Method for evaluating reliability of rolling bearing under variable-speed and variable-load working conditions

Abstract

The invention relates to a rolling bearing reliability evaluation method, in particular to a rolling bearing reliability evaluation method under variable-speed and variable-load working conditions, which comprises the following steps of: firstly, acquiring full-life-cycle time-domain vibration signals and variable working condition parameters of a rolling bearing under the variable-speed and variable-load working conditions, and extracting characteristic parameters of the vibration signals; secondly, establishing a system agent model based on a radial basis function neural network, taking the rotating speed, the load and the vibration signal AR power spectrum root-mean-square as model input, and realizing accurate fitting of time domain root-mean-square at different moments; and then extracting model parameters, performing dimension reduction by using an auto-encoder, constructing a performance degradation index of the rolling bearing, and evaluating the running reliability of the rolling bearing in combination with a logistic regression model. According to the method, the influence of working condition interference on bearing reliability evaluation can be eliminated, the constructed degradation index can reflect the real performance degradation state of the bearing, and accurate evaluation of the running reliability of the rolling bearing under the variable-speed and variable-load working condition is realized.

Description

Technical Field

[0001] The invention relates to a rolling bearing evaluation method, in particular to a rolling bearing reliability evaluation method under variable speed and variable load 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] The purpose of the present invention is to provide a method for evaluating the reliability of rolling bearings under variable speed and variable load conditions. The method uses machine learning and data-driven technology to construct rolling bearing performance degradation indicators under variable conditions, and combines a logistic regression model to complete reliability evaluation.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for evaluating the reliability of a rolling bearing under variable speed and variable load conditions, the method comprising the following steps:

[0007] Step 1: Collect the full life vibration acceleration signal and working condition parameters of the rolling bearing under variable speed and variable load conditions through the data acquisition system;

[0008] Step 2: Extract the root mean square of the rolling bearing vibration signal in time domain and the root mean square of the AR power spectrum in frequency domain;

[0009] Step 3: Take the speed, load and signal AR power spectrum root mean square as model input, take the time domain vibration signal root mean square as model output, build a system proxy model based on the neural network for fitting, adaptively update the model parameters at each moment, and perform a goodness of fit test;

[0010] Step 4: Select model parameters, perform dimensionality reduction through autoencoders, and construct degradation indicators;

[0011] Step 5: Evaluate rolling bearing reliability through logistic regression model.

[0012] In the method for evaluating the reliability of rolling bearings under variable speed and variable load conditions, the operating condition of the rolling bearing in step 1 is a complex condition of variable speed and variable load.

[0013] The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions, the implementation process of step 2 is: firstly, the root mean square of each time domain signal sample is calculated to represent the system model response, and the calculation formula is as follows:

[0014]

[0015] In the formula, i is the number of sample points of each signal. Then, each time domain vibration signal sequence sample is represented by the AR model:

[0016]

[0017] Where x(t) is the original signal; a m represents the AR model parameters; m represents the model order, m = 1, 2, ..., p; u(t) represents the mean value of 0 and the variance of σ 2 The AR power spectrum is fitted for all collected samples. The AR power spectrum calculation process is:

[0018]

[0019] In the formula, 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; the final prediction error criterion and Burg algorithm are used to determine the AR model order and solve the AR model parameters respectively; the AR power spectrum root mean square of all signal samples is calculated as the characteristic parameter to characterize the bearing performance status.

[0020] The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions, the process of constructing a system proxy model in step three includes:

[0021] Based on the radial basis neural network, a system proxy model is built with a model structure of 3-6-1. The speed, load and signal AR power spectrum root mean square are used as the input of the model. The time domain signal root mean square is used to characterize the bearing operation status trend as the output of the model. The accurate fitting of the signal status trend is achieved through multivariate regression, avoiding the establishment of complex mathematical or physical models.

[0022] The neural network input layer to the hidden layer is a nonlinear mapping, which can be expressed as:

[0023]

[0024] 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:

[0025]

[0026] In the formula, ω i is the weight from the hidden layer to the output layer;

[0027] The running state trend of the bearing at each moment is fitted, and the minimum fitting error is used as the loss function, which is expressed as:

[0028]

[0029] 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;

[0030] 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:

[0031]

[0032]

[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] Where λ is the learning rate, λ∈[0,1]; ρ is the momentum factor, ρ=[0,1]; the model fit goodness test formula is as follows:

[0038]

[0039] Where Y q is the true value; is the fitted value; is the average value of the true value; Q is the total number of data. 2 The closer it is to 1, the higher the model fitting accuracy.

[0040] The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions, the degradation index construction in step 4, comprises:

[0041] Parameters in the system proxy model are extracted, and parameters that can well characterize the performance degradation trend of rolling bearings are selected as target feature parameters. An autoencoder is used to reduce its dimensionality. The autoencoder compresses the high-dimensional input data into a low-dimensional representation, and then a decoder is used to reconstruct the original input data from the low-dimensional data. The low-dimensional representation of the original data in the autoencoder is selected as the performance degradation indicator of the rolling bearing.

[0042] The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions, the bearing reliability evaluation in step 5, comprises:

[0043] Use the logistic regression model to evaluate the reliability of rolling bearings. The logistic regression model can be used to analyze the relationship between the equipment operating status and the probability distribution of historical data, and is often used to evaluate the reliability of mechanical equipment. When using the logistic regression model to evaluate the reliability of rolling bearings, it is necessary to select the characteristic parameter set X(t) = {x 1 (t),x 2 (t),…,x n (t)} as the covariate in the logistic regression model, where n is the number of characteristic parameters; the bearing is in normal state at time t and z is used t =1 indicates that the fault state is represented by z t =0, then the reliability function of the bearing can be expressed as:

[0044]

[0045] In the formula, α 0 ,α 1 ,α 2 ,…,α n is the co-regression coefficient of the model. After logarithmic transformation of the formula, it is shown as follows:

[0046]

[0047] Let A = {α 0 ,α 1 ,α 2 ,…α n}, the maximum likelihood method is used to solve the model parameters, and the likelihood equation is shown as follows:

[0048]

[0049] After solving the model parameters, the reliability of the bearing at different times can be calculated.

[0050] The beneficial effects of the present invention are:

[0051] The present invention evaluates the operating reliability of rolling bearings under complex working conditions of variable speed and variable load. The present invention proposes a system proxy model based on a neural network, which avoids the establishment of traditional complex mathematical and physical models and constructs a new type of degradation index based on model parameters. The system proxy model parameters are used to characterize the bearing performance state, and the selected model parameters are reduced in dimension through an autoencoder to accurately and real-time evaluate the reliability of the bearing under operating conditions.

[0052] The present invention avoids the establishment of traditional complex mathematical and physical models. The proposed method can eliminate the influence of working condition interference on bearing reliability evaluation. The constructed degradation index can reflect the actual performance degradation state of the bearing and realize accurate evaluation of the operating reliability of the rolling bearing under variable speed and variable load conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is the overall flow chart of the present invention;

[0054] Figure 2 It is the speed and load spectrum in the experiment of the present invention;

[0055] Figure 3 Extract characteristic parameter diagram in the experiment of the present invention;

[0056] Figure 4 It is the structure diagram of the system agent model in the experiment of the present invention;

[0057] Figure 5 This is a diagram of the model fitting results in the experiment of the present invention;

[0058] Figure 6It is the model parameter diagram in the experiment of the present invention;

[0059] Figure 7 is a graph showing the bearing performance degradation index in the experiment of the present invention;

[0060] Figure 8 This is a full life cycle reliability curve of the bearing in the experiment of the present invention. DETAILED DESCRIPTION

[0061] 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.

[0062] The present invention provides a method for evaluating the reliability of rolling bearings under variable speed and variable load conditions. Figure 1 , specifically including the following steps:

[0063] Step 1: Collect the full life vibration acceleration signal and operating parameters of the rolling bearing under variable speed and variable load conditions through the data acquisition system.

[0064] The operating condition of the rolling bearing is a complex condition in which 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. In the middle 120 minutes, the speed is set to change sinusoidally from 1260r / min to 1890r / min, and the radial load is set to change sinusoidally from 13kN to 19kN, with a phase angle of 180° different from the speed; in the next 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. 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. The speed and load spectrum of the full life experiment are as follows. Figure 2 shown.

[0065] Step 2: Extract the RMS value of the rolling bearing vibration signal in time domain and the RMS value of the AR power spectrum in frequency domain.

[0066] First, the root mean square of each time domain signal sample is calculated to represent the system model response. The calculation formula is as follows:

[0067]

[0068] In the formula, i is the number of sample points of each signal. Then, each time domain vibration signal sequence sample is represented by the AR model:

[0069]

[0070] Where x(t) is the original signal; a m represents the AR model parameters; m represents the model order, m = 1, 2, ..., p; u(t) represents the mean value of 0 and the variance of σ 2 The AR power spectrum is fitted for all collected samples. The AR power spectrum calculation process is:

[0071]

[0072] In the formula, 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. The final prediction error criterion and Burg algorithm are used to determine the AR model order and solve the AR model parameters respectively. The AR power spectrum root mean square of all signal samples is calculated as the characteristic parameter to characterize the bearing performance status.

[0073] The RMS of the time domain signal and AR power spectrum of the rolling bearing over the entire life cycle is as follows Figure 3 Shown

[0074] Step 3: Use the RMS of speed, load and signal AR power spectrum as model input, and the RMS of time domain vibration signal as model output. Build a system proxy model based on neural network for fitting, adaptively update the model parameters at each moment, and perform goodness of fit test.

[0075] Based on the radial basis neural network, a system agent model is built, and the model structure is 3-6-1, such as Figure 4 The speed, load and signal AR power spectrum root mean square are used as the input of the model; the time domain signal root mean square is used to characterize the bearing operation state trend as the output of the model, and the accurate fitting of the signal state trend is achieved through multivariate regression, avoiding the establishment of a complex mathematical model.

[0076] The neural network input layer to the hidden layer is a nonlinear mapping, which can be expressed as:

[0077]

[0078] 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:

[0079]

[0080] In the formula, ω i is the weight from the hidden layer to the output layer.

[0081] The running state trend of the bearing at each moment is fitted, and the minimum fitting error is used as the loss function, which is expressed as:

[0082]

[0083] 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.

[0084] 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:

[0085]

[0086]

[0087]

[0088] ω i (q) = ω i (q-1)+Δω i (q)+ρ[ω i (q-1)-ω i (q-2)]

[0089] b i (q) = b i (q-1)+Δb i +ρ[b i (q-1)-b i (q-2)]

[0090] c il (q) = c il (q-1)+Δc il +ρ[c il (q-1)-c il (q-2)]

[0091] In the formula, λ is the learning rate, λ∈[0,1]; ρ is the momentum factor, ρ=[0,1]. The model fit goodness test formula is as follows:

[0092]

[0093] Where Y q is the true value; is the fitted value; is the average value of the true value; Q is the total number of data. 2 The closer it is to 1, the higher the model fitting accuracy.

[0094] The model fitting effect is as follows Figure 5 As shown, the goodness-of-fit test R 2 The accuracy is 99.52%, achieving high-precision fitting.

[0095] Step 4: Select model parameters, perform dimensionality reduction through autoencoder, and construct degradation indicators.

[0096] Extract the parameters in the system proxy model and select the parameters that can well characterize the performance degradation trend of the rolling bearing as the target feature parameters. The width of the hidden layer radial basis function changes as follows: Figure 6 As shown in the figure, its early fluctuation is smaller and its monotonicity is stronger, showing a trend consistent with the performance degradation of rolling bearings. The width of the radial basis is selected as the target parameter to characterize the bearing performance degradation process.

[0097] The autoencoder is used to reduce the dimension. The autoencoder compresses the high-dimensional input data into a low-dimensional representation, and then the decoder is used to reconstruct the original input data from the low-dimensional data. The low-dimensional representation of the original data in the autoencoder is selected as the performance degradation index of the rolling bearing, and it is normalized as follows Figure 7 shown.

[0098] The degradation index constructed in this paper is not seriously affected by changes in operating conditions and shows better monotonicity and robustness. In the early stage of bearing operation, due to the good performance of the bearing itself, the degradation index value is relatively constant and has not changed significantly. As the bearing operation time increases, the bearing performance begins to decline, and a mutation occurs near 1130 points of the degradation index, reaching a maximum value at 1308 points, which corresponds to the failure time of the test bearing. The early degradation position and failure position can be intuitively found through its mutation point and maximum value. The constructed degradation index can better reflect the true operating status of the rolling bearing.

[0099] Step 5: Evaluate rolling bearing reliability through logistic regression model.

[0100] Use the logistic regression model to evaluate the reliability of rolling bearings. The logistic regression model can be used to analyze the relationship between the equipment operating status and the probability distribution of historical data, and is often used to evaluate the reliability of mechanical equipment. When using the logistic regression model to evaluate the reliability of rolling bearing status, it is necessary to select the characteristic parameter set X(t) = {x 1 (t),x 2(t),…,x n (t)} as the covariate in the logistic regression model, where n is the number of characteristic parameters; the bearing is in normal state at time t and z is used t =1 indicates that the fault state is represented by z t =0, then the reliability function of the bearing can be expressed as:

[0101]

[0102] In the formula, α 0 ,α 1 ,α 2 ,…,α n is the co-regression coefficient of the model. After logarithmic transformation of the formula, it is shown as follows:

[0103]

[0104] Let A = {α 0 ,α 1 ,α 2 ,…α n}, the maximum likelihood method is used to solve the model parameters, and the likelihood equation is shown as follows:

[0105]

[0106] After solving the model parameters, the reliability of the bearing at different times can be calculated.

[0107] The constructed degradation index is used as a covariate in the logistic regression model to complete the running reliability evaluation of rolling bearings. The reliability curve is as follows: Figure 8 shown.

Claims

1. A method for evaluating the reliability of rolling bearings under variable speed and variable load conditions, characterized in that: The method comprises the following steps: Step 1: Collect the full life vibration acceleration signal and working condition parameters of the rolling bearing under variable speed and variable load conditions through the data acquisition system; Step 2: Extract the root mean square of the rolling bearing vibration signal in time domain and the root mean square of the AR power spectrum in frequency domain; Step 3: Take the speed, load and signal AR power spectrum root mean square as model input, take the time domain vibration signal root mean square as model output, build a system proxy model based on the neural network for fitting, adaptively update the model parameters at each moment, and perform a goodness of fit test; Step 4: Select model parameters, perform dimensionality reduction through autoencoders, and construct degradation indicators; Step 5: Evaluate rolling bearing reliability through logistic regression model.

2. The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions according to claim 1 is characterized in that: The operating condition of the rolling bearing in step 1 is a complex condition of variable speed and variable load.

3. The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions according to claim 1 is characterized in that: The implementation process of step 2 is as follows: first, the root mean square of each time domain signal sample is calculated to represent the system model response, and the calculation formula is as follows: In the formula, i is the number of signal sample points; then, each time domain vibration signal sequence sample is represented by the AR model: Where x(t) is the original signal; a m represents the AR model parameters; m represents the model order, m = 1, 2, ..., p; u(t) represents the mean value of 0 and the variance of σ 2 white noise sequence; AR power spectrum fitting is performed on all collected samples; the AR power spectrum calculation process is: In the formula, 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; the final prediction error criterion and Burg algorithm are used to determine the AR model order and solve the AR model parameters respectively; the AR power spectrum root mean square of all signal samples is calculated as the characteristic parameter to characterize the bearing performance status.

4. The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions according to claim 1 is characterized in that: The process of building the system agent model in step 3 includes: Based on the radial basis neural network, a system proxy model is built with a model structure of 3-6-1. The speed, load and signal AR power spectrum root mean square are used as the input of the model. The time domain signal root mean square is used to characterize the bearing operation status trend as the output of the model. The accurate fitting of the signal status trend is achieved through multivariate regression, avoiding the establishment of complex mathematical or physical models. The neural network input layer to the hidden layer is a nonlinear mapping, which 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 fitted, and the minimum fitting 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)] Where λ is the learning rate, λ∈[0,1]; ρ is the momentum factor, ρ=[0,1]; the model fit goodness test formula is as follows: Where Y q is the true value; is the fitted value; is the average value of the true value; Q is the total number of data; R 2 The closer it is to 1, the higher the model fitting accuracy.

5. The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions according to claim 1 is characterized in that: The process of constructing the degradation index in step 4 includes: Parameters in the system proxy model are extracted, and parameters that can well characterize the performance degradation trend of rolling bearings are selected as target feature parameters. An autoencoder is used to reduce its dimensionality. The autoencoder compresses the high-dimensional input data into a low-dimensional representation, and then a decoder is used to reconstruct the original input data from the low-dimensional data. The low-dimensional representation of the original data in the autoencoder is selected as the performance degradation indicator of the rolling bearing.

6. The method for evaluating the reliability of rolling bearings under variable speed and variable load conditions according to claim 1, characterized in that: The bearing reliability assessment in step 5 includes the following steps: Use the logistic regression model to evaluate the reliability of rolling bearings. The logistic regression model can be used to analyze the relationship between the equipment operating status and the probability distribution of historical data, and is often used to evaluate the reliability of mechanical equipment. When using the logistic regression model to evaluate the reliability of rolling bearings, it is necessary to select the characteristic parameter set X(t) = {x1(t), x2(t), …, x n (t)} as the covariate in the logistic regression model, where n is the number of characteristic parameters; the bearing is in normal state at time t and z is used t =1 indicates that the fault state is represented by z t =0, then the reliability function of the bearing can be expressed as: In the formula, α0, α1, α2, …, α n is the co-regression coefficient of the model; after logarithmic transformation of the formula, it is shown as follows: Let A = {α0, α1, α2, … α n }, the maximum likelihood method is used to solve the model parameters, and the likelihood equation is shown as follows: After solving the model parameters, the reliability of the bearing at different times can be calculated.

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