Rotating machine fault diagnosis method and system based on Gaussian boundary constraint network

Abstract

The invention discloses a rotating machine fault diagnosis method and system based on a Gaussian boundary constraint network, and relates to the technical field of fault diagnosis, and the method comprises the steps: obtaining vibration signal data of a rotating machine under a single source domain working condition, and forming a marked source domain training set; training the Gaussian boundary constraint network based on the source domain training set to obtain a trained Gaussian boundary constraint network; the Gaussian boundary constraint network comprises a feature extractor, a feature decoupling module, a Gaussian boundary constraint module and a known category prediction head, the Gaussian boundary constraint module comprises a Gaussian classifier, and the Gaussian classifier trains an input first feature through negative logarithm likelihood loss and confidence perception boundary loss; and acquiring vibration signal data of the rotating machine, inputting the vibration signal data into the trained Gaussian constraint network for fault diagnosis, and outputting a fault diagnosis result. The method can deal with various label inconsistent scenes, and realizes accurate identification of shared categories and robust rejection of unknown categories.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fault diagnosis, and in particular to a rotating machinery fault diagnosis method and system based on a Gaussian boundary constraint network. BACKGROUND

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute the prior art.

[0003] Rotating machinery is a key component in mechanical systems and is widely used in the core transmission link of modern industry. Its running state is directly related to production efficiency. However, when the equipment is running in a complex, variable and harsh working environment for a long time, it is prone to failure, which seriously interferes with the normal production process and even causes huge economic losses and safety hazards. Therefore, the development of an efficient fault diagnosis system is of great significance to improve system reliability and reduce maintenance costs.

[0004] With the acceleration of industrial informatization, a large amount of data is generated during the operation of mechanical equipment, which provides new development opportunities for data-driven fault diagnosis methods. Among many methods, deep learning has become a research hotspot because it does not need to rely on prior physical models and can automatically learn effective features. At present, various deep network architectures such as convolutional neural network (CNN), recurrent neural network (RNN) and Transformer have been successfully applied to fault diagnosis tasks. However, the effectiveness of these methods is usually based on two key assumptions: one is that there is a sufficient amount of training data, and the other is that there is a consistent data distribution between the training set and the test set. However, in practical applications, rotating machinery often faces changes in operating conditions such as different speeds and loads, which can cause significant distribution differences between vibration signals collected under different working conditions. In addition, it is costly and difficult to label all working condition data, and models trained based on single working condition data often experience a sharp decline in performance when transferred to unknown working conditions, which is known as domain shift.

[0005] To alleviate the influence of domain shift, researchers have proposed methods such as domain adaptation (DA) and domain generalization (DG). The goal of domain adaptation is to align the feature distributions between the labeled source domain and the unlabeled target domain, thereby improving the model's performance on the target domain. According to the relationship between the label spaces of the source and target domains, DA methods are generally divided into closed-set DA (CDA), partial-set DA (PDA), and open-set DA (ODA). Among them, CDA assumes that the source and target domains have the same label set, and there are various methods based on maximum mean discrepancy (MMD) and adversarial training that have been widely applied in the field of fault diagnosis. PDA assumes that the target domain only contains a subset of the source domain's label set, while ODA considers the presence of unknown classes in the target domain that are not present in the source domain. PDA focuses on avoiding aligning target samples to private classes in the source domain, while ODA aims to accurately identify shared class samples and uniformly determine unknown class samples as "unknown classes."

[0006] Although the above methods have achieved certain results in specific tasks, they generally rely on prior knowledge of the relationship between the label spaces of the source and target domains. In actual industrial scenarios, the label space of the target domain is often unknown, making it difficult to choose an appropriate adaptation strategy. In addition, current research has paid less attention to the more challenging open-partial-set DA (OPDA) problem. To address such problems, the concept of universal domain adaptation (UniDA) has been proposed. "Universal" reflects the possibility of the target domain containing both shared classes and private unknown classes. UniDA can handle various DA scenarios such as CDA, PDA, ODA, and OPDA, and its goal is to accurately identify shared class samples while effectively determining unknown classes. However, achieving efficient UniDA under the condition of complete unknown target domain still faces significant challenges.

[0007] In contrast, domain generalization (DG) aims to train a model using only multiple source domain data to achieve good generalization performance in unseen target domains. To further cope with more complex scenarios where the class space is completely uncertain, universal domain generalization (UniDG) is proposed. Currently, UniDG has taken shape in the field of computer vision, but its research in mechanical fault diagnosis is still relatively scarce. To fill this gap, the prior art proposes an adaptive intermediate class distribution alignment (AICDA) method that aligns source and target domain features using an intermediate distribution. The prior art also proposes a domain-private suppression meta-recognition network (DPSMR) that suppresses domain-specific noise through channel-level transferability estimation and strengthens domain-invariant feature learning; it also introduces a meta-recognition calibration mechanism to alleviate the overconfidence of the model when dealing with new classes, and combines a double-consistency loss to improve the stability of feature expression. However, both AICDA and DPSMR rely on multiple source domains or synthetic target domains, which makes them difficult to deploy in situations where only single source domain data is available. SUMMARY

[0008] To overcome the deficiencies of the prior art described above, the present application provides a rotating machinery fault diagnosis method and system based on a Gaussian boundary constraint network, proposes a single-source universal domain generalization method based on a Gaussian boundary constraint network, which can handle multiple label inconsistency scenarios and achieve accurate identification of shared classes and robust rejection of unknown classes.

[0009] To achieve the above-mentioned purpose, one or more embodiments of the present application provide the following technical solutions: In a first aspect, the present application provides a rotating machinery fault diagnosis method based on a Gaussian boundary constraint network, comprising: Obtaining vibration signal data of a rotating machinery under a single source domain working condition to form a labeled source domain training set; Training a Gaussian boundary constraint network based on the source domain training set to obtain a trained Gaussian boundary constraint network; the Gaussian boundary constraint network includes a feature extractor, a feature decoupling module, a Gaussian boundary constraint module, and a known class prediction head, the Gaussian boundary constraint module includes a Gaussian classifier, and the Gaussian classifier trains the input first feature through a negative log-likelihood loss and a confidence-aware boundary loss; Obtaining vibration signal data of a rotating machinery and inputting it into the trained Gaussian constraint network for fault diagnosis to output a fault diagnosis result.

[0010] Further technical solutions, the feature decoupling module receives the global features output by the feature extractor, adopts a gating mechanism to decompose the global features into first gating features and second gating features, respectively maps the first gating features and the second gating features through full connection layers to obtain first features and second features, inputs the first features into the Gaussian boundary constraint module, and inputs the second features into the known class prediction head.

[0011] Further technical solutions, when the Gaussian boundary constraint network is trained, covariance loss is adopted to constrain between the first features and the second features.

[0012] Further technical solutions, the negative log-likelihood loss encourages the first features to conform to a Gaussian distribution satisfying a constraint condition, and is expressed as:

[0013] Wherein, represents the i-th source domain sample, represents the i-th dimension of the feature represents the i-th dimension of the feature of the i-th source domain sample, represents a true label of the feature represents the i-th Gaussian distribution mean value belonging to the class

[0014] Further technical solutions, the confidence-aware boundary loss constrains the distribution range and position of the first features, and is expressed as:

[0015]

[0016]

[0017]

[0018] Wherein, represents an inner confidence boundary threshold value, represents the i-th sample normalized Mahalanobis distance, represents an outer confidence boundary threshold value, represents the i-th sample feature vector, represents the i-th sample feature vector, represents the i-th sample feature vector, represents the i-th sample feature vector, ​​​​​​​​​​​The category to which each sample belongs The mean vector, Indicates the first The category to which each sample belongs The standard deviation vector, The cumulative distribution function represents the standard normal distribution. The confidence coefficient represents the inner boundary. This represents the confidence coefficient for the outer boundary.

[0019] A further technical solution is that the total loss during training of the Gaussian boundary constraint network is:

[0020] in, , , Represents the weight coefficients of the loss function. This represents the training loss of the Gaussian classifier. Represents the binary cross-entropy. This represents the covariance loss.

[0021] A further technical solution is that the fault diagnosis process of the trained Gaussian constrained network is as follows: The vibration signal data of rotating machinery is initially classified using a known category prediction head to obtain candidate known categories; Based on the candidate known categories, obtain their corresponding Gaussian mean vector and standard deviation vector; The standardized distance is calculated using the first feature of the vibration signal data and the Gaussian mean vector and standard deviation vector of the candidate known categories. The standardized distance is compared with the confidence threshold. If the standardized distance is greater than the confidence threshold, the vibration signal data is determined to be of an unknown category. Otherwise, the predicted label output by the known category prediction head is used as the final classification result.

[0022] Secondly, the present invention provides a rotating machinery fault diagnosis system based on Gaussian boundary constraint networks, comprising: The training set construction module is configured to acquire vibration signal data of rotating machinery under a single source domain condition and form a labeled source domain training set. The model training module is configured to: train the Gaussian boundary constraint network based on the source domain training set to obtain a trained Gaussian boundary constraint network; the Gaussian boundary constraint network includes a feature extractor, a feature decoupling module, a Gaussian boundary constraint module, and a known class prediction head; the Gaussian boundary constraint module includes a Gaussian classifier, which is trained on the first input feature using negative log-likelihood loss and confidence-aware boundary loss; A model prediction module configured to: acquire vibration signal data of the rotating machinery, input the vibration signal data to the trained Gaussian constraint network for fault diagnosis, and output a fault diagnosis result.

[0023] In a third aspect, the present application provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the rotating machinery fault diagnosis method based on the Gaussian boundary constraint network according to the first aspect.

[0024] In a fourth aspect, the present application provides a computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the rotating machinery fault diagnosis method based on the Gaussian boundary constraint network according to the first aspect when executing the program.

[0025] The above one or more technical solutions have the following beneficial effects: The present application realizes unified and robust diagnostic capability for general domain generalization (UDG) scenarios, innovatively applies the Gaussian boundary constraint network to single-source-domain fault diagnosis, and effectively solves the generalization problem in various complex scenarios such as closed set (CDG), partial set (PDG), open set (ODG), and open-partial set (OPDG) in a unified framework through the unique structure design and loss function of the Gaussian boundary constraint network. The model does not need to know the scene type of the target domain in advance, and can automatically adapt and make reliable decisions, improving the practicality and universality.

[0026] The present application completes training based on only source domain labeled data without relying on target domain data and label priori, and provides a unified "known / unknown" judgment process in the inference stage, which is convenient for reproduction and deployment in actual monitoring systems.

[0027] The present application jointly uses negative log-likelihood (NLL) and confidence-aware boundary (CAB) loss in the Gaussian boundary constraint network (GBCN), jointly constrains to reduce overconfidence and misjudgment of unknown samples in the target domain, suppresses feature over-clustering and keeps cautious to out-of-bound samples, reduces the risk of misjudging unknown categories as known categories from the mechanism, and enables the Gaussian boundary constraint network to have high-confidence rejection ability when there are both shared and unknown categories.

[0028] The present application improves feature separation effect through gated feature decoupling and covariance-based statistical independent regularization, and solves the problem of insufficient class separability caused by deep feature semantic coupling.

[0029] The present application shapes the feature distribution under the condition of no target prior by means of Gaussian boundary constraint, unifies and is compatible with closed-set domain generalization (CDA), partial domain generalization (PDA), open-set domain adaptation (ODA) and open-partial domain generalization (OPDA) and the like scenes, realizes accurate identification of shared classes and robust rejection of unknown classes, and solves the generalization bottleneck when only single source is available and multi-source alignment cannot be used. BRIEF DESCRIPTION OF DRAWINGS

[0030] The accompanying drawings, which form a part of the present description, are included to provide a further understanding of the present application, and are incorporated in and constitute a part of this application. The embodiments of the present application, and their

[0031] Figure 1 is a structural diagram of a Gaussian boundary constraint network of an embodiment of the present application; Figure 2 is a confidence-aware boundary loss schematic diagram of a Gaussian boundary constraint module of an embodiment of the present application; Figure 3 is a graph of the influence of ACA and H-score in experiments of an embodiment of the present application; Figure 4 is a graph of average accuracy of CDG, PDG, ODG and OPDG tasks under different confidence intervals in an embodiment of the present application. DETAILED DESCRIPTION

[0032] It should be noted that the following detailed description is merely exemplary in nature and is intended to provide further description of the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0033] It is to be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments consistent with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, devices, components and / or combinations thereof, but do not preclude the presence or addition of one or more other features, steps, operations, devices, components and / or combinations thereof.

[0034] The embodiments in the present application and the features in the embodiments can be combined with each other without conflict. ​

[0035] Embodiment One As shown in the figure, the embodiment discloses a rotating machinery fault diagnosis method based on a Gaussian boundary constraint network, which comprises the following steps: Figure 1 S1: obtaining vibration signal data of the rotating machinery under a single source domain working condition to form a labeled source domain training set; In the embodiment, in the rotating machinery fault diagnosis, the universal domain generalization (UDG) aims to learn a model that can be generalized to an unseen domain under the condition that there is distribution migration and label inconsistency at the same time. Under the single-source universal domain generalization (SUDG) setting, the model is trained based on a single labeled source domain .

[0036] The present application faces the actual industrial scene of rotating machinery fault diagnosis, and the source domain dataset and the target domain sample are both derived from mechanical vibration signals. Specifically, the source domain dataset can include labeled vibration signal data collected under a certain working condition (for example, rotating speed 900 rpm, load 0 hp, room temperature environment), which can cover typical categories such as healthy state, outer ring fault, inner ring fault, rolling body fault and mixed fault. These data can be derived from a test bench, an industrial production line or a public rotating machinery fault diagnosis dataset (such as CWRU, PU, etc.), to ensure representativeness and verifiability. The target domain sample corresponds to the unlabeled vibration signal collected under the working condition different from the source domain (such as rotating speed 1500 rpm, load 1 hp, temperature 30℃), which can contain the signal of the existing categories of the source domain, and can also appear unknown fault categories that do not exist in the source domain. Through such design, the cross-domain generalization ability of the present application under complex working conditions can be embodied, and the actual needs of unknown category identification in industrial field can also be met.

[0037] The model is expected to be generalized to an unseen target domain , whose data comes from a different distribution than the source domain , i.e. , and has . The target domain can contain both shared categories and private categories with the source domain. Let and be the label sets of the source domain and the target domain, respectively, and the shared category set be defined as ; and and ​respectively represent the source domain private and target domain private class set. To quantify the overlap of the two, the Jaccard similarity coefficient (J) is introduced:

[0038] The lower the value, the greater the label difference, and the more difficult the model generalizes to the target domain.

[0039] UDG involves generalization in different class transfer scenarios, including closed-set domain generalization (CDG), partial-set domain generalization (PDG), open-set domain generalization (ODG), and open-partial-set domain generalization (OPDG). ; Partial-set domain generalization (PDG): ; Open-set domain generalization (ODG): ; Open-partial-set domain generalization (OPDG): , and .

[0040] The goal of SUDG is to train a model using a source domain so that it meets the following conditions during the inference phase: (1) Each sample from an unseen target domain is either correctly classified into a known class in the source domain label space or identified as an unknown class; (2) The model is robust to both domain distribution shift and label space shift without using any target domain data during training.

[0041] Vibration signal data of rotating machinery under single source domain working conditions is collected to form a labeled source domain training set, where each sample is labeled with a fault class label. The original vibration signal is preprocessed, including noise reduction, standardization and segmentation.

[0042] S2: Based on the source domain training set, the Gaussian boundary-constrained network is trained to obtain the trained Gaussian boundary-constrained network; In this embodiment, the goal of the Gaussian boundary-constrained network (Gaussian Boundary-Constrained Network, GBCN) is to achieve feature decoupling and optimize the decision boundary under the condition of unknown classes, so that the model can resist both domain migration and label distribution differences when deployed. As shown in Figure 1As shown, the Gaussian boundary constraint network includes a feature extractor, a feature decoupling module, a Gaussian boundary constraint module, and a known-class prediction head. The feature decoupling module separates the global features extracted by the feature extractor into two branches. One branch is input to the Gaussian boundary constraint module to model the Gaussian distribution and apply confidence boundary constraints, while the other branch is input to the known-class prediction head for regular classification of known classes. A covariance loss is applied between the two branches to reduce redundancy and ensure that the "Gaussian features" and "supplementary features" are independent. This retains the discriminative ability of the traditional classification head for known classes while utilizing the Gaussian boundary constraint module to achieve robust rejection of unknown classes.

[0043] The Gaussian boundary constraint module is trained using a joint loss, specifically consisting of Negative Log-Likelihood (NLL) loss and Confidence-Aware Boundary (CAB) loss. NLL aligns features with the class-conditional Gaussian distribution; CAB confines features within the confidence boundary region, preventing excessive clustering towards class centers and thus impairing generalization ability. Through this dual constraint of "distribution alignment + geometric boundary," the Gaussian classifier becomes more robust to domain and label space transfer.

[0044] (a) Feature decoupling module The feature decoupling module consists of a trainable gating mechanism and two independent branches. The feature extractor uses a convolutional neural network (CNN) to extract features, decomposing the global feature vector output by the CNN into two branches. Each branch is gated by a sigmoid activation mechanism, enabling the network to map features to different subspaces.

[0045] First, the global feature vector output by the feature extractor... The input is passed to a fully connected layer (in this embodiment, the number of nodes is 2, and the activation function is Sigmoid) to form a gating unit, resulting in two sets of gating coefficients. The first gating coefficient... With the second gating Subsequently, they respectively and and Element-wise multiplication yields the first gating feature after gating. With the second gating feature In other words, the global features are processed through two independent gating mechanisms, namely the first gating mechanism. With the second gating Scaling yields the first gating feature. With the second gating feature .Then, , The first feature is obtained by further mapping through a fully connected layer (in this embodiment, the number of nodes is 256 and the activation function is ReLU). With the second feature Finally, regarding and Covariance loss is introduced to constrain the statistical independence of the two branches, reduce redundancy, and enhance diversity.

[0046] To reduce redundancy between branches and improve representation diversity, and Covariance loss is used between them:

[0047] in, Indicates covariance loss. This represents the Frobenius norm (the square root of the sum of the squares of the elements of a matrix, used to measure the size of the matrix). This represents the covariance matrix (i.e., the covariance of two sets of features in each dimension, used to characterize the statistical correlation between features).

[0048] The network employs a sigmoid-based multi-branch binary classification strategy, where each output independently predicts the existence of its corresponding class, thus obtaining a more uncertainty-aware decision boundary. The classification loss is defined as the binary cross-entropy:

[0049] in, Represents the binary cross-entropy. Indicates the first The true labels of the source domain samples Indicates the first The predicted probability of a source domain sample.

[0050] The feature decomposition method described above is based on trainable gating coefficients, which is equivalent to decomposing from the same input features. Two different features are obtained, enabling the network to automatically learn a branch biased towards a Gaussian distribution constraint. ) and a branch that is biased towards predicting known categories ( ).

[0051] The first branch primarily targets the Gaussian boundary constraint module, extracting features aligned with a Gaussian distribution. It constrains these features using negative log-likelihood (NLL) and confidence boundary (CAB) losses to better fit the Gaussian probability space, thus achieving accurate modeling of known classes and robust rejection of unknown classes. The second branch primarily targets the known class prediction head, preserving supplementary information closer to traditional discriminative features. It maintains the classification ability of known classes through cross-entropy loss. The difference between the two branches lies in their focus: the first branch emphasizes probability distribution and boundary constraints, with features leaning towards "Gaussianizable" semantic components; the second branch emphasizes discriminability and supplementary information, with features leaning towards conventional classification. By introducing covariance loss to constrain the two branches, they are encouraged to be statistically independent, reducing redundancy and forming a complementary relationship.

[0052] (ii) Gaussian boundary constraint module First characteristic Gaussian classifier The input to the Gaussian boundary constraint module is a Gaussian classifier. Includes each category Class mean vector With variance vector ( (For feature dimensions).

[0053] The training objectives consist of negative log-likelihood loss (NLL) and confidence-aware boundary loss (CAB).

[0054] (1) Negative log-likelihood loss

[0055] The encouraged features follow a Gaussian distribution that satisfies the constraints:

[0056] in, Indicates the first One source domain sample, Representation of features The One dimension, Indicates the first The features of the source domain sample of the first One dimension, Expression characteristics The true label, Indicates belonging to a category The The mean of a Gaussian distribution Indicates belonging to a category The The variance of a Gaussian distribution.

[0057] (2) Confidence perception boundary loss

[0058] For constraining the distribution range and position of features:

[0059]

[0060]

[0061]

[0062] wherein, represents the inner confidence boundary threshold, used to limit the minimum range of sample distance from the class center; represents the Mahalanobis distance of the th sample after normalization, i.e. the distance between the sample feature and its class center; represents the outer confidence boundary threshold, used to limit the maximum range of sample distance from the class center; represents the feature vector of the th sample; represents the mean vector of the class to which the th sample belongs; represents the standard deviation vector of the class to which the th sample belongs; represents the cumulative distribution function (CDF) of the standard normal distribution, represents the confidence coefficient of the inner boundary, used to calculate ; represents the confidence coefficient of the outer boundary, used to calculate .

[0063] is the threshold value determined by the confidence (such as 85%, 90%, 95% confidence interval), and the scaling coefficient is used to tighten the inner boundary to construct the confidence interval. The features are limited within the annular band around the class center defined by the confidence: as shown in Figure 2 , the points within the inner boundary are considered overconfident and are penalized; the points beyond the outer boundary are considered uncertain samples and are also penalized. This constraint helps to maintain a semantically reasonable, confidence-controllable feature space, avoiding excessive clustering or divergence, and promoting robust recognition and rejection of unknown classes.

[0064] The confidence-aware boundary loss determines the double confidence boundary through Gaussian distribution inversion, and simultaneously incorporates the constraints of in-class convergence and out-of-class rejection, thereby significantly enhancing the stability of known class discrimination and the rejection ability of unknown classes without relying on artificial thresholds, which is fundamentally different from existing single threshold or cross-entropy loss.

[0065] The training loss of the Gaussian classifier G is: .

[0066] The total loss of the Gaussian boundary constraint network training is:

[0067]

[0068] wherein, 、 、 is the normalized loss function weight coefficient, , 、 、 is the learnable loss weight coefficient.

[0069] Input into the Gaussian boundary constraint module, which is trained through negative log likelihood (NLL) and confidence boundary (CAB) loss on The back propagation process transmits the gradient of probability modeling and geometric boundary constraint to , so that its features gradually conform to the statistical properties of Gaussian distribution, thereby realizing accurate modeling of known classes and robust rejection of unknown classes.

[0070] (Three) Known class prediction head Input the known class prediction head to maintain the discrimination ability of known classes through the conventional classification loss. The two branches complement each other, on the one hand to ensure alignment distribution in the Gaussian probability space and improve the rejection ability of unknown classes, and on the other hand to ensure retaining discriminative features to maintain the classification accuracy of known classes.

[0071] S3: Obtain the vibration signal data of the rotating machinery, input it into the trained Gaussian constraint network for fault diagnosis, and output the fault diagnosis result.

[0072] During prediction, the model aggregates the outputs of the known class classification network and the Gaussian classifier for multi-branch decision. For a given input, the feature extractor generates two routes of gated features, one for uncertainty-aware Gaussian scoring and the other for standard classification prediction.

[0073] The Gaussian classifier judges whether the target sample belongs to the known class by calculating the standardized distance between the target sample and the mean of each class. In the prediction stage, the target domain sample is preliminarily classified by the known class prediction head, and the prediction probability of each class is output , and the class with the highest probability is selected as the candidate known class of the sample. According to the candidate class, the corresponding Gaussian mean vector and standard deviation vector can be directly obtained. Then, the standardized distance is calculated by using the first feature of the sample and the Gaussian parameters of the class. For the class , the definition is:

[0074] wherein, is the feature of the target domain sample.

[0075] The standardized distance is compared with the confidence threshold set in the training stage . If the minimum Gaussian distance of the target domain sample is greater than the confidence threshold , it is determined that the sample is an unknown class, and if is less than or equal to , it is determined that the sample is a known class. The prediction label of the class output by the known class prediction head is directly used as the final classification result, which is represented as:

[0076] wherein, represents the prediction probability of .

[0077] To sum up, in order to overcome the challenges of the prior art, the present application faces the single-source universal domain generalization (SUniDG) task, proposes a Gaussian boundary constraint network (GBCN), and realizes effective identification of rotating machinery faults in unknown target domains. The model is composed of two core modules: a feature decoupling module and a Gaussian boundary constraint module. Among them, the feature decoupling module uses a learnable gating mechanism to disassemble global features into independent semantic representations, which are used by the known class prediction head and the Gaussian boundary module. The feature decoupling module realizes statistical decorrelation and effective decoupling between features under the guidance of the covariance loss. The Gaussian boundary constraint module further optimizes the structure of the feature space by introducing a confidence-aware boundary mechanism. The intra-class distribution is constructed within the defined confidence boundary range, and the joint optimization of the negative log-likelihood loss (NLL) and the confidence-aware boundary loss (CAB) is used to introduce probability geometric constraints, effectively suppress intra-class over-concentration, and improve the robustness of the model to unknown class interference.

[0078] The experiment is described below.

[0079] The experiment was performed on a computer equipped with an NVIDIA RTX 4090D Ti GPU. Keras was used for deep learning tasks, and TensorFlow was used as the Keras backend. The Adam optimizer was used for optimization, with an initial learning rate of , which was reduced by 10% every 100 epochs. The batch size was set to 512. The number of training epochs was 1500. Early stopping was used for model training, with 10% of the source domain dataset used as the validation dataset. Classification accuracy and H-score were used as evaluation indicators for performance comparison. For known fault categories, the new fault type was classified as the category, representing the unknown category.

[0080] (1) Comparative method To evaluate the effectiveness of the proposed framework, GBCN was compared with the latest UDG methods.

[0081] Adaptive Intermediate Class-wise Distribution Alignment (AICDA) (Q. Qian, J. Luo, Y. Qin, Adaptive intermediate class-wise distribution alignment: a universal domain adaptation and generalization method for machine fault diagnosis, IEEE transactions on neural networks and learning systems, 2024): AICDA introduces a class alignment mechanism that adaptively selects intermediate domain representations to minimize class mismatch between source and target domains.

[0082] Domain Private Suppression Meta-recognition Network (DPSMR) (M. Xu, Y. Zhang, B. Lu, Z. Liu, Q. Sun, A novel domain-private-suppress meta-recognition network based universal domain generalization for machinery fault diagnosis, Knowledge-Based Systems 309 (2025) 112775): DPSMR adopts a meta-learning strategy to suppress domain-private features while enhancing the discriminability of domain-shared representations.

[0083] GBCN without Covariance Loss (GBCN-NC): This variant removes the covariance loss component to isolate and evaluate its contribution to overall performance.

[0084] GBCN without Confidence-Aware Boundary Loss (GBCN-NCAB): This ablation variant removes the Confidence-Aware Boundary Loss (CAB), which aims to enhance class boundary clarity and reduce misclassification of unknown target samples.

[0085] (2) Evaluation method The present invention uses two indicators to evaluate the effectiveness of each method: average classification accuracy (average class accuracy) and H-score.

[0086] Average Classification Accuracy (ACA): To ensure fair evaluation in the presence of class imbalance, the present invention calculates the average classification accuracy of all target domain classes (including unknown classes). The definition is as follows:

[0087] where, is the classification accuracy of the class , represents the source domain class set, represents the target domain known class set, and the extra class in represents the target domain unknown class in ODG and OPDG.

[0088] H-score: To better reflect the trade-off between known class and unknown class identification in ODG and OPDG, the present application also adopts H-score, defined as the harmonic mean between the average accuracy of known classes (OS) and the accuracy of unknown classes (UK):

[0089] where, is the average accuracy of known classes, is the accuracy of unknown classes.

[0090] (3) CWRU dataset The present application uses the Case Western Reserve University (CWRU) bearing dataset to evaluate the performance of the proposed method under different domain conditions. The dataset contains ten health states, including one normal state and nine fault types based on fault location (inner ring, ball, outer ring) and severity (0.007 inches, 0.014 inches, 0.021 inches). As shown in Table 1, all fault types are labeled from 0 to 9.

[0091] Table 1 Label of CWRU dataset

[0092] Each signal is collected at a sampling rate of 48 kHz. The signal is divided into overlapping windows, each window having 4096 samples and a step size of 256. The segmented samples are saved to four domain-specific subsets: D0 to D3, each representing one operating condition: 1796 rpm, 1775 rpm, 1755 rpm, and 1732 rpm. For each domain, 400 samples are randomly selected for each class to ensure class balance. These domains simulate distribution shift and are used as source domains or target domains in various transfer tasks.

[0093] Table 2 Task settings of SUDG on CWRU dataset. A total of 14 tasks (C1-C14) are constructed and divided into four scenarios: CDG, PDG, ODG, and OPDG. Each task is composed of a source-target domain pair ) definitions, and their Jaccard similarity. CDG tasks (C1-C3) assume that the source and target domains share the exact same set of labels, with a Jaccard similarity of 1.00. PDG tasks (C4-C6) consider partial label overlap, where the target domain contains only a subset of the source domain labels. The Jaccard similarity ranges from 0.40 to 0.67, reflecting varying degrees of partial alignment between the source and target domains. ODG tasks (C7-C10) introduce unknown classes in the target domain that are not observed in the source domain. This setup tests the model's ability to recognize both seen and unseen classes simultaneously. OPDG tasks (C11-C14) combine partial and open-set conditions, being the most challenging. The target domain includes unseen and partially overlapping classes, with a Jaccard similarity ranging from 0.20 to 0.71.

[0094] Table 2 Different UDG task settings and Jaccard similarity on the CWRU dataset

[0095] (4) Impact of confidence region on model accuracy To investigate the impact of the confidence region on model performance, the present invention evaluated the accuracy for values ranging from 0.5 to 0.9, with the confidence region fixed at 95%. Different values led to significant changes in classification performance. As can be seen from Table 3, PDG tasks achieved the highest average accuracy and H-score with = 0.9. (5) Impact of confidence region on model accuracy To investigate the sensitivity of GBCN under different confidence thresholds, the present invention compared its performance under the four UDG scenarios shown in Table 2. These comparisons were conducted with the confidence region set ranging from 45% to 95%, and in the experiments, . Figure 3 As can be seen from Table 4, PDG tasks achieved 100% accuracy even at lower thresholds, indicating that they are relatively less affected by domain shift and unknown class interference. In contrast, ODG and OPDG scenarios showed more pronounced improvement as the confidence region increased, indicating that the boundary is crucial for rejecting unknown samples.

[0096] (6) Impact of confidence region on model accuracy To investigate the sensitivity of GBCN under different confidence thresholds, the present invention compared its performance under the four UDG scenarios shown in Table 2. These comparisons were conducted with the confidence region set ranging from 45% to 95%, and in the experiments, . As can be seen from Table 4, PDG tasks achieved 100% accuracy even at lower thresholds, indicating that they are relatively less affected by domain shift and unknown class interference. In contrast, ODG and OPDG scenarios showed more pronounced improvement as the confidence region increased, indicating that the boundary is crucial for rejecting unknown samples.

[0097] As can be seen from Table 4, PDG tasks achieved 100% accuracy even at lower thresholds, indicating that they are relatively less affected by domain shift and unknown class interference. In contrast, ODG and OPDG scenarios showed more pronounced improvement as the confidence region increased, indicating that the boundary is crucial for rejecting unknown samples. Figure 4

[0098] ​​​​​ACA steadily increases with the increase of confidence threshold and peaks at 95%. In the rest of the experiments of the present invention, we use = 95% and = 0.9.

[0099] (6) Performance analysis on CWRU dataset Table 3 and Table 4 show the performance comparison of 14 UDG tasks on the CWRU dataset. The evaluation includes four domain generalization scenarios: CDG, PDG, ODG, and OPDG. The present invention compares GBCN with its ablation variants (GBCN-NC and GBCN-NCAB) and two state-of-the-art baseline methods AICDA and DPSMR.

[0100] In terms of ACA (Table 3), GBCN achieves the highest overall performance in all scenarios, with an average improvement of 5%-49% over the best-performing baseline. GBCN reaches 100% accuracy on 8 out of 14 tasks, demonstrating strong generalization ability even in the presence of domain shift and label inconsistency.

[0101] Table 3 Average class accuracy on CWRU dataset (tasks C1-C14) under UDG settings

[0102] For H-score (Table 4), which jointly evaluates the performance of known and unknown classes, GBCN leads with an average accuracy of 96.93%, significantly outperforming all baseline methods. The ablation variant GBCN-NCAB performs poorly on open-domain tasks, especially in ODG and OPDG tasks, with H-score dropping to 0%. This highlights the crucial role of confidence-aware boundary loss (CAB) in handling unknown classes.

[0103] The results confirm that GBCN provides robust domain generalization and effective unknown class rejection capability, especially in ODG and OPDG scenarios.

[0104] Table 4 H-score on 12k-CWRU dataset (tasks C7-C14) under UDG settings

[0105] Embodiment Two The present embodiment discloses a rotating machinery fault diagnosis system based on a Gaussian boundary constraint network, comprising: A training set construction module configured to: acquire vibration signal data of a rotating machinery under a single source domain working condition, and constitute a labeled source domain training set; The model training module is configured to train the Gaussian boundary constraint network based on a source domain training set to obtain a trained Gaussian boundary constraint network; the Gaussian boundary constraint network comprises a feature extractor, a feature decoupling module, a Gaussian boundary constraint module, and a known class prediction head, the Gaussian boundary constraint module comprises a Gaussian classifier, and the Gaussian classifier is trained on the input first feature through a negative log-likelihood loss and a confidence-aware boundary loss; The model prediction module is configured to obtain vibration signal data of the rotating machinery, input the vibration signal data into the trained Gaussian constraint network for fault diagnosis, and output a fault diagnosis result.

[0106] Embodiment three The purpose of this embodiment is to provide a computing device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method of embodiment one.

[0107] Embodiment four The purpose of this embodiment is to provide a computer-readable storage medium, a computer-readable storage medium having a computer program stored thereon, wherein the program is executed by a processor to perform the steps of the method of embodiment one.

[0108] The steps involved in the devices of embodiments three and four above correspond to the method of embodiment one, and the specific implementation can be referred to the relevant description of embodiment one. The term "computer-readable storage medium" should be understood to include a single medium or multiple media of one or more instruction sets; it should also be understood to include any medium capable of storing, encoding, or carrying instruction sets for execution by a processor and causing the processor to perform any of the methods in the present application.

[0109] Those skilled in the art should understand that the above-mentioned modules or steps of the present application can be realized by a general computer device, alternatively, they can be realized by program codes executable by a computing device, so that they can be stored in a storage device for execution by a computing device, or they can be made into individual integrated circuit modules, or a plurality of modules or steps among them can be made into a single integrated circuit module. The present application is not limited to any specific combination of hardware and software.

[0110] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

[0111] The above describes the specific embodiments of the present application in combination with the drawings, but is not a limitation on the protection scope of the present application. Those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the protection scope of the present application.

Claims

1. A method for fault diagnosis of rotating machinery based on Gaussian boundary constraint networks, characterized in that, include: Vibration signal data of rotating machinery under single source domain conditions are acquired to form a labeled source domain training set; Based on the source domain training set, the Gaussian boundary constraint network is trained to obtain the trained Gaussian boundary constraint network. The Gaussian boundary constraint network includes a feature extractor, a feature decoupling module, a Gaussian boundary constraint module, and a known class prediction head. The Gaussian boundary constraint module includes a Gaussian classifier, which is trained on the first input feature through negative log-likelihood loss and confidence-aware boundary loss. The vibration signal data of the rotating machinery is acquired, input into a trained Gaussian constraint network for fault diagnosis, and the fault diagnosis results are output.

2. The rotating machinery fault diagnosis method based on Gaussian boundary constraint network as described in claim 1, characterized in that, The feature decoupling module receives the global features output by the feature extractor, and uses a gating mechanism to decompose the global features into a first gating feature and a second gating feature. After being mapped by a fully connected layer, the first feature and the second feature are obtained respectively. The first feature is input into the Gaussian boundary constraint module, and the second feature is input into the known category prediction head.

3. The rotating machinery fault diagnosis method based on Gaussian boundary constraint network as described in claim 2, characterized in that, When training a Gaussian boundary-constrained network, covariance loss is used to constrain the first and second features.

4. The rotating machinery fault diagnosis method based on Gaussian boundary constraint network as described in claim 1, characterized in that, The negative log-likelihood loss encourages the first feature to follow a Gaussian distribution that satisfies the constraints, expressed as: in, Indicates the first One source domain sample, Representation of features The One dimension, Indicates the first The features of the source domain sample of the first One dimension, Expression characteristics The true label, Indicates belonging to a category The The mean of a Gaussian distribution Indicates belonging to a category The The variance of a Gaussian distribution.

5. The rotating machinery fault diagnosis method based on Gaussian boundary constraint network as described in claim 1, characterized in that, The distribution range and location of the first feature constrained by the confidence-aware boundary loss are expressed as follows: in, Indicates the built-in confidence boundary threshold. Indicates the first Normalized Mahalanobis distance for each sample Indicates the outer confidence boundary threshold. Indicates the first The feature vector of each sample Indicates the first The category to which each sample belongs The mean vector, Indicates the first The category to which each sample belongs The standard deviation vector, The cumulative distribution function represents the standard normal distribution. The confidence coefficient represents the inner boundary. This represents the confidence coefficient for the outer boundary.

6. The rotating machinery fault diagnosis method based on Gaussian boundary constraint network as described in claim 1, characterized in that, The total loss during training the Gaussian boundary constraint network is: in, , , Represents the weight coefficients of the loss function. This represents the training loss of the Gaussian classifier. Represents the binary cross-entropy. This represents the covariance loss.

7. The rotating machinery fault diagnosis method based on Gaussian boundary constraint network as described in claim 1, characterized in that, The fault diagnosis process of the trained Gaussian constrained network is as follows: The vibration signal data of rotating machinery is initially classified using a known category prediction head to obtain candidate known categories; Based on the candidate known categories, obtain their corresponding Gaussian mean vector and standard deviation vector; The standardized distance is calculated using the first feature of the vibration signal data and the Gaussian mean vector and standard deviation vector of the candidate known categories. The standardized distance is compared with the confidence threshold. If the standardized distance is greater than the confidence threshold, the vibration signal data is determined to be of an unknown category. Otherwise, the predicted label output by the known category prediction head is used as the final classification result.

8. A rotating machinery fault diagnosis system based on Gaussian boundary constraint networks, characterized in that, include: The training set construction module is configured to acquire vibration signal data of rotating machinery under a single source domain condition and form a labeled source domain training set. The model training module is configured to: train the Gaussian boundary constraint network based on the source domain training set to obtain a trained Gaussian boundary constraint network; the Gaussian boundary constraint network includes a feature extractor, a feature decoupling module, a Gaussian boundary constraint module, and a known class prediction head; the Gaussian boundary constraint module includes a Gaussian classifier, which is trained on the first input feature using negative log-likelihood loss and confidence-aware boundary loss; The model prediction module is configured to: acquire vibration signal data of rotating machinery, input it into a trained Gaussian constraint network for fault diagnosis, and output fault diagnosis results.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the rotating machinery fault diagnosis method based on Gaussian boundary constraint network as described in any one of claims 1-7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the rotating machinery fault diagnosis method based on Gaussian boundary constraint network as described in any one of claims 1-7.

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