Fault Diagnosis Method and System Based on Improved Residual and GRF Feature Fusion

Abstract

This invention discloses a fault diagnosis method and system based on improved residual and GRF feature fusion. The method includes integrating multi-source sensor signals; using kernel principal component analysis for dimensionality reduction; extracting features in parallel using an improved residual network, LSTM, and Transformer; normalizing and projecting the outputs of each branch, then using a dynamic gating weight mechanism for feature weighted fusion, and using a gated recursive unit to enhance the temporal modeling capability; finally, introducing stage label embedding and dynamic scaling processing, and outputting diagnostic results through a fully connected layer and Softmax classification. This invention integrates global and local information in the time and frequency domains of multiple sensors, significantly improving the diagnostic accuracy of complex rolling bearing faults.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology for mechanical equipment, and particularly relates to a fault diagnosis method and system based on the fusion of improved residual and GRF features. Background Technology

[0002] As a core transmission component of mechanical systems, the health of rolling bearings directly determines the operating efficiency and lifespan of equipment. Statistics show that approximately 30% of mechanical failures in industrial equipment originate from bearing failure, and sudden failures can not only cause unplanned downtime but also potentially lead to serious safety accidents. Therefore, condition monitoring and intelligent fault diagnosis of rolling bearings have become an important research direction in the field of industrial operation and maintenance, possessing significant engineering application value and economic benefits.

[0003] With the rapid development of artificial intelligence and machine learning technologies, intelligent diagnostic methods based on deep learning have been widely researched and applied. These methods can automatically extract fault features from massive amounts of sensor data, reducing reliance on expert prior knowledge and manual feature engineering. In existing technologies, some methods use convolutional neural networks (CNNs) to fuse spatial features from multiple vibration sensor signals; others combine CNNs with long short-term memory networks (LSTMs) to simultaneously capture the spatiotemporal dependencies of signals; still others attempt to introduce Transformer structures combined with LSTMs to enhance the modeling ability of long-sequence signals, thereby achieving fusion diagnosis of multi-sensor information in the time or frequency domains.

[0004] However, existing fusion diagnostic methods still have a significant drawback: most methods only extract and fuse features from multi-sensor signals in a single domain (such as the time domain or frequency domain), lacking the ability to collaboratively represent global and local information in the time and frequency domains. This results in limited ability to identify complex fault modes and makes it difficult to achieve comprehensive and robust fault diagnosis. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a fault diagnosis method based on improved residual and GRF feature fusion that can integrate global and local information in the time and frequency domains of multiple sensors to improve the accuracy of complex fault diagnosis of rolling bearings; on the other hand, it provides a fault diagnosis system based on improved residual and GRF feature fusion.

[0006] Technical solution: The fault diagnosis method of the present invention includes the following steps:

[0007] Step S1: Integrate and standardize the raw signals from multiple sensors to form a multi-channel dataset; use kernel principal component analysis to perform nonlinear feature extraction and dimensionality reduction on the multi-channel dataset to obtain a low-dimensional fusion feature matrix;

[0008] Step S2: Input the low-dimensional fused feature matrix into three parallel feature extraction branches: the first branch uses a residual network containing a fast Fourier convolution module for feature extraction; the second branch uses a long short-term memory network for feature extraction; and the third branch uses a Transformer encoder for feature extraction.

[0009] Step S3: Normalize and project the features output from the three branches; calculate the dynamic gating weights between the features of each branch, and perform weighted fusion of each feature to generate the fused feature vector.

[0010] Step S4: Recursively process the fused feature vector using a gated recursive unit; introduce stage label embedding and dynamically scale the feature vector.

[0011] Step S5: Input the processed feature vector into the fully connected layer, classify it using the Softmax function, and output the fault diagnosis result.

[0012] The fault diagnosis method described in this invention effectively improves data consistency and comparability by integrating and standardizing raw signals from multiple sensors; it significantly enhances feature representation and reduces computational complexity by using kernel principal component analysis for nonlinear feature extraction and dimensionality reduction; it achieves efficient extraction of spatial local features, temporal dependent features, and global context features by employing three branches in parallel: a residual network (including fast Fourier convolution), a long short-term memory network, and a Transformer encoder; it fully preserves the complementary advantages of multi-source features by using a feature normalization and weighted fusion mechanism based on dynamic gating weights; it further optimizes the representation capability of feature sequences by combining recursive processing of gating recursive units and dynamic scaling of stage marker embedding; and finally, it comprehensively improves the accuracy and robustness of fault diagnosis through fully connected layers and Softmax classification output.

[0013] Preferably, step S1, which involves integrating and standardizing the raw signals from multiple sensors, includes:

[0014] Raw signals from multiple heterogeneous sensors are aligned and integrated according to time points to construct a multi-channel raw data matrix:

[0015]

[0016] In the formula Each row corresponds to multi-source sensor data at a specific time point. n Indicates the number of sampling points. m Indicates the number of channels;

[0017] The original multi-channel data matrix is ​​standardized as follows:

[0018]

[0019] In the formula and The first j The mean and standard deviation of each channel.

[0020] By aligning and integrating raw signals from multiple heterogeneous sensors at specific times, a unified multi-channel data matrix was effectively constructed, eliminating time delay differences and format barriers between multiple data sources. Furthermore, standardization processing based on the mean and standard deviation of each channel was adopted, which significantly eliminated dimensional differences and distribution biases between sensors, laying a high-quality data foundation for subsequent feature extraction and fusion.

[0021] Preferably, step S1, which involves using kernel principal component analysis to perform nonlinear feature extraction and dimensionality reduction on the multi-channel dataset, includes:

[0022] For the standardized multichannel dataset, a nonlinear kernel function is used to map the original data space to a high-dimensional feature space:

[0023]

[0024] In the formula σ The kernel parameter controls the scale of the nonlinear mapping;

[0025] Calculate the kernel values ​​for all sample pairs to obtain a symmetric kernel matrix, where the elements are:

[0026]

[0027] The kernel matrix is ​​then centered.

[0028]

[0029] In the formula L N It is all elements are 1 / N of N × N matrix;

[0030] Solve the characteristic equation for the centered kernel matrix:

[0031]

[0032] Obtain eigenvalues With feature vectors And select the top k principal components based on the set cumulative contribution rate threshold, satisfying:

[0033]

[0034] Map the original data to the front k By considering the principal component directions, a low-dimensional fusion feature matrix is ​​obtained:

[0035]

[0036] in It is the first m The th eigenvector of the th feature vector j Each component is a faulty component, and the principal component of the fault is obtained. .

[0037] By employing kernel principal component analysis (KPCA), the original data is mapped to a high-dimensional feature space using a nonlinear kernel function, effectively capturing the complex nonlinear relationships in multi-channel data. By constructing, centering, and decomposing the kernel matrix, the principal components with the largest variance contribution are extracted, significantly enhancing the feature representation capability. Adaptively selecting principal components based on the cumulative contribution rate achieves data dimensionality reduction while retaining key fault information, eliminating redundant noise, and providing a low-dimensional, highly discriminative fusion feature matrix for subsequent diagnostic processes.

[0038] Preferably, the first branch described in step S2 uses a residual network containing a fast Fourier convolution module for feature extraction, including:

[0039] Based on input feature map Spatial domain convolution is converted into frequency domain operations using fast Fourier convolution:

[0040]

[0041] For intermediate features Perform batch normalization and ReLU activation operations:

[0042] ;

[0043] In the formula, The average of the batch data. and These are the scaling factor and the translation factor, respectively. It is a small positive number that is not equal to 0;

[0044] Perform Fast Fourier Convolution and Batch Normalization operations again on the processed features:

[0045]

[0046]

[0047] The channel dimension of the features in the skip connection path is adjusted by using 1×1 convolutions to match the dimension of the output features of the main path:

[0048]

[0049] The main path output features are added element-wise to the skip connection path features, and the final output is obtained by applying an activation function:

[0050] ;

[0051] .

[0052] By employing a residual network containing a Fast Fourier Convolution module, the first branch transforms spatial convolution into frequency domain operations, significantly improving computational efficiency and enhancing the ability to capture frequency domain features. Combined with batch normalization and the ReLU activation function, the training convergence process is effectively accelerated and gradient flow is improved. 1×1 convolutions are used to adjust the channel dimension of skip connection paths, ensuring dimensionality matching for feature fusion. Finally, element-wise addition of residual connections highlights detailed features while preserving the original information, significantly improving the model's ability to extract spatial local patterns and complex fault features.

[0053] Preferably, step S3, which involves normalizing and projecting the features output from the three branches, includes:

[0054] The original output features of the first, second, and third branches are each subjected to layer normalization. The normalized features of each branch are then transformed using a learnable linear projection matrix to map them to a feature space of uniform dimension, as shown in the following formula:

[0055] ; ; ;

[0056] In the formula F f , F l , F t These represent the original output features of the three branches respectively; It is a learnable projection matrix; LayerNorm is a layer normalization operation, calculated as follows:

[0057]

[0058] in and These are the mean and standard deviation of the features. and These are learnable scaling and offset parameters.

[0059] By performing layer normalization on the features output from the three branches, the distribution of features was effectively stabilized and the internal covariate shift was reduced, enhancing the stability of the training process. Subsequently, a learnable linear projection matrix was used to map the features of each branch to a feature space of a unified dimension. This not only eliminated the scale and structural differences between different feature sources, but also created a compatible and comparable representation basis for subsequent feature fusion, significantly improving the coordination and effectiveness of multi-source heterogeneous feature fusion.

[0060] Preferably, step S3, calculating the dynamic gating weights between the features of each branch, includes:

[0061] Calculate the output feature vector for every two branches i and j Mean cosine similarity at different time steps:

[0062]

[0063] in and ; T Indicates the total number of time steps; t For index ; and Indicates at time t Two vectors;

[0064] The average cosine similarity is input into the Softmax function to generate dynamic fusion weights for each branch:

[0065]

[0066] The sum of all weights is 1.

[0067] By calculating the average cosine similarity of the output feature vectors of each pair of branches at different time steps, the dynamic correlation between different feature sources is effectively quantified. Then, the average cosine similarity is input into the Softmax function to generate dynamic fusion weights, realizing the normalization and adaptive adjustment of weight allocation. This mechanism can dynamically adjust the contribution ratio of each branch according to the real-time correlation between features, significantly enhancing the flexibility and discriminativeness of multi-source feature fusion, and ultimately improving the representation quality and robustness of the fused feature vector.

[0068] Preferably, the weighted fusion of features in step S3 includes:

[0069] At each time step, the three normalized branch features are linearly weighted according to the dynamically generated gating weights:

[0070]

[0071] in t Indicates a time step. C t This represents the fused feature vector; the weighted calculation result is used as the fused feature vector at this time step.

[0072] By linearly weighting the three normalized branch features according to dynamically generated gating weights at each time step, adaptive fusion of multi-source features is achieved. This mechanism can dynamically adjust the contribution ratio of each branch based on the real-time correlation between features, which not only fully preserves the complementary advantages of spatial local features, temporal dependent features and global context features, but also significantly enhances the discriminativeness and information integrity of the fused feature vector, providing high-quality feature representation for subsequent temporal modeling and classification.

[0073] Preferably, step S4, which involves recursively processing the fused feature vector using a gated recursive unit, includes:

[0074] The fused feature vector is processed using an LSTM unit. The LSTM unit calculates the input gate, forget gate, output gate, and candidate states based on the input at the current time step and the state at the previous time step. The gate signals are calculated as follows:

[0075]

[0076] in i t , f t , o t、 g t This represents the input gate, forget gate, output gate, and candidate state in the gating mechanism; The sigmoid activation function is represented by sigmoid; the hyperbolic tangent activation function is represented by tanh. This represents the state vector from the previous moment; b Represents the bias vector;

[0077] Update the state of the current time step based on the gating signal and calculate the output state:

[0078] The state update formula is as follows:

[0079]

[0080] The output is calculated as follows:

[0081] .

[0082] By using dynamic gating weights to linearly weight and fuse the features of each branch, an adaptive optimization allocation of the contribution of multi-source features is achieved, which significantly enhances the discriminativeness and information integrity of the fused feature vector. By utilizing the recursive processing of the gated recursive unit (GRU) and the collaborative mechanism of its update gate and reset gate, the long-short-term dependencies in the feature sequence are effectively captured, and important historical information is selectively retained, thereby further improving the characterization ability and diagnostic robustness of time-series dynamic fault modes.

[0083] Preferably, step S4, which involves introducing stage-specific embeddings and dynamically scaling the feature vectors, includes:

[0084] The stage label embedding vector is generated based on the severity of the fault. The stage label embedding is calculated as follows:

[0085]

[0086] in It is a learnable stage embedding vector;

[0087] The stage marker embedding vector is combined with the recursively processed features, and the combined features are dynamically scaled.

[0088]

[0089] in α It is a scalar hyperparameter. It is the stage weight matrix; after the above processing, GRFU at time step t The output is and pass the state Moving on to the next time step.

[0090] By introducing learnable stage marker embedding vectors, prior knowledge of fault severity is encoded into the feature representation, effectively enhancing the model's ability to distinguish fault evolution stages. By combining stage markers with recursive features and performing dynamic scaling, adaptive adjustment of feature representation is achieved, highlighting key information highly relevant to the current fault stage while suppressing interference from irrelevant features, significantly improving the model's representation accuracy and diagnostic robustness for complex fault states.

[0091] Secondly, the fault diagnosis system of the present invention includes:

[0092] The data layer fusion module is used to integrate and standardize the raw signals from multiple sensors, and to extract and reduce nonlinear features using the kernel principal component analysis method, outputting a low-dimensional fusion feature matrix.

[0093] The feature extraction module contains three parallel branches:

[0094] The first branch is an improved residual network, which includes a fast Fourier convolution module to extract joint frequency and spatial features of the input features.

[0095] The second branch is a long short-term memory network, used to extract the temporal dependency features of the input features;

[0096] The third branch is the Transformer encoder, which is used to extract long-range dependency features of the input features;

[0097] The feature fusion module is used to normalize and project the output features of the three branches, calculate the dynamic gating weights between the features of each branch, and perform weighted fusion of each feature to generate a fused feature vector; it also includes a gating recursive unit for recursively processing and updating the state of the fused features.

[0098] The fault classification module receives features output by the feature fusion module, performs calculations using a fully connected layer and the Softmax function, and outputs the fault classification result.

[0099] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: 1. It innovatively integrates global and local information in the time and frequency domains of multiple sensors, which significantly improves the diagnostic accuracy of complex rolling bearing faults; 2. It automatically calculates dynamic weights based on feature importance, realizing adaptive optimal fusion of features of each branch; 3. It uses gated recursive units to capture long-range dependencies in fault signals, which strengthens the model's temporal state memory capability; 4. It introduces fault stage markers, enabling the model to perceive the severity of the fault and dynamically scale features, making the diagnosis more precise. Attached Figure Description

[0100] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0101] Figure 2 This is a schematic diagram of the FFC-ResNet model of the present invention;

[0102] Figure 3 This is a structural diagram of the GRF of the present invention;

[0103] Figure 4 This is a schematic diagram of the FRLT bearing fault diagnosis model framework of the present invention;

[0104] Figure 5 This is a schematic diagram of the diagnostic process of the fusion model of the present invention;

[0105] Figure 6 This is a schematic diagram of the accuracy and loss curves for the training and validation sets of the present invention;

[0106] Figure 7 This is a schematic diagram of the test set confusion matrix of the present invention;

[0107] Figure 8 This is a visualization of the t-SNE of the present invention;

[0108] Figure 9 This is a schematic diagram of the confusion matrix of each comparison model of the present invention. Detailed Implementation

[0109] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0110] This invention provides a fault diagnosis method based on improved residual and GRF feature fusion, such as... Figure 1 As shown, it includes the following steps:

[0111] Step S1: Data layer fusion based on kernel principal component analysis

[0112] The basic idea of ​​kernel principal component analysis (KPI) is to transform the original data space into a high-dimensional feature space using a nonlinear kernel function. The relationships between variables are linear in this high-dimensional feature space, therefore linear principal component analysis can be used. Given the diverse information collected by multiple sensors and the complexity of faults, KPI is employed for data-level fusion to obtain kernel principal components.

[0113] First, heterogeneous sensor signals are integrated into a unified multi-channel dataset, preserving the spatiotemporal correlation of the original data and providing structured input for subsequent fusion. The multi-channel original data matrix is ​​represented as follows:

[0114]

[0115] In the formula Each row corresponds to multi-source sensor data at a specific time point. n Indicates the number of sampling points. m Indicates the number of channels.

[0116] Secondly, to prevent numerical scale differences from causing some signals to dominate the principal component direction and to ensure a balanced contribution of each channel in the kernel space, the data is standardized to eliminate dimensional differences, as shown in the following formula:

[0117]

[0118] In the formula and The first j The mean and standard deviation of each channel.

[0119] The complex relationships between multi-sensor signals are implicitly captured using a nonlinear kernel function. A Gaussian kernel function is used to map the data to a high-dimensional feature space, as shown in the following formula:

[0120]

[0121] In the formula σ The kernel parameter controls the scale of the nonlinear mapping. The kernel values ​​for all sample pairs are calculated, resulting in a symmetric kernel matrix with the following elements:

[0122]

[0123] Then, in order to eliminate mean bias in high-dimensional space, ensure that principal component analysis conforms to the zero-mean assumption, and guarantee the validity of covariance matrix calculation, the kernel matrix is ​​centered:

[0124]

[0125] In the formula L N It is all elements are 1 / N of N × N Matrix. To extract the direction with the largest variance in high-dimensional space, retain the main feature patterns of multi-sensor data, and suppress noise and redundant information, the characteristic equation is solved:

[0126]

[0127] Obtain eigenvalues and eigenvectors Based on the cumulative contribution rate threshold (e.g.) θ =95%), before selection k One principal component, satisfying:

[0128]

[0129] Finally, the multi-channel nonlinear correlation information is compressed into a low-dimensional representation, achieving data layer fusion, minimizing information loss, and providing highly discriminative features for subsequent tasks. The original data is mapped to the front... k By considering the principal component directions, we obtain the fused low-dimensional feature matrix:

[0130]

[0131] in It is the first m The th eigenvector of the th feature vector j The principal components of the fault can be obtained using kernel principal component analysis.

[0132]

[0133] Step S2: Improve the residual network model

[0134] The core of the Fast Fourier Convolution (FFC) module is to transform traditional spatial domain convolution into the frequency domain using the Fast Fourier Transform (FFT). This transformation significantly improves computational efficiency and model accuracy. Furthermore, the module introduces Local Fourier Units (LFUs), learnable filters that operate in the frequency domain, further optimizing feature representations and enhancing model performance. FFC not only possesses a non-local receptive field but also fuses cross-scale information within the convolution itself.

[0135] FFC consists of two interconnected paths: a spatial (local) path that performs ordinary convolutions on a portion of the input feature channels, and a spectral (global) path that operates in the spectral domain. Each path can capture complementary information with different receptive fields.

[0136] Therefore, to compensate for the shortcomings of traditional residual local convolutions and enhance long-range dependency modeling, the regular convolutions in ResNet are replaced with Fast Fourier Convolutions, simultaneously processing local details and global context. The main path extracts features through joint frequency-spatial convolutions, while 1×1 convolutional paths adjust the dimensionality, achieving a combination of residual learning and global feature extraction. Compared to traditional residual blocks, FFC-ResNet retains the advantages of residuals (alleviating gradient vanishing and supporting deep training) while enhancing global information capture and improving feature expressiveness. The FFC-ResNet feature extraction model is as follows: Figure 2 As shown.

[0137] Input feature map The computation process of the FFC-ResNet model is as follows: First, the spatial domain convolution is converted into a frequency domain operation using Fast Fourier Convolution to efficiently extract global features, as shown in the following formula:

[0138]

[0139] Following FFC, batch normalization (BN) is introduced to normalize intermediate features, accelerating convergence, reducing gradient vanishing, and improving model stability. Simultaneously, the ReLU activation function introduces non-linearity, enhancing the model's expressive power and avoiding the degradation problem of stacked linear layers. The formula is as follows:

[0140] ;

[0141] In the formula, The average of the batch data. and These are the scaling factor and the translation factor, respectively. This is a small positive number that is not equal to 0. To further extract frequency domain features, a second FFC is performed, as shown in the following formula:

[0142]

[0143] Then, to ensure the stability of the feature distribution, batch normalization is performed again:

[0144]

[0145] To ensure the feasibility of residual addition, the number of channels is adjusted using 1×1 convolution to achieve dimension matching. The skip connection path is calculated as follows:

[0146]

[0147] Finally, residual summation and activation are performed, using a residual learning mechanism to add elements one by one. y The final output of the FFC-ResNet model:

[0148] ; .

[0149] Step S3: Feature layer fusion based on gated recursive fusion (GRF)

[0150] (1) Input feature preprocessing

[0151] The outputs of the three feature extraction branches (FFC-ResNet frequency domain features, LSTM temporal features, and Transformer long-range features) are first normalized to eliminate the distribution differences between the features of different branches. Then, a linear projection transformation is used to map the features to a unified feature space, ensuring dimensionality consistency and comparability, as shown in the following formula:

[0152] ; ; ;

[0153] In the formula F f , F l、 F t These represent the original output features of the three branches respectively; It is a learnable projection matrix; LayerNorm is a layer normalization operation, calculated as follows:

[0154]

[0155] in and These are the mean and standard deviation of the features. and These are learnable scaling and offset parameters.

[0156] (2) Dynamic gating weight generation

[0157] Cross-modal mutual information among the three features is calculated, and the complementarity strength between different feature modalities is quantified by cosine similarity. Specifically, the cosine similarity of each pair of feature vectors at each time step is calculated and averaged along the time dimension. Finally, a dynamic fusion weight is generated using the Softmax function to ensure that the sum of the weights is 1. This mechanism can automatically reduce the weight of highly correlated features, avoid information redundancy, and at the same time increase the weight of highly complementary features.

[0158] Calculation features i With features j Mean cosine similarity:

[0159]

[0160] in and ; T Indicates the total number of time steps; t For index ; and Indicates at time t Two vectors.

[0161] Generate dynamic fusion weights:

[0162]

[0163] (3) Weighted feature fusion

[0164] Based on dynamically generated gating weights, the three normalized features are linearly weighted and fused. This step is performed independently at each time step, generating a combined feature vector containing multimodal information. This weighting method can adaptively adjust the contribution of each branch according to the strength of complementarity between features. The calculation formula is as follows:

[0165]

[0166] in t Indicates a time step. C t This represents the fused feature vector.

[0167] (4) Recursive state update

[0168] LSTM units are used to process fused features and maintain the temporal evolution state of fault features. LSTM consists of four core components: input gate, forget gate, output gate, and candidate state.

[0169] The gating signal is calculated as follows:

[0170]

[0171] in i t , f t , o t、 g t This represents the input gate, forget gate, output gate, and candidate state in the gating mechanism; The sigmoid activation function is represented by sigmoid; the hyperbolic tangent activation function is represented by tanh. This represents the state vector from the previous moment; b This represents the bias vector.

[0172] The state update formula is as follows:

[0173]

[0174] The output calculation is as follows:

[0175]

[0176] (5) Enhanced fault stage perception

[0177] Stage-based labeling embeddings are added based on fault severity (minor / moderate / severe), and the feature representation is dynamically scaled. Fault stages are automatically classified according to the energy intensity of frequency domain features: minor faults are characterized by predominantly low-frequency energy, while severe faults are characterized by significant high-frequency impacts. This mechanism enables the model to adaptively adjust the feature representation intensity for different fault stages.

[0178] The stage marker embedding is calculated as follows:

[0179]

[0180] in It is a learnable stage embedding vector.

[0181] Feature dynamic scaling:

[0182]

[0183] in α It is a scalar hyperparameter (which may be used to control the scaling strength of the weights). It is the stage weight matrix.

[0184] After the above processing, GRFU at time step t The output is and pass the state Moving to the next time step. The structure diagram is as follows: Figure 3 As shown.

[0185] Based on a similar inventive concept, this invention also provides a fault diagnosis system corresponding to the aforementioned fault diagnosis method, comprising three modules: data layer fusion, feature layer fusion, and fault classification. The model framework is as follows: Figure 4 As shown.

[0186] First, the data layer fusion process preprocesses and partitions the collected multi-sensor signals to construct multi-channel datasets corresponding to different fault types. Then, in the feature layer fusion stage, the multi-channel datasets fused from the data layer are input into three feature extraction branches for feature extraction. Branch 1 employs a Fast Fourier Convolutional Residual Network (FFC-ResNet), achieving global receptive field coverage through frequency domain convolution kernels and extracting multi-scale frequency domain features using residual skip connections. This design effectively captures local impulse components and global frequency shift characteristics in the signal. Branch 2 uses an LSTM network to capture the global temporal dependence of the signal and extract its temporal features. Branch 3 uses a Transformer encoder to capture long-range features of the temporal signal, establishing cross-time step feature associations using a multi-head self-attention mechanism, significantly improving the model's ability to capture long-range correlations of fault features. The three feature paths are fused using the GRF feature layer fusion method and finally fed into a fully connected layer (FC) for classification using the Softmax function (SM), achieving fault diagnosis from multi-sensor data.

[0187] like Figure 5 As shown, the fault diagnosis process corresponding to the fusion model includes:

[0188] Step S1: Data Acquisition and Preprocessing. Fault signals from the bearing equipment are acquired using a data acquisition device and then appropriately preprocessed.

[0189] Step S2: Dataset Construction. This involves dividing the preprocessed signal data into training, validation, and test sets.

[0190] Step S3: Establish the FRLT model. A fault diagnosis model is established based on the FFC-ResNet-LSTM-Transformer three-branch feature extraction method.

[0191] Step S4: FRLT Model Training and Validation. The model constructed in Step 3 is trained and validated using the training and validation sets obtained in Step 2.

[0192] Step S5: FRLT Model Testing. Save the optimal training parameters of the model from step 4, input the test set generated by the same preprocessing in step 2 into the model, and output the corresponding results for analysis.

[0193] To verify the effectiveness of the FRLT model in bearing fault diagnosis, experiments were conducted using Python 3.9 and PyTorch 2.1. The network model can output accuracy and loss plots, confusion matrix plots, and scatter plots. The fault diagnosis accuracy and classification performance are analyzed based on these results to evaluate the performance of the proposed network model.

[0194] Step S1: Dataset partitioning

[0195] Deep learning-based intelligent diagnosis often requires a large amount of data. For the Southeast University bearing dataset, a segmented overlapping truncation method was used to preserve the correlation between adjacent signals and expand the data sample set. To ensure that each sample and the overlapping portion contains at least one cycle, 1024 data points were selected as one sample, and samples were truncated with an overlap rate of 50%. Samples were generated using the above method, with 2000 samples for each fault type, for a total of 10000 samples. Next, the training set, validation set, and test set were evenly divided in a 7:2:1 ratio.

[0196] Step S2: Network Training and Result Analysis

[0197] The network training was set to 50 epochs, a batch size of 64 samples, and a learning rate of 0.0003. The Adam optimization algorithm was used to update the network parameters. The performance of deep learning networks needs to be evaluated using a series of metrics, with accuracy and loss introduced as evaluation standards. Accuracy is the ratio of correctly classified samples to the total number of samples, while loss measures the degree of difference between the network's predicted labels and the true labels during training.

[0198] The accuracy and loss curves of the model on the training and validation sets are as follows: Figure 6 As shown in the figure. The maximum number of iterations for the model was set to 50. After 10 iterations of training, the model network stabilized, and the final training accuracy reached 100%. The accuracy on the validation set also reached 100%, and the loss value approached 0, indicating that the model training was complete and the accuracy was high. The model was applied to the test set, and the final results are shown in the figure. Figure 7 As shown in the confusion matrix, the model achieves 100% accuracy in identifying different categories of faults, and there is no overfitting, indicating that the model training is effective.

[0199] Step S3: Network Test Visualization Analysis

[0200] To more intuitively demonstrate the changes in inter-class and intra-class distances after network classification, the t-distributed stochastic neighbor embedding (t-SNE) algorithm was used. t-SNE is a data dimensionality reduction visualization technique that reduces high-dimensional data to two or three dimensions by preserving the similarity relationships between data.

[0201] By visualizing the raw test set data using t-SNE and plotting a scatter plot, such as... Figure 8 As shown in (a), the features of the input layer are intertwined, and there is no clear boundary between different fault types. After feature extraction through the FRLT model, the output of the fully connected layer is reduced to two dimensions, and samples of different categories are distinguished using different colored points. Figure 8 (b) shows that for the output of FRLT, data of the same class are clustered and are significantly distant from other classes, with no overlapping sample points, and the diagnostic accuracy reaches 100%.

[0202] Step S4: Model Comparison Analysis

[0203] To further verify the effectiveness of the FRLT model, the proposed FRLT model is compared and analyzed with classic deep learning models ResNet, CNN-LSTM, LSTM-Transformer and ResNet-LSTM-Transformer (RLT) using the same dataset.

[0204] To visually observe the fault classification performance of each model, confusion matrices were plotted for comparison and analysis of the classification results. The confusion matrices of the four comparison models are shown below. Figure 9 As shown. Taking the confusion matrix of the RLT model as an example, as... Figure 9 As shown in (d), other models are analyzed similarly. This model incorrectly predicted 11 samples from bearing rolling element failure C2 as outer ring failure C3. For the RLT model improvement, after introducing Fast Fourier Convolution, the classification accuracy reached 100%, as shown in (d). Figure 7 As shown, the FRLT model has higher recognition accuracy compared with the other four classic models, verifying the advantages of the FRLT model in multi-sensor signal bearing fault condition identification.

Claims

1. A fault diagnosis method based on improved residual and GRF feature fusion, characterized in that, Includes the following steps: Step S1: Integrate and standardize the raw signals from multiple sensors to form a multi-channel dataset; use kernel principal component analysis to perform nonlinear feature extraction and dimensionality reduction on the multi-channel dataset to obtain a low-dimensional fusion feature matrix; Step S2: Input the low-dimensional fused feature matrix into three parallel feature extraction branches: the first branch uses a residual network containing a fast Fourier convolution module for feature extraction; the second branch uses a long short-term memory network for feature extraction; and the third branch uses a Transformer encoder for feature extraction. Step S3: Normalize and project the features output from the three branches; calculate the dynamic gating weights between the features of each branch, and perform weighted fusion of each feature to generate the fused feature vector. Step S4: Recursively process the fused feature vector using a gated recursive unit; introduce stage label embedding and dynamically scale the feature vector. Step S5: Input the processed feature vector into the fully connected layer, classify it using the Softmax function, and output the fault diagnosis result.

2. The fault diagnosis method according to claim 1, characterized in that, Step S1, which involves integrating and standardizing the raw signals from multiple sensors, includes: Raw signals from multiple heterogeneous sensors are aligned and integrated according to time points to construct a multi-channel raw data matrix: In the formula Each row corresponds to multi-source sensor data at a specific time point. n Indicates the number of sampling points. m Indicates the number of channels; The original multi-channel data matrix is ​​standardized as follows: In the formula and The first j The mean and standard deviation of each channel.

3. The fault diagnosis method according to claim 1, characterized in that, Step S1, which involves using kernel principal component analysis to perform nonlinear feature extraction and dimensionality reduction on the multi-channel dataset, includes: For the standardized multichannel dataset, a nonlinear kernel function is used to map the original data space to a high-dimensional feature space: In the formula σ The kernel parameter controls the scale of the nonlinear mapping; Calculate the kernel values ​​for all sample pairs to obtain a symmetric kernel matrix, where the elements are: The kernel matrix is ​​then centered. In the formula L N It is all elements are 1 / N of N × N matrix; Solve the characteristic equation for the centered kernel matrix: ; Obtain eigenvalues With feature vectors And select the top k principal components based on the set cumulative contribution rate threshold, satisfying: Map the original data to the front k By considering the principal component directions, a low-dimensional fusion feature matrix is ​​obtained: ;in It is the first m The th eigenvector of the th feature vector j Each component is identified, and the principal component of the fault is obtained. .

4. The fault diagnosis method according to claim 1, characterized in that, Step S2 describes the first branch using a residual network containing a Fast Fourier Convolution module for feature extraction, which includes: Based on input feature map Spatial domain convolution is converted into frequency domain operations using fast Fourier convolution: ; for intermediate features Perform batch normalization and ReLU activation operations: ; In the formula, The mean of the batch data. and These are the scaling factor and the translation factor, respectively. It is a small positive number that is not equal to 0; Perform Fast Fourier Convolution and Batch Normalization operations again on the processed features: ; Adjust the channel dimension of features in the skip connection path using 1×1 convolutions to match the dimension of the output features of the main path: The main path output features are added element-wise to the skip connection path features, and the final output is obtained by applying an activation function. ; .

5. The fault diagnosis method according to claim 1, characterized in that, Step S3, which involves normalizing and projecting the features output from the three branches, includes: The original output features of the first, second, and third branches are each subjected to layer normalization. The normalized features of each branch are then transformed using a learnable linear projection matrix to map them to a feature space of uniform dimension, as shown in the following formula: ; ; In the formula F f , F l , F t These represent the original output features of the three branches respectively; It is a learnable projection matrix; LayerNorm is a layer normalization operation, calculated as follows: ;in and These are the mean and standard deviation of the features. and These are learnable scaling and offset parameters.

6. The fault diagnosis method according to claim 1, characterized in that, Step S3, which involves calculating the dynamic gating weights between the features of each branch, includes: Calculate the output feature vector for every two branches i and j Mean cosine similarity at different time steps: ;in and ; T Indicates the total number of time steps; t For index ; and Indicates at time t Two vectors; The average cosine similarity is input into the Softmax function to generate dynamic fusion weights for each branch: The sum of all weights is 1.

7. The fault diagnosis method according to claim 1, characterized in that, Step S3, which involves weighted fusion of the features, includes: At each time step, the three normalized branch features are linearly weighted according to the dynamically generated gating weights: ;in t Indicates a time step. C t This represents the fused feature vector; the weighted calculation result is used as the fused feature vector at this time step.

8. The fault diagnosis method according to claim 1, characterized in that, Step S4, which involves recursively processing the fused feature vector using a gated recursive unit, includes: The fused feature vector is processed using an LSTM unit. The LSTM unit calculates the input gate, forget gate, output gate, and candidate states based on the input at the current time step and the state at the previous time step. The gate signals are calculated as follows: ;in i t , f t , o t、 g t This represents the input gate, forget gate, output gate, and candidate state in the gating mechanism; The sigmoid activation function is represented by sigmoid; the hyperbolic tangent activation function is represented by tanh. This represents the state vector from the previous moment; b Represents the bias vector; Update the state of the current time step based on the gating signal and calculate the output state: The state update formula is as follows: The output calculation is as follows: .

9. The fault diagnosis method according to claim 1, characterized in that, Step S4, which involves introducing stage-labeled embeddings and dynamically scaling the feature vectors, includes: The stage label embedding vector is generated based on the severity of the fault. The stage label embedding is calculated as follows: ;in It is a learnable stage embedding vector; The stage marker embedding vector is combined with the recursively processed features, and the combined features are dynamically scaled. ;in α It is a scalar hyperparameter. It is the stage weight matrix; after the above processing, GRFU at time step t The output is and pass the state Moving on to the next time step.

10. A fault diagnosis system based on the fusion of improved residual and GRF features, characterized in that, include: The data layer fusion module is used to integrate and standardize the raw signals from multiple sensors, and to extract and reduce nonlinear features using the kernel principal component analysis method, outputting a low-dimensional fusion feature matrix. The feature extraction module contains three parallel branches: The first branch is an improved residual network, which includes a fast Fourier convolution module to extract joint frequency and spatial features of the input features. The second branch is a long short-term memory network, used to extract the temporal dependency features of the input features; The third branch is the Transformer encoder, which is used to extract long-range dependency features of the input features; The feature fusion module is used to normalize and project the output features of the three branches, calculate the dynamic gating weights between the features of each branch, and perform weighted fusion of each feature to generate a fused feature vector; it also includes a gating recursive unit for recursively processing and updating the state of the fused features. The fault classification module receives features output by the feature fusion module, performs calculations using a fully connected layer and the Softmax function, and outputs the fault classification result.

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