CN114662226A - Time-varying Kalman filtering-based method for predicting residual service life of rolling bearing - Google Patents

Time-varying Kalman filtering-based method for predicting residual service life of rolling bearing Download PDF

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CN114662226A
CN114662226A CN202210173117.4A CN202210173117A CN114662226A CN 114662226 A CN114662226 A CN 114662226A CN 202210173117 A CN202210173117 A CN 202210173117A CN 114662226 A CN114662226 A CN 114662226A
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崔玲丽
王鑫
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乔文生
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Abstract

The invention discloses a rolling bearing residual service life prediction method based on time-varying Kalman filtering, which can automatically match the characteristics of different degradation stages of a rolling bearing, respectively establish a time-varying Kalman filter model based on a primary linear function and a secondary nonlinear function, judge the degradation state of the bearing in a self-adaptive manner by using a time-shifting window filtering relative error index factor, automatically switch a Kalman filter to process monitoring data of different stages, and realize effective prediction of the residual service life of the bearing.

Description

Time-varying Kalman filtering-based method for predicting residual service life of rolling bearing
Technical Field
The invention belongs to the technical field of mechanical fault prediction, health management and signal processing, and relates to a residual service life prediction method based on time-varying Kalman filtering.
Background
The supporting and driving parts of mechanical equipment such as bearings, gears, rotating shafts and the like are key parts. Once the part fails, mechanical equipment cannot work normally if the part is light, and serious safety accidents occur if the part is heavy, which bring huge losses to production and life. If the fault can be detected as early as possible, even the occurrence of the fault can be predicted, and the method has more application value in practice. Because the rolling bearing is widely applied to rotary machinery and is easy to break down, more and more attention is paid to the research on the prediction of the residual service life of the rolling bearing.
Currently, a life prediction technology based on a data-driven method is researched more. According to the rolling bearing state data monitored by the sensor, the dynamic behavior of the rolling bearing is tracked in real time, and the degradation process is predicted. In the data driving method for predicting the remaining service life of the rolling bearing, one key problem is to determine the time for starting the service life prediction. Generally, the health index of the whole life cycle of the rolling bearing is tracked, and the health stage is divided. Therefore, the establishment and the selection of the health indexes are very important, the proper indexes can accurately measure different degradation stages of the bearing, the established model is simplified, and the efficiency and the accuracy of life prediction are improved. The traditional method adopts a 3 sigma principle to divide the bearing degradation process into two stages, namely a healthy stage and a degradation stage; determining a starting life prediction point by using the degradation speed; and judging the stage of the bearing at each moment by using a switch Kalman filtering method to track the degradation process of the bearing and the like. However, these methods still have some problems to be solved. First, determining the degradation point according to the 3 σ principle is susceptible to interference by outliers. Second, the degradation speed is a dimensional physical quantity, and whether it exceeds a certain positive value to determine the start prediction point may differ depending on individual bearing differences. Finally, the switching Kalman filtering method uses three models for filtering and estimates the probabilities of the three models at each calculation point, and the calculation cost is high.
In order to accurately judge the initial service life prediction point and effectively predict the residual service life of the rolling bearing, the invention provides a service life prediction method based on time-varying Kalman filtering.
Disclosure of Invention
The invention aims to provide a residual service life prediction method based on time-varying Kalman filtering, so as to solve the problems in the service life prediction of a rolling bearing.
In order to achieve the purpose, the technical scheme adopted by the invention is a rolling bearing residual service life prediction method based on time-varying Kalman filtering, the method can automatically match the characteristics of the rolling bearing in different degradation stages, time-varying Kalman filter models based on a primary linear function and a secondary nonlinear function are respectively established, the degradation state of the bearing is judged in a self-adaptive manner by using time-varying window filtering relative error index factors, and the Kalman filter is automatically switched to process monitoring data in different stages, so that the effective prediction of the residual service life of the bearing is realized.
S1, a time-varying Kalman filter model;
defining a state vector X of a random discrete time processkE, R, the linear system discrete random difference equation is as follows:
Xk＝AXk-1+Wk
wherein XkN is the n multiplied by 1 dimensional system state vector at the time of k, and n is the number of state variables; xk-1Is the system state vector at the moment of k-1; a is an nxn dimensional one-step state transition matrix; w is a group ofkIs n × 1 dimensional process excitation noise at time k;
to XkSatisfies a linear relationship, defines a measurement vector ZkE r, the measurement equation is:
Zk＝HXk+Vk
wherein ZkIs the state measurement at time k; h is a 1 Xn dimensional measurement matrix; vkIs the measurement noise at time k;
suppose Wk、VkThe method is mutually independent and normally distributed white noise, a process excitation noise covariance matrix is Q, a measurement noise covariance matrix is R, namely: wk～N(0,Q),Vk～N(0,R)；
And (3) state one-step prediction:
Figure BDA0003519284180000031
covariance one-step prediction:
Figure BDA0003519284180000032
kalman gain:
Figure BDA0003519284180000033
and (3) state updating:
Figure BDA0003519284180000034
and (3) covariance updating:
Figure BDA0003519284180000035
in the formula
Figure BDA0003519284180000036
Representing the estimated value of the a priori state at the time k,
Figure BDA0003519284180000037
representing the a priori covariance estimate at time K, KkRepresenting the Kalman gain, Xk,Xk-1The posterior state estimated value at the k moment and the k-1 moment is represented, namely the optimal estimated value at the moment to be output is represented, and the value is the result of Kalman filtering; pk,Pk-1Representing posterior covariance estimated values at the k moment and the k-1 moment;
the degradation process of the rolling bearing has diversity and different degradation stages generally, the Kalman filtering algorithm highly depends on the accuracy of the established model, if the filtering is carried out by only using a single filter model, the actual degradation rule is not conformed, so the data processing and prediction are difficult to be effectively carried out, aiming at the general evolution rule of the degradation process of the bearing, two types of filter models are provided, namely, a Kalman filter based on a primary function model and a Kalman filter based on a secondary function model, the new bearing is considered to be in a healthy state without losing the generality, so the Kalman filter based on the primary function model is firstly used for filtering a health index, meanwhile, a section of data near a current monitoring point before and after the filtering is respectively intercepted, the average value of the two is calculated to obtain a relative error, the relative error index is defined as a time-shifting window filtering relative error factor, the index is used for judging the switching of the models, an allowable error limit is preset, if the calculated error value does not exceed the threshold, the current monitoring data evolution trend is considered to be in accordance with the established filter model, the monitoring calculation of the next point can be carried out, once the obtained error value exceeds the range, the evolution trend of the monitoring data is considered to be no longer a linear degradation process and not be in accordance with the established Kalman filter based on the primary function model, the accelerated degradation process is started, the moment is a prediction point, the process of the accelerated degradation of the general bearing has the characteristic of high nonlinearity, therefore, the health index obtained by the subsequent monitoring is filtered by the Kalman filter based on the quadratic function model, after each step of filtering, the future data is predicted by using the updated model parameters, and whether the preset failure threshold is exceeded or not is judged, if the failure threshold is exceeded, the bearing fails, the machine is stopped for maintenance, if the failure threshold is not exceeded, the remaining service life is calculated, guidance is made for state monitoring and maintenance decisions, and the established two types of filter models are described as follows:
s1.1, a Kalman filter based on a linear function model;
state vector:
Figure BDA0003519284180000041
wherein xkIs the health indicator at time k;
state transition matrix:
A1＝[1]
measuring a matrix:
H1＝[1]
process noise covariance matrix:
Q1＝q[Δt]
wherein, Δ t is the sampling time interval of the health index, q is the process noise for measuring the uncertainty of the system, and can be obtained by debugging a filter model by using the historical bearing full-life failure data, and in addition, the measurement error R can also be measured by using the root mean square value of the degradation stage index in the historical bearing full-life failure data;
s1.2, a Kalman filter based on a quadratic function model;
state vector:
Figure BDA0003519284180000051
state transition matrix:
Figure BDA0003519284180000052
measuring a matrix:
H2＝[1 0 0]
process noise covariance matrix:
Figure BDA0003519284180000053
s2, filtering the relative error factor by the time-shift window;
the Kalman filtering algorithm is an algorithm strictly based on a model, the requirement on the accuracy of the model is high, once the established model is inconsistent with the actual condition, a filtering result has a large error, and for the degradation process of a bearing, when the degradation process of the bearing enters an accelerated degradation stage, the evolution process of the root mean square value of state monitoring data is not linear change any more, so that the filtering is performed by using an initially established Kalman filter based on a linear function model, the large error is caused, based on the result, a time-shift window filtering relative error index factor is established, once an index deviates from an acceptable threshold value, the currently used filter model is considered to be inconsistent with the actual condition, and the bearing can be judged to enter the accelerated degradation stage, and the established index is specifically described as follows:
root mean square value of the original monitoring is expressed as RMSmea(k) The filtering result is expressed as RMSfil(k) From the current moment, respectively backward intercepting n data points from the two groups of data, calculating the mean value of the data points, and defining the relative error of the two groups of data as a relative error factor of time shift window filtering:
Figure BDA0003519284180000061
s3 residual service life prediction;
the current moment k is set to enter an accelerated degradation stage, the future state monitoring data can be predicted by applying a Kalman filtering algorithm, and when the predicted value RMS is usedfore(t) is more than or equal to the failure threshold value, the bearing is judged to be in the failure state, and the moment is recorded as tfailFrom this, the remaining service life can be obtained:
RUL(k)＝tfail-k
in addition, uncertainty evaluation of the service life is also an important evaluation index, uncertainty evaluation can be calculated through a covariance matrix P, and at a 95% confidence interval, the predicted upper and lower limits of the health index are respectively as follows:
RMSlb(t)＝RMSfore(t)-1.96×P(1,1)
RMSub(t)＝RMSfore(t)+1.96×P(1,1)
the upper and lower limits of remaining useful life may then be RMSlbAnd RMSubThe time at which the failure threshold is exceeded.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a novel time-varying Kalman filtering method for predicting the residual service life of a rolling bearing. The degradation process of the bearing is divided into a normal working stage and a degradation stage. And establishing a Kalman filter based on a linear function model aiming at the normal working stage. And establishing a Kalman filter based on a quadratic function model aiming at the degradation stage. Based on the characteristic that Kalman filtering algorithm has high requirement on model accuracy, a time-shifting window filtering relative error index factor is constructed and used for judging the health state of a bearing so as to switch two filter models. A model switching threshold of 5% is proposed. The filter can be adaptively switched from the filter based on the primary function model to the filter based on the secondary function model, meanwhile, the future state data prediction is started, and the predicted data is judged to exceed a preset failure threshold point, so that the residual service life of the bearing is estimated.
Drawings
FIG. 1 is a schematic flow chart of a time-varying Kalman filtering algorithm-based remaining service life prediction method.
Fig. 2 is a schematic diagram of construction of a time-shift window filtering relative error index.
FIG. 3 is a time-varying Kalman filtering algorithm filtering result of a time-domain health indicator.
Fig. 4 is a real-time-shifted window filter relative error indicator.
Fig. 5 is a prediction result of the condition monitoring index. t is t1＝148.5h，t2＝150.5h。
Fig. 6 is a real-time remaining service life prediction result.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
(1) Actually measuring the acceleration performance degradation data of the rolling bearing, and calculating a root mean square value as a health index. Take the experimental data of the accelerated degradation performance of the rolling bearing disclosed by the university of cincinnati in the United states as an example. The rotating shaft is supported by 4 Rexhord ZA-2115 double-row rolling bearings, and a bearing seat of each bearing is provided with a sensor for collecting data simultaneously. A 6000lbs load was applied radially to accelerate the bearing degradation process. Data are collected every 10min, 980 times of data are collected by the end of the experiment, and the total time is about 160 h. Wherein the health indicator evolution curve of the bearing 2 is shown in the marked line of fig. 3.
(2) Firstly, a kalman filter based on a linear function model is applied to filter the health index, and the result is shown in an O-line in fig. 3. The calculation of the relative error indicator of the time-shift window filtering is shown in fig. 4. From fig. 4, the time when the bearing enters degradation can be automatically determined as the start life prediction point.
(3) When the relative error index of the time shift window filtering exceeds the allowable error, the health index of the Kalman filter based on the quadratic function model is switched to carry out filtering processing, and the result is shown as a delta marked line of figure 3. At the same time, a prediction of future health indicators is initiated, as shown in fig. 5.
(4) And finally, judging the moment when the predicted health index exceeds a preset failure threshold value to obtain an estimation result of the residual service life, as shown in fig. 6.

Claims (2)

1. A rolling bearing residual service life prediction method based on time-varying Kalman filtering is characterized in that: the method automatically matches the characteristics of different degradation stages of the rolling bearing, respectively establishes a time-varying Kalman filter model based on a primary linear function and a secondary nonlinear function, adaptively judges the degradation state of the bearing according to a time-shifting window filtering relative error index factor, automatically switches the Kalman filter to process monitoring data of different stages, and realizes effective prediction of the residual service life of the bearing;
s1 a time-varying kalman filter model;
defining a state vector X of a random discrete time processkE, R, the linear system discrete random difference equation is as follows:
Xk＝AXk-1+Wk
wherein XkN is the n multiplied by 1 dimensional system state vector at the time of k, and n is the number of state variables; xk-1Is the system state vector at the moment of k-1; a is an nxn dimensional one-step state transition matrix; wkIs n × 1 dimensional process excitation noise at time k;
to XkSatisfies a linear relationship, defines a measurement vector ZkE, R, the measurement equation is as follows:
Zk＝HXk+Vk
wherein ZkIs the state measurement at time k; h is a 1 Xn dimensional measurement matrix; vkIs the measurement noise at time k;
suppose Wk、VkThe method is mutually independent, normally distributed white noise, the process excitation noise covariance matrix is Q, the measurement noise covariance matrix is R, namely: wk～N(0，Q)，Vk～N(0，R)；
And (3) state one-step prediction:
Figure FDA0003519284170000011
covariance one-step prediction:
Figure FDA0003519284170000012
kalman gain:
Figure FDA0003519284170000013
and (3) state updating:
Figure FDA0003519284170000021
and (3) covariance updating:
Figure FDA0003519284170000022
in the formula
Figure FDA0003519284170000023
Representing the estimated value of the a priori state at the time k,
Figure FDA0003519284170000024
represents the prior covariance estimate of time K, KkDenotes the Kalman gain, Xk，Xk-1Indicates time k and after time k-1Checking a state estimation value, namely an optimal estimation value at the moment to be output, wherein the value is a Kalman filtering result; p isk，Pk-1Representing posterior covariance estimated values at the k moment and the k-1 moment;
the established two types of filter models are specifically described as follows:
s1.1, a Kalman filter based on a linear function model;
state vector:
Figure FDA0003519284170000025
wherein xkIs the health indicator at time k;
state transition matrix:
A1＝[1]
measuring a matrix:
H1＝[1]
process noise covariance matrix:
Q1＝q[Δt]
wherein, Δ t is the sampling time interval of the health index, q is the process noise for measuring the uncertainty of the system, and can be obtained by debugging a filter model by using the historical bearing full-life failure data, and in addition, the measurement error R can also be measured by using the root mean square value of the degradation stage index in the historical bearing full-life failure data;
s1.2, a Kalman filter based on a quadratic function model;
state vector:
Figure FDA0003519284170000026
state transition matrix:
Figure FDA0003519284170000031
measuring a matrix:
H2＝[1 0 0]
process noise covariance matrix:
Figure FDA0003519284170000032
s2, filtering the relative error factor by the time-shift window;
the established indexes are described in detail as follows:
root mean square value of the original monitoring is expressed as RMSmea(k) The filtering result is expressed as RMSfil(k) From the current moment, respectively backward intercepting n data points from the two groups of data, calculating the mean value of the data points, and defining the relative error of the two groups of data as a relative error factor of time shift window filtering:
Figure FDA0003519284170000033
s3 residual service life prediction;
the current moment k is set to enter an accelerated degradation stage, the future state monitoring data can be predicted by applying a Kalman filtering algorithm, and when the predicted value RMS is usedfore(t) is more than or equal to the failure threshold value, the bearing is judged to be in the failure state, and the moment is recorded as tfailFrom this, the remaining service life can be obtained:
RUL(k)＝tfail-k
in addition, uncertainty evaluation of the service life is also an important evaluation index, uncertainty evaluation can be calculated through a covariance matrix P, and the upper and lower limits of the predicted health index are respectively:
RMSlb(t)＝RMSfore(t)-1.96×P(1，1)
RMSub(t)＝RMSfore(t)+1.96×P(1，1)
then, RMS is used to lower and upper limits on remaining useful lifelbAnd RMSubThe time at which the failure threshold is exceeded.
2. The rolling bearing residual service life prediction method based on the time-varying Kalman filtering according to claim 1 is characterized in that:
(1) respectively establishing a time-varying Kalman filter model based on a linear function and a nonlinear function;
(2) the degradation state of the bearing is judged in a self-adaptive mode through the time-shifting window filtering relative error index factors, monitoring data of different stages are processed through a Kalman filter in an automatic switching mode, and the residual service life of the bearing is effectively predicted.
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