CN114896861A - Rolling bearing residual life prediction method based on square root volume Kalman filtering - Google Patents

Rolling bearing residual life prediction method based on square root volume Kalman filtering Download PDF

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CN114896861A
CN114896861A CN202210342484.2A CN202210342484A CN114896861A CN 114896861 A CN114896861 A CN 114896861A CN 202210342484 A CN202210342484 A CN 202210342484A CN 114896861 A CN114896861 A CN 114896861A
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王宇
刘秋发
訾艳阳
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Xian Jiaotong University
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Abstract

The invention discloses a rolling bearing residual life prediction method based on square root volume Kalman filtering, which comprises the steps of extracting multi-dimensional features from vibration signals of rolling bearing historical failure samples, constructing a sensitive feature set, training a self-organizing mapping neural network with a Mahalanobis distance measurement operator based on sensitive feature data of an early stable running stage of the rolling bearing, reducing dimensions, constructing a health index, determining a self-adaptive degradation threshold value of the rolling bearing based on the health index, dividing the health stage and the degradation stage of the rolling bearing by adopting a continuous trigger mechanism, and predicting the residual life of the rolling bearing by establishing an exponential degradation model considering unequal sampling intervals. The method can better keep the topological structure of the multidimensional characteristics in the high-dimensional space in the dimension reduction process, overcomes the dependence on online monitoring data sampled at equal intervals, and simultaneously improves the utilization rate of the life-cycle data of historical failure samples with different sampling intervals.

Description

Rolling bearing residual life prediction method based on square root volume Kalman filtering
Technical Field
The invention belongs to the technical field of bearing residual life prediction, and particularly relates to a rolling bearing residual life prediction method based on square root volumetric Kalman filtering.
Background
With the rapid development of modern industrial technologies, the safety, stability, reliability, etc. of electromechanical devices are subject to higher and higher requirements. The rolling bearing is used as a key part of the rotating machinery, is a weak link in equipment reliability, and once mechanical failure occurs, equipment failure is caused, so that economic loss is caused. Therefore, real-time state monitoring and performance degradation evaluation of the rolling bearing have urgent needs for ensuring the reliability of equipment operation. On the basis, the residual life of the rolling bearing is predicted, and a reasonable and feasible basis can be provided for the operation and maintenance plan of the equipment.
At present, in order to predict the residual life of the rolling bearing, a data driving method is mostly adopted. Because the remaining life of the rolling bearing is influenced by various factors, the health state of the rolling bearing cannot be well reflected by a single characteristic, so that many researches take the vibration signal of the rolling bearing as the basis, multi-dimensional characteristics are extracted from the vibration signal, and then data are mapped to a low-dimensional space to obtain a comprehensive health index. At present, the commonly used dimensionality reduction technology comprises principal component analysis, linear discriminant analysis, a self-organizing mapping neural network and the like, and in the engineering practice, because unbalance exists between the number of normal samples and the number of failure samples, the self-organizing mapping neural network trained only by means of normal state feature vectors is widely used for monitoring the health state of the rolling bearing. However, in the training process, the self-organizing map neural network adopts the euclidean distance to calculate the similarity between the input layer feature vector and the output layer neuron node weight, and does not consider the correlation between elements in the feature vector.
Next, in a life-cycle degradation test of a rolling bearing, a researcher often takes a method of sampling at equal intervals when acquiring a vibration signal of the rolling bearing. However, in actual engineering, due to factors such as changes in monitoring plans, failures of sensors, and operator errors, the monitoring data of the rolling bearings that are being operated may not meet the requirement of the equal interval distribution. On the other hand, rolling bearing historical failure samples at different times may also have different monitoring intervals. In addressing these issues, the effectiveness of such remaining life prediction methods based on equally spaced sampling may be limited.
Disclosure of Invention
Aiming at the defect that the correlation among variables and the inconsistency of monitoring intervals are not considered in the prior art, the invention aims to provide a rolling bearing residual life prediction method based on square root volumetric Kalman filtering.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for predicting the residual life of a rolling bearing based on square root volume Kalman filtering comprises the following steps:
extracting multi-dimensional features from vibration signals of the rolling bearings, and reducing dimensions through a self-organizing mapping neural network with a Mahalanobis distance measurement operator to construct a health index;
constructing a self-adaptive degradation threshold of the rolling bearing based on the health index, and dividing a health stage and a degradation stage of the rolling bearing by adopting a continuous trigger mechanism;
and predicting the residual life of the rolling bearing by considering an exponential degradation model with unequal sampling intervals.
The invention is further improved in that the method specifically comprises the following steps:
1) extracting and screening features based on the collected rolling bearing vibration signals according to the failure mode of the rolling bearing, and constructing a multi-dimensional sensitive feature set;
2) mapping the multidimensional sensitive features in the multidimensional sensitive feature set to a low-dimensional space through a trained self-organizing mapping neural network with a Mahalanobis distance measurement operator to construct health indexes of the rolling bearing;
3) constructing a dynamic failure threshold of the rolling bearing based on the health index of the rolling bearing, and adopting a continuous trigger mechanism as a method for judging degradation to realize the division of the health stage and the degradation stage of the rolling bearing;
4) establishing an exponential degradation model considering unequal sampling intervals, and updating degradation model parameters through an expectation maximization algorithm based on health index data of a rolling bearing degradation stage;
5) and updating the health state of the rolling bearing through square root volume Kalman filtering according to the updated degradation model parameters, and calculating point estimation and probability density estimation of the residual life of the rolling bearing.
The further improvement of the invention is that the specific steps in the step 1) are as follows:
according to the failure mode of the rolling bearing, based on collected rolling bearing historical failure samples, analyzing collected rolling bearing vibration signals, calculating a plurality of correlation characteristics including root mean square, peak value, wavelet energy entropy and the like of a time domain, a frequency domain and a time-frequency domain, calculating Spearman correlation coefficients between each correlation characteristic and an operation time sequence, screening out the characteristic with the Spearman correlation coefficient higher than an average value as a primary selection sensitive characteristic, calculating a covariance matrix of the primary selection sensitive characteristic, eliminating redundant characteristics according to the correlation between the characteristics, and determining a multi-dimensional sensitive characteristic set.
The further improvement of the invention is that the specific steps in the step 2) are as follows:
selecting data of a section of rolling bearing in a steady operation period as a random sample in a health stage, calculating characteristics in a multi-dimensional sensitive characteristic set, normalizing, and calculating a mean value and a covariance of sensitive characteristics in the steady operation period;
training a self-organizing mapping neural network with a Mahalanobis distance measurement operator through sensitive characteristics in a stable operation period;
and mapping the multidimensional sensitive features to a low-dimensional space through the trained self-organizing mapping neural network with the Mahalanobis distance measurement operator to construct the health index of the rolling bearing.
The further improvement of the invention is that the specific steps in the step 3) are as follows:
calculating the dynamic failure threshold value z-Q of the rolling bearing according to the health index of the rolling bearing 3 +1.5IQR，IQR＝Q 3 -Q 1 In the formula, Q 3 Is the third quantile of the health index from the initial time to the current time, Q 1 The first quantile of the health index from the initial moment to the current moment, and the IQR is the difference of the two quantiles;
judging the health state of the rolling bearing according to the failure threshold value z, and judging that the rolling bearing enters a degradation stage when the health index continuously exceeds the failure threshold value z for n times and the health index presents an increasing trend for n times, so that the health stage and the degradation stage of the rolling bearing are divided.
The further improvement of the invention is that the specific steps in the step 4) are as follows:
1) establishing an exponential degradation model considering unequal sampling intervals:
Figure BDA0003579837990000041
in the formula, x k ＝(x 1,k ,x 2,k ) T Is an implicit variable, y k Is an observed value of a health index, h (x) k )＝x 1,k exp(x 2,k t k ) + c is an exponential degeneration model which is,
Figure BDA0003579837990000042
is process noise and is adjacent to the monitoring time interval tau k ＝t k+1 -t k ，
Figure BDA0003579837990000043
r k N (0, R) is measurement noise, c is offset;
2) based on the initial time t in the degradation phase by an expectation maximization algorithm 1 To the current time t T And updating the parameters of the degradation model.
The invention is further improved in that the specific steps of the step 5) are as follows:
5.1) substituting the updated parameters of the degradation model into the degradation model to realize the recursive update of the health state of the rolling bearing;
5.2) extrapolating the health index sequence to obtain the point estimation and the probability distribution estimation of the residual life.
The further improvement of the invention is that the specific steps of 5.1) are as follows:
a) memory m k-1 At a time t k-1 Latent variable x k-1 Is expected to be estimated, S P,k-1 At a time t k-1 Latent variable x k-1 Estimation of the square root of the covariance of S Q,k-1 At a time t k-1 Process noise q k-1 Square root of covariance of (a), the next time t from the regression model k Expectation of latent variable prediction values
Figure BDA0003579837990000044
Square root of sum covariance
Figure BDA0003579837990000045
Establishing an augmented latent variable
Figure BDA0003579837990000046
S R,k At a time t k Measurement noise r k Square root of variance of (1), time t by square root volumetric Kalman filtering k Expectation estimation of augmented hidden variables
Figure BDA0003579837990000047
Estimation of the square root of sum covariance
Figure BDA0003579837990000048
Decomposition of a matrix into desired estimates m of hidden variables k Estimation of the square root of sum covariance S P,k ；
b) Every time a new monitoring value is obtained, the current time t is obtained by performing the steps of prediction updating and measurement updating in the step a) T An estimate of the health indicator of (1).
The further improvement of the invention is that the specific steps of 5.2) are as follows:
point estimation of remaining life
Figure BDA0003579837990000049
Obtaining the particles by Monte Carlo method
Figure BDA00035798379900000410
The remaining life
Figure BDA00035798379900000411
The probability distribution of the remaining life is estimated as
Figure BDA0003579837990000051
Wherein w is a set failure threshold value t T Is the current time, m T ＝(m 1,T ,m 2,T ) T For the desired estimation of hidden variables at the present moment, P T And estimating the covariance of the hidden variables at the current moment.
Compared with the prior art, the invention has the beneficial effects that:
the method constructs the health index based on the vibration signal characteristics of the rolling bearing, realizes the mapping of the characteristic vector from a high-dimensional space to a low-dimensional space through the self-organizing mapping neural network with the Mahalanobis distance measurement operator, and considers the correlation among variables in the dimension reduction process, so that the topological structure in the high-dimensional space is better reserved. The method better retains the topological structure of the multidimensional characteristics in the high-dimensional space in the dimension reduction process, overcomes the dependence on online monitoring data sampled at equal intervals, and improves the utilization rate of the life-cycle data of historical failure samples with different sampling intervals.
Furthermore, the combination of quantiles is used as a self-adaptive dynamic threshold, and the degradation stage is judged through a continuous trigger mechanism, so that the interference of noise is small, and different rolling bearings with individual differences can be better adapted;
furthermore, the exponential degradation model adopted by the method considers the condition of unequal sampling intervals, and can better adapt to degradation evaluation in the actual engineering environment;
furthermore, the square root volume Kalman filtering in the form of augmentation adopted by the method has better numerical stability compared with particle filtering and the like, and the parameters of the model are updated by adopting an expectation maximization algorithm, so that the result of long-term online operation is more reliable.
Drawings
FIG. 1 is a flow chart of the method for predicting the remaining life of a rolling bearing based on square root volumetric Kalman filtering;
FIG. 2 is a life-cycle vibration waveform of a rolling bearing;
FIG. 3 is a life-cycle health index map of a rolling bearing;
fig. 4 is a diagram showing the result of predicting the remaining life of the rolling bearing at the latter stage of the prediction cycle.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
Referring to fig. 1, a method for predicting the remaining life of a rolling bearing based on square root volumetric kalman filtering includes the following steps:
(1) according to the main failure mode of the rolling bearing, based on the acquired rolling bearing historical failure samples, analyzing the acquired rolling bearing vibration signals, and calculating a plurality of relevant characteristics of a time domain, a frequency domain and a time-frequency domain, including a root mean square, a peak value, a wavelet energy entropy and the like.
And calculating the Spearman correlation coefficient between each correlation characteristic and the running time sequence, and screening out the characteristic with the Spearman correlation coefficient higher than the average value as a primary selection sensitive characteristic. And then, calculating a covariance matrix of the initially selected sensitive features, eliminating redundant features according to the correlation among the features, and finally determining a simplified multi-dimensional sensitive feature set.
(2) In the early operation stage of the rolling bearing, selecting data of a period of stable operation as a random sample of a health stage, calculating sensitive characteristics in a multi-dimensional sensitive characteristic set, normalizing the sensitive characteristics, and calculating the mean value mu and the covariance sigma of the sensitive characteristics in the selected period of stable operation. As shown in fig. 2, the mean and covariance of sensitive features are susceptible to outliers when calculated due to fluctuations in the presence of noise. Therefore, to obtain a more robust mean and covariance estimate, a subset of the number of samples h is determined by the minimum covariance determinant, and the mean μ and covariance Σ of the sensitive feature are calculated from this subset.
Then, training the self-organizing mapping neural network with the Mahalanobis distance measurement operator by using the sensitive characteristics in the selected stationary operation period, wherein the specific process is as follows:
1) initializing the network: determining the number n of neuron nodes of an output layer, and initializing weight vectors m of the neuron nodes of the output layer j ，m j ∈R n ；
2) In the k +1 th iteration, the ith input sample x i ，x i ∈R n Calculating x i And each neuron node weight vector of the output layer
Figure BDA0003579837990000061
The degree of similarity of (c):
Figure BDA0003579837990000062
in the formula | · | non-conducting phosphor M Represents the mahalanobis distance;
3) determining a neutralization sample x in output layer neuron nodes i Corresponding best matching unit c (x) i ) Its weight vector
Figure BDA0003579837990000063
Satisfy the requirement of
Figure BDA0003579837990000071
4) Updating the best matching unit c (x) i ) Weight of neuron node in neighborhood:
Figure BDA0003579837990000072
in the formula (I), the compound is shown in the specification,
Figure BDA0003579837990000073
is a sample x i Corresponding best matching unit c (x) i ) The weight vector of the neuron nodes in the neighborhood,
Figure BDA0003579837990000074
is a function of the neighborhood of the object,
Figure BDA0003579837990000075
alpha is the learning rate, 0<α<1, and σ controls the neighborhood monotonically decreasing with increasing number of iterationsThe range, also monotonically decreasing with increasing number of iterations;
5) and repeating the steps 2) to 4) until the requirement of the iteration times is met.
After the training of the self-organizing mapping neural network is completed, the sensitive characteristic vector x of the rolling bearing is monitored in real time i Inputting the data into a self-organizing mapping neural network, and determining the best matching unit c (x) in an output layer i ) Calculating the minimum quantization error, i.e.
Figure BDA0003579837990000076
Thereby realizing the mapping of the sensitive characteristic vector from a high-dimensional space to a low-dimensional space. As shown in fig. 3, the health index of the rolling bearing is constructed using the obtained minimum quantization error.
(3) Calculating a dynamic failure threshold value z-Q according to the health index of the rolling bearing 3 +1.5IQR，IQR＝Q 3 -Q 1 In the formula, Q 3 Is the third quantile of the health index from the initial time to the current time, Q 1 The first quantile of the health index from the initial time to the current time, and the IQR is the difference of the two quantiles.
Then, the health state of the rolling bearing is judged according to the dynamic failure threshold value z, and in order to reduce the influence of noise, as shown in fig. 3, when the health index continuously exceeds the dynamic failure threshold value z for n times and the health index for n times shows an increasing trend, the rolling bearing is judged to enter a degradation stage, so that the health stage and the degradation stage of the rolling bearing are divided.
(4) And establishing a degradation model and realizing the online updating of the parameters of the degradation model.
1) Establishing an exponential degradation model considering unequal sampling intervals:
Figure BDA0003579837990000077
in the formula, x k ＝(x 1,k ,x 2,k ) T Is an implicit variable, y k Is an observed value of a health index, h (x) k )＝x 1,k exp(x 2,k t k ) + c is an exponential degeneration model which is,
Figure BDA0003579837990000078
is process noise and is adjacent to the monitoring time interval tau k ＝t k+1 -t k ，
Figure BDA0003579837990000079
r k N (0, R) is measurement noise, c is offset;
in the degradation model, process noise is time-dependent, and as the sampling interval increases, the covariance of the process noise increases and the uncertainty of the hidden variable increases.
2) Based on the initial time t in the degradation phase by an expectation maximization algorithm 1 To the current time t T Updating the parameters of the exponential degradation model
Figure BDA0003579837990000081
E, step E:
Figure BDA0003579837990000082
in the formula, theta (n) For the parameter obtained from the last iteration, m 1 Is an initial time t 1 Latent variable x 1 Is expected to be estimated, P 1 Is an initial time t 1 Latent variable x 1 The estimation of the covariance of (a),
Figure BDA0003579837990000083
for an initial time t estimated after smoothing 1 Latent variable x 1 In the expectation that the position of the target is not changed,
Figure BDA0003579837990000084
for an initial time t estimated after smoothing 1 Latent variable x 1 The covariance of (a).
And M:
Figure BDA0003579837990000085
Figure BDA0003579837990000086
Figure BDA0003579837990000087
Figure BDA0003579837990000088
Figure BDA0003579837990000089
where the desired solution can be obtained by RTS smoothing and volume transformation. The degradation model can be trained by using the life-cycle data of the historical failure samples, and a reasonable initial value is determined for the maximum expectation algorithm.
(5) As shown in fig. 4, the state of the rolling bearing is estimated, and the remaining life of the rolling bearing is predicted.
1) And (3) adopting square root volume Kalman filtering in an augmentation form, substituting the updated degradation model parameter theta into the degradation model, and realizing the recursive update of the health state of the rolling bearing:
and (3) prediction updating: memory m k-1 At a time t k-1 Latent variable x k-1 Is expected to be estimated, S P,k-1 At a time t k-1 Latent variable x k-1 Estimation of the square root of the covariance of S Q,k-1 At a time t k-1 Process noise q k-1 The square root of the covariance of (a), and thus the time t, from the model of degradation k Expectation of latent variable prediction values
Figure BDA0003579837990000091
Square root of sum covariance
Figure BDA0003579837990000092
Measurement updating: establishing an augmented latent variable
Figure BDA0003579837990000093
S R,k At a time t k Measurement noise r k Square root of variance of (1), time t being obtained by square root volumetric Kalman filtering k Expectation estimation of augmented hidden variables
Figure BDA0003579837990000094
Estimation of the square root of sum covariance
Figure BDA0003579837990000095
The expected estimation m of the hidden variable can be further obtained by matrix decomposition k Estimation of the square root of sum covariance S P,k 。
When a new monitoring value is obtained, the current time t can be obtained by performing the steps of prediction updating and measurement updating T An estimate of the health indicator of (1).
2) The health indicator sequence is extrapolated to obtain a point estimate and a probability distribution estimate of the remaining life.
The point of remaining life is estimated as
Figure BDA0003579837990000096
w is the set failure threshold.
Obtaining the particles by Monte Carlo method
Figure BDA0003579837990000097
The remaining life
Figure BDA0003579837990000098
The probability distribution of the remaining life is estimated as
Figure BDA0003579837990000099
Wherein w is a set failure threshold, t T Is the current time, m T ＝(m 1,T ,m 2,T ) T Expectation of hidden variable for current timeEstimate, P T And estimating the covariance of the hidden variables at the current moment.
In order to prove the effectiveness of the method, a whole life sample of the rolling bearing is utilized, and performance degradation evaluation and residual life prediction are carried out by the method:
as shown in fig. 2, the vibration signal of the rolling bearing is relatively stable in an early stage and has random fluctuation, and after a period of stability, the vibration signal enters a degradation stage.
As shown in fig. 3, after the sensitive features are determined, dimension reduction is performed through a self-organizing mapping neural network with a mahalanobis distance measurement operator, a comprehensive health index of the rolling bearing can be further constructed based on the minimum quantization error, and the health stage and the degradation stage of the rolling bearing can be divided based on the health index.
As shown in FIG. 4, the residual life prediction of the rolling bearing is realized by utilizing square root cubature Kalman filtering and extrapolating a sequence. With the increase of the monitoring data, the predicted value of the residual life is closer to the true value.
The invention can better reserve the topological structure of multi-dimensional characteristics in a high-dimensional space in the process of dimensionality reduction, overcomes the dependence on online monitoring data sampled at equal intervals, simultaneously improves the utilization rate of the whole life data of historical failure samples with different sampling intervals, and can better adapt to the actual engineering environment.

Claims (9)

1. A method for predicting the residual life of a rolling bearing based on square root volume Kalman filtering is characterized by comprising the following steps:
extracting multi-dimensional features from vibration signals of the rolling bearings, and reducing dimensions through a self-organizing mapping neural network with a Mahalanobis distance measurement operator to construct a health index;
constructing a self-adaptive degradation threshold of the rolling bearing based on the health index, and dividing a health stage and a degradation stage of the rolling bearing by adopting a continuous trigger mechanism;
and predicting the residual life of the rolling bearing by considering an exponential degradation model with unequal sampling intervals.
2. The method for predicting the residual life of the rolling bearing based on the square root volumetric Kalman filtering is characterized by comprising the following steps of:
1) extracting and screening features based on the collected rolling bearing vibration signals according to the failure mode of the rolling bearing, and constructing a multi-dimensional sensitive feature set;
2) mapping the multidimensional sensitive features in the multidimensional sensitive feature set to a low-dimensional space through a trained self-organizing mapping neural network with a Mahalanobis distance measurement operator to construct health indexes of the rolling bearing;
3) constructing a dynamic failure threshold of the rolling bearing based on the health index of the rolling bearing, and adopting a continuous trigger mechanism as a method for judging degradation to realize the division of the health stage and the degradation stage of the rolling bearing;
4) establishing an exponential degradation model considering unequal sampling intervals, and updating degradation model parameters through an expectation maximization algorithm based on health index data of a rolling bearing degradation stage;
5) and updating the health state of the rolling bearing through square root volume Kalman filtering according to the updated degradation model parameters, and calculating point estimation and probability density estimation of the residual life of the rolling bearing.
3. The method for predicting the residual life of the rolling bearing based on the square root volumetric Kalman filtering according to claim 2, characterized in that the specific steps in the step 1) are as follows:
according to the failure mode of the rolling bearing, based on collected rolling bearing historical failure samples, analyzing collected rolling bearing vibration signals, calculating a plurality of correlation characteristics including root mean square, peak value, wavelet energy entropy and the like of a time domain, a frequency domain and a time-frequency domain, calculating Spearman correlation coefficients between each correlation characteristic and an operation time sequence, screening out the characteristic with the Spearman correlation coefficient higher than an average value as a primary selection sensitive characteristic, calculating a covariance matrix of the primary selection sensitive characteristic, eliminating redundant characteristics according to the correlation between the characteristics, and determining a multi-dimensional sensitive characteristic set.
4. The method for predicting the residual life of the rolling bearing based on the square root volumetric Kalman filtering as recited in claim 2, wherein the specific steps in the step 2) are as follows:
selecting data of a section of rolling bearing in a steady operation period as a random sample in a health stage, calculating characteristics in a multi-dimensional sensitive characteristic set, normalizing, and calculating a mean value and a covariance of sensitive characteristics in the steady operation period;
training a self-organizing mapping neural network with a Mahalanobis distance measurement operator through sensitive characteristics in a stable operation period;
and mapping the multidimensional sensitive features to a low-dimensional space through the trained self-organizing mapping neural network with the Mahalanobis distance measurement operator to construct the health index of the rolling bearing.
5. The method for predicting the residual life of the rolling bearing based on the square root volumetric Kalman filtering as recited in claim 2, wherein the specific steps in the step 3) are as follows:
calculating the dynamic failure threshold value z-Q of the rolling bearing according to the health index of the rolling bearing 3 +1.5IQR，IQR＝Q 3 -Q 1 In the formula, Q 3 Is the third quantile of the health index from the initial time to the current time, Q 1 The first quantile of the health index from the initial moment to the current moment, and the IQR is the difference of the two quantiles;
judging the health state of the rolling bearing according to the failure threshold value z, and judging that the rolling bearing enters a degradation stage when the health index continuously exceeds the failure threshold value z for n times and the health index presents an increasing trend for n times, so that the health stage and the degradation stage of the rolling bearing are divided.
6. The method for predicting the residual life of the rolling bearing based on the square root volumetric Kalman filtering as recited in claim 2, wherein the specific steps in the step 4) are as follows:
1) establishing an exponential degradation model considering unequal sampling intervals:
Figure FDA0003579837980000031
in the formula, x k ＝(x 1,k ,x 2,k ) T Is an implicit variable, y k Is an observed value of a health index, h (x) k )＝x 1,k exp(x 2,k t k ) + c is an exponential degeneration model which is,
Figure FDA0003579837980000032
is process noise and is adjacent to the monitoring time interval tau k ＝t k+1 -t k ，
Figure FDA0003579837980000033
r k N (0, R) is measurement noise, c is offset;
2) based on the initial time t in the degradation phase by an expectation maximization algorithm 1 To the current time t T And updating the parameters of the degradation model.
7. The method for predicting the residual life of the rolling bearing based on the square root volumetric Kalman filter according to claim 6, wherein the specific steps of the step 5) are as follows:
5.1) substituting the updated parameters of the degradation model into the degradation model to realize the recursive update of the health state of the rolling bearing;
5.2) extrapolating the health index sequence to obtain the point estimation and the probability distribution estimation of the residual life.
8. The method for predicting the residual life of the rolling bearing based on the square root volumetric Kalman filtering according to claim 7, characterized in that the concrete steps of 5.1) are as follows:
a) memory m k-1 At a time t k-1 Latent variable x k-1 Is expected to be estimated, S P,k-1 At a time t k-1 Latent variable x k-1 Estimation of the square root of the covariance of S Q,k-1 At a time t k-1 Process noise q k-1 Square root of covariance of (a), the next time t from the regression model k Expectation of latent variable prediction values
Figure FDA0003579837980000034
Square root of sum covariance
Figure FDA0003579837980000035
Establishing an augmented latent variable
Figure FDA0003579837980000036
S R,k At a time t k Measurement noise r k Square root of variance of (1), time t by square root volumetric Kalman filtering k Expectation estimation of augmented hidden variables
Figure FDA0003579837980000037
Estimation of the square root of sum covariance
Figure FDA0003579837980000038
Decomposition of a matrix into desired estimates m of hidden variables k Square root estimation of sum covariance S P,k ；
b) Every time a new monitoring value is obtained, the current time t is obtained by performing the steps of prediction updating and measurement updating in the step a) T An estimate of the health indicator of (a).
9. The method for predicting the residual life of the rolling bearing based on the square root volumetric Kalman filtering according to claim 7, characterized in that the concrete steps of 5.2) are as follows:
point estimation of remaining life
Figure FDA0003579837980000041
Obtaining the particles by Monte Carlo method
Figure FDA0003579837980000042
The remaining life
Figure FDA0003579837980000043
The probability distribution of the remaining life is estimated as
Figure FDA0003579837980000044
Wherein w is a set failure threshold value t T Is the current time, m T ＝(m 1,T ,m 2,T ) T For the desired estimation of hidden variables at the present moment, P T And estimating the covariance of the hidden variables at the current moment.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115047894A (en) * 2022-04-14 2022-09-13 中国民用航空总局第二研究所 Unmanned aerial vehicle track measuring and calculating method, electronic equipment and storage medium
CN116738868A (en) * 2023-08-16 2023-09-12 青岛中德智能技术研究院 Rolling bearing residual life prediction method

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115047894A (en) * 2022-04-14 2022-09-13 中国民用航空总局第二研究所 Unmanned aerial vehicle track measuring and calculating method, electronic equipment and storage medium
CN115047894B (en) * 2022-04-14 2023-09-15 中国民用航空总局第二研究所 Unmanned aerial vehicle track measuring and calculating method, electronic equipment and storage medium
CN116738868A (en) * 2023-08-16 2023-09-12 青岛中德智能技术研究院 Rolling bearing residual life prediction method
CN116738868B (en) * 2023-08-16 2023-11-21 青岛中德智能技术研究院 Rolling bearing residual life prediction method

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