CN102279928A - Product performance degradation interval prediction method based on support vector machine and fuzzy information granulation - Google Patents

Abstract

The invention discloses a product performance degradation interval prediction method based on support vector machine (SVM) and fuzzy information granulation, comprising the following steps of: step 1, collecting product multi-parameter performance degradation data; step 2, analyzing principal components of the multi-parameter degradation data; step 3, executing fuzzy information granulation on the obtained principal component data; step 4, executing SVM modeling for the granulated data; step 5, executing interval prediction on product performance degradation trends. In the method, a fuzzy information granulation method and a SVM method are combined, the interval prediction method for the product performance degradation trends is presented for the first time, and the problem of prediction on the degradation trends of performance state and the changing space in the product running process is solved. The method solves the problem of evaluation and prediction under a condition that a plurality of output performance characteristic parameters of some products with complex structures concurrently degrade, based on the principal component analysis method.

Description

Properties of product degenerate interval Forecasting Methodology based on support vector machine and fuzzy message granulation

Technical field

The present invention relates to a kind of interval prediction method of the properties of product degradation trend based on support vector machine and fuzzy message granulation, belong to the forecasting technique in life span field.

Background technology

Along with the development of progress of science and technology and industrial requirement, all kinds of advanced products on the one hand constantly to complicated, at a high speed, efficient, miniature or large-scale direction develops, but faces harsh more work and running environment on the other hand.In case the critical component of product breaks down, just may influence whole process of production, cause the tremendous economic loss.Therefore, how to assess the running status of product, thereby can reasonably formulate maintenance plan, guarantee that equipment is in normal, stable operating mode, the incidents that is against any misfortune be the problem that current every profession and trade is paid close attention to the most and paid attention to.

Product will pass through a series of different performance degradation states usually from the normal condition to complete failure.The performance degradation of product is the influence that constantly is subjected to various environmental activity power because of it in the course of the work, deform, wear and tear, fatigue, corrosion, aging, loosening etc. and cause physics and chemical characteristic change, the function of product and the phenomenon that performance progressively reduces appear.It is impaired that performance degradation means that product has occurred, and will inevitably produce functional fault if develop as one pleases.The external manifestation of performance degradation is that the output performance characteristic parameter of product progressively departs from its normally interval, and this is because predetermined function and some output performance characteristic parameters of product are closely related.Therefore; if can be by product output performance characteristic parameter is carried out on-line monitoring; degree and trend that assessment and predicted are degenerated; and formulate maintenance plan as required; just can avoid the product catastrophic failure effectively; production loss and product maintenance expense that minimizing causes because of the product hang-up, thus enterprises production efficiency improved, reduce maintenance cost and security risk.Properties of product are degenerated and are assessed the technology that just is based on a kind of active maintenance pattern of above thought proposition with trend prediction, have important scientific theory meaning and engineering using value.

In recent years, as failure prediction and health control (Prognostic and Health Management, PHM) and intelligent maintenance system (Intelligent Maintenance System, IMS) core technology, properties of product are degenerated to assess with trend prediction technology and have been obtained a large amount of theory and practice research.The PHM technology is set about from seeking product bug and take place, develop really law of regularity, and analysis-by-synthesis product in use oneself state changes and the external environmental condition data of product experience, thus prediction and assess product serviceable life or residual life.This technology has been applied in fault detect, life prediction and the safety assessment of substantial equipment such as large aircraft, electromechanical equipment, road and bridge, Generator Set.Intelligent maintenance system is a kind of brand new concept, is proposed at first by U.S. intelligent maintenance system research centre director Jay professor Lee.The core concept of intelligent maintenance system is that (early prediction that comprises fault) predicted and assessed to the performance degradation process of equipment and product, and then realizes failure prediction.

The essence of properties of product degeneration assessment and trend prediction is the pattern-recognition to the product running status.No matter be the fault prediction with health control in the product residual life evaluation, still the properties of product in the intelligent maintenance are degenerated and are assessed and prediction, its essence all is by the analysis to product data, the current running status of identification product, and the state tendency predicted, so that reach and to take corresponding measure before the receive status in properties of product, avoid the generation of chance failure.Comprehensive present research, the method that is used for properties of product degeneration assessment and trend prediction mainly contains: ARMA time series models, neural network, Bayesian decision method, Logistic recurrence, hidden Markov (HMM) model method etc.But, many performance degradation forecast assessment algorithms also are in theoretical research stage, and effect also is not very desirable, exist such as not being suitable for small sample, crossing problems such as study, dimension disaster, local minimum, and this is first problem that prior art exists.

In actual engineering problem, some baroque product often has a plurality of output performance characteristic parameters to degenerate simultaneously, yet present research method is launched at the degraded data of single performance characteristic often, and this is second problem that state of the art exists.For assessing properties of product degenerate state and trend exactly, need effectively merge the degeneration of different performance characteristic parameter, thereby obtain more accurately the performance degradation assessment and predict the outcome.At present, the research of relevant product multiparameter performance degradation assessment also seldom.List of references [1] WANG Peng, COIT David.Reliability Prediction Based on Degradation Modeling for Systems with Multiple Degradation Measures//Proceedings of the 2004Reliability﹠amp; Maintainability Symposium (RAMS) .Los Angeles, CA, Wang﹠amp among the 2004:302-307; The situation that Coit degenerates simultaneously at a plurality of performance parameters in the same system has been studied the Reliability Calculation Model under a plurality of performance parameters independences and the correlation circumstance.If separate, the similar cascade system of solution; If be correlated with, then estimate the joint probability density function of a plurality of performance degradation parameters, estimate the fiduciary level of product then in view of the above.Under a lot of situations, be correlated with physically between a plurality of performance parameters of same product, and the result of mathematical computations may be independently that this method is not considered this point.In addition, joint probability density function is to determine by supposing in this method, may be quite different with actual conditions.

Degenerate assessment and trend prediction of properties of product lays particular emphasis on the trend of properties of product degenerate state overall process estimated and predicted, and is not limited to the accurately predicting of the performance state of certain time point.For enterprise, be very helpful if can understand the degradation trend of performance state in the product operational process and change the space.Therefore, the research of carrying out properties of product degenerate interval Forecasting Methodology just seems more meaningful.At present, still blank at home and abroad about the research of this respect, this is the 3rd problem that state of the art exists.

(Support Vector Machine SVM) is the machine learning method based on statistical theory that is proposed in nineteen ninety-five by people such as Vapnik to support vector machine, and its outstanding characteristics are to solve few sample learning problem preferably.In the small sample that solves, non-linear and higher-dimension pattern recognition problem, shown distinctive advantage.It is based upon on the VC dimension theory and structure risk minimum principle basis of Statistical Learning Theory, replace empiric risk to minimize with structural risk minimization, effectively avoided crossing the problem that exists in the conventional machines study such as study, dimension disaster, local minimum, under condition of small sample, still had good generalization ability.Support vector machine also utilizes kernel function to solve high problem of dimension dexterously, and its algorithm complex and sample dimension are irrelevant.

(Information Granulation, IG) this notion is proposed in 1979 by Fuzzy collection founder L. A.Zadeh the information granulation first.L. A.Zadeh thinks that human understanding and reasoning is to be made of three key concepts: granulation (Granulation), tissue (Organization) and cause and effect (Causation); granulation is that integral body is resolved into part; organizing then is that Synthesis Department is divided into integral body, and cause and effect is meant cause-effect relationship.At present, mainly contain three kinds of information granulation models both at home and abroad: based on the model of fuzzy set theory, based on the model of rough set theory, based on the model of quotient space theory.With fuzzy set time series is blured granulation, mainly can be divided into two steps: divide window and obfuscation.Divide window and be exactly the time series of will be given and be divided into one by one boy's row, as action pane one by one; Obfuscation then is that each window that the first step produces is carried out obfuscation, generates fuzzy set one by one, just obscure particle.These two kinds of broad sense patterns combine be exactly the fuzzy message granulation (Fuzzy Information Granulation, FIG).

Summary of the invention

The objective of the invention is to have proposed the stronger properties of product degradation trend interval prediction method of a kind of versatility based on support vector machine and fuzzy message granulation in order to overcome the problem that above-mentioned existing method exists.The present invention comprehensively adopts principal component analytical method, fuzzy message granulation method and support vector machine method; the product multiparameter performance degradation data that obtain by the on-line monitoring means are handled, thereby realized the performance degradation trend of product and the prediction in variation space.

The present invention is a kind of properties of product degradation trend interval prediction method based on support vector machine and fuzzy message granulation, comprises following step:

The collection of step 1, product multiparameter performance degradation data;

The principal component analysis (PCA) of step 2, multiparameter degraded data;

Step 3, the number of principal components that obtains is handled according to carrying out the fuzzy message granulation;

The support vector machine modeling of step 4, granulation data;

Step 5, the interval prediction of properties of product degradation trend.

The invention has the advantages that:

(1) the present invention has proposed the interval prediction method of properties of product degradation trend first with fuzzy message granulation method and support vector machine method combination, has solved the degradation trend of performance state in the product operational process and the problem of variation spatial prediction.

(2) the present invention adopts the method for principal component analysis (PCA) to solve some complex structure product a plurality of output performance characteristic parameters assessment and forecasting problem under the degenerate case takes place simultaneously.

(3) Forecasting Methodology of the present invention's proposition has been avoided present state of the art problem, the problem includes: be not suitable for problems such as small sample, study excessively, dimension disaster, local minimum.

Description of drawings

Fig. 1 is the process flow diagram of the method for the invention;

Fig. 2 is the subordinate function of triangular form obscure particle of the present invention;

Fig. 3 is original many performance parameters degraded data of embodiment of the invention microwave electron product G PZJ-2007;

Fig. 4 is the 1st major component of embodiment of the invention product multiparameter performance degradation data;

Fig. 5 is the fuzzy message granulation result of the 1st major component of the embodiment of the invention;

Fig. 6 is that the degenerate interval of embodiment of the invention particular product performance parameters major component predicts the outcome.

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention is directed to the product that a plurality of output performance characteristic parameters are degenerated simultaneously in the operational process, determine how to discern the current running status of product, and predict, thereby provide foundation for the product maintenance decision-making playing a performance degradation state tendency.Supposing that product has p performance parameter, is M time to the detection total degree of particular product performance parameters.The particular product performance parameters observed reading is respectively x ₁, x ₂..., x _M, x wherein _i=(x _I1, x _I2..., x _Ip) ', i=1,2 ..., M.Then the particular product performance parameters observation matrix is:

$X=\left[\begin{array}{c}{x}_1^{\′}\\ x_2^{\′}\\ .\\ .\\ .\\ x_M^{\′}\end{array}\right]=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1p}\\ x_{21}& x_{22}& ...& x_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{M1}& x_{M2}& ...& x_{\mathrm{Mp}}\end{array}\right]---\left(1\right)$

Wherein, x ' _i, i=1,2 ..., M represents x _iTransposition, x _Ij, i=1,2 ..., M, j=1,2 ..., p represents that j performance parameter of product carried out the i time detects the observed reading that obtains.

The present invention is a kind of properties of product degenerate interval Forecasting Methodology based on support vector machine and fuzzy message granulation, and method flow diagram comprises following step as shown in Figure 1:

The collection of step 1, product multiparameter performance degradation data;

By the mode of on-line monitoring, collect M detected value x of a product p performance parameter _Ij, i=1 wherein, 2 ..., M, j=1,2 ..., p.Utilize these observed readings to make up particular product performance parameters observation matrix X:

$X=\left[\begin{array}{c}{x}_1^{\′}\\ x_2^{\′}\\ .\\ .\\ .\\ x_M^{\′}\end{array}\right]=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1p}\\ x_{21}& x_{22}& ...& x_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{M1}& x_{M2}& ...& x_{\mathrm{Mp}}\end{array}\right]$

Step 2, determine the major component of multiparameter degraded data;

Adopt the sample correlation coefficient matrix

Determine major component, concrete steps are as follows:

(1) obtains the correlation matrix of particular product performance parameters observation matrix X

$S=\frac{1}{M-1}\underset{i-1}{\overset{M}{\mathrm{\Σ}}}(x_i-\stackrel{\‾}{x}){(x_i-\stackrel{\‾}{x})}^{\′}={\left(\frac{1}{M-1}\underset{i-1}{\overset{M}{\mathrm{\Σ}}}(x_{\mathrm{is}}-{\stackrel{\‾}{x}}_s)(x_{\mathrm{it}}-{\stackrel{\‾}{x}}_t)\right)}_{p\×p}={\left(s_{\mathrm{st}}\right)}_{p\×p},s,t=\mathrm{1,2},...,p$

(2)

$\hat{R}=\left(r_{\mathrm{st}}\right),r_{\mathrm{st}}=\frac{s_{\mathrm{st}}}{\sqrt{s_{\mathrm{ss}}}\sqrt{s_{\mathrm{tt}}}}=\frac{\frac{1}{M-1}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}(x_{\mathrm{is}}-{\stackrel{\‾}{x}}_s)(x_{\mathrm{it}}-{\stackrel{\‾}{x}}_t)}{\sqrt{\frac{1}{M-1}\underset{i-1}{\overset{M}{\mathrm{\Σ}}}{(x_{\mathrm{is}}-{\stackrel{\‾}{x}}_s)}^2}\sqrt{\frac{1}{M-1}\underset{i-1}{\overset{M}{\mathrm{\Σ}}}{(x_{\mathrm{it}}-{\stackrel{\‾}{x}}_t)}^2}},s,t=\mathrm{1,2},...,p$

In the formula, x _i=(x _I1, x _I2..., x _Ip) ', i=1,2 ..., M, S are the covariance matrix of sample X,

Be sample average, s _StThe s row of expression sample X and the covariance of t row, r _StThe s row of expression sample X and the related coefficient of t row, s _SsThe s row of expression sample X and the covariance of s row, s _TtThe t row of expression sample X and the covariance of t row.

(2) obtain correlation matrix

Eigenwert and proper vector;

Through type (3) obtains correlation matrix

P eigenvalue=(λ ₁, λ ₂..., λ _p) and corresponding proper vector a=(a ₁, a ₂..., a _p), λ wherein ₁〉=λ ₂〉=... λ _p〉=0.

$(\hat{R}-\mathrm{\λI})a=0---\left(3\right)$

Wherein, λ is

Eigenwert, a is corresponding proper vector, I is a unit matrix.

(3) determine major component;

Be the contribution rate of accumulative total of a preceding k major component, reflect how much information is k major component extracted from original variable.Select among the present invention contribution rate of accumulative total reach 90% k (k＜p) individual variable determines that as major component k the major component that obtains is:

y _i＝Xa _i，i＝1，2，...，k (4)

Step 3, the number of principal components that obtains is handled according to carrying out the fuzzy message granulation;

(described time series is the sequences y that k major component formed to adopt W. Pedrycz time series fuzzy message granulation method _i), at first to the 1st major component y ₁Carry out the fuzzy message granulation and handle, the specific implementation process is as follows:

(1) divides window;

Determine the big or small w of granulation window, with major component y ₁With w is that sub-row length is divided into [M/w] height row, is designated as Δ y _n, n=1,2 ..., [M/w, wherein [M/w] expression M/w round numbers forward.

(2) at a sub-row window delta y _nOn set up obscure particle A;

1) form of selection obscure particle A;

Obscure particle commonly used mainly contains following several citation form: triangular form, ladder type, Gaussian, parabolic type etc., the present invention adopts the triangular form obscure particle, its subordinate function as the formula (5), image is as shown in Figure 2.

$A(x,a,m,b)=\left\{\begin{array}{cc}0,& x<a\\ \frac{x-a}{m-a},& a\&le;x\&le;m\\ \frac{b-x}{b-m},& m<x\&le;b\\ 0,& x>b\end{array}\right.---\left(5\right)$

Wherein, b and a are respectively the upper and lower boundaries of support of obscure particle A; M is the nuclear of obscure particle A.

2) determine the nuclear of triangular form obscure particle A;

The nuclear of triangular form fuzzy number is a point, and it is designated as m, and the present invention gets the median of sub-column data collection of major component as the nuclear of obscure particle (fuzzy set) A.

3) set up the subordinate function of obscure particle A;

Determine the parameter of obscure particle A subordinate function by finding the solution the described optimization problem of formula (6);

$\mathrm{Maximize}{Q}_A=\frac{\underset{i=1}{\overset{w}{\mathrm{\&Sigma;}}}A\left(\mathrm{\&Delta;}{y}_{\mathrm{ni}}\right)}{\mathrm{measure}\left(\mathrm{supp}\left(A\right)\right)}=\frac{\underset{i=1}{\overset{w}{\mathrm{\&Sigma;}}}A\left(\mathrm{\&Delta;}{y}_{\mathrm{ni}}\right)}{b-a}---\left(6\right)$

Wherein, Q _ABe that Maximize represents maximization operation, Δ y according to a function about obscure particle A of W. Pedrycz fuzzy message granulation modelling _NiBe sub-row Δ y _nIn element, w represents sub-row Δ y _nLength, A (Δ y _Ni) expression Δ y _NiSubordinate function,

The degree of membership of expression obscure particle A and, the support of measure (supp (A)) expression obscure particle A is estimated, b and a are respectively the upper and lower boundaries of the support of obscure particle A.Because the nuclear m of obscure particle A determines that the present invention adopts the method for data traversing operation to seek two other parameter a and the b of A subordinate function.Determine three parameter m, a and b of subordinate function, then just on a sub-row window, set up triangular form obscure particle A.

(3) major component y ₁Fuzzy message granulation result

According to the method for on a sub-row window, setting up obscure particle, can be respectively at y ₁[M/w] height row window on set up corresponding triangular form obscure particle A _i, determine three parameter: a of its subordinate function _i, m _i, b _i, i=1,2 ..., [M/w].Therefore, by to major component y ₁Carry out the fuzzy message granulation, can obtain following granulation data result:

$\left\{\begin{array}{c}\mathrm{Low}={[a_1,a_2,...,a_{[M/w]}]}^{\&prime;}\\ R={[{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA0000077054610000012.png"\; state="\{\{state\}\}">m</figure-callout>}}_1,m_2,...,m_{[M/w]}]}^{\&prime;}\\ \mathrm{Up}={[{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA0000077054610000012.png"\; state="\{\{state\}\}">b</figure-callout>}}_1,b_2,...,b_{[M/w]}]}^{\&prime;}\end{array}\right.---\left(7\right)$

Wherein, that the Low parametric description is corresponding major component y ₁The minimum value that changes, the R parametric description be corresponding major component y ₁The average level of the cardinal principle that changes, the Up parametric description be corresponding major component y ₁The maximal value that changes.

Other number of principal components obtains the granulation data result of all major components at last according to handling in the same way.

Step 4, the granulation data are set up hold the vector machine regression model

In order to carry out the support vector machine modeling and forecasting better, earlier the granulation data are carried out phase space reconfiguration, excavate big as far as possible quantity of information to obtain the incidence relation between data, concrete grammar is:

To one group of data X _N={ x ₁, x ₂..., x _N, carry out phase space reconfiguration, be about to the time series X of one dimension _NBe converted into following matrix form:

In the formula, X _ReBe the dimension of the h after reconstruct matrix, Y _ReBe its corresponding one-dimensional vector, h is generally 3～10 for prediction embeds exponent number among the present invention.

Then, according to support vector machine regression modeling method, with X _ReBe the input matrix of support vector machine regression model, Y _ReBe the object vector (output) of support vector machine regression model, set up mapping f:R ^h→ R, supported vector machine regression model is:

Y _re＝f(X _re) (9)

Also can be write as

$x_i=f\left({\stackrel{\&RightArrow;}{x}}_i\right)=f\left(\right\{x_{i-h},x_{i-h+1},...,x_{i-2},x_{i-1}\left\}\right)---\left(10\right)$

In the formula, I=h+1, h+2 ..., N is the h dimension matrix X after the reconstruct _ReI-h capable, expression data X _NMiddle x _iThe set of the h of front point.The essence of support vector machine regression model is to utilize x _iThe value of h preceding point is predicted x _iValue.

Respectively granulation data Low, R, Up are carried out Space Reconstruction according to formula (8), it is h that prediction embeds exponent number.Then, set up the support vector machine regression model of granulation data Low, R, Up respectively according to formula (9) and (10).

Step 5, the interval prediction of properties of product degradation trend.

Utilize the support vector machine regression model of setting up (10) that following data are predicted, be specially:

For data X _NIn x _N+1Point, the value of h the point in its front is all known, then according to formula (10) can supported vector machine one-step prediction model be:

${\hat{x}}_{N+1}=f\left({\stackrel{\&RightArrow;}{x}}_{N+1}\right)=f\left(\right\{x_{N-h+1},x_{N-h+2},...,x_N\left\}\right)---\left(11\right)$

In the formula,

The predicted value of N+1 point of expression raw data, Representing matrix X _ReN-h+1 capable, X just _NIn x _N+1The set of front h point of point.

Utilize

But structural matrix X _ReN-h+2 capable, promptly Promptly can obtain X with its input as the support vector machine regression model _NIn N+2 the point predicted value.By that analogy, can obtain l step SVM prediction model is

${\hat{x}}_{N+l}=f\left({\stackrel{\&RightArrow;}{x}}_{N+l}\right)=f\left(\right\{x_{N-h+l},x_{N-h+l+1},...,x_N,{\hat{x}}_{N+1},...,{\hat{x}}_{N+l}\left\}\right)---\left(12\right)$

In the formula,

Expression data X _NThe predicted value of N+l point,

Representing matrix X _ReN-h+l capable.

According to the l step SVM prediction model of formula (12), granulation data Low, R, the Up to each major component sets up l step SVM prediction model respectively, and carries out the recursion prediction, obtains the variation tendency of k major component and changes the space.Wherein, what the predicted value of Low was described is the following lower bound that changes of major component, and what the predicted value of R was described is the following cardinal principle average level that changes of major component, and what the predicted value of Up was described is the following upper bound that changes of major component.The present invention obtains the prediction of performance degenerate state in the product operational process at last by above-mentioned steps, thereby provides foundation for product maintenance.

Embodiment 1:

With certain microwave electron product G PZJ-2007 is example, and the properties of product degenerate interval Forecasting Methodology based on support vector machine and fuzzy message granulation that adopts the present invention to propose predicts that to its performance state degradation trend and variation space applying step and method are as follows:

The collection of step 1, product multiparameter performance degradation data.By the mode of on-line monitoring,, collect altogether and obtain 9 * 200 performance parameter estimator data, as shown in Figure 3 detecting once 9 performance parameters every days of certain microwave electron product G PZJ-2007.

Step 2, determine the major component of multiparameter degraded data.Obtain by above-mentioned steps two, the contribution rate of accumulative total of the 1st major component reaches more than 90%, therefore only selects 1 variable as major component, and the major component of selection as shown in Figure 4.

The fuzzy message granulation of step 3, major component.Adopt W.Pedrycz time series fuzzy message granulation method, the 1st major component handled.The granulation window size of determining is 3, major component is divided into 66 sub-row windows with 3 for sub-row length, and has set up corresponding obscure particle on each height row window.The fuzzy message granulation result of the 1st major component as shown in Figure 5; wherein; the Low parametric description be the minimum value that corresponding major component changes, the R parametric description be the average level of the cardinal principle that changes of corresponding major component, the Up parametric description be the maximal value that corresponding major component changes.

The support vector machine regression modeling of step 4, granulation data.Respectively granulation data Low, R, Up are carried out phase space reconfiguration according to formula (8), with corresponding X after the reconstruct _ReAs input matrix, Y _ReAs object vector, set up corresponding support vector machine regression model.

Step 5, the interval prediction of properties of product degradation trend.Utilize the l step SVM prediction model of setting up, respectively granulation data Low, R, Up are set up 160 step SVM prediction forecast models, and carry out the recursion prediction, can obtain chief composition series y ₁Variation tendency and change the space, as shown in Figure 6.Wherein, what the predicted value of Low was described is the following lower bound that changes of major component, and what the predicted value of R was described is the following cardinal principle average level that changes of major component, and what the predicted value of Up was described is the following upper bound that changes of major component.Can be seen that by Fig. 6 predicting the outcome conforms to properties of product virtual condition (actual value corresponding curve), therefore, the method that the present invention proposes is accurately feasible.

Claims (3)

1. the properties of product degenerate interval Forecasting Methodology based on support vector machine and fuzzy message granulation is characterized in that, comprises following step:

The collection of step 1, product multiparameter performance degradation data;

Collect the observed reading x of M detection of p performance parameter of product _Ij, i=1 wherein, 2 ..., M, j=1,2 ..., p makes up particular product performance parameters observation matrix X:

$X=\left[\begin{array}{c}{x}_1^{\&prime;}\\ x_2^{\&prime;}\\ .\\ .\\ .\\ x_M^{\&prime;}\end{array}\right]=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1p}\\ x_{21}& x_{22}& ...& x_{2p}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ x_{M1}& x_{M2}& ...& x_{\mathrm{Mp}}\end{array}\right]---\left(1\right)$

Wherein, x _IjExpression is carried out the i time to j performance parameter of product and is detected the observed reading that obtains, i=1, and 2 ..., M, j=1,2 ..., p;

Step 2, determine the major component of multiparameter degraded data;

Adopt the sample correlation coefficient matrix

Determine major component, concrete steps are as follows:

(1) obtains the correlation matrix of particular product performance parameters observation matrix X

$S=\frac{1}{M-1}\underset{i-1}{\overset{M}{\mathrm{\&Sigma;}}}(x_i-\stackrel{\&OverBar;}{x}){(x_i-\stackrel{\&OverBar;}{x})}^{\&prime;}={\left(\frac{1}{M-1}\underset{i-1}{\overset{M}{\mathrm{\&Sigma;}}}(x_{\mathrm{is}}-{\stackrel{\&OverBar;}{x}}_s)(x_{\mathrm{it}}-{\stackrel{\&OverBar;}{x}}_t)\right)}_{p\&times;p}={\left(s_{\mathrm{st}}\right)}_{p\&times;p},s,t=\mathrm{1,2},...,p$

(2)

$\hat{R}=\left(r_{\mathrm{st}}\right),r_{\mathrm{st}}=\frac{s_{\mathrm{st}}}{\sqrt{s_{\mathrm{ss}}}\sqrt{s_{\mathrm{tt}}}}=\frac{\frac{1}{M-1}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}(x_{\mathrm{is}}-{\stackrel{\&OverBar;}{x}}_s)(x_{\mathrm{it}}-{\stackrel{\&OverBar;}{x}}_t)}{\sqrt{\frac{1}{M-1}\underset{i-1}{\overset{M}{\mathrm{\&Sigma;}}}{(x_{\mathrm{is}}-{\stackrel{\&OverBar;}{x}}_s)}^2}\sqrt{\frac{1}{M-1}\underset{i-1}{\overset{M}{\mathrm{\&Sigma;}}}{(x_{\mathrm{it}}-{\stackrel{\&OverBar;}{x}}_t)}^2}},s,t=\mathrm{1,2},...,p$

In the formula, x _i=(x _I1, x _I2..., x _Ip) ', i=1,2 ..., M, S are the covariance matrix of sample X,

Be sample average, s _StThe s row of expression sample X and the covariance of t row, r _StThe s row of expression sample X and the related coefficient of t row, s _SsThe s row of expression sample X and the covariance of s row, s _TtThe t row of expression sample X and the covariance of t row;

(2) obtain correlation matrix Eigenwert and proper vector;

Through type (3) obtains correlation matrix

P eigenvalue=(λ ₁, λ ₂..., λ _p) and corresponding proper vector a=(a ₁, a ₂..., a _p), λ wherein ₁〉=λ ₂〉=... 〉=λ _p〉=0;

$(\hat{R}-\mathrm{\&lambda;I})a=0---\left(3\right)$

Wherein, λ is

Eigenwert, a is corresponding proper vector, I is a unit matrix;

(3) determine major component;

The contribution rate of accumulative total of a current k major component

Then k variable is major component, and k＜p determines that k the major component that obtains is:

y _i＝Xa _i，i＝1，2，...，k (4)

Step 3, the number of principal components that obtains is handled according to carrying out the fuzzy message granulation;

At first to the 1st major component y ₁Carry out the fuzzy message granulation and handle, the specific implementation process is as follows:

(1) divides window;

Determine the big or small w of granulation window, with major component y ₁With w is that sub-row length is divided into [M/w] height row, is designated as Δ y _n, n=1,2 ..., [M/w, wherein [M/w] expression M/w round numbers forward;

(2) at a sub-row window delta y _nOn set up obscure particle A;

1) form of selection obscure particle A;

Adopt the triangular form obscure particle, its subordinate function is specially as the formula (5):

$A(x,a,m,b)=\left\{\begin{array}{cc}0,& x<a\\ \frac{x-a}{m-a},& a\&le;x\&le;m\\ \frac{b-x}{b-m},& m<x\&le;b\\ 0,& x>b\end{array}\right.---\left(5\right)$

Wherein, b and a are respectively the upper and lower boundaries of support of obscure particle A; M is the nuclear of obscure particle A;

2) determine the nuclear of triangular form obscure particle A;

The median of sub-column data collection of getting major component is as the nuclear of obscure particle A;

3) set up the subordinate function of obscure particle A;

Determine the parameter of obscure particle A subordinate function by finding the solution the described optimization problem of formula (6);

$\mathrm{Maximize}{Q}_A=\frac{\underset{i=1}{\overset{w}{\mathrm{\&Sigma;}}}A\left(\mathrm{\&Delta;}{y}_{\mathrm{ni}}\right)}{\mathrm{measure}\left(\mathrm{supp}\left(A\right)\right)}=\frac{\underset{i=1}{\overset{w}{\mathrm{\&Sigma;}}}A\left(\mathrm{\&Delta;}{y}_{\mathrm{ni}}\right)}{b-a}---\left(6\right)$

Wherein, Maximize represents maximization operation, Δ y _NiBe sub-row Δ y _nIn element, w represents sub-row Δ y _nLength, A (Δ y _Ni) expression Δ y _NiSubordinate function,

The degree of membership of expression obscure particle A and, the support of measure (supp (A)) expression obscure particle A is estimated, b and a are respectively the upper and lower boundaries of the support of obscure particle A; The nuclear m of obscure particle A determines that the method for employing data traversing operation is determined two other parameter a and the b of A subordinate function; Determine three parameter m, a and b of subordinate function, just on a sub-row window, set up triangular form obscure particle A;

(3) major component y ₁Fuzzy message granulation result;

According to step (2), respectively at y ₁[M/w] height row window on set up corresponding triangular form obscure particle A _i, determine three parameter: a of its subordinate function _i, m _i, b _i, i=1,2 ..., [M/w]; Therefore, by to major component y ₁Carry out the fuzzy message granulation, can obtain following granulation data result:

$\left\{\begin{array}{c}\mathrm{Low}=[a_1,a_2,...,a_{[M/w]}]\\ R=[m_1,m_2,...,m_{[M/w]}]\\ \mathrm{Up}=[b_1,b_2,...,b_{[M/w]}]\end{array}\right.---\left(7\right)$

Wherein, that the Low parametric description is corresponding major component y ₁The minimum value that changes, the R parametric description be corresponding major component y ₁The average level of the cardinal principle that changes, the Up parametric description be corresponding major component y ₁The maximal value that changes;

Other number of principal components obtains the granulation data result of all major components at last according to handling in the same way;

Step 4, the granulation data are set up hold the vector machine regression model;

The granulation data are carried out phase space reconfiguration, and concrete grammar is:

To one group of data X _N={ x ₁, x ₂..., x _N, carry out phase space reconfiguration, be about to the time series X of one dimension _NBe converted into following matrix form:

In the formula, X _ReBe the dimension of the h after reconstruct matrix, Y _ReBe its corresponding one-dimensional vector, h embeds exponent number for prediction;

Then, according to support vector machine regression modeling method, with X _ReBe the input matrix of support vector machine regression model, Y _ReBe the object vector of support vector machine regression model, set up mapping f:R ^h→ R, supported vector machine regression model is:

Y _re＝f(X _re) (9)

Promptly

In the formula, I=h+1, h+2 ..., N is the h dimension matrix X after the reconstruct _ReI-h capable, expression data X _NMiddle x _iThe set of the h of front point;

Respectively granulation data Low, R, Up are carried out Space Reconstruction according to formula (8), it is h that prediction embeds exponent number; Then, set up the support vector machine regression model of granulation data Low, R, Up respectively according to formula (9) and (10);

Step 5, the interval prediction of properties of product degradation trend;

Be specially:

For data X _NIn x _N+1Point, the value of h the point in its front is all known, then according to the supported vector machine one-step prediction of formula (10) model is:

${\hat{x}}_{N+1}=f\left({\stackrel{\&RightArrow;}{x}}_{N+1}\right)=f\left(\right\{x_{N-h+1},x_{N-h+2},...,x_N\left\}\right)---\left(11\right)$

In the formula,

The predicted value of N+1 point of expression raw data,

Representing matrix X _ReN-h+1 capable, X just _NIn x _N+1The set of front h point of point;

Utilize

Structural matrix X _ReN-h+2 capable, promptly

Promptly can obtain X with its input as the support vector machine regression model _NIn N+2 the point predicted value; By that analogy, obtaining l step SVM prediction model is

${\hat{x}}_{N+l}=f\left({\stackrel{\&RightArrow;}{x}}_{N+l}\right)=f\left(\right\{x_{N-h+l},x_{N-h+l+1},...,x_N,{\hat{x}}_{N+1},...,{\hat{x}}_{N+l}\left\}\right)---\left(12\right)$

In the formula,

Expression data X _NThe predicted value of N+l point,

Representing matrix X _ReN-h+l capable;

According to the l step SVM prediction model of formula (12), granulation data Low, R, the Up to each major component sets up l step SVM prediction model respectively, and carries out the recursion prediction, obtains the variation tendency of k major component and changes the space; Wherein, what the predicted value of Low was described is the following lower bound that changes of major component, and what the predicted value of R was described is the following cardinal principle average level that changes of major component, and what the predicted value of Up was described is the following upper bound that changes of major component; The present invention obtains the prediction of performance degenerate state in the product operational process at last by above-mentioned steps.

2. a kind of properties of product degenerate interval Forecasting Methodology based on support vector machine and fuzzy message granulation according to claim 1 is characterized in that, in the step 1, collects the observed reading xij of M detection of a product p performance parameter by the mode of on-line monitoring.

3. a kind of properties of product degenerate interval Forecasting Methodology according to claim 1 based on support vector machine and fuzzy message granulation; it is characterized in that; in the step 3, adopt W.Pedrycz time series fuzzy message granulation method, main composition is carried out the fuzzy message granulation handle.

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