery faults with a small sample size and variable operating conditions according to claim 1, characterized in that: The tasks of the training task set are composed of the support set of the source domain conditions. and the support set of the target domain conditions The verification task set consists of a query set of source domain conditions. and the query set of the target domain conditions Sampling composition: the test task set consists of data samples that have not been used in the target domain working condition data set.

5. The method for diagnosing rotating machinery faults with a small sample size and variable operating conditions according to claim 4 is characterized in that: The support set From the source domain working condition data set K samples are extracted from N categories, and the support set The target domain working condition dataset K samples are extracted from N categories, and the query set From the source domain working condition data set The query set consists of J samples extracted from N categories. From the source domain working condition data set J samples are drawn from N categories; among them, represents the i'th source domain condition sample, represents the sample label of the i'th source domain condition, represents the j-th target domain working condition sample, represents the label of the j-th target domain working condition sample, n represents the total number of categories of source domain working condition samples, m represents the total number of categories of target domain working condition samples, and N is less than both n and m.

6. The method for diagnosing rotating machinery faults with a small sample size and variable operating conditions according to claim 1, characterized in that: Loss function of the inner loop Among them, k is the number of steps of multi-step optimization in the inner loop training, λ1 and λ2 are the hyperparameters of weight balance, and L b represents the loss function of the inner loop feature screening module, L m represents the loss function of the inner loop migration feature domain adaptation module, L c represents the classification loss function of the inner loop classification module, x s Indicates the source domain condition to extract the support set The characteristic of -i is x s The smallest singular value of the i″th feature matrix, p is the number of singular values ​​that need to be suppressed, E P (·) and E q (·) represents the expected value, φ(·) represents the mapping function that maps the sample to the high-dimensional space, and x t Indicates the target domain condition to extract the support set Features, represents the feature space, |D S | is the cardinality of the source domain working condition data set, y represents the s The corresponding true label, y I Represents x s The corresponding predicted label, O represents the number of samples of the task.

7. The method for diagnosing rotating machinery faults with a small sample size and variable operating conditions according to claim 6 is characterized in that: Each task T i The optimal parameters for each step of training Where θ represents the randomly initialized meta-transfer learning fault diagnosis model parameters, represents the updated gradient, L Ti Represents task T i The inner cycle loss, f θ represents a parameterized function of θ.

8. The method for diagnosing rotating machinery faults with a small sample size and variable operating conditions according to claim 6, characterized in that: Outer loop training loss function 9. The method for diagnosing rotating machinery faults with a small sample size and variable operating conditions according to claim 8, characterized in that: The total loss of the outer training loop γ1<γ2<…γ i1 …<γ k , and γ1+γ2+…+γ k =1, where is the total loss of the outer loop training, γ k is the weight balancing parameter.

10. The method for diagnosing rotating machinery faults with a small sample size and variable operating conditions according to claim 9, characterized in that: The total loss of the outer loop training after weight allocation is used to update the randomly initialized meta-transfer learning fault diagnosis model parameters θ and the inner loop learning rate α: Among them, β is the outer loop learning rate, T′ i ~p(T), p(T) is a batch of tasks extracted from the verification task set, is each task T′ i Relative to the parameters θ obtained by each step of inner loop training i ′ ,k The gradient of represents the updated gradient of α.

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