Small sample fault diagnosis method based on noise elasticity element learning framework

Abstract

The present application relates to a kind of based on noise elasticity element learning framework Small Sample Fault Diagnosis Method, belong to the technical field of fault diagnosis, comprising the following steps: S1: acquisition vibration signal is divided into source domain and target domain, respectively construct support set and query set, generate the task required for element training and element test;S2: the original input signal is mapped into low-dimensional embedding feature;S3: construct energy threshold subspace prototype;S4: calculate task adaptive damping factor;S5: after embedding and normalizing query sample, construct one-dimensional subspace and its projection matrix, calculate its noise perception damping distance with each class prototype by means of damping factor, output classification;S6: construct total loss, update model parameters by back propagation;S7: in element test stage, freeze model parameters, construct prototype for new task and adaptively calculate damping factor, classify according to noise perception damping distance, diagnose the health status of noisy sample in target domain.

Description

Technical Field

[0001] This invention belongs to the field of fault diagnosis technology and relates to a small-sample fault diagnosis method based on a noise elastic element learning framework. Background Technology

[0002] The rise of artificial intelligence has propelled the intelligent transformation of industrial systems to the forefront. In this paradigm, intelligent fault diagnosis and predictive maintenance are crucial for ensuring the reliability, efficiency, and safety of complex machinery. Traditional fault diagnosis methods primarily rely on supervised learning, typically requiring a large amount of accurately labeled fault data to effectively train the model. However, obtaining sufficient labeled fault samples poses a significant challenge in many real-world industrial scenarios. This scarcity stems from various factors, including the inherent rarity of certain key fault types, the high cost and disruption to production caused by data acquisition, and the limited operational history of new equipment. This widespread data scarcity directly leads to the critical issue of few-shot fault diagnosis (FSFD), which requires building robust diagnostic models using only a small number of available samples. This challenge is particularly pronounced in industrial robots. Because industrial robots operate under complex conditions for extended periods, critical components such as rolling bearings and RV (rotary vector) reducers are highly susceptible to failure. Bearings are fundamental components that withstand continuous rotational stress, while RV reducers, typically installed at joints such as the base, boom, and forearm, are core transmission units responsible for motion and load-bearing functions. However, collecting large amounts of fault data for these components is both expensive and often impractical, making FSFD indispensable.

[0003] Meta-learning has emerged as a promising paradigm for solving the FSFD problem. By leveraging meta-knowledge acquired from various related meta-tasks, meta-learning models can rapidly adapt to new and unseen tasks with limited labeled data. Among various meta-learning methods, metric-based methods, especially those employing prototype networks, have achieved significant success. These methods typically learn an embedding space where similar samples cluster around a representative prototype and classify based on the distance of the query sample to these learned prototypes. While other FSFD strategies exist, such as data augmentation or transfer learning, they often face inherent limitations. Data augmentation techniques are generally ineffective at increasing the diversity of a small number of classes and involve constructing complex generative models. Transfer learning methods are often domain-specific, requiring high transferability between the source and target domains and still necessitating sufficient source domain samples, thus failing to fundamentally enhance the model's adaptability in truly small-sample scenarios.

[0004] While meta-learning offers promise for FSFD, industrial data presents a more significant challenge: inherent noise. Industrial signals are inherently contaminated with substantial levels of noise due to sensor defects, environmental interference, variable operating conditions, and mechanical vibrations. The scarcity of labeled samples makes traditional meta-learning methods highly susceptible to noise contamination. With small sample settings, noise can easily mask fault characteristics and distort fault modes, potentially leading to a significant deviation between the estimated prototype and the calculated value, resulting in substantial degradation of model performance.

[0005] To address these challenges, a growing body of research has emerged, primarily focusing on enhancing the robustness and adaptability of FSFD models. Some studies have dedicated themselves to developing robust feature learning techniques. For example, Zhong et al. proposed an adaptive hypergraph feature learning method based on structural conditional diffusion, which enhances discriminative ability in small-sample scenarios by constructing higher-order relationships between samples and utilizing the diffusion process to attenuate noise. You et al. designed a contrastive variational graph autoencoder feature fusion module that separates fault-related patterns from noisy embeddings, achieving robust small-sample diagnosis. Other studies have employed attention mechanisms to mitigate the impact of strong noise and limited samples. Li et al. designed a feature-enhanced small-sample bearing fault diagnosis method based on a dynamic sparse attention mechanism, prioritizing key fault features under strong noise and limited sample conditions. Huang et al. developed a meta-learning framework comprising an adaptive denoising multi-scale attention enhancement network and a soft thresholding module for adaptive denoising. Furthermore, some work focuses on stabilizing the meta-learning process itself. Wen et al. constructed a backtracking prototype network that captures complex class distributions through a center difference metric to mitigate prototype oscillations and achieve robust small-sample diagnosis. Zhang et al. proposed an attention-enhanced Transformer with prototype alignment, in which a reliable median-based estimator is employed to obtain stable prototypes, and query embeddings are aligned with these prototypes. Xia et al. proposed a prototype refinement method based on deep reinforcement learning, designing a comprehensive reward mechanism to stably extract effective information from a finite number of samples.

[0006] While these studies have shown encouraging results regarding FSFD in inherently noisy industrial environments, several key questions remain: 1) Current distance functions often lack sufficient robustness to noise and are highly susceptible to noise disturbances, leading to misclassification under contaminated data.

[0007] 2) When there are only a few samples for each category, noise can significantly distort the estimated category prototypes, leading to inaccurate representations and thus affecting diagnostic performance.

[0008] 3) Most existing small-sample fault diagnosis methods operate in Euclidean space, implicitly assuming a linear data structure. However, real-world monitoring signals often exhibit complex nonlinear geometric structures, making it difficult for these methods to achieve optimal discriminative power and feature representation in sparse, high-dimensional embedding spaces. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a novel noise-resilient meta-learning (NRML) framework for noisy environments, used for small-sample fault diagnosis.

[0010] To achieve the above objectives, the present invention provides the following technical solution: A few-sample fault diagnosis method based on a noisy elastic element learning framework includes the following steps: S1: Collect vibration signals from an industrial robot, divide them into a source domain and a target domain. The source domain contains no noise, while the target domain contains noise of varying degrees. Construct support sets and query sets respectively, and generate the tasks required for meta-training and meta-testing. S2: The original input signal is mapped into low-dimensional embedded features through a feature extractor; S3: Perform singular value decomposition on the feature matrix of support samples for each category, adaptively determine the subspace dimension based on the cumulative energy ratio threshold, and select the dominant left singular vector to form the prototype of the energy threshold subspace. S4: Quantify the noise level and structural complexity of the current meta-task using the projected residual and the average prototype dimension, and calculate the task adaptive damping factor via the learnable base scale and the Softplus function. S5: After embedding and normalizing the query samples, construct a one-dimensional subspace and its projection matrix. Calculate the noise-perceived damping distance between the query samples and various prototypes using the damping factor, and output the classification probability via Softmax. S6: Construct the total loss by combining cross-entropy loss with ratio-based structural loss that combines intra-class compactness and inter-class separation, and update the model parameters through backpropagation; S7: Freeze model parameters during the meta-testing phase, quickly build prototypes for new tasks and adaptively calculate damping factors, and classify based on noise-perceived damping distance to diagnose the health status of noisy samples in the target domain.

[0011] Furthermore, step S2, which involves mapping the original input signal into low-dimensional embedded features using a feature extractor, includes: for the original input signal... x Feature extractor Map it to d Dimensional embedding space:

[0012] For supporting specific fault categories n ,use K Construct a feature matrix from the embedded features:

[0013] in This indicates the specific supporting sample features.

[0014] Furthermore, step S3 specifically includes the following steps: right Perform singular value decomposition:

[0015] in Describes a left singular vector matrix. Represents a singular value matrix. Describes a right singular vector matrix. The column composition A set of orthonormal bases for the column space of ; Determining the subspace dimension using an energy threshold. ,forward p The cumulative energy ratio of each component is:

[0016] in Indicates the first j One portion, Indicates the first i Embedded features, K Indicates that the support is concentrated. K One sample, Indicates the first j The energy in each direction, i.e., the square of the singular value, is similarly... express i Energy in one direction; Given an energy threshold , The smallest integer that satisfies the following conditions:

[0017] category n The energy threshold subspace prototype is obtained by taking the front. Constructing by using left singular vectors and forming a projection matrix:

[0018]

[0019] in Indicates category n The prototype of the energy threshold subspace. This indicates taking the left singular vector matrix. The former List, This represents the projection matrix corresponding to the prototype.

[0020] Furthermore, step S4 specifically includes: For a single query sample feature Its corresponding query subspace With projection matrix The structure is as follows:

[0021] in Representing Grassmanifold The one-dimensional subspace on, i.e. d The set of undirected axes passing through the origin in the dimensional embedding space; Indicates projection mapping; The estimated noise level within the current meta-task is quantified by the projected residuals:

[0022] in This indicates the estimated noise level within the current meta-task. Indicates the number of categories. Represents the Frobenius norm; make The average prototype dimension; Task adaptive damping factor The calculation is as follows:

[0023] in This is the Softplus activation function, used to ensure a positive value; For scaling parameters, including Learnable parameters are randomly initialized and shared across tasks.

[0024] Furthermore, in step S5, the prototype With query subspace The noise sensing damping distance between them is:

[0025] in To query subspace The corresponding projection matrix.

[0026] Furthermore, the softmax output classification probability mentioned in step S5 specifically includes: for those containing K Categories in the query set of each sample n The iQuery sample Its corresponding subspace is This sample belongs to category n The probability is obtained by using the softmax function on negative NADD: .

[0027] Furthermore, the construction of the total loss in step S6, which combines cross-entropy loss with a ratio-based structural loss of intra-class compactness and inter-class separation, includes: The classification loss is the standard cross-entropy:

[0028] in For the first i One-hot encoding of the real labels of each query sample; Intra-class compaction loss will help pull samples toward their prototype:

[0029] Inter-class separation loss pushes different prototypes apart:

[0030] The ratio-based structural loss is:

[0031] in It is a small positive number used to ensure numerical stability; The total loss is:

[0032] in It is a hyperparameter that controls the degree of compromise.

[0033] Furthermore, during the meta-training phase, the feature extractor parameters and the original scaling parameters... By minimizing task distribution Joint optimization of expected loss on:

[0034] During the meta-testing phase, the parameters are frozen; for each new task, an energy threshold subspace prototype is first constructed, and then the damping factor is calculated. The query and classification are then completed, and no further parameter updates are performed throughout the process.

[0035] The beneficial effects of this invention are as follows: 1) This invention proposes a noise-sensing damping distance on a Grassmann manifold. Aware-Damped Distance (NADD) is used to achieve accurate similarity measurement for small-sample fault diagnosis under noise perturbation. NADD has a task-adaptive damping mechanism that can dynamically balance discrimination sensitivity and noise robustness according to the current noise level. In addition, by embedding the target into a common environmental space, NADD naturally ensures comparability between subspaces of different dimensions while maintaining computational efficiency.

[0036] 2) This invention develops a prototype construction method, called the energy threshold subspace prototype. Thresholded subspace prototypes (ETSPs) are used to adaptively obtain compact class representations on optimal-dimensional Grassmann manifolds. Even with extremely limited samples, ETSPs suppress noise and capture the dominant, energy-concentrated directions in each fault category.

[0037] 3) Based on the above innovations, this invention constructs a novel small-sample fault diagnosis framework called NRML. Comprehensive experiments have verified that the NRML proposed in this invention is superior to classical methods and state-of-the-art methods. of the The superiority and noise robustness of the art (SOTA) method.

[0038] 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

[0039] 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: Figure 1 This is a flowchart of a small-sample fault diagnosis method based on a noise elastic element learning framework. Detailed Implementation

[0040] 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.

[0041] 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.

[0042] 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.

[0043] Example 1: like Figure 1 As shown, this invention provides a small-sample fault diagnosis method based on a noise elastic element learning framework, comprising the following steps: 1) Using the collected vibration signals of industrial robots, the source domain and target domain are divided. The source domain is noise-free while the target domain has different levels of noise. Support sets and query sets are constructed respectively to generate the tasks required for meta-training and meta-testing. 2) The original input signal is mapped into low-dimensional embedded features using a feature extractor; 3) Perform singular value decomposition on the feature matrix of support samples for each category, adaptively determine the subspace dimension based on the cumulative energy ratio threshold, and select the dominant left singular vector to form the prototype of the energy threshold subspace; 4) Quantify the noise level and structural complexity of the current meta-task using the projection residual and the average prototype dimension, and calculate the task adaptive damping factor via the learnable base scale and the Softplus function. 5) After embedding and normalizing the query samples, construct a one-dimensional subspace and its projection matrix. Calculate the noise-perceived damping distance between the query samples and various prototypes using the damping factor, and output the classification probability via Softmax. 6) Construct the total loss by combining cross-entropy loss with ratio-based structural loss that balances intra-class compactness and inter-class separation, and update the model parameters through backpropagation; 7) Freeze model parameters during the meta-testing phase, quickly build prototypes for new tasks and adaptively calculate damping factors, and classify based on noise-perceived damping distance to diagnose the health status of noisy samples in the target domain.

[0044] In metric-based meta-learning, the function that compares the distance between a query sample and a prototype fundamentally determines classification accuracy. Traditional distance methods often struggle to maintain sufficient discriminative power under conditions of severe noise contamination and limited data. Therefore, this invention proposes a novel Noise-Aware Damped Distance (NADD) on the Grassmann manifold, which possesses task-adaptive damping properties and can dynamically balance sensitivity and robustness.

[0045] Grassmann manifold It can be represented as:

[0046] in for q An identity matrix of order 1. It should be noted that... Each point on the graph represents a matrix consisting of a set of orthogonal columns. q A linear subspace. If the column vectors of several matrices span the same linear subspace, then these matrices represent an equivalence class.

[0047] The Grassmann manifold was chosen because it leverages the compact subspace structure inherent in high-dimensional monitoring signals, which often exhibit strong correlations and significant redundancy. The Grassmann manifold naturally provides a geometric paradigm for exploring robust discriminative power and feature representation.

[0048] To compare two q 3D linear subspace Their similarities can be seen from their main characters To depict these main characters, they are derived through singularity decomposition:

[0049] To facilitate distance calculation and ensure comparability between subspaces of different dimensions, a projection mapping is used:

[0050] This mapping will be each q 3D linear subspace X Mapped to surrounding space The only symmetric projection matrix in Y .

[0051] The Frobenius norm between projections is directly related to the protagonist between the two subspaces:

[0052] This relationship suggests that using the Frobenius norm in the surrounding space can geometrically faithfully and computationally efficiently replace direct computation of the protagonist. However, while the above formula provides a reasonable measure of similarity, its fixed sensitivity can be problematic in noisy, small-sample scenarios, leading to misleading scores. The lack of a rigid distance function that can adjust its sensitivity according to the current noise level amplifies the influence of spurious components. To enhance robustness to noise, NADD is designed as follows:

[0053] in This is the task-adaptive damping factor.

[0054] NADD is bounded, and its saturation properties limit the upper bound of the influence of large noise bias, preventing it from dominating similarity assessment.

[0055] Meanwhile, NADD exhibits quasi-linearity for small differences, preserving the sensitivity required to distinguish neighboring subspaces.

[0056] Therefore, damping factor As a control parameter, it functions by compressing the range of variation and adjusting the slope: smaller Sharpening sensitivity, and larger Enhance robustness.

[0057] Constructing reliable class prototypes from a small number of noisy support samples is extremely challenging. Simple averaging fails to suppress noise and may discard crucial intra-class geometry. Monitoring signals from rotating machinery are typically embedded in high-dimensional spaces, but often exhibit strong correlation and redundancy, making it possible to represent samples of the same class compactly with low-dimensional structures. Therefore, this invention proposes an Energy Threshold Subspace Prototype (ETSP), which represents each class as a low-dimensional linear subspace on a Grassmann manifold, and adaptively selects the subspace dimension by retaining only the directions with the highest energy concentration in the learned embedding space.

[0058] Specifically, for the original input signal x Feature extractor Map it to d Dimensional embedding space:

[0059] For supporting specific fault categories n ,use K Construct a feature matrix from the embedded features:

[0060] To obtain a category that can be captured n Robust prototype of the main direction of change, this invention directly addresses Perform singular value decomposition:

[0061] in The column composition A set of orthonormal bases for the column space.

[0062] To suppress noise while preserving discriminative information, the subspace dimension is determined using an energy threshold. This avoids fixed, artificially set dimensions. (Previous) p The cumulative energy ratio of each component is:

[0063] Given an energy threshold , The smallest integer that satisfies the following conditions:

[0064] Its upper limit guarantees the stability of subspace estimation.

[0065] Energy threshold This invention strikes a balance between dimensionality reduction and information preservation. Set to 0.80 to discard low-energy dimensions while preserving the dominant components in the embedding space.

[0066] ETSP of category n by taking the first Constructing by using left singular vectors and forming a projection matrix:

[0067]

[0068] This projection mapping encodes the subspace into the surrounding space, directly supporting NADD computation. This is determined by category. ETSP captures the most salient common features of each category while suppressing noise-induced interference. It effectively achieves non-linear dimensionality reduction by focusing on the most informative components, thus making the class representation robust to noisy data.

[0069] Similarly, for a single query sample feature Its corresponding query subspace With projection matrix The structure is as follows:

[0070] in Representing Grassmanifold The one-dimensional subspace on, i.e. d The set of undirected axes passing through the origin in the dimensional embedding space.

[0071] The estimated noise level within the current meta-task is quantified by the projected residuals, i.e., the energy that cannot be explained by the estimated ETSP but exists in its orthogonal complement:

[0072] make This represents the average prototype dimension. Here... This reflects the overall structural complexity of the current task. A larger value indicates that each category requires a richer subspace description, which is typically accompanied by more severe noise pollution. Task-adaptive damping factor. The calculation is as follows:

[0073] in This is the Softplus activation function, used to ensure a positive value; For scaling parameters, including Learnable parameters are randomly initialized and shared across tasks.

[0074] The exponential form is used because it can increase dramatically under high noise conditions, thus powerfully damping large disturbances, while remaining moderate under clean conditions. Incorporating task complexity into the damping mechanism makes It adapts not only to the noise level but also to the dimension selected by the prototype.

[0075] Therefore, the prototype With query subspace The NADD in between can be rewritten as:

[0076] Integrating the NADD and ETSP proposed in this invention forms a complete Noise Elastic Meta-Learning (NRML) framework. For those containing... K Categories in the query set of each sample n The i Query sample Its corresponding subspace is This sample belongs to category n The probability is obtained by using the softmax function on negative NADD:

[0077] The classification loss is the standard cross-entropy:

[0078] in For the first i One-hot encoding of the real labels of each query sample.

[0079] To further impose favorable geometry on the Grassmann manifold, this invention designs a prototype structure loss, comprising two terms: intra-class compactness and inter-class separability. The intra-class loss supports samples towards their prototype:

[0080] Inter-class loss separates different prototypes:

[0081] The structural loss is then constructed in ratio form to inherently balance these two objectives:

[0082] in is a small positive number used to ensure numerical stability. This ratio-based expression aims to implicitly minimize intra-class distance and maximize inter-class distance simultaneously, thereby forcing robust and well-structured embeddings on the Grassmann manifold.

[0083] The total loss of a meta-task is a weighted sum:

[0084] in It is a hyperparameter that controls the degree of compromise.

[0085] During the meta-training phase, the feature extractor parameters and the original scaling parameters... By minimizing task distribution Joint optimization of expected loss on:

[0086] During the meta-testing phase, the parameters are frozen. For each new task, the ETSP is constructed first, and then the damping factor is calculated. The query and classification are then completed, and no further parameter updates are performed throughout the process.

[0087] In summary, this invention constructs a novel fault diagnosis framework, NRML, which can achieve robust small-sample fault diagnosis under diverse and unknown noise conditions.

[0088] In this invention, all comparison methods adhere to their original configurations and optimal hyperparameter settings to ensure fair evaluation. All methods employ the same data preprocessing and scenario sampling methods. Each sample contains 1024 data points. A meta-training task is constructed using 20 samples per class, and a meta-test is performed using 200 samples per class. Each meta-task consists of one... N -way K-shot clip, in which K = 5. The experimental results are based on the average of five random seeds. The diagnostic accuracy and standard deviation (SD) were recorded at six signal-to-noise ratio (SNR) levels from -8 dB to the original noise-free scenario.

[0089] This invention compares the proposed NRML with six other methods: Relation Net (RelaNet), Prototype Network (ProtoNet), Model-agnostic Meta-learning (MAML), General Model-agnostic Meta-learning (GMAML), Adaptive Generic Prototype Network (AGPN), and Retrospective Prototype Network (RPN). Tables 1 and 2 summarize the quantitative results on the two datasets.

[0090] Table 1

[0091] Table 2

[0092] As shown in Table 1, NRML consistently achieves the highest accuracy across the entire SNR range. Under noise-free conditions, all methods perform well, but NRML reaches 99.99%. NRML's advantage becomes increasingly pronounced with increasing noise. At -8 dB, NRML achieves 61.63% accuracy, while the strongest baseline method, RPN, only achieves 48.49%, representing a relative improvement of over 27%. NRML's average accuracy across all noise levels is 90.17%, significantly outperforming RPN's 79.28% and AGPN's 68.51%. Classical methods such as ProtoNet and MAML exhibit a sharp performance drop below 0 dB, confirming their vulnerability in noisy, small-sample scenarios. The performance gap at low SNR can be attributed to the damping mechanism of NADD and the robust prototyping of ETSP. NADD automatically saturates large noise-induced biases, while a fixed distance lacks the flexibility to adapt to different noise levels. Meanwhile, ETSP suppresses noise-dominant dimensions, thus producing compact and stable class representations even under severe contamination.

[0093] Table 2 presents the results on the more challenging IRF dataset. Under noise-free conditions, NRML achieves an accuracy of 95.08%, outperforming AGPN's 93.56% and RPN's 93.22%. At -8 dB, NRML achieves 78.16%, more than 8% higher than the suboptimal methods. NRML's mean accuracy is 88.06%, compared to RPN's 83.55% and AGPN's 83.31%. Importantly, the performance gap widens at the lowest SNR levels, confirming that adaptive damping mechanisms and prototyping provide the greatest benefit when noise severely impairs discriminative ability and class representation.

[0094] Example 2: An electronic device, including a memory and a processor; The memory is used to store computer programs; The processor is configured to implement the method described in Embodiment 1 when executing the computer program.

[0095] Example 3: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0096] Example 4: A computer program product includes a computer program that, when executed by a processor, implements the method described in Example 1.

[0097] 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.

[0098] 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.

[0099] 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.

[0100] 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.

[0101] 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.

[0102] 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.

[0103] 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.

[0104] 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.

[0105] 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 small-sample fault diagnosis method based on a noisy elastic element learning framework, characterized in that: Includes the following steps: S1: Collect vibration signals from an industrial robot, divide them into a source domain and a target domain. The source domain contains no noise, while the target domain contains noise of varying degrees. Construct support sets and query sets respectively, and generate the tasks required for meta-training and meta-testing. S2: The original input signal is mapped into low-dimensional embedded features through a feature extractor; S3: Perform singular value decomposition on the feature matrix of support samples for each category, adaptively determine the subspace dimension based on the cumulative energy ratio threshold, and select the dominant left singular vector to form the prototype of the energy threshold subspace. S4: Quantify the noise level and structural complexity of the current meta-task using the projected residual and the average prototype dimension, and calculate the task adaptive damping factor via the learnable base scale and the Softplus function. S5: After embedding and normalizing the query samples, construct a one-dimensional subspace and its projection matrix. Calculate the noise-perceived damping distance between the query samples and various prototypes using the damping factor, and output the classification probability via Softmax. S6: Construct the total loss by combining cross-entropy loss with ratio-based structural loss that combines intra-class compactness and inter-class separation, and update the model parameters through backpropagation; S7: Freeze model parameters during the meta-testing phase, quickly build prototypes for new tasks and adaptively calculate damping factors, and classify based on noise-perceived damping distance to diagnose the health status of noisy samples in the target domain.

2. The small-sample fault diagnosis method based on the noise elastic element learning framework according to claim 1, characterized in that: Step S2, which involves mapping the original input signal into low-dimensional embedded features using a feature extractor, includes: for the original input signal x Feature extractor Map it to d Dimensional embedding space: For supporting specific fault categories n ,use K Construct a feature matrix from the embedded features: in This indicates the specific supporting sample features.

3. The small-sample fault diagnosis method based on the noise elastic element learning framework according to claim 1, characterized in that: Step S3 specifically includes the following steps: right Perform singular value decomposition: in Describes a left singular vector matrix. Represents a singular value matrix. Describes a right singular vector matrix. The column composition A set of orthonormal bases for the column space of ; Determining the subspace dimension using an energy threshold. ,forward p The cumulative energy ratio of each component is: in Indicates the first j One portion, Indicates the first i Embedded features, K Indicates that the support is concentrated. K One sample, Indicates the first j The energy in each direction, i.e., the square of the singular value, is similarly... express i Energy in one direction; Given an energy threshold , The smallest integer that satisfies the following conditions: category n The energy threshold subspace prototype is obtained by taking the front. Constructing by using left singular vectors and forming a projection matrix: in Indicates category n The prototype of the energy threshold subspace. This indicates taking the left singular vector matrix. The former List, This represents the projection matrix corresponding to the prototype.

4. The small-sample fault diagnosis method based on the noise elastic element learning framework according to claim 1, characterized in that: Step S4 specifically includes: For a single query sample feature Its corresponding query subspace With projection matrix The structure is as follows: in Representing Grassmanifold The one-dimensional subspace on, i.e. d The set of undirected axes passing through the origin in the dimensional embedding space; Indicates projection mapping; The estimated noise level within the current meta-task is quantified by the projected residuals: in This indicates the estimated noise level within the current meta-task. Indicates the number of categories. Represents the Frobenius norm; make The average prototype dimension; Task adaptive damping factor The calculation is as follows: in This is the Softplus activation function, used to ensure a positive value; For scaling parameters, including Learnable parameters are randomly initialized and shared across tasks.

5. The small-sample fault diagnosis method based on the noise elastic element learning framework according to claim 1, characterized in that: In step S5, the prototype With query subspace The noise sensing damping distance between them is: in To query subspace The corresponding projection matrix.

6. The small-sample fault diagnosis method based on the noisy elastic element learning framework according to claim 1, characterized in that: The step S5, which involves outputting the classification probability via Softmax, specifically includes: for cases containing... K Categories in the query set of each sample n The i Query sample Its corresponding subspace is This sample belongs to category n The probability is obtained by using the softmax function on negative NADD: 。 7. The small-sample fault diagnosis method based on the noisy elastic element learning framework according to claim 1, characterized in that: Step S6, which involves constructing the total loss by combining cross-entropy loss with a ratio-based structural loss that balances intra-class compactness and inter-class separation, includes: The classification loss is the standard cross-entropy: in For the first i One-hot encoding of the real labels of each query sample; Intra-class compaction loss will help pull samples toward their prototype: Inter-class separation loss pushes different prototypes apart: The ratio-based structural loss is: in It is a small positive number used to ensure numerical stability; The total loss is: in It is a hyperparameter that controls the degree of compromise.

8. The small-sample fault diagnosis method based on the noise elastic element learning framework according to claim 1, characterized in that: During the meta-training phase, the feature extractor parameters and the original scaling parameters... By minimizing task distribution Joint optimization of expected loss on: During the meta-testing phase, the parameters are frozen; for each new task, an energy threshold subspace prototype is first constructed, and then the damping factor is calculated. The query and classification are then completed, and no further parameter updates are performed throughout the process.

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