Unbalanced small sample fault diagnosis method based on preference calibration meta-learning

Abstract

The application relates to an unbalanced small sample fault diagnosis method based on preference calibration meta learning, and belongs to the technical field of fault diagnosis. The method comprises the following steps: obtaining mechanical equipment operation data and dividing the operation data into source domain samples and target domain samples; a fault diagnosis model is constructed based on meta learning, and the model comprises a multi-scale attention enhanced feature extractor and a Stiefel linear layer connected in sequence; in the model training stage, meta tasks are generated based on a source domain support set and a query set, and a double-layer optimization mechanism adopting an integrated preference calibration Riemann optimization strategy is used to update model parameters; in the parameter updating process, a dynamic class weighting matrix is updated through an adaptive preference updating mechanism, so that the focus of the model is shifted to learning insufficient classes, and effective learning of the model on all fault classes is ensured; in the model testing stage, the model is tested based on meta tasks generated based on a target domain support set and a query set. The application can improve the accuracy of mechanical equipment fault diagnosis.

Description

Technical Field

[0001] This invention belongs to the field of fault diagnosis technology and relates to an imbalanced small sample fault diagnosis method based on preference calibration meta-learning. Background Technology

[0002] Ensuring the safe and reliable operation of machinery and equipment is a fundamental prerequisite for achieving high-quality industrial production. During high-intensity, long-cycle operation, key components are prone to various failures, leading to frequent maintenance, economic losses, and frequent safety accidents. With the increasing complexity and intelligence of modern mechanical systems, the importance of timely and accurate fault diagnosis is becoming increasingly prominent. By correlating monitoring data with the health status of machinery, fault diagnosis can effectively detect potential faults and minimize unplanned downtime. In recent years, data-driven methods, especially deep learning technology, have achieved significant success in the field of intelligent fault diagnosis. However, their effectiveness heavily relies on the assumption of a large amount of labeled data and balanced class distribution. In real-world industrial scenarios, due to low failure rates or limitations imposed by protection mechanisms, certain fault samples are difficult to obtain, resulting in extreme data scarcity. Furthermore, the sample size may differ by orders of magnitude between normal and fault states, and between different fault types. Such small samples and imbalanced datasets (S&I) pose a severe challenge to traditional data-driven models, often leading to overfitting, biased learning, and weakened generalization ability.

[0003] To address this challenge, numerous studies have emerged, broadly categorized into data-level and algorithm-level approaches. At the data level, Liu et al. proposed a feature-reconstruction-based data augmentation method, reconstructing a balanced dataset by upsampling minority class samples and downsampling majority class samples. Ye et al. developed a feature-fusion deep convolutional generative adversarial network architecture to generate high-quality pseudo-samples for rare fault types. Shang et al. constructed a physical information autoencoder based on digital twins, achieving interpretable data augmentation under S&I conditions. However, generating diverse and high-quality minority class samples in extremely small sample scenarios remains challenging. Furthermore, these methods often require the construction of complex generative models, significantly increasing system complexity and computational cost. At the algorithm level, Wang et al. proposed a semi-supervised diagnostic method based on stacked capsule autoencoders to address the challenges of data scarcity and class imbalance. Dong et al. constructed a cost-sensitive ensemble learning framework to deeply mine potential diagnostic knowledge in S&I data. Xu et al. developed an adaptive sample-level nonlinear reweighting method, effectively mitigating the learning deficiencies under imbalanced information by prioritizing key sample learning.

[0004] Meta-learning-based methods have demonstrated outstanding performance, exhibiting significant advantages in rapid learning and adaptability. Li et al. proposed a boundary-reinforcement meta-learning classification framework based on the Bayesian imbalance influence index. Wen et al. developed a retrospective prototype network to achieve high-precision diagnosis with limited information. However, traditional meta-learning algorithms tend to neglect intrinsic geometric information when optimizing in high-dimensional Euclidean parameter spaces, leading to slow convergence or even getting trapped in local suboptimal solutions, which is particularly evident when samples are scarce and distributions are imbalanced. To address this, some researchers have introduced Riemannian geometric constraints into meta-learning frameworks to ensure the stability and efficiency of the optimization process.

[0005] While existing research has shown potential in solving the S&I problem, it still has the following limitations: 1) Meta-learning algorithms lack class preference awareness during the optimization process, leading to the acquisition of biased meta-knowledge. Most optimization-based meta-learning paradigms aim to achieve rapid cross-task adaptation by learning the globally optimal initialization through a small number of samples. In diagnostic scenarios with class imbalance, this process is easily dominated by the majority class (such as the normal state), suppressing the limited fault information of the minority class and exacerbating the difficulty of acquiring effective and reliable meta-knowledge. 2) Although existing Riemannian geometric constraint frameworks can ensure stable optimization of the parameter space, they do not explicitly calibrate the priority learning of minority class discriminative features. This results in bias in the model's internal feature representation under S&I data, weakening its sensitivity to key rare fault patterns. 3) The meta-learning process lacks a direct and adaptive mechanism for adjusting class importance. As the learning process progresses, the model's mastery of different classes changes dynamically, and fixed preferences cannot autonomously shift the focus, which may lead to a decline in generalization performance as training progresses. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide an imbalanced small sample fault diagnosis method based on preference-calibrated meta-learning (PCML) to solve the problems existing in the prior art and meet the actual needs of real-world scenarios.

[0007] To achieve the above objectives, the present invention provides the following technical solution: An imbalanced small-sample fault diagnosis method based on preference calibration meta-learning, comprising: Acquire mechanical equipment operation data and divide it into source domain samples and target domain samples. Divide support sets and query sets on both source domain samples and target domain samples to generate meta-tasks for training and testing phases. A fault diagnosis model is constructed based on meta-learning. The model includes a multi-scale attention-enhanced feature extractor and a Steifel linear layer connected in sequence. The feature extractor is used to extract features from the input samples. The Steifel linear layer obtains the probability of the fault category to which the sample belongs based on the extracted features and converts the probability value into the fault category output. During the model training phase, the model parameters are updated using a two-layer optimization mechanism based on the meta-task generated from the source domain support set and query set and the integrated preference calibration Riemann optimization strategy. During the parameter update process, the dynamic class weighting matrix is ​​updated through an adaptive preference update mechanism, so that the model focuses on the under-learned categories and ensures that the model learns effectively on all fault categories. During the model testing phase, the model is tested based on meta-tasks generated from the target domain support set and query set.

[0008] Furthermore, the feature extractor includes a convolutional module, an Inception module, and a channel attention module connected in sequence; the convolutional module extracts hierarchical representations from the input data; the Inception module uses parallel convolutional branches with different kernel sizes to capture multi-scale fault features; the channel attention module dynamically learns the importance of each channel, amplifying information-rich features and suppressing features with low relevance.

[0009] Furthermore, the two-layer optimization mechanism includes: in the inner loop, multiple gradient updates are performed for a specific meta-task to update the task-specific parameters of the model for that meta-task; when each gradient parameter is updated, the updated parameters are mapped back to the Steifel manifold through the preference-aware symmetric perturbation shrinkage function built into the preference calibration Riemann optimization strategy; in the outer loop, meta-updates of the model parameters are performed by aggregating the gradients computed across all selected meta-tasks.

[0010] The beneficial effects of this invention are as follows: (1) This invention proposes a Preference-calibrated Riemannian optimization (PCRO) strategy in the Steifel manifold space to mitigate meta-knowledge learning bias by fusing category preferences. Specifically, a Preference-aware symmetry-perturbed retraction (PAPR) function is designed to guide the optimization trajectory in the manifold space through calibrated perturbations. This ensures the balance of meta-updates and enhances the learning of discriminative features for a few fault classes, fully exploiting the information value of S&I data.

[0011] (2) This invention proposes an adaptive preference update mechanism (APUM), which dynamically adjusts the class weight matrix based on the real-time performance of the model, shifts the learning focus to the under-learned class, and improves the generalization ability and training stability.

[0012] (3) This invention integrates PCRO, APUM, and a feature extractor to construct a novel fault diagnosis framework, PCML. Comparative experiments on bearing and robot reducer datasets show that the PCML proposed in this invention significantly outperforms existing diagnostic methods in all evaluation metrics.

[0013] 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

[0014] 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 schematic flowchart of an imbalanced small sample fault diagnosis method based on preference calibration meta-learning, provided in an embodiment of the present invention. Detailed Implementation

[0015] 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.

[0016] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0017] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0018] like Figure 1 As shown, an embodiment of the present invention provides an imbalanced small-sample fault diagnosis method based on preference calibration meta-learning, which is described as follows: 1. Divide the samples using vibration monitoring signals from the dataset.

[0019] Second, divide the source domain into support sets and query sets to generate the meta-task set used in the training phase, and at the same time divide the target domain into support sets and query sets to generate the meta-task set used in the testing phase.

[0020] 3. Use the designed feature extractor to extract features from the input samples.

[0021] In this embodiment, a multi-scale attention-enhanced extractor (MSAEE) is designed, whose architecture includes a convolutional module, an Inception module, and a channel attention module.

[0022] The MSAEE processing procedure is as follows: First, the input vibration signal is fed into three consecutive convolutional blocks to extract hierarchical representations from the raw data. Then, an Inception module is employed, which utilizes parallel convolutional branches with different kernel sizes to capture multi-scale fault features. However, the standard Inception architecture treats all feature channels equally during the fusion process, ignoring the varying importance of different feature channels for fault diagnosis. To address this limitation, this embodiment introduces a channel attention module to adaptively recalibrate the channel-level feature responses. This channel attention module is placed after the Inception module and dynamically learns the importance of each channel, thereby amplifying information-rich features and suppressing less relevant features.

[0023] The multi-scale attention-enhanced extractor combines a hybrid architecture of multi-scale feature extraction and attention-guided recalibration, enhancing the model's discriminative feature extraction capability on imbalanced data with small samples.

[0024] IV. Train the model.

[0025] 1. The extracted features are used to obtain classification results through a Steifel manifold linear layer.

[0026] The classification probabilities are transformed using the softmax function:

[0027] For the sample x exist N Predicted probability distributions for each category For category c The score output.

[0028] 2. Calculate the loss based on the classification results and update the dynamic class weighting matrix.

[0029] In this embodiment, the classification error is evaluated by calculating the cross-entropy loss based on the classification result. The cross-entropy loss is calculated as follows:

[0030] In the formula, Samples under one-hot encoding The true label, K This represents the number of samples in a few-sample task. During training, the model parameters are updated with the goal of minimizing the classification error.

[0031] In this embodiment, the dynamic class-weighted matrix is ​​updated using an adaptive preference update mechanism (APUM). APUM dynamically calibrates class importance based on real-time performance metrics. The update process is as follows: The initial category weights are calculated as follows:

[0032] in, Indicates the category in the first training round c The initial weights, and They represent the training datasets respectively. Belongs to the category c and n The number of samples, As a sample, Assign labels to the samples. By assigning higher initial weights to the minority class, we ensure that all classes contribute more evenly in early gradient updates, thus preventing the model from overfitting to the dominant class prematurely.

[0033] Subsequently, the initial class weights are normalized to obtain the standard weights:

[0034] Then, the dynamic class weighting matrix is ​​weighted using standard weights. Initialize as a diagonal matrix:

[0035] During training, APUM quantifies diagnostic capability gaps using query set metrics. Indicates the first t Category in each training cycle c The average accuracy, and Representing categories c True positive count and category j Misclassified as a category c The number of false positives. The global average accuracy is given by the following formula:

[0036] in, This indicates the number of query samples for each category.

[0037] The difference in calculation accuracy is: , For accuracy gap. This accuracy gap metric captures the category c The extent to which it lags behind average performance.

[0038] In addition, to account for inter-class confusion, this embodiment sets a boundary encroachment index:

[0039] The boundary encroachment index reflects the impact of other categories on the category. c The pressure of misclassification applied.

[0040] So, the first t+ The class weights in the first iteration are based on the... t The class weights are updated as follows in the next iteration:

[0041] The updated weights are then normalized:

[0042] Finally, the t+ The dynamic class weight matrix is ​​updated in one iteration as follows:

[0043] The adaptive preference update mechanism operates by continuously adjusting the class weight matrix based on real-time model performance. This design ensures that the model's focus gradually shifts to under-learned classes—those with significant accuracy gaps or large boundary encroachments. Simultaneously, the adaptive preference update mechanism prevents overfitting of the diagnostic model and stabilizes the training process, ensuring effective learning across all fault classes. Its self-calibration properties remain consistent with the evolving learning dynamics, ultimately enhancing robustness to performance degradation caused by imbalance and improving generalization ability for both common and rare fault classes.

[0044] 3. Use a preference-calibrated Riemann optimization strategy to update model parameters through backpropagation.

[0045] To achieve effective and reliable meta-knowledge acquisition on S&I data, this invention proposes a Preference-calibrated Riemannian optimization (PCRO) strategy running in the Steifel manifold space, which mitigates meta-knowledge learning bias by fusing category preferences.

[0046] Let the parameter space be subject to the Steifer manifold Constraints, mathematically defined as:

[0047] in, V This refers to the Steifer descriptor. express 1-order matrix space, express An identity matrix of order n. Therefore, Satisfying the orthogonality condition of 1-th order matrix V Composition. A Steifel manifold can also be equivalently represented as a quotient space:

[0048] in This represents an orthogonal group.

[0049] Reconstructing the orthogonally constrained optimization problem in Euclidean space into an unconstrained optimization problem on a Steifel manifold, the inherent advantage of choosing the Steifel manifold lies in its orthogonality constraints, which promote feature decoupling and stabilize gradient flow in the meta-learning process. Ignoring such geometric constraints can lead to slower optimization or convergence to a suboptimal solution, especially when the data is limited and imbalanced.

[0050] manifold The dimension is This significantly reduces the number of parameters compared to a standard linear layer. For example, a layer with a size of [missing information] After replacing the linear layer with a Steifel-constrained linear layer, the number of parameters decreased from approximately 4.2 million to less than 3.7 million. This characteristic offers a significant advantage when processing finite unbalanced fault data.

[0051] manifold at point V tangent space Defined as:

[0052] in It is the tangent vector.

[0053] Riemannian metric It is given by the following formula:

[0054] , All are tangent vectors. For a smooth scalar field on a manifold. Its Riemann gradient Defined as the unique tangent space element that satisfies the following equation:

[0055] in Represents a scalar field exist V The directional derivative at that point.

[0056] Arbitrary matrix Towards The projection mapping can be represented as:

[0057] The Riemann gradient can be obtained by projecting the Euclidean gradient onto the tangent space using the above equation:

[0058] in Represents mathematical operators.

[0059] The linear layers at the end of the model employ Steiffel manifold constraints. This is achieved using Steiffel descriptors. V For the model parameters, during the initial training phase, the linear layers undergo orthogonal initialization to ensure that the Steifel descriptors used as model parameters lie on the manifold. Parameters The update process proceeds along the manifold curve, in the direction of... , and They represent the first t Steifer descriptors and learning rates for each training epoch. The updated result needs to be mapped back to the manifold using the Preference-awaresymmetry-perturbed retraction (PAPR) function, preserving its manifold constraints. The expression is:

[0060] in A dynamic category weighted matrix that reflects the current learning focus in real time; This is the learning rate.

[0061] PASPR ​​via the main descent direction Ensure the second-order calibration perturbation term is used along the fastest convergence path of the manifold. The design is based on dynamically adjusting the trajectory curvature. This symmetric interactive form is compatible with the Steifel manifold orthogonal constraint, maintaining geometric stability while directly enhancing minority class feature representation through geometric recalibration during feature learning. Model parameters are then updated via backpropagation.

[0062] The meta-learning framework integrating the PCRO strategy can be formulated as a two-layer optimization problem as follows:

[0063] in Indicates from task distribution Meta-loss of all selected tasks in the mid-sample Expectations For diagnostic models, For meta-task i query set, For meta-parameters, This corresponds to the loss.

[0064] Inner loop optimization targets specific meta-tasks:

[0065] In the formula, Passing through the inner ring j Task-specific parameters after each gradient step For meta-task i Support set, For the inner loop adaptive learning rate, For the corresponding diagnostic model, To correspond to the loss, For mathematical operators. PASPR ​​ensures that the updated parameters remain on the Steifel manifold after each gradient step.

[0066] The outer loop optimizes the gradient aggregation update in the Riemann space:

[0067] In the formula For iteration t+ Meta-parameters at time 1 For meta-task i query set, For the outer loop learning rate, These are mathematical operators.

[0068] Outer loop optimization performs optimization by aggregating gradients computed across all selected meta-tasks. The meta-update is performed. For each meta-task, the Euclidean gradient is derived through the inner loop optimization trajectory and then projected onto the current meta-parameters. In the tangent space, a shrinking mapping is then applied to obtain new meta-parameters while preserving manifold constraints.

[0069] In summary, the preference-calibrated Riemannian optimization framework systematically combines the geometric constraints of the Steifel manifold with category-aware calibration through a preference-aware symmetric perturbation contraction mapping. By reformulating the optimization problem on the Riemannian manifold and embedding real-time category preferences into the contraction mechanism, preference-calibrated Riemannian optimization ensures geometric stability and adaptive bias mitigation during the meta-learning process. This method not only reduces the parameter dimensionality and enhances discriminative feature learning, but also fundamentally solves the problems of meta-knowledge acquisition bias and insufficient optimization performance in small-sample imbalanced fault diagnosis scenarios.

[0070] Fifth, by using a trained PCML model, quickly adapt to the meta-tasks of the target domain and diagnose the health status of samples in the target domain.

[0071] Based on the proposed imbalanced small sample fault diagnosis method, this embodiment uses two different datasets to comprehensively evaluate the proposed method.

[0072] One of the datasets is the Jiangnan University (JNU) dataset. This publicly available dataset contains vibration signals under four operating conditions: normal condition (NC), inner race fault (IF), ball fault (BF), and outer race fault (OF). The sampling frequency is 50 kHz, and the data is acquired at a constant speed of 1000 rpm. During the measurement process, the load is randomly varied under manual control.

[0073] Another dataset is the Industrial Robot Fault (IRF) dataset. Data was collected from a BRTIRUS1510A six-DOF industrial robot equipped with a high-sensitivity PCB accelerometer. Given the high torque on the second bearing and the significant cyclic stress on the reduction gear, monitoring focused on the RV40E-121 reducer mounted on this critical axis. This dataset covers five health conditions: Normal condition (NC), Sun gear tooth pitting (SGTP), Sun gear tooth fracture (SGTF), Planetary gear tooth cracking (PGTC), and Planetary gear tooth fracture (PGTF). Data was collected at a speed of 2400 rpm and a load of 9.6 kg.

[0074] Twelve fault diagnosis tasks were constructed on the JNU and IRF datasets. These tasks were specifically designed to simulate real-world industrial scenarios, where normal state data dominates while fault samples are extremely limited, reflecting the data scarcity and class imbalance problems commonly found in practical fault diagnosis applications. Each task is characterized by severe data scarcity and uses either a 2-fold or 5-fold run setting. Furthermore, the tasks exhibit a highly imbalanced distribution, with imbalance ratios (defined as the ratio of minority class samples to majority class samples) as low as 0.005 or 0.01. Simultaneously, the tasks contain different imbalance patterns; the difference in sample size between the minority class leads to diverse skewed distributions within each task. Specific settings are shown in Tables 1 and 2, including the number of training samples used for each class and the K-fold run settings corresponding to each experimental scenario.

[0075] Table 1 Task configuration for the JNU dataset

[0076] Table 2 Task Configuration for IRF Datasets

[0077] To verify the effectiveness of the proposed framework, this embodiment conducts a comprehensive comparison with six existing diagnostic methods on S&I data, including Relation Net (RelaNet), Prototype Network (ProtoNet), Model-agnostic Meta-learning (MAML), General Model-agnostic Meta-learning (GMAML), Adaptive Generic Prototype Network (AGPN), and Multi-source Information Fusion Transformer (MSIFT). Each vibration signal sample contains 1024 data points, and 200 samples are used to test each health state. Each experiment is run independently five times to ensure reliability, and the mean accuracy and standard deviation (SD) are recorded.

[0078] The experimental results are summarized in Tables 3 and 4, which show the diagnostic accuracy and standard deviation (SD) for all 12 tasks on the JNU and IRF datasets, respectively. The results clearly demonstrate that, in various S&I scenarios, the PCML model proposed in this embodiment achieves superior and consistent performance compared to all baseline methods.

[0079] Table 3 Experimental results for six tasks on the JNU dataset

[0080] Table 4 Experimental results for six tasks on the IRF dataset

[0081] As shown in Table 3, on the JNU dataset (tasks T1–T6), PCML achieves an average accuracy of 97.59%, significantly outperforming the second-best method, AGPN (leading by 6.84%). Notably, in the five tasks (T1–T3) with an imbalance ratio of 0.01, PCML's diagnostic accuracy consistently exceeds 99%, reaching a peak of 99.23% in task T3. This represents a significant improvement over the current best method (AGPN at only 94.92% on the same task). In the two more challenging scenarios (T4–T6, imbalance ratio 0.005), PCML's performance advantage is even more pronounced, with accuracy ranging from 95.89% to 96.16%. In contrast, the performance of the comparison methods drops sharply under these extreme data-scarce conditions. For example, MAML drops to 61.25% on T4, and even the comparison method AGPN only reaches 84.35%, a performance gap of 11.54% compared to PCML. Furthermore, the standard deviation of PCML (0.35%–2.29%) was significantly lower than that of the comparative method, indicating that it has superior stability and reliability in multiple runs. IRF dataset (tasks T7–T) 12 The more complex failure modes present a more challenging diagnostic problem. Despite this, PCML still demonstrates superior performance, achieving an average accuracy of 95.21%, outperforming AGPN by 8.31%, as shown in Table 4. In five tasks (T7–T9), PCML's accuracies were 98.52%, 97.75%, and 94.39%, respectively, representing improvements of 12.58%, 6.72%, and 6.46% compared to the suboptimal method. In two tasks where fault data was extremely scarce (T... 10 –T 12 In the IRF dataset, the performance advantage is further expanded. It is particularly noteworthy that traditional meta-learning methods such as MAML and ProtoNet show a significant performance drop on the IRF dataset, with average accuracies falling to 53.18% and 62.33%, respectively, highlighting the inherent difficulty of these industrial scenarios.

[0082] As shown in Tables 3 and 4, the imbalanced small-sample fault diagnosis method proposed in this embodiment effectively mitigates meta-knowledge bias by directly incorporating class preferences into the manifold optimization process through the PCRO strategy, ensuring balanced meta-updates across all classes. Its built-in PASPR ​​function guides the optimization trajectory by applying calibration perturbations on the Steifel manifold, promoting the learning of discriminative features for a few fault classes. Simultaneously, by constraining the parameter space to the Riemannian manifold, PCRO reduces optimization difficulty and enhances the ability to learn from scarce training data. Furthermore, the APUM mechanism dynamically adjusts class importance based on real-time model performance, enabling the framework to autonomously shift its learning focus to under-learned classes, thereby improving generalization ability. The synergistic integration of these components allows the PCML model to fully utilize limited fault information while maintaining robustness under severe class imbalance conditions, ultimately establishing a new framework for fault diagnosis of S&I data.

[0083] Furthermore, to evaluate the contributions of the PCRO strategy, APUM mechanism, and feature extractor (MSAEE), and to verify the effectiveness of the proposed method in addressing small sample sizes and class imbalance challenges, this embodiment also conducted systematic ablation experiments on the T1 task. Table 5 shows the experimental results for six configurations.

[0084] Table 5

[0085] As shown in Table 5, the complete model achieved a diagnostic accuracy of 99.05 ± 0.58%, demonstrating excellent performance with a very small standard deviation. This result validates the effectiveness of the collaborative work among all components of the model. Furthermore, the continuous decrease in standard deviation across ablation variants indicates that the complete framework not only provides higher accuracy but also enhances stability and reliability.

[0086] Removing MSAEE resulted in a drop in accuracy to 94.64%, highlighting its crucial role in learning robust representations from limited and skewed data. Removing APUM reduced accuracy to 95.82%, indicating that static class importance (not updated after initialization) failed to adaptively refocus the learning emphasis on the few poorly learned faults during training, thus impacting model performance.

[0087] When other optimization strategies are replaced with the PCRO strategy, the performance degradation is more significant. When the PCRO strategy is replaced with other optimization strategies, i.e., when PCRO is ablated, APUM is also removed from the model along with PCRO. Using the Cayley transform as a shrinking mapping on the Steifel manifold leads to unstable and biased optimization (91.86% accuracy), while traditional Euclidean updates cause severe performance collapse (85.46% accuracy). This stark contrast shows that PCRO is not only a manifold constraint but also a key bias mitigation mechanism. Its PASPR ​​function explicitly calibrates the optimization trajectory by injecting preference-aware perturbations, ensuring balanced meta-updates and enhancing the learning of discriminative features for minority classes, thus solving the bias problem of meta-knowledge acquisition under class imbalance. Finally, replacing the entire PCML framework with the traditional MAML baseline yields the lowest accuracy (68.99%). Due to the lack of a clear mechanism to offset the influence of class bias, MAML's meta-knowledge is dominated by the majority class, leading to the marginalization of rare failure modes.

[0088] In summary, this invention provides an imbalanced small-sample fault diagnosis method based on preference calibration meta-learning. Based on preference calibration Riemann optimization, an adaptive preference update mechanism, and a feature extractor, a comprehensive fault diagnosis framework for imbalanced small-sample data is constructed, namely preference calibration meta-learning. This framework integrates manifold geometric constraints and category preference calibration, effectively solving the problems of meta-knowledge acquisition bias and insufficient optimization efficiency in S&I scenarios, and significantly improving the model diagnostic performance in practical industrial scenarios.

[0089] 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 method for diagnosing imbalanced small-sample faults based on preference calibration meta-learning, characterized in that, The method includes: Acquire mechanical equipment operation data and divide it into source domain samples and target domain samples. Divide support sets and query sets on both source domain samples and target domain samples to generate meta-tasks for training and testing phases. A fault diagnosis model is constructed based on meta-learning. The model includes a multi-scale attention-enhanced feature extractor and a Steifel linear layer connected in sequence. The feature extractor is used to extract features from the input samples. The Steifel linear layer obtains the probability of the fault category to which the sample belongs based on the extracted features and converts the probability value into the fault category output. During the model training phase, the model parameters are updated using a two-layer optimization mechanism based on the meta-task generated from the source domain support set and query set and the integrated preference calibration Riemann optimization strategy. During the parameter update process, the dynamic class weighting matrix is ​​updated through an adaptive preference update mechanism, so that the model focuses on the under-learned categories and ensures that the model learns effectively on all fault categories. During the model testing phase, the model is tested based on meta-tasks generated from the target domain support set and query set.

2. The method according to claim 1, characterized in that, The feature extractor consists of a convolutional module, an Inception module, and a channel attention module connected in sequence. The convolutional module extracts hierarchical representations from the input data. The Inception module uses parallel convolutional branches with different kernel sizes to capture multi-scale fault features. The channel attention module dynamically learns the importance of each channel, amplifying information-rich features and suppressing features with low relevance.

3. The method according to claim 1, characterized in that, The two-layer optimization mechanism includes: in the inner loop, multiple gradient updates are performed for a specific meta-task to update the task-specific parameters of the model for that meta-task; when each gradient parameter is updated, the updated parameters are mapped back to the Steifel manifold through the preference-aware symmetric perturbation shrinkage function built into the preference calibration Riemann optimization strategy; in the outer loop, meta-updates of the model parameters are performed by aggregating the gradients computed across all selected meta-tasks.

4. The method according to claim 3, characterized in that, The preference-perceived symmetric perturbation shrinkage function is expressed as: In the formula, A dynamic category weighted matrix that reflects the current learning focus in real time; V For Steifer descriptor; The learning rate; The Riemann gradient; Represents a scalar field exist V Directional derivative at point; Represents any Matrix of order Z Tangential space The projection mapping, where the tangent space For Steifer manifold in V The tangent space at the point, , It is the tangent vector; During training, the Steifer descriptor is used. The linear layer parameters of the model are constrained by the Steifel manifold; in the inner loop, for a specific meta-task, the parameters are processed... j The task-specific parameters after each gradient step are: The updated parameters are obtained through a preference-aware symmetric perturbation shrinkage function. The mapping is shrunk back onto the Steifel manifold, as shown below: In the formula, Passing through the inner ring j Task-specific parameters after each gradient step For meta-task i Support set, The inner loop adaptive learning rate; For the corresponding diagnostic model; For the corresponding loss; Mathematical operators; In the outer loop, a meta-update of the model parameters is performed by aggregating gradients computed across all selected meta-tasks, and the updated meta-parameters are then mapped back to the Steifel manifold using a preference-aware symmetric perturbation shrinkage function, as shown below: In the formula, For iteration t+ The model meta-parameters at time 1. For meta-task i query set, The outer loop learning rate; Indicates from task distribution Meta-loss of all selected tasks in the mid-sample Expectations; For the corresponding diagnostic model; These are mathematical operators.

5. The method according to claim 4, characterized in that, The model parameters are updated through backpropagation during training.

6. The method according to claim 4, characterized in that, The dynamic class-weighted matrix is ​​updated using an adaptive preference update mechanism. The update process includes: Initialize class weights: In the formula, Indicates the category in the first training round c The initial weights, and They represent the training datasets respectively. Belongs to the category c and n The number of samples, N The number of classes; by assigning higher initial weights to minority classes, we ensure that all classes contribute more evenly in early gradient updates, preventing the model from overfitting to the dominant class too early; Normalize the initial class weights to obtain the standard weights: The dynamic class weighting matrix is ​​calculated using standard weights. Initialize as a diagonal matrix: By quantifying diagnostic capability gaps through query set indicators, Indicates the first t Category in each training cycle c The average accuracy, and Representing categories c True positive count and category j Misclassified as a category c The number of false positives; the global average accuracy is calculated as follows: In the formula, This indicates the number of query samples for each category; The difference in calculation accuracy is: This precision gap metric captures the category c The degree to which it lags behind average performance; To address inter-class obfuscation, set a boundary encroachment metric: The boundary encroachment index reflects the impact of other categories on the category. c The pressure of misclassification applied; Then the first t+ The class weights in the first iteration are based on the... t The class weights are updated as follows in the next iteration: Normalize the updated weights: Finally, the t+ The dynamic class weighted matrix is ​​updated in one iteration as follows: .

7. The method according to claim 1, characterized in that, The model training process aims to minimize the classification error, which is represented by the cross-entropy loss function. In the formula, Samples under one-hot encoding The true label, K This refers to the number of samples in a small sample task. For the sample x exist N Predicted probability distributions for each category For category c The score output, N This represents the number of categories.

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