Cross-domain few-sample fault diagnosis method based on geometric perception coordinated penalty prototype network

Abstract

The invention relates to a cross-domain few-sample fault diagnosis method based on a geometric perception coordinated penalty prototype network, and belongs to the technical field of fault diagnosis, and the method comprises the following steps: S1, dividing samples through employing vibration monitoring signals in a data set; s2, obtaining respective support sets and query sets through source domain samples and target domain samples, and generating meta-tasks used in training and testing stages; s3, extracting input sample features by using a feature extractor; s4, mining an internal geometric structure of the data by using an adaptive manifold mapping module (AMMM), and converting sample features to manifolds; s5, calculating to obtain a coordination penalty prototype HPP; s6, classification is carried out through a dynamic high-sensitivity distance DHSD, loss is calculated, model parameters are updated through back propagation, and training of the GAHPPN is completed; and S7, quickly adapting to the meta-task of the target domain through the trained GAHPPN model, and diagnosing the health state of the target domain sample.

Description

Technical Field

[0001] This invention belongs to the field of fault diagnosis technology and relates to a cross-domain few-sample fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network. Background Technology

[0002] Rotating machinery is widely used in various industrial applications, including speed reducers, turbines, and engines. Due to the long-term operation of such equipment under extreme conditions, critical components such as bearings, gears, and shafts are highly susceptible to failure. Therefore, accurate and timely fault diagnosis of critical components is crucial for reducing maintenance costs and preventing catastrophic accidents. In recent years, data-driven methods, particularly deep learning-based fault diagnosis models for rotating machinery, have demonstrated good performance. However, these methods face significant challenges in the real world because obtaining large amounts of labeled data is expensive. Consequently, diagnostic models typically operate in sparse embedding spaces, limiting the practical usability of data-driven methods.

[0003] To address the challenge of insufficient labeled data, few-shot learning has been introduced. These methods enhance the model's adaptability by rapidly acquiring knowledge from a limited number of samples. However, such models are prone to overfitting the training set. This limitation becomes particularly pronounced when faced with domain shift. Due to factors such as mechanical structure, operating conditions, and environmental disturbances, there are often distributional differences between the training and test sets. Therefore, traditional few-shot learning methods exhibit suboptimal performance when deployed in real-world industrial scenarios.

[0004] Another prominent research direction is transfer learning, which transfers knowledge from a source domain to a target domain for effective model deployment. While these methods have shown potential in cross-domain adaptation, they typically rely on a large number of labeled samples in the source domain. Furthermore, these methods are often tailored to specific source and target domains, failing to fundamentally enhance the model's adaptability. These limitations result in transfer learning performing poorly in real-world applications.

[0005] Therefore, there is an urgent need to research more practical cross-domain, low-sample fault diagnosis methods for rotating machinery. Several recent studies have focused on this area. An et al. constructed a domain adaptation framework utilizing semantic information encoding and contrastive learning to obtain more accurate prototypes under conditions of insufficient samples. Wang et al. proposed a novel meta-learning method to handle task conflicts and biases in low-sample cross-domain diagnosis. Li et al. designed an enhanced spiking neural network for effectively transferring knowledge across machines in low-sample scenarios. Xia et al. constructed a semantic transfer framework that utilizes a general semantic space built from finite single-fault samples to achieve cross-domain composite fault diagnosis. Mu et al. designed an adaptive meta-model for accurate and robust diagnosis under severe domain bias and low sample conditions. Li et al. proposed a novel continuous learning network for efficient cross-machine fault diagnosis with limited samples.

[0006] However, existing research on cross-domain small-sample fault diagnosis of rotating machinery still faces three significant limitations: 1) Traditional distance methods cannot sensitively reflect subtle differences under conditions of high inter-class similarity; at the same time, diagnostic classifiers based on fixed distances are often unsuitable due to distribution variations and scale differences between the source and target domains. 2) Existing prototype estimation methods struggle to cope with limited samples because the available samples in a certain class may be underrepresented. This situation is exacerbated by intra-class variability, leading to biased prototypes. 3) Discriminative feature extraction faces challenges in sparse high-dimensional embedding spaces. Most existing models ignore the intrinsic geometric structure of mechanical vibration signals, increasing the difficulty of parameter optimization and feature unwrapping under limited sample conditions. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a cross-domain few-sample fault diagnosis method based on a geometry-aware harmonized penalty prototype network (GAHPPN). The method uses a geometry-aware harmonized penalty prototype network (GAHPPN) based on dynamic high-sensitivity distance (DHSD) to achieve cross-domain few-sample rotating machinery fault diagnosis, so as to meet the actual needs of real-world scenarios.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network includes the following steps:

[0010] S1: Divide the samples using vibration monitoring signals from the dataset;

[0011] S2: Obtain the support set and query set of the source domain and target domain samples respectively, and generate the meta-task used in the training and testing phases;

[0012] S3: Use a feature extractor to extract features from the input samples;

[0013] S4: Utilize the adaptive manifold mapping module (AMMM) to mine the inherent geometric structure of the data and transform sample features onto a manifold;

[0014] S5: Calculate the harmonized penalty prototype (HPP);

[0015] S6: Classification is performed using dynamic high-sensitivity distance (DHSD), loss is calculated, and model parameters are updated through backpropagation to complete the training of the geometrically perceptual coordinated penalty prototype network GAHPPN.

[0016] S7: Using a well-trained GAHPPN model, quickly adapt to the meta-tasks of the target domain and diagnose the health status of samples in the target domain.

[0017] Furthermore, by performing sliding window sampling on the original vibration monitoring signal, samples of various health states with a length of 1024 were obtained.

[0018] Furthermore, a meta-training task is generated from source domain samples, and a meta-testing task is generated from target domain samples.

[0019] Furthermore, features are extracted from the input raw vibration signal samples using a neural network to mine sample features.

[0020] Furthermore, the adaptive manifold mapping module consists of a linear layer and a transformation layer; the linear layer transforms the output of the feature extractor into more representative and separable features; the transformation layer maps the final features to the manifold space.

[0021] Furthermore, the linear layer processing steps are as follows:

[0022] Given a Riemannian manifold And a smooth scalar field f on it, initializing the weights of the linear layer. The gradient at point W0 is the only element in the tangent space that satisfies the following equation, denoted as the Riemann gradient gradf(W0):

[0023]

[0024] In the formula, δ(·,·) is the Riemann metric, and Df(W0) is the directional derivative of the scalar field f at point W0; for a scalar field in Euclidean space, gradf(W0) naturally simplifies to ▽f(W0);

[0025] The Riemann gradient on the Stiefel manifold in AMMM is calculated as follows:

[0026]

[0027] The updated direction calculation is as follows:

[0028]

[0029] In the formula Step size;

[0030] Given a shrinkage mapping If it guarantees that the parameter updates remain on the manifold, then the iteration of the Riemann gradient descent method is as follows:

[0031]

[0032] make Using the Cayley transform as the effective shrinkage mapping in AMMM, the following is employed:

[0033]

[0034] The optimization process of the linear layer is constrained within the Riemann space, i.e., an unconstrained optimization process on the Stiefel manifold.

[0035] Furthermore, the conversion layer processing steps are as follows:

[0036] The final characteristics are described as follows:

[0037] x L =Linear(φ(x))

[0038] In the formula, φ(·) is the feature extractor of GAHPPN, and x is the original vibration signal sample of the input model;

[0039] A learnable degree matrix A is given through random initialization, which is used to adjust the intensity of subsequent scale-dependent rotations. Its dimension d×d is related to the output dimension d of the linear layer; a strictly antisymmetric matrix is ​​constructed from A as follows:

[0040]

[0041] Then, a scale-dependent rotation matrix is ​​constructed using matrix exponential mapping:

[0042]

[0043] In the formula ||x L ||For x L The modulus length;

[0044] Θ∈SO(d), where SO(d) denotes a special orthogonal group, in which x L The scale information is selectively preserved; x is right-multiplied by Θ. L The direction is finely adjusted while retaining some scale information. The result after rotation is normalized as follows:

[0045]

[0046] and It is easy to prove that X is used to denote an undirected axis passing through the origin in the d-dimensional embedding space;

[0047] Finally, the final output X is mapped onto the Grassman manifold as follows:

[0048]

[0049] Through the above operations, the final features are mapped one by one to a point on the Grassmann manifold.

[0050] Furthermore, the Grassmann manifold It is a space where points are q-dimensional hyperplanes, i.e. The set of q-dimensional subspaces:

[0051] O(d) / O(k)×O(dk)

[0052] Where O(d) is a d-dimensional orthogonal group;

[0053] Represented as:

[0054]

[0055] Among them I q It is a q-dimensional identity matrix;

[0056] Each point on the matrix represents a q-dimensional linear subspace consisting of a set of matrices with orthogonal columns; if the column vectors of a matrix span the same linear subspace, then the matrix is ​​considered an equivalence class; equivalence classes are defined by projection mappings and analytic manifolds. The points on the screen correspond one-to-one:

[0057]

[0058] Embedded As a submanifold of Euclidean space;

[0059] Two points The Riemann metric between them is given in the form of an inner product:

[0060]

[0061] In an analytic manifold, the geodesic distance derived from the inner product is a projective metric:

[0062]

[0063] Furthermore, the classification using Dynamic High-Sensitivity Distance (DHSD), loss calculation, and model parameter updating via backpropagation specifically include the following steps:

[0064] The dynamic high-sensitivity distance (DHSD) function is expressed as:

[0065]

[0066] Where α is the sensitivity factor;

[0067] First, initialize the sensitivity factor, and then calculate the F-norm that supports the difference between sample pairs:

[0068]

[0069] In the formula To analyze the point in the manifold space corresponding to the i-th sample of class n in the support set;

[0070] Initialize α to the reciprocal of the standard deviation of this set of norms:

[0071]

[0072] Use the activation function as:

[0073] α = max(ReLU(α), ε)

[0074] Where ε represents a small positive constant;

[0075] After initialization, the intra-class clustering degree and inter-class separation degree are calculated as follows:

[0076]

[0077] in Represents the prototype of a class;

[0078] Then, these two loss terms are merged to form the adaptive loss L. adaptation This indicates the degree to which DHSD is adapted to the current task;

[0079]

[0080] Simultaneously, the class prototype is calculated, and then DHSD is used for classification, as follows:

[0081]

[0082] In the formula, p(y=n) is The probability of belonging to the nth class. To find the point in the analytic manifold space corresponding to the i-th sample of the n-th class in the query set;

[0083] By calculating the classification loss L c To adjust the classification risk of the model:

[0084]

[0085] in for The true label;

[0086] Finally, the total loss L is obtained by combining the adaptation loss and the classification loss. t for:

[0087] L t =L adaptation +λL c

[0088] In the formula, λ represents the hyperparameter of the loss term weights;

[0089] Finally, the network parameters, degree matrix A, and sensitivity factor α are updated through backpropagation.

[0090] Furthermore, the calculation method for the coordination penalty prototype is as follows:

[0091] We propose the harmonized penalty mean (HPM) and define it as the solution to the following optimization problem:

[0092]

[0093] Combining HPM with DHSD generates the coordinated penalty prototype HPP as follows:

[0094]

[0095] in As a prototype of a class, This represents the weight of the k-th sample in this class.

[0096] The beneficial effects of this invention are as follows:

[0097] 1) A task-adaptive sensitivity-adjusted DHSD is proposed. It exhibits enhanced discriminative power by improving responsiveness to changes in inter-sample similarity. Furthermore, its normalized scaling properties ensure metric consistency across heterogeneous domains, implicitly aligning the source and target domain distributions.

[0098] 2) A prototype estimation method suitable for DHSD, namely the Coordinated Penalized Mean (HPM), was designed to reduce the bias caused by small samples. When combined with DHSD, this method generates the Coordinated Penalized Prototype (HPP), which improves the fidelity of prototype representation in scenarios with few samples.

[0099] 3) An Adaptive Manifold Mapping Module (AMMM) is proposed. It incorporates Riemannian geometric constraints to mine and utilize the intrinsic geometric structure of finite samples. AMMM enhances the effectiveness and separability of sample features through geometry-aware updates and transformations.

[0100] 4) Based on the above innovations, a novel cross-domain small-sample fault diagnosis framework, GAHPPN, was constructed. In situations where data is scarce, this diagnostic framework achieves accurate fault classification across different equipment and operating conditions, outperforming classic and state-of-the-art methods.

[0101] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0102] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0103] Figure 1 This is a flowchart of a cross-domain few-shot fault diagnosis method based on a geometric perception-based coordinated penalty prototype network. Detailed Implementation

[0104] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0105] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0106] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0107] Example 1:

[0108] like Figure 1 As shown, this invention provides a cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network, comprising the following steps:

[0109] 1) Divide the samples using vibration monitoring signals from the dataset;

[0110] 2) Obtain the support set and query set of the source domain and target domain samples respectively, and generate the meta-task used in the training and testing phases;

[0111] 3) Use a feature extractor to extract features from the input samples;

[0112] 4) Utilize the adaptive manifold mapping module to mine the inherent geometric structure of the data and transform sample features onto a manifold;

[0113] 5) The prototype of the coordinated penalty is calculated;

[0114] 6) Classify using dynamic high-sensitivity distance, calculate loss, and update model parameters through backpropagation;

[0115] 7) By using the trained GAHPPN model, it can quickly adapt to the meta-task of the target domain and diagnose the health status of the target domain samples.

[0116] Specifically, to address the challenge of discriminative feature extraction in sparse high-dimensional embedding spaces, an adaptive manifold mapping module (AMMM) consisting of a linear layer and a transformation layer is proposed. The geometry-aware linear layer transforms the output of the feature extractor into more representative and separable features, which is essential for accurate classification.

[0117] Given a Riemannian manifold And a smooth scalar field f on it, initializing the weights of the linear layer. The gradient at point W0 is the only element in the tangent space that satisfies the following equation, denoted as the Riemann gradient gradf(W0):

[0118]

[0119] In the formula, δ(·,·) is the Riemann metric, and Df(W0) is the directional derivative of the scalar field f at point W0. For a scalar field in Euclidean space, gradf(W0) naturally simplifies to ▽f(W0).

[0120] Specifically, we calculate the Riemann gradient on the Stiefel manifold in AMMM as follows:

[0121]

[0122] The updated direction calculation is as follows:

[0123]

[0124] In the formula The step size.

[0125] Given a shrinkage mapping If it guarantees that the parameter updates remain on the manifold, then the iteration of the Riemann gradient descent method is as follows:

[0126]

[0127] make Using the Cayley transform as the effective shrinkage mapping in AMMM, the following is employed:

[0128]

[0129] Therefore, the optimization process of the linear layer is constrained within the Riemann space, i.e., an unconstrained optimization process on the Stiefel manifold. This method reduces the search space, thereby improving the efficiency of the optimization process, which is particularly beneficial for scenarios with few samples. Furthermore, the linear layer constrained by Riemann geometry can reduce feature redundancy while mining the inherent geometric structure of the data.

[0130] Another important part of AMMM is the transformation layer. It is responsible for mapping the final features to the manifold space, preparing for subsequent distance calculations and prototype estimation. The final features are expressed as:

[0131] x L =Linear(φ(x))

[0132] In the formula, φ(·) is the feature extractor of GAHPPN, and x is the original vibration signal sample of the input model.

[0133] A learnable degree matrix A is given through random initialization, which is used to adjust the intensity of subsequent scale-dependent rotations. Its dimension d×d is related to the output dimension d of the linear layer. We construct a strictly antisymmetric matrix A as follows:

[0134]

[0135] Then, a scale-dependent rotation matrix is ​​constructed using matrix exponential mapping:

[0136]

[0137] In the formula ||x L ||For x L The length of the module.

[0138] At this stage, we obtain Θ∈SO(d), where SO(d) denotes a special orthogonal group. In this matrix, x L The scale information is selectively preserved.

[0139] Next, x is multiplied by Θ on the right. L The direction is finely adjusted while retaining some scale information. The result after rotation is normalized as follows:

[0140]

[0141] and This is easily proven. Therefore, X can be used to represent an undirected axis passing through the origin in the d-dimensional embedding space. Finally, the final output X is mapped onto the Grassman manifold as follows:

[0142]

[0143] Through the above operations, the final features are mapped one by one to a point on the Grassmann manifold.

[0144] By incorporating Riemannian geometric constraints into feature unwrapping and transformation, the model is able to better utilize the intrinsic geometric structure of a finite number of samples. This gives the GAHPPN model a strong ability to perceive and utilize geometry, thereby improving its performance.

[0145] Grassmann manifold It is a space where points are q-dimensional hyperplanes, i.e. The set of q-dimensional subspaces can be considered as the quotient space:

[0146] O(d) / O(k)×O(dk)

[0147] Where O(d) is a d-dimensional orthogonal group.

[0148] For simplicity, It can be represented as:

[0149]

[0150] Among them I q It is a q-dimensional identity matrix. In other words, Each point on the matrix represents a q-dimensional linear subspace consisting of a set of matrices with orthogonal columns. A matrix is ​​considered an equivalence class if its column vectors span the same linear subspace. Therefore, equivalence classes are determined by projection mappings and analytic manifolds. The points on the screen correspond one-to-one:

[0151]

[0152] therefore, Embedded As a submanifold of Euclidean space. Then two points. The Riemann metric between them is given in the form of an inner product:

[0153]

[0154] Then, the geodesic distance derived from the inner product in the analytic manifold is the projective metric:

[0155]

[0156] In this study, the following methods were used:

[0157] To address the limitations of traditional distance measurement methods in terms of discriminativeness and adaptability, we designed a dynamic high-sensitivity distance (DHSD) function, which is expressed as:

[0158]

[0159] Where α is the sensitivity factor.

[0160] The DHSD function is designed to be smooth, i.e., infinitely differentiable. A key characteristic of DHSD is its non-uniform sensitivity. Its slope is large when the differences between samples are small, and gradually decreases as the differences between samples increase. This property allows DHSD to emphasize subtle variations between similar samples, thereby enhancing its responsiveness. This distance is crucial for improving the fault detection capability of diagnostic models, especially in scenarios with high inter-class similarity. Furthermore, DHSD features task-adaptive sensitivity tuning, enabling it to dynamically adjust its response capability according to specific tasks.

[0161] In DHSD applications, initializing the sensitivity factor is a crucial step. The initialization process begins by calculating the F-norm that supports the differences between sample pairs:

[0162]

[0163] In the formula To resolve the point in the manifold space corresponding to the i-th sample of class n in the support set.

[0164] Initialize α to the reciprocal of the standard deviation of this set of norms:

[0165]

[0166] When the support set is relatively concentrated, the calculated standard deviation is smaller, resulting in a larger initial value for the sensitivity factor. This ensures that DHSD exhibits rapid growth and increased sensitivity to small changes, thus responding positively to changes in sample similarity. Conversely, a larger standard deviation indicates a more dispersed support set, leading to a smaller initial sensitivity.

[0167] To ensure that α remains positive during the update process, an activation function is used as:

[0168] α = max(ReLU(α), ε)

[0169] Where ε represents a small positive constant.

[0170] After initialization, the intra-class clustering degree and inter-class separation degree are calculated as follows:

[0171]

[0172] in It represents the prototype of a class.

[0173] Then, these two loss terms are merged to form the adaptive loss L. adaptation This indicates the degree to which DHSD is adapted to the current task.

[0174]

[0175] Simultaneously, the class prototype is calculated, and then DHSD is used for classification, as follows:

[0176]

[0177] In the formula, p(y=n) is The probability of belonging to the nth class. To find the point in the analytic manifold space corresponding to the i-th sample of the n-th class in the query set.

[0178] By calculating the classification loss L cTo adjust the classification risk of the model:

[0179]

[0180] in for The true label.

[0181] Finally, the total loss L is obtained by combining the adaptation loss and the classification loss. t for:

[0182] L t =L adaptation +λL c

[0183] In the formula, λ represents the hyperparameter of the loss term weight.

[0184] Finally, the network parameters, as well as the degree matrix A and sensitivity factor α, are updated through backpropagation.

[0185] Accurate prototype estimation remains a challenge because the model needs to represent the entire class distribution through a single prototype, when only a few examples are seen. This situation worsens when the available samples are insufficiently representative, leading to biased prototypes. Furthermore, the intra-class variability common in vibration monitoring signals due to fluctuations in rotating machinery operating conditions makes obtaining reliable class representations from limited samples even more difficult.

[0186] To mitigate this bias and thus more representatively estimate class prototypes, we propose the harmonized penalty mean (HPM) and define it as the solution to the following optimization problem:

[0187]

[0188] HPM is designed for DHSD (Distributed Data Sorting), using a proportion-based approach to balance the influence of different samples, producing a more representative prototype that accurately reflects the overall data distribution. Unlike traditional methods that impose a uniform penalty based on distance, HPM penalizes larger distances much more than the conventional Fréchet mean, while penalizing smaller distances relatively mildly. This allows HPM to not only see clustered regions but also ensures that the generated prototype is more representative of the entire class distribution, even in the presence of intraclass variations.

[0189] Next, HPM will be combined with DHSD to generate HPP as follows:

[0190]

[0191] in As a prototype of a class, This represents the weight of the k-th sample in this class.

[0192] Compared to traditional prototypes, HPP places greater emphasis on more distant samples. In cases of limited samples, each sample becomes increasingly important. Identifying outliers simply because they are far from the majority of samples is unwise, leading to the loss of limited information. In cases of intra-class variability, samples themselves may follow a distribution different from the majority. In HPP, distant samples are given greater weight than in traditional prototypes because they may contain crucial information about intra-class variability that helps distinguish different failures. It's important to note that this does not mean distant samples are always assigned higher weights than nearby samples. The weights are modulated by both proximity and a sensitivity factor. Incorporating a sensitivity factor into the weight calculation allows HPP to implicitly consider the dispersion in the distribution and dynamically adjust to accommodate different distribution patterns. Therefore, HPP provides a more representative and flexible approach to prototype estimation, especially when samples are limited and intra-class variability exists.

[0193] Based on the method proposed above, this invention constructs a novel fault diagnosis framework GAHPPN, and uses GAHPPN to conduct detailed experiments on the following four datasets:

[0194] 1) Case Western Reserve University (CWRU) Bearing Dataset. This dataset contains four bearing health conditions: normal condition (NC), inner race fault (IF), ball fault (BF), and outer race fault (OF).

[0195] 2) Southeast University (SEU) Bearing Dataset. This dataset provides five different health states: NC, IF, BF, OF, and compound inner-outer race fault (IOF).

[0196] 3) Bearing fault detection (BFD) experimental dataset. The experiment used a self-made bearing test bench to collect vibration signals of the SKF-61908 bearing under time-varying operating conditions. This self-collected dataset contains four health states: NC, IF, BF, and OF.

[0197] 4) Industrial Robot Fault (IRF) Dataset. We used PCB accelerometers to collect fault data from a BRTIRUS1510A six-DOF industrial robot. Due to the high torque load on the two axes and the long-term cyclic stress on the reducer, we specifically monitored the RV40E-121 reducer (located on the two axes). The obtained dataset includes five health states: NC, sun gear tooth pitting, sun gear tooth fracture, planetary gear tooth fracture, and planetary gear tooth fracture.

[0198] Table 1 shows the details of the four datasets mentioned above.

[0199] Table 1

[0200]

[0201] Six 5-sample tasks across bearings were constructed using datasets A, B, and C (Table 2), while six 5-sample tasks across devices were constructed through transfer between the above datasets and dataset D (Table 3). These cross-domain few-sample tasks collectively reflect the diagnostic challenges in real-world applications, including cross-load, cross-speed, and cross-device scenarios with limited samples.

[0202] To verify the effectiveness and advantages of the proposed method, several well-known cross-domain few-sample methods, including Relation Net (RelaNet), ProtoNet (Prototype Network), MAML (Model-agnostic Meta-learning), GMAML (General Model-agnostic Meta-learning), and AGPN (Adaptive Generic Prototype Network), were compared and analyzed. Twenty samples were allocated to each healthy state for training, and 200 samples were allocated to each healthy state for testing. All experiments were repeated five times to mitigate the impact of randomness. The average accuracy and standard deviation (SD) of the experiments were recorded.

[0203] As shown in Table 2, the proposed method achieves an average accuracy of 92.46% in cross-domain few-shot tasks, a 4.28% improvement over the strongest comparative method, AGPN. This progress is attributed to GAHPPN's strong discriminative power and its ability to mine and utilize limited information. Notably, significant improvements were observed in challenging scenarios, particularly in the A→C (7.41% improvement) and B→C (10.68% improvement) tasks, where knowledge transfers from constant velocity to time-varying conditions with non-stationary signals. These results demonstrate that GAHPPN exhibits superior adaptability in complex cross-domain scenarios due to the task-adaptive sensitivity and normalization properties of DHSD and the accurate class representation of HPP. The failure of MAML-based methods on some tasks can be explained by their reliance on classifiers with fixed outputs, which becomes a limitation when dealing with variations in the number of classes in specific domains. In contrast, metric-based meta-learning methods demonstrate greater versatility due to their flexible similarity classification framework. The proposed method also exhibits superior stability in diagnostic accuracy compared to other comparative methods, namely, minimum standard deviation, due to its strong dynamic adjustment capability.

[0204] Table 2

[0205]

[0206]

[0207] As knowledge shifts from laboratory bearings to industrial robot reducers, diagnostic tasks become more challenging, as shown in Table 3. The proposed method achieves the highest mean accuracy of 88.72% across six cross-device few-sample tasks, representing a 2.65% improvement over AGPN and a 25.30% improvement over the baseline ProtoNet. Particularly in the B→D task, the proposed method outperforms the suboptimal AGPN method by 7.30%. These results demonstrate the versatility and strong adaptability of GAHPPN, even with significant domain differences, ranging from laboratory bearings to industrial reducer gears.

[0208] Table 3

[0209]

[0210] To evaluate the contribution of each component in the proposed method, a comprehensive ablation study was conducted using the A→B task as an example. As shown in Table 4, the complete model achieved superior performance. Removing DHSD resulted in a 7.21% performance decrease, highlighting the crucial role of this highly sensitive yet normalized distance in fault identification. Similarly, eliminating HPP reduced accuracy by 3.50%, demonstrating its effectiveness in representing class distributions using a small number of samples. The absence of linear and transform layers in AMMM led to a decrease in accuracy, confirming that the geometry-aware component mines and utilizes the inherent geometric structure of the data to obtain more representative and separable features, thereby making subsequent fault identification more reliable. Notably, the complete model improved performance by 37.32% compared to the baseline ProtoNet, validating the substantial improvements achieved through architectural innovation.

[0211] Table 4

[0212]

[0213] Example 2:

[0214] An electronic device, comprising a memory and a processor;

[0215] The memory is used to store computer programs;

[0216] The processor is configured to implement the method described in Embodiment 1 when executing the computer program.

[0217] Example 3:

[0218] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0219] Example 4:

[0220] A computer program product includes a computer program that, when executed by a processor, implements the method described in Example 1.

[0221] In the above embodiments, the reference to "this embodiment" in the specification indicates that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily refer to the same embodiment.

[0222] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0223] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0224] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0225] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.

[0226] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0227] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0228] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0229] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network, characterized in that: Includes the following steps: S1: Divide the samples using vibration monitoring signals from the dataset; S2: Obtain the support set and query set of the source domain and target domain samples respectively, and generate the meta-task used in the training and testing phases; S3: Use a feature extractor to extract features from the input samples; S4: Utilize the Adaptive Manifold Mapping (AMMM) module to mine the intrinsic geometric structure of the data and transform sample features onto a manifold; S5: Calculate the coordination penalty prototype HPP; S6: Classify using Dynamic High Sensitivity Distance (DHSD), calculate loss, and update model parameters through backpropagation to complete the training of the Geometric Awareness Coordination Penalty Prototype Network (GAHPPN). S7: Using a well-trained GAHPPN model, quickly adapt to the meta-tasks of the target domain and diagnose the health status of samples in the target domain.

2. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 1, characterized in that: Step S1, which involves dividing the samples using vibration monitoring signals from the dataset, specifically includes: obtaining samples of each health state with a length of 1024 by performing sliding window sampling on the original vibration monitoring signals.

3. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 1, characterized in that: Step S2 describes obtaining support sets and query sets from source and target domain samples, and generating meta-tasks for the training and testing phases. Specifically, this includes generating meta-training tasks from source domain samples and generating meta-testing tasks from target domain samples.

4. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 1, characterized in that: Step S3, which involves extracting features from the input sample using a feature extractor, specifically includes: extracting features from the original vibration signal sample using a neural network to mine sample features.

5. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 1, characterized in that: The adaptive manifold mapping module consists of a linear layer and a transformation layer; the linear layer transforms the output of the feature extractor into more representative and separable features; the transformation layer maps the final features to the manifold space.

6. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 5, characterized in that: The linear layer processing steps are as follows: Given a Riemannian manifold And a smooth scalar field f on it, initializing the weights of the linear layer. The gradient at point W0 is the only element in the tangent space that satisfies the following equation, denoted as the Riemann gradient gradf(W0): In the formula, δ(·,·) is the Riemann metric, and Df(W0) is the directional derivative of the scalar field f at point W0; for a scalar field in Euclidean space, gradf(W0) naturally simplifies to The Riemann gradient on the Stiefel manifold in AMMM is calculated as follows: The updated direction calculation is as follows: G0 = -θgradf(W0) In the formula, θ is the step size; Given a shrinkage mapping If it guarantees that the parameter updates remain on the manifold, then the iteration of the Riemann gradient descent method is as follows: make Using the Cayley transform as the effective shrinkage mapping in AMMM, the following is employed: The optimization process of the linear layer is constrained within the Riemann space, i.e., an unconstrained optimization process on the Stiefel manifold.

7. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 5, characterized in that: The conversion layer processing steps are as follows: The final characteristics are described as follows: x L =Linear(φ(x)) In the formula, φ(·) is the feature extractor of GAHPPN, and x is the original vibration signal sample of the input model; A learnable degree matrix A is given by random initialization, which is used to adjust the intensity of subsequent scale-related rotations; Its dimension d×d is related to the output dimension d of the linear layer; a strictly antisymmetric matrix can be constructed using A as follows: Then, a scale-dependent rotation matrix is ​​constructed using matrix exponential mapping: In the formula ||x L ||For x L The modulus length; Θ∈SO(d), where SO(d) denotes a special orthogonal group, in which x L The scale information is selectively preserved; By right-multiplying Θ on x L The direction is finely adjusted while retaining some scale information. The result after rotation is normalized as follows: and It is easy to prove that X is used to denote an undirected axis passing through the origin in the d-dimensional embedding space; Finally, the final output X is mapped onto the Grassman manifold as follows: Through the above operations, the final features are mapped one by one to a point on the Grassmann manifold.

8. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 7, characterized in that: The Grassmann manifold It is a space where points are q-dimensional hyperplanes, i.e. The set of q-dimensional subspaces: O(d) / O(k)×O(dk) Where O(d) is a d-dimensional orthogonal group; Represented as: Among them I q It is a q-dimensional identity matrix; Each point on the matrix represents a q-dimensional linear subspace consisting of a set of matrices with orthogonal columns; if the column vectors of a matrix span the same linear subspace, then the matrix is ​​considered an equivalence class; equivalence classes are defined by projection mappings and analytic manifolds. The points on the screen correspond one-to-one: Embedded As a submanifold of Euclidean space; Two points The Riemann metric between them is given in the form of an inner product: In an analytic manifold, the geodesic distance derived from the inner product is a projective metric:

9. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 1, characterized in that: The process of classifying using Dynamic High-Sensitivity Distance (DHSD), calculating the loss, and updating the model parameters through backpropagation specifically includes the following steps: The dynamic high-sensitivity distance (DHSD) function is expressed as: Where α is the sensitivity factor; First, initialize the sensitivity factor, and then calculate the F-norm that supports the difference between sample pairs: In the formula To analyze the point in the manifold space corresponding to the i-th sample of class n in the support set; Initialize α to the reciprocal of the standard deviation of this set of norms: Use the activation function as: α = max(ReLU(α), ε) Where ε represents a small positive constant; After initialization, the intra-class clustering degree and inter-class separation degree are calculated as follows: in Represents the prototype of a class; Then, these two loss terms are merged to form the adaptive loss L. adaptation This indicates the degree to which DHSD is adapted to the current task; Simultaneously, the class prototype is calculated, and then DHSD is used for classification, as follows: In the formula, p(y=n) is The probability of belonging to the nth class. To find the point in the analytic manifold space corresponding to the i-th sample of the n-th class in the query set; By calculating the classification loss L c To adjust the classification risk of the model: in for The true label; Finally, the total loss L is obtained by combining the adaptation loss and the classification loss. t for: THE t =L adaptation +λL c In the formula, λ represents the hyperparameter of the loss term weights; Finally, the network parameters, degree matrix A, and sensitivity factor α are updated through backpropagation.

10. The cross-domain few-shot fault diagnosis method based on a geometrically perceptual coordinated penalty prototype network according to claim 1, characterized in that: The calculation method for the coordination penalty prototype is as follows: We propose the harmonized penalty mean (HPM) and define it as the solution to the following optimization problem: Combining HPM with DHSD generates the coordinated penalty prototype HPP as follows: in As a prototype of a class, This represents the weight of the k-th sample in this class.

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