CN106228026A - A kind of predicting residual useful life algorithm based on optimum degenerative character amount - Google Patents

Abstract

The invention discloses a kind of predicting residual useful life algorithm based on optimum degenerative character amount, including the extraction of equipment optimum degenerative character amount with set up the Weiner process predicting residual useful life model of band stochastic effect, compared with prior art, the problem that the present invention overcomes artificial subjective selection degenerative character amount, break away from single degenerative character amount and can not characterize the adverse effect of equipment state comprehensively, and the combination genetic programming algorithm proposed in the present invention and the Weiner process model pluses and minuses of band stochastic effect, select optimal predicted time first, set up predicting residual useful life algorithm based on optimum degenerative character amount, in simulation result, can be seen that this algorithm improves in prediction accuracy really.

Description

A kind of predicting residual useful life algorithm based on optimum degenerative character amount

Technical field

The present invention relates to a kind of combination genetic programming algorithm and the predicting residual useful life algorithm of random Weiner process, especially Relate to a kind of predicting residual useful life algorithm based on optimum degenerative character amount.

Background technology

Existing predicting residual useful life technology, is obtained by the key characterization parameter during monitoring device performance degradation and moves back Change data, and then utilize degraded data pre-measurement equipment residual life, determine equipment Maintenance Policy.But Study on residual life at present Work is essentially all artificial subjective selection degenerative character amount.In order to effectively solve this problem, in recent years, L.X.Liao proposes Use the method that genetic programming builds optimum degenerative character amount, and use paris equation simulation bearing expansion process, but the party Method is using genetic programming to extract optimal characteristics amount, does not considers predicted time first, builds from normal data to fail data There is the problem that data volume is the biggest in excellent degenerative character amount, their quantity is the most, and the scope of algorithm search will be the biggest, after expansion Hunting zone code can be caused to expand and affect search efficiency, optimal solution can be made undesirable.It addition, use paris equation Simulation bearing expansion process there is also problem, marble and morton carries out series of experiment research with regard to bearing fragmentation extension, he Point out that the process that fragmentation is formed is the result germinated by multiple crackles and assemble, rather than single lead crack extension process, Therefore, traditional paris formula is not particularly suited for bearing.

Summary of the invention

The purpose of the present invention is that provides a kind of residue based on optimum degenerative character amount to solve the problems referred to above Biometry algorithm.

For the problem of the most artificial subjective selection degenerative character amount, and the degenerative character amount chosen is all single degeneration Index, single degeneration index comprises the Limited information that equipment is degenerated, it is impossible to reflect the life-cycle operation characteristic of equipment all sidedly, because of This, the present invention is considered as genetic programming algorithm and extracts the optimum degenerative character amount in sign equipment degenerative process, uses comprehensive The optimum degenerative character amount of multiple degenerative character amounts comprehensively portrays running status and the degradation trend of equipment, specifically, originally Invent using the dimensionless index in time domain, determine the time that equipment initial failure occurs, first predicted time FPT, profit Data construct optimum degenerative character amount after occurring by equipment initial failure, will be incorporated into genetic programming algorithm by predicted time first In, data volume can be dramatically reduced, it is easy to construct the degenerative character amount of optimum.Extracting optimum degenerative character amount On the basis of, the present invention intends building equipment predicting residual useful life model based on optimum degenerative character amount, design a kind of based on Bayesian updates the method for parameter estimation with expectation-maximization algorithm, finally realizes the residual life Accurate Prediction to equipment.

The present invention is achieved through the following technical solutions above-mentioned purpose:

The present invention comprises the following steps:

(1) extraction of equipment optimum degenerative character amount: use waveform index, pulse index, margin index, kurtosis index and Peak index, these 5 dimensionless indexs, and root value, meansigma methods, root-mean-square value, peak value, these 4 have dimension index conduct Full stop collection, uses and adds, subtracts, multiplication and division, seeks absolute value, opens radical sign as operator collection, by generating initial population, carries out Duplication between body, intersect and the operation such as variation, using monotonicity effect as judging the criterion of individual good and bad degree, constantly to kind Group evolves, and finally under algorithm stop criterion, obtains optimum degenerative character amount；

(2) the Weiner process predicting residual useful life model of band stochastic effect is set up: extracting optimum degenerative character amount On the basis of, build predicting residual useful life model based on optimum degenerative character amount, plan to build the band stochastic effect that is based on The degradation model of Wiener process prescription, it was predicted that the residual life of rotating machinery, in terms of model parameter estimation, will use based on Bayesian method cooperates down with expectation-maximization algorithm and carries out model parameter estimation, is predicted mould by Bayesian method The renewal of type random parameter Posterior distrbutionp, utilizes EM algorithm to carry out model parameter estimation, makes full use of monitoring information and carries out equipment Residual life estimate.

The beneficial effects of the present invention is:

The present invention is a kind of predicting residual useful life algorithm based on optimum degenerative character amount, compared with prior art, and this The bright problem overcoming artificial subjective selection degenerative character amount, breaks away from single degenerative character amount can not characterize equipment state not comprehensively Profit impact, and the combination genetic programming algorithm proposed in the present invention and the Weiner process model pluses and minuses of band stochastic effect, choosing Select optimal predicted time first, set up predicting residual useful life algorithm based on optimum degenerative character amount, in simulation result, can To find out that this algorithm improves in prediction accuracy really.

Accompanying drawing explanation

Fig. 1 is the vibrational waveform figure under normal condition；

Fig. 2 is the vibrational waveform figure under failure state；

Fig. 3 is root value curve chart；

Fig. 4 is Mean curve figure；

Fig. 5 is waveform index curve chart；

Fig. 6 is kurtosis index curve chart；

Fig. 7 is optimum degenerative character discharge curve figure；

Fig. 8 is the optimum degenerative character amount degradation trend curve chart of eight groups of equipment；

Fig. 9 is parameter estimation curve chart；In figure: (a) μ_β,(b)σ_β, and (c) σ；

Figure 10 is the mean degradation track comparison diagram that different model is estimated.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings:

The present invention comprises the following steps:

(1) extraction of equipment optimum degenerative character amount: use waveform index, pulse index, margin index, kurtosis index and Peak index, these 5 dimensionless indexs, and root value, meansigma methods, root-mean-square value, peak value, these 4 have dimension index conduct Full stop collection, uses and adds, subtracts, multiplication and division, seeks absolute value, opens radical sign as operator collection, by generating initial population, carries out Duplication between body, intersect and the operation such as variation, using monotonicity effect as judging the criterion of individual good and bad degree, constantly to kind Group evolves, and finally under algorithm stop criterion, obtains optimum degenerative character amount；Owing to single degenerative character amount comprises Information is less, it is impossible to reflection equipment state general characteristic all sidedly, and predicting residual useful life model uses optimum degenerative character amount, The adverse effect of single degenerative character amount can be broken away from, it is thus achieved that predict the outcome more accurately.And genetic programming is as a kind of intelligence Problem solver optimized algorithm, have in terms of Characteristic Extraction and have great advantage, by initial parameter is reconfigured Optimize, form new complex parameter；

(2) the Weiner process predicting residual useful life model of band stochastic effect is set up: extracting optimum degenerative character amount On the basis of, build predicting residual useful life model based on optimum degenerative character amount, plan to build the band stochastic effect that is based on The degradation model of Wiener process prescription, it was predicted that the residual life of rotating machinery, in terms of model parameter estimation, will use based on Bayesian method cooperates down with expectation-maximization algorithm and carries out model parameter estimation, is predicted mould by Bayesian method The renewal of type random parameter Posterior distrbutionp, utilizes EM algorithm to carry out model parameter estimation, makes full use of monitoring information and carries out equipment Residual life estimate.

With rotating machinery as experimental subject, this rotating machinery is made up of motor, axle and bearing.Use acceleration transducer Gathering unit vibration signal, sample frequency is 1 KHz, and each sample packages contains 4096 data, the rotating speed of equipment is 1800 turns/ Minute, the failure threshold of equipment determines according to ISO2372 and ISO10816, and we record the out-of-service time that equipment is each (being shown in Table 1).

Table 1. out-of-service time

Time domain vibrational waveform under No. 1 rotating machinery time domain vibrational waveform in normal state and failure state is (see figure 1)。

By the analysis to vibration waveform signal, can calculate five dimensionless indexs (waveform index, pulse index, Margin index, kurtosis index, peak index) and four have dimension index (root value, meansigma methods, root-mean-square value, peak value).At this In nine kinds of indexs, the index with optimal monotonicity is root value (see Fig. 3), but it have been found that in this index of incipient stage bent Line presents the most stable variation tendency, but, present larger fluctuation change at after-stage curve.The monotonicity effect of mean value specification Worst (see Fig. 4), in whole life cycle, only only has flashy fluctuation before occurring losing efficacy.

(1) determination of predicted time FPT first

The determination result of predicted time FPT is shown in Fig. 5-6 first.Waveform index and the early stage event to equipment bearing of the kurtosis index Hindering very sensitive, by the two dimensionless index, we can determine whether predicted time FPT first, namely equipment bearing occurs The time of initial failure, equipment is divided into two stages from normal operating condition to failure state by predicted time FPT first.? First before predicted time, waveform index and kurtosis desired value are very steady, but after predicted time first, their value has individual prominent Right increase.Therefore, predicted time FPT=630h first as the initial time of predicting residual useful life, is predicted by first Degraded data after time FPT=630h is using as the input data building optimum degenerative character amount.

(2) structure of optimum degenerative character amount

Genetic programming build in predicting residual useful life optimum degenerative character amount to implement step as follows:

1) experimental data is obtained.Unit is fully obtained from normal condition to inefficacy by rotating machinery and vibration measuring system The experimental data of state, often group packet has dimension desired value containing five kinds of dimensionless index values and four kinds.

2) determine genetic programming basic parameter, be shown in Table 2.Five kinds of dimensionless index values that what full stop collection led to selection is and four kinds Have dimension desired value, collection of functions selected add, subtract, the basic mathematical computing such as multiplication and division, logarithm is as collection of functions.

Table 2. basic parameter

3) m initial individuals of stochastic generation, initial individuals N represents, N represents degenerative character amount, N=f (W, L, I, T, K, R, M, P, S), i.e. degenerative character amount is about waveform index, peak index, pulse index, margin index, kurtosis index, mean square Root, meansigma methods, peak value, the function of root amplitude.

4) using the data after the 630h of predicted time first of each index as the input data of degenerative character amount, degenerate special The monotonicity quality of the degenerated curve of the amount of levying is as weighing individual quality.The present invention designs fitness function

$fitness=\left|\frac{\#ofd/dN>0}{n-1}-\frac{\#ofd/dN<0}{n-1}\right|$

In formula, n represents the quantity of observation, and N represents degenerative character amount, and d/dN represents N derivation.Fitness function value is more Greatly, represent degenerative character amount monotonicity the best.

5) according to genetic parameter, produce new individual by operations described below:

1) replicate.Application tournament selection method, randomly chooses 5 individualities (championship scale) from the i-th generation colony and enters Row fitness size compares, and by individual inheritance the highest for wherein fitness to of future generation, repeats said process M time, so that it may obtain I+1 is individual in colony M.

2) intersect.Whether choose with certain probability (crossover probability) to carry out intersecting and operate, the operation that intersects is so to enter Row: randomly choosing one " father " and " mother " from the i-th generation individual, two cross points are individual " father " and " mother " respectively Body randomly selects, is interchangeable from two node subtrees below, generate two offspring individuals.

3) variation.Choosing whether carry out mutation operation with certain probability (mutation probability), mutation operation is so to enter Row: from the i-th generation colony, select a single parent at random, delete the subtree that this single parent is individual, this subtree is random choosing Fixed, replace with another new subtree, this new subtree also randomly generates, and produces method and the product of new subtree The method of raw 0th generation individuality is identical.

6) repeatedly (3), (4) and (5) are performed, until it reaches algorithm runs abort criterion.

By the operation to genetic programming algorithm, one optimum degenerative character amount of final acquisition is as follows:

$N=ln(T-e^S)+(\frac{W}{P}+R*\sqrt{T})/S$

The degenerated curve (see Fig. 7) as shown below of optimum degenerative character amount.

(3) predicting residual useful life based on optimum degenerative character amount

First, utilize the Wiener process of band stochastic effect to portray the performance degradation process of product, drift parameter is regarded For the stochastic variable of Normal Distribution, use a kind of method for parameter estimation based on EM algorithm, efficiently obtained model ginseng The maximum likelihood estimator of number.

Wiener degenerative process model with stochastic effect

X (t)=β t+ σ B (t) (1)

β represents that drift parameter, obedience average are μ_βAnd variance isNormal distribution, characterize the impact of random factor.B (t) be one for the standard Brownian motion process characterizing degenerative process randomness, σ represents diffusion parameter, features and manufactured The random factor impacts on properties of product such as discordance, measurement error and external interfering noise in journey.Therefore, carried and being moved back Change and model needs the parameter estimated include μ_β,σ 2, for convenience described below, we are by a vector form here Represent the parameter of model

Equipment residual life T is defined as T=inf{t | X (t) >=η } and, when Degradation path X (t) reaches predefined first During threshold value η, equipment is just considered end-of-life.The probability density function PDF of equipment and being desired for of life-span T

$f_T\left(t\right)=\frac{\mathrm{\&eta;}}{\sqrt{2{\mathrm{\&pi;t}}^3({\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2}t+{\mathrm{\&sigma;}}^2)}}\&times;\exp (-\frac{{(\mathrm{\&eta;}-{\mathrm{\&mu;}}_{\mathrm{\&beta;}}t)}^2}{2t({\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2}t+{\mathrm{\&sigma;}}^2)})$ $\left(8\right)$

$E\left(T\right)=E\left(E\right(T|\mathrm{\&beta;}\left)\right)=E\left(\frac{\mathrm{\&eta;}}{\mathrm{\&beta;}}\right)=\frac{\mathrm{\&eta;}}{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^2}\exp (-\frac{{\mathrm{\&mu;}}_{\mathrm{\&beta;}}^2}{2{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^2}){\&Integral;}_0^{{\mathrm{\&mu;}}_{\mathrm{\&beta;}}}\exp (\frac{x^2}{2{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^2}x=\frac{\sqrt{2}\mathrm{\&eta;}}{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}}D(\frac{{\mathrm{\&mu;}}_{\mathrm{\&beta;}}}{\sqrt{2}{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}})---\left(9\right)$

WhereinRepresent the Dawson integration about real number z.

OrderRepresent unknown-model parameter, calculate unknown parameter below with EM algorithmMaximal possibility estimation.Assume have n sample to participate in degradation experiment, for the degeneration number that i-th is individual According to Y_i, at t₁,…,t_mShi Keyou degeneration observed quantity y_i1,…,y_im.Order

Y=(Y₁,...,Y_n)ˊ

Y_i=(y_i0,...,y_im)ˊ

Δy_ij=y_ij-y_i,j-1Represent that i-th is individual from moment t_j-1To moment t_jDegeneration increment.Δt_j=t_j-t_j-1Table Show time interval.

Method based on Maximum-likelihood estimation, makes Ω=(β₁,...,β_n), wherein β_iRepresent the drift individual corresponding to i-th Shifting parameter.At given β_iAnd Y_iUnder conditions of, the degenerative conditions joint density function of i-th individuality is:

$f\left(Y_i\right|\mathrm{\&Theta;},{\mathrm{\&beta;}}_i)=\frac{1}{{\&Pi;}_{j=1}^m\sqrt{2{\mathrm{\&pi;\&sigma;}}^2{\mathrm{\&Delta;t}}_j}}\&times;\exp (-\underset{j=1}{\overset{m}{\&Sigma;}}\frac{{({\mathrm{\&Delta;y}}_{ij}-{\mathrm{\&beta;}}_i{\mathrm{\&Delta;t}}_j)}^2}{2{\mathrm{\&sigma;}}^2{\mathrm{\&Delta;t}}_j})$

So its log-likelihood function is

$\begin{array}{c}l\left(\mathrm{\&Theta;}\right|Y,\mathrm{\&Omega;})=\underset{i=1}{\overset{n}{\&Sigma;}}\&lsqb;\ln p\left(Y_i\right|{\mathrm{\&beta;}}_i,\mathrm{\&Theta;})+\ln p\left({\mathrm{\&beta;}}_i\right|\mathrm{\&Theta;})\&rsqb;\\ =-\frac{1}{2}\underset{i=1}{\overset{n}{\&Sigma;}}\&lsqb;(m+1)\ln 2\mathrm{\&pi;}+\underset{j=1}{\overset{m}{\&Sigma;}}{\mathrm{ln\&Delta;t}}_j+m{\mathrm{ln\&sigma;}}^2+\underset{j=1}{\overset{m}{\&Sigma;}}\frac{{({\mathrm{\&Delta;y}}_{ij}-{\mathrm{\&beta;}}_i{\mathrm{\&Delta;t}}_j)}^2}{{\mathrm{\&sigma;}}^2{\mathrm{\&Delta;t}}_j}+{\mathrm{ln\&sigma;}}_{\mathrm{\&beta;}}^2+\frac{{({\mathrm{\&beta;}}_i-{\mathrm{\&mu;}}_{\mathrm{\&beta;}})}^2}{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^2}\&rsqb;\end{array}$

Owing to Ω is unobservable, the immediate constraint optimization of above-mentioned log-likelihood function calculates and is difficulty with, generally A solution cannot be converged to.Therefore, EM algorithm is used to process this problem.EM algorithm is generally passed through anti-by two basic steps Multiple iteration completes.First, this algorithm calculates the expectation of log-likelihood function, commonly referred to E-step about hidden variable；Then, Log-likelihood function after asking expectation is maximized, commonly referred to M-step.Above-mentioned two step passes through iterative repetition Carry out, until reaching the convergence criterion specified.

AssumeRepresent in the i-th step based on the degraded data Y estimation to unknown-model parameter Value.As previously mentioned, it is assumed that drift parameter β_iIt is μ for obeying average_βAnd variance isNormal distribution.Therefore, at known Y_iAnd Θ Under conditions of (k), β_iPosterior estimator still Normal Distribution, make its average beAnd varianceAt Bayesian frame Under frame, β_iPosterior distrbutionp can be easy to be updated by Bayesian formula, as follows

$\begin{array}{c}p\left({\mathrm{\&beta;}}_i\right|Y_i,{\mathrm{\&Theta;}}^k)\&Proportional;p\left(Y_i\right|{\mathrm{\&beta;}}_i,{\mathrm{\&Theta;}}^k)p\left({\mathrm{\&beta;}}_i\right|{\mathrm{\&Theta;}}^k)\\ \&Proportional;\&lsqb;-\underset{j=1}{\overset{m}{\&Sigma;}}\frac{{({\mathrm{\&Delta;y}}_{ij}-{\mathrm{\&beta;}}_i{\mathrm{\&Delta;t}}_j)}^2}{2{\mathrm{\&sigma;}}^{2\left(k\right)}{\mathrm{\&Delta;t}}_j}\&rsqb;\exp \&lsqb;-\frac{{({\mathrm{\&beta;}}_i-{\mathrm{\&mu;}}_{\mathrm{\&beta;}}^{\left(k\right)})}^2}{2{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}}\&rsqb;\\ \&Proportional;\exp \{-\frac{1}{2}\&lsqb;\underset{j=1}{\overset{m}{\&Sigma;}}\frac{{\mathrm{\&beta;}}_i^2{\mathrm{\&Delta;t}}_j}{{\mathrm{\&sigma;}}^{2\left(k\right)}}-\underset{j=1}{\overset{m}{\&Sigma;}}\frac{2{\mathrm{\&beta;}}_i{\mathrm{\&Delta;y}}_{ij}}{{\mathrm{\&sigma;}}^{2\left(k\right)}}+\frac{{\mathrm{\&beta;}}_i^2-2{\mathrm{\&beta;}}_i{\mathrm{\&mu;}}_{\mathrm{\&beta;}}^{\left(k\right)}+{\left({\mathrm{\&mu;}}_{\mathrm{\&beta;}}^{\left(k\right)}\right)}^2}{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}}\&rsqb;\}\\ \&Proportional;\exp \{-\frac{1}{2}\&lsqb;(\frac{t_m}{{\mathrm{\&sigma;}}^{2\left(k\right)}}-\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}}){\mathrm{\&beta;}}_i^2-2(\frac{y_{im}}{{\mathrm{\&sigma;}}^{2\left(k\right)}}+\frac{{\mathrm{\&mu;}}_{\mathrm{\&beta;}}^{\left(k\right)}}{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}}){\mathrm{\&beta;}}_i\&rsqb;\}\\ \&Proportional;\exp \{-\frac{\&lsqb;{\mathrm{\&beta;}}_i-(y_{im}{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}+{\mathrm{\&mu;}}_{\mathrm{\&beta;}}^{\left(k\right)}{\mathrm{\&sigma;}}^{2\left(k\right)})/(t_m{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}+{\mathrm{\&sigma;}}^{2\left(k\right)})\&rsqb;}{2{\mathrm{\&sigma;}}^{2\left(k\right)}{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}/(t_m{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}+{\mathrm{\&sigma;}}^{2\left(k\right)})}\}\end{array}$

At known Y_iAnd Θ^(k)Under conditions of, β_iThe character of Normal Distribution.

$p\left({\mathrm{\&beta;}}_i\right|Y_i,{\mathrm{\&Theta;}}^k)=\frac{1}{\sqrt{2{\mathrm{\&pi;\&sigma;}}_i^{2\left(k\right)}}}\exp \&lsqb;-\frac{{({\mathrm{\&beta;}}_i-{\mathrm{\&mu;}}_i^{\left(k\right)})}^2}{2{\mathrm{\&sigma;}}_i^{2\left(k\right)}}\&rsqb;$

Wherein,

${\mathrm{\&mu;}}_i^{\left(k\right)}=\frac{y_{im}{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}+{\mathrm{\&mu;}}_{\mathrm{\&beta;}}^{\left(k\right)}{\mathrm{\&sigma;}}^{2\left(k\right)}}{t_m^2{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}+{\mathrm{\&sigma;}}^{2\left(k\right)}}$

${\mathrm{\&sigma;}}_i^{2\left(k\right)}=\frac{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}{\mathrm{\&sigma;}}^{2\left(k\right)}}{t_m^2{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2\left(k\right)}+{\mathrm{\&sigma;}}^{2\left(k\right)}}$

In the E-step stage, calculateExpectationCan obtain:

In the M-step stage, orderThen can try to achieve up-to-date estimates of parameters Θ^(k+1)

${\mathrm{\&sigma;}}_{\mathrm{\&beta;}}^{2(k+1)}=\frac{1}{n}\underset{i=1}{\overset{n}{\&Sigma;}}\&lsqb;{\left({\mathrm{\&mu;}}_i^{\left(k\right)}\right)}^2+{\mathrm{\&sigma;}}_i^{2\left(k\right)}-2{\mathrm{\&mu;}}_i^{\left(k\right)}{\mathrm{\&mu;}}_{\mathrm{\&beta;}}^{(k+1)}+{\left({\mathrm{\&mu;}}_{\mathrm{\&beta;}}^{(k+1)}\right)}^2\&rsqb;$

${\mathrm{\&sigma;}}^{2(k+1)}=\frac{1}{nm}\underset{i=1}{\overset{n}{\&Sigma;}}\underset{j=1}{\overset{m}{\&Sigma;}}\frac{{\left({\mathrm{\&Delta;y}}_{ij}\right)}^2-2{\mathrm{\&mu;}}_i^{\left(k\right)}{\mathrm{\&Delta;y}}_{ij}{\mathrm{\&Delta;t}}_j+{\left({\mathrm{\&Delta;t}}_j\right)}^2{\left({\mathrm{\&mu;}}_i^{\left(k\right)}\right)}^2+{\mathrm{\&sigma;}}_i^{2\left(k\right)}}{{\mathrm{\&Delta;t}}_j}$

Above-mentioned steps can produce a series of estimated value { Θ after successive ignition⁽⁰⁾,Θ⁽¹⁾,Θ⁽²⁾..., until meeting Convergence criterion, it is thus achieved that a good approximation of actual parameter value Θ

We are using the optimal characteristics amount extracted in step (2) as prediction index, and finally we obtain these eight groups degenerations The data trend figure (see Fig. 8) of experiment, wherein failure threshold is 8.25.Based on eight groups of above-mentioned degraded datas, we by this eight The degenerative process of group experiment is built into the Wiener model of band stochastic effect mentioned above and uses EM algorithm to estimate in model The maximal possibility estimation of unknown parameter.Fig. 9 gives the sequence of iterations of each parameter produced by EM algorithm, it may be seen that Can be stablized near true value by parameter after four iteration.The estimated value finally trying to achieve each parameter is respectively

According to the parameter value of above-mentioned estimation, the mean time to failure, MTTF that can be easy to try to achieve correspondence is

$E\left(T\right)=\frac{\sqrt{2}\mathrm{\&eta;}}{{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}}D\left(\frac{{\mathrm{\&mu;}}_{\mathrm{\&beta;}}}{\sqrt{2}{\mathrm{\&sigma;}}_{\mathrm{\&beta;}}}\right)=289$

Due to predicted time FPT=630h first, therefore the meansigma methods in the life-span of final prediction is 919h.Contrast eight groups of inefficacies Life-span meansigma methods 932h of experiment, the algorithm that the present invention proposes can predict the residual life of rotating machinery very accurately, it addition, The algorithm of the present invention and the forecast model Model1 of single index degraded data are compared by we, and Figure 10 gives this calculation The mean degradation track that method is estimated, the mean degradation track of model 1 and degraded data sample average, as seen from the figure, this algorithm pair The mean degradation track answered finally reaches unanimity with the curve of degraded data sample average, illustrates that the carried model of this algorithm has very The good goodness of fit.Above-mentioned analysis fully demonstrates the effectiveness of carried algorithm.

The ultimate principle of the present invention and principal character and advantages of the present invention have more than been shown and described.The technology of the industry Personnel, it should be appreciated that the present invention is not restricted to the described embodiments, simply illustrating this described in above-described embodiment and description The principle of invention, without departing from the spirit and scope of the present invention, the present invention also has various changes and modifications, and these become Change and improvement both falls within scope of the claimed invention.Claimed scope by appending claims and Equivalent defines.

Claims (1)

1. a predicting residual useful life algorithm based on optimum degenerative character amount, it is characterised in that: comprise the following steps:

(1) extraction of equipment optimum degenerative character amount: use waveform index, pulse index, margin index, kurtosis index and peak value Index, these 5 dimensionless indexs, and root value, meansigma methods, root-mean-square value, peak value, these 4 have dimension index as termination Symbol collection, uses and adds, subtracts, multiplication and division, seeks absolute value, opens radical sign as operator collection, by generating initial population, carry out individuality Between duplication, intersect and the operation such as variation, using monotonicity effect as judging the criterion of individual good and bad degree, constantly population is entered Travelingization, finally under algorithm stop criterion, obtains optimum degenerative character amount；

(2) the Weiner process predicting residual useful life model of band stochastic effect is set up: at the base extracting optimum degenerative character amount On plinth, build predicting residual useful life model based on optimum degenerative character amount, plan to build the Wiener mistake of the band stochastic effect that is based on The degradation model that journey describes, it was predicted that the residual life of rotating machinery, in terms of model parameter estimation, will use based on Bayesian Method cooperates down with expectation-maximization algorithm and carries out model parameter estimation, is predicted model by Bayesian method and joins at random The renewal of number Posterior distrbutionp, utilizes EM algorithm to carry out model parameter estimation, makes full use of monitoring information and carry out the residue longevity of equipment Life is estimated.