CN-115587450-B - Degradation process modeling method based on wiener principle and Gaussian process regression

Abstract

The invention relates to the technical field of degradation reliability modeling, and provides a degradation process modeling method based on a wiener principle and Gaussian process regression, which comprises the following steps: according to the actual workpiece vibration signals measured at equal interval sampling moments, a data set is obtained through feature extraction and dimension reduction, a wiener process considering the random effect of drift parameters is adopted to describe the workpiece vibration signals, an analysis form of a wiener kernel is obtained, gaussian process regression is introduced, a Gaussian regression model is obtained, based on a training set, the Gaussian process regression model is subjected to parameter estimation through maximum likelihood estimation, and a testing set is predicted through the Gaussian regression model, so that the effects of reliability estimation and life prediction of equipment are obtained. The invention realizes the combination of the data driving method and the physical mechanism, the excavation of the data information is more thorough, and the prediction precision of the wiener kernel in the Gaussian process regression is obviously improved.

Inventors

• ZHANG TIANXIAO
• Cao Licai
• CUI JIN

Assignees

• 北京航空航天大学

Dates

Publication Date

20260512

Application Date

20221103

Claims (3)

1. 1. A degradation process modeling method based on wiener theory and gaussian process regression, comprising: S1, processing vibration signals of a workpiece according to actual equidistant sampling moment measurement to obtain a training set G and a test set G * , wherein the training set G= { x, y }, the test set G * ={x * ,y * }, x is an actual equidistant sampling training set moment set, and x = Y is an actual training set degradation set corresponding to actual equidistant sampling time, y= { y 1 ,y 2 ,…,y M }, and M is the total number of samples of the training set; S2, establishing a wiener degradation model based on a wiener principle considering a random effect of drift parameters; s3, introducing the wiener degradation model into a Gaussian process to obtain a Gaussian process model; S4, based on the training set, acquiring a parameter estimation value of the Gaussian process model by adopting a negative log-likelihood function, and performing posterior distribution prediction by utilizing the training set and the Gaussian process model to acquire a Gaussian regression model; wherein, the expression of the wiener degradation model is as follows; y'(n) =x 0 + ω(n)+σB(n)+ε(1) where y' (n) is the degradation measure at time n, x 0 is the initial value of degradation, For drift parameters, ω (n) is the drift function, σ is the divergence coefficient, B (n) is the standard brownian motion, ε is the white noise, ε obeys the normal distribution, and it is noted that: (2) Wherein, the Is the standard deviation; giving drift parameters Introducing a random effect such that the drift parameter Obeying normal distribution, noted as: (3) Wherein, the Is that Is used for the average value of (a), Is that Is a variance of (2); The Brownian motion sigma B (n) is used for representing vibration signal change caused by working condition change encountered in the working process of a workpiece, and the distribution rule is recorded as: (4) When the drift function is an exponential function, the Venus exponential function degradation model is: (5) wherein q is a parameter of an exponential function; Based on the Venus exponential function degradation model, a column vector y' = [ y 1 ,y 2 ,…,y M ] T ] of degradation test quantity is obtained, and the column vector is subjected to multi-element normal distribution and is recorded as: y'~MVN(x 0 + ) (6) (7) (8) (9) Wherein, the Is an identity matrix of order M, t is an exponentially mapped column vector of training set time, t= [ ] T ; Is the transpose of t and, =[ ]; Is a wiener covariance matrix; For the ith element of the column vector t, As the j-th element of the column vector t, i is more than or equal to 1 and less than or equal to M, j is more than or equal to 1 and less than or equal to M; Obtaining a gaussian process model based on the training set: Y( )=f( )+ε(10) Wherein Y is Gaussian degradation test quantity, f # ) Is the amount of gaussian degradation at time n subject to the gaussian process, expressed as: (11) Wherein, the Representing a mean function of the gaussian process; covariance function representing gaussian process covariance function, And are respectively expressed as: (12) ;(13) according to the Gaussian process model, obtaining a Gaussian process degradation test quantity Y, wherein Y obeys a multi-element normal distribution: ;(14) Wherein m (t) is the mean vector of Y, Is a Gaussian process covariance matrix; substituting formula (6) into formula (14) to obtain a mean function: (15) Substituting formula (9) into formula (14) to obtain wiener kernel: (16) Wherein, the As covariance matrix M=m; obtaining parameters of a gaussian process model based on m (t) and wiener kernels: (17) according to equation (14), a negative log likelihood function NLML is obtained: (18) Based on the training set, obtaining parameter values of the Gaussian process model by adopting a minimized negative log-likelihood function: (19)。
2. 2. the degradation process modeling method of claim 1, wherein the vibration signal of the bearing is processed by a judgment method to obtain a training set and a test set.
3. 3. The degradation process modeling method according to claim 2, wherein posterior distribution prediction is performed using a training set and a gaussian process model, and a joint prior distribution of training set and gaussian regression testing data is obtained: ;(20) Wherein, the A column vector mapped for the index of test set time; Obtaining a column vector for the degradation amount of the test set corresponding to the sampling time at equal intervals; obtaining posterior distribution of degradation prediction values: ;(21) Obtaining a Gaussian regression model: ;(22) ;(23) Wherein, the Is the mean vector of the degradation prediction value; Is the covariance matrix of the degradation prediction value.

Description

Degradation process modeling method based on wiener principle and Gaussian process regression Technical Field The invention relates to the technical field of degradation reliability modeling, in particular to a degradation process modeling method based on a wiener principle and Gaussian process regression. Background The traditional reliability evaluation method is based on the assumption of two states, namely that a product can only be in two states of normal and fault, however, for modern high-reliability and long-service-life products, the more difficult the acquisition of failure data of the product becomes due to the limitations of test duration and cost, so that the reliability modeling method based on performance degradation is developed, and aims to fully discover statistical information in a reliability test, establish a corresponding physical or mathematical model to evolve degradation rules of performance, and further develop reliability evaluation and service life prediction. The degradation modeling is an important foundation for performance degradation reliability assessment and residual life prediction, and is favored by the students at sea and abroad in recent years, and a modeling method based on a random process and based on data driving is adopted. However, the existing data driving method such as deep learning, support vector machine, gaussian process regression and the like is suitable for large data conditions, and accuracy is low when the sample size is small, while the random process-based method essentially belongs to a Markov process, only the correlation between two adjacent data is considered, and the data mining degree is low. Disclosure of Invention In view of the above, the invention provides a degradation process modeling method based on wiener principle and Gaussian process regression, which solves the problems that the prior art is only suitable for big data and has low data correlation, and can still obtain higher accuracy when samples are fewer. The invention provides a degradation process modeling method based on a wiener principle and Gaussian process regression, which comprises the following steps: S1, processing vibration signals of a workpiece according to workpiece vibration signals obtained through actual equidistant sampling time measurement to obtain a training set G and a test set G *, wherein the training set G= { x, y } and the test set G *＝{x*,y* } are respectively a practical equidistant sampling training set time set, x= { x 1,x2,…,xM } and y is a practical training set degradation amount set corresponding to the practical equidistant sampling time, y= { y 1,y2,…,yM } and M is the total number of samples of the training set; S2, establishing a wiener degradation model based on a wiener principle considering a random effect of drift parameters; s3, introducing the wiener degradation model into a Gaussian process to obtain a Gaussian process model; s4, based on the training set, obtaining a parameter estimation value of the Gaussian process model by adopting a negative log-likelihood function, carrying out posterior distribution prediction by utilizing the training set and the Gaussian process model to obtain a Gaussian regression model, and verifying a prediction result of the Gaussian regression model by utilizing the testing set. Optionally, a judgment method is adopted to process the vibration signal of the workpiece to obtain a training set and a testing set. Optionally, the wiener degradation model is obtained based on wiener principles that consider the random effect of drift parameters: y'(n)=x0+θω(n)+σB(n)+ε; (1) Wherein y' (n) is degradation measurement at time n, x 0 is degradation initial value, θ is drift parameter, ω (n) is drift function, σ is divergence coefficient, B (n) is standard brownian motion, ε is white noise, ε is normal distribution, and it is recorded that: ε~N(0,λ2); (2) wherein lambda is the standard deviation; introducing a random effect to the drift parameter theta so that the drift parameter theta follows a normal distribution, and recording as: Wherein mu θ is the average value of theta, Variance of θ; The Brownian motion sigma B (n) is used for representing vibration signal change caused by working condition change encountered in the working process of a workpiece, and the distribution rule is recorded as: σB(n)~N(0,σ2n)。 (4) Optionally, the drift function comprises a linear function, an exponential function, or a power function. Optionally, when the drift function is an exponential function, the wiener exponential function degradation model is: y'(n)=x0+θqn+σB(n)+ε; (5) where q is a parameter of the exponential function. Optionally, based on the wiener exponential function degradation model, a column vector y 'of the degradation test quantity is obtained= [ y 1,y2,…,yM]T, and the column vector y' of the wiener exponential function degradation test quantity obeys a multivariate normal distribution, and is recorded as: Ω=σ2Q+λ