Method for evaluating reliability of rolling bearing under complex working condition
Through the core principal component analysis and Weibull proportional fault model, combined with autoregressive power spectrum fitting and signal feature mapping model, the challenge of rolling bearing reliability evaluation under complex operating conditions is solved, and accurate evaluation and real-time monitoring of rolling bearing performance degradation is achieved. .
Patent Information
- Application Number
- CN202411474935.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-22
- Publication Date
- 2025-02-21
AI Technical Summary
The prior art is difficult to accurately evaluate the reliability of rolling bearings under complex operating conditions, especially in environments where speed and load change simultaneously, the vibration signal is seriously affected, making it difficult to extract characteristic parameters that reflect the actual operating conditions of the bearings.
The core principal component analysis algorithm is used to reduce the dimensionality of the model parameters, combine with the Vibor proportional fault model, build rolling bearing performance degradation indicators, adaptively update the model parameters, and extract the changes in the vibration signal through the signal feature mapping model and autoregressive power spectrum fitting. Feature parameters.
It realizes accurate evaluation of rolling bearing reliability under complex working conditions, eliminates the interference of working conditions on bearing vibration signals, and can accurately characterize the bearing performance degradation process, improving the accuracy and real-time evaluation.
Smart Images
Figure CN119494082A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of rolling bearing reliability assessment, and in particular relates to a rolling bearing reliability assessment method under complex working conditions. Background Art
[0002] Since rolling bearings are used intensively and their operating conditions are complex and changeable, they are prone to performance degradation and failure. The reliability of rolling bearings is often the weak link in the entire mechanical system, and its reliability directly affects the operating conditions of the entire mechanical system. Once an abnormality occurs in the mechanical system, the equipment may be shut down to affect production quality, or even cause major safety accidents such as casualties. Therefore, it is of great significance to monitor the operating status of rolling bearings in real time and accurately evaluate their reliability.
[0003] Most existing research on the running performance of rolling bearings is limited to constant speed and constant load conditions or single variable speed conditions. However, in actual engineering applications, the running environment of rolling bearings is a situation where the speed and load change simultaneously. Faced with such complex conditions, multiple nonlinear factors in the bearing system are coupled with each other, and the collected vibration signals are seriously affected. They have strong time-varying and strong nonlinear characteristics, making it difficult to extract characteristic parameters that reflect the actual running status of the bearings, and the degradation starting point is difficult to identify, which brings challenges to the accurate assessment of the reliability of rolling bearings. Summary of the invention
[0004] In view of the actual operating conditions of rolling bearings and the deficiencies of existing research technologies, the purpose of the present invention is to provide a method for evaluating the reliability of rolling bearings under complex operating conditions. The method uses a kernel principal component analysis algorithm to reduce the dimension of model parameters, constructs a rolling bearing performance degradation index, and combines the Weibull proportional fault model to evaluate the operating reliability of the rolling bearing. The present invention can eliminate the interference of the operating conditions on the bearing vibration signal and realize accurate reliability evaluation.
[0005] The present invention provides a rolling bearing reliability assessment method under complex working conditions, the method comprising the following steps:
[0006] Step 1: Collect the vibration acceleration signal of the rolling bearing during operation under complex working conditions through the data acquisition system.
[0007] Step 2: Perform AR power spectrum fitting on the original vibration signal of the rolling bearing and extract characteristic parameters reflecting the changes of the vibration signal.
[0008] Step 3: Build a signal feature mapping model, adaptively update the model parameters at each moment, and perform a goodness of fit test.
[0009] Step 4: Select model parameters, perform dimensionality reduction through kernel principal component analysis algorithm, and construct degradation indicators.
[0010] Step 5: Evaluate rolling bearing reliability using the Weibull proportional failure model.
[0011] The step 2 further comprises:
[0012] 2.1 Each original vibration signal sequence sample is represented by an autoregressive model:
[0013]
[0014] Among them, s(τ) is the original signal; a m represents the AR model parameters; m represents the model order, m = 1, 2, ..., p; u(τ) represents the mean of 0 and the variance of σ 2 White noise sequence.
[0015] 2.2 Perform autoregressive power spectrum fitting on all collected samples. The autoregressive power spectrum calculation process is:
[0016]
[0017] Among them, a m represents the AR model parameters; m represents the model order, m=1,2,…,p; σ 2 is the variance of the signal white noise sequence.
[0018] 2.3 Extract features from the autoregressive power spectrum of all sample signals. The power spectrum features include power spectrum root mean square, power spectrum mean, power spectrum peak, and power spectrum area. At the same time, calculate the root mean square of the original time domain vibration signal.
[0019] The step 2.2 further comprises:
[0020] 2.2.1 Use the final prediction error criterion to determine the order of the model.
[0021] 2.2.2 Use Burg algorithm to solve model parameters.
[0022] The step 3 further comprises:
[0023] Based on the radial basis neural network, a signal feature mapping model is built with a model structure of 4-8-1. The characteristic parameters extracted from the AR power spectrum are used as the input of the model; the root mean square of the original signal is calculated to characterize the bearing operating state trend as the output of the model, and the accurate fitting of the signal state trend is achieved through multivariate regression.
[0024] The mapping from the input layer to the hidden layer is nonlinear and can be expressed as:
[0025]
[0026] In the formula, is the Gauss function; is the center vector of the Gauss function of the i-th hidden layer node, l is the number of input nodes; b i is the width; ||Xc i || is the Euclidean distance between the input vector and the center. The mapping from the hidden layer to the output layer is the linear superposition of the hidden layer data, which can be expressed as:
[0027]
[0028] In the formula, ω i is the weight from the hidden layer to the output layer.
[0029] The running state trend of the bearing at each moment is predicted, and the minimum prediction error is used as the loss function, which is expressed as:
[0030]
[0031] Where I is the total number of samples; y(i) is the actual value of the i-th sample; is the model output value corresponding to the i-th sample.
[0032] The gradient descent algorithm is used to adaptively update the parameters in the model in real time to minimize the objective function until the expected error is reached. The model parameters include the center and width of the radial basis function of the hidden layer nodes, and the connection weights from the hidden layer to the output layer. The parameter update formula is as follows:
[0033]
[0034] ω i (q) = ω i (q-1)+Δω i (q)+ρ[ω i (q-1)-ω i (q-2)]
[0035] b i (q) = b i (q-1)+Δb i +ρ[b i (q-1)-b i (q-2)]
[0036] c il (q) = c il (q-1)+Δc il +ρ[c il (q-1)-c il (q-2)]
[0037] Among them, λ is the learning rate, λ∈[0,1]; ρ is the momentum factor, ρ=[0,1].
[0038] The step 4 further comprises:
[0039] 4.1 Extract the parameters in the signal feature mapping model and select the parameters that can well characterize the performance degradation trend of the rolling bearing as the target feature parameters.
[0040] 4.2 The kernel principal component algorithm is used to reduce its dimension, and the first principal component with a contribution rate of more than 90% is selected as the bearing performance degradation indicator.
[0041] The step 5 further comprises:
[0042] 5.1 Select the Weibull distribution function as the basis function of the proportional failure model to evaluate the reliability of rolling bearings. The failure rate function can be expressed as:
[0043]
[0044] Among them, t is time; β is the shape parameter; η is the scale parameter; γ is the covariate regression coefficient; Z is the state characteristic monitoring quantity.
[0045] The reliability function is:
[0046]
[0047] 5.2 Solve the model parameters to calculate the rolling bearing reliability.
[0048] Let θ = {β, η, γ}, use the maximum likelihood method to estimate the model parameters, and after collecting the monitoring data, the joint probability density function can be obtained as:
[0049]
[0050] In the formula, F is the failure sample set, and D is the total sample set. Taking the logarithm of both sides of the likelihood function, we can get:
[0051]
[0052] Where, d f is the number of failed data; d is the total number of data. According to the maximum likelihood estimation principle, taking the partial derivative of lnL(θ) with respect to β, η, and γ respectively can obtain a nonlinear equation system:
[0053]
[0054] By solving the nonlinear equations and determining the unknown parameters, the parameters are introduced into the Weibull proportional fault model to obtain the reliability at any time.
[0055] Further, step 5.2 includes:
[0056] The Gray Wolf optimization algorithm is used to solve the parameters of the Weibull proportional fault model. The model parameters are substituted into the Weibull proportional fault model, and the bearing reliability evaluation is completed based on the constructed bearing degradation index.
[0057] The beneficial effects of the present invention are:
[0058] 1. The present invention is the first to evaluate the operating reliability of rolling bearings under complex working conditions of variable speed and variable load.
[0059] 2. The present invention performs autoregressive power spectrum fitting on the bearing vibration signal and extracts multiple features therefrom, which fully characterizes the randomness, nonlinearity and non-stationary characteristics of the rolling bearing vibration signal under complex working conditions.
[0060] 3. The present invention proposes a signal feature mapping model based on autoregressive power spectrum characteristics and radial basis neural network, and constructs a new type of degradation index based on model parameters. The signal feature mapping model parameters are used to characterize the bearing performance status, and the selected model parameters are reduced in dimension through the kernel principal component analysis algorithm for accurate and real-time evaluation of the reliability of the bearing under operating conditions. The present invention can accurately characterize the performance degradation process of rolling bearings under complex working conditions, eliminate the interference of complex working conditions on rolling bearing signals, and achieve accurate evaluation of rolling bearing reliability. BRIEF DESCRIPTION OF THE DRAWINGS
[0061] Figure 1 It is the overall flow chart of the present invention;
[0062] Figure 2 This is the autoregressive power spectrum of the rolling bearing full life cycle signal in the experiment of the present invention;
[0063] Figure 3 It is the autoregressive power spectrum feature map extracted in the experiment of the present invention;
[0064] Figure 4 It is the RMS diagram of the original time domain signal over the entire life cycle in the experiment of the present invention;
[0065] Figure 5 This is a structural diagram of the signal feature mapping model of the present invention;
[0066] Figure 6 This is a diagram of the model prediction results in the experiment of the present invention;
[0067] Figure 7 It is the model parameter diagram in the experiment of the present invention;
[0068] Figure 8 It is a degradation index diagram in the experiment of the present invention;
[0069] Fig. 9 This is a full life cycle reliability curve of the bearing in the experiment of the present invention. DETAILED DESCRIPTION
[0070] The present invention is further described below by combining the accompanying drawings and specific embodiments. The described embodiments are only part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of this application.
[0071] The present invention provides a method for evaluating the reliability of rolling bearings under complex working conditions. Figure 1 , specifically including the following steps:
[0072] Step 1: Collect the vibration acceleration signal of the rolling bearing during operation under complex working conditions through the data acquisition system.
[0073] The rolling bearing operating conditions are complex conditions where the speed and load change simultaneously, with a change cycle of 360 minutes. In the first 120 minutes, the speed is set to be constant at 1575r / min, and the radial load is set to be constant at 16kN (the load will fluctuate slightly due to the influence of the hydraulic oil flow). In the middle 120 minutes, the speed is set to change in a sinusoidal law from 1260r / min to 1890r / min, and the radial load is set to change in a sinusoidal law from 13kN to 19kN, which is 180° phase angle away from the speed; in the last 120 minutes, the speed is set to change randomly from 1260r / min to 1890r / min, and the radial load is set to change randomly from 13kN to 19kN. The test bearing model is HRB 6306-2RZ. The sampling frequency is set to 10240Hz, the sampling interval is set to 10 minutes, the sampling time is 2 seconds, and each sample contains 20480 data points.
[0074] Step 2: Perform AR power spectrum fitting on the original vibration signal of the rolling bearing and extract characteristic parameters reflecting the changes of the vibration signal.
[0075] 2.1 Each original vibration signal sequence sample is represented by an autoregressive model:
[0076]
[0077] Among them, s(τ) is the original signal; a m represents the AR model parameters; m represents the model order, m = 1, 2, ..., p; u(τ) represents the mean of 0 and the variance of σ 2 White noise sequence.
[0078] 2.2 Perform autoregressive power spectrum fitting on all collected samples. The autoregressive power spectrum calculation process is:
[0079]
[0080] Among them, a m represents the AR model parameters; m represents the model order, m=1,2,…,p; σ 2 is the variance of the signal white noise sequence.
[0081] 2.2.1 Use the final prediction error criterion to determine the order of the model.
[0082] 2.2.2 Use Burg algorithm to solve model parameters.
[0083] The power spectrum of all signal samples during the entire life cycle of the rolling bearing is as follows: Figure 2 shown.
[0084] 2.3 Extract features from the autoregressive power spectrum of all sample signals. Extract power spectrum features according to Table 1, including power spectrum root mean square, power spectrum mean, power spectrum peak, and power spectrum area, such as Figure 3 (a)-(d) are shown. At the same time, the original time domain vibration signal root mean square is calculated as follows Figure 4 shown.
[0085] Table 1 Vibration signal power spectrum characteristic indicators
[0086]
[0087] Note: S k is the power spectrum sequence of the signal; K is the number of spectral lines; f k is the frequency value of the kth spectral line.
[0088] Step 3: Build a signal feature mapping model, adaptively update the model parameters at each moment, and perform a goodness of fit test.
[0089] Based on the radial basis neural network, a signal feature mapping model is built. The model structure is 4-8-1. The model structure is as follows Figure 5 The characteristic parameters extracted from the AR power spectrum are used as the input of the model; the root mean square of the original signal is calculated to characterize the trend of the bearing operation status, which is used as the output of the model, and the accurate fitting of the signal status trend is achieved through multivariate regression.
[0090] The mapping from the input layer to the hidden layer is nonlinear and can be expressed as:
[0091]
[0092] In the formula, is the Gauss function; is the center vector of the Gauss function of the i-th hidden layer node, l is the number of input nodes; b i is the width; ||Xc i || is the Euclidean distance between the input vector and the center. The mapping from the hidden layer to the output layer is the linear superposition of the hidden layer data, which can be expressed as:
[0093]
[0094] In the formula, ω i is the weight from the hidden layer to the output layer.
[0095] The running state trend of the bearing at each moment is predicted, and the minimum prediction error is used as the loss function, which is expressed as:
[0096]
[0097] Where I is the total number of samples; y(i) is the actual value of the i-th sample; is the model output value corresponding to the i-th sample.
[0098] The gradient descent algorithm is used to adaptively update the parameters in the model in real time to minimize the objective function until the expected error is reached. The model parameters include the center and width of the radial basis function of the hidden layer nodes, and the connection weights from the hidden layer to the output layer. The parameter update formula is as follows:
[0099]
[0100] ω i (q) = ω i (q-1)+Δω i (q)+ρ[ω i (q-1)-ω i (q-2)]
[0101] b i (q) = b i (q-1)+Δb i +ρ[b i (q-1)-b i (q-2)]
[0102] c il (q) = c il (q-1)+Δc il +ρ[c il (q-1)-c il (q-2)]
[0103] Among them, λ is the learning rate, λ∈[0,1]; ρ is the momentum factor, ρ=[0,1].
[0104] The model fitting effect is as follows Figure 6 shown.
[0105] Step 4: Select model parameters, perform dimensionality reduction through kernel principal component analysis algorithm, and construct degradation indicators.
[0106] The width of the hidden layer radial basis function changes as follows Figure 7 As shown in . Its early fluctuation is smaller and its monotonicity is stronger, showing a trend consistent with the rolling bearing performance degradation. The width of the radial basis is selected as the target parameter to characterize the bearing performance degradation. The kernel principal component analysis algorithm is used to reduce its dimension, and the first principal component with a contribution of more than 90% is selected as the rolling bearing performance degradation indicator. After normalization, it is as follows Figure 8 shown.
[0107] Compared with the original signal RMS, the constructed degradation index is not seriously affected by the change of working conditions, and the amplitude of the fault sample relative to the normal sample is enhanced, reaching the maximum value at the moment of bearing failure, with a slight mutation near 1130, and a significant increase in its amplitude can be observed near 1160. The early degradation position can be intuitively found through its mutation point. The constructed degradation index can better reflect the real operating status of the rolling bearing.
[0108] Step 5: Evaluate rolling bearing reliability using the Weibull proportional failure model.
[0109] 5.1 Select the Weibull distribution function as the basis function of the proportional failure model to evaluate the reliability of rolling bearings. The failure rate function can be expressed as:
[0110]
[0111] Among them, t is time; β is the shape parameter; η is the scale parameter; γ is the covariate regression coefficient; Z is the state characteristic monitoring quantity.
[0112] The reliability function is:
[0113]
[0114] 5.2 Solve the model parameters to calculate the rolling bearing reliability.
[0115] Let θ = {β, η, γ}, use the maximum likelihood method to estimate the model parameters, and after collecting the monitoring data, the joint probability density function can be obtained as:
[0116]
[0117] In the formula, F is the failure sample set, and D is the total sample set. Taking the logarithm of both sides of the likelihood function, we can get:
[0118]
[0119] Where, d f is the number of failed data; d is the total number of data. According to the maximum likelihood estimation principle, taking the partial derivative of lnL(θ) with respect to β, η, and γ respectively can obtain a nonlinear equation system:
[0120]
[0121] By solving the nonlinear equations and determining the unknown parameters, the parameters are introduced into the Weibull proportional fault model to obtain the reliability at any time.
[0122] The model parameters are obtained by solving the likelihood equation using the Grey Wolf optimization algorithm. Substituting the parameters into the WPHM, the rolling bearing reliability curve is obtained as follows: Fig. 9 As shown. Due to the coupling of multiple faults in rolling bearings under complex working conditions, the rate of decline of their reliability increases. In the early degradation stage, its reliability fluctuates slightly. When the degradation degree increases, its reliability fluctuates significantly. At the failure point, the calculated reliability value is 0.13%, which is close to 0, and the bearing reliability is accurately evaluated. The effectiveness of the method proposed in the present invention is proved.
Claims
1. A rolling bearing reliability assessment method under complex working conditions, characterized in that: The method comprises the following steps: Step 1: Collect the vibration acceleration signal of the rolling bearing during operation under complex working conditions through the data acquisition system; Step 2: Perform AR power spectrum fitting on the original vibration signal of the rolling bearing and extract characteristic parameters reflecting the change of the vibration signal; Step 3: Build a signal feature mapping model, adaptively update the model parameters at each moment, and perform a goodness of fit test; Step 4: Select model parameters, perform dimensionality reduction through kernel principal component analysis algorithm, and construct degradation indicators; Step 5: Evaluate rolling bearing reliability using the Weibull proportional failure model.
2. The method for evaluating the reliability of rolling bearings under complex working conditions according to claim 1, characterized in that: In step 1, the rolling bearing operating conditions are variable speed and variable load.
3. The method for evaluating the reliability of rolling bearings under complex working conditions according to claim 1, characterized in that: The implementation process of step 2 is: 2.1 Each original vibration signal sequence sample is represented by an autoregressive model: Among them, s(τ) is the original signal; a m represents the AR model parameters; m represents the model order, m = 1, 2, ..., p; u(τ) represents the mean of 0 and the variance of σ 2 White noise sequence; 2.2 Perform autoregressive power spectrum fitting on all collected samples; the autoregressive power spectrum calculation process is: Among them, a m represents the AR model parameters; m represents the model order, m=1,2,…,p; σ 2 is the variance of the signal white noise sequence; 2.3 Perform feature extraction on the autoregressive power spectrum of all sample signals; the power spectrum features include power spectrum root mean square, power spectrum mean, power spectrum peak, and power spectrum area; and calculate the root mean square of the original time domain vibration signal at the same time.
4. The method for evaluating the reliability of rolling bearings under complex working conditions according to claim 3, characterized in that: Step 2.2 includes: 2.2.1 Determine the order of the model using the final prediction error criterion; 2.2.2 Use Burg algorithm to solve model parameters.
5. The method for evaluating the reliability of rolling bearings under complex working conditions according to claim 1, characterized in that: Step 3 builds a signal feature mapping model, and the process includes: Based on the radial basis function neural network, a signal feature mapping model is built with a model structure of 4-8-1. The feature parameters extracted from the AR power spectrum are used as the input of the model. The root mean square of the original signal is calculated to characterize the trend of the bearing operation status, which is used as the output of the model. The accurate fitting of the signal status trend is achieved through multivariate regression. The mapping from the input layer to the hidden layer is nonlinear and can be expressed as: In the formula, is the Gauss function; is the center vector of the Gauss function of the i-th hidden layer node, l is the number of input nodes; b i is the width; ||Xc i || is the Euclidean distance between the input vector and the center; the mapping from the hidden layer to the output layer is the linear superposition of the hidden layer data, which can be expressed as: In the formula, ω i is the weight from the hidden layer to the output layer; The running state trend of the bearing at each moment is predicted, and the minimum prediction error is used as the loss function, which is expressed as: Where I is the total number of samples; y(i) is the actual value of the i-th sample; is the model output value corresponding to the i-th sample; The gradient descent algorithm is used to adaptively update the parameters in the model in real time to minimize the objective function until the expected error is reached; the model parameters include the center and width of the radial basis function of the hidden layer nodes, and the connection weight from the hidden layer to the output layer; the parameter update formula is as follows: oh i (q)=ω i (q-1)+Do i (q)+ρ[ω i (q-1)-ω i (q-2)] b i (q)=b i (q-1)+Δb i +ρ[b i (q-1)-b i (q-2)] c il (q)=c il (q-1)+Δc il +ρ[c il (q-1)-c il (q-2)] Among them, λ is the learning rate, λ∈[0,1]; ρ is the momentum factor, ρ=[0,1].
6. The method for evaluating the reliability of rolling bearings under complex working conditions according to claim 1, characterized in that: The degradation index construction process in step 4 includes: 4.1 Extract the parameters in the signal feature mapping model and select the parameters that can well characterize the performance degradation trend of the rolling bearing as the target feature parameters; 4.2 The kernel principal component algorithm is used to reduce its dimension, and the first principal component with a contribution rate of more than 90% is selected as the bearing performance degradation indicator.
7. The method for evaluating rolling bearing reliability under complex working conditions according to claim 1, characterized in that: The bearing reliability assessment process in step 5 includes: 5.1 Select the Weibull distribution function as the basis function of the proportional failure model to evaluate the reliability of rolling bearings. The failure rate function can be expressed as: Among them, t is time; β is the shape parameter; η is the scale parameter; γ is the covariate regression coefficient; Z is the state characteristic monitoring quantity; The reliability function is: 5.2 Solve the model parameters to calculate the rolling bearing reliability; Let θ = {β, η, γ}, use the maximum likelihood method to estimate the model parameters, and after collecting the monitoring data, the joint probability density function can be obtained as: In the formula, F is the failure sample set, and D is the total sample set. Taking the logarithm of both sides of the likelihood function, we can get: Where, d f is the number of failure data; d is the total number of data; according to the maximum likelihood estimation principle, taking the partial derivative of lnL(θ) with respect to β, η, and γ respectively can obtain the nonlinear equation system: By solving the nonlinear equations and determining the unknown parameters, the parameters are introduced into the Weibull proportional fault model to obtain the reliability at any time.
8. The method for evaluating the reliability of rolling bearings under complex working conditions according to claim 7, characterized in that: Step 5.2 uses the Grey Wolf optimization algorithm to solve the Weibull proportional fault model parameters; substitute the model parameters into the Weibull proportional fault model, and complete the bearing reliability evaluation based on the constructed bearing degradation index.