Mechanical system small sample fault diagnosis method based on physical feature entanglement fusion

Abstract

The application discloses a mechanical system small sample fault diagnosis method based on physical feature entanglement fusion, relates to the field of mechanical system state monitoring and intelligent fault diagnosis, and comprises the following steps: acquiring a vibration signal of a mechanical system; constructing a multi-physical view capsule feature extraction main part composed of a short-time Fourier transform branch, a wavelet transform branch and a blind deconvolution branch; performing causal invariant space-time mode retrieval on the multi-physical view capsule feature; obtaining a historical category prior probability; performing space-time causal entanglement decoupling on the multi-physical view capsule feature; generating clean multi-physical view features; based on a maximum evidence aggregation routing fusion mechanism, iteratively routing and outputting a category capsule; performing cross-domain fault diagnosis under a meta-learning framework and outputting a fault category result. The application improves the accuracy, robustness and explainability of small sample fault diagnosis in cross-condition, cross-equipment, composite fault and fault degree migration scenarios.

Description

Technical Field

[0001] This invention relates to the fields of mechanical system condition monitoring, intelligent fault diagnosis, cross-domain few-shot learning, and multi-physical view feature fusion, specifically to a method for few-shot fault diagnosis of mechanical systems based on physical feature entanglement fusion. Background Technology

[0002] Vibration signal-based intelligent fault diagnosis has been widely used in bearings, gearboxes, bogies, reducers, and other rotating machinery components. In actual industrial settings, equipment operates in a healthy state most of the time, making it difficult to continuously collect fault samples. Furthermore, changes in equipment operating conditions, speed, load, measurement point location, or fault severity lead to significant distribution shifts between the source domain training data and the target domain test data. The combination of small sample sizes, cross-domain shifts, and class imbalance makes diagnostic models prone to relying on accidental correlations within a limited sample set, resulting in instability in the target domain category prototype and an increase in misjudgments between complex faults and similar fault severity levels.

[0003] Existing publicly available solutions have been improved from the perspectives of meta-learning, transfer learning, and feature fusion. Chinese patent CN112418013A discloses a method for diagnosing bearing faults under complex operating conditions based on meta-learning with a small sample size. It uses N-class K-sample tasks for meta-training and meta-testing to reduce the model's dependence on the number of samples. Chinese patent CN117390411B discloses a method for diagnosing bearing faults under varying operating conditions based on meta-transfer learning. It combines a relational network with domain adaptation loss for diagnosing varying operating conditions with a small number of labeled target samples. Chinese patent CN118013289B discloses a method, device, medium, and product for diagnosing faults under varying operating conditions with a small sample size based on information fusion meta-transfer learning. It utilizes multi-sensor signal fusion images and a two-dimensional meta-convolutional network to achieve state recognition.

[0004] Regarding multi-source feature fusion, Chinese patent CN113780151A discloses a bearing fault diagnosis method and system based on bilinear feature fusion, which interacts with time-domain and time-frequency domain data through a mutual attention mechanism. Chinese patent CN114970715B discloses a fault diagnosis method and system under varying operating conditions constrained by small sample sizes and unbalanced data. It uses capsule feature construction to create graph convolutional networks and combines MMD and domain adaptation to improve diagnostic performance under different load transitions. These solutions can alleviate, to some extent, the problems of insufficient samples, changing operating conditions, or inadequate utilization of multi-source information.

[0005] However, several more subtle issues remain in cross-domain diagnosis with extremely small sample sizes. First, historical fault knowledge is often implicit in network parameters or global embeddings, making the spatiotemporal correspondence between target samples and historical samples insufficiently traceable. Even when similar samples are retrieved, it's difficult to determine whether the similarity stems from stable fault mechanisms or domain-specific factors such as rotational speed, load, measurement points, or background noise. Second, multi-physical views, such as short-time Fourier transform, wavelet transform, and blind deconvolution, are often spliced, attention-weighted, or fused at multiple levels. Complementary fault evidence, redundant responses, and domain perturbations are not clearly distinguished, and direct fusion may amplify non-transferable components. Third, supporting features for entering category prototypes or capsule routes lack sample-level and physical view-level reliability criteria, and the consistency of traditional routes may be caused by spurious correlation features. Therefore, cross-domain fault diagnosis with small sample sizes still needs to address issues such as judging the transferability of historical patterns, decoupling entanglement among multi-physical views, and aggregating reliable evidence. Summary of the Invention

[0006] The purpose of this invention is to provide a small-sample fault diagnosis method for mechanical systems based on physical feature entanglement fusion, in order to solve the problems of low accuracy in cross-domain small-sample fault diagnosis caused by the difficulty in reliably transferring historical fault knowledge, the mixing of multi-physical view feature coupling and domain perturbation, the lack of reliability quantitative evaluation of features, and the instability of category prototypes when there are very few labeled samples in the target domain.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A small-sample fault diagnosis method for mechanical systems based on entanglement fusion of physical features includes the following steps: S1: Acquire vibration signals from the mechanical system, perform sample segmentation and standardization, and construct a meta-diagnostic task; S2: Construct a multi-physics view capsule feature extraction backbone consisting of a short-time Fourier transform branch, a wavelet transform branch, and a blind deconvolution branch to extract multi-physics view capsule features containing time-frequency energy, multi-scale transient impact, and sparse impact envelope structure from the input vibration signal; S3: Construct a historical fault pattern library, perform causal invariant spatiotemporal pattern retrieval on the multi-physical view capsule features of the current target sample to obtain an enhanced retrieval representation; obtain the prior probability of historical categories based on the fault labels in the historical fault pattern library; S4: Perform spatiotemporal causal entanglement decoupling on the features of multi-physical view capsules. Combine the three types of physical view features, namely short-time Fourier transform, wavelet transform and blind deconvolution, with the retrieval enhancement representation to perform constrained cross-view interaction. Calculate the similarity between different view capsules as a capsule consistency measure, and obtain candidate clean features through channel decoupling. S5: Calculate the spatiotemporal causal invariant cleanliness score of the candidate cleanliness features, and use this score to weight the candidate cleanliness features to generate clean multi-physical view features. S6: Based on the spatiotemporal causal invariant cleanliness score-guided maximum evidence aggregation routing fusion mechanism, it combines clean multi-physical view features, historical category priors and capsule consistency measures to perform iterative routing and output category capsules; S7: Under the meta-learning framework, combined with the meta-diagnostic task, a cleanliness-weighted category prototype is constructed based on category capsules to perform cross-domain fault diagnosis on the target domain query sample and output the fault category results.

[0008] To optimize the above technical solution, the specific limitations also include: In step S1, the meta-diagnostic task includes a support set and a query set. The support set is used for few-sample task adaptation and category prototype construction, and the query set contains query samples for meta-optimization or diagnostic performance evaluation.

[0009] Preferably, in step S3, each historical sample in the historical fault mode library corresponds to a spatiotemporal mode key, which includes a time mode key, a structure mode key, and a spatiotemporal interaction mode key, specifically: ; in, Let Norm(·) be the spatiotemporal mode key for the m-th view, and Norm(·) be the normalization operation. , and These are the time mode key, the structure mode key, and the spatiotemporal interaction mode key, respectively. The historical fault mode library is as follows: ; in, Here, j is the historical pattern library, and j is the historical sample index. For the spatiotemporal pattern key of the j-th historical sample, For pattern value, For fault labels, For domain identifier, This refers to the capacity of the pattern library.

[0010] Preferably, in step S3, the causal invariant spatiotemporal pattern retrieval includes: calculating the causal dynamic transition residual between the query sample and the historical samples, determining the causal invariance score of the retrieval sample based on the causal dynamic transition residual, and fusing the retrieval results with the causal invariance score as the weight to obtain the retrieval enhancement representation.

[0011] Further, in step S4, the spatiotemporal causal entanglement decoupling specifically involves: calculating the entanglement weight matrix based on the current view features, cross-view features, causal dynamic differences, and retrieval enhancement representation; weighting and fusing different physical view capsule features with the entanglement weight matrix to obtain entanglement enhancement features; calculating the channel covariance matrix of the entanglement enhancement features; applying spectral norm orthogonal constraints to suppress channel redundancy; and generating candidate clean features by combining the retrieval enhancement representation.

[0012] Furthermore, in step S5, the spatiotemporal causal invariant cleanliness score is determined jointly by the retrieval relevance score, causal invariance score, entanglement consistency score, decoupling sufficiency score, and domain perturbation penalty, as specified in the formula: ; in, Scoring for spatiotemporal causal invariance cleanliness; , , and The scores are for retrieval relevance, causal invariance, entanglement consistency, and decoupling adequacy, respectively. Penalty for domain disturbance; (·) is an S-shaped function; , , , ,and is the weighting coefficient; b is the bias term.

[0013] Further, in step S6, the maximum evidence aggregation route fusion mechanism guided by the spatiotemporal causal invariant cleanliness score uses the spatiotemporal causal invariant cleanliness score as a bias term in the initial logarithmic weight of the route, and initializes the logarithmic weight of the route in conjunction with the prior probability of historical categories: ; in, The initial logarithmic weights for the routes, and These represent the cleanliness score and causal invariance score of sample i in view m, respectively. Let be the probability that the historical retrieval pattern belongs to category j. , and These are the weighting coefficients.

[0014] Further, in step S6, the iterative routing includes: in each routing iteration, updating the route log weights based on the consistency between the low-level capsule prediction vector and the high-level capsule output, the cosine similarity between the historical retrieval pattern and the high-level capsule, and the redundancy penalty term. ; in, Let r+1 be the logarithmic weight of the route update. Let the logarithmic weight of the route be the value in the r-th iteration. This is the prediction vector for the lower-level capsules. For high-level capsule output, To enhance the representation for retrieval, As a redundancy penalty item, , This is the balance coefficient.

[0015] Preferably, in step S7, the cleanliness weighted category prototype is specifically: using the mean of the spatiotemporally causal invariant cleanliness scores of the support set samples on each physical view as weights, a weighted average is performed on the diagnostic embeddings of the support set samples to obtain category prototypes for each category: ; in, For the cleanliness-weighted prototype of category c in the meta-task τ, To support a subset of samples of the central class c, and For the i-th supporting sample and its label, The average cleanliness weight of the sample is used. For diagnostic embedding, For the number of physical views, Rate the cleanliness of sample i in view m.

[0016] Preferably, the training of the method adopts a two-stage optimization strategy: the first stage pre-trains the multi-physical view capsule feature extraction backbone, and the pre-training loss includes capsule classification loss, reconstruction loss and branch classification loss; the second stage adopts episodic meta-training, and the overall loss includes pre-training loss, episodic classification loss, dynamic consistency loss, decoupling loss and scoring regularization term.

[0017] Compared with the prior art, the beneficial effects of the present invention are: The present invention provides a small-sample fault diagnosis method for mechanical systems based on physical feature entanglement fusion. Through multi-physical view capsule feature extraction, causal invariant spatiotemporal pattern retrieval, spatiotemporal causal entanglement decoupling, spatiotemporal causal invariant cleanliness scoring, maximized evidence aggregation routing fusion, and meta-learning diagnostic output, it achieves cross-domain small-sample fault diagnosis. It effectively solves the problems of unreliable transfer of historical knowledge under the condition of very few labeled samples in the target domain, the mixture of multi-view feature coupling and domain perturbation, and the instability of category prototypes. It improves the diagnostic accuracy, robustness, and interpretability in scenarios of cross-operating conditions, cross-equipment, composite faults, and fault degree transfer.

[0018] This invention employs a causal invariant spatiotemporal pattern retrieval, utilizing causal dynamic transfer residuals to filter historical samples with stable fault dynamics, thus avoiding the pseudo-similarity problem caused by temporal noise caused by relying solely on feature similarity retrieval. By decoupling spatiotemporal causal entanglement, it suppresses domain-specific perturbations and channel redundancy, enabling the model to construct reliable category prototypes even with very few labeled samples in the target domain, thereby improving diagnostic accuracy in scenarios involving cross-operating conditions, cross-equipment, composite faults, and fault degree migration.

[0019] This invention treats three types of physical views—short-time Fourier transform, wavelet transform, and blind deconvolution—as response projections of the same fault source in different analysis domains. It preserves physical correlations and suppresses domain noise correlations through a cross-view entanglement weight matrix with causal constraints, and then performs channel-level decoupling through spectral norm orthogonal constraints. This allows the fused features to retain complementary fault evidence while suppressing redundant information and domain-specific perturbations.

[0020] The spatiotemporal causal invariant cleanliness score proposed in this invention integrates five dimensions: retrieval relevance, causal invariance, entanglement consistency, decoupling sufficiency, and domain perturbation penalty, to quantitatively evaluate candidate cleanliness features and improve the reliability of the diagnostic process.

[0021] This invention uses the spatiotemporal causal invariant cleanliness score as a bias term for the initial logarithmic weight of the route, and combines historical category priors and capsule consistency measures for iterative routing. This allows capsule features with high cleanliness, strong causal reliability, and consistency with historical category evidence to obtain higher credibility in the initial stage of routing, avoiding the interference of spurious correlation features caused by uniform initialization of traditional routing. Attached Figure Description

[0022] Figure 1 : A flowchart illustrating the small-sample fault diagnosis method for mechanical systems based on physical feature entanglement fusion of the present invention.

[0023] Figure 2 A schematic diagram of the process of causal invariant spatiotemporal pattern retrieval, cross-view spatiotemporal causal entanglement, channel decoupling, and spatiotemporal causal invariant cleanliness scoring.

[0024] Figure 3 : Schematic diagram of the mechanism for maximizing evidence aggregation and routing fusion.

[0025] Figure 4 Comparison of fault diagnosis accuracy of different models under different sample settings in dataset 1 and dataset 2.

[0026] Figure 5 Confusion matrix of different models under different sample settings in dataset 1 and dataset 2.

[0027] Figure 6: Visualization of the t-distribution random neighborhood embeddings of source and target domain features in datasets 1 and 2.

[0028] Figure 7 Comparison of time-domain waveforms, spectra, and envelope spectra of the target query sample and the first three historical retrieval patterns under wavelet transform view.

[0029] Figure 8 Comparison of retrieval similarity and post-retrieval reliability distributions for three types of physical views: wavelet transform, short-time Fourier transform, and blind deconvolution.

[0030] Figure 9 The channel covariance matrix and structured cross-channel dependency suppression results of representative target samples before and after feature decoupling are shown in the figure.

[0031] Figure 10 : Efficient evidence aggregation route distribution map from multi-physical view feature capsules to primary capsules under different target categories.

[0032] Figure 11 The diagram illustrates the changes in the evidence aggregation route from the initial state to the final iterative state and the route stabilization process. Detailed Implementation

[0033] The present invention will be further described in detail below through specific embodiments, but it should not be construed as limiting the scope of the subject matter of the present invention to the following embodiments. All technologies implemented based on the above content of the present invention fall within the scope of the present invention.

[0034] In one embodiment, this invention proposes a small-sample fault diagnosis method for mechanical systems based on the entanglement fusion of physical features, the flowchart of which is shown below. Figure 1 and Figure 2 As shown, the entire method includes the following steps: S1: Acquire vibration signals from the mechanical system, perform sample segmentation and standardization, and construct a meta-diagnostic task; S2: Construct a multi-physics view capsule feature extraction backbone consisting of a short-time Fourier transform branch, a wavelet transform branch, and a blind deconvolution branch to extract multi-physics view capsule features containing time-frequency energy, multi-scale transient impact, and sparse impact envelope structure from the input vibration signal; S3: Construct a historical fault pattern library, perform causal invariant spatiotemporal pattern retrieval on the multi-physical view capsule features of the current target sample to obtain an enhanced retrieval representation; obtain the prior probability of historical categories based on the fault labels in the historical fault pattern library; S4: Perform spatiotemporal causal entanglement decoupling on the features of multi-physical view capsules. Combine the three types of physical view features, namely short-time Fourier transform, wavelet transform and blind deconvolution, with the retrieval enhancement representation to perform constrained cross-view interaction. Calculate the similarity between different view capsules as a capsule consistency measure, and obtain candidate clean features through channel decoupling. S5: Calculate the spatiotemporal causal invariant cleanliness score of the candidate cleanliness features, and use this score to weight the candidate cleanliness features to generate clean multi-physical view features. S6: Based on the spatiotemporal causal invariant cleanliness score-guided maximum evidence aggregation routing fusion mechanism, it combines clean multi-physical view features, historical category priors and capsule consistency measures to perform iterative routing and output category capsules; S7: Under the meta-learning framework, combined with the meta-diagnostic task, a cleanliness-weighted category prototype is constructed based on category capsules to perform cross-domain fault diagnosis on the target domain query sample and output the fault category results.

[0035] In step S1, firstly, vibration signals of the mechanical system under different operating conditions, different fault types, or different fault degrees are acquired. The original vibration signals are then segmented into fixed-length sample segments, and each segment is standardized to eliminate amplitude scale differences. The processed samples are divided into a source domain and a target domain, where the source domain contains a large number of labeled samples, and the target domain contains a small number of labeled samples.

[0036] Under the meta-learning framework, meta-diagnostic tasks are constructed in the form of N classes and K samples. Each meta-diagnostic task consists of a support set and a query set. The support set is used for few-sample task adaptation and class prototype construction, while the query set is used for meta-optimization or diagnostic performance evaluation.

[0037] The meta-diagnostic task is specifically represented as follows: (1); in, For the first Individual diagnostic tasks To support the collection, For query set.

[0038] In step S2, a multi-physics view capsule feature extraction backbone is constructed, consisting of a short-time Fourier transform branch, a wavelet transform branch, and a blind deconvolution branch. The vibration signal is input into each of the three branches: the short-time Fourier transform branch extracts local time-frequency energy distribution features, the wavelet transform branch extracts multi-scale transient impact features, and the blind deconvolution branch extracts sparse impact envelope structure features. Each branch extracts primary features through a shared convolutional layer, and the primary features are encapsulated into capsules through a dynamic routing mechanism, resulting in capsule feature sequences for the three physical views, constituting the multi-physics view capsule features.

[0039] The capsule feature sequence of the three physical views is represented as follows: (2); Where x is a one-dimensional vibration sample of length L, It is an L-dimensional real number space; This represents the capsule feature corresponding to the m-th physical view. d represents the number of capsules, and d represents the capsule dimension. This refers to the m-th branch and its parameters; m is the physical view index. This is a set of physical views, where s, w, and b correspond to the views of short-time Fourier transform, wavelet transform, and blind deconvolution, respectively.

[0040] In step S3, a historical failure mode library is constructed for each physical view. The historical failure mode library is specifically as follows: (3); in, Here, j is the historical pattern library, and j is the historical sample index. For the spatiotemporal pattern key of the j-th historical sample, For pattern value, For fault labels, For domain identifier, This refers to the capacity of the pattern library.

[0041] Each historical sample in the historical failure mode library corresponds to a spatiotemporal mode key, which is obtained by concatenating and normalizing the temporal mode key, structural mode key, and spatiotemporal interaction mode key. Specifically, the spatiotemporal mode key is as follows: (4); in, Let Norm(·) be the spatiotemporal mode key for the m-th view, and Norm(·) be the normalization operation. , and These are the time mode key, the structure mode key, and the spatiotemporal interaction mode key, respectively. Perform causal invariant spatiotemporal pattern retrieval on the multi-physical view capsule features of the current target sample. For the current target sample, calculate the similarity between its query pattern key and the pattern keys of each historical sample in the historical fault pattern database: (5); in, To retrieve similarity, and These are the spatiotemporal pattern keys for the query sample and the j-th historical sample, respectively. To retrieve the temperature coefficient.

[0042] Select the K most similar historical samples as candidate search results and calculate the normalized search weights: (6); in, To normalize the retrieval weights, TopK selects the top K patterns with the highest similarity.

[0043] The candidate search results are weighted and fused using normalized search weights to obtain the enhanced search representation: (7); in, To enhance the representation for retrieval, For historical pattern library, This is the pattern value.

[0044] To further calculate the causal dynamic transition residuals between the query sample and each candidate historical sample, the capsule features are first decomposed into causal invariant dynamic variables and domain-specific perturbation variables: (8); in, and Let be the causal invariant dynamic variable and the domain-specific perturbation variable at time t, respectively. and These are causal dynamic encoders and domain perturbation encoders, respectively. The view features at time t; Calculate the causal dynamic transfer residuals using the causal dynamic transfer function: (9); in, The dynamic transfer residual at time t; (·) represents the causal dynamic transfer function; The causal invariance score for each candidate retrieval sample is determined based on the variance of the causal dynamic transfer residuals. (10); in, Scoring for causal invariance, The scaling factor. For dynamic transfer of residuals, Var(·) is used for variance calculation.

[0045] Simultaneously, based on the fault labels of the retrieved historical samples, the prior probabilities of historical categories are statistically obtained. , This represents the probability that the historical retrieval pattern belongs to category j.

[0046] In step S4, as Figure 2 As shown, a spatiotemporal causal entanglement decoupling operation is performed on the features of the multi-physics view capsule.

[0047] First, constrained cross-view interactions are performed. Based on current view features, cross-view features, causal dynamic differences, and retrieval enhancement representations, the entanglement weight matrix is ​​calculated: (11); Then, the entanglement weight matrix is ​​used to weight and fuse the features of different physical view capsules to obtain entangled enhanced features: (12); in, Let be the entanglement weight of view n at time t′ with view m at time t; 'a' is the attention vector. , , and It is a learnable mapping matrix; and It is a causal invariant dynamic variable; and For the corresponding view features; Enhanced representation for retrieval; Entanglement enhancement features; This is a cross-view information mapping matrix.

[0048] Channel decoupling includes: Calculate the channel covariance matrix of the entanglement enhancement feature: (13); Applying spectral norm orthogonality constraints to suppress channel redundancy: (14); in, Let m be the channel covariance matrix of the m-th view. To standardize the entanglement features, P represents the total number of time positions and capsule positions. To decouple the orthogonal loss, σ(·) is the spectral norm, and I is the identity matrix; Candidate clean features are generated by combining retrieval augmentation representation. : (15); in, The candidate clean features are defined by LN(·), which is layer normalization, and Attn(·) is scaled dot product attention. , and For query, key, and value mapping matrix, is the channel mask, [·;·] is for concatenation, and ⊙ is for Hadamard product.

[0049] In step S5, the spatiotemporal causal invariant cleanliness score is determined jointly by the retrieval relevance score, causal invariance score, entanglement consistency score, decoupling adequacy score, and domain perturbation penalty, using the following formula: (16); in, Scoring for spatiotemporal causal invariance cleanliness; , , and These are the retrieval relevance score, causal invariance score, entanglement consistency score, and decoupling sufficiency score, respectively. Penalty for domain disturbance; (·) is an S-shaped function; , , , ,and is the weighting coefficient; b is the bias term.

[0050] (17); (18); (19); (20); in, The retrieval relevance score represents the mean of the similarity scores of the top K retrievals; The causal dynamic increment is represented by cos(·,·), where cos(·,·) is the cosine similarity, and T is the number of time positions. This is the scaling factor; Let L2 be the domain-specific perturbation variable. and , respectively, are candidate features of the source and target domains, and MMD(·) is the maximum mean difference.

[0051] Candidate cleanliness features are weighted using a spatiotemporally causal invariant cleanliness score to generate cleanliness multi-physical view features: (twenty one); in, It is characterized by cleanliness. These are candidate cleanliness characteristics.

[0052] In step S6, iterative routing is performed based on a maximum evidence aggregation routing fusion mechanism guided by a spatiotemporal causal invariant cleanliness score. The structural diagram is shown below. Figure 3 As shown. First, the prediction vector of low-level capsule i for category capsule j is defined as: (twenty two); in, For the prediction vector, Let be the transformation matrix from the lower-level capsule to the category capsule, where i and j are the indices of the lower-level capsule and the category capsule, respectively.

[0053] The maximum evidence aggregation route fusion mechanism guided by spatiotemporal causal invariant cleanliness scores uses the spatiotemporal causal invariant cleanliness score as a bias term for the initial logarithmic weights of the routes, and initializes the logarithmic weights of the routes in conjunction with the prior probabilities of historical categories. (twenty three); in, The initial logarithmic weights for the routes, and These represent the cleanliness score and causal invariance score of sample i in view m, respectively. Let be the probability that the historical retrieval pattern belongs to category j. , and These are the weighting coefficients.

[0054] The routing coupling coefficient is: (twenty four); in, Let be the routing coupling coefficient for the r-th iteration. This indicates normalization along the category dimension. This represents the routing temperature coefficient.

[0055] The branch-level fusion weights are: (25); in, For branch fusion weights, and The average rating for the m-th view. and These are the weighting coefficients.

[0056] In each routing iteration, the input and output of the category capsule are: (26); in, and Let be the input and output of the j-th category capsule in the r-th iteration, respectively, and squash(·) be the capsule compression function.

[0057] The route logarithmic weight is updated as follows: (27); in, Let r+1 be the logarithmic weight of the route update. Let the logarithmic weight of the route be the value in the r-th iteration. This is the prediction vector for the lower-level capsules. For high-level capsule output, To enhance the representation for retrieval, As a redundancy penalty item, , This is the balance coefficient.

[0058] After R iterations, the final fault category probability is given by the category capsule modulus: (28); in, Let x be the probability that sample x belongs to class j, and R be the total number of routing iterations. For the length of the category capsule.

[0059] In step S7, under the meta-learning framework, a cleanliness-weighted category prototype is constructed based on category capsules: using the mean of the spatiotemporally causal invariant cleanliness scores of the support set samples on each physical view as weights, a weighted average is applied to the diagnostic embeddings of the support set samples to obtain category prototypes for each category. (29); in, For the cleanliness-weighted prototype of category c in the meta-task τ, To support a subset of samples of the central class c, and For the i-th supporting sample and its label, The average cleanliness weight of the sample is used. For diagnostic embedding, For the number of physical views, Rate the cleanliness of sample i in view m.

[0060] For a target domain query sample, calculate the distance between its diagnostic embedding and the prototype of each category, and combine the confidence of the category capsule to output the final fault category result.

[0061] The training of this method employs a two-stage optimization strategy: the first stage pre-trains the multi-physical view capsule feature extraction backbone, and the pre-training loss includes capsule classification loss, reconstruction loss, and branch classification loss, specifically: (30); in, The total pre-training loss, For capsule classification loss, To reconstruct the loss, Let m be the single-branch classification loss for the m-th physical view. and These are the weighting coefficients.

[0062] The second stage employs episodic meta-training. The overall loss includes pre-training loss, episodic classification loss, dynamic consistency loss, decoupling loss, and a scoring regularization term, specifically: (31); (32); (33); in, For the overall training objective, , and These are dynamic consistency loss, decoupling orthogonality loss, and scoring regularization term, respectively. , and These are the corresponding weighting coefficients; To query the set of plot-based classification loss, For query set, To query the number of samples, For querying tags, exp(·) is the exponential function; For query samples The classification logarithm of category c, The original distance. The original temperature coefficient, For the confidence weight of capsules, Output for category c capsule.

[0063] To further understand the technical solution of the present invention, a detailed description is provided in conjunction with specific embodiments: This embodiment uses a publicly available bogie dataset and a publicly available bearing dataset to verify the effectiveness of the method of the present invention in two types of cross-domain small sample tasks: composite fault migration and fault degree migration. These datasets are named Dataset 1 and Dataset 2, respectively. The dataset and cross-domain task settings are shown in Table 1.

[0064] Table 1 Dataset and Cross-Domain Task Settings

[0065] Dataset 1 is a publicly available bogie dataset with a sampling frequency of 64kHz and a sample length of 2048 points. Dataset 1 is used to construct a composite fault transfer task. The source domain consists of single gear fault and bearing fault categories, while the target domain consists of composite fault categories formed by combinations of gear faults and bearing inner ring faults. The source domain contains 8 single fault categories: tooth root crack, tooth surface wear, missing tooth, broken tooth, inner ring fault, outer ring fault, rolling element fault, and cage fault. The target domain contains 4 composite fault categories: broken tooth plus bearing inner ring fault, tooth surface wear plus bearing inner ring fault, missing tooth plus bearing inner ring fault, and tooth root crack plus bearing inner ring fault.

[0066] Dataset 2 is a publicly available bearing dataset with a sampling frequency of 25.6 kHz and a sample length of 2048 points. Dataset 2 is used to construct a fault severity transfer task. The source domain consists of normal conditions and minor fault categories, while the target domain consists of corresponding severe fault categories. The source domain contains 5 categories: normal bearing, minor inner race fault, minor outer race fault, minor rolling element fault, and minor combined fault. The target domain contains 4 categories: severe inner race fault, severe outer race fault, severe rolling element fault, and severe combined fault.

[0067] Four existing methods—GMAML, TS-ANIL, ADML, and CIRNet—were selected as comparative models and compared with the method of this invention. These methods, along with the physical feature entanglement fusion meta-learning framework of this invention, are denoted in order as M1 (GMAML), M2 (TS-ANIL), M3 (ADML), M4 (CIRNet), and M5 (this invention). GMAML represents optimized meta-learning and channel-interactive feature encoding; TS-ANIL emphasizes feature reuse and task-supervised inner-loop adaptation; ADML improves cross-machine few-shot recognition capability through signal enhancement and discriminative prototypes; and CIRNet introduces causal intervention and relational measurement.

[0068] All models used the same data partitioning, support sample size, and evaluation method. Experimental results are as follows: Figure 4 As shown in the figure, in dataset 1, the diagnostic accuracy of M5 under the conditions of 1 sample, 3 samples, 5 samples, and 10 samples are 91.85±0.08%, 93.33±0.25%, 94.62±0.41%, and 96.10±0.46%, respectively; in dataset 2, the corresponding accuracies of M5 reach 98.81±0.51%, 99.53±0.24%, 99.58±0.07%, and 99.78±0.17%, respectively. Specific results are shown in Table 2.

[0069] Table 2. Diagnostic accuracy of the method of the present invention under different sample settings.

[0070] The above results demonstrate that even with only a very small number of labeled support samples for each target domain, this invention can still dynamically construct a relatively reliable target domain category prototype using historical failure modes and stable failures in multi-physics views. As the number of support samples increases, the method of this invention maintains its leading edge, verifying its superiority under extremely small sample conditions.

[0071] like Figure 5As shown in the confusion matrices, the diagonal response of each model's confusion matrix generally increases with the increase in the number of supporting samples for each class. Compared with M1-M4, the method of this invention exhibits a more concentrated diagonal distribution in both dataset 1 and dataset 2, with a significant reduction in the number of misclassifications in the off-diagonal regions. This phenomenon is particularly evident under the conditions of 1 sample and 3 samples, indicating that this invention can effectively distinguish between easily confused composite fault categories and fault severity categories.

[0072] like Figure 6 As shown, the source domain features of both datasets 1 and 2 form relatively clear category clustering structures. Target domain samples still exhibit some degree of intra-class dispersion and inter-class overlap under the condition of 1 sample. As the number of supporting samples increases, target domain samples of the same category gradually cluster, and the interval between different fault categories further increases. This indicates that the present invention can gradually establish the correspondence between stable fault modes in the source domain and target domain samples, and reduce cross-domain distribution shift.

[0073] like Figure 7 The historical pattern extraction based on post-retrieval reliability, shown in the example of a target query sample in a wavelet transform view, exhibits similarities of approximately 0.981, 0.980, and 0.979 for the three retrieved historical patterns, with corresponding post-retrieval reliability of approximately 0.806, 0.789, and 0.789. While the time-domain waveforms of the target query sample and the retrieved historical patterns do not completely overlap, they show consistent trends in major spectral peaks, energy distribution, and envelope modulation structure. This indicates that causal invariant spatiotemporal pattern retrieval can locate historical reference patterns with similar fault dynamics and modulation patterns.

[0074] like Figure 8 The retrieval similarity score and post-retrieval reliability score shown indicate that the blind deconvolution view has the highest overall retrieval similarity and the most concentrated distribution, but its post-retrieval reliability is not the highest. The wavelet transform view has a relatively high overall post-retrieval reliability, while the short-time Fourier transform view falls in between. This result suggests that high retrieval similarity does not necessarily imply high cross-domain transfer value of the retrieval pattern. This invention can filter out highly similar but low-reliability historical patterns through causal dynamic residuals and domain perturbation evaluation.

[0075] like Figure 9 The decoupling effect analysis shown reveals significant off-diagonal responses in the channel covariance matrices of the two representative target samples before decoupling, indicating strong redundant coupling between different characteristic channels. After channel decoupling, the main diagonal responses are preserved, while the off-diagonal responses are significantly reduced. The off-diagonal dispersion of sample 1 decreased from 0.238 to 0.033, achieving a structured cross-channel dependency suppression rate of 86.1%; the off-diagonal dispersion of sample 2 decreased from 0.246 to 0.036, achieving a suppression rate of 85.4%.

[0076] Table 3. Composition of Cleanliness Scores for Representative Target Query Samples

[0077] Table 3 presents the spatiotemporal causal invariant cleanliness score composition and corresponding fusion weights for representative target query samples. As shown in Table 3, the average retrieval relevance of wavelet transform, short-time Fourier transform, and blind deconvolutional view are approximately 0.989, 0.994, and 0.999, respectively, but their average spatiotemporal causal invariant cleanliness scores are approximately 0.893, 0.888, and 0.882, respectively, with corresponding average fusion weights of approximately 0.342, 0.333, and 0.326. Although the blind deconvolutional view has the highest average retrieval relevance, its final fusion weight is not the highest, indicating that the spatiotemporal causal invariant cleanliness score can comprehensively consider causal stability, entanglement consistency, decoupling sufficiency, and domain perturbation strength, avoiding the final diagnostic result being solely dominated by physical views with high retrieval similarity.

[0078] like Figure 10 As shown, the maximized evidence aggregation routing matrices corresponding to different target categories have different distribution structures, indicating that the model can adaptively organize three types of physical evidence—Short-Time Fourier Transform, Wavelet Transform, and Blind Deconvolution—according to the target fault category. Taking target category 0 as an example, the effective routing weight from the wavelet transform feature capsule to primary capsule 1 is 0.154, the effective routing weight from the Short-Time Fourier Transform feature capsule to primary capsule 4 is 0.118, and the effective routing weight from the blind deconvolution feature capsule to primary capsule 0 is 0.112, indicating that this category requires evidence from different feature capsules in multiple physical views. The effective routing distribution from target category 1 to target category 3 also shows different high-weight positions.

[0079] like Figure 11 As shown, the evidence-maximizing aggregation routing maintains a predominantly high-weight structure from the initial state to the final iteration state, with only minor adjustments in some local units. The changes in most routing units are approximately 0.001–0.004, with the largest local change occurring in the routing unit from the blind deconvolution feature capsule to primary capsule 4, where the change is 0.014. The average update of all routing units is approximately 0.003. These results indicate that spatiotemporal causal invariant cleanliness scores, causal reliability, and retrieval category priors can provide relatively stable initial evidence for the routing process, with subsequent iterations primarily used for local corrections.

[0080] To evaluate the contribution of each core module to the diagnostic results, six ablation models (A0-A5) were set up. A0 represents the complete method of this invention; A1 removes historical spatiotemporal pattern retrieval; A2 removes cross-view spatiotemporal causal entanglement; A3 removes feature decoupling; A4 removes spatiotemporally causal invariant cleanliness score weighting; and A5 removes maximizing evidence aggregation route fusion. Except for the removed modules, all ablation models adopted the same physical view capsule backbone, training strategy, data partitioning, and testing task settings. The experimental results are shown in Table 4.

[0081] Table 4 Ablation Experiment Results

[0082] As shown in Table 4, the complete method A0 achieved the highest accuracy in all sample settings. Under the 1-sample condition, removing historical spatiotemporal pattern retrieval (A1) resulted in a 5.13 percentage point decrease in accuracy, and removing cross-view spatiotemporal causal entanglement (A2) resulted in a 4.53 percentage point decrease, indicating that the retrieval and entanglement modules made the most significant contributions under extremely small sample conditions.

[0083] This invention can be applied to bearings, gearboxes, bogies, reducers, industrial robot transmission systems, wind power transmission chains, and other mechanical systems where vibration signals are the primary monitoring target. For mechanical systems that simultaneously collect information such as current, acoustics, temperature, or rotational speed, the corresponding signals can be constructed into an additional physical view and integrated into the multi-physical view capsule feature extraction backbone. The number of physical view branches, the number of capsules, the capsule dimensions, the capacity of the historical pattern library, the number of the top K retrieval patterns, and the number of routing iterations can be adjusted according to the type of mechanical equipment, sensor arrangement, sampling frequency, and the number of available target domain labeled samples.

[0084] In summary, the mechanical system small-sample fault diagnosis method based on physical feature entanglement fusion provided by this invention can effectively utilize historical fault knowledge and complementary information from multiple physical views to achieve highly accurate and robust cross-domain small-sample fault diagnosis under the condition that there are very few labeled samples in the target domain. It has good interpretability and practical value.

[0085] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent substitutions, and improvements made by those skilled in the art to the above embodiments without departing from the scope of the technical solution of the present invention, based on the technical essence of the present invention, shall still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for small-sample fault diagnosis of mechanical systems based on entanglement fusion of physical features, characterized in that, Includes the following steps: S1: Acquire vibration signals from the mechanical system, perform sample segmentation and standardization, and construct a meta-diagnostic task; S2: Construct a multi-physics view capsule feature extraction backbone consisting of a short-time Fourier transform branch, a wavelet transform branch, and a blind deconvolution branch to extract multi-physics view capsule features containing time-frequency energy, multi-scale transient impact, and sparse impact envelope structure from the input vibration signal; S3: Construct a historical fault pattern library, perform causal invariant spatiotemporal pattern retrieval on the multi-physical view capsule features of the current target sample to obtain an enhanced retrieval representation; obtain the prior probability of historical categories based on the fault labels in the historical fault pattern library; S4: Perform spatiotemporal causal entanglement decoupling on the features of multi-physical view capsules. Combine the three types of physical view features, namely short-time Fourier transform, wavelet transform and blind deconvolution, with the retrieval enhancement representation to perform constrained cross-view interaction. Calculate the similarity between different view capsules as a capsule consistency measure, and obtain candidate clean features through channel decoupling. S5: Calculate the spatiotemporal causal invariant cleanliness score of the candidate cleanliness features, and use this score to weight the candidate cleanliness features to generate clean multi-physical view features. S6: Based on the spatiotemporal causal invariant cleanliness score-guided maximum evidence aggregation routing fusion mechanism, it combines clean multi-physical view features, historical category priors and capsule consistency measures to perform iterative routing and output category capsules; S7: Under the meta-learning framework, combined with the meta-diagnostic task, a cleanliness-weighted category prototype is constructed based on category capsules to perform cross-domain fault diagnosis on the target domain query sample and output the fault category results.

2. The method for small-sample fault diagnosis of mechanical systems based on physical feature entanglement fusion according to claim 1, characterized in that: In step S1, the meta-diagnostic task includes a support set and a query set. The support set is used for few-sample task adaptation and category prototype construction, and the query set contains query samples for meta-optimization or diagnostic performance evaluation.

3. The method for small-sample fault diagnosis of mechanical systems based on physical feature entanglement fusion according to claim 1, characterized in that: In step S3, each historical sample in the historical fault mode library corresponds to a spatiotemporal mode key, which includes a time mode key, a structure mode key, and a spatiotemporal interaction mode key, specifically: ； in, Let Norm(·) be the spatiotemporal mode key for the m-th view, and Norm(·) be the normalization operation. , and These are the time mode key, the structure mode key, and the spatiotemporal interaction mode key, respectively. The historical fault mode library is as follows: ； in, Here, j represents the historical pattern library, and j is the historical sample index. For the spatiotemporal pattern key of the j-th historical sample, For pattern value, For fault labels, For domain identifier, This refers to the capacity of the pattern library.

4. The method for small-sample fault diagnosis of mechanical systems based on physical feature entanglement fusion according to claim 1, characterized in that: In step S3, the causal invariant spatiotemporal pattern retrieval includes: calculating the causal dynamic transition residual between the query sample and the historical samples, determining the causal invariance score of the retrieval sample based on the causal dynamic transition residual, and fusing the causal invariance score as a weight to obtain the retrieval enhancement representation.

5. The method for small-sample fault diagnosis of mechanical systems based on physical feature entanglement fusion according to claim 1, characterized in that: In step S4, the spatiotemporal causal entanglement decoupling specifically involves: calculating an entanglement weight matrix based on the current view features, cross-view features, causal dynamic differences, and retrieval enhancement representation; and using the entanglement weight matrix to perform weighted fusion of different physical view capsule features to obtain entanglement enhancement features. Calculate the channel covariance matrix of the entanglement enhancement features and apply spectral norm orthogonality constraints to suppress channel redundancy; Candidate clean features are generated by combining search enhancement representation.

6. The method for small-sample fault diagnosis of mechanical systems based on physical feature entanglement fusion according to claim 1, characterized in that: In step S5, the spatiotemporal causal invariant cleanliness score is determined jointly by the retrieval correlation score, causal invariance score, entanglement consistency score, decoupling adequacy score, and domain perturbation penalty, and the specific formula is as follows: ； in, Scoring for spatiotemporal causal invariance cleanliness; , , and The scores are for retrieval relevance, causal invariance, entanglement consistency, and decoupling adequacy, respectively. Penalty for domain disturbance; (·) is an S-shaped function; , , , ,and is the weighting coefficient; b is the bias term.

7. The method for small-sample fault diagnosis of mechanical systems based on physical feature entanglement fusion according to claim 1, characterized in that: In step S6, the maximum evidence aggregation route fusion mechanism guided by the spatiotemporal causal invariant cleanliness score uses the spatiotemporal causal invariant cleanliness score as a bias term for the initial logarithmic weight of the route, and initializes the logarithmic weight of the route in conjunction with the prior probability of historical categories. ； in, The initial logarithmic weights for the routes, and These represent the cleanliness score and causal invariance score of sample i in view m, respectively. Let be the probability that the historical retrieval pattern belongs to category j. , and These are the weighting coefficients.

8. The method for small-sample fault diagnosis of mechanical systems based on physical feature entanglement fusion according to claim 7, characterized in that: In step S6, the iterative routing includes: in each routing iteration, updating the route log weights based on the consistency between the low-level capsule prediction vector and the high-level capsule output, the cosine similarity between the historical retrieval pattern and the high-level capsule, and the redundancy penalty term. ； in, Let r+1 be the logarithmic weight of the route update. Let the logarithmic weight of the route be the value in the r-th iteration. This is the prediction vector for the lower-level capsules. For high-level capsule output, To enhance the representation for retrieval, As a redundancy penalty item, , This is the balance coefficient.

9. The method for small-sample fault diagnosis of mechanical systems based on entanglement fusion of physical features according to claim 1, characterized in that: In step S7, the cleanliness weighted category prototype is specifically obtained by: using the mean of the spatiotemporally causally invariant cleanliness scores of the support set samples on each physical view as weights, and performing a weighted average of the diagnostic embeddings of the support set samples to obtain category prototypes for each category. ； in, For the cleanliness-weighted prototype of category c in the meta-task τ, To support a subset of samples of the central category c, and For the i-th supporting sample and its label, The average cleanliness weight of the sample is used. For diagnostic embedding, For the number of physical views, Rate the cleanliness of sample i in view m.

10. The method for small-sample fault diagnosis of mechanical systems based on physical feature entanglement fusion according to claim 1, characterized in that: The training of the method adopts a two-stage optimization strategy: the first stage is to pre-train the multi-physical view capsule feature extraction backbone, and the pre-training loss includes capsule classification loss, reconstruction loss and branch classification loss; The second stage employs episodic meta-training, with the overall loss including pre-training loss, episodic classification loss, dynamic consistency loss, decoupling loss, and scoring regularization term.

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