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CN110222855B - Method and device for processing train wheel degradation data and storage medium - Google Patents

Method and device for processing train wheel degradation data and storage medium Download PDF

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CN110222855B
CN110222855B CN201910505718.9A CN201910505718A CN110222855B CN 110222855 B CN110222855 B CN 110222855B CN 201910505718 A CN201910505718 A CN 201910505718A CN 110222855 B CN110222855 B CN 110222855B
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康凤伟
李权福
王洪昆
王文刚
边志宏
卢宇星
王蒙
方琪琦
王萌
刘洋
蒋增强
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China Shenhua Energy Co Ltd
Shenhua Rail and Freight Wagons Transport Co Ltd
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Shenhua Rail and Freight Wagons Transport Co Ltd
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Abstract

The invention relates to the technical field of train maintenance, discloses a method and a device for processing train wheel degradation data and a storage medium, and solves the problem that in the prior art, the accuracy of prediction of the residual service life of a wheel is caused by neglecting sequence correlation and difference between degradation data. The method comprises the following steps: acquiring degradation monitoring data of a specific wheel of a train and a corresponding monitoring moment; obtaining updated degradation monitoring data and corresponding monitoring time by using a preset root-mean-square matrix; obtaining the mean value and the variance of the updated monitoring time according to the preset fixed effect vector, the preset random effect vector and the updated monitoring time; and obtaining the estimated value of the residual life of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time and a preset conditional probability density function. The method and the device are suitable for predicting the residual service life of the train wheels.

Description

Method and device for processing train wheel degradation data and storage medium
Technical Field
The invention relates to the technical field of train maintenance, in particular to a method and a device for processing train wheel degradation data and a storage medium.
Background
Under the condition of heavy-duty railway transportation, the wheel wear in service for a long time is the most serious, and if the wheel with serious wear is not timely warned, the safety and the stability of train operation can be finally and directly influenced. When wheel degradation data is researched in the prior art, only the certainty and average behavior of the data are often concerned, and the sequence correlation and the difference existing between individuals or groups are ignored, so that the accuracy of the residual life prediction of the wheel is influenced.
Disclosure of Invention
The embodiment of the invention aims to provide a method, a device and a storage medium for processing train wheel degradation data, which solve the problem that the accuracy of residual life prediction of wheels is caused by neglecting sequence correlation and difference existing between degradation data in the prior art.
In order to achieve the above object, an embodiment of a first aspect of the present invention provides a method for processing train wheel degradation data, where the method includes: acquiring degradation monitoring data of a specific wheel of a train and a corresponding monitoring moment; performing independence conversion on the degradation monitoring data and the corresponding monitoring time by using a preset root-mean-square matrix to obtain updated degradation monitoring data and corresponding monitoring time; obtaining the mean value and the variance of the updated monitoring moment according to a preset fixed effect vector, a preset random effect vector and the updated monitoring moment; and obtaining the estimated value of the residual life of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time and a preset conditional probability density function.
Further, before the obtaining of the updated degradation monitoring data and the corresponding monitoring time, the method further includes: acquiring historical degradation data of all wheels of the train; from a linear mixture effect model yi＝Xiβ+Zibi+εiObtaining a fixed effect vector beta and a random effect vector biAnd a measurement error eiWherein i is 1i～N(0,ψ)，εi～N(0,Ri)，
Figure BDA0002091767050000021
m is the number of all wheels of the train, yiFor historical degradation data of the ith wheel, XiDesigning the matrix for the fixing effect of the ith wheel, ZiDesign of the matrix for the random effects of the ith wheel, biThe distribution of (a) follows a normal distribution with a mean of 0 and a covariance matrix of phi ∈iDistribution obeys a mean of 0 and a variance of RiNormal distribution of (a) ("a")i 2Is the residual variance of the ith wheel,
Figure BDA0002091767050000022
is an identity matrix; according to
Figure BDA0002091767050000023
Obtaining an updated error effect variance matrix RiWherein σ isi 2Is the residual variance, Γ, of the ith wheeliFor an autocorrelation structure matrix, HiIs of a heteroscedastic structure; according to BiBi＝RiObtaining a preset root-mean-square matrix B of the ith wheeli。
Further, the performing, by using a preset root-mean-square matrix, independence conversion on the degradation monitoring data and the corresponding monitoring time to obtain updated degradation monitoring data and corresponding monitoring time includes: according to y*＝B-1×y，x*＝B-1×x，z*＝B-1×z，ε*＝B-1X epsilon to obtain updated degradation monitoring data y*And updated monitoring time x*Wherein B is-1An inverse matrix of the preset root mean square matrix is set, y is the acquired degradation monitoring data, x is the monitoring time corresponding to the acquired degradation monitoring data, z is a subset of the acquired monitoring time, and z is*For an updated subset of said monitoring instants, ε is a predetermined measurement error of said particular wheel, ε*The updated preset measurement error.
Further, theObtaining a mean value and a variance of the updated monitoring time according to a preset fixed effect vector, a preset random effect vector and the updated monitoring time comprises: according to
Figure BDA0002091767050000031
Obtaining a mean value mu of a posterior estimation value beta' of the preset fixed effect vector betaβ',k(ii) a According to
Figure BDA0002091767050000032
Obtaining the mean value mu of the posterior estimated value b' of the preset random effect vector bb',k(ii) a According to
Figure BDA0002091767050000033
Obtaining the standard deviation sigma of the posterior estimated value beta' of the preset fixed effect vector beta2 β',k(ii) a According to
Figure BDA0002091767050000034
Obtaining the standard deviation sigma of the posterior estimation value b' of the preset random effect vector b2 b',k(ii) a According to
Figure BDA0002091767050000035
Obtaining a posterior estimation value p of the orthogonal eigenvector p of the error effect variance matrixkWherein k is a total number of the degradation monitoring data of the specific wheel,
Figure BDA0002091767050000036
for the updated ith degradation monitoring data,
Figure BDA0002091767050000037
for the updated i-th monitoring instant, σ2Is the residual variance of the degradation monitoring data,
Figure BDA0002091767050000038
is the residual variance of the preset constant effect vector beta,
Figure BDA0002091767050000039
the residual variance of the preset random effect vector b is obtained; according to
Figure BDA00020917670500000310
Obtaining the mean value of the updated monitoring time
Figure BDA00020917670500000311
And variance
Figure BDA00020917670500000312
Wherein x is the specific wheel at the monitoring time
Figure BDA00020917670500000313
The remaining life of the battery pack is,
Figure BDA00020917670500000314
for the updated 1 st to kth degradation monitoring data,
Figure BDA00020917670500000315
Figure BDA0002091767050000041
further, the obtaining the estimated value of the remaining life of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time, and a preset conditional probability density function includes: according to
Figure BDA0002091767050000042
Obtaining a conditional cumulative distribution function
Figure BDA0002091767050000043
Wherein T is the time of the specific wheel
Figure BDA0002091767050000044
H is the failure threshold of wheel wear, Z isA standard normal distribution of the random variable x,
Figure BDA0002091767050000045
phi (-) is a cumulative distribution function of a standard normal distribution random variable; according to
Figure BDA0002091767050000046
Obtaining a preset conditional probability density function
Figure BDA0002091767050000047
Where φ (·) is a probability density function of a standard normally distributed random variable, g' (x) is the derivative of g (x); and obtaining a maximum variable corresponding to the preset conditional probability density function according to a function maximization algorithm, and determining the maximum variable as the estimated value of the residual life of the specific wheel.
In a second aspect, the present invention provides a device for processing train wheel degradation data, including: the system comprises an acquisition unit, a monitoring unit and a control unit, wherein the acquisition unit is used for acquiring degradation monitoring data of a specific wheel of a train and corresponding monitoring time; the independence conversion unit is used for carrying out independence conversion on the degradation monitoring data and the corresponding monitoring time by using a preset root-mean-square matrix to obtain updated degradation monitoring data and the corresponding monitoring time; the processing unit is used for obtaining the mean value and the variance of the updated monitoring time according to a preset fixed effect vector, a preset random effect vector and the updated monitoring time; and the residual life estimation unit is used for obtaining the estimated value of the residual life of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time and a preset conditional probability density function.
Further, the obtaining unit is further configured to obtain historical degradation data of all wheels of the train; the processing unit is further configured to generate a linear mixing effect model yi＝Xiβ+Zibi+εiObtaining a fixed effect vector beta and a random effect vector biAnd a measurement error eiWherein i is 1..,m，bi～N(0,ψ)，εi～N(0,Ri)，
Figure BDA0002091767050000051
m is the number of all wheels of the train, yiFor historical degradation data of the ith wheel, XiDesigning the matrix for the fixing effect of the ith wheel, ZiDesign of the matrix for the random effects of the ith wheel, biThe distribution of (a) follows a normal distribution with a mean of 0 and a covariance matrix of phi ∈iDistribution obeys a mean of 0 and a variance of RiNormal distribution of (a) ("a")i 2Is the residual variance of the ith wheel,
Figure BDA0002091767050000052
is an identity matrix; according to
Figure BDA0002091767050000053
Obtaining an updated error effect variance matrix RiWherein σ isi 2Is the residual variance, Γ, of the ith wheeliIn the form of a matrix of an autocorrelation structure,
Figure BDA0002091767050000054
is of a heteroscedastic structure; according to BiBi＝RiObtaining a preset root-mean-square matrix B of the ith wheeli。
Further, the independence transformation unit is also used for transforming the independence according to y*＝B-1×y，x*＝B-1×x，z*＝B-1×z，ε*＝B-1X epsilon to obtain updated degradation monitoring data y*Updated monitoring time x*Wherein B is-1An inverse matrix of the preset root mean square matrix is set, y is the acquired degradation monitoring data, x is the monitoring time corresponding to the acquired degradation monitoring data, z is a subset of the acquired monitoring time, and z is*For an updated subset of said monitoring instants, ε is a predetermined measurement error of said particular wheel, ε*Is an updated postThe preset measurement error is described.
Further, the processing unit is also used for
Figure BDA0002091767050000055
Obtaining the mean value mu of the posterior estimated value of the preset fixed effect vector betaβ',k(ii) a According to
Figure BDA0002091767050000056
Obtaining the mean value mu of the posterior estimated value of the preset random effect vector bb',k(ii) a According to
Figure BDA0002091767050000061
Obtaining the standard deviation sigma of the posterior estimated value of the preset fixed effect vector beta2 β',k(ii) a According to
Figure BDA0002091767050000062
Obtaining the standard deviation sigma of the posterior estimated value of the preset random effect vector b2 b',k(ii) a According to
Figure BDA0002091767050000063
Obtaining a posterior estimation value p of the orthogonal eigenvector p of the error effect variance matrixkWherein k is a total number of the degradation monitoring data of the specific wheel,
Figure BDA0002091767050000064
for the updated ith degradation monitoring data,
Figure BDA0002091767050000065
for the updated i-th monitoring instant, σ2Is the residual variance of the degradation monitoring data,
Figure BDA0002091767050000066
is the residual variance of the preset constant effect vector beta,
Figure BDA0002091767050000067
the residual variance of the preset random effect vector b is obtained; according to
Figure BDA0002091767050000068
Obtaining the mean value of the updated monitoring time
Figure BDA0002091767050000069
And variance
Figure BDA00020917670500000610
Wherein x is the specific wheel at the monitoring time
Figure BDA00020917670500000611
The remaining life of the battery pack is,
Figure BDA00020917670500000612
for the updated 1 st to kth degradation monitoring data,
Figure BDA00020917670500000613
Figure BDA00020917670500000614
further, the remaining life estimating unit is further configured to estimate the remaining life based on
Figure BDA00020917670500000615
Obtaining a conditional cumulative distribution function
Figure BDA00020917670500000616
Wherein T is the time of the specific wheel
Figure BDA00020917670500000617
H is the failure threshold for wheel wear, Z is the standard normal distribution of the random variable x,
Figure BDA00020917670500000618
phi (-) is a cumulative distribution function of a standard normal distribution random variable; according to
Figure BDA0002091767050000071
Obtaining a preset conditional probability density function
Figure BDA0002091767050000072
Where φ (·) is a probability density function of a standard normally distributed random variable, g' (x) is the derivative of g (x); and obtaining a maximum variable corresponding to the preset conditional probability density function according to a function maximization algorithm, and determining the maximum variable as the estimated value of the residual life of the specific wheel.
A third embodiment of the present invention provides a storage medium having stored therein instructions that, when run on a computer, cause the computer to perform a method of processing train wheel degradation data as described above.
According to the technical scheme, degradation monitoring data and corresponding monitoring time of a specific wheel of a train are obtained, the degradation monitoring data and the corresponding monitoring time are subjected to independent conversion by using a preset root-mean-square matrix to obtain updated degradation monitoring data and corresponding monitoring time, then the mean value and the variance of the updated monitoring time are obtained according to a preset fixed effect vector, a preset random effect vector and the updated monitoring time, and then the estimated value of the residual life of the specific wheel is obtained according to the updated monitoring time, the updated degradation monitoring data, the mean value and the variance of the updated monitoring time and a preset conditional probability density function. The method and the device solve the problem that the accuracy of the residual service life prediction of the wheel is caused by neglecting the sequence correlation and difference existing between the degradation data in the prior art, and improve the accuracy of the estimated value of the residual service life, reduce the maintenance cost of the wheel and improve the use efficiency of the wheel due to the fact that the result of the non-independence measurement error is considered.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic flow chart of a method for processing train wheel degradation data according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a processing device for train wheel degradation data according to an embodiment of the present invention;
FIG. 3 is a comparison graph of fit residuals of a conventional regression model and a selected model of substantially linear mixed effects provided by an embodiment of the present invention;
FIG. 4 is a graph of the degradation parameter intercept update changes for the wheel provided by an embodiment of the present invention;
FIG. 5 is a graph illustrating updated changes in the slope of the degradation parameter for the wheel provided by an embodiment of the present invention;
fig. 6 is a comparison graph of the residual life prediction of the general linear mixed effect model and the linear mixed effect model adjusted by the error effect matrix provided by the embodiment of the invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present invention, are given by way of illustration and explanation only, not limitation.
Fig. 1 is a schematic flow chart of a method for processing train wheel degradation data according to an embodiment of the present invention. As shown in fig. 1, the method comprises the steps of:
step 101, obtaining degradation monitoring data of a specific wheel of a train and a corresponding monitoring moment;
102, performing independence conversion on the degradation monitoring data and the corresponding monitoring time by using a preset root-mean-square matrix to obtain updated degradation monitoring data and the corresponding monitoring time;
103, obtaining a mean value and a variance of the updated monitoring time according to a preset fixed effect vector, a preset random effect vector and the updated monitoring time;
and 104, obtaining the estimated value of the residual service life of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time and a preset conditional probability density function.
The method comprises the steps that degradation monitoring data and corresponding monitoring time of a monitoring point are obtained when a train passes through the monitoring point, and before the degradation monitoring data and the corresponding monitoring time are subjected to independence conversion, historical degradation data of all wheels of the train are obtained, so that parameters needed by follow-up calculation are obtained. In the embodiment of the invention, the historical degradation data and the degradation monitoring data comprise the circumferential wear of the tread of the wheel, the running time, the intercept and the like.
Firstly, historical degradation data is used for carrying out data pre-analysis of a traditional regression model, and the linearity, normality, heterogeneity and abnormal data of the historical degradation data are tested. And then establishing a series of linear mixed effect models, taking historical degradation data of the wheels as model input, realizing parameter solution of the models by using an expectation-maximization algorithm, selecting the optimal models for evaluation index calculation, adjusting error effect matrixes of the optimal models, and realizing selection of an autocorrelation structure and an heteroscedastic structure so as to obtain the optimal mixed effect models. And then, taking an error effect matrix in a degradation rule obtained by historical degradation data as a conversion point of the non-independent measurement error, carrying out spectral decomposition on the error effect matrix to realize the independent conversion of the degradation monitoring data, and taking the updated degradation monitoring data and the degradation model parameters of the historical degradation data as input to calculate the degradation parameters of the online wheel individuals in real time under a Bayesian updating frame. And finally, predicting the estimated value of the residual life of the single wheel by using a preset conditional probability density function met by the residual life.
Wherein the selection of a general linear model is performed using historical degradation data of the train. Because the influence factor which can be monitored by the historical degradation data (namely the circumferential abrasion of the wheel tread) is the traveling mileage, the historical degradation data of the wheel is preprocessed and analyzed, the detection of linearity, normality and variance of the historical degradation data and the elimination of outlier data points are realized, and the method is used for constructing a subsequent mixed effect model. Based on linear detection, normality detection, homodyne detection and anomaly point detection on the historical degradation data, the historical degradation data of the wheel diameter can be obtained to meet linear and normality assumptions, but the model has the phenomenon of heteroscedasticity, so that the heteroscedasticity needs to be considered and eliminated in subsequent model construction. A linear mixed effect model is given as formula (1), which is a typical model describing a degradation accumulation process, and a fixed effect and a random effect in the model appear in a linear relationship, and the fixed effect and the random effect are combined in the model to explain the relevance and the difference of historical degradation data.
Figure BDA0002091767050000101
Wherein, i is 1
Figure BDA0002091767050000102
In addition, yiHistorical degradation data for the ith wheel, including niMaintaining historical degradation data of the monitoring points; m is the number of all wheels of the train; xiIs niX p dimension (n)iThe fixed effect design matrix of the ith wheel of the monitoring points and p fixed effect parameters); ziIs niX q dimension (n)iThe random effect design matrix of the ith wheel of the q monitoring points and the q random effect parameters); β is the p-dimensional fixed effect vector (mileage and intercept); biIs a q-dimensional random effect vector (distance traveled and intercept); biThe distribution of (a) follows a normal distribution with a mean value of 0 and a variance covariance matrix of ψ; epsiloniIs the measurement error, the distribution obeys a mean of 0, the variance is RiNormal distribution of (2); sigmai 2Is the residual variance of the ith wheel;
Figure BDA0002091767050000103
is an identity matrix. Wherein a random effect vector b is assumediAnd measurement error eiAre independent of each other, yiHas a marginal distribution of yi～N(XiBeta, sigma), where sigma is ZiψZi'+Ri。
In the basic linear mixed effect model, the assumption condition is that the two measurements are independent of each other, however, the repetitive measurements cause correlation between the observed results, so the problems of heterogeneity and correlation of errors need to be considered. Due to the existence of the two cases, the method can be directly introduced through the materialization of the error effect matrix. In order to improve the accuracy of prediction, the model is improved, and the problem of measurement error independence is solved better through adjustment of an error effect matrix.
Wherein the error effect variance matrix can be updated as shown in equation (2):
Figure BDA0002091767050000104
wherein R isiFor the updated error effect variance matrix, σi 2Is the residual variance, Γ, of the ith wheeliFor an autocorrelation structure matrix, HiIs in a heteroscedastic structure.
Wherein the autocorrelation structure matrix gammaiExpressing the time series correlation of individual repeated measurement data, the main structural form comprises: the method comprises a first-order autoregressive matrix model (AR (1)), a matrix model (ARMA (1,1)) formed by combining the first-order autoregressive model and a moving average model and a composite symmetric matrix model (CS), wherein rho is a correlation coefficient, gamma is a parameter to be estimated, and the specific structure is represented as follows:
Figure BDA0002091767050000111
Figure BDA0002091767050000112
Figure BDA0002091767050000113
variance structure HiThe error variance of the simulation may vary as the dependent variable increases for data representing individual repetitive measurements. The main structural forms comprise: fixed functions (var Fixed), Power functions (var Power), and exponential functions (var Exp). Wherein, the var Fixed function only has one variance variable and no variance parameter; the expression of var Power function is var (epsilon)ij)＝σ2|vij|2δI.e. g (v)ij,δ)＝|vij|δ. The expression of the var Exp function is var (epsilon)ij)＝σ2exp(δvij) I.e. g (v)ij,δ)＝exp(δvij). Wherein v isijThe dependent variable estimated for the fixed effect, δ is the power of the dependent variable, which is the parameter to be estimated.
In the embodiment of the invention, a first-order autoregressive matrix model (AR (1)) is adopted as an autocorrelation structural matrix gammaiTaking a Fixed function (var Fixed) as a heteroscedastic structure Hi。
In the error effect variance matrix RiAnd carrying out spectrum decomposition, and then carrying out appropriate data independence transformation on the original model by using a preset root-mean-square matrix obtained by spectrum decomposition. The decomposition process is as follows:
Figure BDA0002091767050000114
wherein P ═ P1,…,pn]Is an orthogonal matrix, column vector p1,…,pnIs the orthogonal eigenvector of R. Λ ═ diag (λ)1,…,λn) Is a diagonal matrix, the values of the diagonals are p corresponding to the eigenvectors1,…,pnBecause R is a symmetric positive definite matrix, the solution of the preset root-mean-square matrix can be realized:
BB＝PΛ1/2P'PΛ1/2P'＝PΛ1/2Λ1/2p ═ R equation (3)
B is a preset root mean square matrix after the variance matrix of the error effect is decomposed, B-1Performing independence conversion on the degradation monitoring data and the corresponding monitoring time by using a preset root-mean-square matrix obtained by spectrum decomposition to obtain updated degradation monitoring data and corresponding monitoring time, wherein the inverse matrix of the preset root-mean-square matrix is a main power equal matrix obtained by spectrum decomposition, and the formula (4) is as follows:
y*＝B-1×y，x*＝B-1×x，z*＝B-1×z，ε*＝B-1x epsilon formula (4)
Obtaining updated degradation monitoring data y according to formula (4)*And updated monitoring time x*Wherein B is-1An inverse matrix of the preset root mean square matrix is set, y is the acquired degradation monitoring data, x is the monitoring time corresponding to the acquired degradation monitoring data, z is a subset of the acquired monitoring time, and z is*For an updated subset of said monitoring instants, ε is a predetermined measurement error of said particular wheel, ε*The updated preset measurement error.
Since the independence conversion is realized by using the above formula (4), it is at this time
Figure BDA0002091767050000121
Independently and equally distributed.
Thus, the mean value μ of the posterior estimates β' of the predetermined fixation effect vector β can be obtained according to equation (5)β',kPresetting mean value mu of posterior estimated value b' of random effect vector bb',kPresetting the standard deviation sigma of the posterior estimate beta' of the fixed effect vector beta2 β',kPresetting the standard deviation sigma of the posterior estimated value b' of the random effect vector b2 b',kPosterior estimate p of the orthogonal eigenvector p of the error-effect variance matrixk：
Figure BDA0002091767050000122
Figure BDA0002091767050000123
Figure BDA0002091767050000131
Figure BDA0002091767050000132
Figure BDA0002091767050000133
Wherein k is a total number of the degradation monitoring data of the specific wheel,
Figure BDA0002091767050000134
for the updated ith degradation monitoring data,
Figure BDA0002091767050000135
for the updated i-th monitoring instant, σ2Is the residual variance of the degradation monitoring data,
Figure BDA0002091767050000136
is the residual variance of the preset constant effect vector beta,
Figure BDA0002091767050000137
and the residual variance of the preset random effect vector b is obtained.
Then, according to the formula (6), the updated average value of the monitoring time is obtained
Figure BDA0002091767050000138
And variance
Figure BDA0002091767050000139
Figure BDA00020917670500001310
Wherein x is the specific wheel at the monitoring time
Figure BDA00020917670500001311
The remaining life of the battery pack is,
Figure BDA00020917670500001312
for the updated 1 st to kth degradation monitoring data,
Figure BDA00020917670500001313
Figure BDA00020917670500001314
the remaining life of the wheel refers to the time interval from the current moment to the moment when the wheel fails, and the wheel at the moment can be known according to the definition of the life
Figure BDA00020917670500001315
The remaining lifetime x of (a) can be expressed as:
Figure BDA00020917670500001316
where H is the failure threshold for wheel wear. Let T denote
Figure BDA00020917670500001317
RUL (Remaining Useful Life) at time, i.e. from the current time
Figure BDA00020917670500001318
The interval to failure time, defined by the above-given definition of degenerate failure, can be such that T should satisfy
Figure BDA0002091767050000141
At a given point
Figure BDA0002091767050000142
The conditional cumulative distribution function for RUL is:
Figure BDA0002091767050000143
wherein use is made of
Figure BDA0002091767050000144
And converting the random variable x into standard normal distribution, wherein Z is the standard normal distribution of the random variable x, and phi (-) is a cumulative distribution function of the random variable of the standard normal distribution. If considering T representation
Figure BDA0002091767050000145
The RUL at a time, and therefore T, is a non-negative random variable, and to ensure this fact, the resulting distribution
Figure BDA0002091767050000146
The following estimation results can be obtained by performing truncation under the condition that T is more than or equal to 0:
Figure BDA0002091767050000147
the corresponding RUL has a predetermined conditional probability density function of:
Figure BDA0002091767050000148
where φ (-) is a probability density function of a standard normally distributed random variable, and g' (x) is the derivative of g (x).
Due to the equation (10), a function maximization algorithm may be adopted to obtain a maximum variable corresponding to the preset conditional probability density function, for example, x corresponding to the preset conditional probability density function when the preset conditional probability density function obtains the maximum density is the maximum variable, that is, the estimated value of the remaining life of the specific wheel.
In the embodiment of the invention, the non-independent errors of the measurement data are considered, and the non-independent analysis of the measurement errors is carried out by adjusting the error effect matrix of the conventional mixed effect model in the degradation modeling process. In the process of predicting the remaining life of the wheel, firstly, carrying out spectral decomposition on an error effect matrix in a degradation model obtained by solving, then, carrying out independence conversion on degradation monitoring data monitored in real time, fusing the degradation monitoring data with historical degradation data based on a Bayesian updating thought, and carrying out real-time remaining life prediction and reliability evaluation on the wheel. The invention considers the result of the non-independent measurement error, so that the residual life estimation shows a relatively more accurate estimation result, the reduction of the uncertainty of the residual life estimation is very important for PHM (fault prediction and Health Management), and the reduction of the uncertainty of the residual life estimation can reduce the maintenance cost of the wheel, improve the use efficiency of the wheel, improve the confidence coefficient of a decision result, has potential engineering practical value and can well guide the development of the state maintenance of the truck.
Correspondingly, fig. 2 is a schematic structural diagram of a processing device for train wheel degradation data according to an embodiment of the present invention. As shown in fig. 2, the apparatus 20 includes: an obtaining unit 21, configured to obtain degradation monitoring data of a specific wheel of the train and a corresponding monitoring time; the independence conversion unit 22 is configured to perform independence conversion on the degradation monitoring data and the corresponding monitoring time by using a preset root-mean-square matrix to obtain updated degradation monitoring data and corresponding monitoring time; the processing unit 23 is configured to obtain a mean value and a variance of the updated monitoring time according to a preset fixed effect vector, a preset random effect vector, and the updated monitoring time; and a remaining life estimating unit 24, configured to obtain an estimated value of the remaining life of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time, and a preset conditional probability density function.
Further, the obtaining unit is also used for obtaining all trains of the trainHistorical degradation data of the wheel; the processing unit is further configured to generate a linear mixing effect model yi＝Xiβ+Zibi+εiObtaining a fixed effect vector beta and a random effect vector biAnd a measurement error eiWherein i is 1i～N(0,ψ)，εi～N(0,Ri)，
Figure BDA0002091767050000151
m is the number of all wheels of the train, yiFor historical degradation data of the ith wheel, XiDesigning the matrix for the fixing effect of the ith wheel, ZiDesign of the matrix for the random effects of the ith wheel, biThe distribution of (a) follows a normal distribution with a mean of 0 and a covariance matrix of phi ∈iDistribution obeys a mean of 0 and a variance of RiNormal distribution of (a) ("a")i 2Is the residual variance of the ith wheel,
Figure BDA0002091767050000152
is an identity matrix; according to
Figure BDA0002091767050000153
Obtaining an updated error effect variance matrix RiWherein σ isi 2Is the residual variance, Γ, of the ith wheeliIn the form of a matrix of an autocorrelation structure,
Figure BDA0002091767050000154
is of a heteroscedastic structure; according to BiBi＝RiObtaining a preset root-mean-square matrix B of the ith wheeli。
Further, the independence transformation unit is also used for transforming the independence according to y*＝B-1×y，x*＝B-1×x，z*＝B-1×z，ε*＝B-1X epsilon to obtain updated degradation monitoring data y*Updated monitoring time x*Wherein B is-1An inverse matrix of the preset root mean square matrix is set, and y is the obtained regressionChanging monitoring data, wherein x is the monitoring time corresponding to the obtained degradation monitoring data, z is the subset of the obtained monitoring time, and z*For an updated subset of said monitoring instants, ε is a predetermined measurement error of said particular wheel, ε*The updated preset measurement error.
Further, the processing unit is also used for
Figure BDA0002091767050000161
Obtaining the mean value mu of the posterior estimated value of the preset fixed effect vector betaβ',k(ii) a According to
Figure BDA0002091767050000162
Obtaining the mean value mu of the posterior estimated value of the preset random effect vector bb',k(ii) a According to
Figure BDA0002091767050000163
Obtaining the standard deviation sigma of the posterior estimated value of the preset fixed effect vector beta2 β',k(ii) a According to
Figure BDA0002091767050000164
Obtaining the standard deviation sigma of the posterior estimated value of the preset random effect vector b2 b',k(ii) a According to
Figure BDA0002091767050000165
Obtaining a posterior estimation value p of the orthogonal eigenvector p of the error effect variance matrixkWherein k is a total number of the degradation monitoring data of the specific wheel,
Figure BDA0002091767050000171
for the updated ith degradation monitoring data,
Figure BDA0002091767050000172
for the updated i-th monitoring instant, σ2Is the residual variance of the degradation monitoring data,
Figure BDA0002091767050000173
is the residual variance of the preset constant effect vector beta,
Figure BDA0002091767050000174
the residual variance of the preset random effect vector b is obtained; according to
Figure BDA0002091767050000175
Obtaining the mean value of the updated monitoring time
Figure BDA0002091767050000176
And variance
Figure BDA0002091767050000177
Wherein x is the specific wheel at the monitoring time
Figure BDA0002091767050000178
The remaining life of the battery pack is,
Figure BDA0002091767050000179
for the updated 1 st to kth degradation monitoring data,
Figure BDA00020917670500001710
Figure BDA00020917670500001711
further, the remaining life estimating unit is further configured to estimate the remaining life based on
Figure BDA00020917670500001712
Obtaining a conditional cumulative distribution function
Figure BDA00020917670500001713
Wherein T is the time of the specific wheel
Figure BDA00020917670500001714
H is the failure threshold of wheel wear, Z is the followingThe standard normal distribution of the machine variable x,
Figure BDA00020917670500001715
phi (-) is a cumulative distribution function of a standard normal distribution random variable; according to
Figure BDA00020917670500001716
Obtaining a preset conditional probability density function
Figure BDA00020917670500001717
Where φ (·) is a probability density function of a standard normally distributed random variable, g' (x) is the derivative of g (x); and obtaining a maximum variable corresponding to the preset conditional probability density function according to a function maximization algorithm, and determining the maximum variable as the estimated value of the residual life of the specific wheel.
Implementation process parameters of the device are implementation process of the processing method of the train wheel degradation data.
Accordingly, an embodiment of the present invention further provides a storage medium, where instructions are stored in the storage medium, and when the storage medium is run on a computer, the storage medium causes the computer to execute the processing method for train wheel degradation data according to the foregoing embodiment.
In order to further illustrate the accuracy of the estimated value of the remaining life of the wheel obtained by the embodiment of the invention, a comparison between a general linear mixed effect model and a linear mixed effect model adjusted by an error effect matrix in the prediction of the remaining life is provided.
Firstly, historical degradation data is used for carrying out data pre-analysis of a traditional regression model, and the linearity, normality, heterogeneity and abnormal data of the historical degradation data are tested. Based on linear detection, normality detection, homodyne detection and anomaly point detection on the historical degradation data, the historical degradation data of the wheel diameter can be obtained to meet linear and normality assumptions, but the model has the phenomenon of heteroscedasticity, so that the heteroscedasticity needs to be considered and eliminated in subsequent model construction.
A series of linear mixed effect models were then built to fit the degradation data as shown in table 1.
TABLE 1
Figure BDA0002091767050000181
In the model, a and b are coefficients of the model fixed effect; a isi' and bi' is the coefficient of the model random effect, obeys the binary normal distribution with the mean value of 0 and the covariance of psi; epsiloniFor error effects, a normal distribution with a mean of 0 and a variance of R is followed, in which case yijThe circumferential degradation of the wheel tread; t is tijThe running time is the running time. The above-mentioned R matrix and ψ matrix are the intra-group and inter-group covariance matrices, respectively. Modeling the historical degradation data of the wheel according to the three models based on the historical degradation data (including the traveling time and the tread circumferential wear), solving parameters of unknown parameters in the models by adopting the EM (Expectation-Maximization algorithm) provided by the above, calculating relevant fitting indexes according to the solved parameter values and the degradation data, and selecting a basic linear mixed effect model:
TABLE 2
Figure BDA0002091767050000191
In table 2, the results of comparing the model (1) and the model (3) are shown.
TABLE 3
Figure BDA0002091767050000192
Table 3 shows the results of comparing model (1) with model (2).
It can be seen from tables 2 and 3 that the elimination of the fixed effect of the model does not significantly improve the fitting effect of the model, and the comparison of the simulation results of the model (2) and the model (1) shows that the likelihood ratio test value is 1.933821, the p value is less than 0.0001, the model (2) has a certain statistical significance, and it indicates that the simulation effect considered is better than the simulation effect without taking the intercept as the fixed effect. Comparing the model (2) with the model (3), wherein the intercept and the instability thereof have the largest influence on the degradation simulation of the wheel diameter, so that in the process of adding the linear mixed effect parameter effect, the travel mileage is taken as a fixed effect, the travel mileage and the intercept are taken as random effects, the model (2) is a selected basic mixed effect model through p-value inspection and according to the AIC and BIC minimization principle. The determined substantially linear mixed effect model of wheel diameter degradation is in the form of model (2) parameter estimates as shown in table 4:
TABLE 4
Figure BDA0002091767050000193
In addition, as shown in fig. 3, a fitting residual comparison graph of a conventional regression model (left graph) in which the absolute value of the wheel diameter estimated by the model and the diameter actually measured increases with the increase of the predicted value and thus presents a trumpet-like divergence and thus explains the problem of the variance phenomenon is compared with a selected basic linear mixed effect model (2)) (right graph). Although the construction of the linear mixed effect model enables heterogeneity among individuals to be decomposed to a certain degree, and the fitting effect of the model is obviously improved, the distribution is not completely uniform, so that the accuracy of model estimation is improved by improving an error effect matrix through a heteroscedastic structure.
The variance structure indicates that the error variance of the simulation may change as the dependent variable of the individual repeatability measurement data increases. The main structural forms comprise: fixed functions (var Fixed), Power functions (var Power), and exponential functions (var Exp). As shown in Table 5, the results of the adjustment for the fixed function and the power function are compared, and Table 6 shows the results of the adjustment for the fixed function and the exponential function
TABLE 5
Figure BDA0002091767050000201
TABLE 6
Figure BDA0002091767050000202
As can be seen from tables 5 and 6, for the solution of the variance matrix, the influence of variance is reduced to some extent by establishing a general mixed effect model, and in the process of adjusting by using the power function and the exponential function, the complexity of the model is increased by the increase of unknown variables, and the model does not pass the hypothesis test. Therefore, in the embodiment of the present invention, the heteroscedastic structure is not adjusted, and the fixed function format in the base model (2) is still adopted.
The autocorrelation structure expresses a time series correlation comprising: a first-order autoregressive matrix model (AR (1)), a matrix model combining first-order autoregressive and moving average models (ARMA (1,1)), and a composite symmetric matrix model (CS) for correlation analysis. Table 7 shows the results of comparison of three autocorrelation structure models, and Table 8 shows the results of comparison of AR (1) with the basic mixture effect model.
TABLE 7
Figure BDA0002091767050000211
TABLE 8
Figure BDA0002091767050000212
From table 7 and table 8, it can be seen that, when the AIC and BIC indexes are compared, the smaller the value is, the better the value is, and the larger the logLik index is, the better the value is, so that the AR (1) structure is selected as the autocorrelation structure to adjust the error effect, and the comparison and verification with the basic mixed effect model are performed, on the premise that the AIC and BIC indexes are smaller and better the p value is less than 0.0001, and the statistical significance is certain, which indicates that the difference is not considered significantly in consideration of the error matrix ratio.
In summary, the degradation model of the wheel can be obtained by selecting the autocorrelation error structure matrix AR (1) for model adjustment on the basis of the model (2), and the finally determined wheel diameter degradation mixed effect model is in the form as follows:
Figure BDA0002091767050000213
Figure BDA0002091767050000214
Figure BDA0002091767050000215
εi～N(O，Ri)
Figure BDA0002091767050000216
Hi＝I
τi(θ)＝AR(1)
the parameters in the above formula are shown in table 9.
TABLE 9
Figure BDA0002091767050000221
A mixed effect model constructed based on historical degradation data of the wheel, and an error effect matrix RiThe spectral decomposition is performed, the main power matrix is used for performing independence conversion on the degradation monitoring data monitored in real time (formula (4)), and then based on the bayesian idea, the parameter update value (formula (5)) of the wheel at each monitoring moment is obtained, and as a result, a degradation parameter intercept update change graph of the wheel shown in fig. 4 and a degradation parameter slope update change graph of the wheel shown in fig. 5 are obtained. It can be seen from the figure that the posterior estimation value of the parameter changes with the measured data in time tracking and self-adapting adjustment.
Since the degradation process of the wheel is linear degradation, degradation modeling and residual life prediction are directly carried out by using degradation data, for stricter comparison and considering the effectiveness of an independence Error, a general linear mixed effect model and the residual life prediction of the linear mixed effect model regulated by an Error effect matrix are compared from the perspective of RMSE (Root-Mean-Square Error), and as can be seen from FIG. 6, the RUL calculation result considering the non-independence Error is kept on a relatively small level, which is a relatively more accurate estimation result due to the consideration of the result of the non-independence measurement Error.
The reduction of the uncertainty of the remaining life estimation is very important for the PHM, because the reduction of the uncertainty of the remaining life can reduce the maintenance cost of the wheel, improve the use efficiency of the wheel, and improve the confidence of the decision result. By modeling of wheel degradation data and prediction of residual life, irrationality of independence error data is obviously seen, and compared with the method, the method provided by the embodiment of the invention can obtain a better result and verify the effectiveness of the method.
The preferred embodiments of the present invention have been described in detail with reference to the accompanying drawings, however, the present invention is not limited to the specific details of the above embodiments, and various simple modifications can be made to the technical solution of the present invention within the technical idea of the present invention, and these simple modifications are within the protective scope of the present invention.
It should be noted that the various features described in the above embodiments may be combined in any suitable manner without departing from the scope of the invention. The invention is not described in detail in order to avoid unnecessary repetition.
In addition, any combination of the various embodiments of the present invention is also possible, and the same should be considered as the disclosure of the present invention as long as it does not depart from the spirit of the present invention.

Claims (7)

1. A method of processing train wheel degradation data, the method comprising:
acquiring degradation monitoring data of a specific wheel of a train and a corresponding monitoring moment;
performing independence conversion on the degradation monitoring data and the corresponding monitoring time by using a preset root-mean-square matrix to obtain updated degradation monitoring data and corresponding monitoring time;
obtaining the mean value and the variance of the updated monitoring moment according to a preset fixed effect vector, a preset random effect vector and the updated monitoring moment;
obtaining the estimated value of the residual service life of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time and a preset conditional probability density function,
wherein, before the obtaining of the updated degradation monitoring data and the corresponding monitoring time, the method further comprises:
acquiring historical degradation data of all wheels of the train;
from a linear mixture effect model yi＝Xiβ+Zibi+εiObtaining a fixed effect vector beta and a random effect vector biAnd a measurement error eiWherein i is 1i～N(0,ψ)，εi～N(0,Ri)，
Figure FDA0003095617330000011
m is the number of all wheels of the train, yiFor historical degradation data of the ith wheel, XiDesigning the matrix for the fixing effect of the ith wheel, ZiDesign of the matrix for the random effects of the ith wheel, biThe distribution of (a) follows a normal distribution with a mean of 0 and a covariance matrix of phi ∈iDistribution obeys a mean of 0 and a variance of RiNormal distribution of (a) ("a")i 2Is the residual variance of the ith wheel,
Figure FDA0003095617330000012
is an identity matrix;
according to
Figure FDA0003095617330000013
Obtaining an updated error effect variance matrix RiWherein σ isi 2Is the residual variance, Γ, of the ith wheeliFor an autocorrelation structure matrix, HiIs of a heteroscedastic structure;
according to BiBi＝RiObtaining a preset root-mean-square matrix B of the ith wheeli；
The obtaining of the updated degradation monitoring data and the corresponding monitoring time by using the preset root-mean-square matrix comprises:
according to y*＝B-1×y，x*＝B-1×x，z*＝B-1×z，ε*＝B-1X epsilon to obtain updated degradation monitoring data y*And updated monitoring time x*Wherein B is-1An inverse matrix of the preset root mean square matrix is set, y is the acquired degradation monitoring data, x is the monitoring time corresponding to the acquired degradation monitoring data, z is a subset of the acquired monitoring time, and z is*For an updated subset of said monitoring instants, ε is a predetermined measurement error of said particular wheel, ε*The updated preset measurement error.
2. The method of claim 1, wherein obtaining the mean and variance of the updated monitoring time based on a predetermined fixed effect vector, a predetermined random effect vector, and the updated monitoring time comprises:
according to
Figure FDA0003095617330000021
Obtaining a mean value mu of a posterior estimation value beta' of the preset fixed effect vector betaβ',k；
According to
Figure FDA0003095617330000022
Obtaining the mean value mu of the posterior estimated value b' of the preset random effect vector bb',k；
According to
Figure FDA0003095617330000023
Obtaining the standard deviation sigma of the posterior estimated value beta' of the preset fixed effect vector beta2 β',k；
According to
Figure FDA0003095617330000024
Obtaining the standard deviation sigma of the posterior estimation value b' of the preset random effect vector b2 b',k；
According to
Figure FDA0003095617330000031
Obtaining a posterior estimation value p of the orthogonal eigenvector p of the error effect variance matrixk，
Wherein k is a total number of the degradation monitoring data of the specific wheel,
Figure FDA0003095617330000032
for the updated ith degradation monitoring data,
Figure FDA0003095617330000033
for the updated i-th monitoring instant, σ2Is the residual variance of the degradation monitoring data,
Figure FDA0003095617330000034
is the residual variance of the preset constant effect vector beta,
Figure FDA0003095617330000035
the residual variance of the preset random effect vector b is obtained;
according to
Figure FDA0003095617330000036
Obtaining the mean value of the updated monitoring time
Figure FDA0003095617330000037
And variance
Figure FDA0003095617330000038
Wherein x is the specific wheel at the monitoring time
Figure FDA0003095617330000039
The remaining life of the battery pack is,
Figure FDA00030956173300000310
for the updated 1 st to kth degradation monitoring data,
Figure FDA00030956173300000311
Figure FDA00030956173300000312
3. the method of claim 2, wherein obtaining the estimated remaining life value of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time, and a preset conditional probability density function comprises:
according to
Figure FDA00030956173300000313
Obtaining a conditional cumulative distribution function
Figure FDA00030956173300000314
Wherein T is the time of the specific wheel
Figure FDA00030956173300000315
Residual service life of, H is the carThe failure threshold of the wheel wear, Z is the standard normal distribution of the random variable x,
Figure FDA00030956173300000316
phi (-) is a cumulative distribution function of a standard normal distribution random variable;
according to
Figure FDA00030956173300000317
Obtaining a preset conditional probability density function
Figure FDA00030956173300000318
Where φ (·) is a probability density function of a standard normally distributed random variable, g' (x) is the derivative of g (x);
and obtaining a maximum variable corresponding to the preset conditional probability density function according to a function maximization algorithm, and determining the maximum variable as the estimated value of the residual life of the specific wheel.
4. An apparatus for processing train wheel degradation data, the apparatus comprising:
the system comprises an acquisition unit, a monitoring unit and a control unit, wherein the acquisition unit is used for acquiring degradation monitoring data of a specific wheel of a train and corresponding monitoring time;
the independence conversion unit is used for carrying out independence conversion on the degradation monitoring data and the corresponding monitoring time by using a preset root-mean-square matrix to obtain updated degradation monitoring data and the corresponding monitoring time;
the processing unit is used for obtaining the mean value and the variance of the updated monitoring time according to a preset fixed effect vector, a preset random effect vector and the updated monitoring time;
a remaining life estimating unit for obtaining a remaining life estimation value of the specific wheel according to the updated monitoring time, the updated degradation monitoring data, the updated mean and variance of the monitoring time, and a preset conditional probability density function,
wherein the obtaining unit is further configured to obtain historical degradation data of all wheels of the train;
the processing unit is further configured to generate a linear mixing effect model yi＝Xiβ+Zibi+εiObtaining a fixed effect vector beta and a random effect vector biAnd a measurement error eiWherein i is 1i～N(0,ψ)，εi～N(0,Ri)，
Figure FDA0003095617330000041
m is the number of all wheels of the train, yiFor historical degradation data of the ith wheel, XiDesigning the matrix for the fixing effect of the ith wheel, ZiDesign of the matrix for the random effects of the ith wheel, biThe distribution of (a) follows a normal distribution with a mean of 0 and a covariance matrix of phi ∈iDistribution obeys a mean of 0 and a variance of RiNormal distribution of (a) ("a")i 2Is the residual variance of the ith wheel,
Figure FDA0003095617330000042
is an identity matrix; according to
Figure FDA0003095617330000043
Obtaining an updated error effect variance matrix RiWherein σ isi 2Is the residual variance, Γ, of the ith wheeliIn the form of a matrix of an autocorrelation structure,
Figure FDA0003095617330000044
is of a heteroscedastic structure; according to BiBi＝RiObtaining a preset root-mean-square matrix B of the ith wheeli；
Wherein the independence conversion unit is further used for converting the independence according to y*＝B-1×y，x*＝B-1×x，z*＝B-1×z，ε*＝B-1X epsilon to obtain updated degradation monitoring data y*Updated monitoringTime x*Wherein B is-1An inverse matrix of the preset root mean square matrix is set, y is the acquired degradation monitoring data, x is the monitoring time corresponding to the acquired degradation monitoring data, z is a subset of the acquired monitoring time, and z is*For an updated subset of said monitoring instants, ε is a predetermined measurement error of said particular wheel, ε*The updated preset measurement error.
5. The apparatus of claim 4, wherein the processing unit is further configured to process the data according to
Figure FDA0003095617330000051
Obtaining the mean value mu of the posterior estimated value of the preset fixed effect vector betaβ',k(ii) a According to
Figure FDA0003095617330000052
Obtaining the mean value mu of the posterior estimated value of the preset random effect vector bb',k(ii) a According to
Figure FDA0003095617330000053
Obtaining the standard deviation sigma of the posterior estimated value of the preset fixed effect vector beta2 β',k(ii) a According to
Figure FDA0003095617330000054
Obtaining the standard deviation sigma of the posterior estimated value of the preset random effect vector b2 b',k(ii) a According to
Figure FDA0003095617330000061
Obtaining a posterior estimation value p of the orthogonal eigenvector p of the error effect variance matrixkWherein k is a total number of the degradation monitoring data of the specific wheel,
Figure FDA0003095617330000062
for updated i-th degradation monitoring numberAccording to the above-mentioned technical scheme,
Figure FDA0003095617330000063
for the updated i-th monitoring instant, σ2Is the residual variance of the degradation monitoring data,
Figure FDA0003095617330000064
is the residual variance of the preset constant effect vector beta,
Figure FDA0003095617330000065
the residual variance of the preset random effect vector b is obtained; according to
Figure FDA0003095617330000066
Obtaining the mean value of the updated monitoring time
Figure FDA0003095617330000067
And variance
Figure FDA0003095617330000068
Wherein x is the specific wheel at the monitoring time
Figure FDA0003095617330000069
The remaining life of the battery pack is,
Figure FDA00030956173300000610
for the updated 1 st to kth degradation monitoring data,
Figure FDA00030956173300000611
Figure FDA00030956173300000612
6. the apparatus of claim 5,
the remaining life estimating unit also usesIn accordance with
Figure FDA00030956173300000613
Obtaining a conditional cumulative distribution function
Figure FDA00030956173300000614
Wherein T is the time of the specific wheel
Figure FDA00030956173300000615
H is the failure threshold for wheel wear, Z is the standard normal distribution of the random variable x,
Figure FDA00030956173300000616
phi (-) is a cumulative distribution function of a standard normal distribution random variable; according to
Figure FDA00030956173300000617
Obtaining a preset conditional probability density function
Figure FDA00030956173300000618
Where φ (·) is a probability density function of a standard normally distributed random variable, g' (x) is the derivative of g (x); and obtaining a maximum variable corresponding to the preset conditional probability density function according to a function maximization algorithm, and determining the maximum variable as the estimated value of the residual life of the specific wheel.
7. A storage medium having stored therein instructions which, when run on a computer, cause the computer to perform the method of processing train wheel degradation data of any of claims 1-3 above.
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