Manifold regularization based cross-condition bearing compound fault diagnosis method

Abstract

The application provides a manifold regularization-based cross-condition bearing compound fault diagnosis method, comprising collecting bearing vibration signals, constructing a source domain data set and a target domain data set; training a classification branch using the source domain data set, and optimizing the classification branch through an improved multi-label focal loss function; predicting the target domain samples using the classification branch, constructing a health state isolation mask matrix, and filtering the initial similarity relationship between the target domain samples; extracting local neighborhood structure information of the target domain samples and constructing a local metric space; predicting the fault component sharing degree between the target domain samples based on a relationship prediction function, obtaining a fault relationship prediction score matrix, and adjusting a discrimination boundary; fusing the filtered sample connection relationship matrix and the fault relationship prediction score matrix to construct a target domain topology adjacency matrix; constructing a manifold regularization constraint and applying it to a target domain top-level classification probability output space to output a fault diagnosis result.

Description

Technical Field

[0001] This application relates to the field of bearing fault diagnosis and intelligent operation and maintenance technology, specifically to a cross-condition bearing composite fault diagnosis method based on manifold regularization. Background Technology

[0002] As a critical fundamental component in rotating equipment, the operating condition of rolling bearings directly affects the stability, reliability, and operational safety of the entire system. Under actual operating conditions, bearings are typically subjected to complex conditions such as variable speed, variable load, and impact disturbances, making them prone to typical damage such as inner ring failure, outer ring failure, and rolling element failure, which can further manifest as complex failures with multiple fault components existing simultaneously. Compared to single faults, bearing complex faults not only have stronger signal coupling but also often exhibit partial overlap with their corresponding single faults at the fault component level, thus making their diagnosis significantly more difficult.

[0003] Existing bearing fault diagnosis methods have the following prominent problems when dealing with complex faults under varying operating conditions:

[0004] First, the scarcity of composite fault samples can easily lead to class imbalance, further affecting the quality of the target domain relation graph construction. In real-world data, healthy samples and single-fault samples are usually plentiful, while composite fault samples are difficult to obtain. During model training, the model tends to favor learning simpler classes, and the discriminative boundary between healthy and fault states is not clear enough. Especially in unsupervised transfer learning scenarios across different operating conditions, existing methods often directly construct relation graphs based on the initial feature similarity of target domain samples. However, under conditions where the target domain lacks label constraints and predictions are unstable, this approach can easily form incorrect connections between healthy and fault samples, thus polluting the target domain sample connection graph and reducing the reliability of subsequent graph structure constraints.

[0005] Secondly, existing methods struggle to accurately model and effectively utilize the complex fault relationships between composite fault samples under cross-operating conditions. Most current methods still treat composite faults as independent categories for global distribution alignment. Although some recent advanced research (such as the Multi-Level Distance-Aware Transfer Learning (MLDT) method) has recognized the unique characteristics of composite faults and proposed multi-level relationship constraints such as "similar, partially similar, and dissimilar," it still heavily relies on manually preset fixed distance interval parameters and rigid neighborhood set partitioning. For bearing composite faults, different categories generally exhibit continuous sharing, transition, and difference relationships at the physical fault component level; these relationships collectively constitute the fault relationship structure between samples. Continuing to use fixed boundaries or relationship modeling methods lacking fault component guidance makes it difficult to adapt to the nonlinear drift of composite fault boundaries caused by changes in target operating conditions, easily leading to severe aliasing at complex feature boundaries.

[0006] Third, existing transfer diagnostic methods based on manifold regularization typically construct adjacency relationships directly based on sample geometric similarity during joint optimization, and apply the corresponding manifold constraints directly to the deep feature space, lacking differentiated modeling of inter-sample connectivity. On the one hand, due to the lack of guiding information on fault component relationships, the constructed local manifold structure struggles to distinguish between genuine and pseudo-associations, easily leading to the erroneous convergence of samples that do not share fault component relationships. On the other hand, when manifold constraints lack effective propagation path control, the network may tend to compress feature distributions to meet local consistency requirements in order to quickly reduce regularization loss, thereby causing excessive uniformity of deep features or even discriminative collapse, reducing the classification ability of complex boundary regions. Summary of the Invention

[0007] This application provides a method and system for diagnosing composite bearing faults across operating conditions based on manifold regularization. It can alleviate the class imbalance problem caused by the scarcity of composite fault samples, improve the quality of target domain relation graph construction, and also be able to more accurately model the local structure of the target domain by combining the relationship of fault components and optimize the action path of manifold regularization constraints, thereby improving the identification accuracy, training stability and generalization ability of composite bearing faults under cross-operating conditions.

[0008] This application provides a method for diagnosing composite bearing faults across operating conditions based on manifold regularization, including the following steps:

[0009] S1. Collect bearing vibration signals under source and target operating conditions, preprocess the vibration signals, and construct labeled source domain datasets and unlabeled target domain datasets respectively.

[0010] S2. Input the source domain dataset and the target domain dataset into a shared feature extractor to extract deep features of the source domain and the target domain, and align the global feature distribution of the source domain and the target domain based on MK-MMD; at the same time, use multi-label annotation of the source domain to train the classification branch, and optimize the classification branch through an improved multi-label focus loss function, which includes a basic multi-label focus loss term and a health-failure mutual exclusion constraint term;

[0011] S3. Use the classification branch to predict the target domain samples, extract the health status prediction probability, construct a health status isolation mask matrix based on the health status prediction probability, filter the initial similarity relationship between the target domain samples, and obtain the filtered sample connection relationship matrix.

[0012] S4. Based on the filtered target domain sample connection relationship matrix, the target domain neighborhood samples are weighted and aggregated to obtain the local neighborhood structure representation of the target domain samples, and the target domain local metric space is constructed based on the local neighborhood structure representation.

[0013] S5. Construct a local neighborhood structure representation of source domain samples based on deep features of the source domain, and construct a fault component sharing degree label for source domain sample pairs using multi-label fault component annotation of the source domain. Supervised training is performed on the relationship prediction function with the local neighborhood structure representation of source domain samples as input. The trained relationship prediction function is applied to the local neighborhood structure representation of target domain samples to predict the fault component sharing degree between target domain samples, and a fault relationship prediction score matrix is ​​obtained. The discrimination boundary is dynamically adjusted according to the difference between the fault relationship prediction scores.

[0014] S6. The filtered sample connection matrix is ​​fused with the fault relationship prediction score matrix to construct the topological adjacency matrix of the target domain.

[0015] S7. Construct manifold regularization constraints based on the topological adjacency matrix, and apply the manifold regularization constraints to the classification probability output space at the top layer of the target domain to optimize the structural consistency of the prediction results in the target domain and output the fault diagnosis results.

[0016] Optionally, in step S2, the improved multi-label focus loss function is expressed as:

[0017]

[0018] in, An improved multi-label focus loss function representing classification branches; This represents the basic multi-label focus loss; This represents a health-failure mutual exclusion constraint. Represents the weight coefficient of the mutual exclusion constraint term;

[0019] The basic multi-label focus loss is defined as:

[0020]

[0021] in, This represents the basic multi-label focus loss; This indicates the number of source domain samples in the current iteration batch; Indicates the total number of output dimensions or status label bits for multi-label output; Represents source domain samples In the The actual label on each status label; This represents the corresponding predicted probability output by the network. Indicates the focus parameter;

[0022] The health-failure mutual exclusion constraint term is defined as follows:

[0023]

[0024] in, This represents a health-failure mutual exclusion constraint. Indicates sample The probability of being predicted as being in a healthy state; Represents the complete set of fault labels; Indicates sample In the Predicted probabilities on each fault label.

[0025] Optionally, step S3 specifically includes the following steps:

[0026] Calculate the features of the target domain samples and Cosine similarity between And obtain the original similarity matrix, the expression of which is:

[0027]

[0028] in, Represents target domain samples With sample The degree of similarity in the deep feature space; Indicates the first in the target domain The deep feature vector corresponding to each sample; Indicates the first in the target domain The deep feature vector corresponding to each sample; t indicates that the feature comes from the target domain; and This represents the sample index in the target domain. This means that negative values ​​in the cosine similarity are truncated to 0 to ensure that the connection weights of the samples constructed subsequently are non-negative.

[0029] Extract the predicted probability of the corresponding health status from the multi-label classification output of the target domain. and ;

[0030] A health status isolation mask matrix is ​​constructed based on the predicted health status probability, and its definition is as follows:

[0031]

[0032] in, Indicates the first in the target domain The predicted probability of health status for each sample; Indicates the first in the target domain The predicted probability of health status for each sample; The confidence threshold for determining health status; and Indicates the sample number in the target domain;

[0033] Perform a Hadamard product between the original similarity matrix and the mask matrix to obtain the filtered sample connection matrix. :

[0034]

[0035] in, This represents the connection matrix of target domain samples after health status isolation filtering; Represents the original similarity matrix; This represents the isolation mask matrix for health status.

[0036] Optionally, in step S4, extracting the local neighborhood structure information of the target domain sample includes the following steps:

[0037] Determine any sample based on the filtered sample connection matrix neighborhood sample set ;

[0038] By weighted aggregation of neighborhood samples, a neighborhood representation reflecting the local structural information of the current sample is obtained. Its expression is:

[0039]

[0040] in, Indicates sample Local neighborhood structure information under the current sample connection constraints; This represents the samples in the filtered sample connection matrix. With sample Connection weights between them; Indicates sample The neighborhood set; Represents the feature mapping function; Indicates sample The corresponding feature vector; These are the normalization coefficients;

[0041] Representing the neighborhood The learnable mapping function is input to generate the intermediate transformation matrix corresponding to the sample, which is represented as follows:

[0042]

[0043] in, Represents the sample output by the learnable mapping function The corresponding intermediate transformation matrix; The parameter is Learnable mapping functions; Indicates sample The neighborhood structure is represented.

[0044] To ensure that the local metric matrix satisfies the positive definiteness requirement, a local positive definite metric matrix corresponding to the sample is constructed based on the intermediate transformation matrix, which is expressed as:

[0045]

[0046] in, Indicates sample The corresponding local positive definite metric matrix; Represents the intermediate transformation matrix Transpose of; This represents a stable term, used to ensure the positive definiteness of the matrix; Represents the identity matrix.

[0047] Optionally, in the local metric space, any two sample features and The distance between them is defined as:

[0048]

[0049] in, Indicates sample With sample Relative distance within the context of the current local structure; Indicates sample The corresponding feature vector; Indicates sample The corresponding feature vector; Indicates sample The corresponding local positive definite metric matrix.

[0050] Optionally, in step S5, the relation prediction function is first pre-trained using the multi-label fault component annotation information of the source domain samples:

[0051] Based on the multi-label fault component annotation information of the source domain samples, construct the corresponding real shared labels:

[0052]

[0053] in, Represents source domain samples With source domain samples Labels indicating the degree of sharing of fault components among them; Represents source domain samples The corresponding set of activated faulty components; Represents source domain samples The corresponding set of activated faulty components; This indicates the number of fault components commonly contained in both samples; This indicates the total number of all distinct fault components contained in the two samples; and This indicates the source domain sample number. When both samples are healthy, the sharing level label is set to 1; when one sample is healthy and the other is faulty, the sharing level label is set to 0.

[0054] Based on the local neighborhood structure representation of source domain samples and The relationship prediction function outputs the predicted value of the degree of sharing of source domain sample pairs:

[0055]

[0056] in, This represents the prediction result of the relation prediction function on the degree of sharing of fault components among source domain samples; Represents the source domain. The local neighborhood structure representation corresponding to each sample Represents the source domain. The local neighborhood structure representation corresponding to each sample; s indicates that both samples come from the source domain. and These represent the two sample indices in the source domain sample pair;

[0057] The source domain relation supervised pre-training loss is constructed as follows:

[0058]

[0059] in, Indicates source domain relation monitoring loss; This represents the set of valid source domain sample pairs in the current training batch after excluding self-pairing. Indicates the number of valid source domain sample pairs; The relation prediction function represents the relationship prediction function for the source domain samples. and source domain samples The predicted value of the degree of sharing of fault components; This indicates the corresponding actual level of sharing.

[0060] Optionally, in step S5, the relationship prediction function outputs a fault component sharing score between samples in the target domain, the expression of which is:

[0061]

[0062] in, This represents the Sigmoid mapping function; Represents a multi-layer nonlinear mapping structure; Represents element-wise product; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Local neighborhood structure information under the current sample connection constraints; Indicates sample Local neighborhood structure information under the current sample connection relationship constraints.

[0063] Optionally, in step S5, dynamically adjusting the discrimination boundary includes:

[0064] For the target sample and any two candidate samples in its neighborhood and If the predicted sample With target sample The component sharing score was higher than that of the sample. With target sample The component sharing score satisfies: Then the discriminant boundary is defined as:

[0065]

[0066] This is the global baseline scaling factor; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Relative to target sample The shared score of fault components;

[0067] Constructing the sorting contrast loss:

[0068]

[0069] in, Indicates target sample With candidate samples Local metric distance between them; Indicates target sample With candidate samples Local metric distance between them; This is the global baseline scaling factor; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Relative to target sample The shared score of the fault components.

[0070] Optionally, in step S6, the construction of the topological adjacency matrix includes:

[0071] The fault relationship prediction score matrix is ​​symmetrically processed:

[0072]

[0073] in, Indicates a sample For reference, sample The directed shared score output when candidates are selected; Indicates a sample For reference, sample The opposite direction of the directed fault component is shared with the candidate output; Indicates sample With sample The strength of the undirected fault relationship between them after symmetry processing; , Indicates the sample number in the target domain;

[0074] The initial connectivity relationship and the symmetric fault relationship strength are fused using element-wise product:

[0075]

[0076] in, Represents the topological adjacency matrix of the target domain The One element; Represents target domain samples and target domain samples The connection weights after being filtered and isolated based on health status; Indicates a sample For reference, based on samples The shared score of the directed fault components obtained during the candidate selection process; This indicates the shared score for directed fault components in the opposite direction; This represents the undirected fault component sharing score obtained after symmetrizing the relationship scores in two directions. This indicates that the connection between the sample itself is excluded;

[0077] Optionally, in step S7, the construction and application of the manifold regularization constraint includes:

[0078] Construct a symmetric normalized Laplace matrix based on the aforementioned topological adjacency matrix A:

[0079]

[0080] in, Represents the target domain fusion topological adjacency matrix; Indicates by The degree matrix formed has diagonal elements that satisfy ; Represents the identity matrix;

[0081] Perform gradient truncation on the Laplacian matrix of the symmetric normalized graph:

[0082]

[0083] in, This represents the symmetric normalized graph Laplacian matrix after gradient truncation. This represents the symmetric normalized graph Laplacian matrix before gradient truncation. This indicates that the input matrix is ​​treated as a constant during backpropagation;

[0084] The truncated Laplacian matrix is ​​applied to the multi-label probability output matrix at the top layer of the target domain to construct the output space manifold regularization loss:

[0085]

[0086] in, This represents the output spatial manifold regularization loss; The output matrix represents the multi-label classification probability of the target domain samples; express Transpose of; This represents the Laplacian matrix of the symmetric normalized graph after gradient truncation. This represents the matrix trace operation.

[0087] This application provides a cross-condition bearing composite fault diagnosis method based on manifold regularization. By introducing an improved multi-label focus loss during the source domain supervised training stage, the physical mutual exclusion relationship between healthy and fault states is explicitly introduced into the classification learning process, enhancing the model's ability to focus on composite fault samples and difficult-to-classify samples, and improving the discrimination and separation effect between healthy and fault states. Furthermore, in the target domain relation construction stage, a healthy state isolation gating mask is generated using the healthy state prediction results to filter the similarity relationship of the initial samples, thereby suppressing untrusted connections between healthy and fault samples, reducing the interference of pseudo-associations on subsequent local manifold structure modeling, solving the problem that the connection relationship of target domain samples is easily contaminated by pseudo-associations, and improving the reliability of fault relation construction.

[0088] Based on the filtered sample connectivity, local neighborhood structure information of the target domain samples is first extracted and a local metric space is constructed. Then, a relation prediction function oriented towards the degree of fault component sharing is introduced, and supervised pre-training is performed using multi-label fault component annotation information from the source domain. This allows the function to learn the inclusion, transition, and difference relationships between composite faults and single faults, as well as between different composite faults. The relation prediction function is then transferred to the target domain to output the component sharing score between samples. The discrimination boundary is dynamically adjusted based on the score difference, so that the local distance constraint strength adapts to the change in the degree of fault component sharing. This effectively reduces class aliasing in complex boundary regions, improves the accuracy of composite fault identification, solves the problem of difficulty in accurately expressing the fault relationship between composite fault samples, and enhances the ability to discriminate complex boundaries.

[0089] By integrating the connection relationships of samples isolated from healthy states with the relationship information of fault components, an adjacency topology that better conforms to the local structural rules of the target domain is constructed. Furthermore, by controlling the gradient truncation of the regularization term propagation path, its direct interference to the underlying feature extraction network is blocked. Finally, consistency constraints are mainly applied to the top-level classification probability output space of the target domain, and the output space manifold regularization constraint is realized under the guidance of fault relationships. This not only enhances the structural consistency of the prediction results, but also effectively avoids deep feature collapse, improves the stability of end-to-end joint training and cross-condition transfer diagnostic performance, and solves the problems of traditional manifold regularization constraints lacking effective relationship guidance and training instability, thus improving the effectiveness and training stability of manifold regularization. Attached Figure Description

[0090] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0091] Figure 1 This is a flowchart illustrating the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application.

[0092] Figure 2a This is the confusion matrix of the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application under the sample balanced test conditions for the 0W→200W task;

[0093] Figure 2b This is the confusion matrix of the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application under the sample balanced test conditions for the 0W→400W task;

[0094] Figure 2cThis is the confusion matrix of the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application for the 200W→400W task under sample equalization test conditions;

[0095] Figure 3 This is the optimized feature t-SNE visualization result of the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application under different migration tasks in sample balanced test conditions;

[0096] Figure 4a This is the confusion matrix of the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application under the sample imbalance test conditions for the 0W→200W task;

[0097] Figure 4b This is the confusion matrix of the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application under the sample imbalance test conditions for the 0W→400W task;

[0098] Figure 4c This is the confusion matrix of the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application for the 200W→400W task under sample imbalance test conditions;

[0099] Figure 5 This is the optimized feature t-SNE visualization result of the cross-condition bearing composite fault diagnosis method based on manifold regularization provided in this application under different migration tasks in sample imbalance test conditions. Detailed Implementation

[0100] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. In addition, it should be understood that the specific embodiments described herein are only for illustration and explanation of this application and are not intended to limit this application. In this application, unless otherwise stated, directional terms such as "up," "down," "left," and "right" generally refer to up, down, left, and right in the actual use or working state of the device, specifically the drawing directions in the accompanying drawings.

[0101] This application provides a method for diagnosing composite bearing faults across operating conditions based on manifold regularization, which will be described in detail below. It should be noted that the order of description of the following embodiments is not intended to limit the preferred order of the embodiments of this application. Furthermore, the descriptions of each embodiment have their own emphasis; parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments.

[0102] Please see Figure 1 This application provides a cross-condition bearing composite fault diagnosis method based on manifold regularization. This method addresses the problems of scarce composite fault samples, easy confusion between healthy and fault states, susceptibility to spurious associations in the local adjacency relationships of target domain samples, and the difficulty of accurately characterizing fault component relationships using traditional constraint methods under complex operating conditions such as variable speed and load. First, an improved label filtering mechanism, combining multi-label focus loss and health state isolation masking, suppresses untrusted connections between healthy and fault samples, improving the reliability of the local adjacency structure of the target domain. Then, based on the filtered sample connections, a relationship modeling and dynamic boundary control mechanism oriented towards fault component sharing relationships is introduced to characterize the fault component relationships among target domain samples, and the discrimination boundary is adaptively adjusted according to the strength of the relationships. Finally, an output space manifold regularization mechanism based on fault relationship guidance and propagation path control is constructed to maintain the consistency of the local manifold structure while avoiding excessive uniformity of deep features, thereby achieving accurate identification of bearing health states, single faults, and composite faults under cross-condition conditions.

[0103] The cross-condition bearing composite fault diagnosis method based on manifold regularization defines the task of diagnosing composite faults under varying operating conditions as a transfer learning task with supervised source domain and unsupervised target domain. Its technical process includes: data preprocessing and global feature alignment, improved label filtering combining multi-label focus loss and health state isolation mask, fault component relationship modeling and dynamic boundary constraints, output space manifold regularization constraints guided by fault relationships, and fault diagnosis output. The overall framework process is as follows: Figure 1 As shown.

[0104] S1. Collect bearing vibration signals under source and target operating conditions, preprocess the vibration signals, and construct labeled source domain datasets and unlabeled target domain datasets respectively.

[0105] First, time-series vibration signals of the bearing were acquired under source and target operating conditions. The source condition samples were labeled with healthy, single-fault, and combined-fault states, while the target condition samples were not included in the label supervision. To reduce amplitude differences between different acquisition conditions and between different samples, the raw vibration signals were then standardized using Z-score normalization. After standardization, source domain datasets were constructed. and target domain dataset .

[0106] in, and These represent the input vibration signal segments in the source and target domains, respectively. and These represent the total number of samples in the source domain and the target domain, respectively. The multi-label annotation vector represents the source domain sample; s represents the source domain, t represents the target domain; i represents the i-th sample in the source domain, j represents the j-th sample in the target domain. Multiple positions in the same label vector are allowed to be 1 at the same time, which is used to represent the composite fault state.

[0107] S2. Input the source domain dataset and the target domain dataset into a shared feature extractor to extract deep features of the source domain and the target domain, and align the global feature distribution of the source domain and the target domain based on MK-MMD; at the same time, use multi-label annotation of the source domain to train the classification branch, and optimize the classification branch through an improved multi-label focus loss function, which includes a basic multi-label focus loss term and a health-failure mutual exclusion constraint term;

[0108] Vibration signals from both the source and target domains are input into a shared feature extractor, which employs a one-dimensional ResNet feature extractor to extract deep features with strong discriminative capabilities. and At the end of the feature extraction layer, a Gaussian multi-kernel maximum mean discrepancy (MK-MMD) loss function is introduced for global distribution adaptation. The loss function is defined as follows:

[0109]

[0110] Among them, the hybrid kernel function It is obtained by weighted linear combination of multiple Gaussian kernels with different bandwidths:

[0111]

[0112] in, This represents the Gaussian multi-kernel maximum mean difference loss; Indicates the first Deep feature vectors of each source domain sample; Indicates the first Deep feature vectors of each target domain sample; and Represent the source domain and the target domain, respectively; and These represent the sample indices of the source and target domains, respectively. Denotes the squared distance norm in the reproducing kernel Hilbert space; and These represent two feature vectors whose kernel similarity is to be calculated. This represents the squared Euclidean distance between two eigenvectors. This represents an exponential function.

[0113] This module improves the quality of the fault relationship graph construction in the target domain, providing initial filtered sample connectivity for subsequent fault relationship modeling and output space manifold regularization. It consists of two parts: an imbalance suppression stage and a label filtering stage. The imbalance suppression stage enhances the ability of the classification branch to distinguish between healthy and faulty states through source domain supervised learning. The label filtering stage, under the condition of no labels in the target domain, uses the health state prediction results output by the classification branch to construct an isolation mask, filtering the initial similarity relationships between samples.

[0114] Because the source domain contains a large number of healthy and single-fault samples, while the number of composite fault samples is relatively small, the network training process tends to favor the simpler category with the larger number of samples, resulting in insufficient learning of composite fault samples. Furthermore, considering that subsequent target domain relationship filtering relies on the "health state prediction probability" to construct a health state isolation mask, if the classification branch's distinction between healthy and fault states is not clear enough, it will further affect the reliability of the target domain topology filtering.

[0115] Therefore, the present invention connects a feature extractor to a feature extractor containing... A fully connected layer of neurons is constructed, and the multi-label prediction probability corresponding to each state label is output through the Sigmoid function. Based on the conventional multi-label focus loss, a physical mutual exclusion constraint between healthy and faulty states is introduced to improve the traditional multi-label focus loss, thereby alleviating the class imbalance problem and explicitly enhancing the discriminative separation ability between healthy and faulty states.

[0116] In step S2, the improved multi-label focus loss function is expressed as:

[0117]

[0118] in, An improved multi-label focus loss function representing classification branches; This represents the basic multi-label focus loss; This represents a health-failure mutual exclusion constraint. Represents the weight coefficient of the mutual exclusion constraint term;

[0119] The basic multi-label focus loss is defined as:

[0120]

[0121] in, This represents the basic multi-label focus loss; This indicates the number of source domain samples in the current iteration batch; Indicates the total number of output dimensions or status label bits for multi-label output; Represents source domain samples In the The actual label on each status label; This represents the corresponding predicted probability output by the network. Indicates the focus parameter;

[0122] When the model encounters easily identifiable healthy samples and single-fault samples, their impact on the overall training is reduced; however, when the model encounters complex fault samples or samples that are easily misclassified, these samples are given greater weight in the training process. In this way, the model will not only focus on learning the numerous and easily classified samples, but will pay more attention to the truly difficult and more critical complex fault samples, thereby improving its ability to identify complex fault states.

[0123] To make the classification branch output more consistent with the physical law that healthy and faulty states are mutually exclusive, the health-fault mutual exclusion constraint term is defined as follows:

[0124]

[0125] in, This represents a health-failure mutual exclusion constraint. Indicates sample The probability of being predicted as being in a healthy state; Represents the complete set of fault labels; Indicates sample In the Predicted probabilities on each fault label.

[0126] When the model classifies the same sample as both "healthy" and "faulty" simultaneously, it indicates a prediction conflict. This constraint penalizes such conflicts, prompting the model to gradually distinguish between healthy and faulty samples more clearly, thereby improving the stability of health status prediction results and providing a more reliable basis for the subsequent construction of health status isolation masks.

[0127] S3. Use the classification branch to predict the target domain samples, extract the health status prediction probability, construct a health status isolation mask matrix based on the health status prediction probability, filter the initial similarity relationship between the target domain samples, and obtain the filtered sample connection relationship matrix.

[0128] Under the aforementioned improved multi-label focus loss, the classification branch can form a relatively stable health status discrimination boundary. Based on this, under the condition of no label in the target domain, the predicted probability of the corresponding "health status" can be extracted from the multi-label classification output of the target domain to filter the initial similarity relationship between samples in the target domain, thereby suppressing erroneous connections between healthy samples and faulty samples, as well as between untrusted sample pairs.

[0129] Step S3 specifically includes the following steps:

[0130] Calculate the features of the target domain samples and Cosine similarity between And obtain the original similarity matrix, the expression of which is:

[0131]

[0132] in, Represents target domain samples With sample The degree of similarity in the deep feature space; This represents the deep feature vector corresponding to the i-th sample in the target domain; Let represent the deep feature vector corresponding to the j-th sample in the target domain; t indicates that the feature originates from the target domain; i and j represent the sample indices in the target domain. This means that negative values ​​in the cosine similarity are truncated to 0 to ensure that the connection weights of the samples constructed subsequently are non-negative.

[0133] Extract the predicted probability of the corresponding health status from the multi-label classification output of the target domain. and ;

[0134] Since the aforementioned health mutual exclusion constraint explicitly suppresses the situation where both health and fault labels have high responses simultaneously, resulting in a clearer distribution separation of health state prediction probabilities between healthy and faulty samples, a health state isolation mask matrix is ​​constructed based on the health state prediction probabilities, defined as follows:

[0135]

[0136] in, This represents the predicted probability of the health status corresponding to the i-th sample in the target domain; This represents the predicted probability of the health status corresponding to the j-th sample in the target domain; The confidence threshold for determining health status is represented; i and j represent the sample numbers in the target domain.

[0137] Perform a Hadamard product between the original similarity matrix and the mask matrix to obtain the filtered sample connection matrix. :

[0138]

[0139] in, This represents the connection matrix of target domain samples after health status isolation filtering; Represents the original similarity matrix; This represents the isolation mask matrix for health status.

[0140] It should be noted that the label filtering process is not determined all at once after all training is completed, but rather is a dynamic iterative process that occurs simultaneously with subsequent relationship modeling and parameter updates. Specifically, in each training batch, the model first predicts the target domain samples based on the current network parameters, and generates the corresponding health status isolation mask and sample connectivity matrix based on the prediction results; then, it models the local relationships between samples in the current batch based on the filtered sample connectivity matrix, and calculates the corresponding relationship constraint loss; the relationship constraint loss further participates in backpropagation to update the feature extractor, classification branch, relationship prediction module, and related parameters.

[0141] As training iteratively continues, the feature representations and health status predictions of the target domain samples are gradually optimized. The resulting health status isolation mask and sample connectivity matrix are also simultaneously corrected and updated. This allows the target domain relation graph to gradually evolve from an initial coarse state to a more stable and accurate state, forming an iterative enhancement process of "health-fault mutual exclusion supervision—health-fault state isolation—relationship modeling—parameter update." Through this process, spurious associations in the target domain relation graph can be continuously suppressed, and a relatively stable foundation of sample connectivity relationships can be provided for subsequent relation modeling and dynamic boundary control oriented towards fault component semantics.

[0142] S4. Based on the filtered sample connection relationship matrix, extract the local neighborhood structure information of the target domain samples and construct a local metric space;

[0143] This module is used to extract local neighborhood structure information of target domain samples based on the sample connectivity relationships obtained from label filtering, and to construct a local metric space adapted to the local structure of the samples, providing a metric basis for subsequent fault component relationship modeling and dynamic boundary constraints. Specifically, the fault component relationships characterize the degree of sharing and compositional relationships among different samples at the fault component level, reflecting the inclusion, transition, and difference relationships between composite faults and single faults, as well as between different composite faults.

[0144] In step S4, extracting the local neighborhood structure information of the target domain sample includes the following steps:

[0145] Determine any sample based on the filtered sample connection matrix neighborhood sample set ;

[0146] By weighted aggregation of neighborhood samples, a neighborhood representation reflecting the local structural information of the current sample is obtained. Its expression is:

[0147]

[0148] in, Indicates sample Local neighborhood structure information under the current sample connection constraints; This represents the samples in the filtered sample connection matrix. With sample Connection weights between them; Indicates sample The neighborhood set; Represents the feature mapping function; This represents the feature vector corresponding to sample j; These are the normalization coefficients;

[0149] Through the above weighted aggregation process, the neighborhood representation... Able to comprehensively reflect the sample Local neighborhood structure information under the current sample connection relationship constraints.

[0150] Subsequently, a local metric space is constructed based on the local neighborhood structure information. Specifically, the neighborhood representation is... The learnable mapping function is input to generate the intermediate transformation matrix corresponding to the sample, which is represented as follows:

[0151]

[0152] in, Represents the sample output by the learnable mapping function The corresponding intermediate transformation matrix; The parameter is Learnable mapping functions; Indicates sample The neighborhood structure is represented.

[0153] To ensure that the local metric matrix satisfies the positive definiteness requirement, a local positive definite metric matrix corresponding to the sample is constructed based on the intermediate transformation matrix, which is expressed as:

[0154]

[0155] in, Indicates sample The corresponding local positive definite metric matrix; Represents the intermediate transformation matrix Transpose of; This represents a stable term, used to ensure the positive definiteness of the matrix; Represents the identity matrix.

[0156] In the local metric space, any two sample features and The distance between them is defined as:

[0157]

[0158] in, Indicates sample With sample Relative distance within the context of the current local structure; This represents the feature vector corresponding to sample j; This represents the feature vector corresponding to sample i; Let represent the local positive definite metric matrix corresponding to sample i.

[0159] This local metric space can adaptively adjust the distance metric based on the neighborhood structure of different samples, thus making the relative positional relationships between samples more consistent with the local structural features of the target domain. It should be noted that, to enable the subsequent relationship prediction function to be trained under supervision using multi-label annotations from the source domain, this embodiment also determines the neighborhood set of the source domain samples based on deep features of the source domain, and performs weighted aggregation of the deep features of the source domain neighborhood samples to obtain a local neighborhood structure representation of the source domain samples. Target domain samples and source domain samples The local neighborhood structure representations are as follows:

[0160]

[0161] in, Represents target domain samples The local neighborhood structure representation; Represents source domain samples The local neighborhood structure representation; Represents target domain samples The neighborhood set; Represents source domain samples The neighborhood set; Represents target domain samples samples in the neighborhood of the target domain Connection weights between them; Represents source domain samples samples from the source domain Connection weights between them; and These represent the normalization coefficients in the aggregation process of the target domain and the source domain neighborhood, respectively; Represents the feature mapping function; and These represent the deep features of samples in the target domain neighborhood and samples in the source domain neighborhood, respectively.

[0162] S5. Using the relationship prediction function obtained by supervised training with multi-label fault component annotation in the source domain, the degree of fault component sharing among samples in the target domain is predicted to obtain the fault relationship prediction score matrix, and the discrimination boundary is dynamically adjusted according to the difference between the fault relationship prediction scores.

[0163] This invention first utilizes the multi-label fault component annotation information of source domain samples to construct the fault component sharing relationship between sample pairs, and then performs supervised pre-training on the relationship prediction function accordingly.

[0164] In step S5, the relation prediction function is first pre-trained using the multi-label fault component annotation information of the source domain samples:

[0165] Based on the multi-label fault component annotation information of the source domain samples, construct the corresponding real shared labels:

[0166]

[0167] in, Represents source domain samples With source domain samples Labels indicating the degree of sharing of fault components among them; Represents source domain samples The corresponding set of activated faulty components; Represents source domain samples The corresponding set of activated faulty components; This indicates the number of fault components commonly contained in both samples; This indicates the total number of all distinct fault components contained in the two samples; and This indicates the source domain sample number. When both samples are healthy, the sharing level label is set to 1; when one sample is healthy and the other is faulty, the sharing level label is set to 0.

[0168] Based on the local neighborhood structure representation of source domain samples and The relationship prediction function outputs the predicted value of the degree of sharing of source domain sample pairs:

[0169]

[0170] in, This represents the prediction result of the relation prediction function on the degree of sharing of fault components among source domain samples; This represents the local neighborhood structure representation corresponding to the p-th sample in the source domain. represents the local neighborhood structure representation corresponding to the q-th sample in the source domain; s indicates that both samples come from the source domain, and p and q represent the sample indices of the two samples in the source domain sample pair, respectively;

[0171] The source domain relation supervised pre-training loss is constructed as follows:

[0172]

[0173] in, Indicates source domain relation monitoring loss; This represents the set of valid source domain sample pairs in the current training batch after excluding self-pairing. Indicates the number of valid source domain sample pairs; The relation prediction function represents the relationship prediction function for the source domain samples. and source domain samples The predicted value of the degree of sharing of fault components; This indicates the corresponding actual level of sharing.

[0174] By minimizing the source domain relation supervision pre-training loss, the relation prediction function can learn the mapping law from the local neighborhood structure representation to the degree of sharing of fault components, thereby having the ability to initially represent the fault component inclusion relation, transition relation and difference relation.

[0175] In step S5, after completing the source domain supervised pre-training, since the preceding MK-MMD has mapped the source and target domains to a shared feature space, the fault component sharing relationship learned in the source domain can be used as a priori for predicting the relationship between unlabeled samples in the target domain. The relationship prediction function is then further used for the transfer representation of fault component relationships between samples in the target domain. Specifically, among samples in the target domain, the relationship prediction function outputs a fault component sharing score between samples, expressed as:

[0176]

[0177] in, This represents the Sigmoid mapping function; Represents a multi-layer nonlinear mapping structure; Represents element-wise product; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Local neighborhood structure information under the current sample connection constraints; Indicates sample Local neighborhood structure information under the current sample connection relationship constraints.

[0178] The fault component sharing score is used to characterize the degree of sharing between two samples at the fault component level. The larger the value, the more fault components they share and the stronger the local correlation; the smaller the value, the fewer fault components they share or the virtually non-existent sharing relationship and the weaker the local correlation.

[0179] Considering the continuous variation in the degree of fault component sharing among different sample pairs, this embodiment further constructs a dynamic boundary control mechanism based on the differences in component relationships. This mechanism no longer sets fixed boundaries for different relationship levels, but instead dynamically constrains the basic boundary based on the differences in fault component sharing scores between samples. This allows the boundary size to change with the degree of fault component sharing among samples, thereby maintaining good consistency between the distance constraint strength and the physical component differences between samples.

[0180] In step S5, dynamically adjusting the discrimination boundary includes:

[0181] For the target sample and any two candidate samples in its neighborhood and If the predicted sample With target sample The component sharing score was higher than that of the sample. With target sample The component sharing score satisfies: Then the discriminant boundary is defined as:

[0182]

[0183] This is the global baseline scaling factor; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Relative to target sample The shared score of fault components;

[0184] In this way, when the component relationships between two candidate samples differ significantly from those of the target sample, the dynamic boundary automatically increases to enhance the separation between different samples.

[0185] Based on the dynamic boundary, a ranking contrast loss function is constructed, such that the relative positional relationship of samples in the local metric space conforms to the ranking result of the degree of sharing of fault components. Specifically, for any target sample... If candidate samples Compared to The component sharing score is higher than that of the candidate samples. Then the expected sample Relative to the sample in the local metric space Closer, and the sample Relative to the sample Further apart; the two should satisfy the constraints given by the aforementioned dynamic boundary. Based on this, a ranking contrast quantity loss is constructed:

[0186]

[0187] in, Indicates target sample With candidate samples Local metric distance between them; Indicates target sample With candidate samples Local metric distance between them; This is the global baseline scaling factor; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Relative to target sample The shared score of the fault components.

[0188] By optimizing the loss function, the relative distance relationships in the feature space can be made to conform to the ranking results of the fault component relationships, without explicitly dividing fixed sets of strong, weak, or transitional associations, or setting independent boundary parameters for different relationship levels, thereby reducing the complexity of model design and tuning. The component relationship information and local metric space structure output by this module can be further used to correct and strengthen the sample connection relationships obtained by label filtering, providing an adjacency structure foundation that combines healthy state filtering results and fault component structure information for subsequent output space manifold regularization.

[0189] S6. The filtered sample connection matrix is ​​fused with the fault relationship prediction score matrix to construct the topological adjacency matrix of the target domain.

[0190] This module is used to fuse the sample connection relationship and fault relationship prediction score matrix after health status isolation filtering to construct the final topological adjacency matrix of the target domain, providing an adjacency structure basis with fault component semantic guidance for subsequent output space manifold regularization constraints.

[0191] Specifically, the initial sample connection matrix obtained by filtering with the health status isolation mask... The fault relationship prediction score matrix output by the relationship modeling module. The elements are fused to construct the final topological adjacency matrix of the target domain. The matrix... elements Indicates sample With sample The strength of the fault relationship between the two is determined by the magnitude of the fault relationship; a larger value indicates that the two are closer in terms of the degree of sharing of fault components and local association structure, while a smaller value indicates that the fault relationship between the two is weaker. Considering that the relationship prediction score may have slight differences under different sample orders, the fault relationship prediction score is first symmetricized. Then, the initial sample connection relationship and the symmetricized fault relationship strength are fused by multiplying the element-to-element fault relationship to construct the final topological adjacency matrix of the target domain.

[0192] The construction of the topological adjacency matrix includes:

[0193] The fault relationship prediction score matrix is ​​symmetrically processed:

[0194]

[0195] in, Indicates a sample For reference, sample The directed shared score output when candidates are selected; Indicates a sample For reference, sample The opposite direction of the directed fault component is shared with the candidate output; Indicates sample With sample The strength of the undirected fault relationship between them after symmetry processing; , Indicates the sample number in the target domain;

[0196] The initial connectivity relationship and the symmetric fault relationship strength are fused using element-wise product:

[0197]

[0198] in, Represents the topological adjacency matrix of the target domain The One element; Represents target domain samples and target domain samples The connection weights after being filtered and isolated based on health status; Indicates a sample For reference, based on samples The shared score of the directed fault components obtained during the candidate selection process; This indicates the shared score for directed fault components in the opposite direction; This represents the undirected fault component sharing score obtained after symmetrizing the relationship scores in two directions. This indicates that the connection between the sample itself is excluded;

[0199] Using the above construction method, the corresponding topological edge weights are only enhanced when two samples retain a reliable connection after being isolated in a healthy state, and their fault relationship is strong; conversely, when samples have an initial geometric adjacency but a weak fault relationship, their connection weights are suppressed. Therefore, the constructed adjacency matrix... It not only inherits the reliable topological foundation after the isolation of healthy states, but also further incorporates the strong and weak information of fault sharing between samples, thereby realizing the explicit guidance of fault relationships on the manifold regularization process.

[0200] S7. Construct manifold regularization constraints based on the topological adjacency matrix, and apply the manifold regularization constraints to the classification probability output space at the top layer of the target domain to optimize the structural consistency of the prediction results in the target domain and output the fault diagnosis results.

[0201] The construction and application of the manifold regularization constraints include:

[0202] Construct a symmetric normalized Laplace matrix based on the aforementioned topological adjacency matrix A:

[0203]

[0204] in, Represents the target domain fusion topological adjacency matrix; Indicates by The degree matrix formed has diagonal elements that satisfy ; Represents the identity matrix;

[0205] Perform gradient truncation on the Laplacian matrix of the symmetric normalized graph:

[0206]

[0207] in, This represents the symmetric normalized graph Laplacian matrix after gradient truncation. This represents the symmetric normalized graph Laplacian matrix before gradient truncation. This indicates that the input matrix is ​​treated as a constant during backpropagation;

[0208] If the adjacency structure guided by the aforementioned fault relationships is directly used for backpropagation of the overall network loss, the gradient of the manifold regularization term will continuously propagate back to the lower-level feature extractor and local relation modeling module. The network may tend to reduce the loss of the regularization term by over-compressing the sample feature distribution, thereby weakening the proper discriminative margin between different categories of samples. In severe cases, this can lead to a collapse of deep features with low discriminativeness. Therefore, to avoid the fault relationship-guided manifold regularization causing excessive perturbation to the lower-level discriminative features, this module performs a gradient truncation operation on the Laplacian matrix corresponding to the graph structure. This blocks the backpropagation path of graph constraints to the lower-level feature extraction network and local structure modeling module, stripping them from the computational graph and solidifying them into constant tensors.

[0209] The truncated Laplacian matrix is ​​applied to the multi-label probability output matrix at the top layer of the target domain to construct the output space manifold regularization loss:

[0210]

[0211] in, This represents the output spatial manifold regularization loss; The output matrix represents the multi-label classification probability of the target domain samples; express Transpose of; This represents the Laplacian matrix of the symmetric normalized graph after gradient truncation. This represents the matrix trace operation.

[0212] By minimizing the output space manifold regularization loss, target domain samples with strong correlations in the fault relationship-guided adjacency structure can maintain higher consistency in the final classification output space; while for samples with weak fault relationships or large differences, the indiscriminate consistency constraint is no longer implemented, thereby avoiding the excessive smoothing effect of traditional manifold regularization on complex boundary regions.

[0213] A cross-condition bearing composite fault diagnosis method based on manifold regularization employs a sample connectivity filtering mechanism that combines an improved multi-label focus loss with a health state isolation mask. This mechanism enhances the model's ability to focus on composite fault samples and hard-to-classify samples by introducing physical mutual exclusion constraints between healthy and fault states into the conventional multi-label focus loss during the source domain training phase, and improves the discriminative separation between healthy and fault states. Subsequently, during the target domain relation construction phase, a health state isolation mask is generated using the health state prediction results to filter the initial sample similarity relations, thereby suppressing untrusted connections between healthy and fault samples. This design allows the target domain sample connectivity relations to be progressively updated and strengthened from coarse to fine and from unstable to stable during training, providing a filtered relational foundation for subsequent fault relation modeling and manifold regularization.

[0214] This method designs a fault component relationship modeling and dynamic boundary constraint mechanism. Based on the filtered sample connectivity, this mechanism first extracts the local relationship structure of the target domain samples through local neighborhood structure information. Then, it introduces a fault relationship prediction function based on the degree of fault component sharing to model the strength of fault relationships between samples. First, it uses the multi-label fault component annotation information of the source domain samples for supervised pre-training, enabling it to learn the degree of sharing and compositional relationships of fault components between composite faults and single faults, and between different composite faults. Then, under the constraint of the target domain sample connectivity, it further refines the transfer learning to model the fault relationships between target domain samples. Based on this, the basic discrimination boundary is dynamically adjusted according to the differences in the strength of fault relationships between different candidate samples relative to the same target sample, so that the strength of the local distance constraint can change with the degree of fault component sharing between samples.

[0215] This method designs an output space manifold regularization smoothing optimization mechanism based on fault relationship guidance and propagation path control. This mechanism addresses the problems of traditional manifold regularization lacking effective relationship guidance and easily causing over-smoothing of features when directly applied to deep feature spaces. It fuses the initial filtering relationship obtained from the preceding steps with the semantic relationship information of fault components to construct the symmetric normalized Laplacian matrix required for local manifold structure constraints in the target domain. Furthermore, it controls the backpropagation path of the regularization term through gradient truncation, blocking its direct gradient interference to the lower-level feature extraction network and local relationship modeling module. Finally, the path-controlled manifold structure constraints are applied to the top-level multi-label probability output space of the target domain, achieving output space manifold regularization under fault relationship guidance. This design effectively improves the risk of over-smoothing and collapse of deep features while enhancing the structural consistency of the prediction results in the target domain, significantly improving the training stability and generalization ability of cross-condition composite fault diagnosis.

[0216] To verify the effectiveness of the proposed manifold regularization-based composite bearing fault diagnosis method under cross-condition migration scenarios, experimental verification was conducted using the HUST bearing fault public dataset. The HUST dataset contains three typical operating conditions, denoted as 0W, 200W, and 400W, respectively.

[0217] The data category distribution remains consistent across all operating conditions, including one healthy state, three single-fault states, and three pairwise composite fault states. Data labels employ a four-dimensional multi-label encoding method, with four label bits representing: N for healthy state, I for inner race fault, O for outer race fault, and B for rolling element fault. Therefore, this dataset comprehensively covers normal states, single-fault states, and composite fault states, effectively reflecting the actual characteristics of multi-label composite fault diagnosis. Consequently, it is suitable for validating the proposed method's application effectiveness in multi-label variable operating condition diagnosis tasks.

[0218] In terms of specific category definitions, the 7 states in the HUST dataset can be represented as: N: healthy state; I: single fault in the inner ring; O: single fault in the outer ring; B: single fault in the rolling element; IO: combined inner and outer ring fault; IB: combined inner and rolling element fault; OB: combined outer ring and rolling element fault.

[0219] Here, IO, IB, and OB represent composite fault samples where two fault components coexist. Since these categories exhibit both significant differences and some component overlap, they are more suitable for verifying the ability of this embodiment to preserve composite fault structure information under the synergistic effect of target domain sample connectivity filtering, fault relationship modeling and dynamic boundary constraint mechanisms, and fault relationship-guided manifold regularization constraint mechanisms.

[0220] To verify the transfer diagnostic capability of this invention under different operating conditions, this embodiment constructs three cross-operating-condition transfer tasks: 0W→200W, 0W→400W, and 200W→400W. The operating condition to the left of the arrow represents the source domain, and the operating condition to the right of the arrow represents the target domain. For example, 0W→200W means using labeled samples under the 0W operating condition as the source domain training data and samples under the 200W operating condition as the target domain transfer object.

[0221] To further evaluate the ability of this invention to identify composite fault categories, this embodiment also statistically analyzes the accuracy of the basic class and the accuracy of the composite class. The basic class accuracy measures the recognition performance of healthy state N and single fault states I, O, and B; the composite class accuracy measures the overall recognition performance of the three composite fault states IO, IB, and OB. A higher composite class accuracy indicates that the model is better able to maintain the structural characteristics of multiple fault components in a composite fault, preventing composite fault samples from being mistakenly absorbed into single fault categories or other similar composite categories.

[0222] Experiment 1: Target Domain Sample Balancing Cross-Condition Migration Diagnosis Experiment

[0223] To eliminate the influence of differences in the number of samples per category on the diagnostic results and to verify the cross-condition migration diagnostic capability of the method of the present invention under the condition that the number of samples in each fault category is consistent, a sample-balanced cross-condition migration diagnostic experiment was set up. Specifically, in the target domain test set, 1300 samples were selected as test samples for each category, totaling 9100 test samples for the 7 states. This experiment was used to evaluate the overall identification capability of the method of the present invention for healthy states, single fault states, and compound fault states under the condition of balanced category distribution.

[0224] Table 1. Results of the Sample Balanced Cross-Working Condition Migration Diagnostic Experiment ,

[0225] As shown in Table 1, under balanced sample testing conditions, the accuracy rates for the basic and composite classes are as follows: In the 0W→200W task, the basic class accuracy is 0.9767, and the composite class accuracy reaches 0.9961; in the 0W→400W task, the basic class accuracy is 0.9951, and the composite class accuracy reaches 0.9846; in the 200W→400W task, the basic class accuracy is 0.9996, and the composite class accuracy reaches 0.9977. It can be seen that the composite class accuracy remains at a high level in all three transfer tasks, indicating that the method of this invention can not only identify single fault states but also effectively maintain the component structure information in composite fault samples such as IO, IB, and OB, reducing the risk of composite faults being absorbed by similar single fault categories.

[0226] The confusion matrix results from the sample balancing experiment show that the confusion matrices for all three transfer tasks exhibit a clear diagonal dominance, indicating that most target domain samples can be correctly classified. Among these, the classification results are most stable in the 200W→400W task, with the main diagonal values ​​approaching the upper limit of the target test sample count. This suggests that under this transfer direction, the feature distribution differences between the source and target domains are relatively small, making it easier for the model to achieve cross-domain feature alignment. For tasks with large workload ranges such as 0W→400W, the method of this invention still maintains high accuracy for both the basic and composite classes, demonstrating good robustness even under significant load changes.

[0227] To further illustrate the alignment effect of the proposed method on feature distributions across operating conditions, Figure 3 The two-dimensional t-SNE visualization results of the three transfer tasks in the optimized feature space are presented.

[0228] Where S represents the source domain sample and T represents the target domain sample; N, I, O and B represent the health status, inner ring fault, outer ring fault and rolling element fault, respectively; IO, IB and OB represent the pairwise compound fault status. Figure 3 The results show that after processing by the method of this invention, samples of the same type in the source and target domains exhibit good clustering in the feature space, and clear separation boundaries are maintained between different categories. Furthermore, in more challenging tasks such as 0W→400W, although some distance fluctuations still exist between some categories, a relatively clear category boundary is maintained overall, indicating that the method still possesses good feature alignment and discrimination capabilities under significant differences in operating conditions.

[0229] Experiment 2: Target Domain Sample Imbalance Cross-Condition Migration Diagnosis Experiment

[0230] To verify the adaptability of this invention to an imbalanced data distribution in actual industrial settings—characterized by a large number of healthy samples, followed by single-fault samples, and a small number of compound-fault samples—a further imbalanced test set cross-condition migration diagnostic experiment was conducted. Specifically, in the target domain test set, the healthy class N was set to 1300 samples, the single-fault classes I, O, and B were each set to 800 samples, and the compound-fault classes IO, IB, and OB were each set to 500 samples. This setup created an imbalanced data distribution with a large number of healthy samples, followed by single-fault samples, and a small number of compound-fault samples, which was used to test the diagnostic capability of the method of this invention under conditions with a small number of compound-fault samples.

[0231] Table 2 Results of the Experiment on Imbalanced Samples Across Operating Conditions ,

[0232] As shown in Table 2, the method of this invention still maintains good diagnostic performance even when the test samples in the target domain are significantly imbalanced. In the 0W→200W task, the accuracy of the basic class of the method of this invention is 0.9905, and the accuracy of the composite class is 0.9680; in the 0W→400W task, the accuracy of the basic class is 0.9870, and the accuracy of the composite class is 0.9920. In the 200W→400W task, the accuracy of the basic class is 0.9951, and the accuracy of the composite class is 0.9767. The above results show that even when the number of composite fault samples is significantly less than that of healthy and single fault samples, the method of this invention can still maintain a high composite fault identification ability. This indicates that the model does not simply favor the healthy or single fault classes with a larger sample size, but rather enhances the separability of a few composite fault categories through structural constraints.

[0233] The results in Table 2, Figure 4, and Figure 5 show that the proposed cross-condition bearing composite fault diagnosis method based on manifold regularization still achieves good diagnostic performance under unbalanced sample conditions. This is because the present invention does not rely solely on a single classifier to directly discriminate target domain samples. Instead, it first reduces the overall distribution shift caused by different load conditions through source-target domain feature alignment, allowing target domain samples to enter the fault discrimination space already learned in the source domain. Then, manifold regularization is used to maintain the local neighborhood structure between target domain samples, ensuring good clustering of similar or identical fault samples in the feature space. More importantly, the present invention does not simply treat composite faults as ordinary independent categories, but rather combines the fault component correlation between composite faults and single faults to perform structured modeling of composite fault categories. For composite fault samples such as IO, IB, and OB, their signals simultaneously contain information from two single fault components, making them more susceptible to confusion with corresponding single fault categories or other composite categories with shared fault components during cross-condition migration. This invention improves the recognition stability of composite faults under conditions of few samples by filtering the connection relationship of target domain samples, modeling fault relationships, dynamic boundary constraints, and fault relationship-guided manifold regularization constraints, so that samples with similar fault components maintain a reasonable proximity relationship in the feature space, while enhancing the discrimination boundary between different categories.

[0234] The results of Experiments 1 and 2 show that the proposed cross-condition bearing composite fault diagnosis method based on manifold regularization achieves good diagnostic performance under both balanced and imbalanced sample conditions. Under balanced sample conditions, the method can stably distinguish between healthy states, single-fault states, and composite fault states, especially demonstrating high recognition ability for composite fault categories such as IO, IB, and OB. Under imbalanced sample conditions, even when the number of composite fault samples is significantly less than that of healthy and single-fault samples, the method still maintains a high accuracy rate for composite faults, demonstrating its adaptability to scenarios with few composite fault samples.

[0235] The cross-condition bearing composite fault diagnosis method based on manifold regularization addresses the problems in existing variable-condition composite fault diagnosis, such as the scarcity of composite fault samples, the susceptibility of target domain sample connectivity to spurious associations, the difficulty in accurately representing fault component relationships, and the tendency of traditional manifold constraints to cause excessive smoothing of deep features. It achieves the following significant benefits:

[0236] This invention improves upon existing methods that directly construct sample relationships based solely on geometric similarity in the target domain. It introduces an improved multi-label focus loss during the source domain supervised training phase, explicitly integrating the physically exclusive relationship between healthy and faulty states into the classification learning process. This enhances the model's ability to focus on composite fault samples and difficult-to-classify samples, and improves the discrimination and separation between healthy and faulty states. Furthermore, it utilizes the target domain health state prediction results to construct a health state isolation mask, filtering initial sample similarity relationships and effectively suppressing untrusted connections between healthy and faulty samples. Compared to traditional direct graph construction methods, this invention weakens the introduction and propagation of pseudo-associations from the source of relationship construction, providing a more reliable foundation for subsequent local relationship modeling and graph constraint optimization.

[0237] This invention overcomes the limitations of traditional methods that simply treat composite faults as independent categories or rely on fixed distance intervals for relationship classification. Based on the filtered sample connectivity, it first extracts local neighborhood structure information of the target domain samples and constructs a local metric space. Then, it introduces a relationship prediction function oriented towards the degree of fault component sharing. Through supervised pre-training using multi-label fault component annotation information from the source domain, the model acquires the initial ability to represent the inclusion, transition, and difference relationships between composite and single faults. Next, under the constraint of the target domain sample connectivity, it performs transfer refinement, outputting component sharing scores between samples, and dynamically adjusts the discrimination boundary based on score differences, so that the strength of the local distance constraint adapts to changes in the degree of fault component sharing. This design effectively reduces the category aliasing phenomenon between composite faults and their corresponding single faults in complex boundary regions, significantly improving the identification accuracy and robustness of composite faults under cross-condition conditions.

[0238] This invention departs from the traditional approach of manifold regularization, which directly operates on deep feature spaces and lacks effective relational guidance. On one hand, it fuses the connection relationships of samples after health state isolation filtering with the relational information of fault components, providing a high-quality adjacency structure foundation with physical semantic guidance for manifold regularization. On the other hand, by performing gradient truncation on the Laplacian constraint term, it controls the backpropagation path of the regularization term, blocking its direct gradient interference to the lower-level feature extraction network and local relational modeling module, and primarily applies consistency constraints to the top-level classification probability output space of the target domain. Compared to traditional manifold constraints that directly operate on deep feature spaces, this invention enhances the structural consistency of the prediction results in the target domain while effectively avoiding the problem of excessive compression of sample feature distribution to reduce the loss of the regularization term. This significantly reduces the risk of low-discriminative feature collapse and improves the stability of the end-to-end joint training process and the overall performance of cross-condition transfer diagnosis.

[0239] The above provides a detailed description of a cross-condition bearing composite fault diagnosis method based on manifold regularization. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for diagnosing composite bearing faults across operating conditions based on manifold regularization, characterized in that, Including the following steps: S1. Collect bearing vibration signals under source and target operating conditions, preprocess the vibration signals, and construct labeled source domain datasets and unlabeled target domain datasets respectively. S2. Input the source domain dataset and the target domain dataset into the shared feature extractor to extract deep features of the source domain and deep features of the target domain, and align the global feature distribution of the source domain and the target domain based on MK-MMD; Simultaneously, the classification branch is trained using source domain multi-label annotation, and the classification branch is optimized by an improved multi-label focus loss function, which includes a basic multi-label focus loss term and a health-fault mutual exclusion constraint term. S3. Use the classification branch to predict the target domain samples, extract the health status prediction probability, construct a health status isolation mask matrix based on the health status prediction probability, filter the initial similarity relationship between the target domain samples, and obtain the filtered sample connection relationship matrix. S4. Based on the filtered target domain sample connection relationship matrix, the target domain neighborhood samples are weighted and aggregated to obtain the local neighborhood structure representation of the target domain samples, and the target domain local metric space is constructed based on the local neighborhood structure representation. S5. Construct a local neighborhood structure representation of source domain samples based on deep features of the source domain, and construct a fault component sharing degree label for source domain sample pairs using multi-label fault component annotation of the source domain. Supervised training is performed on the relationship prediction function with the local neighborhood structure representation of source domain samples as input. The trained relationship prediction function is applied to the local neighborhood structure representation of target domain samples to predict the fault component sharing degree between target domain samples, and a fault relationship prediction score matrix is ​​obtained. The discrimination boundary is dynamically adjusted according to the difference between the fault relationship prediction scores. S6. The filtered sample connection matrix is ​​fused with the fault relationship prediction score matrix to construct the topological adjacency matrix of the target domain. S7. Construct manifold regularization constraints based on the topological adjacency matrix, and apply the manifold regularization constraints to the classification probability output space at the top layer of the target domain to optimize the structural consistency of the prediction results in the target domain and output the fault diagnosis results.

2. The cross-condition bearing composite fault diagnosis method based on manifold regularization according to claim 1, characterized in that, In step S2, the improved multi-label focus loss function is expressed as: ， in, An improved multi-label focus loss function representing classification branches; This represents the basic multi-label focus loss; This represents a health-failure mutual exclusion constraint. Represents the weight coefficient of the mutual exclusion constraint term; The basic multi-label focus loss is defined as: ， in, This represents the basic multi-label focus loss; This indicates the number of source domain samples in the current iteration batch; Indicates the total number of output dimensions or status label bits for multi-label output; Represents source domain samples In the The actual label on each status label; This represents the corresponding predicted probability output by the network. Indicates the focus parameter; The health-failure mutual exclusion constraint term is defined as follows: ， in, This represents a health-failure mutual exclusion constraint. Indicates sample The probability of being predicted as being in a healthy state; Represents the complete set of fault labels; Indicates sample In the Predicted probabilities on each fault label.

3. The method for diagnosing composite bearing faults across operating conditions based on manifold regularization according to claim 1, characterized in that, Step S3 specifically includes the following steps: Calculate the features of the target domain samples and Cosine similarity between And obtain the original similarity matrix, the expression of which is: ， in, Represents target domain samples With sample The degree of similarity in the deep feature space; Indicates the first in the target domain The deep feature vector corresponding to each sample; Indicates the first in the target domain The deep feature vector corresponding to each sample; This indicates that the feature originates from the target domain; and This represents the sample index in the target domain. This means that negative values ​​in the cosine similarity are truncated to 0 to ensure that the connection weights of the samples constructed subsequently are non-negative. Extract the predicted probability of the corresponding health status from the multi-label classification output of the target domain. and ; A health status isolation mask matrix is ​​constructed based on the predicted health status probability, and its definition is as follows: ， in, Indicates the first in the target domain The predicted probability of health status for each sample; Indicates the first in the target domain The predicted probability of health status for each sample; The confidence threshold for determining health status; and Indicates the sample number in the target domain; Perform a Hadamard product between the original similarity matrix and the mask matrix to obtain the filtered sample connection matrix. : ， in, This represents the connection matrix of target domain samples after health status isolation filtering; Represents the original similarity matrix; Represents the isolation mask matrix for health status.

4. The cross-condition bearing composite fault diagnosis method based on manifold regularization according to claim 1, characterized in that, In step S4, extracting the local neighborhood structure information of the target domain sample includes the following steps: Determine any sample based on the filtered sample connection matrix neighborhood sample set ; By weighted aggregation of neighborhood samples, a neighborhood representation reflecting the local structural information of the current sample is obtained. Its expression is: ， in, Indicates sample Local neighborhood structure information under the current sample connection constraints; This represents the samples in the filtered sample connection matrix. With sample Connection weights between them; Indicates sample The neighborhood set; Represents the feature mapping function; Indicates sample The corresponding feature vector; These are the normalization coefficients; Representing the neighborhood The learnable mapping function is input to generate the intermediate transformation matrix corresponding to the sample, which is represented as follows: ， in, Represents the sample output by the learnable mapping function The corresponding intermediate transformation matrix; The parameter is Learnable mapping functions; Indicates sample The neighborhood structure representation, To ensure that the local metric matrix satisfies the positive definiteness requirement, a local positive definite metric matrix corresponding to the sample is constructed based on the intermediate transformation matrix, which is expressed as: ， in, Indicates sample The corresponding local positive definite metric matrix; Represents the intermediate transformation matrix Transpose of; This represents a stable term, used to ensure the positive definiteness of the matrix; Represents the identity matrix.

5. The cross-condition bearing composite fault diagnosis method based on manifold regularization according to claim 4, characterized in that, In the local metric space, any two sample features and The distance between them is defined as: ， in, Indicates sample With sample Relative distance within the context of the current local structure; Indicates sample The corresponding feature vector; Indicates sample The corresponding feature vector; Indicates sample The corresponding local positive definite metric matrix.

6. The method for diagnosing composite bearing faults across operating conditions based on manifold regularization according to claim 1, characterized in that, In step S5, the relation prediction function is first pre-trained using the multi-label fault component annotation information of the source domain samples: Based on the multi-label fault component annotation information of the source domain samples, construct the corresponding real shared labels: ， in, Represents source domain samples With source domain samples Labels indicating the degree of sharing of fault components among them; Represents source domain samples The corresponding set of activated faulty components; Represents source domain samples The corresponding set of activated faulty components; This indicates the number of fault components commonly contained in both samples; This indicates the total number of all distinct fault components contained in the two samples; and This indicates the source domain sample number. When both samples are healthy, the sharing degree label is set to 1; when one sample is healthy and the other is faulty, the sharing degree label is set to 0. Based on the local neighborhood structure representation of source domain samples and The relationship prediction function outputs the predicted value of the degree of sharing of source domain sample pairs: ， in, This represents the prediction result of the relation prediction function on the degree of sharing of fault components among source domain samples; Represents the source domain. The local neighborhood structure representation corresponding to each sample Represents the source domain. The local neighborhood structure representation corresponding to each sample; s indicates that both samples come from the source domain. and These represent the two sample indices in the source domain sample pair; The source domain relation supervised pre-training loss is constructed as follows: ， in, Indicates source domain relation monitoring loss; This represents the set of valid source domain sample pairs in the current training batch after excluding self-pairing. This indicates the number of valid source domain sample pairs; The relation prediction function represents the relationship prediction function for the source domain samples. and source domain samples The predicted value of the degree of sharing of fault components; This indicates the corresponding actual level of sharing.

7. The cross-condition bearing composite fault diagnosis method based on manifold regularization according to claim 6, characterized in that, In step S5, the relationship prediction function outputs a fault component sharing score between samples in the target domain, the expression of which is: ， in, This represents the Sigmoid mapping function; Represents a multi-layer nonlinear mapping structure; Represents element-wise product; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Local neighborhood structure information under the current sample connection constraints; Indicates sample Local neighborhood structure information under the current sample connection relationship constraints.

8. The method for diagnosing composite bearing faults across operating conditions based on manifold regularization according to claim 7, characterized in that, In step S5, dynamically adjusting the discrimination boundary includes: For the target sample and any two candidate samples in its neighborhood and If the predicted sample With target sample The component sharing score was higher than that of the sample. With target sample The component sharing score satisfies: Then the discriminant boundary is defined as: ， This is the global baseline scaling factor; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Relative to target sample The shared score of fault components; Constructing the sorting contrast loss: ， in, Indicates target sample With candidate samples Local metric distance between them; Indicates target sample With candidate samples Local metric distance between them; This is the global baseline scaling factor; Indicates sample Relative to target sample The shared score of fault components; Indicates sample Relative to target sample The shared score of the fault components.

9. The method for diagnosing composite bearing faults across operating conditions based on manifold regularization according to claim 1, characterized in that, In step S6, the construction of the topological adjacency matrix includes: The fault relationship prediction score matrix is ​​symmetrically processed: ， in, Indicates a sample For reference, sample The directed shared score output when candidates are selected; Indicates a sample For reference, sample The opposite direction of the directed fault component is shared with the candidate output; Indicates sample With sample The strength of the undirected fault relationship between them after symmetry processing; , Indicates the sample number in the target domain; The initial connectivity relationship and the symmetric fault relationship strength are fused using element-wise product: ， in, Represents the topological adjacency matrix of the target domain The One element; Represents target domain samples and target domain samples The connection weights after being filtered and isolated based on health status; Indicates a sample For reference, based on samples The shared score of the directed fault components obtained during the candidate selection process; This indicates the shared score for directed fault components in the opposite direction; This represents the undirected fault component sharing score obtained after symmetrizing the relationship scores in two directions. This indicates that the connection of the sample itself is excluded.

10. The method for diagnosing composite bearing faults across operating conditions based on manifold regularization according to claim 9, characterized in that, In step S7, the construction and application of the manifold regularization constraint includes: Construct a symmetric normalized Laplace matrix based on the aforementioned topological adjacency matrix A: ， in, Represents the target domain fusion topological adjacency matrix; Indicates by The degree matrix formed has diagonal elements that satisfy ; Represents the identity matrix; Perform gradient truncation on the Laplacian matrix of the symmetric normalized graph: ， in, This represents the symmetric normalized graph Laplacian matrix after gradient truncation. This represents the symmetric normalized graph Laplacian matrix before gradient truncation. This indicates that the input matrix is ​​treated as a constant during backpropagation; The truncated Laplacian matrix is ​​applied to the multi-label probability output matrix at the top layer of the target domain to construct the output space manifold regularization loss: ， in, This represents the output spatial manifold regularization loss; The output matrix represents the multi-label classification probability of the target domain samples; express Transpose of; This represents the Laplacian matrix of the symmetric normalized graph after gradient truncation. This represents the matrix trace operation.

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