End-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and kolmogorov-arnold network

Abstract

The application discloses a rolling bearing end-to-end fault diagnosis system based on multi-scale convolution and Kolmogorov-Arnold network, and relates to the technical field of industrial machine fault diagnosis.The system comprises an input module, which is used for receiving a one-dimensional original vibration signal of a rolling bearing, and completing initial signal input and dimension matching; a Stem preprocessing module, which is used for performing preliminary coding, batch normalization, nonlinear activation and time dimension compression on the original vibration signal, and outputting compact initial features to a multi-level feature extraction module; and the multi-level feature extraction module, which is used for inputting the compact initial features, adopting a multi-branch deep separable convolution structure, and capturing local impact components and global modulation features of the fault signal in parallel, and outputting multi-scale fusion features.The system has compact structure, excellent diagnosis precision, and can maintain ultra-high accuracy and robust performance in multi-load and cross-platform scenes, and can be deployed on industrial edge devices in a light weight manner, thereby providing an efficient and reliable scheme for intelligent operation and maintenance of rolling bearings.

Description

Technical Field

[0001] This invention relates to the field of industrial machinery fault diagnosis technology, specifically to an end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks. Background Technology

[0002] Rolling bearings are core components of rotating machinery, widely used in key industrial sectors such as manufacturing, transportation, energy and power, and heavy equipment. Their operating condition directly determines equipment reliability, service life, and system operational safety. Under high-speed, heavy-load, high-impact, complex coupling, and high-noise conditions, rolling bearings are prone to wear, cracks, spalling, and fatigue failure. Early-stage fault characteristics are subtle, the degradation process is insidious, and vibration signals are easily contaminated by noise. Failure to diagnose these faults promptly and accurately can lead to equipment performance degradation, abnormal vibration, unplanned downtime, and even major safety accidents and economic losses. Therefore, achieving efficient, accurate, and robust intelligent fault diagnosis for rolling bearings under complex operating conditions, high noise, and variable loads is a core technological requirement in the field of industrial intelligent operation and maintenance and condition monitoring.

[0003] Existing rolling bearing fault diagnosis technologies are mainly divided into two categories: traditional signal processing and artificial feature engineering methods, and deep learning diagnostic methods. Both have obvious technical shortcomings. Traditional diagnostic methods rely heavily on manual preprocessing and expert experience, resulting in poor generalization ability. In real-world scenarios with strong noise, large operating condition fluctuations, and complex sample distribution, they exhibit weak feature representation capabilities, low diagnostic accuracy, and insufficient robustness, making them difficult to adapt to complex industrial scenarios such as multi-load and cross-platform environments. Existing deep learning methods rely on complex preprocessing, have redundant model structures and limited generalization, and their multi-branch, multi-module stacked structures result in a large number of parameters and high computational complexity, which is not conducive to lightweight deployment in industrial settings. Currently, the field of rolling bearing fault diagnosis lacks an end-to-end intelligent diagnostic system that requires no complex signal preprocessing, directly addresses one-dimensional raw vibration signals, has a compact structure, strong multi-scale feature extraction capabilities, adaptive attention enhancement, and excellent nonlinear fitting and generalization performance. This system fails to meet the practical needs of modern industry for efficient, stable, and accurate fault diagnosis of core components of rotating machinery. To address this, we propose an end-to-end rolling bearing fault diagnosis system based on multi-scale convolution and Kolmogorov-Arnold networks. Summary of the Invention

[0004] To address the aforementioned technical issues, an end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks is provided. This technical solution solves the problems of relying on manual preprocessing and expert experience, poor generalization ability, large number of parameters, and high computational complexity.

[0005] To achieve the above objectives, the technical solution adopted in this invention is: an end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks, the system comprising:

[0006] The input module is used to receive the one-dimensional original vibration signal of the rolling bearing and complete the initial signal input and dimension matching. The Stem preprocessing module is used to perform preliminary encoding, batch normalization, nonlinear activation and time dimension compression on the original vibration signal, and output compacted initial features to the multi-level feature extraction module. A multi-level feature extraction module is used to input compact initial features, adopts a multi-branch depthwise separable convolution structure, captures local impact components and global modulation features of fault signals in parallel, and outputs multi-scale fused features. The SE channel attention module is used to adaptively recalibrate the channel dimension of the multi-scale fused features, enhance key fault features, suppress noise and redundant information, and obtain deep features that are input into the KAN classification module. The KAN classification module uses the Kolmogorov-Arnold network for nonlinear mapping from deep features to fault categories and fault identification, outputting the final fault diagnosis result.

[0007] Preferably, the Stem preprocessing module includes a one-dimensional convolutional layer, a batch normalization layer, a GELU activation function layer, and an average pooling layer; The one-dimensional convolutional layer performs local feature extraction and channel expansion on the original vibration signal. The one-dimensional convolutional layer has 1 input channel and 32 output channels. It performs sliding filtering on the original signal of length 1024 and outputs a 32-channel feature map to the batch normalization layer. The batch normalization layer takes a 32-channel feature map as input, performs batch normalization processing, unifies the feature distribution to a standard range with a mean of 0 and a variance of 1, and outputs a normalized feature map. The GELU activation function layer is used to perform nonlinear transformation on the normalized feature map to mine nonlinear fault correlation features. The average pooling layer samples the associated features in the time dimension and uses average pooling to compress redundant time dimensions, outputting compacted initial features.

[0008] Preferably, the multi-level feature extraction module includes: a channel mapping unit, a multi-scale deep convolution unit, a nonlinear normalization unit, and a multi-scale fusion unit; The channel mapping unit uses 1×1 pointwise convolution to remap the channels of the input compacted initial features, regularizes the channel dimensions, and outputs a channel-normalized feature map. Multi-scale deep convolutional units receive channel normalized feature maps and set up multiple sets of parallel branches. Each set of branches uses deep convolution with convolution kernels of different lengths to capture the local impact components and global modulation features of the fault vibration signal respectively. Nonlinear normalization units are set for each deep convolutional branch. The output features of each branch are sequentially connected in a batch normalization layer and a GELU activation function layer to complete feature normalization and nonlinear activation. The multi-scale fusion unit receives the features from each branch after nonlinear normalization, splices them along the channel dimension, and further enhances the feature expression through secondary normalization and nonlinear activation, outputting multi-scale fusion features.

[0009] Preferably, the set of convolution kernel lengths of the multi-scale depth convolution unit is K = (3, 5, 7, 9), where (3, 5) are small-sized convolution kernels and (7, 9) are large-sized convolution kernels; wherein the small-sized convolution kernels are used to extract local transient impact components in the fault vibration signal, and the large-sized convolution kernels are used to capture global periodic modulation features and long-range dependency information in the fault signal. Each group of branches is calculated in parallel and independently to complete the extraction of multi-granularity fault features under different receptive fields.

[0010] Preferably, the nonlinear normalization unit is correspondingly set at the output end of each multi-scale depth convolution unit, and the batch normalization layer and the GELU activation function layer are connected in series. The multi-scale fusion unit is configured to splice and fuse the single-branch enhancement features output by each group of deep convolutional branches along the channel dimension to form a high-dimensional multi-scale composite feature; after splicing, the feature expression is further enhanced by batch normalization and nonlinear activation, and the output is a multi-scale fusion feature.

[0011] Preferably, the SE channel attention module includes: a global compression unit, a channel excitation unit, and a feature recalibration unit; The global compression unit is used to perform global average pooling on the input multi-scale fusion features along the feature temporal dimension, complete the aggregation of temporal global information, generate a global feature descriptor corresponding to each channel, and extract global context information in the channel dimension. The channel excitation unit uses a lightweight gated network to perform nonlinear transformation on the global feature descriptor and learn the inter-channel dependencies. Through a combination of two fully connected layers and activation functions, it automatically learns and generates the weight coefficients of each channel, suppressing noise and redundant channels. The feature recalibration unit is used to multiply the learned channel weight coefficients with the original multi-scale fusion features channel by channel to complete the reweighting of feature channels, enhance the critical response of the fault and suppress irrelevant information, and output the adaptively optimized deep features.

[0012] Preferably, the KAN classification module includes: a global feature compression unit, a KAN linear mapping unit, and a classification output unit; The global feature compression unit uses global average pooling to compress the temporal dimension of the input deep features, transforming high-dimensional temporal features into a compact global feature vector of fixed length, and inputting the features of uniform dimension to the KAN linear mapping unit. The KAN linear mapping unit replaces the traditional fully connected layer with a KANLinear layer and replaces the combination of fixed linear weights and conventional activation functions with a learnable univariate nonlinear function to map the global feature vector to the fault category space. By adaptively fitting complex nonlinear decision boundaries, the model's ability to distinguish between different fault types and different damage levels is enhanced.

[0013] Preferably, the classification output unit normalizes the classification logits output by the KANLinear layer using the Softmax function, generates the predicted probability of each fault category, and outputs the final fault diagnosis result.

[0014] Preferably, the classification output unit uses the cross-entropy loss function as the optimization objective to measure the difference between the predicted and the true labels. The expression is: Where N is the number of samples and C is the number of categories. Let represent the true label of the i-th sample for class c. To predict the probability that the sample belongs to class c, the predicted probability is obtained through the Softmax function.

[0015] Preferably, the Softmax function The expression is: actually The output score for class c; For the i-th sample, the original output score of class c is... Perform exponentiation; The original scores of all categories for the i-th sample are exponentially calculated and then summed.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention proposes using one-dimensional raw vibration signals as input, eliminating the need for complex preprocessing such as manual feature engineering, time-frequency transformation, and signal decomposition to achieve end-to-end fault diagnosis. This simplifies the diagnostic process, reduces deployment costs, and is suitable for industrial real-time monitoring scenarios. It employs a multi-scale, depthwise separable convolutional structure to simultaneously capture the local impact and global modulation features of the fault signal. Compared to traditional single-scale convolution, this provides more comprehensive feature representation with fewer parameters and higher computational efficiency. Combining SE channel attention mechanisms and residual connections, it adaptively enhances key fault features, suppresses noise redundancy, and mitigates gradient degradation in deep networks, improving the model's diagnostic stability and generalization ability under varying operating conditions and strong noise. Replacing traditional fully connected layers with a Kolmogorov-Arnold network significantly enhances the ability to fit complex nonlinear mappings and identify fault boundaries, resulting in higher accuracy in recognizing non-stationary, multi-class coupled fault signals. With its compact structure and excellent diagnostic accuracy, it maintains ultra-high accuracy and robust performance under multi-load and cross-platform scenarios, and can be lightweightly deployed on industrial edge devices, providing an efficient and reliable solution for intelligent operation and maintenance of rolling bearings. Attached Figure Description

[0017] Figure 1 This is a system framework diagram of the present invention. Detailed Implementation

[0018] The following description is intended to disclose the invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious variations will occur to those skilled in the art.

[0019] Example 1 Reference Figure 1 As shown, an end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks is presented. The system includes: The input module is used to receive the one-dimensional original vibration signal of the rolling bearing and complete the initial signal input and dimension matching. The Stem preprocessing module is used to perform preliminary encoding, batch normalization, nonlinear activation and time dimension compression on the original vibration signal, and output compacted initial features to the multi-level feature extraction module. A multi-level feature extraction module is used to input compact initial features, adopts a multi-branch depthwise separable convolution structure, captures local impact components and global modulation features of fault signals in parallel, and outputs multi-scale fused features. The SE channel attention module is used to adaptively recalibrate the channel dimension of the multi-scale fused features, enhance key fault features, suppress noise and redundant information, and obtain deep features that are input into the KAN classification module. The KAN classification module uses the Kolmogorov-Arnold network for nonlinear mapping from deep features to fault categories and fault identification, outputting the final fault diagnosis result.

[0020] Input module The input module is used to receive the one-dimensional raw vibration signal of the rolling bearing, and complete the initial signal input, format verification and dimension matching. The input signal is a single-channel one-dimensional time-domain vibration signal, which is directly acquired by the accelerometer without manual processing such as filtering, noise reduction and decomposition. The sample length is fixed at 1024 sampling points and the input dimension is 1×1024. The input module performs length verification and numerical normalization preprocessing on the signal, unifies the signal amplitude to the range of [-1, 1], eliminates the amplitude difference caused by the acquisition equipment and the working condition, and outputs a standard format signal to the Stem preprocessing module.

[0021] Stem preprocessing module The Stem preprocessing module is used to perform preliminary encoding, batch normalization, nonlinear activation, and time dimension compression on the original vibration signal, and output compacted initial features. The Stem preprocessing module consists of: a one-dimensional convolutional layer, a batch normalization layer, a GELU activation function layer, and an average pooling layer. A one-dimensional convolutional layer performs local feature extraction and channel expansion on the original vibration signal. The input channel number is 1, the output channel number is 32, the convolutional kernel size is 15, and the stride is 2. The original signal with a length of 1024 is subjected to sliding filtering to complete the preliminary temporal feature extraction and channel dimensionality expansion, and outputs a 32-channel feature map with a size of 32×512. The batch normalization layer takes 32-channel feature maps as input, performs batch normalization processing, unifies the feature distribution to a standard distribution with a mean of 0 and a variance of 1, eliminates feature distribution bias, accelerates the convergence of subsequent network training, and outputs normalized feature maps. The GELU activation function layer performs nonlinear transformation on the normalized feature map, introduces nonlinear mapping capability, mines the hidden nonlinear correlation features in the fault signal, and improves the feature expression capability. The average pooling layer downsamples the nonlinear features in the time dimension with a pooling kernel size of 2 and a stride of 2. The average pooling method is used to compress redundant time dimensions, retain key fault features, and output compacted initial features with a size of 32×256. Multi-level feature extraction module The multi-level feature extraction module takes compacted initial features as input, adopts a multi-branch depthwise separable convolution structure, captures local impact components and global modulation features of fault signals in parallel, and outputs multi-scale fused features. The multi-level feature extraction module includes a channel mapping unit, a multi-scale deep convolution unit, a non-linear normalization unit, and a multi-scale fusion unit; The channel mapping unit uses 1×1 pointwise convolution to remap the channel of the input compacted initial features, thereby achieving channel dimension regularization and feature fusion, reducing the computational cost of subsequent multi-branch deep convolution, and outputting a channel-regularized feature map. The multi-scale deep convolutional unit receives the channel normalized feature map and sets up four sets of parallel deep convolutional branches with a kernel length set of K={3,5,7,9}. Among them, kernels 3 and 5 are small-sized kernels used to extract local transient impact components in fault vibration signals, which are adapted to the early weak fault features of bearings; kernels 7 and 9 are large-sized kernels used to capture global periodic modulation features and long-range dependency information in fault signals, which are adapted to the fault evolution features under fluctuating operating conditions. Each set of branches is computed in parallel and independently to complete multi-granularity fault feature extraction under different receptive fields. Nonlinear normalization units are set for each deep convolutional branch. Batch normalization layers and GELU activation function layers are sequentially connected to the output features of each branch to complete feature normalization and nonlinear activation, suppress internal covariate shift, and stabilize the branch feature distribution. The multi-scale fusion unit splices the features of each branch after nonlinear normalization along the channel dimension to form a high-dimensional multi-scale composite feature; after splicing, it is further enhanced by batch normalization and GELU activation to output multi-scale fusion features. A three-level serial structure is adopted, and the number of channels is increased to 64, 128 and 256 in stages, while the time dimension is compressed to 128, 64 and 32 in parallel, so as to gradually complete the abstraction from shallow local features to high-level fault semantic features.

[0022] SE Channel Attention Module The SE channel attention module performs adaptive recalibration of the channel dimension for multi-scale fused features, enhances key fault features, suppresses noise and redundant information, and outputs deep features to the KAN classification module. The SE channel attention module includes: a global compression unit, a channel excitation unit, and a feature recalibration unit; The global compression unit performs global average pooling on the input multi-scale fusion features along the feature temporal dimension, aggregating the temporal features of each channel into a single global descriptor, completing the aggregation of temporal global information, and realizing the extraction of global contextual information in the channel dimension; The channel excitation unit adopts a lightweight gated network, which is composed of two fully connected layers and ReLU and Sigmoid activation functions. The first fully connected layer compresses the number of channels to 1 / 16 of the original number of channels and introduces nonlinear transformation. The second fully connected layer restores the original number of channels and outputs the channel weight coefficients in the range of 0 to 1 through Sigmoid, automatically learning the dependencies between channels and suppressing noise and redundant channels. The feature recalibration unit multiplies the learned channel weight coefficients with the original multi-scale fusion features channel by channel to complete the feature channel reweighting, thereby enhancing the critical fault response and suppressing irrelevant information, and outputting the adaptively optimized deep features.

[0023] KAN classification module The KAN classification module uses a Kolmogorov-Arnold network to achieve nonlinear mapping from deep features to fault categories and fault identification, outputting the final fault diagnosis result. The KAN classification module includes: a global feature compression unit, a KAN linear mapping unit, and a classification output unit; The global feature compression unit uses global average pooling to compress the temporal dimension of the input deep features, transforming high-dimensional temporal features into a fixed-length compact global feature vector with a dimension of 256, eliminating temporal length differences and providing a unified dimensional input for classification.

[0024] The KAN linear mapping unit replaces the traditional fully connected layer with a KANLinear layer and replaces the combination of fixed linear weights and conventional activation functions with a learnable univariate nonlinear function to map the global feature vector to the fault category space. By adaptively fitting complex nonlinear decision boundaries, it enhances the model's ability to distinguish between different fault types, different damage levels, and similar fault modes.

[0025] The classification output unit normalizes the classification logits output by the KANLinear layer using the Softmax function, generates the predicted probability of each fault category, selects the category corresponding to the maximum probability as the diagnosis result, and outputs the final fault type.

[0026] The classification output unit uses the cross-entropy loss function as its optimization objective to measure the difference between the predicted and the true labels. The expression is: Where N is the number of samples and C is the number of categories. Let represent the true label of the i-th sample for class c. To predict the probability that the sample belongs to class c, the predicted probability is obtained through the Softmax function.

[0027] The Softmax function The expression is: actually The output score for class c; For the i-th sample, the original output score of class c is... Perform exponentiation; The original scores of all categories for the i-th sample are exponentially calculated and then summed.

[0028] Model training and inference implementation steps Data preprocessing One-dimensional vibration signals were collected under various conditions, including normal rolling bearing, inner ring fault, outer ring fault, and rolling element fault. The samples were divided into 1024 points per sample using a sliding window with a window overlap rate of 0.5 to increase the number of samples and improve training stability. The samples were divided into training, validation, and test sets in a 7:2:1 ratio. To comprehensively verify the effectiveness, robustness, and generalization ability of the proposed KanMSConv one-dimensional convolutional bearing fault diagnosis model (combining the KAN classification head and SE attention mechanism), this study selected three mainstream bearing fault datasets from Case Western Reserve University (CWRU), the University of Paderborn (PU), and Shandong University of Science and Technology (SDUST). Multi-condition, multi-class comparative experiments were designed. By comparing the model's performance with representative methods in the current field, and combining data processing strategies and experimental settings, the fault diagnosis performance and advantages of the model were systematically analyzed, providing reliable experimental support and theoretical reference for intelligent fault diagnosis of rolling bearings.

[0029] Experimental Design and Infrastructure This experiment revolves around the core principles of "multi-dataset validation, multi-condition testing, and multi-method comparison," unifying the experimental benchmark to ensure the objectivity and validity of the comparison results. The specific basic setup is as follows: Dataset selection and processing Three bearing fault datasets with different characteristics were selected to cover different fault types, operating conditions, and damage degrees, comprehensively testing the model's adaptability and generalization ability: CWRU dataset: Vibration signals from the drive end (DE) channel with a sampling frequency of 12 kHz were selected. Ten classification tasks were constructed according to fault type (inner race, outer race, rolling element fault), outer race fault location (3 o'clock, 6 o'clock, 12 o'clock), and normal operating conditions. At the same time, four motor load conditions of 0 hp, 1 hp, 2 hp, and 3 hp were set to simulate the impact of speed and load changes on vibration signals in actual operation and to verify the robustness of the model under multiple operating conditions.

[0030] PU dataset: Covers normal conditions and various artificial damage faults, including four different working conditions (shaft diameter, radial force, and rotational speed), and constructs six classification tasks to focus on verifying the model's fault identification capabilities under complex industrial working conditions.

[0031] SDUST dataset: Focusing on the differences in different fault sizes (damage levels), samples were collected at a constant speed of 1800 r / min, and a ten-class classification task was constructed to evaluate the model's ability to distinguish faults with different damage levels.

[0032] Data preprocessing employs a uniform sliding window strategy, with each sample containing 1024 consecutive sampling points and an overlap rate of 0.5. This ensures consistency in sample length while also increasing the number of effective samples and improving training stability through data augmentation. All datasets are divided into training, validation, and test sets in a 7:2:1 ratio, and the model input is a single-channel 1024-point sequence to ensure consistency in experimental conditions.

[0033] Experimental platform and comparative model The experimental platform was configured uniformly: the software environment was PyTorch 2.5.1 and CUDA 12.1, and the hardware was an Intel Core i7-14650H CPU and an RTX 4060 Laptop GPU, ensuring that all models ran under the same computing resources and avoiding the impact of hardware differences on the experimental results; The selection of comparison models follows the principles of "representativeness and full coverage," encompassing different technical approaches such as traditional machine learning, classic deep learning, and advanced fusion models, as detailed below: The CWRU dataset selects five models: VMD-CNN-Transformer, WDCNN, Deep ResNet, CWT-CNN, and AlexNet, covering mainstream technical routes such as signal decomposition + deep learning, wide convolution, residual networks, time-frequency transform + convolution, and classic convolution.

[0034] The P dataset selects six models: AMDC-CNN, MRSFN, Matrix-CNN, MCFCNN, CWT-RepLKNet, and SDP-CNN, covering different feature extraction and fusion strategies such as simple feature fusion, temporal modeling, data reconstruction, time-frequency transformation, and image representation.

[0035] The SDUST dataset was used to select four models: SVM (traditional machine learning), ResNet, WDCNN, and FCN-Desnet, covering the technical span from shallow classifiers to typical deep learning models, to verify the advantages of deep learning over traditional methods and the performance improvement of the proposed models.

[0036] Evaluation indicators Four core evaluation metrics—accuracy, precision, recall, and F1 score—are used to comprehensively measure the model's classification performance: accuracy reflects the overall correctness of classification; precision reflects the proportion of samples predicted as positive that are actually positive; recall reflects the proportion of actual positive samples that are correctly predicted; and the F1 score combines precision and recall to avoid the limitations of a single metric and ensure a comprehensive evaluation of the model's performance.

[0037] Experimental Results and Detailed Analysis of Multiple Datasets CWRU Dataset Experimental Results Analysis The experiments on the CWRU dataset focused on verifying the model's fault diagnosis performance and feature extraction capabilities under various load conditions. The experimental results are as follows: The comparative experimental results show a clear stratification in the performance of different models: Deep ResNet and CWT-CNN performed moderately, with accuracies of 93.15% and 94.06%, respectively. This indicates that relying solely on residual connections to deepen the network layers or simply on time-frequency transformations to extract features is insufficient to fully capture the key discriminative information embedded in complex fault modes and cannot effectively address the differences in signal features caused by load variations. AlexNet and WDCNN showed significant performance improvements, with accuracies of 95.82% and 96.02%, respectively. This demonstrates that convolutional architectures are inherently suited for extracting local features from vibration signals. In particular, the wide convolutional kernel design of WDCNN has a significant advantage in capturing local impact features in vibration signals. VMD-CNN-Transformer performed best, with an accuracy of 99.48%. This shows that the combination of signal decomposition, local feature extraction, and global dependency modeling can effectively enhance fault identification capabilities and mitigate the impact of load variations on diagnostic performance.

[0038] The proposed KanMSConv model performs optimally on this dataset, achieving 100% across all four evaluation metrics, significantly outperforming all comparative models. This result demonstrates that KanMSConv's multi-scale feature extraction mechanism effectively mines multi-dimensional key features from the original vibration signal, while the SE attention mechanism enhances useful features and suppresses redundant information. Combined with the strong nonlinear fitting capability of the KAN classification head, it achieves efficient collaborative representation of features at different levels, thereby accurately distinguishing between various faults and normal operating conditions. Furthermore, the confusion matrix visualization results show that under the four load conditions, all category samples are completely concentrated on the main diagonal of the confusion matrix, proving that the model maintains stable diagnostic performance even when load changes lead to alterations in rotational speed, load path, and vibration response characteristics. It possesses strong generalization ability and can adapt to the fluctuations in operating conditions in real-world industrial scenarios.

[0039] Analysis of Experimental Results of PU Dataset The PU dataset experiments focused on the model's fault diagnosis capabilities under complex industrial conditions (multiple shaft diameters, multiple radial forces, and multiple rotational speeds). The experimental results are as follows: The performance differences between the models are significant: AMDC-CNN performed the worst, with all four metrics below 87%, indicating that relying solely on simple feature extraction and fusion methods is insufficient to fully represent fault characteristics under complex conditions and struggles to cope with the increased signal complexity resulting from multiple overlapping conditions. MRSFN, by introducing a richer temporal modeling structure, improved its accuracy to 91.78%, but still significantly lagged behind the proposed model, demonstrating the limitations of traditional single-layer or shallow feature fusion strategies in uncovering deep correlations among multi-source information. Matrix-CNN and MCFCNN further improved their performance, achieving accuracies of 96.49%. The accuracy rates of 95.21% and 98.80% respectively demonstrate that data recombination or matrix representation can enhance feature representation capabilities and improve the model's ability to identify fault modes. However, these methods focus on modeling local related information and fail to fully utilize the deep interaction relationships between different information sources, limiting further performance improvement. The accuracy rates of CWT-RepLKNet and SDP-CNN reached 98.80% and 97.71% respectively, indicating that feature extraction methods based on time-frequency transformation or image representation can enhance the separability of fault features. However, both methods rely on signals from a single source, making it difficult to integrate complementary information from multiple sources and fully explore the potential correlations of fault signals.

[0040] The KanMSConv model achieved a best-in-class performance with 99.93% across all four evaluation metrics on this dataset, fully demonstrating the effectiveness of its multi-level information fusion framework. This framework overcomes the limitations of single feature extraction methods, fully exploring complementary features and potential correlations between multi-source data, effectively addressing signal variations under complex operating conditions. Even with multiple overlapping operating conditions and ambiguous fault features, it still achieves high-precision fault identification, further validating the model's robustness and adaptability.

[0041] Analysis of Experimental Results on the SDUST Dataset The experiments on the SDUST dataset primarily evaluate the model's ability to distinguish between different fault sizes (damage levels). The experimental results are as follows: Significant performance differences were observed among different types of models: SVM, a traditional machine learning method, achieved an accuracy of only 74.50%, significantly lower than deep learning models. This indicates that traditional machine learning methods have limited feature extraction capabilities when processing high-dimensional nonlinear vibration signals, failing to fully extract the deep discriminative information contained in the original signal and making it difficult to distinguish faults of different damage degrees. ResNet, WDCNN, and FCN-Desnet, three deep learning models, performed well, with accuracies of 97.08%, 98.33%, and 97.50%, respectively, fully demonstrating the advantages of deep learning in vibration signal feature extraction and pattern discrimination. ResNet alleviated the gradient vanishing problem caused by network deepening through residual connections, enhancing feature learning capabilities. WDCNN, with its wide convolutional kernel design, excelled in local feature extraction and classification stability. Although FCN-Desnet achieved good performance, there is still room for improvement in class prediction balance, with an F1 score of only 95.27%, lower than the other two deep learning models.

[0042] The KanMSConv model achieved over 99.80% across all four metrics on this dataset, demonstrating its significant performance advantage once again. This result shows that the proposed model's multi-scale feature extraction mechanism can accurately capture subtle feature differences caused by different fault sizes, the SE attention mechanism can specifically enhance key information related to fault features and damage degree, and the KAN classification head can efficiently fit the feature distribution of faults with different damage degrees, thereby achieving accurate differentiation of different fault sizes and further validating the model's ability in refined fault identification.

[0043] Summary of Experimental Conclusions and Model Advantages Based on the comparative experimental results of the three major datasets, the following core conclusions can be drawn, clarifying the advantages and experimental value of the KanMSConv model: Superior feature extraction capability: The combination of KanMSConv's multi-scale feature extraction mechanism can effectively mine multi-dimensional and deep-level key features in the original vibration signal, solving the problem that traditional models are unable to fully capture complex fault features. Compared with single feature extraction methods (such as time-frequency transformation and simple convolution), it can more comprehensively represent fault modes.

[0044] Stronger robustness and generalization ability: KanMSConv achieved the best performance in CWRU multi-load conditions, PU complex industrial conditions, and SDUST multi-fault size scenarios. It can still maintain high-precision diagnosis even when the operating conditions change, the fault characteristics are ambiguous, and the damage degree is small. This proves that the model has strong environmental adaptability and generalization ability and can adapt to the complex needs of actual industrial scenarios.

[0045] More stable classification performance: KanMSConv performs excellently in all four metrics: accuracy, precision, recall, and F1 score, with no obvious weaknesses. Compared to the comparison models (some of which are excellent in one metric but weak in others), its classification performance is more balanced and stable, effectively avoiding missed diagnoses and misdiagnoses.

[0046] Compared to traditional methods and existing deep learning methods, KanMSConv achieves a significant improvement in diagnostic performance while maintaining a compact model structure, balancing model efficiency and diagnostic accuracy, and providing a new, efficient, and reliable method for intelligent fault diagnosis of rolling bearings.

[0047] In summary, this experiment, through comprehensive comparison of multiple datasets, operating conditions, and methods, fully verified the effectiveness and superiority of the proposed KanMSConv model in rolling bearing fault diagnosis, laying a solid experimental foundation for the practical engineering application of this model.

[0048] Application Case 1 Online fault diagnosis for large-scale wind farms: The main shafts and gearbox bearings of 50 wind turbines in a certain wind farm are subject to complex outdoor conditions for extended periods, making them prone to various faults. Traditional manual inspections are inefficient, have a high rate of missed and false diagnoses, and result in significant downtime losses. The system collects 10kHz, 1024-point one-dimensional raw vibration signals from sensors. After dimension matching by the input module, the Stem module preprocesses the signals to reduce noise and compress dimensions. A multi-level feature extraction module captures multi-scale fault features in parallel, the SE module enhances key features, and the KAN module performs accurate classification. After deployment, it achieves 24 / 7 real-time monitoring with a diagnostic latency of ≤50ms and an early fault accuracy rate of 99.2%, significantly reducing missed and false diagnoses and saving over 8 million yuan in downtime losses annually, thus improving operational efficiency.

[0049] Application Case 2 Precise fault diagnosis for CNC machine tools: The spindle bearings of 30 machines in a precision machinery company are prone to failure under high-speed operation, leading to decreased machining accuracy and scrapped workpieces. Traditional manual inspection is time-consuming and labor-intensive, and cannot provide real-time early warnings. The system collects 15kHz vibration signals through sensor linkage, with the input module directly receiving and adapting. The Stem module filters interference and compresses dimensions, a multi-level feature extraction module captures fault features at different scales, the SE module suppresses redundancy, and the KAN module distinguishes fault types and damage degrees. The system has a diagnostic accuracy of 99.5%, a latency of ≤30ms, and provides early warnings of faults 7-15 days in advance, reducing workpiece scrap losses by more than 3 million yuan annually and ensuring production continuity.

[0050] Application Case 3 Diagnosis of axle box bearings in urban rail transit vehicles; the axle box bearings of 80 subway trains operated by a certain company operate under complex conditions, and faults can easily lead to safety accidents. Traditional periodic maintenance poses significant risks. The system collects 12kHz vibration signals through wireless sensors. The input module adapts to the signal format, the Stem module reduces noise and compresses dimensions, a multi-level feature extraction module captures interwoven fault features, the SE module enhances key information, and the KAN module accurately identifies faults. After deployment, real-time monitoring latency is ≤40ms, early fault accuracy is 99.0%, and warnings are issued 10-20 days in advance, reducing operational losses by more than 5 million yuan annually and ensuring train operation safety.

[0051] In summary, the three case studies cover the wind power, precision machining, and rail transit industries, all demonstrating the advantages of end-to-end system diagnostics. They eliminate the need for manual intervention, effectively address the pain points of traditional diagnostics, improve operation and maintenance efficiency, reduce costs, and ensure safety. They are applicable to various industrial equipment equipped with rolling bearings and have broad application value.

[0052] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. An end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks, characterized in that the system... include: The input module is used to receive the one-dimensional original vibration signal of the rolling bearing and complete the initial signal input and dimension matching. The Stem preprocessing module is used to perform preliminary encoding, batch normalization, nonlinear activation and time dimension compression on the original vibration signal, and output compacted initial features to the multi-level feature extraction module. A multi-level feature extraction module is used to input compact initial features, adopts a multi-branch depthwise separable convolution structure, captures local impact components and global modulation features of fault signals in parallel, and outputs multi-scale fused features. The SE channel attention module is used to adaptively recalibrate the channel dimension of the multi-scale fused features, enhance key fault features, suppress noise and redundant information, and obtain deep features that are input into the KAN classification module. The KAN classification module uses the Kolmogorov-Arnold network for nonlinear mapping from deep features to fault categories and fault identification, outputting the final fault diagnosis result.

2. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 1, characterized in that: The Stem preprocessing module includes a one-dimensional convolutional layer, a batch normalization layer, a GELU activation function layer, and an average pooling layer. The one-dimensional convolutional layer performs local feature extraction and channel expansion on the original vibration signal. The one-dimensional convolutional layer has 1 input channel and 32 output channels, and performs sliding filtering on the original signal with a length of 1024. Output 32-channel feature maps to the batch normalization layer; The batch normalization layer takes a 32-channel feature map as input, performs batch normalization processing, unifies the feature distribution to a standard range with a mean of 0 and a variance of 1, and outputs a normalized feature map. The GELU activation function layer is used to perform nonlinear transformation on the normalized feature map to mine nonlinear fault correlation features. The average pooling layer samples the associated features in the time dimension and uses average pooling to compress redundant time dimensions, outputting compacted initial features.

3. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 1, characterized in that, The multi-level feature extraction module includes: a channel mapping unit, a multi-scale deep convolution unit, a nonlinear normalization unit, and a multi-scale fusion unit; The channel mapping unit uses 1×1 pointwise convolution to remap the channels of the input compacted initial features, regularizes the channel dimensions, and outputs a channel-normalized feature map. The multi-scale deep convolutional unit receives channel normalized feature maps and sets up multiple parallel branches. Each branch uses deep convolution with convolution kernels of different lengths to capture the local impact components and global modulation features of the fault vibration signal respectively. Nonlinear normalization units are set for each deep convolutional branch. The output features of each branch are sequentially connected in a batch normalization layer and a GELU activation function layer to complete feature normalization and nonlinear activation. The multi-scale fusion unit receives the features from each branch after nonlinear normalization, splices them along the channel dimension, and further enhances the feature expression through secondary normalization and nonlinear activation, outputting multi-scale fusion features.

4. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 3, characterized in that: The set of convolution kernel lengths for the multi-scale depth convolutional unit is K = (3, 5, 7, 9), where (3, 5) are small-sized convolution kernels and (7, 9) are large-sized convolution kernels. The small-sized convolution kernels are used to extract local transient impact components in the fault vibration signal, while the large-sized convolution kernels are used to capture global periodic modulation features and long-range dependency information in the fault signal. Each group of branches is calculated in parallel and independently to complete the extraction of multi-granularity fault features under different receptive fields.

5. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 3, characterized in that: The nonlinear normalization unit is set at the output of each multi-scale depth convolution unit, and the batch normalization layer and the GELU activation function layer are connected in series in sequence. The multi-scale fusion unit is configured to splice and fuse the single-branch enhancement features output by each group of deep convolution branches along the channel dimension to form a high-dimensional multi-scale composite feature. After concatenation, the features are further enhanced by batch normalization and nonlinear activation, and the output is a multi-scale fusion feature.

6. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 1, characterized in that, The SE channel attention module includes: a global compression unit, a channel excitation unit, and a feature recalibration unit; The global compression unit is used to perform global average pooling on the input multi-scale fusion features along the feature temporal dimension, complete the aggregation of temporal global information, generate a global feature descriptor corresponding to each channel, and extract global context information in the channel dimension. The channel excitation unit uses a lightweight gated network to perform nonlinear transformation on the global feature descriptor and learn the inter-channel dependencies. Through a combination of two fully connected layers and activation functions, it automatically learns and generates the weight coefficients of each channel, suppressing noise and redundant channels. The feature recalibration unit is used to multiply the learned channel weight coefficients with the original multi-scale fusion features channel by channel to complete the reweighting of feature channels, enhance the critical response of the fault and suppress irrelevant information, and output the adaptively optimized deep features.

7. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 1, characterized in that, The KAN classification module includes: a global feature compression unit, a KAN linear mapping unit, and a classification output unit; The global feature compression unit uses global average pooling to compress the temporal dimension of the input deep features, transforming high-dimensional temporal features into a compact global feature vector of fixed length, and inputting the features of uniform dimension to the KAN linear mapping unit. The KAN linear mapping unit replaces the traditional fully connected layer with a KANLinear layer and replaces the combination of fixed linear weights and conventional activation functions with a learnable univariate nonlinear function to map the global feature vector to the fault category space. By adaptively fitting complex nonlinear decision boundaries, the model's ability to distinguish between different fault types and different damage levels is enhanced.

8. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 7, characterized in that, The classification output unit normalizes the classification logits output by the KANLinear layer using the Softmax function, generates the predicted probability of each fault category, and outputs the final fault diagnosis result.

9. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 8, characterized in that: The classification output unit uses the cross-entropy loss function as its optimization objective to measure the difference between the predicted and the true labels. The expression is: Where N is the number of samples and C is the number of categories. Let represent the true label of the i-th sample for class c. To predict the probability that the sample belongs to class c, the predicted probability is obtained through the Softmax function.

10. The end-to-end fault diagnosis system for rolling bearings based on multi-scale convolution and Kolmogorov-Arnold networks according to claim 9, characterized in that: The Softmax function The expression is: actually The output score for class c; For the i-th sample, the original output score of class c is... Perform exponentiation; The original scores of all categories for the i-th sample are exponentially calculated and then summed.

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