Rolling bearing reliability evaluation and prediction method based on hybrid noise reduction and MKRVM

Abstract

The invention discloses a rolling bearing reliability evaluation and prediction method based on hybrid noise reduction and MKRVM, and the method comprises the steps: obtaining the vibration signal data of the whole life of a rolling bearing; carrying out mixed noise reduction on the vibration signal by using maximum kurtosis deconvolution improved by an intrinsic time scale decomposition algorithm ITD and an arithmetic optimization algorithm to obtain a vibration signal subjected to secondary noise reduction; respectively carrying out feature extraction on the vibration signal subjected to secondary noise reduction by using three feature extraction methods, namely a time domain feature extraction method, a frequency domain feature extraction method and a time-frequency domain feature extraction method; forming a feature vector set by the respectively extracted features; a stacked auto-encoder dimension reduction method and a logistic regression reliability evaluation model are adopted to obtain a reliability curve for evaluating the current bearing; inputting the feature vector set into a bearing reliability prediction model for constructing a hybrid kernel relevance vector machine, and predicting bearing degradation features to obtain predicted degradation features; and the predicted degradation characteristics are embedded into the logistic regression reliability evaluation model to obtain a bearing reliability prediction curve with higher precision.

Description

Technical Field

[0001] The present invention relates to the field of fault prediction and health management, and in particular to a method for evaluating and predicting the reliability of a rolling bearing based on hybrid noise reduction and MKRVM. Background Art

[0002] Reliability assessment and prediction of bearings is an important area of ​​reliability research. Reliability assessment of bearings can help us better understand the operating conditions of bearings, and reliability prediction of bearings can predict the failure time of bearings, providing important prompt information for equipment maintenance and avoiding accidents. However, the cost of reliability analysis through physical objects is huge and the process is complicated. Therefore, the vibration signals collected by smart sensors can be analyzed, and the reliability analysis of bearings can be carried out with the help of machine learning methods, which can effectively control costs and improve efficiency. The vibration signal of rolling bearings contains a lot of effective information about the bearings. However, in engineering practice, the operation of mechanical equipment will generate a lot of noise signals. In addition, the signal will generate noise due to various factors during acquisition, transmission and subsequent processes, which will cause great inconvenience to the monitoring of the equipment and will also affect the judgment of the bearing status.

[0003] The reliability assessment methods of bearings mainly include statistical methods and artificial intelligence model-based methods. The statistical method requires the use of a large number of bearing samples combined with operating parameters such as ambient temperature, humidity, load and stress during operation to construct a bearing reliability assessment model; in actual working conditions, since the load and speed of the bearing are uncertain, it is very difficult to use traditional statistical methods to assess the reliability of the bearing. Summary of the invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a method for evaluating and predicting the reliability of rolling bearings based on hybrid denoising and MKRVM, and accurately evaluates the reliability of rolling bearings based on the hybrid denoising method and the stacked autoencoder-logistic regression bearing reliability evaluation method; a reliability prediction model based on a hybrid kernel correlation vector machine is proposed to predict future bearing reliability and improve the accuracy of the prediction.

[0005] Technical solution: To achieve the above purpose, the method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM of the present invention comprises the following steps:

[0006] Step 1: Obtain vibration signal data of the rolling bearing over its entire lifespan; use the intrinsic time scale decomposition algorithm ITD to decompose the vibration signal to obtain several PR components;

[0007] Step 2: A hybrid evaluation index combining fine composite multi-scale scatter entropy, Pearson correlation coefficient and root mean square error value is used to screen several PR components, and the screened PR components are reconstructed to obtain a primary denoised vibration signal; the primary denoised vibration signal is subjected to secondary denoising through maximum kurtosis deconvolution improved by an arithmetic optimization algorithm to obtain a secondary denoised vibration signal containing effective information;

[0008] Step 3, using three feature extraction methods in time domain, frequency domain and time-frequency domain to extract time domain features, frequency domain features and time-frequency domain features of the secondary noise reduction vibration signal respectively, and the extracted features constitute a feature vector set;

[0009] Step 4: Use the stacked autoencoder dimensionality reduction method to reduce the parameters of the feature vector set, and use the reduced-dimensional feature vector set as degradation feature information to input the constructed logistic regression reliability assessment model to obtain a reliability curve for evaluating the current bearing;

[0010] Step 5. Input the feature vector set into the bearing reliability prediction model constructed by the hybrid kernel correlation vector machine, predict the bearing degradation characteristics to obtain the predicted degradation characteristics; embed the predicted degradation characteristics into the logistic regression reliability assessment model to obtain the bearing reliability prediction curve.

[0011] Furthermore, in the step 2, the mixed evaluation index K of PR is obtained by combining the fine composite multi-scale spread entropy, the Pearson correlation coefficient and the root mean square error value. The calculation process of the K value of the i-th PR component is as follows:

[0012]

[0013] In the formula, is the Pearson correlation coefficient between the original vibration signal and , is the root mean square error between the original vibration signal and several PR components, RCMDE i is the fine composite multi-scale scatter entropy of the i-th PR component, L is the number of PR components, x is the original vibration signal, x i is the i-th PR component;

[0014] Calculate the K values ​​corresponding to several PR components, and calculate the average value of all K values ​​as T; select the PR component whose K value is greater than T as the screened PR component;

[0015]

[0016] Furthermore, the calculation process of calculating the PR component fine composite multi-scale spread entropy is as follows:

[0017]

[0018] Where P k is the probability value of the spread entropy corresponding to the kth coarse-grained sequence; X is the input signal; m is the embedding dimension; c is the number of categories into which the data is divided; d represents the delay; τ is the scale factor during division;

[0019] The Pearson correlation coefficient between the original vibration signal and the PR component The calculation process is as follows:

[0020]

[0021] Among them, cov(x,x i ) represents x and x i The covariance between x and are the sample mean differences between the original vibration signal and the i-th PR component after decomposition;

[0022] The root mean square error RMSE between the original vibration signal and the PR component is calculated as follows:

[0023]

[0024] Where N is the number of sample points in the vibration signal.

[0025] Furthermore, in step 4, the i-th dimension feature vector set at time t is set to X i (t)=(x1(t),x2(t),...,x i (t)), X i (t)=(x1(t),x2(t),...,x i (t)) Input the reliability solution formula, set y(t) = 0 for the normal operation of the bearing at time t, and y(t) = 1 for the failure of the bearing at time t; input the eigenvalue into the sigmoid function, and input the reliability solution formula of the i-th dimension eigenvector set at time t as follows:

[0026]

[0027] In the formula, β0, β1, β2,…,β i is the regression coefficient of the feature vector set;

[0028] Transform the reliability solution formula to obtain:

[0029]

[0030] Let C=β0, β1, β2,...,β i Substituting the above formula into the regression coefficient, we can solve the equation as follows:

[0031]

[0032] The gradient descent method is used to solve the regression coefficient solution equation to obtain the regression coefficient of the feature vector set. The regression coefficient is substituted into the reliability solution formula to obtain the logistic regression reliability assessment model.

[0033] Furthermore, in step 5, the bearing reliability prediction model of the hybrid kernel relevance vector machine uses the local Laplace kernel function and the global linear kernel as kernel functions, and uses the linear weighted combination of the kernel functions to combine the local Laplace kernel function and the global linear kernel to obtain the hybrid kernel function H; the calculation process is as follows:

[0034]

[0035] H=pH1+(1-p)H2

[0036] Where p is the weight coefficient of the kernel function, 0≤p≤1, and δ is the width of the kernel function.

[0037] Furthermore, the hybrid kernel function is substituted into the relevance vector machine to obtain the hybrid kernel function relevance vector machine MKRVM; the parameters of the kernel function are trained according to the nonlinear mapping relationship between the input data and the output data, and the bearing reliability prediction model of the hybrid kernel relevance vector machine is constructed; the training samples are set to be input {x n} N and the target value {t n} N The correspondence between the input and target values ​​in the hybrid kernel correlation vector machine is constructed and the calculation process is as follows:

[0038]

[0039] Where ω is the weight vector of the model, H is the hybrid kernel function, ε is the offset, and N is the total number of training samples.

[0040] Furthermore, the Bayesian theory is used to add constraints to the weight vector ω, and each weight vector ω is defined as a vector with zero mean. The Gaussian prior probability distribution formula is as follows:

[0041]

[0042] In the formula, α=[α0, α1,...,α N ] T is a hyperparameter vector, each hyperparameter corresponds to a weight vector, and the weight vectors are independently distributed;

[0043] The posterior distribution weight of the weight vector ω is obtained by the Bayesian formula, and the calculation process is as follows:

[0044]

[0045] In the formula, ∑=(σ -2 Φ T Φ+C) is the covariance matrix, μ=σ -2 ∑Φ T t is the posterior matrix of the target value, C represents the main diagonal elements α = [α0, α1, ..., α N ] T The matrix of .

[0046] Furthermore, the hyperparameters α and σ 2 , so that the hyperparameters are uniformly defined as follows:

[0047]

[0048] E=σ 2 I+ΦC -1 Φ T .

[0049] The hyperparameters α and σ of the hybrid kernel function related vector machine are adjusted by an iterative algorithm. 2 Solve for the hyperparameters α and σ 2 Perform iterative calculations until the convergence conditions are met. The calculation process is as follows:

[0050]

[0051] Where M ii is the i-th diagonal element of the covariance matrix.

[0052] Beneficial effects: The method for evaluating and predicting the reliability of rolling bearings based on hybrid denoising and MKRVM of the present invention can remove redundant noise in the bearing vibration signal through secondary denoising to obtain data containing a large amount of effective signals; three extraction methods in time domain, frequency domain and time-frequency domain are used to extract features of the denoised vibration signal and form a feature vector set, and the stacked autoencoder SAE dimension reduction method is used to reduce the parameters of the vector set, which can greatly improve the computational efficiency of the reliability evaluation model; a MKRVM reliability prediction model based on a hybrid kernel correlation vector machine is used to predict the bearing operating status through the model, and the prediction results are input into a logistic regression reliability evaluation model to obtain the bearing reliability prediction results; the error of the bearing reliability prediction results is small, and the prediction accuracy is further improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The overall flow chart of the method for reliability assessment and prediction of rolling bearings;

[0054] Figure 2 It is the time domain characteristic diagram of the bearing;

[0055] Figure 3 is the frequency domain characteristic diagram of the bearing;

[0056] Figure 4 It is the time-frequency domain characteristic diagram of the bearing;

[0057] Figure 5 It is the feature map after dimensionality reduction of multi-dimensional features;

[0058] Figure 6 This is the bearing reliability curve. DETAILED DESCRIPTION

[0059] The present invention will be further described below in conjunction with the accompanying drawings.

[0060] like Figure 1 As shown, the method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM includes the following steps:

[0061] Step 1: Obtain vibration signal data of the rolling bearing over its entire lifespan; use the intrinsic time scale decomposition algorithm ITD to decompose the vibration signal to obtain several PR components;

[0062] Step 2: A hybrid evaluation index combining fine composite multi-scale scatter entropy, Pearson correlation coefficient and root mean square error value is used to screen several PR components, and the screened PR components are reconstructed to obtain a primary denoised vibration signal; the primary denoised vibration signal is subjected to secondary denoising through maximum kurtosis deconvolution improved by an arithmetic optimization algorithm to obtain a secondary denoised vibration signal containing effective information;

[0063] Step 3, using three feature extraction methods in time domain, frequency domain and time-frequency domain to extract time domain features, frequency domain features and time-frequency domain features of the secondary noise reduction vibration signal respectively, and the extracted features constitute a feature vector set;

[0064] Step 4: Use the stacked autoencoder dimensionality reduction method to reduce the parameters of the feature vector set to obtain a reduced-dimensional feature vector set, and use the reduced-dimensional feature vector set as the degradation feature information input to construct a logistic regression reliability assessment model for evaluation, so as to obtain a reliability curve for evaluating the current bearing, thereby evaluating the reliability of the current rolling bearing;

[0065] Step 5. Input the feature vector set into the bearing reliability prediction model constructed by the hybrid kernel correlation vector machine, predict the bearing degradation characteristics to obtain the predicted degradation characteristics; embed the predicted degradation characteristics into the logistic regression reliability assessment model to obtain the bearing reliability prediction curve, and then predict the reliability of the rolling bearing in the future.

[0066] In the step 2, the calculation process of calculating the PR component fine composite multi-scale spread entropy is as follows:

[0067]

[0068]

[0069] Where P k is the probability value of the spread entropy corresponding to the kth coarse-grained sequence; X is the input signal; m is the embedding dimension; c is the number of categories into which the data is divided; d represents the delay; τ is the scale factor during division;

[0070] The Pearson correlation coefficient between the original vibration signal and the PR component The calculation process is as follows:

[0071]

[0072] Among them, cov(x,x i ) represents x and x i The covariance between x and are the sample mean differences between the original vibration signal and the i-th PR component after decomposition;

[0073] The root mean square error RMSE represents the deviation between the measured value and the sample value. The lower the value, the smaller the deviation value. The root mean square error RMSE between the original vibration signal and the PR component is calculated as follows:

[0074]

[0075] Where N is the number of sample points in the vibration signal.

[0076] The mixed evaluation index K of PR is obtained by combining the fine composite multi-scale scatter entropy, Pearson correlation coefficient and root mean square error value. The complexity of the signal, the correlation with the original signal and the deviation value can be comprehensively considered to screen out the PR components with more effective information. Since the number of PR components obtained by decomposing each signal is different, the number of screened components is also different. The calculation process of the K value of the i-th PR component is as follows:

[0077]

[0078] In the formula, is the Pearson correlation coefficient between the original vibration signal and , is the root mean square error between the original vibration signal and several PR components, RCMDE i is the fine composite multi-scale scatter entropy of the i-th PR component, L is the number of PR components, x is the original vibration signal, x i is the i-th PR component;

[0079] Calculate the K values ​​corresponding to several PR components, and calculate the average value of all K values ​​as T; select the PR component whose K value is greater than T as the screened PR component;

[0080]

[0081] The filtered PR components are reconstructed to obtain a vibration signal with primary denoising. The maximum kurtosis deconvolution is improved by an arithmetic optimization algorithm. The key parameters of the MCKD, the displacement number M and the filter length L, are optimized by the arithmetic optimization algorithm. That is, the improved MCKD algorithm performs secondary denoising on the vibration signal with primary denoising to obtain a vibration signal with secondary denoising containing effective information.

[0082] In the step three, the time domain features include standard deviation, kurtosis, root mean square, impulse factor, variance and rectified mean; the frequency domain features include spectral skewness, spectral kurtosis, spectral variance, spectral mean, mean square frequency, centroid frequency domain, frequency domain feature parameter 1, frequency domain feature parameter 2 and frequency domain feature parameter 3; the time-frequency domain features include wavelet packet entropy and singular value entropy; all features such as standard deviation, kurtosis, root mean square, impulse factor, variance, rectified mean, spectral skewness, spectral kurtosis, spectral variance, spectral mean, mean square frequency, centroid frequency domain, frequency domain feature parameter 1, frequency domain feature parameter 2, frequency domain feature parameter 3, wavelet packet entropy and singular value entropy constitute a feature vector set.

[0083] According to the formulas corresponding to the standard deviation, kurtosis, root mean square, impulse factor, variance and rectified average value in the time domain characteristics, the standard deviation, kurtosis, root mean square, impulse factor, variance and rectified average value of the vibration signal of the secondary noise reduction are calculated respectively; the standard deviation formula is as follows:

[0084]

[0085] The kurtosis formula is as follows:

[0086]

[0087] The RMS formula is as follows:

[0088]

[0089] The pulse factor formula is as follows:

[0090]

[0091] The variance formula is as follows:

[0092]

[0093] The rectified average value formula is as follows:

[0094]

[0095] Where N is the number of sample points in the vibration signal, x m It is the mean of the signal. It is convenient to extract the time domain features of the signal, and the change of the signal can be clearly observed. It can well describe the change process of the bearing signal, so as to carry out reliability evaluation and prediction of the bearing.

[0096] According to the formulas corresponding to the spectrum skewness, spectrum kurtosis, spectrum variance, spectrum mean, mean square frequency, center of gravity frequency domain, frequency domain characteristic parameter 1, frequency domain characteristic parameter 2 and frequency domain characteristic parameter 3 in the frequency domain characteristics, the spectrum skewness, spectrum kurtosis, spectrum variance, spectrum mean, mean square frequency, center of gravity frequency domain, frequency domain characteristic parameter 1, frequency domain characteristic parameter 2 and frequency domain characteristic parameter 3 of the vibration signal of the secondary noise reduction are calculated respectively; the spectrum skewness formula is as follows:

[0097]

[0098] The spectrum kurtosis formula is as follows:

[0099]

[0100] The spectrum variance formula is as follows:

[0101]

[0102] The spectrum mean formula is as follows:

[0103]

[0104] The mean square frequency formula is as follows:

[0105]

[0106] The center of gravity frequency domain formula is as follows:

[0107]

[0108] The frequency domain characteristic parameter 1 formula is as follows:

[0109]

[0110] The frequency domain characteristic parameter 2 formula is as follows:

[0111]

[0112] The frequency domain characteristic parameter 3 formula is as follows:

[0113]

[0114] Where L is the total number of frequency components, y(l) is the frequency spectrum of the vibration signal, and f l is the frequency value of the lth spectral line.

[0115] According to the formulas corresponding to the wavelet packet entropy and singular value entropy in the frequency domain characteristics, the wavelet packet entropy and singular value entropy of the vibration signal of the secondary noise reduction are calculated respectively; the wavelet packet entropy is based on the information entropy theory established by wavelet packet decomposition, and the information entropy calculation formula for the variable X is as follows:

[0116]

[0117] In the formula, q j is the frequency of occurrence of the corresponding signal, and the sum of the probabilities of all signals occurring is 1.

[0118] The singular value entropy is achieved by performing singular value decomposition on the signal. The singular value entropy can well describe the distribution of the signal. The singular value decomposition can map the relevant wavelet packets and project them into the linear space, and describe the signal change by the energy change of the signal. Assuming that the characteristic matrix V, its corresponding singular value is σ i , the expression for summing the singular values ​​is:

[0119]

[0120] According to the probability formula and information entropy formula, the singular value entropy S can be obtained as:

[0121]

[0122] All the features of the extracted bearing signals are used to form a feature vector set, and the stacked autoencoder SAE dimensionality reduction method is used to reduce the parameters of the vector set; the logistic regression reliability assessment model is used to evaluate the reliability of the bearing, and the feature vector set after dimensionality reduction is selected as the degradation feature information. As the input of the logistic regression reliability assessment model, the reliability curve of the bearing can be obtained; the reliability of the rolling bearing can be evaluated based on the reliability curve of the bearing.

[0123] In the step 4, in the constructed logistic regression reliability assessment model, the i-th dimension feature vector set at time t is set to X i (t)=(x1(t),x2(t),...,x i (t)), X i (t)=(x1(t),x2(t),...,x i(t)) Input the reliability solution formula, set y(t) = 0 for the normal operation of the bearing at time t, and y(t) = 1 for the failure of the bearing at time t; input the eigenvalue into the sigmoid function, and input the reliability solution formula of the i-th dimension eigenvector set at time t as follows:

[0124]

[0125] In the formula, β0, β1, β2,..., β i is the regression coefficient of the feature vector set;

[0126] Transform the reliability solution formula to obtain:

[0127]

[0128] Let C=β0, β1, β2,...,β i Substituting the above formula into the regression coefficient, we can solve the equation as follows:

[0129]

[0130] The gradient descent method is used to solve the regression coefficient solution equation to obtain the regression coefficient of the feature vector set. The regression coefficient is substituted into the reliability solution formula to obtain the logistic regression reliability assessment model.

[0131] In the step five, the bearing reliability prediction model of the hybrid kernel correlation vector machine, the correlation vector machine RVM is a model based on the kernel function; in the prediction process of the correlation vector machine, different kernel functions and kernel parameter settings will affect the prediction performance of the model, and the kernel function is roughly divided into global kernel and local kernel; the global kernel can extract the global features in the sample very well, and the data at a long distance can affect the kernel function value; the local kernel will only affect the kernel function value when the data distance is close, but it has stronger learning ability than the global kernel function. Therefore, two or more kernel functions can be selected, and the combination of kernel functions can make full use of the advantages of each kernel function to construct a new kernel function with better performance; firstly, a hybrid kernel function RVM is proposed, using the local Laplace kernel function and the global linear kernel as the kernel function, and using the linear weighted combination of the kernel function to combine the local Laplace kernel function H1 with the global linear kernel H2 to obtain the hybrid kernel function H, which can effectively improve the prediction accuracy of the RVM model; the calculation process is as follows:

[0132]

[0133] H=pH1+(1-p)H2

[0134] Where p is the weight coefficient of the kernel function, 0≤p≤1, and δ is the width of the kernel function.

[0135] Relevant vector machine (RVM) is a kernel sparse machine learning method based on the Bayesian framework. Sparse machine learning can increase the capacity of the model and greatly improve the efficiency of the machine learning method. Relevant vector machine (RVM) is very similar to the support vector machine (SVM) method, but it breaks through the limitations of SVM to a certain extent. RVM adds a probability term on the basis of SVM to illustrate the impact of the deviation of model prediction on the final result. RVM does not need to set too many parameters, and RVM is not restricted by Messi's theorem in the selection of kernel functions. It is more suitable for use in the case of large data volume. The number of its related vectors will increase with the increase of the number of samples, but compared with SVM, the increase rate is slower; RVM can produce a relatively sparse model, improve the speed of running on the test set, and can also retain a certain generalization error.

[0136] Substitute the hybrid kernel function into the relevance vector machine to obtain the hybrid kernel function relevance vector machine MKRVM; train the parameters of the kernel function based on the nonlinear mapping relationship between the input data and the output data, and construct the bearing reliability prediction model of the hybrid kernel relevance vector machine; set the training samples to be input {x n} N and the target value {t n} N The correspondence between the input and target values ​​in the hybrid kernel correlation vector machine is constructed and the calculation process is as follows:

[0137]

[0138] Where ω is the weight vector of the model, H is the hybrid kernel function, ε is the offset, and N is the total number of training samples.

[0139] The target value {t n} N is an independent variable, and the conditional probability of the target value t is calculated as follows:

[0140]

[0141] Where Φ is an N×(N+1) matrix composed of mixed kernel functions, σ 2 is the noise variance;

[0142] In the calculation process, since a large number of hyperparameters are referenced, directly using the maximum likelihood estimation method to find the value of ω may result in overfitting. To solve this problem, the Bayesian theory is used to add constraints to the weight vector ω, and each weight vector ω is defined as a vector with zero mean. The Gaussian prior probability distribution formula is as follows:

[0143]

[0144] In the formula, α[α0, α1,...,αN ] T is a hyperparameter vector, each hyperparameter corresponds to a weight vector, and the weight vectors are independently distributed; the size of the hyperparameter can affect the sparsity of the model. Therefore, the key to RVM is to find the hyperparameter, calculate the corresponding weights and kernel functions to ensure the sparsity of the model, and combine the noise variance to obtain the final regression model.

[0145] The posterior distribution weight of the weight vector ω is obtained by the Bayesian formula, and the calculation process is as follows:

[0146]

[0147] In the formula, ∑=(σ -2 Φ T Φ+C) is the covariance matrix, μ=σ -2 ∑Φ T t is the posterior matrix of the target value, C represents the main diagonal elements α[α0, α1, ..., α N ] T The matrix of .

[0148] During the calculation process, the hyperparameters α and σ 2 , so that the hyperparameters are uniformly defined as follows:

[0149]

[0150] E=σ 2 I+ΦC -1 Φ T .

[0151] The hyperparameters α and σ of the hybrid kernel function related vector machine are adjusted by an iterative algorithm. 2 Solve for the hyperparameters α and σ 2 Perform iterative calculations until the convergence conditions are met. The calculation process is as follows:

[0152]

[0153] Where M ii is the i-th diagonal element of the covariance matrix. During the training process, most hyperparameters tend to infinity. According to the above formula, we can know that the weight vector ω is 0 when the hyperparameters tend to infinity. Therefore, we should discard the samples with the weight vector ω being 0 because it has little impact on the results. For the samples with ω not being 0, we call them the relevance vector, which can reflect the most core regression features.

[0154] Substitute the hybrid kernel function into the RVM to obtain the hybrid kernel RVM, and use the input {x n} Nand the target value {t n} N The samples that constitute the training are used to train the hybrid kernel relevance vector machine. During the training, a constraint is imposed on the weight vector, and the hyperparameters α and σ are solved through an iterative algorithm. 2 , and finally obtain the bearing reliability prediction model of the hybrid kernel correlation vector machine; the feature vector set after denoising is input into the bearing reliability prediction model of the hybrid kernel correlation vector machine to obtain the predicted degradation characteristics, at this time the predicted degradation characteristics can be embedded in the logistic regression reliability assessment model, and the prediction curve of the bearing reliability can be obtained; this scheme can evaluate the reliability of the current rolling bearing according to the vibration signal of the current rolling bearing, and at the same time can predict the reliability of the future rolling bearing according to the vibration signal of the current rolling bearing.

[0155] The mean absolute error (MAE) and mean absolute percentage error (MAPE) are used to evaluate the prediction results. MAE is measured in original units and is not easily affected by extreme values. It is expressed in the form of a linear fraction. Directly averaging the error values ​​can avoid the problem of error values ​​canceling each other out. MAPE is an indicator commonly used to measure the accuracy of predictions. It measures the average percentage of prediction errors and gives the size of the average prediction error in percentage, with a range of [0, +∞]. The calculation formulas are:

[0156]

[0157] To address the problem of excessive noise in rolling bearing vibration signals, a hybrid denoising method based on intrinsic time-scale decomposition (ITD) and maximum correlated kurtosis deconvolution (AOA-MCKD) improved by arithmetic optimization algorithm is proposed; to address the difficulty in evaluating the reliability of rolling bearings, a bearing reliability evaluation method based on a stacked autoencoder (SAE-logistic regression) is proposed; to address the problem of poor reliability prediction of rolling bearings, a reliability prediction model based on a mixed kernel relevance vector machine (MKRVM) is proposed to predict bearing reliability.

[0158] Example

[0159] For further verification, in a specific embodiment, the XJTU-SY bearing data set is used for experimental verification, and bearing 3-2 is used for the experiment.

[0160] First, the noisy signal is decomposed by ITD to obtain a total of 6 PR components. Next, the PR evaluation index K proposed in the present invention is used to screen the decomposed PR. First, the RCMDE value, P value and RMSE value of each component are respectively obtained according to the formula. The calculation formula of the signal component evaluation index K proposed in the present invention is used to calculate the K value of each PR component. The results are shown in Table 1 below. Then, the average value T of the evaluation index K is calculated to be 1.93. The K values ​​of the PR1, PR2, and PR3 components are greater than the average value T. Therefore, the decomposed PR1, PR2, and PR3 components contain most of the effective information of the vibration signal. PR1, PR2, and PR3 are reconstructed to obtain the effective signal after denoising by the ITD decomposition algorithm; that is, the vibration signal with one denoising.

[0161] Table 1 PRs evaluation indicators

[0162]

[0163] Next, the improved MCKD algorithm is used to perform secondary denoising on this effective signal. Since the parameters in MCKD will affect its operating effect, the present invention optimizes the key parameters in MCKD through an arithmetic optimization algorithm; first, according to the existing experimental conclusions, the initialization ranges of the displacement number M and the filter length L in the MCKD algorithm are set to [1, 7] and [50, 400] respectively, the initial population size N of AOA is 30, and the number of iterations n is 100. Through continuous iterations, the optimal displacement number M and filter length L are 1.8 and 386 respectively.

[0164] Generally speaking, the signal-to-noise ratio (SNR) is used to indicate the amount of noise signal in a signal. SNR indicates the ratio of signal power to noise power. The higher the value, the better the signal quality, and vice versa. The proposed method is compared with the existing commonly used signal denoising methods ITD-MCKD, ITD, LCD, and LMD. It can be seen from Table 2 below that compared with other decomposition-based denoising algorithms, the denoising method proposed by the present invention, ITD-AMCKD, has the highest signal-to-noise ratio of -2.3754. This shows that the use of ITD-AMCKD can accurately reduce bearing noise signals, improve signal quality, and provide sufficient data preparation for studying the reliability of bearings.

[0165] Table 2 Comparison of signal-to-noise ratio

[0166]

[0167] like Figure 2-4As shown in the figure, the signal after noise reduction contains a lot of effective information. Next, 17 time domain, frequency domain and time-frequency domain features are extracted from the noise-reduced rolling bearing 3-2 vibration signal, such as mean, standard deviation, kurtosis, waveform factor, etc.; spectral skewness, spectral kurtosis and mean square frequency, etc.; time-frequency domain feature wavelet packet entropy and singular value factor; the extracted bearing signal features constitute a feature vector set, such as Figure 2-4 shown.

[0168] The 17 features extracted form a multi-domain feature parameter set of the bearing, which is also a feature vector set. However, directly substituting the parameter set into the reliability assessment model will bring great difficulties to the modeling. The present invention uses a three-layer stacked autoencoder to reduce the dimension of the feature parameter set of bearing 3-2, sets the input layer neurons to 17 dimensions, sets the learning rate to 0.01, sets the epochs to 100, and sets the batch-size to 80. The 3-dimensional feature set after dimension reduction is obtained, such as Figure 5 As shown in the figure. In comparison, the SAE algorithm can divide the operation cycle of the bearing more clearly, the intervals between each cycle are more obvious, and the data points at different stages can be well distinguished. This shows that the dimensionality reduction result of the algorithm can well describe the degradation condition of the bearing.

[0169] The reliability assessment model is created based on the three-dimensional degradation feature vector of bearing 3-2 obtained after dimensionality reduction. The present invention uses a more efficient logistic regression model to perform reliability assessment on the bearing. The feature vector set after dimensionality reduction is selected as the degradation feature information and as the input of the logistic regression model. The regression coefficient values ​​of the logistic regression model are calculated using the solution formula as β0=3.679, β1=-5.618, β2=1.175, β3=-2.074. The above regression coefficients are brought into the logistic regression model reliability calculation formula to establish a bearing reliability assessment model:

[0170]

[0171] The obtained bearing reliability curve is as follows: Figure 6 As shown, the reliability of the current rolling bearing can be evaluated to determine the reliability of the rolling bearing at this time.

[0172] Finally, the future bearing reliability is predicted; first, the first 2096 samples are selected from the bearing 3-2 sample set to train the model, and the last 400 samples are used as the test set. After many experiments, when the coefficient p of the hybrid kernel function is set to 0.6, the performance of the hybrid kernel correlation vector machine reaches the best, and the bearing reliability prediction is carried out after the training data and parameters are determined.

[0173] In order to verify the prediction accuracy of the hybrid kernel relevance vector machine model, this study used Bayesian optimized relevance vector machine model BOA-RVM, relevance vector machine model RVM, least squares support vector machine LSSVM, ELMAN neural network, extreme learning machine Extreme Learning Machine, ELM and back propagation Back-Propagation, BP neural network prediction model to predict the reliability of bearings and compared them with the MKRVM method. At the same time, the proposed bearing reliability evaluation and prediction method was verified using bearings 3-1 and bearings 3-4; and the average absolute error and average absolute percentage error generated by each prediction model were calculated, as shown in Table 3 below.

[0174] Table 3 Error comparison of prediction models

[0175]

[0176] It can be seen that the MAE mean absolute error of RVM is smaller than that of other prediction models, but the MAPE mean absolute percentage error is much larger than that of other prediction models; the MKRVM of the present invention reduces the MAPE mean absolute percentage error lower than other prediction models, while ensuring that the MAE mean absolute error of the MKRVM of the present invention is lower than other prediction models; so as to meet the higher accuracy of the prediction of rolling bearing reliability.

[0177] The above is only a description of the preferred embodiments of the present invention. Ordinary technicians in this technical field can make several modifications and optimizations based on the above disclosure without departing from the above basic principles. These improvements and optimizations should be regarded as the understood protection scope of the present invention.

Claims

1. A method for reliability assessment and prediction of rolling bearings based on hybrid noise reduction and MKRVM, characterized by: The following steps are involved: Step 1: Obtain vibration signal data of the rolling bearing over its entire lifespan; use the intrinsic time scale decomposition algorithm ITD to decompose the vibration signal to obtain several PR components; Step 2: A hybrid evaluation index combining fine composite multi-scale scatter entropy, Pearson correlation coefficient and root mean square error value is used to screen several PR components, and the screened PR components are reconstructed to obtain a primary denoised vibration signal; the primary denoised vibration signal is subjected to secondary denoising through maximum kurtosis deconvolution improved by an arithmetic optimization algorithm to obtain a secondary denoised vibration signal containing effective information; Step 3, using three feature extraction methods in time domain, frequency domain and time-frequency domain to extract time domain features, frequency domain features and time-frequency domain features of the secondary noise reduction vibration signal respectively, and the extracted features constitute a feature vector set; Step 4: Use the stacked autoencoder dimensionality reduction method to reduce the parameters of the feature vector set, and use the reduced-dimensional feature vector set as degradation feature information to input the constructed logistic regression reliability assessment model to obtain a reliability curve for evaluating the current bearing; Step 5. Input the feature vector set into the bearing reliability prediction model constructed by the hybrid kernel correlation vector machine, predict the bearing degradation characteristics to obtain the predicted degradation characteristics; embed the predicted degradation characteristics into the logistic regression reliability assessment model to obtain the bearing reliability prediction curve.

2. The method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM according to claim 1, characterized in that: In the step 2, the mixed evaluation index K of PR is obtained by combining the fine composite multi-scale scatter entropy, the Pearson correlation coefficient and the root mean square error value. The calculation process of the K value of the i-th PR component is as follows: In the formula, is the Pearson correlation coefficient between the original vibration signal and , is the root mean square error between the original vibration signal and several PR components, RCMDE i is the fine composite multi-scale scatter entropy of the i-th PR component, L is the number of PR components, x is the original vibration signal, x i is the i-th PR component; Calculate the K values ​​corresponding to several PR components, and calculate the average value of all K values ​​as T; select the PR component whose K value is greater than T as the screened PR component; 3. The method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM according to claim 2, characterized in that: The calculation process of calculating the PR component fine composite multi-scale scatter entropy is as follows: Where P k is the probability value of the spread entropy corresponding to the kth coarse-grained sequence; X is the input signal; m is the embedding dimension; c is the number of categories into which the data is divided; d represents the delay; τ is the scale factor during division; The Pearson correlation coefficient between the original vibration signal and the PR component The calculation process is as follows: Among them, cov(x,x i ) represents x and x i The covariance between x and are the sample mean differences between the original vibration signal and the i-th PR component after decomposition; The root mean square error RMSE between the original vibration signal and the PR component is calculated as follows: Where N is the number of sample points in the vibration signal.

4. The method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM according to claim 1, characterized in that: In step 4, the i-th dimension feature vector set at time t is set to X i (t)=(x1(t),x2(t),...,x i (t)), X i (t)=(x1(t),x2(t),...,x i (t)) Input the reliability solution formula, set y(t) = 0 for the normal operation of the bearing at time t, and y(t) = 1 for the failure of the bearing at time t; input the eigenvalue into the sigmoid function, and input the reliability solution formula of the i-th dimension eigenvector set at time t as follows: In the formula, β0, β1, β2,..., β i is the regression coefficient of the feature vector set; Transform the reliability solution formula to obtain: Let C=β0,β1,β2,…,β i Substituting the above formula into the regression coefficient, we can solve the equation as follows: The gradient descent method is used to solve the regression coefficient solution equation to obtain the regression coefficient of the feature vector set. The regression coefficient is substituted into the reliability solution formula to obtain the logistic regression reliability assessment model.

5. The method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM according to claim 1, characterized in that: In step 5, the bearing reliability prediction model of the hybrid kernel correlation vector machine uses the local Laplace kernel function and the global linear kernel as kernel functions, and uses the linear weighted combination of the kernel functions to combine the local Laplace kernel function and the global linear kernel to obtain the hybrid kernel function H; the calculation process is as follows: H=pH1+(1-p)H2 Where p is the weight coefficient of the kernel function, 0≤p≤1, and δ is the width of the kernel function.

6. The method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM according to claim 5, characterized in that: Substitute the hybrid kernel function into the relevance vector machine to obtain the hybrid kernel function relevance vector machine MKRVM; train the parameters of the kernel function based on the nonlinear mapping relationship between the input data and the output data, and construct the bearing reliability prediction model of the hybrid kernel relevance vector machine; set the training samples to be input {x n } N and the target value {t n } N The correspondence between the input and target values ​​in the hybrid kernel correlation vector machine is constructed and the calculation process is as follows: Where ω is the weight vector of the model, H is the hybrid kernel function, ε is the offset, and N is the total number of training samples.

7. The method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM according to claim 6, characterized in that: Bayesian theory is used to add constraints to the weight vector ω, and each weight vector ω is defined as a vector with zero mean. The Gaussian prior probability distribution formula is as follows: In the formula, α = [α0, α1, ..., α N ] T is a hyperparameter vector, each hyperparameter corresponds to a weight vector, and the weight vectors are independently distributed; The posterior distribution weight of the weight vector ω is obtained by the Bayesian formula, and the calculation process is as follows: In the formula, ∑=(σ -2 Φ T Φ+C) is the covariance matrix, μ=σ -2 ΣΦ T t is the posterior matrix of the target value, C represents the main diagonal elements α = [α0, α1, ..., α N ] T The matrix of .

8. The method for evaluating and predicting rolling bearing reliability based on hybrid noise reduction and MKRVM according to claim 7, characterized in that: The hyperparameters α and σ 2 , so that the hyperparameters are uniformly defined as follows: E=σ 2 I+ΦC -1 Φ T 。 The hyperparameters α and σ of the hybrid kernel function related vector machine are adjusted by an iterative algorithm. 2 Solve for the hyperparameters α and σ 2 Perform iterative calculations until the convergence conditions are met. The calculation process is as follows: Where M ii is the i-th diagonal element of the covariance matrix.

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