CN117291290A - Rolling bearing integrated service life prediction method based on double-flow infinite particle filtering - Google Patents

Rolling bearing integrated service life prediction method based on double-flow infinite particle filtering Download PDF

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CN117291290A
CN117291290A CN202310950277.XA CN202310950277A CN117291290A CN 117291290 A CN117291290 A CN 117291290A CN 202310950277 A CN202310950277 A CN 202310950277A CN 117291290 A CN117291290 A CN 117291290A
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崔玲丽
李文杰
刘东东
王华庆
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Abstract

The invention discloses a rolling bearing integrated life prediction method based on double-flow infinite particle filtering. In rotating machines, the degradation process is complex due to the poor consistency of the rolling bearings, making accurate predictions of their remaining service life a great challenge. In this regard, the invention discloses a rolling bearing life prediction method based on double-flow infinite particle filtering to estimate the integrated life of a bearing. Firstly, adopting a similarity measurement-based method to adaptively identify the degradation stage of the rolling bearing; secondly, based on the characteristics of an exponential model and a polynomial model, a double-flow infinite particle filter model is constructed, and the effective mining of the whole degradation trend and the local fluctuation double-flow information of the rolling bearing is realized; in order to comprehensively evaluate the overall health state of the rolling bearing, a comprehensive fusion strategy based on dynamic Bayes is provided for quantitatively evaluating the failure probability of the double-flow information source, so that the effective estimation of the integrated service life of the rolling bearing is realized.

Description

Rolling bearing integrated service life prediction method based on double-flow infinite particle filtering
Technical Field
The invention belongs to the technical field of fault prediction and health management, and relates to a rolling bearing integrated life prediction method based on double-flow infinite particle filtering.
Background
Rolling bearings are used as key components of rotary machines, and their health state is directly related to whether the machine can operate well or not. When a rolling bearing fails, the machine should be shut down as soon as possible to avoid catastrophic consequences, which often occurs at inconvenient times, thus often resulting in considerable time wastage and economic loss. If the health state of the bearing can be monitored in real time, predictive maintenance is adopted for the equipment, so that not only can major safety accidents be effectively avoided, but also the unplanned maintenance cost of the machine can be reduced. Therefore, it is important to monitor the running state of the bearing and predict its remaining service life.
Currently, lifetime prediction methods can be generally classified into two categories: data driven methods and model-based methods. The data driving method utilizes artificial intelligence technology, convolutional neural network, related vector machine, fuzzy neural system and the like to estimate the operation state of the mechanical equipment by learning historical observation data and then predict the residual life of the mechanical equipment. However, such methods rely on large amounts of high quality experimental data, which is extremely difficult to obtain in engineering practice. The model-based method is to build a model reflecting the health state of the bearing to describe the degradation process of the bearing, and then update model parameters in real time and predict the residual life of the model parameters based on the monitoring data. Such methods do not require a clear bearing failure mechanism nor a large amount of data to train, and therefore find extremely wide application in bearing life prediction. The use of the infinite particle filter as a powerful nonlinear filtering technique has received increased attention in health estimation and life prediction. However, the model of the infinite particle filter constructed empirically has poor robustness, and particularly when the bearing degradation process is complex, the prediction accuracy is low.
Disclosure of Invention
The invention aims to provide a rolling bearing integrated life prediction method based on double-flow infinite particle filtering so as to improve the life prediction precision of a rolling bearing in a fluctuation degradation process.
In order to achieve the above purpose, the invention provides a rolling bearing integrated life prediction method based on double-flow unscented particle filtering. Firstly, adopting a similarity measurement-based method to adaptively identify the degradation stage of the rolling bearing; secondly, based on the characteristics of an exponential model and a polynomial model, a double-flow infinite particle filter model is constructed, and effective mining of double-flow information of overall degradation trend and local fluctuation of the bearing is realized; in order to comprehensively evaluate the overall health state of the bearing, a comprehensive fusion strategy based on dynamic Bayes is provided for quantitatively evaluating the failure probability of the double-flow information source, so that the effective estimation of the integrated service life of the rolling bearing in the fluctuation process is realized.
S1, an infinite particle filter theory;
particle Filtering (PF) is an approximate Bayesian filtering algorithm based on Monte Carlo simulation, and the core idea is to approximate the probability density function of the system random variable with a set of discrete random sampling points, and replace the integral operation with the sample mean value, thereby obtaining the minimum variance estimation of the state. Because of the superiority presented in dealing with non-linear, non-gaussian problems, PF technology has been proposed to be widely used in various fields, since orcard et al first introduced PF into life prediction in 2005, and many students at home and abroad began to use PF algorithm to predict the remaining life of rolling bearings.
In PF-based rolling bearing life prediction, the degradation process of a bearing system is often described by constructing a state model, consisting in particular of a set of state equations and measurement equations, as follows:
x k ＝f k (x k-1 ，v k-1 )
y k ＝h k (x k ，w k )
wherein x is k Is the health state of the bearing system, and subscript k represents time; v k Is bearing system noise, often manifested as gaussian white noise; f (f) k The state transfer function of the bearing system often reflects the relation between the working state of the bearing at the current moment and the working state of the bearing at the previous moment and is often expressed as a linear or nonlinear relation; y is k Is the measured value of the bearing system at the moment k; w (w) k Measuring noise for the sensor, the mean and variance of which are inherent properties of the sensor; h is a k The relationship between the bearing state and the measurement result is expressed as a bearing system measurement function, and is often expressed as a linear relationship.
However, the conventional PF often has a particle degradation problem, that is, after several iterations, the weight of most of the bearing state particles is small to a negligible extent, and continuing the iterations not only causes a waste of computing resources, but also causes inaccurate bearing state estimation.
Whereas UPF constructs the importance sample distribution of particle filtering by Unscented Kalman Filtering (UKF). When the mean value and variance of the state of the bearing are calculated, UKF utilizes the latest measurement information based on unscented transformation, so that the tracking precision of the state particles is improved, and the degradation problem of the state particles can be improved to a certain extent.
The UPF algorithm flow is as follows:
1) And (3) initializing. When k=0, the distribution p (x 0 ) Sampling M bearing state particles to generate an original state particle setSetting the weight of each state particle to +.>When k is more than 0, k=k+1, then sequentially iterating to obtain the state particle group +.>
2) Importance sampling stage. Firstly, calculating the mean value of each state particle by using UKF algorithmSum covarianceAccording to Gaussian distribution->The sample update state particles are calculated as follows:
then, the weight of each state particle is updated by using the measurement value:
finally, normalizing the weight of the bearing state particles:
3) And (3) resampling. The state particles are weighted according to the weightAnd sorting, namely discarding the state particles with smaller weights under the condition that the number of the particles is unchanged, and copying the state particles with larger weights. The common resampling algorithms now include random resampling, systematic resampling, polynomial resampling and residual resampling, and resampling the resampled state particlesAnd (3) carrying out equivalence treatment on the weight values of the components.
4) And a state estimation stage. The state particles are weighted and summed to achieve an effective estimate of the bearing health.
Wherein P is k Is the covariance matrix of the UPF at time k.
S3, a rolling bearing integrated service life prediction method based on double-flow unscented particle filtering;
s3.1, determining initial degradation Time (TSD);
after determining the Health Index (HI) of the rolling bearing's full life cycle, real-time monitoring of when the bearing enters the degradation phase is the first step in life prediction work.
The method of similarity is used herein to estimate the initial degradation moment of the bearing, i.e., the TSD point. The specific estimation flow is as follows: firstly, setting a fixed window with the length of M, selecting HI in a health state as a basic reference data set, simultaneously setting a sliding window 1 with the same length, intercepting M latest state estimated values, and finally calculating Euclidean distance between two groups of data to measure similarity between the two groups of data:
by calculating the Euclidean distance between the sliding window and the fixed window data at each moment, the variation curve of the Euclidean distance along with time is obtained, and the average value mu of the Euclidean distance in the health stage is calculated Dist And mu Dist Is taken as a degradation threshold DT that determines the bearing entering the degradation phase. When the Euclidean distance at a certain moment is monitored to exceed DT for the first time, the bearing is indicated to enter a degradation stage, and the sliding window is at the momentThe mouth contains partial health data and degradation data, has better trend and contains certain early weak fault information. To make full use of the degradation data, the moment before the sliding window is chosen here as the moment when the bearing enters the degradation phase, i.e. the TSD point.
S3.2, starting to determine a prediction Time (TSP) and a Failure Threshold (FT);
when the bearing is monitored to enter the degradation stage, in order to effectively utilize degradation data, the health state of the bearing needs to be estimated in the latest period, and when the length of the health state estimated value reaches the predicted length requirement, the RUL of the bearing can be predicted. The state of health of the bearing at this stage is estimated using a hybrid model comprising an exponential model and a quadratic polynomial as the state model for the UPF.
Wherein a is 1 ，a 2 ，a 3 ，a 4 ，a 5 Are coefficient vectors of the mixed model, t is different monitoring moments, v k To measure noise.
In determining TSP point, a sliding window 2 with length L is firstly set, L HI which just enters degradation stage are intercepted, and then the degradation state of the bearing when TSD+L is estimated by adopting UPF based on mixed modelThen move the sliding window forward and estimate the health status at the next moment +.>And the process is repeated in a circulating way. When the length of the state estimation value set is greater than L min At the moment, the RUL of the bearing can be estimated min Is the preset predicted bearing RUL minimum length. And the current time is set as the TSP point of the bearing.
After determining the TSP point, the FT of the bearing is then estimated. Firstly, it is necessary to intercept the state of healthHealth index z of (2) 1 ，z 2 ，...，z TSP-1 The mean μ and variance σ of the set of data sets are then calculated, and finally the Failure Threshold (FT) of the bearing is calculated:
FT＝μ+λσ
where λ is a complete failure criterion coefficient, the value of which depends on the specific bearing operating condition.
S3.2 integrated life (IRUL) prediction;
in the working process of the bearing, the performance degradation process of the bearing wholly presents a fluctuation rising trend. The degradation trend of the bearing shows the evolution trend of the health state, and the local fluctuation hides the latest defect expansion condition of the bearing, and the degradation trend of the bearing is respectively revealed from different time scales, so that the IRUL of the bearing is predicted to fully consider the whole health state and the local health state.
The provided integrated life prediction flow is as follows:
1) Stream one: long-term RUL prediction based on global degradation trend:
in the performance degradation process of the bearing, HI of the bearing is in an overall rising trend, and one of research hotspots of life prediction is to mine trend information of the degradation process. In a common life prediction model, the index model has extremely high stability, so that the index model is used as a UPF state model to analyze the degradation trend of the whole bearing, and the long-term prediction of RUL of the bearing is realized as follows:
wherein a is 1 ，a 2 Coefficient vectors of the index model, t is different monitoring moments, v k To measure noise.
When the bearing is monitored to enter the RUL predictable degradation stage, all state estimation values are intercepted, and then index model parameters are estimated based on UPF to obtain a global optimal degradation modelAnd predicting future degradation state of bearingIn order to estimate the global failure life of the bearing, a dynamic Bayesian is proposed to estimate the failure probability at each time in the future, as follows:
wherein,indicating that the bearing is at t 0 To t 0 All are healthy at time +j-1, and at t 0 Probability of beginning failure at time +j, +.>Is from t 0 To t 0 Probability that the bearings remain healthy at moment +j-1,/->At t 0 Probability of failure at +j moment, probability value of the invention is 0-1; q is a standard Gaussian distribution function, and sigma is a standard deviation in a certain time period.
Thus, the failure probability of the bearing at each time in the future is obtained, wherein the maximum failure probability LT_p k The corresponding time is the long-term failure time LPre_t 0 The following formula:
thus t 0 The long-term bearing RUL estimated at the moment is:
LT_RUL k ＝LPre_t k -t k
2) Stream two: short-term RUL prediction based on local fluctuation information:
in the performance degradation process of the bearing, the expansion condition of the defects and the health index are not in a simple linear mapping relation, but have a complex mechanism. For example, the fatigue spalling process of a bearing may involve one or several fluctuations, each of which may contain failure information that directly leads to failure of the bearing. Modeling and life prediction for the wave process is extremely difficult because the time, duration and amplitude of each wave generation are uncertain. In order to maximally utilize fault information hidden in the fluctuation process, a mixed model of a high-order polynomial and an index is adopted for predicting short-term fluctuation service life. In the mixed model, the exponential model can well track local degradation trend, and due to the existence of the high-order polynomial, the mixed model can timely respond to mutation of the local degradation trend, so that the latest local degradation information is effectively utilized.
When the bearing enters a predictable degradation stage, prediction of its short term fluctuation life may begin. Firstly, a sliding window 3 with the length of N needs to be set to intercept the nearest HI, then a mixed model is used as a UPF state model, and finally the short-term fluctuation life SF_RUL is obtained based on a dynamic Bayesian algorithm k Probability of failure SF_p k The specific calculation flow is the same as the long-term trend life calculation process in the previous section.
However, in predicting short-term fluctuation life with complex degradation process, there is a high probability that mixed model failure occurs, and the local optimal degradation model cannot effectively predict future degradation trend, and the failure probability value lf_p k And is well below normal. Therefore, in order to cope with such a situation, it is necessary to set a model minimum failure probability p min . When the failure probability of the mixed model prediction is smaller than p min When the hybrid model is replaced by a more stable oneAnd predicting by an index model. When the exponential model also fails, indicating a more complex degradation process of the bearing, the local prediction cannot provide an effective RUL prediction value, and the SF_RUL is caused to be k ＝0，SF_p k =0, i.e. the long-term trend lifetime is defaulted as the final lifetime prediction result.
3) Integrated lifetime IRUL estimation:
after a long-term trend lifetime lt_rul is obtained k And short-term fluctuation life SF_RUL k Then, based on the double-flow failure probability, the integrated service life ERUL of the bearing k And (3) predicting:
s3.3, performance evaluation indexes;
in order to quantitatively measure the predictive performance of the proposed algorithm, several predictive models are introduced herein, a minimum mean square error RMSE and an accumulated relative accuracy CRA.
RMSE is a measure reflecting the difference between the estimated value and the true value, and can better reflect the accuracy of prediction, and the calculation method is as follows:
wherein,predicting a lifetime value for time t, < >>Is the real life value at the moment t, t Eol To reach the corresponding failure time t when the failure threshold value is reached TSP To start the predicted time.
Relative accuracy refers to the relative prediction error at a particular instant:
to comprehensively measure the overall prediction effect, an accumulated relative precision index (CRA) is obtained by accumulating weights for the relative precision at each time instant:
wherein omega λ Is a normalized weight coefficient, and K is the length of the predicted result.
Compared with the prior art, the invention has the following beneficial effects:
the technical scheme adopted by the invention is a rolling bearing integrated life prediction method based on double-flow infinite particle filtering. Firstly, the method realizes the self-adaptive identification of the bearing degradation stage based on the similarity principle; secondly, aiming at the problems of low prediction precision caused by poor consistency and complex degradation process of the rolling bearing, an exponential model and a polynomial model are respectively adopted to analyze long-term degradation trend and short-term local fluctuation of the rolling bearing, so that the utilization rate of bearing degradation information is improved, and the generalization capability of the model in predicting the service life of bearings with different trends is also enhanced; meanwhile, dynamic Bayes are introduced to estimate the failure probability of the long-period degradation process, and the prediction accuracy and the robustness of the model in predicting the bearing life with the fluctuation process are effectively improved by fusing the life information of different time scales.
Drawings
FIG. 1 is a flow chart of a rolling bearing integrated life prediction method based on double-flow infinite particle filtering.
Fig. 2 is a graph of rolling bearing degradation phase monitoring based on a similarity measure.
Fig. 3 is a western-style test stand picture.
FIG. 4 is a selected rolling bearing full life cycle vibration signal.
FIG. 5 is an enlarged view of RMS index and degradation interval of rolling bearing
FIG. 6 is a graph showing the prediction results of the proposed method and its lifetime probability density distribution
FIG. 7 is a graph of probability density distribution and predicted lifetime versus real lifetime estimated at four different times.
Fig. 8 is a graph comparing rolling bearing life predictions of the proposed method with those of several other methods.
Fig. 9 is a performance evaluation index of the bearing life prediction results of the five methods.
Table 1 is a performance evaluation index of several life prediction algorithms.
Detailed Description
The invention is further described below with reference to the drawings and the detailed description.
(1) And (5) monitoring the degradation stage. In rolling bearing life prediction, the degradation phase is the important research phase, so monitoring whether a bearing enters the degradation phase in real time is the first step in predicting bearing life. The TSP point is determined by a method based on similarity measurement, and the specific process is shown in fig. 2. Firstly, intercepting healthy data with fixed length as a basic reference data set in a stable operation stage of the bearing, simultaneously setting a sliding window 1 with the same length to intercept the latest monitoring data, and finally calculating Euclidean distance between two groups of data to measure the similarity between the two groups of data. Thus, a time-dependent euclidean distance curve is obtained. And the 3 sigma criterion is used as the basis for the bearing to enter the degradation stage, and in order to fully utilize the degradation data, the moment before the sliding window is selected as the moment when the bearing enters the degradation stage, namely the calculated TSP point. When the bearing is monitored to enter the degradation phase, the UPF based on the mixed model estimates the health state of the bearing in the current sliding window.
(2) And (5) integrating life prediction. When the bearing is monitored to enter the degradation stage, the bearing life can be predicted, and the specific prediction process is shown in fig. 1. Firstly, all degradation data are intercepted, and a relatively stable exponential model is utilized to predict the overall degradation trend of the bearing and the uncertainty interval thereof; and then intercepting the latest monitoring data and capturing the latest fluctuation trend information of the bearing by adopting a flexible polynomial model. And finally, estimating the integrated service life of the bearing by adopting a comprehensive fusion strategy based on dynamic Bayes. Fig. 6 shows the probability density distribution of failure and the uncertainty interval of the predicted result of the proposed method, fig. 7 shows the probability density curves of failure of the proposed method at 2390min, 2407min, 2465min and 2524min, respectively, the red and cyan dashed lines represent the integrated life and the real life, respectively. Fig. 8 shows the results of the proposed method compared to several other pure model-driven life prediction methods.
(3) And actually measuring the accelerated performance degradation data of the rolling bearing. The data are provided by the university of Shaanxi traffic science and basic research institute. To collect the vibration signal of the bearing under test, two PCB 352C33 accelerometers are placed in the 90 orientation of the shaft, respectively. The sampling frequency was set to 25.6kHz, sampling intervals of 1min, and sampling duration of 1.28s each time. When the vibration acceleration of the bearing exceeds 20g, the bearing is considered to be invalid, and the experiment is stopped. A first set of experimental data for condition 3 was analyzed, with the data in the figures all from the bearing.
(4) In the prediction performance evaluation section of the life prediction method, two indexes of RMSE and CRA were used, and the evaluation results of several methods are shown in table 1.
TABLE 1

Claims (1)

1. A rolling bearing integrated life prediction method based on double-flow unscented particle filtering is characterized in that the implementation steps of the method are as follows,
s1, an infinite particle filter theory;
in PF-based rolling bearing life prediction, the degradation process of a bearing system is described by constructing a state model, which is composed of a set of state equations and measurement equations, as follows:
x k ＝f k (x k-1 ，v k-1 )
y k ＝h k (x k ，w k )
wherein x is k Is the health state of the bearing system, and subscript k represents time; v k Is bearing system noise, often manifested as gaussian white noise; f (f) k A state transfer function for the bearing system; y is k Is the measured value of the bearing system at the moment k; w (w) k Measuring noise for the sensor, the mean and variance of which are inherent properties of the sensor; h is a k Measuring a function for the bearing system;
the UPF algorithm constructs importance sampling distribution of particle filtering through unscented Kalman filtering UKF; the UPF algorithm flow is as follows:
1) An initialization stage; when k=0, the distribution p (x 0 ) Sampling M bearing state particles to generate an original state particle setSetting the weight of each state particle to +.>When k is more than 0, k=k+1, then sequentially iterating to obtain the state particle group +.>
2) An importance sampling stage; calculating the mean value of each state particle by using UKF algorithmSum of covariance->According to Gaussian distribution->The sample update state particles are calculated as follows:
then, the weight of each state particle is updated by using the measurement value:
finally, normalizing the weight of the bearing state particles:
3) A resampling stage; the state particles are weighted according to the weightSorting, namely discarding state particles with small weights under the condition that the number of particles is unchanged, and copying state particles with large weights at the same time;
4) A state estimation stage; carrying out weighted summation on the state particles so as to realize effective estimation on the health state of the bearing;
wherein P is k Covariance matrix of UPF at k moment;
s3, a rolling bearing integrated service life prediction method based on double-flow unscented particle filtering;
s3.1, determining an initial degradation moment TSD;
after determining the health index HI of the full life cycle of the rolling bearing, monitoring when the bearing enters a degradation stage in real time;
estimating initial degradation time of the bearing, namely TSD point, by adopting a similarity method; the specific estimation flow is as follows: firstly, setting a fixed window with the length of M, selecting HI in a health state as a basic reference data set, simultaneously setting a sliding window 1 with the same length, intercepting M latest state estimated values, and finally calculating Euclidean distance between two groups of data to measure similarity between the two groups of data:
the Euclidean distance between the sliding window and the fixed window data at each moment is calculated, so that the variation curve of the Euclidean distance along with the time is obtained, and the average mu of the Euclidean distance in the health stage is calculated Dist And mu Dist As a degradation threshold DT for determining the bearing entering the degradation phase; when the Euclidean distance at a certain moment is monitored to exceed DT for the first time, the bearing is indicated to enter a degradation stage, and the sliding window contains part of health data and degradation data; for utilizing the degradation data, selecting the previous moment of the sliding window as the moment of the bearing entering the degradation phase, namely a TSD point;
s3.2, starting to determine a prediction time TSP and a failure threshold FT;
when the bearing is monitored to enter a degradation stage, in order to effectively utilize degradation data, the health state of the bearing needs to be estimated in the latest period, and when the length of the health state estimated value reaches the requirement of the predicted length, the RUL of the bearing is predicted; estimating the health state of the bearing at the stage by taking a mixed model comprising an exponential model and a quadratic polynomial as a UPF state model;
wherein a is 1 ，a 2 ，a 3 ，a 4 ，a 5 Are coefficient vectors of the mixed model, t is different monitoring moments, v k For measuringNoise;
in determining TSP point, a sliding window 2 with length L is firstly set, L HI which just enters degradation stage are intercepted, and then the degradation state of the bearing when TSD+L is estimated by adopting UPF based on mixed modelThen move the sliding window forward and estimate the health status at the next moment +.>Circularly reciprocating; when the length of the state estimation value set is greater than L min At the moment, the RUL of the bearing can be estimated min The method comprises the steps of setting a preset minimum length of a predictive bearing RUL; setting the current moment as the TSP point of the bearing;
after determining the TSP point, estimating FT of the bearing; first, it is necessary to intercept the health index z in the health state 1 ，z 2 ，...，z TSP-1 Then the mean μ and variance σ of the set of data sets are calculated, and finally the failure threshold FT of the bearing is calculated:
FT＝μ+λσ
wherein lambda is a complete failure criterion coefficient, and the value of lambda depends on the specific bearing working condition;
s3.2 integrated life IRUL prediction;
the provided integrated life prediction flow is as follows:
1) Stream one: long-term RUL prediction based on global degradation trend:
and (3) taking the index model as a UPF state model to analyze the degradation trend of the whole bearing, so as to realize long-term prediction of RUL thereof, wherein the method comprises the following steps:
wherein a is 1 ，a 2 Coefficient vectors of the index model, t is different monitoring moments, v k For measuring noise;
when the shaft is monitoredWhen the bearing enters the RUL predictable degradation stage, all state estimation values are intercepted, and then the index model parameters are estimated based on UPF to obtain a global optimal degradation modelAnd predicting future degradation state of bearingIn order to estimate the global failure life of the bearing, a dynamic Bayes is proposed to estimate the failure probability at each time in the future, as follows:
wherein,indicating that the bearing is at t 0 To t 0 All are healthy at time +j-1, and at t 0 Probability of beginning failure at time +j, +.>Is from t 0 To t 0 Probability that the bearings remain healthy at moment +j-1,/->At t 0 Probability of failure at +j moment, probability value of the invention is 0-1; q is a standard Gaussian distribution function, sigma is a standard within a certain time periodThe accuracy is poor;
thus obtaining the failure probability of the bearing at each time in the future, wherein the maximum failure probability LT_p k The corresponding time is the long-term failure time LPre_t 0 The following formula:
t 0 the long-term bearing RUL estimated at the moment is:
LT_RUL k ＝LPre_t k -t k
2) Stream two: short-term RUL prediction based on local fluctuation information:
predicting short-term fluctuation life by adopting a mixed model of a high-order polynomial and an index;
when the bearing enters a predictable degradation stage, the prediction of the short-term fluctuation life of the bearing can be started; firstly, a sliding window 3 with the length of N needs to be set to intercept the nearest HI, then a mixed model is used as a UPF state model, and finally the short-term fluctuation life SF_RUL is obtained based on a dynamic Bayesian algorithm k Probability of failure SF_p k The specific calculation flow is the same as the long-term trend life calculation process of the previous section;
setting a model minimum failure probability p min The method comprises the steps of carrying out a first treatment on the surface of the When the failure probability of the mixed model prediction is smaller than p min When the mixed model is replaced by a more stable index model for prediction; when the index model also fails, the bearing is shown to have a more complex degradation process, and the local prediction cannot provide an effective RUL prediction value, so that SF_RUL is ensured k ＝0，SF_p k =0, i.e. the long-term trend lifetime is defaulted as the final lifetime prediction result;
3) Integrated lifetime IRUL estimation:
after a long-term trend lifetime lt_rul is obtained k And short-term fluctuation life SF_RUL k Then, based on the double-flow failure probability, the integrated service life ERUL of the bearing k And (3) predicting:
s3.3, performance evaluation indexes;
in order to quantitatively measure the prediction performance of the proposed prediction method, a minimum mean square error (RMSE) and accumulated relative precision (CRA) are introduced to evaluate several prediction models;
RMSE is a measure reflecting the difference between predicted life and real life, calculated as follows:
wherein,predicting a lifetime value for time t, < >>Is the real life value at the moment t, t Eol To reach the corresponding failure time t when the failure threshold value is reached TSP The starting prediction time is the starting prediction time;
relative accuracy refers to the relative prediction error at a particular instant:
to comprehensively measure the overall prediction effect, the relative accuracy at each time is weighted by accumulation to obtain an accumulated relative accuracy index CRA:
wherein omega λ Is a normalized weight coefficient, and K is the length of the predicted result.
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