CN113962020A - Vehicle bearing residual life prediction method based on wiener process with measurement error - Google Patents

Vehicle bearing residual life prediction method based on wiener process with measurement error Download PDF

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CN113962020A
CN113962020A CN202111142187.5A CN202111142187A CN113962020A CN 113962020 A CN113962020 A CN 113962020A CN 202111142187 A CN202111142187 A CN 202111142187A CN 113962020 A CN113962020 A CN 113962020A
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CN113962020B (en
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魏秀琨
管青鸾
贾利民
尹贤贤
魏德华
张慧贤
汤庆锋
周航
刘运超
尹新强
王棣青
赵春生
赵天可
魏东华
李江帅
刘志强
高方庆
沈星
胡新杨
傅兵
袁若岑
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Beijing Jiaotong University
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Abstract

The invention provides a vehicle bearing residual life prediction method based on a wiener process with a measurement error. The method comprises the following steps: collecting bearing data of a full life cycle by using a bearing test bed, and extracting a time domain characteristic value of a bearing; establishing a two-stage linear wiener degradation process model of the bearing, defining the service life of the bearing by using first arrival time, determining a failure threshold of the bearing, and deducing a probability density function of the residual service life of the bearing; obtaining a log-likelihood function of the model parameter vector, and obtaining an optimal estimation value of the parameter vector through multiple iterations by using an expectation expression of iterative operation through an expectation maximization algorithm; substituting the optimal estimated value of the parameter vector into the probability density function of the residual service life of the bearing to obtain the final predicted expected residual service life of the bearing. The invention can predict the residual service life of the bearing to determine the optimal maintenance time and maintenance strategy and provide a targeted bearing maintenance suggestion for a maintenance department.

Description

Vehicle bearing residual life prediction method based on wiener process with measurement error
Technical Field
The invention relates to the technical field of vehicle bearing residual life prediction, in particular to a vehicle bearing residual life prediction method based on a wiener process with a measurement error.
Background
With the rapid development of urban rail trains, higher requirements are put forward on the safety and reliability of the trains. Many operation lines are in overload operation in the morning and evening peak hours, so that each key system of the train is required to be safe and reliable, and the phenomenon that the train can not run in a fault or failure state is required. The bearing is one of indispensable elements in rail transit, is also the most fragile element simultaneously, and its validity directly leads to the operational safety of train. The degradation mechanism and the complex and variable running environment (load, smoothness of the track, temperature, etc.) inherent in the bearing have a great influence on the health state of the bearing. When a certain part in the bearing breaks down, a chain reaction is generated, which can lead to the damage of related systems of the vehicle and the shutdown of the vehicle and even the injury and death of people.
In the existing bearing residual life prediction research, the influence of measurement errors in the degradation process on the residual life prediction is less considered. The bearing exhibits a two-stage degradation mode: the bearing is in a relatively stable state in a slow degradation stage, and after an unknown change point, the bearing enters a more rapid degradation stage, and the peak value of the bearing shows a rapid growth trend. The fading characteristics of the bearings at different stages are very different and the results of the residual life prediction will also be very different. Therefore, a two-stage residual life prediction method of a bearing based on a wiener process with measurement errors requires intensive research.
A bearing remaining life prediction scheme in the prior art includes:
step 1, feature extraction and data processing
The bearing test bed is used for collecting bearing data in a full life cycle, then rolling axis characteristic values are extracted, time domain characteristic values with obvious change characteristics are selected to represent the bearing degradation process, and change points can be detected by a common method, such as a 3 sigma principle and Bayesian detection. And sequentially obtaining relevant data of the service life, the sampling interval, the change time and the failure threshold of the bearing.
Step 2, two-stage degradation modeling based on wiener process with measurement errors
(1) Let X (t) represent the degradation track of the bearing at time t, and neglecting the measurement error, the bearing degradation process can be described as
X(t)＝x0+exp(μt) (1)
In the formula, x0Representing the initial state of the degradation process, here generally taken as x00; μ as a random parameter.
Logarithmic transformation is carried out on two sides of the formula (1), and random influence and measurement error in the degradation process are considered, then
Figure BDA0003284176110000021
Where the change time τ (i.e., the time at which the change point occurs) is defined as the last monitored time of the first phase; x is the number ofτIs defined as the state of degradation at the point of change, where y0＝0，yτ＝ln(xτ)；μ1And mu2The drift coefficients, σ, of the first and second stages, respectively1And σ2Diffusion coefficients for the first and second stages, respectively; b (t) and B (t- τ) are standard wiener processes; epsilon1And ε2Are Gaussian errors and are respectively obeyed
Figure BDA0003284176110000022
And
Figure BDA0003284176110000023
step 3, predicting the residual life of two stages based on wiener process with measurement error
(1) In order to accurately predict the residual life of the product, the first-arrival time is used for defining the life of the bearing, the bearing degradation process { Y (t) > 0} is characterized in that the time of operation when the failure threshold omega is reached for the first time is represented, and then the life is defined as
T＝inf{t:Y(t)≥ω|Y(0)≤ω} (3)
In the formula, ω is a constant which is set in advance based on conventional industrial experience and is a failure threshold value.
From equation (2), the degradation process of both stages is a linear wiener process with measurement error. To derive the remaining life distributions of the two phases, the remaining life distribution of the first phase is first derived.
According to Y1(tk) From tkThe initial degradation process can be expressed approximately as
Figure BDA0003284176110000024
According to formula (5), let z (l) be Y1(tk+l)-ykThen { Z (l), l ≧ 0} can be considered as the threshold w-ykWiener model with drift term and measurement error.
At tkTime of day, degradation process { Y1(t), t ≧ 0} is equivalent to the first arrival time of { Z (l), l ≧ 0 }. According to { Z (l), l ≧ 0}, at ykUnder the condition, the probability density function of l under the first arrival time of { Z (l), l is obtained by derivation and is:
Figure BDA0003284176110000025
furthermore,. epsilon1Is a Gaussian error
Figure BDA0003284176110000026
The probability density function is:
Figure BDA0003284176110000031
according to the formula of total probability at ykAnd mu1Under the condition that the first arrival time of { Z (l) ≧ 0} is
Figure BDA0003284176110000032
At tkThe first arrival time of time, { Z (l), l ≧ 0} is equivalent to { Y ≧ 0}1(t), t.gtoreq.0 }. Thus based on ykAnd mu1Obtaining { Y1(t), t ≧ 0} a probability density function of the remaining lifetime l.
Figure BDA0003284176110000033
According to the degradation data y0:kFor a bearing that is actually running, will { Y1(t), t ≧ 0} at time tkThe remaining life of (a) is defined as:
Lk＝inf{lk:Y1(tk+lk)≥ω|y0:k} (10)
(2) assuming that τ is constant and known, the parameters of the degradation model are defined as random variables describing the random effects in the degradation process. Suppose μ in the model of equation (2)1And mu2Subject to a gaussian distribution,
Figure BDA0003284176110000034
μ1has a probability density function of
Figure BDA0003284176110000035
At ykAnd mu1Under the condition that the probability density function of the remaining life is
Figure BDA0003284176110000036
(3) First, theOne step is to deduce and find gτ(yτ|μ1,P1). Due to the fact that1Randomness of (g) according to the formula of total probabilityτ(yτ|μ1,P1) Can be expressed as
Figure BDA0003284176110000037
For a linear Wiener process Y1(t)＝μ1t+σ1B(t)+ε1If the drift coefficient mu1Garment
Figure BDA0003284176110000038
The transition intensity function under the first arrival time concept is
Figure BDA0003284176110000041
(4) In calculating the lifetime, consider μ1And mu2Is random. According to equation (12) and the overall probability theorem, if μ1And mu2Subject to a gaussian distribution,
Figure BDA0003284176110000042
the probability density function of the lifetime with a time of change τ of the constant value based on the two-stage degradation model is then:
Figure BDA0003284176110000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003284176110000044
Figure BDA0003284176110000051
Figure BDA0003284176110000052
Figure BDA0003284176110000053
(5) therefore, from the relationship between the lifetime and the remaining lifetime, a probability density function of the remaining lifetime can be obtained.
Case 1: current time tkLess than τ
Figure BDA0003284176110000054
In the formula (I), the compound is shown in the specification,
Figure BDA0003284176110000055
Figure BDA0003284176110000061
Figure BDA0003284176110000062
Figure BDA0003284176110000063
case 2: at a current time τ greater than tk
Figure BDA0003284176110000064
Step 4, model parameter estimation
To update the model parameters for both phases, at the point of change (i.e., t)kTau is less than or equal to) only the parameters of the first stage model are updated, otherwise, at the changing point (tau is less than or equal to t)k) Then, the RUL estimation can be performed only by updating the parameters of the second stage model. In the two stages, expectation maximization algorithm is introducedThe unknown parameters are estimated. The model parameter estimation step of the first stage based on the expectation-maximization algorithm is as follows.
(1) Establishing a state equation and an observation equation based on a state space model
Figure BDA0003284176110000065
In the formula, wk～N(0,Q1)，Δtk＝tk-tk-1，ΔBk＝B(tk)-B(tk-1) Initial parameter μ1,0～N(μ0,P0) Random parameter μ1,kThe expectation and variance of the a posteriori estimates are defined as
Figure BDA0003284176110000066
And P1,k|k＝var(μ1,k|Y0:k)。
(2) Unknown model parameters are represented by vectors
Figure BDA0003284176110000067
Is expressed as omega1Has a log-likelihood function of
Figure BDA0003284176110000068
In the formula, mu1＝{μ1,0,μ1,1,μ1,2,···,μ1,k},μ1,jIs tkThe gaussian distribution at a time, j ═ 1,2, ·, k.
(3) By passing
Figure BDA00032841761100000714
Determine omega1Maximum likelihood estimate of
Figure BDA0003284176110000071
(4) Solving for implicit variables using expectation maximization algorithmsΩ1Estimated value in the sense of the maximum likelihood function, expectation step
Figure BDA0003284176110000072
In the formula (I), the compound is shown in the specification,
Figure BDA0003284176110000073
the result obtained for the ith EM iteration.
(5) And (4) a maximization step, namely solving the iterative estimation of the step i +1 to obtain model parameters:
Figure BDA0003284176110000074
(6) obtaining the drift coefficient mu by using Rauch-Tung-Striebel (RTS) optimal smoothing algorithm1Condition expectation of
Figure BDA0003284176110000075
(7) Based on
Figure BDA0003284176110000076
Obtaining the optimal estimation value of the model parameter by the i +1 step iteration estimation
Figure BDA0003284176110000077
Figure BDA0003284176110000078
Figure BDA0003284176110000079
Figure BDA00032841761100000710
Figure BDA00032841761100000711
Figure BDA00032841761100000712
Wherein m is a constant and m > Δ tj，Δtj＝tj-tj-1，Δyj＝yj-yj-1。
Unknown model parameters of the second stage (i.e.
Figure BDA00032841761100000713
) The same methods and steps can be used for updating and estimating.
The method is performed by an artificial intelligence based method; only few residual life predictions of bearings are based on binary and multi-stage (degradation is divided into normal stage, slow degradation stage and accelerated degradation stage, and a multi-stage random degradation model of the bearing is built according to the degradation stage) wiener processes.
The disadvantages of the above-mentioned prior art bearing residual life prediction scheme include: the calculation process and the related algorithm are complex; the influence of complex environmental factors on the residual life prediction result and the measurement error in the degradation process are not fully considered; an analytic solution of the probability density function of the residual service life cannot be obtained, reliability analysis cannot be carried out based on the analytic solution, and a targeted bearing maintenance suggestion cannot be provided for a maintenance department.
Disclosure of Invention
The invention provides a vehicle bearing residual life prediction method based on a wiener process with a measurement error, so as to effectively predict the residual life of a vehicle bearing.
In order to achieve the purpose, the invention adopts the following technical scheme.
A vehicle bearing residual life prediction method based on a wiener process with measurement errors comprises the following steps:
step 1, collecting full-life cycle bearing data by using a bearing test bed, and extracting a time domain characteristic value of a bearing from the full-life cycle bearing data;
step 2, selecting a peak value in the time domain characteristic value of the bearing to represent a bearing degradation process, and establishing a two-stage linear wiener degradation process model of the bearing based on the time domain characteristic value of the bearing;
step 3, defining the service life of the bearing by using first arrival time by using the two-stage linear wiener degradation process model of the bearing, determining a failure threshold value of the bearing, obtaining a probability density function of the remaining service life of the first stage, and deducing the probability density function of the remaining service life of the two-stage linear wiener degradation process model according to a transition intensity function at a variable point;
step 4, solving a log-likelihood function of a parameter vector of a two-stage linear wiener degradation process model of the bearing, solving a maximum likelihood estimation value of the parameter vector through the log-likelihood function, solving an expected expression of iterative operation according to the maximum likelihood estimation value of the parameter vector, and obtaining an optimal estimation value of the parameter vector through multiple iterations by utilizing the expected expression of iterative operation through an expected maximization algorithm;
and 5, substituting the optimal estimated value of the parameter vector of the two-stage linear wiener degradation process model of the bearing into the residual life probability density function of the bearing, and obtaining the final predicted residual life expectation of the bearing by utilizing an expectation definition on the basis of the residual life probability density function of the bearing.
Preferably, the step 1 specifically includes:
the method comprises the steps of collecting full-life cycle bearing data by using a bearing test bed, and extracting time domain characteristic values of a rolling bearing from the full-life cycle bearing data, wherein the time domain characteristic values comprise a mean value, an absolute mean value, a maximum value, a minimum value, a peak value, a root mean square value and a variance.
Preferably, the step 2 specifically includes:
let x (t) represent the degradation trajectory at time t of the bearing, describing the bearing degradation process as:
X(t)＝x0+exp(μt) (1)
in the formula, x0Represents the initial state of the degradation process, and mu is a random parameter;
and (2) carrying out logarithmic transformation on two sides of the formula (1), and considering random influence and measurement error in the degradation process, then:
Figure BDA0003284176110000091
wherein, the change time tau is defined as the last monitoring time of the linear wiener degradation process model of the first stage; x is the number ofτIs defined as the state of degradation at the point of change, where y0＝0，yτ＝ln(xτ)；μ1And mu2The drift coefficients, σ, of the linear wiener degradation process model in the first and second stages, respectively1And σ2Diffusion coefficients for the first and second stages, respectively; b (t) and B (t- τ) are standard wiener processes; epsilon1And ε2Are Gaussian errors and are respectively obeyed
Figure BDA0003284176110000092
And
Figure BDA0003284176110000093
preferably, the step 3 specifically includes:
defining the service life of the bearing by using the first arrival time and determining the failure threshold of the bearing by using a two-stage linear wiener degradation process model of the bearing, obtaining a probability density function of the residual service life of the first stage, and obtaining a transition intensity function and mu at a variable point1And mu2The method comprises the steps of estimating expectation and variance of a drift coefficient at each monitoring point through Kalman filtering, predicting a peak degradation track of a bearing, and deducing a bearing residual life probability density function based on a two-stage linear wiener degradation process model, wherein parameters of the bearing residual life probability density function are unknown.
Preferably, the step 4 specifically includes:
the parameter vector of the two-stage linear degradation model is
Figure BDA0003284176110000094
Initial parameter mu comprising a drift coefficient1,0～N(μ0,P0)，
Figure BDA0003284176110000095
Is the diffusion coefficient σ of the first stage1The variance of (a);
Figure BDA0003284176110000096
is the first stage Gaussian error ε1The variance of (a);
for parameter vector omega1Performing ln conversion processing to obtain parameter vector omega by log likelihood function1According to said parameter vector omega1The maximum likelihood estimation value of the bearing determines an expected expression of iterative computation, a state equation and an observation equation are established based on a state space model, the expectation and the variance of the posterior estimation of the drift coefficient at each monitoring time point are estimated through Kalman filtering by using the state equation and the observation equation, the peak value degradation track of the bearing is predicted, and the optimal estimation value of the parameter vector is obtained through multiple iterations by using the expected expression of the iterative computation based on the peak value degradation track of the bearing through an expectation maximization algorithm.
Preferably, the desired definition in step 5 is:
Figure BDA0003284176110000101
Epre(tk) Is tkThe bearing residual life expectancy at the moment; lkThe residual life of the bearing;
Figure BDA0003284176110000102
for the residual life l of the bearingkIs determined.
According to the technical scheme provided by the embodiment of the invention, the method not only can estimate the degradation amount of the peak time domain characteristic value of the bearing, but also can predict the residual service life so as to determine the optimal maintenance time and maintenance strategy and provide a targeted bearing maintenance suggestion for a maintenance department, thereby reducing the time and economic cost and improving the reliability of the urban rail vehicle. And the algorithm of the method is easy to program by using related software, and the method is simple in calculation, convenient and practical.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic flow chart of a bearing two-stage remaining life prediction method based on a wiener process with measurement errors according to an embodiment of the present invention:
fig. 2 is a schematic diagram of a degradation trace of a peak signal of a bearing according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a comparison between an actual degraded track and a predicted degraded track according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating an update of model parameters according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a probability density function of the remaining life of a bearing (the last 10 monitoring points) based on model parameters according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a calculated prediction result of the residual life of the bearing according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
The embodiment of the invention provides a bearing two-stage residual life prediction method based on a wiener process with measurement errors, fully considers the influence of complex environmental factors on a residual life prediction result and the measurement errors in a degradation process, simultaneously considers the randomness of a degradation state at a variable point, improves the residual life prediction precision, and perfects the monitoring on the health state of a bearing.
The embodiment of the invention provides a bearing two-stage residual life prediction method based on a wiener process with a measurement error, which realizes the prediction of a degradation track and the prediction of residual life of a bearing and provides operation and maintenance support for a vehicle maintenance department. The processing flow of the method is shown in fig. 1, and comprises the following processing steps:
step 1, feature extraction and data processing.
The method comprises the steps of collecting full-life cycle Bearing data by using a Bearing test bed, wherein Bearing1-3 is an outer ring fault Bearing, and extracting time domain characteristic values of a rolling Bearing from the full-life cycle Bearing data, wherein the time domain characteristic values comprise a mean value, an absolute mean value, a maximum value, a minimum value, a peak value, a root mean square value, a variance and the like. The peak value is selected to characterize the bearing degradation process, since the peak value variation characteristics of the bearing degradation process are obvious and easy to calculate.
The degradation data for Bearing1-3 is shown in Table 1.
TABLE 1 degradation data of Bearing1-3
Figure BDA0003284176110000121
And 2, modeling based on two-stage degradation of the wiener process with the measurement error.
Based on the two-stage wiener process, degradation modeling is carried out on the time domain characteristic value of the peak value of the rolling bearing, and the measurement error in the degradation process is considered in the modeling process. The wiener process is a random process with Gaussian distribution increment, is convenient for estimating parameters and solving the analytic solution of residual life distribution, and is suitable for a non-strict monotonous degradation process. The Wiener process x (t) is generally of the form x (t) ═ θ t + σ b (t), where θ is the drift coefficient, σ > 0 is the diffusion coefficient, and b (t) is the standard brownian motion.
The invention establishes a two-stage linear wiener degradation process model of the bearing to describe the degradation track, discusses the problem of the residual service life of the bearing under a probability theory frame, obtains the probability density distribution of the residual service life, and can well describe the uncertainty of a prediction result.
In the embodiment, the bearing peak value y after linear transformationkIs a bearing degradation index;
determining the failure threshold of the bearing by using a relative method when the effective value of the bearing exceeds 10 xAhThen, judging that the bearing has completely failed, wherein AhThe failure threshold is determined from the value at which the bearing has completely failed, for the maximum characteristic indicator of the bearing in a healthy state. The failure threshold value is not less than the value at the time of complete failure.
And 3, predicting the residual life of the two stages based on the wiener process with the measurement error.
Fig. 2 shows a schematic diagram of a degradation trajectory of a peak signal of each test bearing provided by an embodiment of the present invention. Defining the service life of the bearing by using the first arrival time and determining the failure threshold of the bearing by using the two-stage linear wiener degradation process model of the bearing, obtaining the probability density function of the residual service life of the first stage, and further considering mu according to the transition intensity function at the transition point1And mu2And deriving a bearing residual life probability density function based on a two-stage linear wiener degradation process model.
And estimating the expectation and the variance of the posterior estimation of the drift coefficient at each monitoring point through Kalman filtering, and predicting the peak value degradation track of the bearing in one step. The monitoring points are monitoring time points, and each monitoring time point corresponds to a peak value.
Fig. 3 is a schematic diagram comparing an actual degraded track and a predicted degraded track according to an embodiment of the present invention. Finally, based on the expectation and variance of the posterior estimation of the total probability formula and the drift coefficient, considering the randomness of the degradation state at the variable point, obtaining the residual life probability density function of the bearing, wherein the residual life probability density function is only an expression, and the value of the variable is unknown, so that the model parameter estimation needs to be carried out in the step 4 to obtain the estimated value of the parameter, namely omega1。
Step 4, model parameter estimation
The parameters of the linear degradation model of the two stages are
Figure BDA0003284176110000131
Initial parameter mu comprising a drift coefficient1,0～N(μ0,P0)，
Figure BDA0003284176110000132
Is the diffusion coefficient σ of the first stage1The variance of (a);
Figure BDA0003284176110000133
is the first stage Gaussian error ε1The variance of (c).
And establishing a state equation and an observation equation based on the state space model, estimating the expectation and the variance of the posterior estimation of the drift coefficient at each monitoring time point through Kalman filtering, and predicting the peak value degradation track of the bearing in one step.
The purpose of estimating the model parameter vector is to calculate the residual life by using the estimated value to the probability density function of the residual life of the bearing and using the expected definition. Firstly, a model parameter vector omega unknown in the first stage is used1Expressing, finding the model parameter vector omega1The log-likelihood function of (a).
For vector omega1The ln conversion processing is carried out, and the expression is shown as formula (18):
Ω1the log-likelihood function of (a) is:
Figure BDA0003284176110000137
determining omega by means of a log-likelihood function1To Ω is calculated as the maximum likelihood estimate of1Iterated at step i in the sense of the maximum likelihood function of
Figure BDA0003284176110000134
The desired expression of (c). Then, the expectation step and the maximization step of the expectation maximization algorithm are carried out, and further, the RTS algorithm is used for solving the drift coefficient mu1The conditions of (1) are expected. Finally, and maximize
Figure BDA0003284176110000135
Obtaining the optimal estimation value of the model parameters obtained by i +1 times of iterative estimation
Figure BDA0003284176110000136
The updating of the model parameters is shown in fig. 4.
And 5, obtaining a residual life probability density function of the bearing by using the optimal estimation value of the parameter vector of the two-stage linear wiener degradation process model of the bearing, and obtaining a final predicted residual life expectation of the bearing by using an expectation definition based on the residual life probability density function of the bearing.
The optimal estimated value of the unknown parameters of the linear degradation models of the two stages is brought into the residual life probability density function formula (15) and the formula (16), and finally, the expected definition is carried out
Figure BDA0003284176110000141
And calculating the predicted residual life expectation of the bearing.
Fig. 5 shows a probability density function of the remaining life of the bearing (the last 10 monitoring points) obtained based on the model parameters, and fig. 6 shows a predicted result of the remaining life of the bearing calculated by the probability density function.
In conclusion, compared with the existing method for predicting the residual life of the bearing, the method provided by the invention can be used for easily estimating the degradation track of the bearing, tracking the degradation process of the bearing is realized, and the prediction accuracy is improved. In addition, the method is simple in calculation and convenient for practical application, and can provide technical support for prediction of the bearing degradation track in engineering practice.
The method considers the random effect and the measurement error influence of the bearings under the influence of environmental factors such as temperature, load, smoothness of the track and the like in the actual operation of the urban rail, and effectively describes the uncertainty and the measurement error of the degradation process. Meanwhile, the randomness of the degradation state at the variable point is considered, the probability density function of the residual service life is deduced based on the wiener process with the measurement error, the analytic solution of the two-stage service life prediction model is obtained, the accuracy of the residual service life prediction is improved, and the reliability analysis, the optimization of the maintenance period and the compilation of the maintenance plan can be further carried out based on the prediction result.
Those of ordinary skill in the art will understand that: the figures are merely schematic representations of one embodiment, and the blocks or flow diagrams in the figures are not necessarily required to practice the present invention.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (6)

1. A method for predicting the residual life of a vehicle bearing based on a wiener process with measurement errors is characterized by comprising the following steps:
step 1, collecting full-life cycle bearing data by using a bearing test bed, and extracting a time domain characteristic value of a bearing from the full-life cycle bearing data;
step 2, selecting a peak value in the time domain characteristic value of the bearing to represent a bearing degradation process, and establishing a two-stage linear wiener degradation process model of the bearing based on the time domain characteristic value of the bearing;
step 3, defining the service life of the bearing by using first arrival time by using the two-stage linear wiener degradation process model of the bearing, determining a failure threshold value of the bearing, obtaining a probability density function of the remaining service life of the first stage, and deducing the probability density function of the remaining service life of the two-stage linear wiener degradation process model according to a transition intensity function at a variable point;
step 4, solving a log-likelihood function of a parameter vector of a two-stage linear wiener degradation process model of the bearing, solving a maximum likelihood estimation value of the parameter vector through the log-likelihood function, solving an expected expression of iterative operation according to the maximum likelihood estimation value of the parameter vector, and obtaining an optimal estimation value of the parameter vector through multiple iterations by utilizing the expected expression of iterative operation through an expected maximization algorithm;
and 5, substituting the optimal estimated value of the parameter vector of the two-stage linear wiener degradation process model of the bearing into the residual life probability density function of the bearing, and obtaining the final predicted residual life expectation of the bearing by utilizing an expectation definition on the basis of the residual life probability density function of the bearing.
2. The method according to claim 1, wherein the step 1 specifically comprises:
the method comprises the steps of collecting full-life cycle bearing data by using a bearing test bed, and extracting time domain characteristic values of a rolling bearing from the full-life cycle bearing data, wherein the time domain characteristic values comprise a mean value, an absolute mean value, a maximum value, a minimum value, a peak value, a root mean square value and a variance.
3. The method according to claim 1, wherein the step 2 specifically comprises:
let x (t) represent the degradation trajectory at time t of the bearing, describing the bearing degradation process as:
X(t)＝x0+exp(μt) (1)
in the formula, x0Represents the initial state of the degradation process, and mu is a random parameter;
and (2) carrying out logarithmic transformation on two sides of the formula (1), and considering random influence and measurement error in the degradation process, then:
Figure FDA0003284176100000021
wherein, the change time tau is defined as the last monitoring time of the linear wiener degradation process model of the first stage; x is the number ofτIs defined as the state of degradation at the point of change, where y0＝0，yτ＝ln(xτ)；μ1And mu2The drift coefficients, σ, of the linear wiener degradation process model in the first and second stages, respectively1And σ2Diffusion coefficients for the first and second stages, respectively; b (t) and B (t- τ) are standard wiener processes; epsilon1And ε2Are Gaussian errors and are respectively obeyed
Figure FDA0003284176100000022
And
Figure FDA0003284176100000023
4. the method according to claim 1, wherein the step 3 specifically comprises:
defining the service life of the bearing by using the first arrival time and determining the failure threshold of the bearing by using a two-stage linear wiener degradation process model of the bearing, obtaining a probability density function of the residual service life of the first stage, and obtaining a transition intensity function and mu at a variable point1And mu2The method comprises the steps of estimating expectation and variance of a drift coefficient at each monitoring point through Kalman filtering, predicting a peak degradation track of a bearing, and deducing a bearing residual life probability density function based on a two-stage linear wiener degradation process model, wherein parameters of the bearing residual life probability density function are unknown.
5. The method according to claim 1, wherein the step 4 specifically comprises:
the parameter vector of the two-stage linear degradation model is
Figure FDA0003284176100000024
Initial parameter mu comprising a drift coefficient1,0～N(μ0,P0)，
Figure FDA0003284176100000025
Is the diffusion coefficient σ of the first stage1The variance of (a);
Figure FDA0003284176100000026
is the first stage Gaussian error ε1The variance of (a);
for parameter vector omega1Performing ln conversion processing to obtain parameter vector omega by log likelihood function1According to said parameter vector omega1Determining an expected expression of iterative computation based on the maximum likelihood estimate, establishing a state based on a state space modelAnd estimating the expectation and the variance of the posterior estimation of the drift coefficient at each monitoring time point through Kalman filtering by using a state equation and an observation equation, predicting the peak value degradation track of the bearing, and obtaining the optimal estimation value of the parameter vector through multiple iterations by using the expectation expression of iterative operation through an expectation maximization algorithm based on the peak value degradation track of the bearing.
6. The method of claim 1, wherein the desired definition in step 5 is:
Figure FDA0003284176100000027
Epre(tk) Is tkThe bearing residual life expectancy at the moment; lkThe residual life of the bearing;
Figure FDA0003284176100000031
for the residual life l of the bearingkIs determined.
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