Zero-Shot Bearing Fault Diagnosis Method Based on High-Dimensional Parameter Multi-Objective Efficient Optimization Using Deep Models

Abstract

This invention discloses a zero-shot bearing fault diagnosis method based on high-dimensional parameter multi-objective efficient optimization using a deep model, relating to the field of intelligent bearing fault diagnosis. The method includes the following steps: construction of a visual feature extractor through high-dimensional spatial domain transformation; construction of a visual feature extractor component optimization strategy based on a surrogate-assisted multi-objective evolutionary algorithm; construction of a semantic matrix assisted by statistical features of sequential signals; and construction of a visual-semantic autoencoder zero-shot mapping strategy for outlier interpolation. This invention improves upon the inherent technical bottlenecks in existing rotating machinery fault diagnosis, such as insufficient extraction of detection and discrimination features, low efficiency in model reconstruction and detection performance, imbalance in the number of various types of samples, and limited identification of outliers / zero-shot samples. It ensures safe and reliable equipment operation, minimizes spare parts costs, mechanical system downtime, and maintenance time, and provides a new method for solving key problems restricting the development of bearing fault diagnosis in current practical engineering scenarios.

Description

Technical Field

[0001] This invention relates to the field of intelligent bearing fault diagnosis, specifically a zero-sample bearing fault diagnosis method based on high-dimensional parameter multi-objective efficient optimization using a deep model. Background Technology

[0002] In the course of modernization, rotating machinery is indispensable in everything from large-scale manufacturing industries such as wind power generation, aerospace components, and mining machinery to automated manufacturing equipment in small businesses. To meet the ever-evolving demands of industrial production and manufacturing, machinery is being designed to be increasingly precise, complex, and intelligent. However, due to factors such as operating environment and manufacturing processes, the failure rate of machinery is gradually increasing.

[0003] Traditional fault diagnosis methods typically employ model-based or signal processing-based approaches. However, with the increasing size and complexity of modern machinery, the former often struggles to establish numerical models that reliably reflect the operating characteristics of the mechanical system, while the latter, relying too heavily on human technical experience, is ill-suited for effectively extracting fault features from massive amounts of data. Currently, data-driven intelligent fault diagnosis algorithms, with their powerful feature extraction capabilities, are gradually replacing the establishment of complex numerical models or cumbersome signal processing, becoming a research hotspot in the field of rotating machinery fault diagnosis both domestically and internationally. However, existing data-driven intelligent fault diagnosis methods heavily rely on large amounts of ideal labeled data. In actual engineering scenarios, although equipment accumulates massive amounts of data through long-term operation, there is a lack of usable data to train intelligent fault diagnosis models, as specifically demonstrated below.

[0004] (1) The problem of no historical training data for fault types, i.e., fault diagnosis under zero-sample conditions. Compared with the typical fault types generated by laboratory process operations, rolling bearings in actual engineering scenarios are prone to complex and diverse fault types due to harsh working conditions such as large loads and strong impacts. As a result, there is no labeled or unlabeled historical training data available for training intelligent fault diagnosis models. Without stopping the machine for inspection, how to identify fault types without historical records (i.e., unseen faults) and improve the accuracy of unseen fault identification using existing condition monitoring data is a key issue in the field of fault diagnosis at present, and it urgently needs to be solved.

[0005] (2) The mainstream fault diagnosis model structure is generally selected manually, which largely depends on the designer's experience and knowledge. It often requires repeated experiments to determine the final model structure, making it difficult to balance multiple indicators such as model diagnosis speed and detection performance. The process is time-consuming, inefficient, and makes it difficult to guarantee the generalization of the diagnostic model. Therefore, how to achieve automatic balance and optimization of diagnostic model performance while providing the optimal model component structure with reliable output still requires further in-depth research. Summary of the Invention

[0006] To further improve the technical bottlenecks inherent in existing rotating machine fault diagnosis, such as insufficient extraction of detection and discrimination features, low efficiency in model reconstruction detection performance, imbalance in the number of various types of samples, and limited identification of abnormal / zero samples, this invention proposes a zero-sample bearing fault diagnosis method based on high-dimensional parameter multi-objective efficient optimization of deep models.

[0007] This invention is achieved through the following technical solution: a zero-sample bearing fault diagnosis method based on high-dimensional parameter multi-objective efficient optimization using a deep model, comprising the following steps:

[0008] 1) Construction of a visual feature extractor for high-dimensional spatial domain transformation:

[0009] Typically, bearing fault diagnosis relies solely on analyzing vibration signals collected by sensors. The resulting one-dimensional time-domain sequences contain insignificant fault feature information and insufficiently express the correlation between features. This invention addresses this issue by constructing a high-dimensional spatial domain transformation visual feature extractor using a deep convolutional neural network model. First, sensors are used to collect sequence signals under various conditions, and the collected data is mapped into a high-dimensional Gramain Angular Summation Field (GASF). Features are decomposed in the high-dimensional space using fully connected layers to explore the feasibility of features in the high-dimensional spatial dimension of the data samples. This is then combined with a convolutional neural network to achieve efficient extraction of visual features from the data samples. The GASF transformation expression function is shown in equation (1). The overall framework of the visual feature extractor is constructed as shown in Table 1.

[0010] (1)

[0011] In the formula The transformed polar coordinate sequence, where I is the unit row vector. The specific transformation process involves encoding the time series in a polar coordinate system to display different information granularities of the samples; each element in the Gram matrix is ​​a trigonometric function value of an angle, and the Gram angle and field are constructed by using the summation operation of trigonometric functions.

[0012] Table 1 Overall framework of the visual feature extractor

[0013]

[0014] 2) Construction of optimization strategy for visual feature extractor components based on surrogate-assisted multi-objective evolutionary algorithm:

[0015] The visual feature extractor constructed in this invention, which involves high-dimensional spatial domain transformation, is only a rough framework. Except for the number of nodes in the final fully connected visual feature extraction layer, the setting of numerous internal structural components and parameters / hyperparameters is unknown. Relying solely on manual experience for operation would be subjective, unreasonable, and costly to redesign. Therefore, this invention constructs a surrogate-assisted evolution algorithm (CDNNEA) based on a constrained dropout neural network as an optimization strategy for visual feature extractor components. This optimization strategy adaptively searches the internal components of the deep model performing visual feature extraction, expanding the optimization objectives to three dimensions: recognition accuracy, model complexity, and training time. Furthermore, to reduce the time and hardware costs of model training and evaluation during single-objective optimization, a highly scalable surrogate model is constructed to assist the search strategy. The specific implementation is as follows:

[0016] The overall framework of the CDNNEA algorithm is as follows: Figure 3 As shown, the inputs are: maximum number of evaluations MaxFE, number of evaluations FE, population size P, decision variable dimension d, cost function f, number of true evaluation solutions σ, evaluation ratio ρ, and the output is the non-dominated solution set (X, Y) of the true problem. The specific steps include:

[0017] ① Initial solution generation part: X=LatinHypercubeSample(11d-1), Y=f(X);

[0018] ②FE=11d-1;

[0019] ③ Start algorithm iteration: WHILE FE ≤ MaxFE DO;

[0020] ④ Train the agent model using the training dataset: C-dropout=TrainingData(X, Y);

[0021] ⑤ Perform an optimization search on the non-dominated solution set in the population: (X1, Y1, ρ1, ρ2) = Estimate(P, C-dropout);

[0022] ⑥ Select σ previously obtained non-dominated solutions for actual evaluation according to the management criteria:

[0023] X2=Selection(X1, Y1, ρ1, ρ2, C-dropout, σ), Y2=f(X2);

[0024] ⑦X'=X∪X2, Y'=Y∪Y2;

[0025] ⑧ Update the training dataset: (X, Y)=Update(X', Y', 11d-1, σ);

[0026] ⑨FE=FE+1, ρ1=ρ2;

[0027] ⑩END WHILE;

[0028] Step ① generates the initial solution by sampling a portion of the initial samples after actual computation and generating the initial training dataset based on these. Steps ③ to ⑩ constitute the main iterative process of the algorithm. Step ④ primarily uses the training dataset to train the surrogate model. Step ⑤ optimizes the non-dominated solution set in the population; the target evaluation involved during this process does not require costly actual computation and can be achieved solely using the computationally inexpensive surrogate model. Finally, since the optimization guidance of the initially built surrogate model may not be correct, the quality of the non-dominated solutions and the accuracy of the model estimation will be difficult to guarantee without any update strategy. Therefore, step ⑥ selects σ previously obtained non-dominated solutions for actual evaluation according to the management criteria, and step ⑧ updates the training dataset.

[0029] Step ①, before optimization begins, CDNNEA uses the Latin hypercube sampling method to generate uniform sampling points of size 11d⁻¹ in the decision space, where d is the dimension of the decision variable. The objective function to be optimized is then used to perform real-world calculations on these points. The obtained decision variables and corresponding objective solutions are used as the dataset to train the surrogate model. The suitability of setting the sampling number to 11d⁻¹ can be found in the relevant literature.

[0030] 3) Semantic matrix construction aided by statistical features of sequence signals:

[0031] Because supervised classification typically uses one-hot codes for label information, there is often no correlation between the labels in supervised classification, making it impossible for supervised classification to classify unseen classes. However, there is a correlation between the auxiliary information of seen and unseen classes. This auxiliary information mainly comes from human-defined semantic description information, word vector information obtained by natural language processing technology, or a mixture of both. In this indirect way, a correlation is created between seen and unseen classes, making it possible for unseen classes to be correctly classified.

[0032] Semantic description information mainly refers to human summaries of category features based on prior knowledge. There are two forms of artificially defined semantic description information: binary description and continuous value description. The design of semantic description information for bearing fault sequence signals needs to meet the following conditions:

[0033] (1) It has semantic meaning, that is, it can be obtained through human descriptive information;

[0034] (2) It has discriminative power, that is, the semantic descriptions of different fault types are different;

[0035] (3) It has consistency, that is, once the number of attributes is determined, the dimension of the fault semantic description vector is fixed, and the same position in the vector represents the same attribute.

[0036] Binary representation primarily indicates the presence or absence of attributes. For fault semantic description, attributes can be various sensor indicators; if abnormal, the attribute value is 1, and if normal, the value is 0. Each fault in the fault semantic description information is represented by a vector, where each attribute value is either 0 or 1. The vector composed of these attribute values ​​constitutes the fault's semantic description information. While constructing semantic description vectors using binary representation is often relatively easy, its description of attributes is often incomplete because the attributes under fault conditions are not always definitive.

[0037] Continuous-valued representations of semantic descriptive information often describe faults more accurately than binary representations. However, continuous-valued representations are more difficult to implement and are more susceptible to individual subjectivity. Therefore, they typically require experts in the field to score the attribute; higher scores indicate more severe anomalies. The final continuous value is obtained by averaging the scores from multiple experts. However, zero-shot learning has been less studied in fault diagnosis, and the semantic descriptive information required for designing continuous-valued semantic descriptions of faults is difficult to express. Therefore, further research is needed on the construction of semantic matrices for sequence signals in fault diagnosis.

[0038] Statistical analysis is a theoretical statistical approach that follows stochastic processes. It primarily utilizes probabilistic and statistical methods to explore and discover the stochastic processes of things. In the intelligent diagnosis of bearing faults, the vibration frequency is uncertain due to the experimental environment and bearing materials, resulting in random components in the collected signals. Therefore, describing such signals with precise mathematical expressions is difficult. However, after extensive experimentation, these random signal data often exhibit specific statistical patterns. In intelligent bearing fault diagnosis, interference signals are often random. Influenced by the internal structure of the material, vibration acceleration signal identification may suffer from acoustic wave deflection and beam distortion. Therefore, a sufficient number of features that accurately reflect the essence of the defect signal are crucial for defect identification. To find semantic vectors that simultaneously represent the essence of the fault signal and are optimal in quantity, 24 time-domain or frequency-domain features are selected as the statistical feature semantic representation model for bearing faults: root mean square value, root square amplitude, absolute average amplitude, standard deviation, maximum value, minimum value, peak-to-peak value, kurtosis, kurtosis, skewness, eighth-order moment coefficient, sixteenth-order moment coefficient, waveform index, peak index, impulse index, margin index, kurtosis index, skewness index, mean square spectrum, spectral centroid, frequency domain variance, correlation factor, harmonic factor, and spectral origin moment. The details are as follows:

[0039] Root mean square value: Root amplitude absolute average amplitude ;

[0040] Standard deviation maximum value minimum value ;

[0041] Peak-to-peak value , cliff Peak state ;

[0042] Skewness Eighth-order moment coefficients Sixteenth-order moment coefficients ;

[0043] Waveform Indicators Peak index Pulse index Margin indicators ;

[0044] kurtosis index skewness index ;

[0045] Mean square spectrum Spectral centroid ;

[0046] Frequency domain variance Related factors ;

[0047] Harmonic factors ; Spectral origin moment .

[0048] 4) Construction of a visual-semantic autoencoder zero-shot mapping strategy for outlier imputation:

[0049] Once the visual-semantic mapping is established, the similarity between any unseen class data and its prototype can be calculated, and the unseen class can be classified based on this similarity. This invention adds specific semantic information constraints to the mapping layer to regulate the reconstruction effect, achieving supervised projection function learning. Semantic attribute descriptions or word vectors are used as transfer knowledge, and the information in the hidden layer is set as the semantic attributes of the samples. An autoencoder maps visual features to the semantic space, and a decoder reconstructs the original visual features. The structure diagram is shown below. Figure 3 As shown. The specific steps are as follows:

[0050] The objective function for constructing a zero-shot learning model is:

[0051] (8)

[0052] In the formula, the input sample data is... d is the feature dimension of the sample, and N is the total number of samples; projection matrix k is the dimension of the sample attributes, and the sample attributes To simplify model calculations, let At the same time, consider resolving constraints. Due to the difficulty, the above formula is rewritten as:

[0053] (9)

[0054] in It is the Frobenius paradigm, the first term It is the zero-shot feature learning term, the second term. λ is the visual semantic constraint term used to constrain the projection matrix W, and λ is the overshoot parameter used to balance these two terms. The optimization of the above equation involves first taking the derivative, then simplifying it using the properties of the matrix trace, with the following result:

[0055] (10)

[0056] Let equation (10) equal to 0, we get:

[0057] (11)

[0058] Again Then the above formula can be finally written in the following form:

[0059] (12)

[0060] Formula (12) is a Sylvester equation, which can be solved using the Bartels-Stewart algorithm to obtain the optimal visual-semantic mapping matrix W. Meanwhile, to eliminate the impact of incomplete outlier data on the rationality of the mapping matrix W during the solution of the Sylvester equation, this invention, based on the average interpolation theory, sets that if outliers are detected in the mapping matrix W, the outliers are replaced by interpolation based on the average value of the current attribute column. That is, outlier data is interpolated using the moving average window method, the average value of the sum of the non-outlier values ​​in the column is used as the interpolated data, the data is assigned to the missing values, and finally the new interpolated column is assigned to the original column. Experiments have verified that the average interpolation data processing method greatly improves the similarity of the mapping from visual space to semantic space and can effectively solve the problem of data anomalies in the visual-semantic space mapping process in the model.

[0061] Finally, in the unseen class sample label prediction stage, using equation (13) combined with cosine similarity, the derived unseen class sample attributes are compared with the unknown class prototype attributes, thereby predicting the labels of the unknown class samples:

[0062] (13)

[0063] In the formula It is the predicted attribute of the i-th sample in the target domain. It is the prototype attribute of the j-th unknown class. It is the cosine distance equation. These are the predicted sample labels.

[0064] Furthermore, in step ④ of step 2), a surrogate model is trained using the training dataset. A constrained Dropout neural network scalable surrogate model is used, aiming to reduce the differences in the distribution of outputs between different sub-models. A new sample padding mechanism and loss constraint term are added to improve the reliability of the surrogate model in solving multi-objective problems. This is done for a training set consisting of samples with a batch size of d. d is consistent with the size of the decision variable, and the original purpose of backpropagation is to minimize the mean square error function shown in equation (2); in the C-dropout process, the training data X of each batch i All samples will be copied, stacked, and then input as new samples. The purpose is to simulate two forward propagation processes of the same data to obtain two distributions of the model's prediction results. and Meanwhile, thanks to the dynamic change of the Dropout network structure, the method of stacking new samples can expand the data to a certain extent for the scarce real computation samples in expensive optimization problems; at this time, the goal of minimizing the error loss changes to Equation (3), and the problem of reducing the difference of the sub-models is transformed into how to constrain the distributions P1 and P2 after the output; combined with the Spearman correlation coefficient as an effective measure of the correlation between variables, it is applied to measure the inconsistency between the two outputs, that is, to construct the constraint term shown in Equation (4), and combine it with l2 to form the final training loss function as shown in Equation (5), thereby reducing the degree of freedom of the parameters in the original network space; after calculating the error, the model will backpropagate according to the set number of iterations, combined with the weights and biases updated by the gradient and chain method, and finally complete the training stage;

[0065] (2)

[0066] (3)

[0067] (4)

[0068] (5).

[0069] Furthermore, in step ⑤ of step 2), the non-dominated solution set in the population is optimized and searched. The PeEA algorithm, which has good performance in solving high-dimensional multi-objective problems, is used to search for the optimal solution set of the surrogate model. By evaluating the sensitivity of Pareto front curvature in high-dimensional space and the similarity between solution sets, solutions with superior performance are searched in an environment where the shape, continuity and other characteristics of Pareto front are unknown. These solutions form a candidate solution set to provide several individuals that need to be evaluated in real time to guide the surrogate model update.

[0070] In its environment selection strategy, PeEA first uses an achievement scaling function to locate the key points that best characterize the Pareto front curvature, and calculates the ratio of distances between points to approximate the front curvature. Then, based on the estimated curvature values, an adaptive scaling function is constructed to select an appropriate index to achieve maximum convergence of the algorithm. Simultaneously, a unique similarity metric is used to improve the consistency of the solution set when outliers exist in high-dimensional environments. In PeEA, for a front surface point x=(x1, x2, …, x…) in an m-dimensional target optimization problem… m Then, the Pareto front shape is estimated using equation (6):

[0071] (6)

[0072] Where q is a positive parameter representing the leading edge curvature, for 0 <q<1、q=1、q> 1 represents a concave, linear, and convex front, respectively. When determining the q-value, PeEA first standardizes the target using the minimum and extreme points on each target to provide a hyperplane equidistant from the target axis as the base plane. When the predicted front shape is concave or linear, linear scaling is used to measure population convergence. When the predicted front shape is convex, Chebyshev distance is used to measure population convergence.

[0073] Step 2) In the application of CDNNEA to the visual feature extraction model, the test time is the total time required for the recognition process of the test set, and the computational load is measured by the number of floating point operations per second (FLOPs) of the model. The test error is calculated using equation (7):

[0074] (7)

[0075] In the formula, t(i) represents the true label, p(i) is the predicted label, and batch is the batch size.

[0076] The present invention provides a zero-sample bearing fault diagnosis method based on high-dimensional parameter multi-objective efficient optimization of deep models. Compared with the prior art, the present invention has the following beneficial effects: ① Most of the current mainstream rolling bearing fault diagnosis models are still in the stage of requiring a large number of labeled samples for training. When faced with some complex / unseen new types of faults that suddenly appear in actual engineering tests, they will be helpless. Therefore, this invention innovatively takes bearing fault diagnosis under conditions of few samples and zero samples as the research object. It aims to establish the coupling relationship between labeled fault categories and newly added unseen fault categories through the embedding space at the visual and semantic levels, extract the semantic vectors of known and unseen categories to build a semantic space, learn the subspace shared between visual features and semantic attributes, and use the mapping function to obtain the visual feature prototype of unknown categories. Finally, it constructs a zero-sample diagnosis model for complex / unseen fault categories, realizing the prediction and recognition of unknown fault categories. ② In the process of intelligent diagnosis of bearing faults, vibration acceleration signal recognition may encounter situations such as sound wave deflection and sound beam distortion, making it difficult to describe the accurate semantic information of signal samples with precise mathematical expressions. In order to construct semantic vectors that reflect the essence of fault signals and have the optimal quantity, this invention innovatively selects 24 time-domain / frequency-domain features, such as root mean square value, root mean square amplitude, absolute average amplitude, mean square spectrum, spectral centroid, and eighth-order moment coefficient, as the statistical feature semantic representation model of bearing faults. This invention aims to discover a suitable amount of features that align with the essence of defect signals. ③ In zero-shot diagnostic methods, if the design of components such as structure and parameters in the visual feature extraction model is manually adjusted, achieving the highest-performance reconstruction model would be extremely time-consuming or even impossible. Furthermore, the structure and parameters in the reconstructed model are likely to be redundant. To effectively improve model generalization and reconstruction performance, and to balance the contradiction between efficiency and accuracy in diagnostic models, this invention constructs a search space for the components of the model architecture to be optimized. It determines the parameters to be optimized in the model and uses them as decision variables, sets the constraints and search range within each variable, and formulates evaluation indicators that reflect requirements such as evaluation speed, accuracy of fault sample evaluation, and model computational complexity. Based on specific engineering needs, it selects appropriate Pareto optimal solutions to optimize the reliability components of the diagnostic model, ultimately achieving a balance between the speed and accuracy requirements of the reconstruction model, and extracting higher-quality sample visual features more efficiently. Attached Figure Description

[0077] Figure 1 This is a flowchart of the CDNNEA application process in step 2) of the present invention.

[0078] Figure 2 The flowchart of the overall framework of algorithm 1 CDNNEA in step 2 of this invention is shown.

[0079] Figure 3 This is a visual-semantic mapping structure diagram for step 4) of the present invention.

[0080] Figure 4 In a specific embodiment of the present invention, the average IGD values ​​obtained by the three proxy methods on the DTLZ test problem (the optimal result is marked in bold).

[0081] Figure 5 In a specific embodiment of the present invention, the average IGD values ​​obtained by the three proxy methods on the WFG test problem (the optimal result is marked in bold) are shown.

[0082] Figure 6 In a specific embodiment of the present invention, the average IGD value obtained by CDNNEA and six comparison algorithms on the 3-m DTLZ test problem is shown.

[0083] Figure 7 In a specific embodiment of the present invention, the average IGD value obtained by CDNNEA and six comparison algorithms on the 40-d DTLZ test problem is shown.

[0084] Figure 8 This is a description table of the CWRU dataset partitioning in a specific embodiment of the present invention.

[0085] Figure 9 This is a table showing the preset ranges of parameters for the visual feature extraction model before optimization, as shown in a specific embodiment of the present invention.

[0086] Figure 10 The table shows the parameter values ​​for the three sets of preference solutions in a specific embodiment of the present invention.

[0087] Figure 11 This is a performance comparison table of four comparison algorithms applied to a feature extraction model, as shown in a specific embodiment of the present invention.

[0088] Figure 12 In a specific embodiment of the present invention, the zero-sample diagnostic model identifies the distribution of unknown class samples. Detailed Implementation

[0089] The following detailed description of this embodiment is provided in conjunction with specific examples.

[0090] A zero-sample bearing fault diagnosis method based on high-dimensional parameter multi-objective efficient optimization using deep models includes the following steps:

[0091] 1) Construction of a visual feature extractor for high-dimensional spatial domain transformation:

[0092] A visual feature extractor with high-dimensional spatial domain transformation is constructed using a deep convolutional neural network model. First, a sensor is used to collect sequential signals under various states, and the collected data is mapped into high-dimensional Gram angle and field GASF. In the high-dimensional space, features are decomposed in a fully connected layer manner to explore the feasibility of features in the high-dimensional space dimension of the data samples. Convolutional neural networks are used to achieve efficient extraction of visual features of the data samples. The GASF transformation expression function is shown in Equation (1), which constructs the overall framework of the visual feature extractor.

[0093] (1)

[0094] In the formula The transformed polar coordinate sequence, where I is the unit row vector. The specific transformation process involves encoding the time series in a polar coordinate system to display different information granularities of the samples; each element in the Gram matrix is ​​a trigonometric function value of an angle, and the Gram angle and field are constructed by using the summation operation of trigonometric functions.

[0095] 2) Construction of optimization strategy for visual feature extractor components based on surrogate-assisted multi-objective evolutionary algorithm:

[0096] A surrogate-assisted evolutionary algorithm, CDNNEA, based on a constrained Dropout neural network, is constructed as an optimization strategy for visual feature extractor components. This optimization strategy is used to adaptively search the internal components of the deep model performing visual feature extraction. The optimization objectives are expanded to three dimensions: recognition accuracy, model complexity, and training time. Furthermore, to reduce the time and hardware costs of model training and evaluation during single-objective optimization, a highly scalable surrogate model is constructed to assist the search strategy. The specific implementation is as follows:

[0097] The overall framework of the CDNNEA algorithm includes the following inputs: maximum number of evaluations (MaxFE), number of evaluations (FE), population size (P), decision variable dimension (d), cost function (f), number of true evaluation solutions (σ), and evaluation ratio (ρ). The output is the non-dominated solution set (X, Y) of the true problem. Specifically, it includes the following steps:

[0098] ① Initial solution generation part: X=LatinHypercubeSample(11d-1), Y=f(X);

[0099] ②FE=11d-1;

[0100] ③ Start algorithm iteration: WHILE FE ≤ MaxFE DO;

[0101] ④ Train the agent model using the training dataset: C-dropout=TrainingData(X, Y);

[0102] ⑤ Perform an optimization search on the non-dominated solution set in the population: (X1, Y1, ρ1, ρ2) = Estimate(P, C-dropout);

[0103] ⑥ Select σ previously obtained non-dominated solutions for actual evaluation according to the management criteria:

[0104] X2=Selection(X1, Y1, ρ1, ρ2, C-dropout, σ), Y2=f(X2);

[0105] ⑦X'=X∪X2, Y'=Y∪Y2;

[0106] ⑧ Update the training dataset: (X, Y)=Update(X', Y', 11d-1, σ);

[0107] ⑨FE=FE+1, ρ1=ρ2;

[0108] ⑩END WHILE;

[0109] In step ④, a surrogate model is trained using the training dataset. A constrained Dropout neural network scalable surrogate model is employed, aiming to reduce the differences in output distribution between different sub-models. A sample padding mechanism and loss constraint terms are added to improve the reliability of the surrogate model in solving multi-objective problems. This is done for a training set consisting of samples with a batch size of d. d is consistent with the size of the decision variable, and the original purpose of backpropagation is to minimize the mean square error function shown in equation (2); in the C-dropout process, the training data X of each batch i All samples will be copied, stacked, and then input as new samples. The purpose is to simulate two forward propagation processes of the same data to obtain two distributions of the model's prediction results. and Meanwhile, thanks to the dynamic change of the Dropout network structure, the method of stacking new samples can expand the data to a certain extent for the scarce real computation samples in expensive optimization problems; at this time, the goal of minimizing the error loss changes to Equation (3), and the problem of reducing the difference of the sub-models is transformed into how to constrain the distributions P1 and P2 after the output; combined with the Spearman correlation coefficient as an effective measure of the correlation between variables, it is applied to measure the inconsistency between the two outputs, that is, to construct the constraint term shown in Equation (4), and combine it with l2 to form the final training loss function as shown in Equation (5), thereby reducing the degree of freedom of the parameters in the original network space; after calculating the error, the model will backpropagate according to the set number of iterations, combined with the weights and biases updated by the gradient and chain method, and finally complete the training stage;

[0110] (2)

[0111] (3)

[0112] (4)

[0113] (5).

[0114] In step ⑤, the non-dominated solution set in the population is optimized and searched. The PeEA algorithm, which has good performance in solving high-dimensional multi-objective problems, is used to search for the optimal solution set of the surrogate model. By evaluating the sensitivity of Pareto front curvature in high-dimensional space and the similarity between solution sets, solutions with superior performance are searched in an environment where the shape, continuity and other characteristics of Pareto front are unknown. These solutions form a candidate solution set to provide several individuals that need to be evaluated in real time to guide the surrogate model update.

[0115] In its environment selection strategy, PeEA first uses an achievement scaling function to locate the key points that best characterize the Pareto front curvature, and calculates the ratio of distances between points to approximate the front curvature. Then, based on the estimated curvature values, an adaptive scaling function is constructed to select an appropriate index to achieve maximum convergence of the algorithm. Simultaneously, a unique similarity metric is used to improve the consistency of the solution set when outliers exist in high-dimensional environments. In PeEA, for a front surface point x=(x1, x2, …, x…) in an m-dimensional target optimization problem… m Then, the Pareto front shape is estimated using equation (6):

[0116] (6)

[0117] Where q is a positive parameter representing the leading edge curvature, for 0 <q<1、q=1、q> 1 represents a concave, linear, and convex front, respectively. When determining the q value, PeEA first standardizes the target by using the minimum and extreme points on each target, aiming to provide a hyperplane equidistant from the target axis as the base plane. When the predicted front shape is concave or linear, the population convergence is measured using linear scaling; when the predicted front shape is convex, the population convergence is measured using Chebyshev distance.

[0118] Figure 1The flowchart of CDNNEA's application to the visual feature extraction model is shown. First, the training set and test set are divided proportionally and the convolutional neural network model is preset. Then, the decision variable dimension of the CDNNEA algorithm is defined, that is, the parameters to be optimized in the network model. Such as: number of convolution kernels, convolution kernel size, activation function in the convolutional layer, pooling method, number of nodes in the fully connected layer, gradient descent function, learning rate, batch size. Among them, the parameters to be determined except for activation function, pooling method, learning rate, and gradient descent function need to be rounded to the first decimal place due to the integer planning problem of information. Then, the CDNNEA algorithm optimization process is entered. In each iteration, the network parameters are optimized to find the minimum value of the three objectives of the network model: test time, computational cost, and test error. In the example, the test time is the total time required for the recognition process of the test set, the computational cost is measured by the number of floating point operations per second (FLOPs) of the model, and the test error is calculated by equation (7).

[0119] (7)

[0120] In the formula, t(i) represents the true label, p(i) is the predicted label, and batch is the batch size.

[0121] 3) Semantic matrix construction aided by statistical features of sequence signals:

[0122] A sufficient number of features that accurately reflect the essence of defect signals have a significant impact on defect identification. To find semantic vectors that simultaneously represent the essence of fault signals and are optimal in quantity, 24 time-domain or frequency-domain features were selected as the statistical semantic representation model for bearing faults: root mean square value, root square amplitude, absolute average amplitude, standard deviation, maximum value, minimum value, peak-to-peak value, kurtosis, kurtosis, skewness, eighth-order moment coefficient, sixteenth-order moment coefficient, waveform index, peak index, impulse index, margin index, kurtosis index, skewness index, mean square spectrum, spectral centroid, frequency domain variance, correlation factor, harmonic factor, and spectral origin moment. The time-domain or frequency-domain features are as follows:

[0123] Root mean square value: Root amplitude absolute average amplitude ;

[0124] Standard deviation maximum value minimum value ;

[0125] Peak-to-peak value , cliff Peak state ;

[0126] Skewness Eighth-order moment coefficients Sixteenth-order moment coefficients ;

[0127] Waveform Indicators Peak index Pulse index Margin indicators ;

[0128] kurtosis index skewness index ;

[0129] Mean square spectrum Spectral centroid Frequency domain variance ;

[0130] Related factors Harmonic factors ;

[0131] Spectral origin moment .

[0132] 4) Construction of a visual-semantic autoencoder zero-shot mapping strategy for outlier imputation:

[0133] By adding specific semantic information constraints to the mapping layer to regulate the reconstruction effect, supervised projection function learning is achieved. Semantic attribute descriptions or word vectors are used as transfer knowledge, and the information from the hidden layer is set as sample semantic attributes. An autoencoder maps visual features to the semantic space, and a decoder reconstructs the original visual features. The objective function for constructing the zero-shot learning model is:

[0134] (8)

[0135] In the formula, the input sample data is... d is the feature dimension of the sample, and N is the total number of samples; projection matrix k is the dimension of the sample attributes, and the sample attributes To simplify model calculations, let At the same time, consider resolving constraints. Due to the difficulty, the above formula is rewritten as:

[0136] (9)

[0137] in It is the Frobenius paradigm, the first term It is the zero-shot feature learning term, the second term. λ is the visual semantic constraint term used to constrain the projection matrix W, and λ is the overshoot parameter used to balance these two terms. The optimization of the above equation involves first taking the derivative, then simplifying it using the properties of the matrix trace, with the following result:

[0138] (10)

[0139] Let equation (10) equal to 0, we get:

[0140] (11)

[0141] Again Then the above formula can be finally written in the following form:

[0142] (12)

[0143] Formula (12) is a Sylvester equation, which can be solved using the Bartels-Stewart algorithm to obtain the optimal visual-semantic mapping matrix. and Meanwhile, based on the average interpolation theory, if an outlier is detected in the mapping matrix W, the outlier is replaced by the average value of the current attribute column. That is, the outlier is interpolated by the moving average window method. The average value is calculated after summing the non-outlier values ​​in the column as the interpolated data. The data is assigned to the missing value. Finally, the new column after interpolation is assigned to the original column.

[0144] Finally, in the unseen class sample label prediction stage, using equation (13) combined with cosine similarity, the derived unseen class sample attributes are compared with the unknown class prototype attributes, thereby predicting the labels of the unknown class samples:

[0145] (13)

[0146] In the formula It is the predicted attribute of the i-th sample in the target domain. It is the prototype attribute of the j-th unknown class. It is the cosine distance equation. These are the predicted sample labels.

[0147] 5) Apply the above process to conduct evaluation and analysis:

[0148] 5.1) Performance verification of the optimization strategy for the CDNNEA visual feature extractor component:

[0149] ① Comparison Algorithm:

[0150] To comprehensively analyze the performance of the CDNNEA algorithm, this embodiment first tests three different agent-assistant models—C-dropout, Dropout, and Kriging—in conjunction with the PeEA algorithm, demonstrating the feasibility of C-dropout as a scalable agent model. Secondly, the performance of CDNNEA is compared with six advanced algorithms in the field. All experiments in this embodiment were designed and implemented using MATLAB R2020b software on a computer with an Intel Core i5-9400F CPU and Microsoft Windows 10 operating system. The results of the algorithm comparisons were obtained on the PlatEMO platform.

[0151] ② Test question set:

[0152] The experiment used DTLZ and WFG test problems as benchmark test problems. For each test problem, the maximum number of decision variables and the number of objectives were set to 100 and 20, respectively. Specifically, on the WFG test set, when the objective dimension m is 3 or 5, the number of relevant location parameters γ is set to m-1, and when m is 10 or 20, the corresponding γ is set to 2(m-1).

[0153] ③ Parameter settings:

[0154] (1) Number of independent runs: For each test problem, each algorithm is run 20 times independently.

[0155] (2) Maximum number of real evaluations: In addition to the initial 11d-1 training data samples, 120 real solutions are used to test and compare the performance of the algorithm. Therefore, the maximum number of real evaluations is set to 11d+119.

[0156] (4) C-dropout related parameters: the inactivation probabilities p1 and p2 of the two layers of neurons are 0.2 and 0.5 respectively, the learning rate is set to 0.01, the batch size is set to be consistent with the number of decision variables, and the number of model training iterations is I. train Set to 1*10 4 Test iteration count I test Set it to 100.

[0157] (5) PeEA algorithm parameters: population size is set to 50, and the maximum number of evaluations of the surrogate model is set to 20.

[0158] (6) Mutation operator: a polynomial mutation method is adopted, with a mutation probability of 1 / d and a distribution index of 20.

[0159] (7) Crossover operator: The simulated binary crossover method is adopted, with a crossover probability of 1.0 and a distribution index of 20.

[0160] ④ Evaluation indicators:

[0161] The Inverted Generational Distance (IGD) metric was selected as the evaluation metric in the experiment. The relevant calculation formula is shown in Equation (14).

[0162] (14)

[0163] In the formula, P is a set of target vectors uniformly distributed on the true Pareto front, and Q is a set of target vectors calculated by the algorithm. dist(v,Q) represents the Euclidean distance from a target vector v∈P to the nearest vector in Q. In this embodiment, |P| is set to 10000, that is, 10000 points are uniformly sampled on the Pareto front as reference points for calculating the IGD index.

[0164] Meanwhile, this embodiment uses the Wilcoxon rank-sum test with a confidence level of 0.05 to statistically test the performance difference between CDNNEA and other comparison algorithms. The symbols '+', '-', and '=' represent that the performance of the CDNNEA algorithm is better, worse, and has no significant difference compared to the comparison algorithms, respectively.

[0165] ⑤ Feasibility of the C-dropout proxy model:

[0166] Figure 4 and Figure 5 This study aims to evaluate the average IGD (Inverse Dimension) of the PeEA algorithm on the DTLZ and WFG problem sets using three surrogate methods: Kriging, Dropout, and C-dropout. Experiments were conducted with the number of objectives m=3, and the dimension d of the decision variable was varied (20, 40, 60, 100) to test the scalability of C-dropout in high-dimensional decision spaces. The results show that in 64 test cases, CDNNEA outperformed the other two methods in 40 cases, was near optimal in 10 cases, and slightly underperformed in 14 cases due to the model management's potential to miss some well-evaluated solutions caused by balancing solution diversity and convergence. Overall, C-dropout as the surrogate model demonstrates better comprehensive performance, and compared to the Kriging surrogate model, CDNNEA achieves better or similar IGD values ​​on most test problems, further proving the applicability of C-dropout in high-dimensional MOPs and verifying the feasibility of using C-dropout as the surrogate model in this embodiment.

[0167] ⑥ Comparative experimental results of CDNNEA and advanced algorithms:

[0168] The algorithms compared to validate the performance of CDNNEA include two evolutionary algorithms without surrogate assistance (ARMOEA and PeEA) and four representative surrogate-assisted evolutionary algorithms (EDN-ARMOEA, ParEGO, K-RVEA, and MOEA / D-EGO). Performance comparisons primarily focus on the impact of decision space dimension and the number of objectives on the algorithms. Therefore, two sets of experiments were conducted on the DTLZ test set: one with a fixed number of objectives m=3 and varying the decision variable dimension d (20, 40, 60, 100), and the other with a fixed decision variable dimension d=40 and varying the number of objectives m (3, 5, 10, 20). Since the ParEGO algorithm is only designed for solving multi-objective problems with no more than four objectives, it was only compared and tested on problems with three objectives. The average IGD results obtained by the seven algorithms are shown below. Figure 6 , Figure 7 As shown, it can be observed that, facing a total of 46 test problems, CDNNEA has the best performance compared to the other comparative algorithms on 23 sets, and its performance is nearly optimal on 15 sets. Moreover, the relevant cases are all in test problems with a high number of decision variables or objectives, indicating that CDNNEA has a better solution capability in high-dimensional problem spaces compared to other algorithms.

[0169] 5.2) Application Examples of Bearing Fault Datasets

[0170] To evaluate the effectiveness and accuracy of the zero-sample bearing fault diagnosis method based on high-dimensional parameter multi-objective efficient optimization of deep models proposed in this embodiment, rolling bearings were used as the object of verification, and bearing data from Case Western Reserve University (CWRU) were used for experimental verification.

[0171] The CWRU dataset, provided by the Case Western Reserve University Data Center, is widely used for rolling bearing fault diagnosis. The test bench mainly consists of a 2-horsepower electric motor, bearing accelerometers, torque sensors, and a power meter. The bearing models tested at the drive end and fan end are 6205-2rs JEM SKF and 6203, respectively. Single-point faults were arranged on the rolling elements, inner raceway, and outer raceway of the bearings using electrical discharge machining (EDM), with fault damage levels ranging from 7 mils, 14 mils, and 21 mils. An accelerometer was placed on the bearing housing at both the motor drive end and the fan end to collect the vibration acceleration signals of the faulty bearings. The vibration signals were acquired by a 16-channel data logger at a sampling frequency of 12 kHz.

[0172] In this example, for sensors originating from different sources on the drive-end and fan-end bearing housings, ten types of faults of varying severity were investigated on the rolling elements, inner raceway, and outer raceway of the drive-end rolling bearing. The sample sets for the ten fault types were generated using a window size of 1024 time points with a window movement step of 1000 time points. Each fault type had 1200 samples, totaling 12000 samples. A detailed description of the experimental data can be found in [link to experimental data]. Figure 8 .

[0173] ① Reliability verification of CDNNEA strategy optimization model components:

[0174] First, the CWRU dataset was divided into training and testing sets in a 6:1 ratio, and the visual feature extraction model shown in Table 1 was pre-defined. Then, the decision variable dimensions of the CDNNEA algorithm, i.e., the parameters to be optimized in the network model, were defined. The visual feature extraction model for the CWRU dataset contains 16 parameters: the number of convolutional kernels (Channel_1, Channel_2, Channel_3), the kernel sizes (C_s_1, C_s_2, C_s_3), the three activation functions in the convolutional layers (Act_1, Act_2, Act_3), the pooling methods (pool_1, pool_2, pool_3), the number of nodes in the first fully connected layer (f_1), the gradient descent function (Op), the learning rate (L_rate), and the batch size. The ranges for each parameter are set as follows: Figure 9 As shown. Among them, the undetermined parameters other than the activation function, pooling method, learning rate, and gradient descent function need to be rounded down to their first decimal place due to the integer planning problem of information. Figure 10 The graph shows the decision variable values ​​for each of the three different preference-type solutions found by the algorithm in the visual feature extraction model after the last iteration. It is clear from the graph that solution A has the shortest network testing time, solution B has the least network computation, and solution C has the lowest test error. Furthermore, the performance of the four comparative algorithms (ARMOEA, PeEA, EDN-ARMOEA, and K-RVEA) mentioned earlier is compared when applied to the optimization process of visual feature extraction model components. Figure 11 As shown, with a maximum of 216 evaluations, the CDNNEA algorithm searches for a network architecture with high recognition accuracy while ensuring low computation time consumption.

[0175] ②Performance verification of the zero-sample bearing diagnostic method

[0176] To validate the effectiveness of the zero-shot method, the dimensional output of the penultimate fully connected layer in the C-term solution model constructed using the CDNNEA algorithm is first extracted as the visual feature X in the zero-shot learning model. The semantic feature S is based on a pre-constructed semantic attribute relation matrix based on statistical features. The visual feature X of the visible evaluation result type data is then trained. Y Combining the visible type semantic features S in the semantic space Y Find the mapping matrix W, and use the visual features X of the unseen class data in the test set. Z The semantic vector is inversely mapped from W and compared with the original unseen class semantic feature matrix S. Z The classification result is obtained by comparing cosine similarity. During the validation process, the visible classes in the CWRU dataset are set as labels 1, 2, 3, 4, and 5 in the Class Label, and the remaining 5 labels are set as unknown classes. Figure 12 The evaluation metrics of the model trained on the visible class and tested on the invisible class, based on the above settings, are shown. The model achieves a classification accuracy of 82.43% on the CWRU dataset for five unseen class samples. Analysis shows that even without using unseen class samples during training, the method described in this embodiment still achieves a high recognition rate for such samples.

[0177] The scope of protection claimed by this invention is not limited to the specific embodiments described above. Moreover, for those skilled in the art, this invention can have various modifications and alterations. Any modifications, improvements, and equivalent substitutions made within the concept and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A zero-sample bearing fault diagnosis method based on deep model high-dimensional parameter multi-objective efficient optimization, characterized by: Comprising the following steps: 1) High-dimensional space domain conversion visual feature extractor construction: A high-dimensional space domain conversion visual feature extractor is constructed using a convolutional neural network deep model. First, a sensor is used to collect sequence signals under multiple states, and the collected data is mapped into a high-dimensional GASF. In the high-dimensional space, the features are disassembled in a fully connected layer manner to explore the feasibility of the features in the high-dimensional space dimension of the data samples, and a convolutional neural network is used to efficiently extract the visual features of the data samples. The GASF change expression function is shown in formula (1), and the overall framework of the visual feature extractor is constructed. （1） In the formula is the converted polar coordinate sequence, I is a unit row vector ; The specific conversion process is to encode the time series in the polar coordinate system to show different information granularity of the samples. Each element in the Gram matrix is the trigonometric function value of the angle, and the Gram angle field is constructed using the sum operation of the trigonometric function. 2) Visual feature extractor component optimization strategy construction based on agent-assisted multi-objective evolutionary algorithm: A CDNNEA based on a constraint-type Dropout neural network is constructed as an agent-assisted evolutionary algorithm for visual feature extractor component optimization strategy. The optimization strategy is used to adaptively search the internal components of the deep model for visual feature extraction, and the optimization target is expanded to three dimensions of recognition accuracy, model complexity, and training time. In order to reduce the time cost and hardware cost in the model training and evaluation process in the single-objective optimization process, an extended agent model is constructed to assist the search strategy, which is implemented as follows: The overall framework of the CDNNEA algorithm, the input is: the maximum evaluation number MaxFE, the evaluation number FE, the population size P, the decision variable dimension d, the cost function f, the number of real evaluation solutions σ, the evaluation ratio ρ, and the output is the non-dominated solution set (X, Y) of the real problem, which comprises the following steps: ① Generate initial solution part: X = LatinHypercubeSample(11d-1), Y = f(X); ② FE = 11d-1; ③ Start algorithm iteration: WHILE FE ≤ MaxFE DO; ④ Train the agent model using the training data set: C-dropout = TrainingData(X, Y); ⑤ Optimize search for the non-dominated solution set in the population: (X1, Y1, ρ1, ρ2) = Estimate(P, C-dropout); ⑥ Select σ non-dominated solutions obtained previously for real evaluation according to the management criteria: X2 = Selection(X1, Y1, ρ1, ρ2, C-dropout, σ), Y2 = f(X2); ⑦ X' = X ∪ X2, Y' = Y ∪ Y2; ⑧ Update the training data set: (X, Y) = Update(X', Y', 11d-1, σ); ⑨ FE = FE + 1, ρ1 = ρ2; ⑩ END WHILE; 3) Semantic matrix construction assisted by sequence signal statistical features: The characteristic quantity which meets the essence of the defect signal and is appropriate has an important influence on the defect recognition. In order to find the semantic vector which meets the essence of the fault signal and is optimal in quantity, the root mean square value, the square root amplitude, the absolute average amplitude, the standard deviation, the maximum value, the minimum value, the peak-peak value, the kurtosis, the peak state, the skewness, the eighth moment coefficient, the sixteenth moment coefficient, the waveform index, the peak value index, the pulse index, the margin index, the kurtosis index, the skewness index, the mean square spectrum, the spectral barycenter, the frequency domain variance, the correlation factor, the harmonic factor, and the spectral origin moment are selected as the 24 kinds of time domain or frequency domain characteristics as the statistical characteristic semantic representation model of bearing fault; 4) The visual-semantic self-encoding zero sample mapping strategy of abnormal value interpolation is constructed: The specific semantic information is added in the mapping layer to constrain the reconstruction effect and realize the projection function learning under the supervision. The semantic attribute description or word vector is used as the transfer knowledge. The information of the hidden layer is set as the sample semantic attribute. The visual features are mapped into the semantic space by using the automatic encoder. The original visual features are reconstructed by using the decoder. The objective function of the zero sample learning model is: （8） In the formula, the input sample data is , d is the feature dimension of the sample, and N is the total number of samples; the projection matrix , k is the dimension of the sample attribute, and the sample attribute ; in order to simplify the model operation, let , and the constraint is difficult to solve, so the formula is rewritten as: （9） where is the Frobenius norm, the first term is the zero sample feature learning term, the second term is the visual semantic constraint term, which is used to constrain the projection matrix W, and λ is the hyper-parameter to balance the two terms; the optimization of the above equation is first derived, and then simplified by using the properties of the matrix trace, and the result is as follows: （10） Let formula (10) equal to 0, and the following can be obtained: （11） Again let Then the above equation can finally be written as follows: （12） Equation (12) is a Sylvester equation, which can be solved by Bartels-Stewart algorithm to obtain the optimal visual-semantic mapping matrix With Meanwhile, based on the average interpolation theory, if there is an abnormal value in the mapping matrix W, the abnormal value is replaced by the average value of the current attribute column, that is, the data abnormal value is interpolated by the moving average window method, the average value of the sum of the non-abnormal values in the column is calculated as the interpolation data, the data is assigned to the missing value, and finally the interpolated new column is assigned to the original column. Finally, in the label prediction stage of the unseen class sample, the derived attribute of the unseen class sample is compared with the prototype attribute of the unknown class by using formula (13) combined with the cosine similarity, so that the label of the unknown class sample is predicted: （13） wherein is a predicted attribute of the i-th sample in the target domain, is a prototype attribute of the j-th unknown class, is a cosine distance equation, is a predicted sample label; The visual features X and the semantic features S are taken as inputs of the constructed zero-shot learning model, the semantic features S are taken as a standard of a constructed statistical feature semantic attribute relationship matrix, and the visual features X of visible evaluation result type data are trained Y , combined with the visible type semantic features S in the semantic space Y , to obtain a mapping matrix W, the unseen class data in the test set are reflected by the visual features X Z of W to obtain semantic vectors, and the original unseen class semantic feature matrix S Z is compared to obtain a classification result by cosine similarity.

2. The zero-shot bearing fault diagnosis method based on deep model high-dimensional parameter multi-objective efficient optimization according to claim 1, characterized in that: In step IV of step 2), the agent model is trained using the training data set, and a constraint type Dropout neural network scalable agent model is used to reduce the difference between the distributions of different sub-model outputs as the starting point, and a new sample filling mechanism and a loss constraint term are added to improve the reliability of the agent model in the multi-objective problem solving process. For a training set composed of samples with a batch size of d , d is consistent with the size of the decision variable, and the purpose of the original back propagation is to minimize the mean square error function shown in equation (2); in the C-dropout process, each batch of training data X i is copied and stacked as new samples for input, the purpose of which is to simulate two forward propagation processes of the same data to obtain two distributions of model prediction results and , and by virtue of the dynamic change of the Dropout network structure, the stacked new sample can perform a certain degree of data expansion on the scarce real calculation samples in the expensive optimization problem; at this time, the target of error loss minimization changes to equation (3), and the reduction of the difference between the sub-models is transformed into how to constrain the distributions P1 and P2 after output; combined with the effective measurement of the correlation between variables by the Spearman correlation coefficient, it is applied to measure the inconsistency of the two outputs, that is, the constraint term shown in equation (4) is constructed, and is combined with l2 to form the final training loss function as shown in equation (5), so as to reduce the degree of freedom of the parameters in the original network space; after the error is calculated, the model will perform back propagation according to the set number of iterations, combined with the updated weights and biases by the gradient and chain method, and finally complete the training phase; （2） （3） （4） （5）。 3. The zero-shot bearing fault diagnosis method based on deep model high-dimensional parameter multi-objective efficient optimization according to claim 2, characterized in that: In step 5) of step 2), the non-dominated solution set in the population is searched, the PeEA algorithm with good high-dimensional multi-objective problem solving performance is used to search the optimal solution set of the proxy model, and the performance of the solution is searched in the environment where the shape and continuity of the Pareto front are unknown, so as to form a candidate solution set to provide a plurality of individuals which need real evaluation to guide the proxy model updating; In the environment selection strategy of PeEA, the achievement scale function is first used to locate the key points which can best represent the curvature of the Pareto front, and the ratio of the distances between the points is used to approximate the front curvature. After the estimated curvature value, the adaptive scaling function is constructed to select the appropriate index to achieve the maximum convergence of the algorithm; at the same time, the consistency of the solution set is improved when there are outliers in high-dimensional environment by using a unique similarity measure; in PeEA, for the point x = (x1, x2, …, xm) on the front surface of the m-objective dimension optimization problem, the Pareto front shape estimation of formula (6) is obtained: m ) （6） Wherein q is a positive parameter representing the front curvature, and 0<q<1, q=1, q>1 represent the front as concave, linear and convex respectively; when determining the value of q, the PeEA first realizes the target standardization by using the minimum value point and the extreme value point on each target, so as to provide a hyperplane equidistant to the target axis as the base plane; when the estimated front shape is concave or linear, the linear scaling form is used to measure the convergence of the population; when the estimated front shape is convex, the Chebyshev distance form is used to measure the convergence of the population.

4. The zero-shot bearing fault diagnosis method based on deep model high-dimensional parameter multi-objective efficient optimization according to claim 3, characterized in that: In the application of the visual feature extraction model of step 2) CDNNEA, the test time is the total time required for the identification process of the test set, the calculation amount is measured by the floating point operation per second FLOPs of the model, and the test error is calculated by formula (7): （7） In the formula, t(i) represents the true label, p(i) is the predicted label, and batch is the batch size.

5. The zero-shot bearing fault diagnosis method based on deep model high-dimensional parameter multi-objective efficient optimization according to claim 1, characterized in that: The time domain or frequency domain characteristics as the statistical characteristic semantic representation model of bearing fault in step 3) are as follows: Root mean square value: , root mean square amplitude , absolute mean amplitude ; standard deviation , maximum value , minimum value ; peak-to-peak value , kurtosis , peakedness ; skewness , coefficient of eight moments , coefficient of sixteen moments ; Waveform indicator , peak indicator , pulse indicator , margin indicator ; kurtosis indicator , skewness indicator ; mean square spectrum , spectral centroid , spectral variance ; correlation factor harmonic factor ; spectral origin moment .

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