A gearbox cross-domain fault diagnosis method and system based on physical information guidance

Abstract

This invention discloses a physical information-guided method and system for cross-domain fault diagnosis of gearboxes. Vibration signals from gearboxes under multiple operating conditions are collected, preprocessed with speed alignment and spectral whitening, and the frequency band spectral entropy is calculated as a physical label. A physical-guided deep transfer diagnostic model is constructed, employing multi-scale deep separable convolution combined with CBAM attention to extract time-frequency features, and constraining feature physical consistency through a physical regression head. A conditional domain adversarial network and a minimum class confusion loss are introduced to align the conditional distributions of the source and target domains. During the training phase, a joint optimization strategy using classification loss, domain adversarial loss, physical regression loss, and minimum class confusion loss is employed. Finally, self-training is performed through parameter freezing and layered fine-tuning, dynamic threshold filtering of pseudo-labels, and adaptive batch normalization statistics adaptation. This invention solves the problems of large differences in feature distribution, lack of physical meaning, and easy collapse of self-training under different operating conditions, significantly improving the accuracy, robustness, and interpretability of fault diagnosis under varying operating conditions while maintaining lightweight design.

Description

Technical Field

[0001] This invention belongs to the field of industrial intelligent fault diagnosis and deep transfer learning technology, specifically involving a method and system for cross-domain fault diagnosis of gearboxes based on physical information guidance. Background Technology

[0002] Gearboxes are a critical component of modern industrial equipment, and their health directly affects the safety and efficiency of the entire production system. Utilizing vibration signals for fault diagnosis is an important means of achieving predictive maintenance. However, in real-world industrial scenarios, equipment often operates under complex conditions such as varying speeds and loads, leading to shifts in the distribution of monitoring data. This makes it difficult to directly apply diagnostic models trained on source domain data to target domain conditions, posing a significant challenge to cross-domain fault diagnosis.

[0003] Current gearbox fault diagnosis methods mainly suffer from the following technical problems: 1. Existing methods lack physical interpretability and constraints: Most existing deep domain adaptation networks are based on pure data-driven approaches, ignoring the explicit physical mechanisms inherent in vibration signals. For example, the model proposed in the paper "Interpretable physics-informed domain adaptation paradigm for cross-machine transfer diagnosis" only fits the statistical distribution of the source domain data by minimizing the classification cross-entropy loss, completely ignoring the explicit physical mechanisms inherent in vibration signals. During feature extraction, due to the lack of explicit constraints from prior physical knowledge, the model tends to learn the distribution of background noise in the data or non-causal statistical biases under specific working conditions. Once the working conditions of the target domain change, such as a change in rotational speed causing a drift in the feature frequency, or a change in load causing nonlinear fluctuations in amplitude, the feature representation learned by the model in the source domain will become invalid. This lack of physical meaning leads to a sharp decline in cross-domain generalization performance, making the diagnostic results uninterpretable from a physical perspective and failing to meet the requirements of reliable diagnosis in industrial settings. 2. Traditional adversarial transfer learning has poor cross-domain conditional distribution alignment: Existing domain adversarial transfer methods mainly focus on minimizing the global marginal distribution differences between the source and target domains through adversarial training. Patent CN116894187A utilizes an adversarial training strategy to reduce the Wasserstein distance between the source and target domains, attempting to eliminate distributional differences. However, gearbox fault signals are highly complex, and different fault categories often overlap in frequency domain features. Simply seeking global distribution consistency ignores the conditional distribution differences of different categories in the feature space. Under variable load conditions, forcibly bringing the overall distributions of the two domains closer together without considering inter-class boundary alignment can easily lead to negative transfer; that is, a certain type of fault feature in the target domain is incorrectly mapped and confused into another type of fault feature cluster in the source domain. This alignment method results in blurred inter-class boundaries, making the distinction between similar faults extremely low. 3. Existing Physical Information Neural Networks (PINNs) have high computational complexity, making it difficult to meet the demands of lightweight models in industrial settings. PINNs improve model accuracy by introducing physical equation constraints, such as the methods proposed in the literature "Hybrid Paris Physics-Informed Neural Network for Predicting Engine Fatigue Failure" and "Physics-Informed Residual Network (PIResNet) for rollingelement bearing fault diagnostics," which rely on solving complex partial differential equations or performing high-dimensional dynamic simulations. These methods typically require calculating higher-order derivatives or performing complex numerical integrations, resulting in huge computational overhead in both training and inference phases. This leads to a large number of model parameters, high inference latency, and stringent hardware requirements.However, edge computing nodes in industrial settings (such as embedded systems, PLCs, and industrial tablets) typically have limited computing power, creating a rigid requirement for lightweight, low-latency, and low-power models. Existing PINN methods suffer from excessive computational complexity, making real-time inference impossible under limited computing power, severely restricting their practical deployment in online gearbox monitoring. 4. Insufficient multi-scale frequency domain feature capture capability: Gearbox vibration signals exhibit significant non-stationarity and multi-scale characteristics, containing both high-frequency transient impact components and low-frequency shaft modulation components. Traditional convolutional neural networks typically use fixed-size convolutional kernels, resulting in a single and fixed receptive field. Patent CN114298288A uses the DarkNet-53 network for feature extraction, relying on standard convolutional layers; while patent CN116223019A introduces dual-tree complex wavelet transform, it still belongs to feature decomposition with fixed basis functions. In these methods, small convolutional kernels struggle to capture long-distance low-frequency periodic trends and modulation sidebands, while large convolutional kernels easily smooth out fleeting high-frequency weak impacts. Furthermore, existing models generally lack frequency-adaptive attention mechanisms, failing to automatically adjust the focus based on the frequency band distribution of fault features. In strong noise environments, key, subtle fault features are easily obscured by broadband background noise or masked by high-energy frequency conversion harmonic components, leading to incomplete feature extraction and reduced accuracy. 5. Existing self-training techniques are susceptible to noise interference and model collapse: Existing methods typically use fixed confidence thresholds to filter pseudo-labels and directly fine-tune the entire network parameters. Patent CN118094106A proposes a fine-tuning mechanism, but it primarily relies on global static strategies such as linearly adjusting the learning rate to accelerate convergence; Patent CN119357776A enhances the model's feature extraction capabilities by fusing CAM and Self-Attention mechanisms, but lacks dynamic filtering of pseudo-label noise in the target domain during the transfer process. This static strategy cannot adapt to the dynamic changes in model capabilities during training; excessively high thresholds result in too few effective samples and training stagnation; excessively low thresholds introduce a large number of incorrect labels. This leads the model to tend to reinforce its training on samples with high confidence in its predictions, causing the error to amplify continuously during iterations. The method of directly fine-tuning all parameters or attention weights in the aforementioned patent causes the feature extractor to cater to the specific distribution bias of the target domain, discarding the general physical features learned in the source domain, triggering feature distribution collapse, and all samples are collapsed into a few categories.

[0004] Although deep learning is widely used in fault diagnosis, existing research rarely transforms the essential physical properties of signals into explicit auxiliary supervision signals or regularization constraints to guide the network in learning physically consistent feature representations. Furthermore, the deep integration of physical mechanism guidance and multi-scale attention mechanisms to deeply integrate gearbox vibration signals with their non-stationary and wide-bandwidth characteristics, while suppressing strong background noise and adaptively capturing transient impact and steady-state modulation features, has not been fully explored in the field of cross-domain fault diagnosis. This results in models often lacking physical interpretability and noise robustness in feature extraction under complex operating conditions.

[0005] In summary, existing cross-domain fault diagnosis methods suffer from problems such as lack of physical meaning, single feature extraction, and unstable self-training, making it difficult to meet the high-precision and high-reliability diagnostic requirements under complex and variable operating conditions. There is an urgent need for a gearbox fault diagnosis technology that can integrate physical information guidance, multi-scale feature enhancement, and adaptive training strategies to meet the industrial field's demand for high-precision, high-reliability, and interpretable fault diagnosis. Summary of the Invention

[0006] To address the shortcomings of traditional data-driven fault diagnosis methods, such as lack of physical interpretability, susceptibility to confusion between similar fault categories, and poor generalization ability under varying operating conditions, this invention proposes a physical information-guided cross-domain fault diagnosis method and system for gearboxes. This is achieved by introducing physical information guidance, multi-scale feature extraction, conditional domain adversarial mechanisms, and self-training. Compared to traditional CNN or DANN models, this invention improves the model's cross-domain adaptability by introducing physical features as auxiliary supervision signals, combined with multi-scale convolutional blocks and pseudo-label filtering strategies. This enhances the physical consistency and robustness of feature extraction, enabling accurate fault type identification based on the vibration signal characteristics of rotating machinery under varying operating conditions.

[0007] To achieve the above objectives, the present invention provides a method and system for cross-domain fault diagnosis of gearboxes based on physical information guidance, the technical solution of which is as follows: A method and system for cross-domain fault diagnosis of gearboxes based on physical information guidance, characterized by comprising the following steps: S1: Acquire vibration signals and perform spectral whitening preprocessing. The original vibration acceleration signals of the gearbox under different speeds and load conditions are collected using an accelerometer, and the target domain signal is resampled based on the source domain speed. The signal is then subjected to a fast Fourier transform to obtain the amplitude spectrum, and spectral whitening is performed to highlight the fault impact characteristics.

[0008] S2: Calculate the physical consistency characteristics based on the frequency band energy distribution. The normalized spectrum is divided into multiple sub-bands, and the normalized spectral entropy in each sub-band is calculated to construct a physical supervision label vector. This label reflects the energy distribution characteristics of the signal in the frequency domain and has domain invariance, which is used to guide the network to learn feature representations that conform to physical mechanisms.

[0009] S3: Construct source and target domain datasets The preprocessed vibration data is divided into source domain and target domain datasets; the source domain contains fault category labels and physical feature labels, while the target domain contains only physical feature labels; the two types of data are encapsulated into tensor formats required by the deep learning framework for subsequent model training.

[0010] S4: Implement data augmentation processing The source domain data is subjected to random cyclic shift, frequency domain random masking, additive white Gaussian noise injection, and random amplitude scaling in sequence to simulate typical signal distortions in industrial settings and enhance the robustness and generalization ability of the model.

[0011] S5: Construct a physically guided deep migration diagnostic model A transfer diagnostic model integrating physical mechanisms and deep learning is constructed, specifically including the following sub-modules: 5.1 Design of a multi-scale feature extraction module: The module employs depth-separable convolutions with different kernel sizes to extract local and global frequency domain features in parallel, providing rich multi-scale feature representations for subsequent processing; 5.2 Introducing the CBAM attention mechanism: After feature fusion, channel attention and spatial attention weighting are performed sequentially to enhance the response of key frequency bands and suppress background noise interference; 5.3 Constructing the bottleneck layer: The extracted high-dimensional features are mapped to a low-dimensional manifold space after global average pooling, and domain-invariant high-level feature representations are extracted; 5.4 Setting up a physical regression head: Based on the spectral entropy of the predicted signal using deep features, the network is guided to learn physically meaningful features through physical consistency constraints; 5.5 Introducing a Conditional Domain Discriminator: The bottleneck layer features and the classifier's predicted probabilities are fused in a multilinear manner, and the conditional distributions of the source and target domains are aligned through conditional adversarial training.

[0012] S6: Implement a model training strategy based on multi-objective joint optimization. A composite loss function is constructed, which includes classification loss, conditional domain adversarial loss, minimum class confusion loss, and physical regression loss. The AdamW optimizer is used in conjunction with a cosine annealing strategy, and a dynamic weighting strategy is introduced to gradually increase the weight of the domain adversarial loss, ensuring that the model converges to the classification task first in the early stage of training. At the same time, label smoothing and feature sparsity constraints are introduced to improve the model's generalization ability and inter-class separability.

[0013] S7: Conduct fine-tuning diagnostics based on self-training and adaptive statistical regularization. The multi-scale feature extractor parameters are frozen, and only the high-level network is fine-tuned; a Teacher-Student self-training mode is adopted, combined with a dynamic confidence threshold to screen high-confidence pseudo-labels; the statistics of the batch normalization layer are updated using target domain data to correct distribution differences; finally, the real-time acquired vibration signals are input into the model to output the fault category and diagnostic confidence, achieving high-precision cross-domain fault diagnosis. Compared with the prior art, this invention has the following beneficial effects: 1. A hybrid architecture driven by both physical and data principles is proposed. By incorporating prior physical knowledge (spectral entropy) into the training process of deep neural networks, a deep transfer learning model is constructed that parallelizes a physical regression head and a multi-scale feature extractor. Unlike existing technologies that only use physical parameters as input, this invention forces the network to retain information capable of reconstructing the physical properties of the signal at the feature extraction layer. The physical regression loss, used as a regularization term, forces deep features to decouple into discriminative features and physically consistent features. This ensures, at the mechanistic level, that the extracted features not only possess statistical correlation but also imply physical causality, significantly enhancing the model's feature extraction capability under strong noise and providing interpretability based on physical laws for diagnostic results.

[0014] 2. Significantly improved the accuracy of cross-domain feature alignment. This invention employs a Conditional Domain Adversarial Network (CDAN) combined with Minimum Class Confusion Loss (MCC) to reduce class confusion caused by global alignment. CDAN fuses feature vectors and class prediction probabilities into tensors through multilinear mapping, performing adversarial training in the joint space of features and classes, ensuring that the source and target domains are strictly aligned according to fault categories. Simultaneously, the MCC loss prompts features to automatically cluster into well-defined, highly separable, compact clusters in the space, improving the discriminability of similar faults.

[0015] 3. A lightweight physical constraint mechanism was designed. A regularization guidance mechanism based on physical knowledge is designed to ensure that physical consistency constraints play a role during the training phase, guiding the feature extractor to learn the correct parameters. During the online inference phase, the model only needs to perform standard forward convolution operations, without requiring additional physical equation solving or frequency domain transformation regression. Furthermore, the application of depthwise separable convolution significantly reduces the number of model parameters and FLOPs. Unlike the method in patent CN202511529090.8, which introduces depthwise separable dilated convolutions with different dilation rates to construct multi-scale features, this invention, specifically targeting the characteristics of gearbox faults, employs a depthwise separable convolution architecture with convolution kernels of different sizes in parallel, and embeds a CBAM attention mechanism. This avoids the mesh effect that dilated convolutions may cause under certain operating conditions, achieving physical scale decoupling between high-frequency transient impacts and low-frequency periodic modulation. While ensuring the accuracy of physical guidance, inference latency is minimized, making it suitable for diagnostic terminals with limited computing power in industrial settings.

[0016] 4. Adaptive capture of multi-scale frequency domain features was achieved. This invention designs a multi-scale feature extraction module that integrates depthwise separable convolutions (DSConv) with different kernel sizes in parallel, simultaneously constructing both large and small receptive fields. The small receptive field accurately captures high-frequency transient impacts, while the large receptive field effectively extracts low-frequency modulation trends, achieving complete coverage of the gearbox's wideband signal. The embedded CBAM attention mechanism automatically learns feature weights from both channel and spatial dimensions, suppressing background noise bands and amplifying the response of key frequency bands containing fault information. This mechanism enables the model to keenly capture subtle early fault features even under low signal-to-noise ratio conditions.

[0017] 5. Enhanced stability of unsupervised adaptation A self-training strategy is introduced, freezing the low-level feature extractor and using a dynamic threshold to filter pseudo-labels, preventing the common model collapse phenomenon during fine-tuning in the target domain. Simultaneously, AdaBN technology is used to correct the statistical distribution difference between the source and target domains. A dynamic confidence threshold that increases linearly with training epochs is employed, utilizing a larger sample size for exploration in the early stages of training and rigorously filtering high-confidence samples in later stages to prevent the accumulation of pseudo-label noise. The strategy of freezing the low-level feature extractor and fine-tuning the high-level feature extractor protects the physical feature extraction capability from being compromised. Combined with AdaBN technology, the statistics of the batch normalization layer (BN) are directly updated using target domain data. Domain offset is corrected from both parameter optimization and statistical distribution perspectives, ensuring the stability of the unsupervised fine-tuning process and preventing model collapse. Attached Figure Description

[0018] Figure 1 This is a flowchart of a cross-domain fault diagnosis method based on physical information in an embodiment of the present invention; Figure 2This is a flowchart of data preprocessing and physical feature calculation in an embodiment of the present invention; Figure 3 This is a diagram of the architecture of the physically guided deep migration diagnostic model in an embodiment of the present invention; Figure 4 This is a diagram illustrating the model training and multi-objective joint optimization strategy in an embodiment of the present invention. Figure 5 This is a flowchart of the fine-tuning diagnostic process for self-training and adaptive statistical regularization in an embodiment of the present invention; Figure 6 This is a confusion matrix diagram of the diagnostic results of the model on the target domain test set in this embodiment of the invention; Figure 7 This is a visualization result of the fault feature distribution (t-SNE) in an embodiment of the present invention. Detailed Implementation

[0019] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0020] This invention provides a method and system for cross-domain fault diagnosis of gearboxes based on physical information guidance, specifically as follows: Figure 1 As shown, it includes: S1. Acquire vibration signals and perform spectral whitening preprocessing. The raw vibration data of the gearbox under different operating conditions are acquired, and the speed differences are aligned through resampling. Then, the transmission path effect and background colored noise are eliminated through spectral whitening technology to highlight the fault impact characteristics. The steps are as follows: Figure 2 As shown.

[0021] First, using an accelerometer mounted on the gearbox, at a sampling frequency... Collect time-domain vibration acceleration signals under different speed and load conditions To address the first-order frequency mismatch problem caused by variable speed operation, the target domain signal is resampled using the speed of the source domain data as a reference. Let the speed of the source domain operation be... The original rotational speed under the target domain operating condition is The original signal length is To align the characteristic frequency positions of the target domain signal with those of the source domain, the length of the resampled target signal is calculated. :

[0022] Using signal resampling algorithms to convert target domain signals Convert to So that its equivalent speed is Consistent. If If so, then zero-filling is performed; if If so, the signal is truncated, and the uniform signal length is... .

[0023] For the aligned time-domain signal A Hanning window is added to reduce spectral leakage, followed by a Fast Fourier Transform (FFT) to obtain the amplitude spectrum.

[0024] in, For the Hanning window function, This is the index of the sampling points for the discrete-time domain signal.

[0025] To eliminate the influence of the gearbox transfer function and suppress colored noise, the amplitude spectrum is whitened. First, the logarithmic amplitude spectrum is calculated: ,in This is the numerical stability constant. The spectral envelope is calculated using a moving average filter. convolution kernel For length is Normalized rectangular window:

[0026] Subtracting the envelope from the logarithmic spectrum yields the whitening spectrum. :

[0027] The whitened spectrum is normalized to obtain the feature vector that is finally input into the neural network. :

[0028] S2. Calculate the physical consistency characteristics based on the frequency band energy distribution. Physical supervision labels are constructed based on the physical statistical features of the spectrum. These features characterize the frequency domain energy distribution of the signal and possess domain invariance, guiding the network to learn feature representations that conform to physical mechanisms. For example... Figure 2 As shown.

[0029] The normalized spectrum obtained in step S1 Divide evenly on the frequency axis into There are subbands. Let the total length of the spectrum be... , No. The length of each sub-band is The length of each sub-band . No. Individual band ( The frequency index range is ,in:

[0030] For the spectral components within each subband Calculate its normalized probability distribution :

[0031] Calculate the spectral entropy of each sub-band according to the definition of information entropy. and divide by the maximum possible entropy value. Normalization is performed to obtain physical eigenvalues. :

[0032]

[0033] All The normalized spectral entropy of each subband is concatenated to form the physical supervision label vector of the sample. :

[0034] S3. Construct source and target domain datasets. Based on the operating conditions, the preprocessed vibration data is divided into source and target domain datasets, and a data input format adapted to the deep transfer learning model is constructed. The source domain dataset is selected based on known operating conditions and complete fault labels. At the rotational speed... ,load The data was collected below. The target domain selection and operating conditions changed, affecting the rotational speed. ,load The dataset to be diagnosed. In the unsupervised transfer learning setting, the fault category labels in the target domain cannot be used for training.

[0035] For the first in the source domain Each sample consists of a triplet. .in The whitening spectrum obtained in step S1, For fault category labels, The physical tag is calculated in step S2.

[0036] For the first in the target domain Each sample, during the training phase, is composed of binary tuples. .in The spectrum after resampling and whitening. The calculated physical labels serve as auxiliary monitoring signals, eliminating the need for manual labeling.

[0037] The processed data is converted into a tensor format required by deep learning frameworks. The source domain dataset is encapsulated as a set of tensors. :

[0038] in, For the source domain batch spectrum input, For the corresponding category index, This is the physical feature vector.

[0039] Batch tensor set of target domain :

[0040] in, This is the batch spectrum input for the target domain, used for unsupervised domain adaptation training.

[0041] After constructing the samples, all samples from the source and target domains are encapsulated into tensor datasets. Finally, a data loader is constructed, the batch size is set, and the source domain data is randomly shuffled to meet the batch-level tensor input requirements for stochastic gradient descent training.

[0042] S4. Implement data augmentation processing A multi-dimensional hybrid data augmentation strategy is applied to the source domain data to reduce the data distribution differences between the source and target domains, thereby improving the robustness of the deep transfer learning model to noise interference, phase shift, and amplitude fluctuations under complex operating conditions. This strategy expands the diversity of training samples by simulating typical signal distortion scenarios in industrial settings, forcing the model to learn essential fault characteristics with domain invariance.

[0043] Specifically, the following four serial enhancement operations are implemented: (1) Random cyclic translation The randomness of the initial position is truncated during the simulated data acquisition process to eliminate the dependence of features on specific time or frequency phase. This applies to the input feature vector. Perform random cyclic displacements along the dimensional direction. The formula is as follows:

[0044] Among them, displacement Follows uniform distribution , The length of the feature vector.

[0045] (2) Frequency domain random mask During analog signal transmission, partial frequency band loss or sudden narrowband interference forces the model to learn a global feature distribution instead of relying on single-frequency band features. A random, continuous region is selected from the feature vector, and its amplitude is forcibly set to zero. The specific implementation is as follows:

[0046] in, For mask ratio, Represents the starting position of the mask. This represents the maximum frequency domain mask ratio.

[0047] (3) Additive white Gaussian noise injection To improve the model's adaptability to low signal-to-noise ratio environments, circuit thermal noise and background environmental noise introduced during sensor data acquisition in simulated industrial settings are introduced. Random noise following a standard normal distribution is superimposed onto the feature vector, as shown in the following formula:

[0048] in, The noise intensity coefficient, It is a random noise vector.

[0049] (4) Random amplitude scaling This simulates the overall signal energy fluctuations caused by sensor sensitivity drift, changes in mounting and tightening force, or differences in transmission path attenuation. The feature vector is multiplied by a randomly generated scaling factor, as shown in the following formula:

[0050] Among them, scaling disturbance amount Follows uniform distribution , This is the upper bound of the amplitude scaling intensity.

[0051] The four enhancement operations described above are applied sequentially to obtain the enhanced source domain sample. During model training, augmented samples are generated online in real time for each iteration, ensuring that the model never sees the exact same input, thereby maximizing the effectiveness of data augmentation.

[0052] S5. Construct a physically guided deep migration diagnostic model A transfer diagnostic model integrating physical mechanisms and deep learning is constructed, with the overall architecture as follows: Figure 3 As shown, the model consists of four parts: a multi-scale feature extractor, a bottleneck layer, a physical regression head, and a conditional domain discriminator. It collaboratively optimizes classification error, domain distribution differences, and physical consistency errors through a multi-task learning mechanism.

[0053] 5.1 Design of a multi-scale feature extraction module To capture fault characteristics across different frequency bands of vibration signals, a multi-scale residual module based on depthwise separable convolution is designed. A cascaded approach combining depthwise convolution and pointwise convolution is used to reduce the number of parameters and improve computational efficiency.

[0054] Let the input features be The output is The calculation formula is as follows:

[0055] in, Perform convolution operations independently for each input channel. use The convolution kernel performs inter-channel information fusion. Specifically, for the ... One channel:

[0056] in, is the sliding index of the convolution kernel.

[0057] The multi-scale attention module contains two parallel depthwise separable convolutional branches with kernel sizes of [sizes to be filled in]. and These two branches are used to extract local transient impact features and global periodic features, respectively. The output features of the two branches are concatenated and fused along the channel dimension.

[0058] 5.2 Introducing the CBAM attention mechanism After feature fusion, a convolutional block attention module is introduced, which sequentially performs channel attention and spatial attention weighting, followed by channel attention. The calculation is as follows:

[0059] Multiply the channel attention weights element-wise with the input features:

[0060] Spatial attention The calculation is as follows:

[0061] in, This is a convolution operation used to fuse channel information to extract spatial attention weights.

[0062] Final output features Combined with residual connection:

[0063] 5.3 Constructing the bottleneck layer Output of feature extractor After global average pooling, it is mapped to a low-dimensional manifold space through a fully connected layer. The formula is as follows:

[0064] in, For weights and biases, Batch normalization is used to extract domain-invariant high-level features.

[0065] 5.4 Setting up the physical regression head To give the model physical interpretability, a physics regression head is designed to directly extract data from the original high-dimensional features. Spectral entropy of the predicted signal Predicted value The calculation formula is:

[0066] in, Using the Sigmoid activation function, the output is constrained to... The module minimizes the physical prediction error within the range. This forces the feature extractor to retain features with clear physical meaning, preventing the model from overfitting to non-causal statistical laws of the source domain.

[0067] 5.5 Introduction of Conditional Domain Discriminator To achieve fine-grained alignment between the source and target domains, a conditional domain adversarial strategy is employed. This involves incorporating bottleneck layer features... The class probability vector predicted by the classifier Perform multilinear fusion, For the bottleneck layer feature dimension, Generate conditional features for the total number of fault categories. To capture domain distribution differences under specific categories:

[0068] Calculate the conditional features of the source and target domains respectively. and The input discriminator is then flattened. The domain discriminator distinguishes the domain origin of the input data, while the feature extractor aims to fool the discriminator through a gradient inversion layer (GRL). The optimization objective is to minimize the conditional domain adversarial loss:

[0069] Through the aforementioned adversarial training mechanism, the model can learn feature representations that maintain both class discriminativeness and domain invariance.

[0070] S6. Implement a model training strategy based on multi-objective joint optimization. Design a composite loss function that takes into account classification error, domain distribution differences, class confusion, and physical consistency constraints, such as... Figure 4 As shown, by minimizing the total loss, the conditional distribution of features in the source and target domains is aligned while ensuring the accuracy of source domain fault classification. Physical mechanism constraints are also introduced to improve the model's generalization ability and interpretability under varying operating conditions.

[0071] 6.1 Overall Optimization Objective The overall optimization objective of the model It consists of four parts, and the calculation formula is as follows:

[0072] in, These are the balancing hyperparameters for each loss term. For source domain classification loss, To mitigate losses in the conditional domain, For minimum class confusion loss, The loss is constrained by physical mechanisms. During training, a dynamic weighting strategy is adopted, gradually increasing the weight of the domain adversarial loss as the training rounds increase, to ensure that the model converges to the classification task preferentially in the early stages of training.

[0073] 6.2 Classification Loss To reduce the risk of overfitting, a cross-entropy loss function with label smoothing is used. Let the true labels of the source domain samples be... The smoothed label is The probability distribution predicted by the model is The loss is calculated as follows:

[0074]

[0075] in, For the source domain batch size, Number of fault categories This is the label smoothing coefficient.

[0076] 6.3 Conditional Domain Adversarial Loss Based on conditional domain adversarial networks, by minimizing the domain discriminator The binary cross-entropy loss is used to train the feature extractor to generate domain-invariant features. Let... For the domain label (source domain is 0, target domain is 1). To incorporate conditional features that combine feature and category prediction, the loss is:

[0077] Where Bt is the batch size of the target domain. The gradient inversion layer inverts the gradient during backpropagation, achieving adversarial alignment of the feature distribution.

[0078] 6.4 Minimal Class Confusion Loss For unlabeled target domain data, minimizing the off-diagonal elements of the class correlation matrix promotes feature cluster separation of target domain samples, reducing inter-class confusion. Let the prediction probability matrix of the target domain batch be... First, calculate the category correlation matrix. :

[0079] right Perform row-wise normalization to obtain :

[0080] The final MCC loss is defined as the sum of the off-diagonal elements:

[0081] This loss term forces the predicted probability distributions of each category in the target domain to become orthogonal, effectively enhancing the discriminative power of features.

[0082] 6.5 Physical Mechanism Constraint Loss The physical mechanism constraint loss includes two components: the mean squared error of physical attribute prediction and the feature sparsity constraint. It aims to ensure that the extracted features conform to physical laws and possess sparse expressive power.

[0083] in, The spectral entropy predicted by the physical regression head. The true spectral entropy label calculated in step S2, Features of the bottleneck layer For the target domain physical consistency weight, is the characteristic sparsity constraint coefficient.

[0084] The physical regression loss guides the feature extractor to retain physical information related to the fault mechanism by supervising the energy distribution characteristics of the signal spectrum; the sparsity constraint makes the feature representation more compact and efficient.

[0085] 6.6 Optimization Strategy The AdamW optimizer is used for parameter updates, and a cosine annealing strategy is used to dynamically adjust the learning rate, as shown in the following formula:

[0086] in, For the current iteration round, This represents the maximum number of iterations.

[0087] To ensure stability during the initial training phase, the weights of the domain adversarial loss are... It grows dynamically as the training progresses:

[0088] in, This represents the current training progress percentage. This mechanism enables the model to prioritize fitting the source domain classification task in the early stages of training, and gradually strengthen the domain alignment strength as training progresses, avoiding early gradient noise from interfering with the convergence of the feature extractor.

[0089] S7. Conduct fine-tuning diagnostics based on self-training and adaptive statistical regularization. Implement a self-training strategy that integrates parameter freezing, dynamic threshold filtering, and statistical adaptation, such as... Figure 5 As shown, the aim is to further improve the model's classification accuracy in the target domain, while avoiding the risks of model collapse and overfitting to noisy pseudo-labels during unsupervised fine-tuning.

[0090] 7.1 Parameter Freezing and Layered Fine-Tuning Before entering the self-training phase, lock the multi-scale feature extractor. All parameters are preserved, retaining the physical feature representations with good generalization ability learned during the source domain adversarial training phase, preventing the low-level feature extraction ability from degrading due to erroneous supervision signals when fine-tuning is only based on pseudo-labels.

[0091] Parameter updates are performed only on higher-level network modules, specifically including: Bottleneck layer

[0092] Fault classifier

[0093] Physical regression head

[0094] This layered fine-tuning strategy effectively protects the underlying physical feature extraction capability from being compromised while adapting to the target domain distribution.

[0095] 7.2 Dynamic Threshold Pseudo-Label Filtering The Teacher-Student training mode is adopted, and pseudo-labels are generated using the current model as the teacher network as the target domain data. High-confidence samples are selected based on dynamic confidence threshold.

[0096] To balance sample utilization in the early stages of training with label quality in later stages, a design was developed that adapts to different training rounds. Dynamic threshold of linear growth Let the total number of fine-tuning rounds be... The initial threshold is The maximum threshold is Then the first The formula for calculating the threshold of a wheel is:

[0097] For target domain samples The model predicts the class probability distribution as follows: Calculate the maximum prediction probability. and corresponding pseudo tags Define the filter mask. A sample is retained if and only if the prediction confidence is higher than the current threshold:

[0098] Backpropagation is performed only on the selected high-confidence sample set:

[0099] in We applied weak perturbations to the target domain samples to enhance the robustness of the fine-tuning process.

[0100] 7.3 Adaptive Batch Normalization Statistics Fitting To eliminate the inherent differences in statistical distribution between the source and target domain data, statistical adaptation is performed on all batch normalization layers in the network before inference. Keeping the network parameters constant, the target domain dataset is... The input model undergoes one forward propagation. Using the moment features of the target domain data, the running mean of all BN layers is recalculated and replaced. and operating variance :

[0101] This operation does not update any network weights; it only corrects the statistics of the normalization layer to match the distribution of the target working condition data, effectively reducing the performance degradation caused by covariate bias. This strategy significantly improves the model's generalization performance in the target domain while maintaining the discriminative ability of features learned from the source domain.

[0102] 7.4 Real-time Diagnosis and Confidence Level Early Warning After completing the above training and adaptation, the model will be deployed to an edge or cloud-based diagnostic system. Real-time acquisition of gearbox vibration acceleration signals will be performed. The resampling, windowed FFT and spectrum whitening operations described in step S1 are performed, and the preprocessed spectrum is input into the fault diagnosis model to output the fault category probability distribution.

[0103] No. Class of faults Sample posterior probability :

[0104] : The original output value of the k-th category of the model output.

[0105] : The total number of fault categories.

[0106] Diagnostic confidence of the current sample :

[0107] The category with the highest probability is taken as the final diagnosis result. . If the value is lower than the preset safety threshold, the current sample is determined to be outside the model's cognitive boundary, and "unknown working condition" is output with a prompt for manual review to avoid the risk of misdiagnosis.

[0108] This mechanism provides configurable confidence warning boundaries for industrial sites, balancing diagnostic accuracy with decision security.

[0109] This technical solution collects vibration signals of the gearbox under different operating conditions using an accelerometer to construct source and target domain datasets. Through speed alignment and spectral whitening preprocessing, and by calculating the spectral entropy of the signal as a physical label, the distribution shift caused by differences in operating conditions is effectively eliminated. Combined with a physical-guided deep transfer diagnostic model, the system first extracts time-frequency features using multi-scale deep separable convolution and CBAM attention mechanisms. After physical consistency is constrained by the physical regression head, the Conditional Domain Adversarial Network (CDAN) and Minimum Class Confusion Loss (MCC) work together to achieve conditional distribution alignment between the source and target domains while preserving effective physical features. Finally, through self-training and AdaBN strategy fine-tuning of the model, the robustness and diagnostic accuracy of fault features under varying operating conditions are significantly improved.

[0110] like Figure 6 As shown, the model achieves a diagnostic accuracy of 99.50% on the target domain test set, with the vast majority of samples correctly classified onto the diagonal of the confusion matrix, exhibiting extremely low inter-class confusion. Comprehensive evaluation results demonstrate that the cross-domain fault diagnosis model based on physical information fusion performs exceptionally well in complex variable operating condition tasks, accurately and reliably identifying the health status and fault type of the gearbox. Figure 7 As shown, the feature distribution visualization (t-SNE) results show that the features of the source domain and the target domain exhibit a high degree of alignment in two-dimensional space, and the feature clusters of different fault categories have high separation and clear boundaries, with significant clustering effect. This indicates that the model effectively overcomes the distribution differences caused by cross-operating conditions and learns discriminative physical features.

[0111] The above embodiments are merely specific examples of the present invention, and their descriptions are quite specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these obvious substitutions all fall within the protection scope of the present invention.

Claims

1. A method for cross-domain fault diagnosis of gearboxes based on physical information guidance, characterized in that, Includes the following steps: S1: Acquire vibration signals and perform spectral whitening preprocessing; S2: Calculate the physical consistency characteristics based on the frequency band energy distribution; S3: Construct source and target domain datasets; S4: Implement data augmentation processing; S5: Construct a physically guided deep migration diagnostic model; S6: Implement a model training strategy based on multi-objective joint optimization; S7: Conduct fine-tuning diagnostics based on self-training and adaptive statistical regularization.

2. The gearbox cross-domain fault diagnosis method based on physical information guidance according to claim 1, characterized in that, The spectral whitening preprocessing described in step S1 specifically includes: taking the logarithm of the amplitude spectrum to obtain the logarithmic amplitude spectrum, calculating the spectral envelope using a moving average filter, subtracting the envelope from the logarithmic spectrum to obtain the whitened spectrum, and finally performing normalization processing.

3. The gearbox cross-domain fault diagnosis method based on physical information guidance according to claim 1, characterized in that, The calculation of normalized spectral entropy in step S2 specifically includes: uniformly dividing the normalized spectrum into M sub-bands on the frequency axis, calculating the normalized probability distribution of the spectral components in each sub-band, calculating the spectral entropy and normalizing it by dividing it by the maximum possible entropy value, and concatenating the normalized spectral entropies of all sub-bands to form a physical supervision label vector.

4. The physical information-guided gearbox cross-domain fault diagnosis method according to claim 1, characterized in that, The multi-scale feature extraction module in step S5 uses depth-separable convolutional branches with different sized convolutional kernels to extract features in parallel, and introduces a convolutional block attention mechanism after feature fusion, performing channel attention and spatial attention weighting in sequence.

5. The gearbox cross-domain fault diagnosis method based on physical information guidance according to claim 1, characterized in that, In step S5, the conditional domain discriminator performs multilinear fusion of the bottleneck layer features and the class probability vector predicted by the classifier to generate conditional features, which are then input into the domain discriminator for adversarial training to achieve conditional distribution alignment between the source and target domains.

6. The gearbox cross-domain fault diagnosis method based on physical information guidance according to claim 1, characterized in that, The minimum class confusion loss described in step S6 minimizes the sum of the off-diagonal elements of the class correlation matrix of the target domain prediction probability matrix, thereby promoting the separation of feature clusters of each class in the target domain and reducing inter-class confusion.

7. The gearbox cross-domain fault diagnosis method based on physical information guidance according to claim 1, characterized in that, The adaptive batch normalization statistic adaptation in step S7 specifically includes: Keeping the network parameters fixed, input the target domain dataset into the model for one forward propagation, and recalculate and replace the running mean and running variance of all batch normalized layers using the moment features of the target domain data.

8. A physical information-guided cross-domain fault diagnosis system for gearboxes, characterized in that, include: A data acquisition and preprocessing module is used to perform the operations described in steps S1 to S3 of claim 1; The model building and training module is used to perform the operations described in steps S4 to S6 of claim 1 to build and train a physically guided deep transfer diagnostic model. The fine-tuning diagnostic module is used to perform the operation described in step S7 of claim 1, to fine-tune the model and output real-time diagnostic results.

9. The gearbox cross-domain fault diagnosis system based on physical information guidance according to claim 8, characterized in that, The fine-tuning diagnostic module also includes a confidence warning unit, which is used to calculate the diagnostic confidence of the sample during real-time diagnosis. If the value is lower than the preset safety threshold, it outputs "unknown working condition" and prompts manual review.

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