CN108776017B - Method for predicting residual life of rolling bearing by improving CHSMM - Google Patents

Method for predicting residual life of rolling bearing by improving CHSMM Download PDF

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CN108776017B
CN108776017B CN201810325011.5A CN201810325011A CN108776017B CN 108776017 B CN108776017 B CN 108776017B CN 201810325011 A CN201810325011 A CN 201810325011A CN 108776017 B CN108776017 B CN 108776017B
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白瑞林
朱朔
李新
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Wuxi Xinje Electric Co Ltd
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Abstract

The invention discloses a prediction method for the residual life of a rolling bearing with an improved CHSMM, which is characterized by comprising the following steps: firstly, extracting a characteristic vector of time domain and time domain of bearing vibration data, and reducing the dimension of the characteristic vector by adopting a PCA algorithm; then, obtaining data of each degradation state by using a k-means algorithm, establishing a degradation state identification model, and establishing a residual life prediction model by using the data of the full life cycle of the bearing; aiming at the problem of low residual life prediction precision caused by the fact that the state residence time probability density function is not practical, introducing a Gaussian mixture probability density function into the CHSMM; compared with the residual life prediction model established based on the original CHSMM, the residual life prediction model established based on the improved CHSMM can better approximate the state residence time probability distribution, so that the residual life of the bearing can be predicted more accurately.

Description

Method for predicting residual life of rolling bearing by improving CHSMM
Technical Field
The invention belongs to the field of residual life prediction of bearings, and particularly relates to a residual life prediction method of a rolling bearing with improved CHSMM.
Background
With the continuous improvement of the industrial and technological levels, mechanical equipment is continuously improved in the aspects of complexity, high efficiency, light weight and the like, and is also faced with a more rigorous working environment. Once the key parts of the equipment are out of order, the whole production process can be affected, huge economic loss can be caused, and even casualties and other problems can be caused. Therefore, equipment maintenance is moving from traditional after-the-fact and scheduled maintenance to state-based, on-the-fly maintenance, and equipment remaining life prediction has also begun to be of great interest as a prerequisite to establishing a reasonable maintenance strategy.
The performance of a rolling bearing, which is one of the key parts in a rotating machine, directly affects the operational reliability of the whole machine. Generally, rolling bearings undergo a process from normal to degraded to failure during use, and during this period, a series of different performance degradation states are usually experienced. If the residual service life of the bearing can be monitored in the process of the performance degradation of the rolling bearing, production can be organized and a reasonable maintenance plan can be formulated in a targeted manner, and the occurrence of abnormal failure of equipment is prevented.
Currently, the prediction of the remaining life of a rolling bearing can be classified into: model-based and data-driven methods. The model-based method is mainly used for establishing a service life model of the bearing according to the physical structure of the bearing by applying a mathematical statistics principle or from the aspect of mechanics, and the methods need a large amount of expert experience and more complex fault mechanism knowledge and limit the application range of the methods. The data driving method is mainly used for predicting the residual service life of the bearing by utilizing a machine learning algorithm according to the running state data of the bearing. The main methods used include Deep Neural Networks (DNNs), Support Vector Machines (SVMs), Kalman Filters (KFs), and CHSMMs (Continuous hidden semi-Markov models), wherein CHSMMs are a dual stochastic process that can well describe the relationship between the degradation process and the state data of the bearing, and many scholars apply them to the field of predicting the remaining life of the bearing. However, in the process of applying CHSMM, it is assumed that the probability density function of the state residence time conforms to gaussian distribution, and in practice, the true distribution function of the state residence time is unknown, which will reduce the prediction accuracy.
Disclosure of Invention
The invention provides a method for predicting the residual life of a rolling bearing by improving CHSMM (chemical mechanical polishing) in order to more accurately predict the residual life of the bearing.
In order to achieve the purpose, the invention is realized by the following technical scheme:
step (1): acquiring vibration data of a bearing in a full life cycle, and performing denoising and normalization pretreatment; extracting time domain and time-frequency domain feature vectors of the vibration data;
step (2): performing feature dimensionality reduction on the multi-domain feature vector by using a Principal Component Analysis (PCA) algorithm;
and (3): dividing the bearing full life cycle data obtained in the step (2) into five degradation states, namely a normal state, a degradation state 1, a degradation state 2, a degradation state 3 and a degradation state 4, and performing clustering analysis on the full life cycle data by using a k-means algorithm to obtain data of each degradation state;
and (4): introducing a Gaussian mixture probability density function into the CHSMM to obtain an improved CHSMM, and training five degradation state recognition models by using the degradation state data obtained in the step (3) to serve as a state classifier of the bearing;
and (5): training a residual life prediction model by using the full life cycle data obtained in the step (2) to obtain the state transition probability of the full life cycle, extracting the characteristic vector of the data to be detected by using the methods provided in the steps (1) and (2), inputting the characteristic vector into the state classifier in the step (4) to obtain the current degradation state of the bearing, and then calculating the current residual life of the bearing by using a residual life calculation formula.
According to the technical scheme, the following beneficial effects can be realized:
(1) according to the method, the time domain of the bearing vibration data and the time-frequency characteristics based on the wavelet packet are extracted, and the characteristic dimension reduction is carried out based on the PCA algorithm, so that redundant information in a high-dimensional characteristic vector is reduced, and the training speed of a model is accelerated;
(2) compared with the conventional CHSMM, the improved model can better approximate the probability distribution of the state residence time, so that the residual life of the bearing can be predicted more accurately.
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FIG. 1 is a schematic flow chart of a method for predicting the remaining life of a rolling bearing with improved CHSMM according to the present invention.
Detailed Description
In order to make the objects, technical solutions, advantages and the like of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings in combination with examples.
As shown in fig. 1, a method for predicting the remaining life of a rolling bearing for improved CHSMM, the method comprising the steps of:
step (1): extracting time domain and time-frequency domain feature vectors of the vibration data;
extracting time domain characteristics RMS (root mean square), AM (absolute mean), SMR (square root amplitude), Kurtosis (Kurtosis), Skewness (Skewness) and Peak (Peak value) of the vibration data of the bearings 1,2 and 3 in a working condition I by using the full life cycle vibration data, and performing three-layer wavelet packet decomposition on the data by using db8 wavelet to obtain a normalized value of the energy of eight nodes as a time-frequency characteristic;
step (2): performing feature dimensionality reduction on the multi-domain feature vector by using a PCA algorithm, wherein the steps are as follows:
1) carrying out zero-averaging on the eigenvector matrix X and solving a covariance matrix of the eigenvector matrix X;
2) calculating eigenvalue lambda of covariance matrixiAnd corresponding feature vector ri(i ═ 1,2, ·, n), n is the feature vector dimension;
3) calculating the contribution ratio k:
Figure BDA0001626301180000041
4) arranging the eigenvectors into a matrix according to the corresponding eigenvalues from large to small, and taking the first k rows to form a matrix J;
5) y is JX which is the characteristic vector from dimensionality reduction to dimensionality k;
and (3): acquiring degradation state data;
dividing the bearing full life cycle data obtained in the step (2) into five degradation states, namely a normal state, a degradation state 1, a degradation state 2, a degradation state 3 and a degradation state 4, and performing clustering analysis on the full life cycle data by using a k-means algorithm to obtain data of each degradation state;
and (4): introducing a Gaussian mixture probability density function into the CHSMM to obtain an improved CHSMM, training five degradation state recognition models by using the degradation state data obtained in the step (3) to serve as a state classifier of the bearing, and comprising the following steps:
1) the CHSMM has the parameter τ ═ (N, M, pi, a, B, C), and the specific meanings are as follows:
① N number of states of Markov chain in model, and marking N states as S1，S2，…,SN,qtRepresenting the state in which the Markov chain is at any time t;
② M number of possible observations, o, corresponding to each state in the modeltRepresents an observed value at an arbitrary time t;
③ pi initial time, state probability distribution of model, pi ═ pi (pi)1,π2,···,πN) In which pii＝P(q1＝Si)1≤i≤N；
④ A is a state transition probability matrix, A ═ aij)N×NWherein a isij＝P(qt+1＝Sj|qt＝Si) I is not less than 1, j is not less than N, and
Figure BDA0001626301180000042
⑤ B observed probability density function, B ═ Bj(ok),1≤j≤N,1≤k≤M}，bj(ok)＝P(ok|qt＝Sj)；
⑥ C probability density function of state dwell time D, C ═ Cj(d),1≤j≤N,1≤d≤E}，cj(d)＝P(d|qt＝Sj) And E is the maximum residence time;
the forward-backward algorithm solves the evaluation problem, namely, the probability of a certain observation sequence is calculated by giving the observation sequence O and the parameter tau; the Viterbi algorithm solves the decoding problem, namely, given an observation sequence O and a parameter tau, an observation sequence which is optimal in a certain sense is searched; the Baum Welch algorithm solves the learning problem, i.e., given a sequence of observations, one τ can be determined so that P (O | τ) is maximized;
define forward variable αt(i)＝P(o1,o2,···,ot,qt＝i,qt+1≠i),
Figure BDA0001626301180000051
Backward variable βt(i)＝P(ot+1，ot+2，···，oT，|qt＝i，qt+1≠i)，
Figure BDA0001626301180000052
Then there are:
Figure BDA0001626301180000053
Figure BDA0001626301180000054
Figure BDA0001626301180000055
Figure BDA0001626301180000056
for a given parameter τ and observation sequence O ═ O (O)1,o2,···,oT) And T is the length of the observation sequence, and the obtained logarithm expression of P (O | tau) is as follows:
Figure BDA0001626301180000057
wherein
Figure BDA0001626301180000058
δt(i,d)＝P(qt＝i,d|O),
Figure BDA0001626301180000061
1≤i,j≤N,1≤d≤T-1,1≤t≤T；
2) Parameter solving:
and (3) solving the partial derivatives of the variables A and pi by the formula:
Figure BDA0001626301180000062
Figure BDA0001626301180000063
and for the observation probability density B, fitting by adopting a Gaussian mixture model, wherein the model parameter expression is as follows:
Figure BDA0001626301180000064
N(ok|Ujg,Σjg) And G represents the number of the Gaussian probability density function. And (3) performing partial derivation on each variable in the B:
Figure BDA0001626301180000065
Figure BDA0001626301180000066
Figure BDA0001626301180000067
wherein the content of the first and second substances,
Figure BDA0001626301180000068
⊙ represents the vector dot product.
For the state residence time D, in the process of predicting the residual life of the bearing by applying CHSMM, the state residence time D is assumed to conform to Gaussian distribution, and in practice, the real distribution function of the state residence time is unknown, so that the prediction precision is reduced by the assumption;
in order to overcome the defects, a Gaussian mixture probability density function is adopted as a probability density function of the state residence time D, and a model expression is as follows:
Figure BDA0001626301180000071
f represents the number of Gaussian probability density functions;
the model parameters for state dwell time D are derived as follows:
Figure BDA0001626301180000072
Figure BDA0001626301180000073
Figure BDA0001626301180000074
wherein the content of the first and second substances,
Figure BDA0001626301180000075
training a state classifier of the bearing by using the improved CHSMM training algorithm, inputting the newly input feature vector into 5 state-quitting models, and calculating the output probability of each model by using a forward-backward algorithm, wherein the model with the maximum output probability is the current degradation state of the bearing;
and (5): predicting the residual life;
for the sample to be measured whose degradation state is known (as can be obtained from step (4)), the remaining life of the bearing is obtained from the following recursion equation (assuming that the bearing is in degradation state i, RUL)iRepresents the remaining life of the bearing in a healthy state i, and d (i) represents the residence time of i macroscopic states):
when the bearing is in a healthy state N-1:
RULN-1＝aN-1,N-1[D(N-1)+D(N)]+aN-1,ND(N)
when the bearing is in a healthy state N-2:
RULN-2＝aN-2,N-2[D(N-2)+RULN-1]+aN-2,N-1RULN-1
when the bearing is in a healthy state i:
RULi＝ai,i[D(i)+RULi+1]+ai,i+1RULi+1
wherein the content of the first and second substances,
Figure BDA0001626301180000081

Claims (2)

1. a prediction method for the residual life of a rolling bearing of an improved CHSMM specifically comprises the following steps:
step (1): acquiring vibration data of a bearing in a full life cycle, and performing denoising and normalization pretreatment; extracting time domain and time-frequency domain feature vectors of the vibration data;
step (2): performing feature dimensionality reduction on the multi-domain feature vector by using a PCA (principal component analysis) algorithm;
and (3): dividing the bearing full life cycle data obtained in the step (2) into five degradation states, namely a normal state, a degradation state 1, a degradation state 2, a degradation state 3 and a degradation state 4, and performing clustering analysis on the full life cycle data by using a k-means algorithm to obtain data of each degradation state;
and (4): introducing a Gaussian mixture probability density function into the CHSMM to obtain an improved CHSMM, and training five degradation state recognition models by using the degradation state data obtained in the step (3) to serve as a state classifier of the bearing;
and (5): training a residual life prediction model by using the full life cycle data obtained in the step (2) to obtain the state transition probability of the full life cycle, extracting the characteristic vector of the data to be detected by using the methods provided in the steps (1) and (2), inputting the characteristic vector into the state classifier in the step (4) to obtain the current degradation state of the bearing, and then calculating the current residual life of the bearing by using a residual life calculation formula.
2. The method of claim 1 for predicting the remaining life of a rolling bearing in an improved CHSMM, wherein: the improvement to CHSMM in said step (4), comprising the steps of:
1) the CHSMM has the parameter τ ═ (N, M, pi, a, B, C), and the specific meanings are as follows:
① N number of states of Markov chain in model, and marking N states as S1，S2，…,SN,qtRepresenting the state in which the Markov chain is at any time t;
② M number of possible observations, o, corresponding to each state in the modeltRepresents an observed value at an arbitrary time t;
③ pi initial time, state probability distribution of model, pi ═ pi (pi)1,π2,…,πN) In which pii＝P(q1＝Si)1≤i≤N；
④ A is a state transition probability matrix, A ═ aij)N×NWherein a isij＝P(qt+1＝Sj|qt＝Si) I is not less than 1, j is not less than N, and
Figure FDA0002353665010000021
⑤ B observed probability density function, B ═ Bj(ok),1≤j≤N,1≤k≤M}，bj(ok)＝P(ok|qt＝Sj)；
⑥ C probability density function of state dwell time D, C ═ Cj(d),1≤j≤N,1≤d≤E}，cj(d)＝P(d|qt＝Sj) And E is the maximum residence time;
the forward-backward algorithm solves the evaluation problem, namely, the probability of a certain observation sequence is calculated by giving the observation sequence O and the parameter tau; the Viterbi algorithm solves the decoding problem, namely, given an observation sequence O and a parameter tau, an observation sequence which is optimal in a certain sense is searched; the Baum Welch algorithm solves the learning problem, i.e. given a sequence of observations, one τ can be determined such that P (O τ) is maximized;
define forward variable αt(i)＝P(o1,o2,…,ot,qt＝i,qt+1≠i),
Figure FDA0002353665010000022
Backward variable βt(i)＝P(ot+1,ot+2,…,oT,|qt＝i,qt+1≠i)，
Figure FDA0002353665010000023
Then there are:
Figure FDA0002353665010000024
Figure FDA0002353665010000025
Figure FDA0002353665010000026
Figure FDA0002353665010000027
for theGiven the parameter τ and the observation sequence O ═ O (O)1,o2,…,oT) And T is the length of the observation sequence, and the obtained logarithm expression of P (O | tau) is as follows:
Figure FDA0002353665010000031
wherein
Figure FDA0002353665010000032
δt(i,d)＝P(qt＝i,d|O),
Figure FDA0002353665010000033
1≤i,j≤N,1≤d≤T-1,1≤t≤T；
2) Parameter solving:
for the state residence time D, in the process of predicting the residual life of the bearing by applying CHSMM, the state residence time D is assumed to conform to Gaussian distribution, and in practice, the real distribution function of the state residence time is unknown, so that the prediction precision is reduced by the assumption;
in order to overcome the defects, a Gaussian mixture probability density function is adopted as a probability density function of the state residence time D, and a model expression is as follows:
Figure FDA0002353665010000034
f represents the number of Gaussian probability density functions;
the model parameters for state dwell time D are derived as follows:
Figure FDA0002353665010000035
Figure FDA0002353665010000036
Figure FDA0002353665010000037
wherein the content of the first and second substances,
Figure FDA0002353665010000038
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