Rolling bearing residual life prediction method based on hybrid filtering and condition monitoring

Abstract

The application discloses a rolling bearing residual life prediction method based on a hybrid filter and state monitoring, first acquires horizontal vibration signals in the operation process of the rolling bearing; then calculates kurtosis and root mean square (RMS) values by using the horizontal vibration signals, and respectively determines the kurtosis and RMS of the horizontal vibration signals as state monitoring indexes and prediction indexes; then adopts a Kalman filter algorithm (KF) to monitor the operation state of the bearing and determine a fault starting point (FST); when the bearing enters a degradation state, a hybrid filter algorithm combining a particle filter (PF) and an unscented Kalman filter (UKF) is adopted to estimate future RMS values; finally, a sliding window and a linear model are established on the obtained RMS estimation values to determine a failure threshold of the bearing, and the moment when the RMS value exceeds the failure threshold is judged to obtain a residual life prediction result. The application determines the fault starting point by monitoring the operation state of the rolling bearing, and obtains an accurate residual life prediction result.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of rotating machinery life prediction, and particularly relates to a rolling bearing residual life prediction method based on hybrid filtering and state monitoring. BACKGROUND

[0002] The rolling bearing is a key component of the rotating machinery, and its running state directly determines the use performance of the machinery. Once a failure occurs, a serious safety accident will be caused. Therefore, it is necessary to monitor the running state of the rolling bearing in real time, analyze the performance degradation process, and research the residual service life prediction method, so as to ensure the safe operation of the machinery.

[0003] In view of the problem that the failure starting point and the failure threshold are difficult to determine in the residual life prediction of the rolling bearing, a residual life prediction method based on hybrid filtering and state monitoring is provided. The method can effectively identify the failure starting point and the failure threshold, and accurately predict the residual life, and has high prediction accuracy, thereby providing a further reference for the residual life prediction of the rolling bearing. SUMMARY

[0004] The purpose of the application is to provide a rolling bearing residual life prediction method based on hybrid filtering and state monitoring. The running state of the rolling bearing is monitored, the failure starting point is determined, and an accurate residual life prediction result is obtained.

[0005] The technical scheme adopted by the application is a rolling bearing residual life prediction method based on hybrid filtering and state monitoring, which is implemented according to the following steps:

[0006] Step 1, obtaining the horizontal vibration signal in the running process of the rolling bearing;

[0007] Step 2, calculating the kurtosis and root mean square (RMS) value by using the horizontal vibration signal obtained in step 1, and determining the kurtosis and RMS of the horizontal vibration signal as the state monitoring index and the prediction index respectively, and then monitoring the running state of the bearing by using the Kalman filtering algorithm (KF) and determining the failure starting point (FST);

[0008] Step 3, when the bearing enters the degradation state, a hybrid filtering algorithm combining particle filtering (PF) and unscented Kalman filtering (UKF) is used to estimate the future root mean square value;

[0009] Step 4, establishing a sliding window and a linear model on the root mean square estimation value obtained in step 3 to determine the failure threshold of the bearing, and determining the time when the root mean square value exceeds the failure threshold to obtain the residual life prediction result.

[0010] The application also has the characteristics of,

[0011] Step 2 is implemented according to the following steps:

[0012] Step 2.1, determination of state monitoring index and prediction index: kurtosis and RMS are selected as state monitoring index and prediction index respectively, and the calculation method is shown in the following formula:

[0013]

[0014]

[0015] wherein, V kurtosis represents kurtosis, V RMS represents RMS value, V i represents the ith vibration signal, represents the average value of vibration signal, and n represents the sampling number;

[0016] Step 2.2, after determining kurtosis as monitoring index in step 2.1, then the KF algorithm is used to monitor the running state of bearing in real time based on kurtosis and determine the FST point. Through analysis of historical data of kurtosis, in the normal running stage, the KF based on linear function model is established as follows:

[0017] State vector:

[0018]

[0019] wherein is the original kurtosis value at k time, is the prior state estimation at k time;

[0020] State transition matrix A:

[0021] A = 1

[0022] Measurement matrix H:

[0023] H = 1

[0024] Process noise covariance Q:

[0025] Q = q [Δt]

[0026] wherein Δt is the sampling interval of original kurtosis value, and q is process error;

[0027] Step 2.3, after filtering kurtosis in step 2.2, a sliding window is established on the filtered value, and the original value KUR raw and the filtered value KUR filthe relative error RE_error between the two, while a permissible error boundary is preset, if the RE_error does not exceed the error boundary, it is considered that the current time is still in the normal state, and the next monitoring point is calculated; if the RE_error exceeds the error boundary, the current time is recorded as the FST point, that is, the bearing enters the degradation state from the normal state, the KF algorithm ends, and the RUL prediction process starts,

[0028]

[0029] where RE_error(l) is the relative error at time l, N s is the length of the sliding window, and KUR raw is the Kurtosis value of the bearing vibration signal. fil (i) is the original value and the filtered value of the i-th kurtosis.

[0030] Step 3 is implemented according to the following steps:

[0031] Step 3.1, the degradation model of the bearing is established as:

[0032] z RMS (t) = a·exp(b·t) + c·exp(d·t)

[0033] where Z RMS (t) is the RMS value at time t, a, b, c, and d are unknown parameters in the model.

[0034] Step 3.2, the state equation and the measurement equation of the bearing degradation system are established as:

[0035]

[0036]

[0037] Let where are the process noises of the parameters a, b, c, and d at time k-1 of the system, respectively, then the state equation and the measurement equation are rewritten in the following form:

[0038] x k = [a k ,b k ,c k ,d k ] T = x k-1 +w k-1

[0039]

[0040] where x k and x k-1are the degradation states of the system at time k and k-1 respectively, a k ,b k ,c k ,d k are the state parameters at time k, is the RMS measurement of the system at time k, x k (1), x k (2), x k (3), x k (4) represent a k ,b k ,c k ,d k ,w k-1 is the process noise at time k-1, v k is the measurement noise at time k, both of which are independent and follow zero-mean Gaussian distribution, and their variances are Q = [Q a ,Q b ,Q c ,Q d ] and R, respectively.

[0041] Step 3.3, determine the predicted starting point SPT, fit the RMS values between the FST point and the SPT point by the degradation model established in step 3.1, calculate the Fréchet distance of the fitting curve and the original curve, and finally select the parameters that make the Fréchet distance reach the minimum as the initial parameters of the bearing degradation model in step 3.1.

[0042] Step 3.4, update the bearing degradation model parameters in step 3.1 and estimate the future root mean square value by using the hybrid filtering algorithm combining particle filtering PF and unscented Kalman filtering UKF.

[0043] Step 3.4 is as follows:

[0044] Step 3.4.1, sample a particle set i = 1, 2,..., N from the prior probability density distribution p(x0) of the rolling bearing system, where is the initial state corresponding to the i-th particle, N is the total number of particles, and the initial weight of each particle is 1 / N;

[0045] Step 3.4.2, sample the updated particle from the proposal distribution At the same time, the initial weight of the particle is updated to the importance weight Then the importance weight is normalized where is the importance weight of the i-th particle corresponding to the state at time k-1, is the normalized importance weight of the i-th particle corresponding to the state at time k-1;

[0046] Step 3.4.3, when the effective particle number N eff <N th , resampling is performed, and the sample originally with weight will become an equal weight sample after resampling wherein is the i-th particle corresponding to the state at time 0 to k-1 after resampling, N th is the effective sample number threshold;

[0047] Step 3.4.4, obtaining the state estimation at time k-1 is:

[0048]

[0049] Step 3.4.5, according to the state estimation at time k-1 obtain a set of sigma point sets based on the sampling strategy and the corresponding weight ω 0 , ω 1 , …,

[0050]

[0051]

[0052] wherein, n s is the dimension of the system state vector, λ represents the scaling parameter, P is the covariance matrix, is the j-th column of the square root matrix, and are the weights when calculating the mean and variance of the first sigma point, respectively, α represents the distribution state of the sigma point, and β is the adjustment parameter;

[0053] Step 3.4.6, calculating one-step prediction of the sigma point set obtained in step 3.4.5 :

[0054]

[0055] wherein is the j-th sigma point in the sigma point set, is the one-step prediction of :

[0056] Step 3.4.7, calculating the predicted mean of the system state quantity and the predicted covariance matrix P k|k-1 :

[0057]

[0058]

[0059] Step 3.4.8, compute the predicted mean of the system observation from the predicted mean of the state and the predicted covariance P k|k-1 Again construct the sigma point set

[0060]

[0061] Step 3.4.9, perform the nonlinear transformation on the sigma point set according to the observation model, compute the predicted sampling points of the observation

[0062]

[0063] Step 3.4.10, compute the predicted mean of the system observation

[0064]

[0065] Step 3.4.11, compute the self-covariance P zz,k|k-1 and the cross-covariance P xz,k|k-1 :

[0066]

[0067]

[0068] Step 3.4.12, compute the Kalman gain K k , update the particles with the latest measurement, and compute the posterior state estimation mean and the covariance matrix P k :

[0069]

[0070]

[0071]

[0072] Step 3.4.13, if the failure threshold has not been reached at the current time, return to Step 3.4.2 to update the particles for the next step, continue the hybrid filtering calculation at time k+1, and terminate the algorithm after the failure threshold is reached, outputting the estimated result of the RMS value.

[0073] Step 4 is as follows:

[0074] Step 4.1, a sliding window is established on the RMS estimation value obtained in step 3, and a linear model shown in the following formula is established on the sliding window, every time an RMS estimation value is obtained, the sliding window moves forward one step to contain the next estimation value and discard the oldest estimation value, the linear model in the window is also updated, and the RMS values in the window are combined to solve the gradient of the model by using the least square method, and the failure threshold of the bearing is determined according to the obtained gradient:

[0075] y RMS =gt s +b s

[0076] Wherein, t s represents a time parameter, y RMS represents the estimation value of RMS, b s represents a model parameter, and the coefficient g represents the gradient of the RMS value relative to time, when g is less than or equal to 0, it indicates that the bearing is in a healthy state, and when g is greater than 0, it indicates that the bearing is in a degradation state, the present application sets that when the window length is 50 and the gradient is greater than or equal to 0.02, the bearing fails;

[0077] Step 4.2, if the RMS exceeds the failure threshold at t fail , then the remaining useful life RUL k' at the current time k' is:

[0078] RUL k' =t fail -k'

[0079] Wherein, t fail is the failure time of the rolling bearing, k' is the current time, and RUL k' is the remaining useful life at the time k'.

[0080] The beneficial effects of the present application are that a rolling bearing remaining life prediction method based on mixed filtering and state monitoring first obtains the horizontal vibration signal in the running process of the rolling bearing, and calculates the kurtosis and root mean square value through the vibration signal; secondly, the kurtosis is taken as a state monitoring index, the Kalman filtering algorithm is used to monitor the running state of the bearing and determine the fault starting point; then the root mean square value is taken as a prediction index, the mixed filtering method combining particle filtering and unscented Kalman filtering is used to estimate the future root mean square value, and a sliding window and a linear model are established on the obtained estimation value to determine the failure threshold of the bearing; finally, the time when the prediction index exceeds the failure threshold is judged, and the remaining life prediction result is calculated. The present application can monitor the working state of the rolling bearing in real time, and the remaining life prediction result of the bearing is obtained by using the mixed filtering algorithm, compared with a single filtering algorithm, the present application has higher prediction accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0081] Figure 1 is a general flow chart of a rolling bearing residual service life prediction method based on hybrid filtering and state monitoring according to the present application;

[0082] Figure 2 is a kurtosis filtering result chart of a rolling bearing residual service life prediction method based on hybrid filtering and state monitoring according to the present application;

[0083] Figure 3 is a relative error chart of a rolling bearing residual service life prediction method based on hybrid filtering and state monitoring according to the present application;

[0084] Figure 4 is a residual life prediction result chart of a rolling bearing residual service life prediction method based on hybrid filtering and state monitoring according to the present application. DETAILED DESCRIPTION

[0085] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0086] The rolling bearing residual service life prediction method based on hybrid filtering and state monitoring according to the present application has a flow chart as shown in Figure 1 and is implemented according to the following steps:

[0087] Step 1, obtaining horizontal vibration signals in the running process of a rolling bearing;

[0088] Step 2, calculating kurtosis and root mean square (RMS) values using the horizontal vibration signals obtained in Step 1, and determining the kurtosis and RMS of the horizontal vibration signals as state monitoring indicators and prediction indicators, respectively, then monitoring the running state of the bearing and determining a failure start time (FST) using a Kalman filter (KF) algorithm;

[0089] Step 2 is implemented according to the following steps:

[0090] Step 2.1, determination of state monitoring indicators and prediction indicators: since the vibration signals collected by the sensor have the characteristics of non-stationary, non-linear and strong noise, the running state of the bearing cannot be directly monitored and the residual life cannot be predicted using the vibration signals, and a suitable health indicator needs to be selected, the present application selects kurtosis and RMS as the state monitoring indicators and prediction indicators, respectively, and the calculation method is shown in the following formula:

[0091]

[0092]

[0093] wherein, V kurtosisdenotes kurtosis, V RMS denotes root mean square value, V i denotes the i-th vibration signal, denotes the average value of the vibration signal, n denotes the sampling number;

[0094] Step 2.2, after determining the kurtosis as the monitoring index in step 2.1, then the KF algorithm is used to monitor the running state of the bearing in real time based on the kurtosis and determine the FST point, through analysis of the historical data of the kurtosis, it can be known that the change trend of the kurtosis can be approximately regarded as a linear process in the normal running stage, therefore, the KF based on the linear function model is established as follows:

[0095] State vector:

[0096]

[0097] wherein is the original kurtosis value at k moment, is the prior state estimation at k moment;

[0098] State transition matrix A:

[0099] A = 1

[0100] Measurement matrix H:

[0101] H = 1

[0102] Process noise covariance Q:

[0103] Q = q [Δt]

[0104] wherein Δt is the sampling interval of the original kurtosis value, and q is the process error;

[0105] Step 2.3, after filtering the kurtosis in step 2.2, a sliding window is established on the filtered value, and the relative error RE_error between the original value KUR raw and the filtered value KUR fil is calculated through the following formula, and meanwhile an allowed error boundary is set in advance, if the RE_error does not exceed the error boundary, it is considered that the current moment is still in the normal state, and the next monitoring point is continued to be calculated; if the RE_error exceeds the error boundary, the current moment is recorded as the FST point, that is, the bearing enters the degradation state from the normal state, the KF algorithm ends, and the RUL prediction process begins, the sliding window length is set to 50 and the error boundary is set to 0.3 through analysis of the kurtosis data.

[0106]

[0107] wherein RE_error (l) is the relative error at l moment, N sKUR is the length of the sliding window raw (i) is the original value and filtered value of the i-th kurtosis. fil (i) is the original value and filtered value of the i-th kurtosis.

[0108] Step 3, when the bearing enters the degradation state, a hybrid filtering algorithm combining particle filter PF and unscented Kalman filter UKF is used to estimate the future root mean square value;

[0109] Step 3 is implemented according to the following steps:

[0110] Step 3.1, the degradation model of the bearing is established as:

[0111] z RMS (t) = a·exp(b·t) + c·exp(d·t)

[0112] wherein, Z RMS (t) is the RMS value at time t, a, b, c, d are unknown parameters in the model;

[0113] Step 3.2, the state equation and measurement equation of the bearing degradation system are established as:

[0114]

[0115]

[0116] For ease of description, let wherein are the process noise of parameters a, b, c, d at time k-1 of the system respectively, then the state equation and the measurement equation are rewritten in the following form:

[0117] x k = [a k ,b k ,c k ,d k ] T = x k-1 +w k-1

[0118]

[0119] wherein, x k and x k-1 are the degradation states at time k and k-1 of the system respectively, a k ,b k ,c k ,d k are state parameters at time k, Z k is the RMS measurement value at time k of the system, xk (1),x k (2),x k (3),x k (4) respectively represent a k ,b k ,c k ,d k , w k-1 is the process noise at time k-1 of the system, v k is the measurement noise at time k of the system, both are independent and follow Gaussian distribution with zero mean, and the variance is Q = [Q a , Q b , Q c , Q d ] and R respectively;

[0120] Step 3.3, determine the predicted start point SPT (Start Prediction Time), fit the RMS value between the FST point and the SPT point by the degradation model established in step 3.1, calculate the Fréchet distance of the fitting curve and the original curve, and finally select the parameters that make the Fréchet distance reach the minimum as the initial parameters of the bearing degradation model in step 3.1;

[0121] Step 3.4, update the bearing degradation model parameters in step 3.1 and estimate the future root mean square value by using the hybrid filtering algorithm combining particle filter PF (Particle Filter) and unscented Kalman filter UKF (Unscented Kalman filter).

[0122] Step 3.4 is as follows:

[0123] Step 3.4.1, sample a particle set i = 1, 2,..., N from the prior probability density distribution p(x0) of the rolling bearing system, where is the initial state corresponding to the i-th particle, N is the total number of particles, and the initial weight of each particle is 1 / N;

[0124] Step 3.4.2, sample the updated particle from the proposal distribution At the same time, the initial weight of the particle is updated to the importance weight Then the importance weight is normalized Where is the importance weight of the i-th particle corresponding to the state at time k-1, is the normalized importance weight of the i-th particle corresponding to the state at time k-1;

[0125] Step 3.4.3, when the effective particle number N eff <N th , the original sample with weight is changed into equal weight sample after resampling where is the ith particle corresponding to the state at time 0 to k-1 after resampling, N th is the effective sample number threshold;

[0126] Step 3.4.4, get the state estimation at time k-1 is:

[0127]

[0128] Step 3.4.5, according to the state estimation at time k-1 get a set of sigma points set based on the sampling strategy and the corresponding weight ω 0 , ω 1 , …,

[0129]

[0130]

[0131] where, n s is the dimension of the system state vector, λ represents the scaling parameter, P is the covariance matrix, is the jth column of the square root matrix, and are the weights when calculating the mean and variance of the first sigma point, α represents the distribution state of the sigma point, and β is the adjustment parameter;

[0132] Step 3.4.6, calculate the one-step prediction of the sigma point set obtained in step 3.4.5 :

[0133]

[0134] where is the jth sigma point in the sigma point set, is the one-step prediction of :

[0135] Step 3.4.7, calculate the predicted mean of the system state quantity and the predicted covariance matrix P k|k-1 :

[0136]

[0137]

[0138] Step 3.4.8, calculate the predicted mean value according to step 3.4.7 and the predicted covariance P k|k-1 Again construct the sigma point set

[0139]

[0140] Step 3.4.9, perform nonlinear transformation on the sigma point set according to the observation model, calculate the predicted sampling points of the observation

[0141]

[0142] Step 3.4.10, calculate the predicted mean value of the system observation

[0143]

[0144] Step 3.4.11, calculate the self-covariance P zz,k|k-1 and the cross-covariance P xz,k|k-1 :

[0145]

[0146]

[0147] Step 3.4.12, calculate the Kalman gain K k , update the particles with the latest measurement value, and calculate the posterior state estimation mean value at time k and the covariance matrix P k :

[0148]

[0149]

[0150]

[0151] Step 3.4.13, if the current time does not reach the failure threshold, return to step 3.4.2 for particle update, continue the mixed filtering calculation at time k+1, until the failure threshold is reached, the algorithm terminates, and the estimation result of the RMS value is output.

[0152] Step 4, establish a sliding window and a linear model on the root mean square estimation value obtained in step 3 to determine the failure threshold of the bearing, and judge the time when the root mean square value exceeds the failure threshold, to obtain the remaining life prediction result.

[0153] Step 4 is as follows:

[0154] Step 4.1: Establish a sliding window based on the RMS estimates obtained in Step 3, and build a linear model on this sliding window as shown in the following formula. Each time an RMS estimate is obtained, the sliding window moves forward one step to include the next estimate and discards the oldest estimate. The linear model within the window is also updated accordingly. Simultaneously, the gradient of the model is calculated using the least squares method, combining the RMS values ​​within the window. The bearing failure threshold is determined based on the obtained gradient.

[0155] y RMS =gt s +b s

[0156] Among them, t s Represents the time parameter, y RMS b represents the estimated value of RMS. s The model parameters are represented by the coefficient g, which represents the gradient of the RMS value relative to time. When g is less than or equal to 0, it indicates that the bearing is in a healthy state, and when g is greater than 0, it indicates that the bearing is in a degraded state. This invention analyzes the historical degradation data of the bearing and sets the bearing to fail when the window length is 50 and the gradient is greater than or equal to 0.02.

[0157] Step 4.2, if RMS is at t fail If the failure threshold is exceeded at time k', then the remaining useful life RUL at the current time k' is... k' for:

[0158] RUL k' =t fail -k'

[0159] Among them, t fail Let k' be the moment of failure of the rolling bearing, and RUL be the current moment. k' This represents the remaining lifetime at time k'.

[0160] Figure 2 The kurtosis filtering results obtained by the present invention are shown in the figure. The solid line with circles in the figure represents the true kurtosis value, and the solid line with asterisks represents the filtered kurtosis value. As can be seen from the figure, the proposed method can effectively filter out the interference of external factors such as noise on the status monitoring data. Figure 3 Given Figure 2 The graph shows the relative error between the original and filtered values ​​of kurtosis. The solid line in the graph represents the preset error boundary, the circled solid line represents the relative error curve, and the dashed line represents the FST point, which is the point from which the bearing enters the degradation state. As can be seen from the graph, the relative error increases as degradation progresses. This is because the trend of kurtosis data during the degradation stage does not conform to a linear process. Figure 4The residual life prediction result figure of the rolling bearing obtained by the application is given, the solid line in the figure is the true residual life curve of the rolling bearing, the solid line with square is the predicted residual life curve, and the dotted line is the 30% error boundary, as can be seen from the figure, the residual life prediction result obtained by the application is very close to the true residual life result, and the prediction result is within the 30% error boundary, and has high prediction accuracy.

Claims

1. A method for predicting the remaining life of rolling bearings based on hybrid filtering and condition monitoring, characterized in that, The specific steps are as follows: Step 1: Acquire the horizontal vibration signal during the operation of the rolling bearing; Step 2: Calculate the kurtosis and root mean square (RMS) values ​​using the horizontal vibration signal obtained in Step 1, and determine the kurtosis and RMS of the horizontal vibration signal as the condition monitoring index and prediction index, respectively. Then, use the Kalman filter algorithm (KF) to monitor the operating status of the bearing and determine the fault initiation point (FST). Step 2 is implemented in the following steps: Step 2.1, Determination of State Monitoring and Predictive Indicators: Kurtosis and RMS are selected as the state monitoring and predictive indicators, respectively, and the calculation methods are shown in the following formulas: in, Indicates kurtosis, Represents the root mean square value. Indicates the first A vibration signal, This represents the average value of the vibration signal. Indicates the number of samples; Step 2.2: After determining kurtosis as the monitoring index in Step 2.1, the KF algorithm is then used to monitor the bearing's operating status in real time and determine the FST point based on kurtosis. Analysis of historical kurtosis data shows that during normal operation, the KF algorithm based on a linear function model is established as follows: State vector: in for The original kurtosis value at time 1. for Prior state estimation at time step; State transition matrix : Measurement Matrix : Process noise covariance : in The sampling interval for the original kurtosis values. It is a process error; Step 2.3: After filtering the kurtosis in Step 2.2, establish a sliding window on the filtered values, and calculate the original values ​​within the window using the following formula. and filter value relative error between At the same time, a permissible error boundary is preset, if If the error boundary is not exceeded, the current time is considered to be in a normal state, and the calculation continues to the next monitoring point; if... If the error boundary is exceeded, the current time is recorded as the FST point, indicating that the bearing has entered a degraded state from its normal state. The KF algorithm ends, and the RUL prediction process begins. in for The relative error in time, The length of the sliding window. and For the first The original and filtered values ​​of each kurtosis; Step 3: After the bearing enters the degradation state, a hybrid filtering algorithm combining particle filter (PF) and unscented Kalman filter (UKF) is used to estimate the future root mean square value. Step 3 is implemented in the following steps: Step 3.1: Establish the degradation model of the bearing as follows: in, for RMS value at time 10:00 These are the unknown parameters in the model; Step 3.2: Establish the state equation and measurement equation for the bearing degradation system as follows: make ,in For each system Parameters at time If the process noise is considered, the state equation and measurement equation can be rewritten in the following form: in, and For each system Time and The state of degradation at any given moment. for State parameters at time, For the system RMS measurement at time 10:00 Represent , For the system Process noise at any given time, For the system The measurement noise at time t is independent of each other and both follow a Gaussian distribution with zero mean, with variances of t and t respectively. and ; Step 3.3: Determine the prediction starting point SPT, fit the RMS value between the FST point and the SPT point using the degradation model established in Step 3.1, calculate the Fréchet distance between the fitted curve and the original curve, and finally select the parameter that minimizes the Fréchet distance as the initial parameter of the bearing degradation model in Step 3.

1. Step 3.4: Update the bearing degradation model parameters in Step 3.1 and estimate the future root mean square value using a hybrid filtering algorithm that combines particle filter (PF) and unscented Kalman filter (UKF). Step 4: Establish a sliding window and a linear model based on the root mean square estimate obtained in step 3 to determine the failure threshold of the bearing and to determine the moment when the root mean square value exceeds the failure threshold, thereby obtaining the remaining life prediction result.

2. The method for predicting the remaining life of rolling bearings based on hybrid filtering and condition monitoring according to claim 1, characterized in that, Step 3.4 is as follows: Step 3.4.1: From the prior probability density distribution of the rolling bearing system Particle set obtained by sampling ,in The state corresponding to the initial time. One particle, Let be the total number of particles, and let the initial weight of each particle be . ; Step 3.4.2, from the suggested distribution Mid-sampling yields updated particles At the same time, the initial weights of the particles are updated to importance weights. Next, the importance weights are normalized. ,in for The state at time corresponds to the 1st The importance weight of each particle. for The state at time corresponds to the 1st The normalized importance weights of each particle; Step 3.4.3, when the number of effective particles When resampling is performed, the original weighted samples will become equally weighted samples after resampling. ,in , For resampling The state corresponding to time step 1 One particle, The threshold for the number of valid samples; Step 3.4.4, obtain State estimation at time 1 for: Steps 3, 4, and 5, according to Moment A set of samples is obtained based on the sampling strategy. dot set and corresponding weights : in, Let be the dimension of the system state vector. This represents the scaling parameter. Let covariance matrix be the variance matrix. The square root matrix is ​​the first... List, The first one The weights used when calculating the mean and variance of points. express The distribution of points To adjust the parameters; Step 3.4.6: Calculate the result obtained in step 3.4.

5. dot set One step of prediction: in for The first point in the set indivual point, for A one-step prediction; Step 3.4.7: Calculate the predicted mean of the system state variables. and predicting covariance matrix : Step 3.4.8: Based on the predicted mean obtained in step 3.4.7 and predicted covariance Reconstruction dot set : Step 3.4.9: Based on the observation model... dot set Perform nonlinear transformation to calculate the predicted sampling points of the observations. : Step 3.4.10: Calculate the predicted mean of the system observations. : Step 3.4.11: Calculate the autocovariance and mutual covariance : Step 3.4.12: Calculate the Kalman gain. Update the particles with the latest measurements and calculate. Mean of posterior state estimate at time step Covariance Matrix : Step 3.4.13: If the failure threshold has not been reached at the current moment, return to step 3.4.2 to perform the next particle update and continue. The algorithm performs mixed filtering calculations at each time step until the failure threshold is reached, at which point it terminates and outputs the estimated RMS value.

3. The method for predicting the remaining life of rolling bearings based on hybrid filtering and condition monitoring according to claim 2, characterized in that, Step 4 is as follows: Step 4.1: Establish a sliding window based on the RMS estimates obtained in Step 3, and build a linear model on this sliding window as shown in the following formula. Each time an RMS estimate is obtained, the sliding window moves forward one step to include the next estimate and discards the oldest estimate. The linear model within the window is also updated accordingly. Simultaneously, the gradient of the model is calculated using the least squares method, combining the RMS values ​​within the window. The bearing failure threshold is determined based on the obtained gradient. in, Indicates time parameter, This represents the estimated value of RMS. Represents model parameters, coefficients This represents the gradient of the RMS value relative to time, when A value less than or equal to 0 indicates that the bearing is in good condition. A value greater than 0 indicates that the bearing is in a degraded state. This invention analyzes the historical degradation data of the bearing and sets the bearing to fail when the window length is 50 and the gradient is greater than or equal to 0.

02. Step 4.2, if RMS is in If the time exceeds the failure threshold, then the current time... Remaining service life for: in, This is the failure moment of the rolling bearing. For the current moment, for The remaining service life at any given moment.

Images