CN110532629A - A kind of method for predicting residual useful life of multi-modal degenerative process - Google Patents

Abstract

The present invention relates to the predicting residual useful life technical fields of industrial process, provide a kind of method for predicting residual useful life of multi-modal degenerative process, comprising the following steps: read in multi-modal degraded data, initialization model parameter；Height is detected using PELT algorithm, Hurst Exponent is recognized based on wavelet estimators device, and estimate remaining unknown-model parameter using layering maximum likelihood algorithm；Finally, the mean square error for being distributed and predicting using the remaining life of weak convergence transformation calculations all parts.Present invention combination fractional Brownian motion characterizes stationary increment and non-stationary increment with time two kinds of non-Markovian random processes of fractional Brownian motion, and furthermore present the probability density function of remaining life, compared to conventional model, institute's climbing form type can explain the random switching between multiple and different mode, broader memory effect is introduced simultaneously, multi-modal non-equilibrium diffusion process suitable for actual industrial system, practicability with higher.

Description

A kind of method for predicting residual useful life of multi-modal degenerative process

Technical field

The present invention relates to the predicting residual useful life fields of industrial process, and in particular to a kind of residue of multi-modal degenerative process Life-span prediction method.

Background technique

Remaining life can be used in real time, quantitatively assessing in-service equipment as an important indicator in Predicting Technique Health degree.Under first-hitting time meaning, remaining life is normally defined as degenerative process distance and crosses failure threshold for the first time Residual time length.For the online process monitoring system of chemical company, the remaining life of Accurate Prediction core component can be effective Avoid the generation of accident.Predictive information generally comprises expectation and the probability density function of remaining life, and engineer inspection is transported Row safety and formulation maintenance strategy play certain reference role.

It is worth noting that, the degraded data of real equipment often has non-stationary property, random oscillation may be presented Or certain recovery effect.In recent years, Wiener-Hopf equation and its generalized form obtain relatively broad pass in degeneration modeling field Note, has pushed the fast development of the method for predicting residual useful life of data-driven.However, Wiener-Hopf equation substantially belongs to a kind of Ma Er Can husband's process, have ignored memory effect that may be present in data set.In response to this problem, some scholars draw fractional Brownian motion Enter to modeling of degenerating, hit time analysis and predicting residual useful life.As the nonlinear extensions form of Wiener-Hopf equation, score Brownian movement can describe long-term, the short-term memory effect in degeneration path using Hurst Exponent, be usually used in practical applications It is fitted specific Nonstationary diffusion processes.

Existing prediction technique is still in the elementary step for the research of multimodal switchover.Chen and Tsui proposes one kind two Stage degradation model, and combination bayesian theory improves the precision of life prediction；Wen et al. is real using linear changeable point model The on-line prediction of remaining life is showed.But such method does not consider non-Markovian, non-stationary characteristic, application conditions compared with For idealization.Particularly, the incremental process of Wiener-Hopf equation and fractional Brownian motion is still stationary process, it is difficult to which simulation is large-scale high The complicated diffusion process of the equipment such as furnace, steam turbine.

Summary of the invention

In view of the above-mentioned problems in the prior art, the present invention provides a kind of predicting residual useful life sides of multi-modal degenerative process Method, for a kind of new non-stationary degradation model, in conjunction with fractional Brownian motion and time two kinds of non-Markovians of fractional Brownian motion with Machine process characterizes stationary increment and non-stationary increment, and furthermore presents the probability density function of remaining life, compared to passing System model, institute's climbing form type can explain the random switching between multiple and different mode, while introduce broader memory effect It answers, the multi-modal non-equilibrium diffusion process suitable for actual industrial system, practicability with higher.

The following technical solution is employed by the present invention:

A kind of method for predicting residual useful life of multi-modal degenerative process, comprising the following steps:

(1) M group degraded data is read in, X (t is denoted as_k)=[x₁(t_k), x₂(t_k) ..., x_M(t_k)]^T, wherein t_kIndicate kth A monitoring moment；

(2) it is based on following structure initialization model parameter

Wherein, for+1 mode of jth of m-th of degenerative process,For degeneration initial value,For coefficient of deviation, λ (t_k-τ^(j)-δ；γ^(j+1)) it is drift function, τ^(j)And τ^(j+1)For two adjacent height moment, δ is monitoring time at intervals, γ^(j+1) For nonlinear factor, σ^(j+1)For diffusion coefficient, I is indicative function,For stationarity detected value, if value is 1, table Show steady increments, if value is 0, indicates increment non-stationary, B_H(t_k-τ^(j)- δ) it is criterion score Brownian movement, For standard time fractional Brownian motion, H is Hurst Exponent；

(3) height τ is detected using PELT algorithm^(1:D+1), and Hurst Exponent H is recognized based on wavelet estimators device；

(4) remaining unknown-model parameter is estimated using layering maximum likelihood algorithm

(5) remaining life of weak convergence transformation prediction all parts is utilized；

(6) mean square error of prediction is calculated, i.e.,

Wherein, N is the degraded data length of each component, f_{M, k}(r_{M, k}) it is the probability density function that m-th of component is estimated, r_{M, k}For remaining life stochastic variable,For t_kWhen inscribe true remaining life, according toValue examine precision of prediction, and most The probability density function of output remaining life eventually.

Further, in step (3), detection of change-point τ^(1:D+1)And the identification of Hurst Exponent H is by Calling MATLAB respectively In findchangepts function and wfbmesti function seek.

Further, in step (4), for+1 mode of jth,And σ^(j+1)Maximum likelihood estimate Meterσ^(1:D+1)It is provided by maximizing log-likelihood function:

Wherein,For degraded data vector,For initial vector, λ^(j+1)For drift function vector, Q^(j+1)'s The position (i, κ) element is

Further, the log-likelihood function are as follows:

Further, in step (4), γ^(j+1)Maximum-likelihood estimation γ^(1:D+1)Pass through the fminsearch in MATLAB Function is sought, i.e. maximization following formula:

Further, in step (4),Maximum-likelihood estimationBy maximizing part log-likelihood function It provides:

Further, the part log-likelihood function are as follows:

Further, in step (5), the remaining life of prediction all parts is converted using weak convergence, specially using weak Former degenerative process is converted approximate Markov process by convergence criterion, i.e.,

Wherein,

WhenWhen, note

Then m-th of component is in t_kWhen the probability density function of remaining life inscribed be expressed as

Wherein,

And have, * indicates convolution symbol,For failure threshold.

The invention has the advantages that:

A kind of new non-stationary degradation model is provided, in conjunction with fractional Brownian motion and time two kinds of non-horses of fractional Brownian motion Er Kefu random process characterizes stationary increment and non-stationary increment, and furthermore presents the probability density letter of remaining life Number；It is capable of handling the complicated degenerative process containing Mode-switch, compared to traditional predicting residual useful life algorithm, since the present invention fills Divide the non-stationary property for considering incremental process, can be that different modalities distribution reasonably be diffused through based on stationarity testing result Journey, therefore institute's climbing form type of the present invention can explain the random switching between multiple and different mode, while introduce broader Memory effect, multi-modal non-equilibrium diffusion process of the method for predicting residual useful life suitable for actual industrial system, practicability It is higher；When detection of change-point result agrees with true Mode-switch process, the residue for all parts that can more calculate to a nicety Service life.

Detailed description of the invention

Fig. 1 is the flow chart that the present invention carries out predicting residual useful life；

Fig. 2 is the Degradation path of example；

Fig. 3 is the detection of change-point result of example；

Fig. 4 is the predicting residual useful life result of example.

Specific embodiment

The present invention is specifically described with reference to the accompanying drawing:

A kind of method for predicting residual useful life of multi-modal degenerative process, when handling degraded data be according to the following steps according to Secondary realization: multi-modal degraded data, initialization model parameter are read in；Detection of change-point is carried out using PELT algorithm, is estimated based on small echo Gauge recognizes Hurst Exponent, and estimates remaining unknown-model parameter using layering maximum likelihood algorithm；Finally, utilizing weak convergence The remaining life of transformation calculations all parts is distributed and the mean square error of prediction.

Refering to fig. 1, specific steps:

1) M group degraded data is read in, X (t is denoted as_k)=[x₁(t_k), x₂(t_k) ..., x_M(t_k)]^T, wherein t_kIt indicates k-th Monitor the moment；

2) it is based on following structure initialization model parameter

Wherein, for+1 mode of jth of m-th of degenerative process,For degeneration initial value,For coefficient of deviation, λ (t_k-τ^(j)-δ；γ^(j+1)) it is drift function, τ^(j)And τ^(j+1)For two adjacent height moment, δ is monitoring time at intervals, γ^(j+1) For nonlinear factor, σ^(j+1)For diffusion coefficient, I is indicative function,For stationarity detected value, if value is 1, table Show steady increments, if value is 0, indicates increment non-stationary, B_H(t_k-τ^(j)- δ) it is criterion score Brownian movement, For standard time fractional Brownian motion, H is Hurst Exponent；

3) the findchangepts function in Calling MATLAB and wfbmesti function realize detection of change-point and conspicuous respectively This refers in particular to the identification of number；

4) remaining unknown-model parameter is estimated using layering maximum likelihood algorithm Specifically, for+1 mode of jth,And σ^(j+1)Maximum-likelihood estimation by maximize log-likelihood Function provides, i.e.,

Log-likelihood function:

Wherein,For degraded data vector,For initial vector, λ^(j+1)For drift function vector, Q^(j+1)'s The position (i, κ) element is

Fminsearch function in Calling MATLAB seeks γ^(j+1)Maximum-likelihood estimation, i.e., maximization following formula

Then it is sought according to part log-likelihood functionMaximum-likelihood estimation, i.e.,

Part log-likelihood function:

5) approximate Markov process is converted by former degenerative process using weak convergence criterion, i.e.,

Wherein,

WhenWhen, note

Then m-th of component is in t_kWhen the probability density function of remaining life inscribed be represented by

Wherein,

And have, * indicates convolution symbol,For failure threshold.

6) mean square error of prediction is calculated, i.e.,

Wherein, N is the degraded data length of each component, f_{M, k}(r_{M, k}) it is the probability density function that m-th of component is estimated, r_{M, k}For remaining life stochastic variable,For t_kWhen inscribe true remaining life.According toValue examine precision of prediction, and most The probability density function of output remaining life eventually.

Example predicting residual useful life result

Simulated environment is as follows:

Type: Intel Core i7-4790 (CPU 3.60Ghz, 8.00GB RAM)；

Operating system: Windows 10；

Software: Matlab R2018b.

By one group of numerical simulation, the detailed description of experimental procedure and the prediction result of remaining life are provided:

1) consider a kind of three mode degeneration systems, 5 groups of degraded datas are generated based on formula (1), design parameter is provided that M=5, H =0.6, δ=0.1,τ⁽¹⁾=11, τ⁽²⁾=22, σ⁽¹⁾=0.3, σ⁽²⁾=0.2, σ⁽³⁾=0.4, γ⁽¹⁾=0.6, γ⁽²⁾=0.9, γ⁽³⁾=0.8, Degradation path such as Fig. 2, failure moment are set as 33；

2) initialization model parameter

3) the findchangepts function in Calling MATLAB and wfbmesti function realize detection of change-point and conspicuous respectively This refers in particular to the identification of number, can obtain:Wherein, the graphical result of detection of change-point Such as Fig. 3, it is clear that estimated result is closer to true value, is conducive to further Model Distinguish；

4) remaining unknown-model parameter is estimated using layering maximum likelihood algorithm As a result as follows: σ⁽¹⁾=0.3741, σ⁽²⁾=0.2269, σ⁽³⁾=0.4245, γ⁽¹⁾=0.6296, γ⁽²⁾=0.9081, γ⁽³⁾=0.8109, it can To find out, parameter estimation result is more accurate, mutually agrees with mentioned model structure；

5) probability density function that the remaining life of all parts is calculated using formula (6) to formula (14), by taking component 5 as an example, Prediction result such as Fig. 4, it can be seen that the probability density function curve of estimation, which is inscribed preferably to cover in each monitoring, works as Preceding remaining life true value has stronger convincingness；

6) mean square error that prediction is calculated using formula (15), can obtain:Illustrate that precision of prediction is higher, thus Demonstrate practicability of the invention.

Certainly, the above description is not a limitation of the present invention, and the present invention is also not limited to the example above, this technology neck The variations, modifications, additions or substitutions that the technical staff in domain is made within the essential scope of the present invention also should belong to of the invention Protection scope.

Claims (8)

1. a kind of method for predicting residual useful life of multi-modal degenerative process, which comprises the following steps:

(1) M group degraded data is read in, X (t is denoted as_k)=[x₁(t_k), x₂(t_k) ..., x_M(t_k)]^T, wherein t_kIndicate k-th of prison Survey the moment；

(2) it is based on following structure initialization model parameter

Wherein, for+1 mode of jth of m-th of degenerative process,For degeneration initial value,For coefficient of deviation, λ (t_k- τ^(j)-δ；γ^(j+1)) it is drift function, τ^(j)And τ^(j+1)For two adjacent height moment, δ is monitoring time at intervals, γ^(j+1)For Nonlinear factor, σ^(j+1)For diffusion coefficient, I is indicative function,It is indicated for stationarity detected value if value is 1 Steady increments indicate increment non-stationary, B if value is 0_H(t_k-τ^(j)- δ) it is criterion score Brownian movement, For standard time fractional Brownian motion, H is Hurst Exponent；

(3) height τ is detected using PELT algorithm^(1:D+1), and Hurst Exponent H is recognized based on wavelet estimators device；

(4) remaining unknown-model parameter is estimated using layering maximum likelihood algorithmγ^(1:D+1), σ^(1:D+1),

(5) remaining life of weak convergence transformation prediction all parts is utilized；

(6) mean square error of prediction is calculated, i.e.,

Wherein, N is the degraded data length of each component, f_{M, k}(r_{M, k}) it is the probability density function that m-th of component is estimated, r_{M, k} For remaining life stochastic variable,For t_kWhen inscribe true remaining life, according toValue examine precision of prediction, and it is final Export the probability density function of remaining life.

2. a kind of method for predicting residual useful life of multi-modal degenerative process according to claim 1, which is characterized in that step (3) in, detection of change-point τ^(1:D+1)And the identification of Hurst Exponent H is by the findchangepts function in Calling MATLAB respectively It is sought with wfbmesti function.

3. a kind of method for predicting residual useful life of multi-modal degenerative process according to claim 1, which is characterized in that step (4) in, for+1 mode of jth,And σ^(j+1)Maximum-likelihood estimationσ^(1:D+1)It is logical Maximization log-likelihood function is crossed to provide:

Wherein,For degraded data vector,For initial vector, λ^(j+1)For drift function vector, Q^(j+1)The position (i, κ) Setting element is

4. a kind of method for predicting residual useful life of multi-modal degenerative process according to claim 3, which is characterized in that described Log-likelihood function are as follows:

5. a kind of method for predicting residual useful life of multi-modal degenerative process according to claim 3, which is characterized in that step (4) in, γ^(j+1)Maximum-likelihood estimation γ^(1:D+1)It is sought by the fminsearch function in MATLAB, that is, under maximizing Formula:

6. a kind of method for predicting residual useful life of multi-modal degenerative process according to claim 1, which is characterized in that step (4) in,Maximum-likelihood estimationIt is provided by maximizing part log-likelihood function:

7. a kind of method for predicting residual useful life of multi-modal degenerative process according to claim 6, which is characterized in that described Part log-likelihood function are as follows:

8. a kind of method for predicting residual useful life of multi-modal degenerative process according to claim 1, which is characterized in that step (5) in, the remaining life of prediction all parts is converted using weak convergence, is specially turned former degenerative process using weak convergence criterion Approximate Markov process is turned to, i.e.,

Wherein,

WhenWhen, note

Then m-th of component is in t_kWhen the probability density function of remaining life inscribed be expressed as

Wherein,

And have, * indicates convolution symbol,For failure threshold.