A rolling bearing degradation trend prediction method based on linear regression and TCN
By combining linear regression and TCN, and using sample entropy as a performance indicator, a TCN model is constructed to predict the degradation trend of rolling bearings. This solves the problem of insufficient prediction accuracy of rolling bearings in existing technologies, and achieves accurate and timely prediction of the degradation trend of rolling bearings, thereby improving the accuracy and stability of the prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- KUNMING UNIV OF SCI & TECH
- Filing Date
- 2021-12-21
- Publication Date
- 2026-06-02
AI Technical Summary
In the existing technology, the degradation trend prediction model of rolling bearings has problems such as inconsistent parameter selection and unstable model performance, resulting in insufficient prediction accuracy and failure to detect the initial degradation time of the bearing in a timely manner.
A method combining linear regression and temporal convolutional network (TCN) is adopted. The sample entropy is used as the performance degradation index to construct a TCN model for predicting the degradation trend of rolling bearings. Local weighted regression and VMD decomposition are used for data processing, and causal convolution and residual connection are combined to improve the prediction accuracy.
It enables accurate and timely prediction of the degradation trend of rolling bearings, avoids the subjectivity of manually selecting the window length based on experience, improves the accuracy and stability of prediction, reduces equipment maintenance costs, and ensures the safe operation of equipment.
Smart Images
Figure CN114595525B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of bearing performance degradation assessment, specifically relating to a method for predicting the degradation trend of rolling bearings based on linear regression and TCN. Background Technology
[0002] With the development of control science and various disciplines, mechanical equipment is trending towards complexity, efficiency, and intelligence. Rolling bearings, as key components of most mechanical equipment, especially high-precision equipment like satellites and space shuttles, have particularly high requirements for bearing vibration performance. Analyzing bearing vibration time series provides crucial assurance for the safe operation of equipment. Statistics show that in mechanical equipment containing rolling bearings, the probability of overall equipment failure due to rolling bearing failure is 50%. If the performance degradation of rolling bearings can be assessed, predictive maintenance can prevent disasters, ensuring safety while minimizing equipment maintenance costs. Timely detection of the initial degradation time of bearings is key to predicting degradation trends. In bearing degradation trend prediction, data-driven methods have become the mainstream, with recurrent neural networks (RNNs) being widely used. However, these models contain a large number of parameters, which directly affect model performance, and there are no universally applicable selection criteria for these parameters. The convolutional architecture of Temporal Convolutional Networks (TCNs) outperforms typical recurrent networks (such as LSTM and GRU) on various tasks and datasets, and TCNs are less sensitive to parameter selection than models such as RNNs. This makes TCNs more stable in performance.
[0003] Therefore, this paper proposes a method for predicting the degradation trend of rolling bearings based on linear regression and TCN. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention designs a method for predicting the degradation trend of rolling bearings based on linear regression and TCN. The sample entropy of the rolling bearing is extracted as a performance degradation index, and the degradation index is input into TCN to achieve prediction of the degradation trend of the rolling bearing, thereby improving the prediction accuracy.
[0005] To achieve the above-mentioned technical effects, the present invention is implemented through the following technical solution: a method for predicting the degradation trend of rolling bearings based on linear regression and TCN, characterized in that:
[0006] Step 1: Collect vibration data of the rolling bearing throughout its entire life cycle using an accelerometer, and divide the data according to the sampling time and sampling frequency;
[0007] Step 2: Calculate the sample entropy of each data group after division, as an indicator of rolling bearing performance degradation;
[0008] Step 3: Perform smoothing preprocessing on the sample entropy;
[0009] Step 4: Use a linear regression model to determine the SPT. If the degradation threshold is exceeded multiple times consecutively, it can be determined that the rolling bearing has undergone initial degradation. Analyze the impact of different window lengths on the determination of SPT.
[0010] Step 5: Use VMD decomposition to determine the number of data groups that have experienced initial degradation, and perform envelope spectrum analysis on the data to determine whether the determined SPT is correct;
[0011] Step 6: Construct the TCN model;
[0012] Step 7: Based on the SPT determined in Step 4, divide the data into training and test sets. The data before the SPT point is used as the training set, and the data after the SPT point is used as the test set. Input the data into the model in Step 6 to realize the prediction of the degradation trend of rolling bearings, and use the evaluation function to evaluate the prediction results.
[0013] Furthermore, in Step 1, the sampling time is 1 second, the sampling frequency is 20000 Hz, and the bearing life cycle data is divided into 984 groups, each containing 20480 data points.
[0014] Furthermore, in Step 2, the partitioned matrix is... Where m = 20480, l = 984.
[0015] Furthermore, in Step 3, the smoothing method employs locally weighted regression. In locally weighted regression, the smoothing value is determined using adjacent data points within a given span, and the regression weight W for each data point is calculated. i The calculation method is as follows Where s i Let s be the adjacent elements of s, and d(s) represent the horizontal distance between the farthest values in the span.
[0016] Furthermore, in Step 4, the linear regression model can be expressed as: Where g corresponds to the sample entropy gradient value, d i For the corresponding time t i The value of the sample entropy at time t, where w is the size of the sliding window. The degradation threshold is determined by μ + 3δ, for an approximately normally distributed dataset, let its mean be μ and its variance be σ. 2 The probability that its value is distributed in (μ-3σ,μ+3σ) is 99.73%, and the number of times it exceeds the degradation threshold is 5; the window length is set to 10, 20, 30, 40, and 50.
[0017] Furthermore, in Step 5, the number of decomposition modes of VMD is 7, and envelope spectrum analysis is performed after reconstructing the signal according to the principle of maximum kurtosis.
[0018] Furthermore, in Step 6, the constructed TCN model includes causal convolution, dilated convolution, residual connections, and one-dimensional full convolution; the causal convolution predicts the current time value y. t The output is only related to the current time s t It is related to previous inputs, and to the value s at future time steps. t+1 Irrelevant, can be represented as: y t = f(s1,s2,...,s t ), t=1,2,...,T, where f(·) denotes the convolution operation; for a one-dimensional input s1,s2,...,s T With filter f, the dilated convolution of the sequence can be expressed as:
[0019] Where d is the dilation factor, n is the filter size, and s x- d ·i This represents the product of sequence elements and elements in the convolution kernel; the larger the dilation factor d, the larger the range of the input, thus increasing the receptive field of the convolutional network; to avoid the gradient vanishing problem caused by deep networks, a residual module is introduced in the output layer of the TCN, and the input s is fused into the output y of the convolutional network, which can be expressed as: y=G(s,{W i})+s, where the function G(s,{W i})+s represents learning the residual mapping; one-dimensional full convolution ensures that the lengths of the input and output sequences of TCN remain consistent.
[0020] Furthermore, in Step 7, fully connected layers in the TCN network are used to predict the output; the prediction evaluation metric is the coefficient of determination R. 2 The closer the value is to 1, the better the prediction effect.
[0021] The beneficial effects of this invention are:
[0022] 1. This invention accurately and timely determines the initial degradation time of rolling bearings using linear regression and the μ+3δ degradation threshold adaptive method;
[0023] 2. The impact of different window lengths on determining SPT was analyzed, avoiding the subjectivity of determining SPT due to manual experience in selecting window length;
[0024] 3. This invention predicts the degradation trend of rolling bearings by inputting sample entropy as a performance degradation index into the TCN network model, which greatly improves the accuracy of prediction compared with the current mainstream recurrent neural networks. Attached Figure Description
[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0026] Figure 1 This is a flowchart of the present invention;
[0027] Figure 2 This is a graph reflecting the trend of bearing performance degradation after sample entropy smoothing;
[0028] Figure 3 SPT determined for different window lengths;
[0029] Figure 4 The image shows the results of envelope spectrum analysis for the 525th data set.
[0030] Figure 5 Here is a diagram of the TCN model structure;
[0031] Figure 6 A comparison chart of degradation trends predicted by different prediction models;
[0032] Figure 7 This is a comparison chart of the prediction accuracy of different models. Detailed Implementation
[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0034] Example 1
[0035] See Figures 1 to 7 As shown, a method for predicting the degradation trend of rolling bearings based on linear regression and TCN is characterized by:
[0036] Step 1: Collect vibration data of the rolling bearing throughout its entire life cycle using an accelerometer, and divide the data according to the sampling time and sampling frequency;
[0037] Step 2: Calculate the sample entropy of each data group after division, as an indicator of rolling bearing performance degradation;
[0038] Step 3: Perform smoothing preprocessing on the sample entropy;
[0039] Step 4: Use a linear regression model to determine the SPT. If the degradation threshold is exceeded multiple times consecutively, it can be determined that the rolling bearing has undergone initial degradation. Analyze the impact of different window lengths on the determination of SPT.
[0040] Step 5: Use VMD decomposition to determine the number of data groups that have experienced initial degradation, and perform envelope spectrum analysis on the data to determine whether the determined SPT is correct;
[0041] Step 6: Construct the TCN model;
[0042] Step 7: Based on the SPT determined in Step 4, divide the data into training and test sets. The data before the SPT point is used as the training set, and the data after the SPT point is used as the test set. Input the data into the model in Step 6 to realize the prediction of the degradation trend of rolling bearings, and use the evaluation function to evaluate the prediction results.
[0043] Furthermore, in Step 1, the sampling time is 1 second, the sampling frequency is 20000 Hz, and the bearing life cycle data is divided into 984 groups, each containing 20480 data points.
[0044] Furthermore, in Step 2, the partitioned matrix is... Where m = 20480, l = 984.
[0045] Furthermore, in Step 3, the smoothing method employs locally weighted regression. In locally weighted regression, the smoothing value is determined using adjacent data points within a given span, and the regression weight W for each data point is calculated. i The calculation method is as follows Where s i Let s be the adjacent elements of s, and d(s) represent the horizontal distance between the farthest values in the span.
[0046] Furthermore, in Step 4, the linear regression model can be expressed as: Where g corresponds to the sample entropy gradient value, d i For the corresponding time t i The value of the sample entropy at time t, where w is the size of the sliding window. The degradation threshold is determined by μ + 3δ, for an approximately normally distributed dataset, let its mean be μ and its variance be σ. 2The probability that its value is distributed in (μ-3σ,μ+3σ) is 99.73%, and the number of times it exceeds the degradation threshold is 5; the window length is set to 10, 20, 30, 40, and 50.
[0047] Furthermore, in Step 5, the number of decomposition modes of VMD is 7, and envelope spectrum analysis is performed after reconstructing the signal according to the principle of maximum kurtosis.
[0048] Furthermore, in Step 6, the constructed TCN model includes causal convolution, dilated convolution, residual connections, and one-dimensional full convolution; the causal convolution predicts the current time value y. t The output is only related to the current time s t It is related to previous inputs, and to the value s at future time steps. t+1 Irrelevant, can be represented as: y t = f(s1,s2,...,s t ), t=1,2,...,T, where f(·) denotes the convolution operation; for a one-dimensional input s1,s2,...,s T With filter f, the dilated convolution of the sequence can be expressed as:
[0049] Where d is the dilation factor, n is the filter size, and s x- d·i represents the product of sequence elements and elements in the convolution kernel; the larger the dilation factor d, the larger the range of inputs, thus increasing the receptive field of the convolutional network; to avoid the gradient vanishing problem caused by deep networks, a residual module is introduced in the output layer of the TCN, and the input s is fused into the output y of the convolutional network, which can be expressed as: y=G(s,{W i})+s, where the function G(s,{W i})+s represents learning the residual mapping; one-dimensional full convolution ensures that the lengths of the input and output sequences of TCN remain consistent.
[0050] Furthermore, in Step 7, fully connected layers in the TCN network are used to predict the output; the prediction evaluation metric is the coefficient of determination R. 2 The closer the value is to 1, the better the prediction effect.
[0051] Example 2
[0052] This invention accurately and timely determines the initial degradation time (SPT) of rolling bearings using linear regression and the μ+3δ degradation threshold adaptive method. It analyzes the impact of different window lengths on determining the SPT, avoiding the subjectivity of manually selecting window lengths. Furthermore, by inputting sample entropy as a performance degradation index into the TCN network model, this invention predicts the degradation trend of rolling bearings, significantly improving prediction accuracy compared to current mainstream recurrent neural networks.
[0053] Example 3
[0054] Verification experiment:
[0055] This experiment used a test dataset from the University of Cincinnati's Intelligent Maintenance Systems Center, documenting the progression of rolling bearings from normal operation to failure. The rolling bearings were driven by an AC motor, model Rexnord ZA-2115, and operated at a constant speed of 2000 r / min. The data sampling frequency was 20000 Hz, the sampling time was 1 second, and the sampling interval was 10 minutes. Each dataset consisted of a single file containing 20480 data points. Bearing 1 ended with an outer ring defect; bearing 3 ended with an inner ring defect; and bearing 4 ended with a rolling element defect. This invention focuses on bearing 1, which ultimately failed, as the subject of the experimental study.
[0056] like Figure 2 As shown, the collected bearing life cycle data is divided into 20480×984 groups of data. The sample entropy value of each group of data is calculated, and finally a 1×980-dimensional sample entropy value is obtained as the bearing performance degradation index. Among them, the last four groups of data in the file are discarded because they have entered the severe degradation stage.
[0057] like Figure 3 As shown, when using linear regression to determine the HI gradient, the smaller the sliding window, the larger the calculated sample entropy gradient, and the more sensitive it is to faults. Combining the μ+3σ method will also allow the degradation threshold to be exceeded earlier. Only by selecting an appropriate value can the SPT be accurately determined. Figure 3 The results are shown in the figure with window lengths of 10, 20, 30, 40, and 50. The red line in the figure represents the fault threshold alarm line determined by the 3σ interval. When the bearing is in normal operation, the sample entropy gradient amplitude is small and does not exceed the fault threshold. When the bearing runs to the 525th data set, the sample entropy gradient value first exceeds the fault threshold until the 532nd data set. It is generally recommended to use exceeding the threshold 5 times consecutively as the basis for determining whether the bearing has degraded. Therefore, it is preliminarily determined that bearing 1 degraded in the 525th data set.
[0058] To verify the accuracy of the determined SPT, it was determined whether bearing 1 degraded in group 525. First, data from group 750, representing the severe degradation stage of the bearing, was extracted and subjected to VMD decomposition with 7 decomposition modes. The signal was reconstructed according to the maximum kurtosis criterion, and envelope spectrum analysis was performed on the reconstructed signal. Figure 4 As shown. In the severe degradation stage of the bearing, a frequency component of 230.7 Hz, which is close to the fault characteristic frequency of the outer ring of bearing 1, and the fourth harmonic of the fault characteristic frequency can be found in the envelope spectrum; similarly, the fault characteristic frequency and the fourth harmonic of the fault characteristic frequency are also found in the 525th data set; while the fault characteristic frequency and harmonics do not appear obviously in the envelope spectrum of the 524th data set. Therefore, it can be determined that bearing 1 underwent early degradation in the 525th data set.
[0059] Based on the determined SPT, the data is divided into training and testing sets. The training set data is then input into the TCN model for training. The TCN model structure is as follows: Figure 5 As shown. Where d is the dilation factor, n is the filter size, and s... x-d·i This represents the product of sequence elements and elements in the convolution kernel. A larger dilation factor *d* results in a larger input range, thus increasing the receptive field of the convolutional network. The residual module enables deeper layers to function correctly, thereby improving model performance. The residual module includes two dilated causal convolutional layers with ReLU activation. WeightNorm normalizes weights to speed up training, and Dropout prevents overfitting during training, acting as a regularization mechanism. Furthermore, a one-dimensional fully convolution ensures that the input and output sequences of the TCN maintain consistent lengths. Finally, a fully connected layer is used to predict the output.
[0060] Figure 6 To evaluate the prediction results of bearing degradation trends using TCN, the coefficient of determination (COD) is used. A COD value closer to 1 indicates better prediction performance. The evaluation results are shown below. Figure 7 As shown, from Figure 7 As can be seen, TCN has higher prediction accuracy compared to LSTM and GRU.
[0061] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.
[0062] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims
1. A method for predicting the degradation trend of rolling bearings based on linear regression and TCN, characterized in that: Step 1: Collect vibration data of the rolling bearing throughout its entire life cycle using an accelerometer, and divide the data according to the sampling time and sampling frequency; Step 2: Calculate the sample entropy of each data group after division, as an indicator of rolling bearing performance degradation; Step 3: Perform smoothing preprocessing on the sample entropy; Step 4: Use a linear regression model to determine the SPT and calculate the gradient value g of the sample entropy. The calculation formula is as follows: Among them, t i For time point d i For the corresponding time t i The sample entropy value at time, w is the sliding window size; the degradation threshold is determined by... Sure, Let be the mean of the sample entropy gradient during normal operation. The standard deviation is used; if the gradient value obtained from 5 consecutive calculations exceeds this threshold, the rolling bearing is determined to have undergone initial degradation. The window lengths w are set to 10, 20, 30, 40, and 50, respectively, and the influence of different window lengths on determining the initial degradation time SPT is analyzed. Step 5: Use VMD decomposition to determine the number of data groups that have experienced initial degradation, and perform envelope spectrum analysis on the data to determine whether the determined SPT is correct; Step 6: Construct the TCN model; Step 7: Based on the SPT determined in Step 4, divide the data into training and test sets. The data before the SPT point is used as the training set, and the data after the SPT point is used as the test set. Input the data into the model in Step 6 to realize the prediction of the degradation trend of rolling bearings, and use the evaluation function to evaluate the prediction results.
2. The method for predicting the degradation trend of rolling bearings based on linear regression and TCN according to claim 1, characterized in that: The sampling time in Step 1 is 1 second, the sampling frequency is 20000 Hz, and the bearing life cycle data is divided into 984 groups, each containing 20480 data points.
3. The method for predicting the degradation trend of rolling bearings based on linear regression and TCN according to claim 1, characterized in that: In Step 2, the partitioned matrix is: ,in , .
4. The method for predicting the degradation trend of rolling bearings based on linear regression and TCN according to claim 1, characterized in that: In Step 3, the smoothing method uses locally weighted regression. In locally weighted regression, the smoothing value is determined using adjacent data points within a given span, and the regression weight of each data point is calculated. The calculation method is as follows ,in for Adjacent elements, This represents the horizontal distance between the farthest values in the span.
5. The method for predicting the degradation trend of rolling bearings based on linear regression and TCN according to claim 1, characterized in that: In Step 4, the linear regression model can be expressed as: ,in, Corresponding sample entropy gradient value, For the corresponding time The value of sample entropy at that time, The size of the sliding window; the degradation threshold is determined by... Given an approximately normally distributed dataset, let its mean be... The variance is Then its numerical distribution is in The probability of it being true is 99.73%.
6. The method for predicting the degradation trend of rolling bearings based on linear regression and TCN according to claim 1, characterized in that: In Step 5, the number of decomposition modes of VMD is 7. After reconstructing the signal according to the principle of maximum kurtosis, envelope spectrum analysis is performed.
7. The method for predicting the degradation trend of rolling bearings based on linear regression and TCN according to claim 1, characterized in that: In Step 6, the constructed TCN model includes causal convolution, dilated convolution, residual connections, and one-dimensional fully convolution; the causal convolution predicts the value at the current time step. The output is only related to the current time. Related to previous inputs, and related to future values. Irrelevant can be expressed as: ,in, This represents a convolution operation; for a one-dimensional input... and filters The dilated convolution of a sequence can be represented as: ,in, It is the expansion factor. For filter size, Indicates the product of sequence elements and the elements in the convolution kernel; the expansion factor. The larger the value, the larger the input range, thus increasing the receptive field of the convolutional network; a residual module is introduced into the output layer of the TCN, while simultaneously increasing the input... The output of the convolutional network is fused into the network. In, it can be represented as: , where the function This represents the learning residual mapping.
8. The method for predicting the degradation trend of rolling bearings based on linear regression and TCN according to claim 1, characterized in that: In Step 7, fully connected layers in the TCN network are used to predict the output; the prediction evaluation metric is the coefficient of determination. The closer the value is to 1, the better the prediction effect.