Rolling bearing residual life prediction method and system based on convolution white box

Abstract

The invention belongs to the technical field of bearing residual service life detection, and discloses a rolling bearing residual service life prediction method and system based on a convolution white box. According to the method, time domain and frequency domain feature extraction, noise reduction processing and health state and degradation state division are carried out on an original vibration signal, and deep neural network training is carried out in combination with a Weibull-MSE loss function, so that prediction of RUL conforms to the actual degradation process of a bearing; and synchronous extraction of long-time dependence information and local degradation characteristics of the bearing signal is completed through a convolution CRATE network architecture fusing an expansion causal convolution attention mechanism DCA and a multi-scale convolution MSC. According to the method, the accuracy of RUL prediction is improved in combination with health state evaluation, the local feature extraction capability is enhanced, the local modeling capability of the model is improved through multi-scale information fusion, and the interpretability and the prediction credibility are improved through a CRATE structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of detecting the remaining service life of bearings, and particularly relates to a method and system for predicting the remaining life of rolling bearings based on a convolutional white box. Background Art

[0002] In modern industrial production, rotating machinery (such as motors, turbines, pumps, and compressors) is widely used in fields such as aerospace, manufacturing, energy, and transportation. During the long-term operation of these devices, the health status of their key component - the rolling bearing directly affects the operation efficiency, reliability, and safety of the devices.

[0003] With the development of industrial intelligence, Prognostics and Health Management (PHM) technology has emerged. The core goal of PHM is to discover potential faults of devices in advance through data analysis and modeling, predict their Remaining Useful Life (RUL), so as to reasonably arrange maintenance plans, reduce device downtime, and improve production efficiency. Currently, PHM mainly includes key links such as data acquisition and processing, health status assessment, fault diagnosis, fault prediction, health management, feedback, and iteration. As the core link of fault prediction, RUL prediction can help enterprises perform maintenance at the right time, avoid unplanned downtime, reduce maintenance costs, and increase the service life of devices. Therefore, researching high-precision RUL prediction methods, especially for key components such as rolling bearings, has important industrial application value.

[0004] Furthermore, the rolling bearing is one of the most common rotating support components in mechanical equipment. During long-term operation, factors such as friction, fatigue, and lubrication degradation will cause it to gradually deteriorate and eventually fail. Therefore, predicting the remaining life (RUL) of rolling bearings can discover potential faults in advance, extend the device life, and improve production safety.

[0005] Currently, RUL prediction mainly relies on the following types of methods: (1) Physical model-based methods.

[0006] This method describes the degradation process of the bearing through mathematical or physical models and updates the model parameters in combination with actual monitoring data. For example, using differential equations to describe the material fatigue process, or using statistical models to estimate the wear condition of the bearing. Such methods rely on a large amount of prior knowledge, are applicable to specific devices, but it is difficult to establish accurate models under complex working conditions.

[0007] (2) Data-driven methods.

[0008] This method directly extracts features from the bearing operation data, learns the degradation pattern through machine learning or deep learning algorithms, and predicts the remaining useful life. The specific process includes data preprocessing, feature extraction, model training, and prediction. This type of method avoids complex mathematical modeling and has strong adaptability, but it often lacks the guidance of physical mechanisms and may lead to prediction errors.

[0009] (3) Based on hybrid methods.

[0010] This method combines physical models with data-driven methods, uses prior knowledge to build an initial model, and optimizes the model parameters through a data-driven approach. For example, first establish a physical model to describe the bearing degradation characteristics, and then use machine learning methods to correct the model parameters to make it more in line with the actual working conditions. This method takes into account the interpretability of physical models and the flexibility of data-driven methods, but it is complex to implement and has high requirements for data and domain knowledge.

[0011] Existing improved schemes based on Transformer have solved the problems of global and local information extraction in RUL prediction to a certain extent, but there are still many deficiencies.

[0012] (1) The health state assessment method is imperfect, affecting the prediction accuracy.

[0013] Existing RUL prediction methods usually assume that the bearing degradation process follows a linear or preset fixed curve. When training the model, all bearing data are directly regarded as a unified input, ignoring the individual differences in the operating environment and usage conditions of different bearings. The latest research proposes a method based on correlation coefficient analysis, which dynamically divides the stable period and degradation period of the bearing using historical data, thus making up for the limitations of the fixed degradation curve to a certain extent and enhancing the adaptability to individual differences. However, this method does not perform more refined processing on the original historical data. Especially in the case of noise interference in vibration signals, the calculated health assessment state often has errors, affecting the accuracy and stability of RUL prediction.

[0014] (2) It is difficult to capture long-term dependence information and local degradation features simultaneously.

[0015] The closest existing technical solution: Convolutional Transformer (COT).

[0016] The Convolutional Transformer (COT) integrates the CNN and Transformer architectures, aiming to simultaneously extract local and global features in RUL prediction to improve the modeling ability of the bearing degradation process. Its basic process is as follows: First, before the Transformer, the CNN is used to extract the local features of the vibration signal to enhance the capturability of the bearing degradation pattern; then, the self-attention mechanism of the Transformer is used to establish long-term dependencies, ensuring that the model can effectively learn the changing trend of the bearing life over time, thereby improving the prediction stability.

[0017] Although this method combines the advantages of CNN and Transformer, there are still certain limitations. Due to the limited receptive field of the CNN, there may still be information loss when extracting local features during the bearing recession period, resulting in an insufficiently detailed characterization of key degradation features. In addition, this architecture mainly focuses on time series modeling and lacks full utilization of the spatial features of the signal (such as frequency domain information), while RUL prediction depends not only on the degradation trend in the time dimension but also on the changes in frequency domain features. The deficiencies of COT in this regard affect the prediction accuracy and generalization ability.

[0018] (3) The interpretability of the model is poor and it is difficult to apply to industrial scenarios.

[0019] The closest existing technical solution: the Multiscale Temporal Convolutional Transformer (MTCT).

[0020] Based on the standard Transformer architecture, the Multiscale Temporal Convolutional Transformer (MTCT) adds a temporal convolution module to strengthen the modeling ability for time series data. Its core idea is as follows: First, an attention mechanism based on temporal convolution is introduced before the Transformer to enhance the ability to capture local features, making the model pay more attention to the key short-term changes during the bearing degradation process when calculating the attention weights; subsequently, the multi-head self-attention mechanism is used to optimize the feature representation, and the Transformer architecture is used to establish long-term dependencies, ensuring that the model can effectively learn the changing trend of the bearing life over time.

[0021] Although the MTCT improves the modeling ability for local information to a certain extent, its interpretability is still weak. This method still relies on the standard Transformer architecture, and the decision-making process of its self-attention mechanism is complex and difficult to trace the specific role of features, making the prediction results of the model difficult to be intuitively understood by engineers or industry experts. Summary of the Invention

[0022] To overcome the problems existing in the related technologies, the disclosed embodiments of the present invention provide a rolling bearing remaining life prediction method and system based on a convolutional white box, specifically related to a rolling bearing remaining service life (RUL) prediction method based on a convolutional white box Transformer.

[0023] The technical solution is as follows: A rolling bearing remaining life prediction method based on a convolutional white box, comprising the following steps: S1, perform time-domain and frequency-domain feature extraction on the original vibration signal, and perform noise reduction processing in combination with singular value decomposition (SVD) to remove random noise and interference in the signal, and provide input features; S2, input the processed data into a deep neural network, and based on the correlation coefficient analysis method, dynamically evaluate the operation process of the bearing, divide the healthy state and the degradation state, and train the deep neural network in combination with the Weibull-MSE loss function to make the prediction of the RUL conform to the actual degradation process of the bearing; S3, complete the synchronous extraction of the long-term dependence information and local degradation features of the bearing signal through a convolutional CRATE network architecture that fuses the dilated causal convolutional attention mechanism (DCA) and the multi-scale convolution (MSC).

[0024] In step S2, based on the correlation coefficient analysis method, dynamically evaluate the operation process of the bearing, divide the healthy state and the degradation state, and train the deep neural network in combination with the Weibull-MSE loss function, including: S201, calculate the correlation between the features at each moment after SVD compression and the features at the initial moment using the Pearson correlation coefficient, and use the moment when the correlation starts to be less than 0.90 as the division point of the healthy state , indicating that the bearing enters the degradation stage from the healthy state; the correlation coefficient calculation is shown in formula (1): (1) In the formula, is the correlation coefficient at the moment, is the singular value of the dimension, is the singular value of the dimension, is the average value of the singular values along the dimension, is the singular value obtained by compressing the features at the zero moment, S202. Construct the RUL life curve. According to the health state of each bearing divided, divide the remaining life label of each bearing into two parts: the stable state and the rapid decline state. Among them, The stable state is: ; The rapid decline state is: ; In the formula, is the remaining life of the bearing at the stable state time, is the total life of the bearing, is the bearing segmentation point time, is the remaining life of the bearing at the rapid decline state time, is the current time; S203. Optimize the loss function.

[0025] In step S203, optimizing the loss function includes: The Weibull cumulative distribution function CDF is defined by the following formula (2). Different corresponds to the shape factor of different curve change trends, is the characteristic life; (2) In the formula, is the bearing failure probability at time, is the natural constant, is the current time; Combining the Weibull cumulative distribution function with the traditional MSE loss function can obtain the Weibull-MSE loss function; the MSE loss function is shown in formula (3), and the Weibull-MSE loss function formula is shown in (4); (3) ; (4) In the formula, is the MSE loss function, is the number of time steps, is the predicted value, is the mixed loss function, is the Weibull cumulative distribution function, is the Weibull-MSE loss function, is the Weibull loss function, is the weight ratio hyperparameter, is the true RUL label value, is the RUL predicted value, is the actual used time of the bearing, is the predicted used time of the bearing; During the training process of the deep neural network, the Weibull-MSE loss function that combines Weibull with the mean square error MSE is used as the loss function in the network. The failure probability of the bearing at different times is fused into the Weibull-MSE loss function through the Weibull cumulative distribution function. The Weibull-MSE loss function is combined with the RUL life curve of the bearing health state evaluation method, so that the prediction of RUL conforms to the actual degradation process of the bearing.

[0026] In step S3, the convolutional CRATE network architecture that fuses the dilated causal convolutional attention mechanism DCA and the multi-scale convolution MSC includes: The dilated causal convolutional attention mechanism DCA is the multi-head subspace convolutional attention that fuses the dilated causal convolution DCC and the CRATE structure, forming the multi-head subspace convolutional sub-attention; Through the multi-scale convolution MSC module, the ability to extract spatial features is enhanced.

[0027] Furthermore, the synchronous extraction of the long-term dependence information and local degradation characteristics of the bearing signal is completed, including: S301, construct the dilated causal convolution DCC. During the attention calculation process of the Transformer structure, the dilated causal convolution DCC is used to replace the standard self-attention mechanism to capture the local features of the bearing signal; S302, embed the multi-scale convolution MSC module. The multi-scale convolution module is embedded in the main loop block of the CRATE structure, placed after the multi-head subspace convolutional attention and before the iterative shrinkage threshold algorithm ISTA to extract the multi-scale features of the bearing signal; S303, regressor optimization and RUL prediction. In the regressor, the average pooling operation is used along the time dimension to capture the long-term dependence relationship; S304, construct the convolutional CRATE network architecture.

[0028] In step S301, constructing the dilated causal convolution DCC includes: (a) Exponential expansion factor ; (b) Unilateral padding strategy. The extracted feature data is , where is the total number of time steps, and each represents the bearing feature at the th time step; To complete the convolution operation, data is padded unilaterally, and the padded sequence is , For padding data, The number of is determined by where is the convolution kernel size, is the dilation factor, and is the number of paddings; In step S302, the multi-scale convolution MSC module is embedded, including: (1) After the attention mechanism, the multi-scale convolution MSC introduces convolution kernels of different sizes to extract features of different scales in parallel; (2) Feature fusion strategy, the input data dimension is , and after feature extraction with different convolution kernel sizes, four parallel output results are generated; As the output of the convolutional pool, ensure that ; is the sequence length, is the dimension of the 1st convolution module, is the dimension of the 2nd convolution module, is the dimension of the 3rd convolution module; (5) In the formula, is the output after splicing of multiple convolution modules, is the splicing operation, are the outputs of the 1st, 2nd, 3rd, and 4th convolution modules, is the selected dimension parameter; (3) ReLU activation function and BatchNorm normalization, the formula is: (6) In the formula, is the activation function, is the batch normalization operation, is the output of the multi-scale convolution module.

[0029] In step S303, the input of the regressor is ; is the input of the regressor at time (i) Average pooling is adopted, and pooling is performed along the time dimension in the regressor to extract long-term dependence information: (7) In the formula, is the output of the pooling layer, is the layer normalization operation, is the average value operation, is the specified dimension parameter, is the original time series; (ii)The fully connected layer outputs the final predicted value, and converts the high-dimensional features into the RUL predicted value through linear mapping: (8) Wherein, is the weight matrix of the fully connected layer, is the bias vector of the fully connected layer, is the output of the regressor.

[0030] In step S304, a convolutional CRATE network architecture is constructed, including: S3041, the encoding reduction principle, defines the encoding rate of a given feature in a specific feature space as follows: (9) Wherein, is the encoding rate after compression of, is the covariance matrix of the feature, indicating the correlation between features, is the regularization parameter, is to calculate the logarithmic determinant of the specified matrix; According to the encoding reduction principle, the multi-head subspace convolutional attention mechanism and feature sparsification operation of the CRATE structure are derived; S3042, perform the transparency of the improved multi-head subspace convolutional attention mechanism MSSA, including: First, the subspace attention mechanism is used for feature decomposition, and the input bearing feature is compressed into the local signal model subspace, and the expression is: (10) Wherein, is the Query matrix in self-attention, is the Key matrix in self-attention, is the Value matrix in sub-attention, is the th non-overlapping subspace; Secondly, the transparent attention mechanism is calculated as: (11) Wherein, is the multi-head self-attention mechanism, is the th subspace, is the th Value matrix, is the activation function, is the a Query matrix, is the th Key matrix, is the Gaussian codebook encoding accuracy, is the feature dimension, is the subspace dimension; S3043, feature sparsification based on the ISTA iterative shrinkage threshold algorithm.

[0031] In step S3043, the feature sparsification based on the ISTA iterative shrinkage threshold algorithm includes: When the ISTA block receives the output C of the previous module, the ISTA compresses and sparsifies the features through the following iterative update process: (12) In the formula, is the output of the ISTA block, is the activation function, is the output of the previous module, is the optimization gradient of the objective optimization function, is the th iteration, is the objective optimization function, is the learning rate.

[0032] Another object of the present invention is to provide a rolling bearing remaining life prediction system based on a convolutional white box, which implements the rolling bearing remaining life prediction method based on the convolutional white box. The system includes: A data preprocessing module for extracting time-domain and frequency-domain features from the original vibration signal, performing noise reduction processing by combining singular value decomposition (SVD) to remove random noise and interference in the signal, and providing input features; A health state evaluation module for inputting the processed data into a deep neural network, dynamically evaluating the operation process of the bearing based on the correlation coefficient analysis method, dividing the health state and the degradation state, and training the deep neural network by combining the Weibull-MSE loss function to make the prediction of the remaining useful life (RUL) conform to the actual degradation process of the bearing; A feature extraction module that completes the synchronous extraction of long-term dependence information and local degradation features of the bearing signal through a convolutional CRATE network architecture that fuses the dilated causal convolutional attention mechanism (DCA) and the multi-scale convolutional (MSC).

[0033] Combining all the above technical solutions, the beneficial effects of the present invention are as follows: Combined with health state evaluation, improve the accuracy of RUL prediction: Use the correlation coefficient analysis method to dynamically divide the health state and degradation state of the bearing, avoid the limitations of the fixed degradation curve, and improve the accuracy of state division.

[0034] Enhance the local feature extraction ability and accurately model the bearing degradation mode: Adopt the dilated causal convolutional attention mechanism (DCA), introduce dilated convolution into the Transformer structure, improve the ability to capture local degradation features, and make up for the deficiency of traditional Transformer in local information extraction.

[0035] Multi-scale information fusion to enhance the local modeling ability of the model: Adopt a feature fusion strategy to splice convolutional features of different scales, enabling the model to capture global trends and local details simultaneously, and improving the adaptability to complex degradation modes.

[0036] CRATE structure to improve interpretability and prediction credibility: For the first time, apply the white-box architecture to the field of RUL prediction, enhance the transparency and interpretability of the model, and contribute to the implementation in the re-engineering of deep learning projects.

[0037] Optimize the CRATE regression structure to enhance the stability of RUL prediction: Introduce average pooling (MeanPooling) into the regressor to obtain long-term dependence information, make the RUL prediction more stable, and reduce the impact of short-term fluctuations.

[0038] The technical solution proposed by the present invention has good engineering generality, is applicable to the predictive maintenance requirements of high-value equipment such as power, wind power, aerospace, and numerically controlled machine tools, and can significantly improve the operation stability and safety guarantee ability of industrial systems. It is expected to reduce the risk of unplanned downtime by more than 30% and effectively extend the service life of key components by more than 10%, with significant economic benefits and engineering application value, and has broad industrialization prospects in the fields of equipment health management and intelligent manufacturing.

[0039] The present invention combines the Weibull-MSE loss function with a health assessment method based on dynamic correlation coefficients for the first time to construct an interpretable CRATE network integrating dilated causal convolution (DCA) and multi-scale convolution (MSC), effectively overcoming problems existing in the actual deployment of traditional methods such as large prediction deviation, complex debugging, and high implementation threshold, and filling the technical gap in the field of a fusion-based RUL prediction architecture based on "white box + multi-scale + health dynamic recognition".

[0040] In the field of RUL prediction, there have long been bottlenecks such as inaccurate health state recognition, weak local feature extraction ability, and poor model deployability. Existing methods mostly rely on static threshold division or fixed degradation curves, making it difficult to adapt to the individual differences of bearings. At the same time, the "black box" characteristics of traditional deep networks make it difficult to interpret and optimize the prediction results. The present invention introduces a dynamic health assessment method based on the Pearson correlation coefficient and optimizes the degradation fitting accuracy by combining the Weibull-MSE composite loss function, significantly improving the prediction reliability. At the same time, CRATE integrating convolution realizes the structural transparency of the network structure. This solution effectively alleviates the core difficulties such as difficult state division, weak degradation modeling, and untraceable prediction in RUL prediction, and constructs a technical foundation for evolving towards an industrial-level interpretable prediction model. There are generally two types of biases in existing methods: First, they overly rely on deep learning to automatically extract health state features and ignore the role of expert knowledge in state division and degradation judgment. Second, they lack attention to model interpretability, restricting the popularization and application of "white box" network architectures in industry. The present invention improves the prediction performance and promotes the in-depth application of interpretable models in the field of RUL prediction by introducing a dynamic health state division mechanism, combining expert experience to determine the degradation starting point, and constructing a CRATE framework integrating a convolution structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings herein are incorporated into the specification and form a part of the specification, showing embodiments consistent with the present disclosure, and are used together with the specification to explain the principles of the present disclosure; Figure 1 is a flowchart of a method for predicting the remaining useful life of a rolling bearing based on a convolutional white box provided by an embodiment of the present invention; Figure 2 is a flowchart of a method for evaluating the health state of a bearing provided by an embodiment of the present invention; Figure 3 is a bearing fault change curve, a "bathtub" curve graph provided by an embodiment of the present invention; Figure 4 is a schematic diagram of the principle of dilated causal convolution provided by an embodiment of the present invention; Figure 5 is a schematic diagram of a multi-scale convolution module provided by an embodiment of the present invention; Figure 6 is a schematic diagram of the principle of the convolutional CRATE network architecture provided by an embodiment of the present invention; Figure 7 is a graph of the health state division and RUL label of Bearing1_4 of the present invention; Figure 8 is a prediction result graph of Bearing1_1 of the present invention; Figure 9 is a prediction result graph of Bearing1_2 of the present invention; Figure 10 This is the Bearing1_3 prediction result diagram of the present invention; Figure 11 This is the Bearing1_4 prediction result diagram of the present invention; Figure 12 This is the Bearing1_5 prediction result diagram of the present invention; Figure 13 This is the Bearing1_6 prediction result diagram of the present invention; Figure 14 This is the prediction result diagram of Bearing1_7 of the present invention. DETAILED DESCRIPTION

[0042] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0043] The innovation of the present invention lies in: the present invention constructs a CRATE network structure that integrates dilated causal convolution (DCA) and multi-scale convolution (MSC), enhances the ability to synchronously capture long-term dependencies and local degradation characteristics, and ensures the interpretability of key steps of the prediction method; at the same time, the dynamic division mechanism of the health state of the Pearson correlation coefficient is introduced, and the Weibull-MSE loss function is combined to improve the fitting ability of the prediction process to the actual degradation curve of the bearing.

[0044] Embodiment 1: The rolling bearing remaining life prediction system based on convolutional white box provided by the embodiment of the present invention comprises: The data preprocessing module is used to extract the time domain and frequency domain features of the original vibration signal, and combine it with singular value decomposition (SVD) for noise reduction, remove random noise and interference in the signal, improve data quality, and provide more stable and accurate input features for subsequent analysis.

[0045] The health status assessment module is used to input the deep neural network after data preprocessing, and dynamically evaluate the operation process of the bearing based on the correlation coefficient analysis method, accurately divide the healthy state and the degradation state, and combine the Weibull-MSE loss function to train the deep neural network so that the RUL prediction is consistent with the actual degradation process of the bearing. The deep neural network can better adapt to the actual degradation law of the bearing and improve the accuracy and robustness of the prediction.

[0046] Through the convolutional CRATE network architecture that fuses the dilated causal convolution attention mechanism (DCA) and multi-scale convolution (MSC), the synchronous extraction of long-term dependence information and local degradation features of bearing signals is completed; The dilated causal convolution attention mechanism (DCA) is the multi-head subspace convolution sub-attention formed by fusing dilated causal convolution (DCC) and the CRATE structure's multi-head subspace convolution attention; through multi-scale convolution (MSC), the ability to extract spatial features is enhanced.

[0047] Example 2, as Figure 1 shown, the method for predicting the remaining useful life of a rolling bearing based on a convolutional white box provided by the embodiment of the present invention includes: S1. Extract time-domain and frequency-domain features from the original vibration signal, and perform noise reduction processing in combination with singular value decomposition (SVD) to remove random noise and interference in the signal and provide input features; Specifically, it includes: S101. Calculate the time-domain statistical features (mean, standard deviation, kurtosis, skewness, etc.) of the original vibration signal to characterize the overall trend of the bearing signal.

[0048] S102. Use the fast Fourier transform (FFT) to extract the frequency-domain features of the vibration signal to enhance the representation ability of the extracted features in the frequency domain of the original vibration signal.

[0049] S103. Perform time-frequency analysis using the discrete wavelet transform (DWT), and enhance the extraction of high-frequency and low-frequency features of the unstable original vibration signal through wavelet transformation to retain the key time-frequency information of bearing faults.

[0050] S104. Normalize the features min-max extracted in steps S101 - S103 to construct the input data of the deep neural network.

[0051] S105. For further dividing the health state later, use singular value decomposition (SVD) for noise reduction, record the singular values obtained by singular value decomposition, and use them to replace the original features to achieve the purpose of removing random noise and compressing the original features.

[0052] S2. Input the processed data into the deep neural network, and based on the correlation coefficient analysis method, dynamically evaluate the operation process of the bearing, divide the health state and degradation state, and combine the Weibull-MSE loss function to train the deep neural network to make the prediction of RUL conform to the actual degradation process of the bearing; In the present invention, the deep neural network is a general term for the overall modeling framework used for RUL prediction. The innovation of the present invention lies in designing a deep neural network with a specific structure, namely a convolutional neural network based on the CRATE (Coding Rate Autoencoding Transformer Explanation) architecture, which integrates dilated causal convolution (DCA) and multi-scale convolution (MSC) modules for simultaneously extracting long-term dependencies and local degradation features. Therefore, the CRATE network itself is the implementation structure of the deep neural network referred to in the present invention, and the specific schematic diagram is as shown in Figure 6 shown.

[0053] Specifically, it includes: S201, calculating the correlation between the features at each moment after SVD compression and the features at the initial moment using the Pearson correlation coefficient, and taking the moment when the correlation starts to be less than 0.90 as the division point p of the healthy state, marking that the bearing enters the degradation stage from the healthy state. The calculation of the correlation coefficient is as shown in formula (1); (1) In the formula, is the correlation coefficient at the moment, is the singular value of the th dimension, is the singular value of the th dimension, is the average value of the dimension singular values along, is the average value of the dimension singular values along, is the singular value obtained by compressing the feature at the zero moment, is the singular value obtained by compressing the feature at the current moment;

[0054] In the healthy state, it is defaulted that the life changes very slowly and does not change. In the degradation stage, linear degradation is adopted so that it can map the actual degradation process of the bearing. According to the healthy state of each bearing divided, the remaining life labels of each bearing can be divided into two parts: the stable state and the rapid decline state. The flow of the bearing health state evaluation method is as shown in Figure 2 shown.

[0055] The stable state is: ; The rapid decline state is: ; In the formula, is the stable state The remaining life of the bearing at a certain moment is the total life of the bearing is the moment of the bearing segmentation point is the rapid decline state The remaining life of the bearing at a certain moment is the current moment S203, optimize the loss function

[0056] In industrial production, the law of the failure rate of bearings changing with time can be summarized as the "bathtub" curve. In the initial stage, the bearings need to run in new equipment, so the failure rate is relatively high; after entering the normal use period, the bearings will enter a relatively long stable period, during which the failure rate is constantly low; after running for a certain period of time, the bearings will inevitably enter the decline period, and the failure rate begins to rise gradually. Among them, the bearing failure change curve, the "bathtub" curve is as Figure 3 shown

[0057] The Weibull cumulative distribution function (CDF) can perfectly represent the three states of the initial stage, normal use period, and decline period of the failure rate changing with time. The CDF is defined as follows (2), different corresponds to the shape factor of different changing trends of the curve is the characteristic life (2) In the formula is the bearing failure probability at a certain moment is the natural constant is the current moment Combining the Weibull cumulative distribution function with the traditional MSE loss function can obtain the Weibull-MSE loss function; the MSE loss function is shown in formula (3), and the Weibull-MSE loss function formula is as shown in (4); (3) ; (4) In the formula is the MSE loss function is the number of time steps is the predicted value is the hybrid loss function is the Weibull cumulative distribution function is the Weibull-MSE loss function is the Weibull loss function is the weight ratio hyperparameter, is the true RUL label value, is the RUL predicted value, is the actual used time of the bearing, is the predicted used time of the bearing; Exemplarily, during the training process of the deep neural network, the Weibull-MSE loss function that combines Weibull and mean square error (MSE) is used as the loss function in the network. The failure probability of the bearing at different times is fused into the Weibull-MSE loss function through the Weibull cumulative distribution function. The Weibull-MSE loss function is combined with the RUL life curve of the bearing health state evaluation method, making the prediction of RUL more in line with the actual degradation process of the bearing.

[0058] S3. Through the convolutional CRATE network architecture that fuses the dilated causal convolutional attention mechanism DCA and the multi-scale convolution MSC, the synchronous extraction of the long-term dependence information and local degradation characteristics of the bearing signal is completed.

[0059] The dilated causal convolutional attention mechanism (DCA) is the multi-head subspace convolutional attention that fuses the dilated causal convolution (DCC) and the CRATE structure, forming the multi-head subspace convolutional sub-attention; through the multi-scale convolution (MSC) module, the ability to extract spatial features is enhanced; Among them, DCA (the dilated causal convolutional attention mechanism) strengthens the ability to extract local features, makes up for the deficiency of the traditional sub-attention mechanism in modeling local degradation information, and ensures that the convolutional CRATE network can accurately capture the short-term change trend of the bearing signal.

[0060] MSC (multi-scale convolution): Add MSC within the basic CRATE structure to extract signal features at different scales, enhance the adaptability to the bearing degradation mode, enable the deep neural network to simultaneously focus on the macroscopic trend and microscopic changes, and improve the comprehensiveness of the prediction.

[0061] Exemplarily, the convolutional CRATE network architecture: adopts a mathematically interpretable optimization objective to make the training and inference processes of the deep neural network transparent, ensuring that the prediction results are more credible and have industrial application value.

[0062] Exemplarily, the synchronous extraction of the long-term dependence information and local degradation characteristics of the bearing signal through the convolutional CRATE network architecture that fuses the dilated causal convolutional attention mechanism (DCA) and the multi-scale convolution (MSC) specifically includes: S301. Construct the dilated causal convolution (DCC). As Figure 4 The schematic diagram of the dilated causal convolution; During the attention calculation process of the Transformer structure, dilated causal convolution (DCC) is adopted to replace the standard self-attention mechanism, so as to improve the ability of the basic CRATE network architecture to capture local features of bearing signals. The specific implementation is as follows: (a) Exponential dilation factor : Ensure that the model can perceive local features of bearing signals at different time scales, taking into account both short-term degradation features and long-term trends.

[0063] (b) Unilateral padding strategy: Ensure the causality of time series data, avoid leakage of future time step information, enable the model to truly simulate the degradation process of bearings, and improve the credibility of prediction.

[0064] Due to the causal characteristics of this convolution, it is required that the features at a certain moment in the next layer can only receive the features at the current moment and the previous moments. Due to this causal limitation, when performing the Padding operation for dilated convolution, in order to keep the sizes of the front and back layers consistent, padding will only be added on one side: Suppose the feature data extracted by the present invention is , where is the total number of time steps, and each represents the bearing feature at the th time step; To complete the convolution operation, the present invention needs to pad data on one side, and the padded sequence is , is the padded data, and the number of is determined by , where is the convolution kernel size, is the dilation factor, is the number of padding ; S302, Embed the multi-scale convolution (MSC) module. As shown in Figure 5 Schematic diagram of the multi-scale convolution module; The multi-scale convolution module is embedded in the main loop block of the CRATE structure, placed after the multi-head subspace convolutional attention and before the iterative shrinkage threshold algorithm (ISTA), so as to fully extract multi-scale features of bearing signals. The specific implementation is as follows: (1) Multi-scale convolution (MSC): After the attention mechanism, convolution kernels of different sizes (such as 1×3, 1×5) are introduced to extract features of different scales in parallel, so as to enhance the model's ability to extract multi-scale spatial information and local features. The convolution kernel size distributions of the 4 parallel extraction routes are 1×1; 1×3 and 1×1; 1×5 and 1×1; 1×2 (pooling) and convolution pool (Branch Pool).

[0065] (2) Feature fusion strategy: Concatenate the output features of different convolutional kernels to simultaneously utilize local information and global trends, and improve the generalization ability of the model.

[0066] Assume the input data dimension is , after feature extraction with different convolutional kernel sizes, four parallel output results are generated. To ensure that the feature dimensions before and after entering the multi-scale convolutional module do not change, as the output of the convolutional pooling, ensures that ; is the sequence length, is the dimension of the first convolutional module, is the dimension of the second convolutional module, is the dimension of the third convolutional module; (5) In the formula, is the output after concatenating multiple convolutional modules, is the concatenation operation, are the outputs of the first, second, third, and fourth convolutional modules, is the selected dimension parameter; (3) ReLU activation function and BatchNorm normalization: Maintain the non-linear expression ability of the network, accelerate convergence, and reduce the gradient vanishing problem. The formula is expressed as follows: (6) In the formula, is the output of the pooling layer, is the layer normalization operation, is the average value operation, is the specified dimension parameter, is the original time series; S303, Regressor optimization and RUL prediction.

[0067] Compared with the traditional CRATE architecture, the present invention has made improvements in the regressor part: To better extract global information, the present invention uses average pooling operation along the time dimension in the regressor to help the model better capture long-term dependence relationships. Assume the input of the regressor is: ; is the input of the regressor at time (i) Adopt average pooling (Mean Pooling): Perform pooling along the time dimension in the regressor to fully extract long-term dependence information and make the RUL prediction more stable.

[0068] (7) In the formula, is the output of the pooling layer, is the layer normalization operation, is the average value operation, is the specified dimension parameter, is the original time series; This operation compresses the original time series Z along the time dimension into a feature vector of a fixed length, that is, by calculating the average value along the time dimension direction, it retains the global feature information of all time steps and enhances the network's capture of long-term information.

[0069] (ii) The fully connected layer outputs the final predicted value: The high-dimensional features are converted into RUL predicted values through linear mapping, improving the model's expressive ability and accuracy.

[0070] (8) In the formula, is the weight matrix of the fully connected layer, is the bias vector of the fully connected layer, is the output of the regressor.

[0071] Since the remaining useful life (RUL) of a rolling bearing is a definite value, while the features extracted and compressed in a deep learning network are usually high-dimensional vectors. To achieve accurate prediction of RUL, it is necessary to map these multi-dimensional features to an RUL value in scalar form through a fully connected layer, so as to complete the regression task of the model and output a clear life prediction result.

[0072] S304. Construct a convolutional CRATE network architecture, as shown in Figure 6 the schematic diagram of the convolutional CRATE network architecture; Principles of the convolutional CRATE network architecture: Through the Coding Rate Reduction principle, high-dimensional input features are mapped to a low-dimensional space, and strict mathematical derivations are carried out on the feature distribution to ensure that each step of feature processing in the model has a clear mathematical basis, enhancing the transparent interpretability of the model for the degradation process. Including: S3041. Coding reduction principle: The CRATE structure is based on the concept of Coding Rate in information theory, aiming to maximize the compression efficiency of meaningful information in the feature space, ensuring that the model only retains the core information related to RUL prediction and reducing redundant and noise interference.

[0073] Define the coding rate of a given feature X in a specific feature space as follows, where is the coding rate after compression of The covariance matrix characterized by represents the correlation between features. is the regularization parameter to prevent numerical instability. is to calculate the log determinant of the specified matrix. (9) In the formula, is the coding rate after compression of. The covariance matrix of the features represents the correlation between features. is the regularization parameter. is to calculate the log determinant of the specified matrix. Based on this principle, the multi-head subspace convolutional attention mechanism and feature sparsification operation of the CRATE structure are derived.

[0074] S3042, perform the transparency of the multi-head subspace convolutional attention mechanism (MSSA).

[0075] The present invention uses an improved multi-head subspace convolutional attention mechanism (MSSA), combined with the coding rate reduction target, to achieve the mathematical inferability of the model attention and improve the transparency of the prediction process.

[0076] First, use the subspace attention mechanism to perform feature decomposition on the input bearing features and compress them into the local signal model subspace: (10) In the formula, is the Query matrix in the self-attention. is the Key matrix in the self-attention. is the Value matrix in the sub-attention. is the th non-overlapping subspace. Secondly, the transparent attention mechanism is calculated as: (11) In the formula, is the multi-head self-attention mechanism. is the kth subspace. is the ith Value matrix. is the activation function. is the ith Query matrix. is the ith Key matrix. is the coding accuracy of the Gaussian codebook. is the feature dimension. is the subspace dimension. The MSSA here is basically similar to the multi-head self-attention operator in the standard Transformer, except that the linear operators are all set to be the same as the subspace basis, that is, ; S3043, feature sparsification based on the ISTA iterative shrinkage threshold algorithm.

[0077] In the convolutional CRATE network architecture, the iterative shrinkage threshold algorithm (ISTA) is used to achieve feature sparsification and retain the key information most relevant to RUL prediction. When the ISTA block receives the output C of the previous module (here referring to the output of the multi-scale convolutional module), ISTA compresses and sparsifies the features through the following iterative update process, defined as follows: (12) where is the output of the ISTA block, is the activation function, is the output of the previous module, is the optimization gradient of the objective optimization function, is the th iteration, is the objective optimization function, is the learning rate.

[0078] As can be seen from the above embodiments, the present invention fully considers the correlation coefficient analysis of time-frequency domain signals for the health state assessment method, and improves the accuracy of degradation stage division by dynamically evaluating the bearing health state.

[0079] A rolling bearing life prediction method that combines the Weibull loss function with the new health state assessment method enables the model to optimize the RUL prediction by combining physical characteristics, improving the prediction accuracy and stability.

[0080] The convolutional white-box Transformer (CRATE) structure is combined, and the local feature extraction ability is enhanced through dilated causal convolution (DCA) and multi-scale convolution (MSC), and the adaptability to bearing degradation modes is improved.

[0081] For the first time, a completely mathematically inferable architecture and a transparent model are applied in the field of rolling bearing remaining life prediction. The CRATE structure is adopted to make the prediction process transparent, improving the interpretability and industrial application value.

[0082] Another exemplary method for evaluating the health state of rolling bearings involves adding common time-frequency domain analysis methods such as wavelet transform and Hilbert-Huang transform to the time-frequency domain analysis means to enhance the feature extraction of vibration signals. In the correlation analysis method, the Pearson correlation coefficient can also be replaced with methods such as cluster analysis, principal component analysis, and dynamic time warping for autocorrelation / cross-correlation / similarity analysis.

[0083] To further illustrate the relevant effects of the embodiments of the present invention, the following experiments are conducted.

[0084] Existing methods usually use fixed degradation curves or simple threshold division to assess the health state of bearings, ignoring individual differences. The present invention dynamically divides the healthy state and the degradation state through the correlation coefficient analysis method of time-frequency domain signals, enabling the model to more accurately capture the true degradation process of bearings and improving the reliability of RUL prediction.

[0085] Most existing deep learning methods use loss functions such as mean squared error (MSE), failing to fully consider the physical degradation laws of bearings, resulting in prediction deviations. The present invention combines Weibull with a new health state evaluation method, fully considering the physical characteristics of rolling bearings and enhancing the model's modeling ability and remaining life prediction accuracy.

[0086] Traditional Transformer structures mainly focus on global information and are difficult to effectively model the local degradation characteristics of bearings. The present invention combines the dilated causal convolutional attention mechanism (DCA) with a multi-scale convolutional module to improve the ability to extract short-term degradation information and make the prediction more accurate.

[0087] Most existing Transformer and deep learning models are "black box" structures, making it difficult to understand their internal decision-making processes and affecting their applications in industrial scenarios. The present invention first introduces the completely mathematically inferable CRATE structure into RUL prediction, making the model optimization process transparent, improving the credibility of prediction results, and providing a more reliable solution for industrial equipment health management.

[0088] The prediction accuracy of the present invention is improved. After obtaining the preprocessed data features, the present invention evaluates the health state of bearings according to the above-mentioned health state division method. See Table 1. Table 1 Bearing health state division

[0089] According to the health state of each bearing divided, the present invention can divide the remaining life labels of each bearing into two parts: a stable state and a rapid decline state. Among them, The stable state is: ; The rapid decline state is as follows: ; In order to more intuitively show the effectiveness of the state division, the present invention compares and shows the original signal corresponding to Bearing1_4, the Person correlation coefficient, and the RUL life curve. Figure 7 It is the health state division and RUL label graph of Bearing1_4, showing the trend consistency between the correlation coefficient curve and the original signal, and transmitting the information to the RUL life curve.

[0090] The prediction results of the present invention for Bearing1_1 to Bearing1_7 are respectively as Figures 8 - 14 shown, and Table 2 shows the specific data. It can be seen from the figure that the method proposed by the present invention has achieved the expected goal on all bearings, distinguished the two working states of the bearings, and accurately extracted the local information near the bearing decline point.

[0091] Table 2 Bearing prediction results

[0092] The above is only a relatively preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modification, equivalent replacement, and improvement made by those skilled in the art within the technical scope disclosed by the present invention, as long as it is made within the spirit and principle of the present invention, shall be covered by the protection scope of the present invention.

Claims

1. A method for predicting the remaining life of a rolling bearing based on convolutional white box, characterized in that: The method comprises the following steps: S1, extract time domain and frequency domain features of the original vibration signal, combine singular value decomposition (SVD) to perform noise reduction processing, remove random noise and interference in the signal, and provide input features; S2, input the processed data into the deep neural network, dynamically evaluate the operation process of the bearing based on the correlation coefficient analysis method, divide the healthy state and the degraded state, and train the deep neural network with the Weibull-MSE loss function to make the RUL prediction consistent with the actual degradation process of the bearing; S3, through the convolutional CRATE network architecture that integrates the dilated causal convolutional attention mechanism DCA and the multi-scale convolution MSC, the synchronous extraction of the long-term dependency information and local degradation features of the bearing signal is completed.

2. The rolling bearing remaining life prediction method based on convolutional white box according to claim 1 is characterized in that: In step S2, based on the correlation coefficient analysis method, the operation process of the bearing is dynamically evaluated, the healthy state and the degraded state are divided, and the deep neural network training is performed in combination with the Weibull-MSE loss function, including: S201, use the Pearson correlation coefficient to calculate the correlation between the features at each moment after SVD compression and the features at the initial moment, and take the moment when the correlation starts to be less than 0.90 as the dividing point of the health state , indicating that the bearing enters the degradation stage from the healthy state; the correlation coefficient is calculated as shown in formula (1): （1） In the formula, for The correlation coefficient of time, for No. Dimension singular values, for No. Dimension singular values, for The average value of the singular value of the extended dimension, for The average of the singular values ​​along the dimension, is the singular value obtained by feature compression at time zero, is the singular value obtained by feature compression at the current moment; S202, constructing a RUL life curve, and dividing the remaining life label of each bearing into two parts: a stable state and a rapid decline state according to the divided health state of each bearing; wherein, The stable state is: ； The rapid decay state is: ； In the formula, For stable state The remaining life of the bearing at that moment, is the total bearing life, is the bearing segmentation point moment, Rapid decline The remaining life of the bearing at that moment, for the current moment; S203, optimize the loss function.

3. The rolling bearing remaining life prediction method based on convolutional white box according to claim 2 is characterized in that: In step S203, the loss function is optimized, including: The Weibull cumulative distribution function CDF is defined as follows: The shape factors corresponding to the different changing trends of the curve, is the characteristic lifespan; （2） In the formula, for The probability of bearing failure at time is a natural constant, for the current moment; Combining the Weibull cumulative distribution function with the traditional MSE loss function can obtain the Weibull-MSE loss function; the MSE loss function is shown in formula (3), and the Weibull-MSE loss function formula is shown in (4); （3） ； （4） In the formula, is the MSE loss function, is the number of time steps, is the predicted value, is the mixed loss function, is the Weibull cumulative distribution function, is the Weibull-MSE loss function, is the Weibull loss function, is the weight ratio hyperparameter, is the real URL label value, is the predicted value of RUL, is the actual bearing usage time, To predict the bearing usage time; During the deep neural network training process, the Weibull-MSE loss function, which is a combination of Weibull and mean square error (MSE), is used as the loss function in the network. The failure probability of the bearing at different times is integrated into the Weibull-MSE loss function through the Weibull cumulative distribution function. The Weibull-MSE loss function is combined with the RUL life curve of the bearing health status assessment method, so that the RUL prediction is consistent with the actual degradation process of the bearing.

4. The rolling bearing remaining life prediction method based on convolutional white box according to claim 1 is characterized in that: In step S3, a convolutional CRATE network architecture is formed by integrating the dilated causal convolutional attention mechanism DCA and the multi-scale convolution MSC, including: the dilated causal convolutional attention mechanism DCA is a multi-head subspace convolutional attention that integrates the dilated causal convolution DCC and the CRATE structure to form a multi-head subspace convolution sub-attention; through the multi-scale convolution MSC module, the ability to extract spatial features is enhanced.

5. The method for predicting the remaining life of a rolling bearing based on a convolutional white box according to claim 4, characterized in that: Complete the simultaneous extraction of the long-term dependence information and local degradation characteristics of the bearing signal, including: S301, constructing the dilated causal convolution DCC. In the attention calculation process of the Transformer structure, the dilated causal convolution DCC is used to replace the standard self-attention mechanism to capture the local features of the bearing signal; S302, embedding a multi-scale convolution MSC module, the multi-scale convolution module is embedded in the main loop block of the CRATE structure, placed after the multi-head subspace convolution attention and before the iterative shrinkage threshold algorithm ISTA, to extract the multi-scale features of the bearing signal; S303, regressor optimization and RUL prediction, using flat pooling operation in the time dimension of the regressor to capture long-term dependencies; S304, construct a convolutional CRATE network architecture.

6. The rolling bearing remaining life prediction method based on convolutional white box according to claim 5 is characterized in that: In step S301, a dilated causal convolution DCC is constructed, including: (a) Exponential Expansion Factor ; (b) One-sided filling strategy, the extracted feature data is ,in, is the total number of time steps, each Representative The bearing features of time steps; to complete the convolution operation, the data is padded on one side, and the padded sequence is , To fill the data, The number of Determine, among which, is the convolution kernel size, is the expansion factor, For filling The number of In step S302, a multi-scale convolutional MSC module is embedded, including: (1) Multi-scale convolution MSC introduces convolution kernels of different sizes after the attention mechanism to extract features of different scales in parallel; (2) Feature fusion strategy, the input data dimension is , after feature extraction with different convolution kernel sizes, generate Four parallel output results; As the output of the convolution pool, ensure ; is the sequence length, is the dimension of convolution module No. 1, is the dimension of convolution module No. 2, is the dimension of convolution module No. 3; （5） In the formula, is the output after concatenation of multiple convolutional modules, For splicing operation, Output of convolution modules 1, 2, 3, and 4. To select dimension parameters; (3) ReLU activation function and BatchNorm normalization, the formula is: （6） In the formula, is the activation function, is the batch normalization operation, It is the output of the multi-scale convolution module.

7. The method for predicting the remaining life of a rolling bearing based on a convolutional white box according to claim 5, characterized in that: In step S303, the input of the regressor is ; for Moment regressor input; (i) Using average pooling, pooling is performed along the time dimension in the regressor to extract long-term dependency information: （7） In the formula, is the output of the pooling layer, is the layer normalization operation, is the average operation, To specify the dimension parameter, is the original time series; (ii) The fully connected layer outputs the final prediction value, converting the high-dimensional features into RUL prediction values ​​through linear mapping: （8） In the formula, is the weight matrix of the fully connected layer, is the bias vector of the fully connected layer, is the output of the regressor.

8. The method for predicting the remaining life of a rolling bearing based on a convolutional white box according to claim 5, characterized in that: In step S304, a convolutional CRATE network architecture is constructed, including: S3041, Coding Reduction Principle, defines a given feature The encoding rate in a specific feature space is as follows: （9） In the formula, for The encoding rate after compression is is the covariance matrix of the features, indicating the correlation between the features. is the regularization parameter, Calculate the logarithmic determinant of the specified matrix; According to the principle of coding reduction, the multi-head subspace convolution attention mechanism and feature sparsification operation of the CRATE structure are derived; S3042, make the improved multi-head subspace convolution attention mechanism MSSA transparent, including: First, the subspace attention mechanism is used to decompose the features and transform the input bearing features into Compression to local signal model The subspace expression is: （10） In the formula, is the Query matrix in self-attention, is the Key matrix in self-attention, is the Value matrix in the sub-attention, For the non-overlapping subspaces; Second, the transparent attention mechanism is calculated as: （11） In the formula, is a multi-head self-attention mechanism, is the kth subspace, is the i-th Value matrix, is the activation function, is the i-th Query matrix, is the i-th Key matrix, is the encoding accuracy of the Gaussian codebook, is the feature dimension, is the subspace dimension; S3043, feature sparsification based on ISTA iterative shrinkage threshold algorithm.

9. The method for predicting the remaining life of a rolling bearing based on a convolutional white box according to claim 8, characterized in that: In step S3043, feature thinning based on the ISTA iterative shrinkage threshold algorithm includes: When the ISTA block receives the output of the previous module When , ISTA compresses and sparses the features through the following iterative update process: （12） In the formula, For the ISTA block output, is the activation function, is the output of the previous module, is the optimization gradient of the target optimization function, For the Iterations, is the target optimization function, is the learning rate.

10. A rolling bearing remaining life prediction system based on convolutional white box, characterized in that: The system implements the rolling bearing remaining life prediction method based on convolution white box as claimed in any one of claims 1 to 9, and the system comprises: The data preprocessing module is used to extract the time domain and frequency domain features of the original vibration signal, and perform noise reduction processing in combination with singular value decomposition (SVD) to remove random noise and interference in the signal and provide input features; The health status assessment module is used to input the processed data into the deep neural network, dynamically evaluate the operation process of the bearing based on the correlation coefficient analysis method, divide the healthy state and the degradation state, and train the deep neural network in combination with the Weibull-MSE loss function to make the RUL prediction consistent with the actual degradation process of the bearing; The feature extraction module completes the simultaneous extraction of long-term dependency information and local degradation features of bearing signals by integrating the convolutional CRATE network architecture of the dilated causal convolutional attention mechanism DCA and the multi-scale convolution MSC.

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