CN111241633A - Chopper residual life prediction method based on principal component analysis and double-exponential model - Google Patents
Chopper residual life prediction method based on principal component analysis and double-exponential model Download PDFInfo
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Abstract
The invention discloses a chopper residual life prediction method based on principal component analysis and a bi-exponential model, which comprises the following steps of: s1 obtaining T by principal component analysis method2Curves consisting of historical values of the statistics, i.e. T2A curve; s2, identifying parameters of the bi-exponential model by adopting a nonlinear least square method; s3, obtaining a pair T of bi-exponential models through identification2Predicting a curve; and S4, subtracting the current time from the time when the value of the double-exponential model reaches the specified threshold value for the first time, and obtaining the remaining service life of the chopper at the current time. The invention obtains T by a principal component analysis method2Curve, identifying parameters of the dual-exponential model by nonlinear least square method, and identifying the obtained dual-exponential model to T2Curve prediction, realizing residual life prediction of chopperThe detection has the advantages of simple detection and high reliability.
Description
Technical Field
The invention belongs to the technical field of magnetic suspension trains, and particularly relates to a chopper residual life prediction method based on principal component analysis and a double-exponential model.
Background
With the popularization of magnetic levitation trains, the safety and reliability of levitation systems are receiving more and more attention, wherein the chopper is a core component of the levitation system. In the running process of the magnetic-levitation train, once the chopper breaks down, the train cannot run. This is largely avoided if the system can be predicted for remaining life before a chopper failure occurs. Therefore, how to accurately predict the residual life of the chopper is a problem which needs to be solved urgently at present.
Disclosure of Invention
The invention aims to provide a chopper residual life prediction method based on principal component analysis and a bi-exponential model, and T is obtained by utilizing the principal component analysis method2Curve, double exponential model pair T2And curve prediction is realized, so that the residual service life of the chopper is predicted, and the method has the advantages of simplicity in detection and high reliability.
The purpose of the invention is realized by the following technical scheme: the chopper residual life prediction method based on the principal component analysis method and the double-exponential model is characterized by comprising the following steps of:
s1 obtaining T by principal component analysis method2Curves consisting of historical values of the statistics, i.e. T2A curve;
s2, identifying parameters of the bi-exponential model by adopting a nonlinear least square method;
s3, using the bi-exponential model pair T obtained by identification2Predicting a curve;
and S4, subtracting the current time from the time when the value of the double-exponential model reaches the specified threshold value for the first time, and obtaining the remaining service life of the chopper at the current time.
As a further improvement, the model of the principal component analysis method is established by the following steps:
(1) assuming that a training data set Y is composed of N samples and M variables, the expression of Y is as follows:
Y＝(yi)∈CM×N(1)
in the formula, CM×NA set of matrices representing M rows and N columns, i 1,2iRepresenting the test data obtained in the training data set Y;
(2) setting the mean value of N samples as 0 and the variance as 1;
(3) the covariance of Y is defined as:
in the formula, YTA transposed matrix that is Y;
and the covariance according to the principal component analysis method Y is also expressed by the following formula:
in the formula, PpcDenotes the principal component part, PresRepresenting the residual part, ΛpcCharacteristic value, Λ, representing the principal component partresCharacteristic value, P, representing residual partpc TIs PpcTransposed matrix of (1), Pres TIs PresThe transposed matrix of (1), wherein:
Ppc＝[p1,...,pγ]∈RM×γ(4)
in the formula, RM×γSet of matrices, p, representing M rows and gamma columns1、pγRespectively representing the feature vectors corresponding to the 1 st and the gamma-th feature values;
in the formula, RM×(M-γ)Set of matrices, p, representing M rows and M-gamma columnsγ+1、pMRespectively representing the characteristic vectors corresponding to the gamma +1 th characteristic value and the Mth characteristic value;
Λpc＝diag(λ1,...,λγ) (6)
in the formula, λ1、λγRespectively represent ΛpcA diagonal element of (a);
Λres＝diag(λγ+1,...,λM) (7)
in the formula, λγ+1、λMRespectively represent ΛresDiagonal element of (2), and λ1≥…≥λγ≥λγ+1≥…λM。
As a further improvement, T2The curve test statistic is calculated according to the formula:
T2 j＝yj TPpcΛ-1PT pcyj(8)
wherein j is 1,22 jDenotes the jth T2Curve test statistic, yj TIs yjThe transposed matrix of (2).
As a further improvement, the expression of the bi-exponential model is:
in the formula, at、bt、ctAnd dtAre all parameters and t represents the time.
As a further improvement, according to T2Curve test statistic and dual index model identification of the parameter at、bt、ctAnd dt。
As a further improvement, the remaining life is solved by the following formula:
RUL(tk)＝inf{r:f(r+tk)≥θ|f(tk)} (10)
wherein, RUL (t)k) Is at the tkThe remaining life of the chopper, f (r + t)k) Is the (r + t) thk) T of time chopper2Curve test statistic T2 pcaValue of f (t)k) Is at the tkT of time chopper2Curve test statistic T2 pcaθ is a preset specified threshold, wherein:
in formulae (11) and (12), atk,btk,ctk,dtkDenotes the t-thkThe parameters obtained at the moment.
The chopper residual life prediction method based on principal component analysis and bi-exponential model obtains T through the principal component analysis method2Curve, identifying parameters of the dual-exponential model by nonlinear least square method, and identifying the obtained dual-exponential model to T2And the curve prediction is realized, so that the residual service life of the chopper is predicted, and the method has the advantages of simple detection and high reliability.
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The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.
FIG. 1 is a flow chart of a chopper remaining life prediction method based on principal component analysis and a bi-exponential model.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following detailed description of the present invention is provided with reference to the accompanying drawings and specific embodiments, and it is to be noted that the embodiments and features of the embodiments of the present application can be combined with each other without conflict.
It should be noted that the following terms are specifically explained for better understanding of the present invention:
principal Component Analysis (PCA), a statistical method. A group of variables which are possibly correlated are converted into a group of linearly uncorrelated variables through orthogonal transformation, and the group of converted variables are called principal components.
Non-linear least squares (Non-linear least squares), a method for estimating parameters of a nonlinear static model using the least square sum of errors as a criterion, where y is the output of the system, x is the input, and θ is a parameter (which may be a vector).
As shown in fig. 1, the chopper residual life prediction method based on principal component analysis and bi-exponential model provided by the embodiment of the present invention includes the following steps:
s1 obtaining T by principal component analysis method2Curves consisting of historical values of the statistics, i.e. T2A curve;
specifically, the model of the principal component analysis method is established by the following steps: (1) assuming that a training data set Y is composed of N samples and M variables, the expression of Y is as follows:
Y＝(yi)∈CM×N(1)
in the formula, CM×NA set of matrices representing M rows and N columns, i 1,2iRepresenting the test data obtained in the training data set Y;
(2) setting the mean value of N samples as 0 and the variance as 1;
(3) the covariance of Y is defined as:
in the formula, YTA transposed matrix that is Y;
and the covariance according to the principal component analysis method Y is also expressed by the following formula:
in the formula, PpcDenotes the principal component part, PresRepresenting the residual part, ΛpcCharacteristic value, Λ, representing the principal component partresCharacteristic value, P, representing residual partpc TIs PpcTransposed matrix of (1), Pres TIs PresThe transposed matrix of (1), wherein:
Ppc＝[p1,...,pγ]∈RM×γ(4)
in the formula, RM×γSet of matrices, p, representing M rows and gamma columns1、pγRespectively representing the eigenvectors corresponding to the 1 st and the gamma-th eigenvalues;
in the formula, RM×(M-γ)Set of matrices, p, representing M rows and M-gamma columnsγ+1、pMRespectively representing the characteristic vectors corresponding to the gamma +1 th characteristic value and the Mth characteristic value;
Λpc＝diag(λ1,...,λγ) (6)
in the formula, λ1、λγRespectively represent ΛpcA diagonal element of (a);
Λres＝diag(λγ+1,...,λM) (7)
in the formula, λγ+1、λMRespectively represent ΛresDiagonal element of (2), and λ1≥…≥λγ≥λγ+1≥…λM。
S2, identifying parameters of the bi-exponential model by adopting a nonlinear least square method;
s3, using the bi-exponential model pair T obtained by identification2Predicting a curve;
and S4, subtracting the current time from the time when the value of the double-exponential model reaches the specified threshold value for the first time, and obtaining the residual life.
As a further preferred embodiment, T2The calculation formula of the curve test statistic value and the expression of the double-exponential model are respectively as follows:
T2 j＝yj TPpcΛ-1PT pcyj(8)
in the formula (8), T2 jDenotes the jth T2Curve test statistic, yj TIs yjThe transposed matrix of (2).
In the formula (9), at、bt、ctAnd dtAre all parameters, and t represents time;
the number of parameters at、bt、ctAnd dtI.e. according to T2Curve test statistic T2 jAnd identifying the double-index model.
Meanwhile, in a further technical solution, the remaining life in step S4 is solved by the following formula:
RUL(tk)＝inf{r:f(r+tk)≥θ|f(tk)} (10)
wherein, RUL (t)k) Is tkThe remaining life of the system at the first moment, f (r + t)k) Is the (r + t) thk) T of time chopper2Curve test statistic T2 pcaValue of f (t)k) Is at the tkT of time chopper2Curve surveyTrial and error value T2 pcaθ is a preset specified threshold, wherein:
in formulae (11) and (12), atk,btk,ctk,dtkDenotes the t-thkThe parameters obtained at the moment.
Therefore, the invention obtains T by a principal component analysis method2Curve, identifying parameters of the dual-exponential model by nonlinear least square method, and identifying the obtained dual-exponential model to T2And the curve prediction is realized, so that the residual service life of the chopper is predicted, and the method has the advantages of simple detection and high reliability.
In the description above, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore should not be construed as limiting the scope of the present invention.
In conclusion, although the present invention has been described with reference to the preferred embodiments, it should be noted that, although various changes and modifications may be made by those skilled in the art, they should be included in the scope of the present invention unless they depart from the scope of the present invention.
Claims (6)
1. The chopper residual life prediction method based on principal component analysis and a bi-exponential model is characterized by comprising the following steps of:
s1 obtaining T by principal component analysis method2Curves consisting of historical values of the statistics, i.e. T2A curve;
s2, identifying parameters of the bi-exponential model by adopting a nonlinear least square method;
s3, using the bi-exponential model pair T obtained by identification2Predicting a curve;
and S4, subtracting the current time from the time when the value of the double-exponential model reaches the specified threshold value for the first time, and obtaining the remaining service life of the chopper at the current time.
2. The chopper residual life prediction method based on principal component analysis and bi-exponential model according to claim 1, characterized in that the model of the principal component analysis method is established by the following steps:
(1) assuming that a training data set Y is composed of N samples and M variables, the expression of Y is as follows:
Y＝(yi)∈CM×N(1)
in the formula, CM×NA set of matrices representing M rows and N columns, i 1,2iRepresenting the ith data in the training data set Y.
(2) Setting the mean value of N samples as 0 and the variance as 1;
(3) the covariance of Y is defined as:
in the formula, YTA transposed matrix that is Y;
and the covariance according to the principal component analysis method Y is also expressed by the following formula:
in the formula, PpcDenotes the principal component part, PresRepresenting the residual part, ΛpcCharacteristic value, Λ, representing the principal component partresCharacteristic value, P, representing residual partpc TIs PpcTransposed matrix of (1), Pres TIs PresThe transposed matrix of (1), wherein:
Ppc＝[p1,...,pγ]∈RM×γ(4)
in the formula, RM×γSet of matrices, p, representing M rows and gamma columns1、pγRespectively representing the eigenvectors corresponding to the 1 st and the gamma-th eigenvalues;
in the formula, RM×(M-γ)Set of matrices, p, representing M rows and M-gamma columnsγ+1、pMRespectively representing the characteristic vectors corresponding to the gamma +1 th characteristic value and the Mth characteristic value;
Λpc＝diag(λ1,...,λγ) (6)
in the formula, λ1、λγRespectively represent ΛpcA diagonal element of (a);
Λres＝diag(λγ+1,...,λM) (7)
in the formula, λγ+1、λMRespectively represent ΛresDiagonal element of (2), and λ1≥…≥λγ≥λγ+1≥…λM。
3. The method for predicting the residual life of the chopper based on the principal component analysis and the bi-exponential model as claimed in claim 2, wherein T is2The curve test statistic is calculated according to the formula:
T2 j＝yj TPpcΛ-1PT pcyj(8)
wherein j is 1,22 jDenotes the jth T2Curve test statistic, yj TIs yjThe transposed matrix of (2).
4. The chopper residual life prediction method based on principal component analysis and the bi-exponential model as claimed in claim 3, wherein the expression of the bi-exponential model is as follows:
in the formula, at、bt、ctAnd dtAre all parameters and t represents the time.
5. The method for predicting the residual life of a chopper based on principal component analysis and bi-exponential model according to claim 4, characterized in that the method is based on T2Curve test statistic and dual index model identification of the parameter at、bt、ctAnd dt。
6. The chopper residual life prediction method based on principal component analysis and bi-exponential model according to claim 5, characterized in that the residual life is solved by the following formula:
RUL(tk)＝inf{r:f(r+tk)≥θ|f(tk)} (10)
wherein, RUL (t)k) Is at the tkThe remaining life of the chopper, f (r + t)k) Is the (r + t) thk) T of time chopper2Curve test statistic T2 jValue of f (t)k) Is at the tkT of time chopper2Curve test statistic T2 jθ is a preset specified threshold, wherein:
in formulae (11) and (12), atk,btk,ctk,dtkDenotes the t-thkThe parameters obtained at the moment.
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| US20100217568A1 (en) * | 2006-02-08 | 2010-08-26 | Nec Corporation | Variation simulation system, method for determining variations, apparatus for determining variations and program |
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