CN105868557A - Online prediction method for remaining life of electromechanical equipment under situation of two-stage degradation - Google Patents

Abstract

The invention discloses an online prediction method for the remaining life of electromechanical equipment under the situation of two-stage degradation. The online prediction method can be applied to online service life prediction and health management of mechanical equipment and electric and electronic devices. The method comprises the steps that a Wiener process model serves as a basic degradation model of an object, and a degradation drifting coefficient is expanded into a state and described with a closed oblique Wiener process. A new algorithm is proposed to overcome prediction deviation caused by the Markovian feature of a common Wiener process. For state estimation in the online prediction stage, an iteration filter algorithm is proposed to obtain an analytical expression of updated states. On parameter estimation, a two-stage parameter estimation algorithm is proposed. An analytical expression related to remaining life prediction results is obtained by using updated states and parameters. The model proposed in the method better conforms to the general degradation rules, more accurate online remaining life prediction results can be obtained, and great significance is achieved on fault prediction and health management in engineering.

Description

Online prediction method for residual life of electromechanical equipment under two-stage degradation condition

Technical Field

The invention belongs to the technical field of reliability engineering, and relates to an online prediction method for the residual life of electromechanical equipment under the condition of two-stage degradation.

Background

Fault Prediction and Health Management (PHM) is critical to the reliability and safety of a product in operation and has been applied to many different products. The core of realizing the fault prediction and the health management lies in the prediction of the residual service life of the equipment. The wiener process model has good mathematical characteristics and physical interpretability, so that the wiener process model is widely applied to the service life data analysis of different industrial fields, such as LEDs of contact image scanners, self-temperature-control heating cables, aluminum electrolysis cells, bridges and bearings. Further, in order to take historical degradation data and current measurement quantities into account, adaptive wiener process models have become widely adopted prediction models. However, for predicting the remaining life of the electromechanical device with two stages of slow degradation and accelerated degradation, the assumption of the existing prediction method based on the wiener process is unreasonable, so that a more accurate prediction effect cannot be obtained.

Disclosure of Invention

Aiming at the prior technical situation, the invention aims to solve the problems in the prior art, and aims to construct a model capable of more reasonably describing the degradation process characteristics according to the performance degradation data which can be obtained by aiming at electromechanical equipment with two-stage degradation characteristics so as to realize online high-accuracy prediction of the residual service life of the equipment.

The concept of the present invention will now be explained as follows:

the invention adopts a wiener process model as a basic degradation model of an object, expands a degradation drift coefficient into a state, and describes the state by using a closed oblique wiener process. In order to overcome the prediction deviation caused by the Markov characteristic of the general wiener process, the invention provides a novel algorithm. Aiming at the state estimation in the online prediction stage, the invention provides an iterative filtering algorithm to obtain an analytical expression of an updated state. In parameter estimation, the invention provides a two-stage parameter estimation algorithm. With the updated states and parameters, the present invention obtains an analytical expression for the remaining life prediction. The model provided by the invention is more consistent with general degradation rules, and more accurate online residual life prediction results can be obtained

According to the invention concept, the invention provides an online prediction method for the residual life of electromechanical equipment under the condition of two-stage degradation, the actual degradation of the equipment is divided into two stages of normal degradation and accelerated degradation, the performance degradation process conforms to a self-adaptive oblique wiener process model, a two-stage parameter estimation algorithm is adopted for parameters of the model, an iterative filtering algorithm is adopted to obtain the degradation state in real time, and after the degradation state estimation and the parameter estimation are completed, the residual life of the equipment is predicted by using an updated degradation drift state, estimated parameters and measurement quantity; the method comprises the following specific steps:

step 1: establishing a performance degradation model describing equipment conforming to the two-stage degradation characteristics, which comprises the following specific steps:

step 1.1: a device degradation model satisfying the two-stage degradation characteristic is expressed as follows:

η_k＝η_k-1+ν_k

_k＝η_k-1τ_k+αΒ(τ_k)

_k＝x_k-x_k-1

wherein, t_kAt the kth sampling instant, η_kIs t_kIs used for characterizing the degradation speed and satisfies a closed oblique gaussian distribution, and the probability density function f (η) is:

$f\left(\mathrm{\η}\right)=\mathrm{\φ}\left(\frac{\mathrm{\η}-\mathrm{\μ}}{\mathrm{\σ}}\right)\mathrm{\Φ}\[\mathrm{\λ}\left(\frac{\mathrm{\η}-\mathrm{\μ}}{\mathrm{\σ}}\right)+\mathrm{\ξ}\]/\[\mathrm{\σ}\mathrm{\Φ}\left(\frac{\mathrm{\ξ}}{\sqrt{1+{\mathrm{\λ}}^2}}\right)\]$

in the above formula, phi (DEG) is a probability density function of the standard Gaussian distribution, phi (DEG) is a cumulative distribution function of the standard Gaussian distribution, mu and sigma are a position parameter and a scale parameter respectively, ξ is a general parameter, lambda is a shape parameter, and v_kIs system white noise, and v_k～N(0,²) α is the diffusion coefficient, and α>0，τ_kIs the sampling time interval, and_k＝t_k-t_k-1，Β(τ_k) Is a standard brownian motion, andx_kcharacterizing the degradation degree of the device at the kth sampling moment;_kthe degradation degree increment of two adjacent sampling moments is obtained;

step 1.2: once the product starts to run, the monitoring system will start to run at t ═ { t ═ t₁,...,t_kIt is monitored for equipment state data, i.e. equipment degradation degree isx₀Generally assume a value of 0, defining the historical degradation increment from product commissioning to the kth sampling time as_1:k＝{₁,...,_k}，₁＝x₁。

Step 2: estimating a degraded hidden state by adopting an iterative filtering algorithm, and specifically comprising the following steps of:

step 2.1: the degradation speed of the electromechanical equipment, namely the hidden degradation drift coefficient of the oblique wiener process model, and the initial state of the model satisfies the closed oblique Gaussian distribution, namelyCSN is closed oblique Gaussian distribution, and unknown parameters of an initial degradation drift state are obtained by fitting initial degradation data of similar products; further, the initial state of the apparatus is (₁|η₀)～N(η₀τ₁,α²τ₁) The unknown parameters are obtained by a maximum likelihood estimation method through historical degradation data and an initial degradation drift state obtained through estimation;

step 2.2: at the kth sampling instant, there is a degenerate hidden state satisfying the distribution

$\left({\mathrm{\η}}_{k-1}\right|{\mathrm{\δ}}_{1:k-1})~CSN({\mathrm{\μ}}_{k-1},{\mathrm{\σ}}_{k-1}^2,{\mathrm{\λ}}_{k-1},{\mathrm{\ξ}}_{k-1})$

With a degree of deterioration (_k|η_k-1,_1:k-1)～N(η_k-1τ_k,α²τ_k)。

Step 2.3: according to the obtained new measurement quantity, the degradation hidden state of the equipment satisfies a closed oblique Gaussian distribution

$\left({\mathrm{\η}}_{k-1}\right|{\mathrm{\δ}}_{1:k})~CSN({\widehat{\mathrm{\μ}}}_{k-1},{\widehat{\mathrm{\σ}}}_{k-1}^2,{\widehat{\mathrm{\λ}}}_{k-1},{\widehat{\mathrm{\ξ}}}_{k-1})$

Wherein,

the estimated value of the parameter is represented with a symbol in the formula;

step 2.4: the posterior distribution of degenerate hidden states is obeyed according to the result of step 2.3

$\left({\mathrm{\η}}_k\right|{\mathrm{\δ}}_{1:k})~CSN({\mathrm{\μ}}_k,{\mathrm{\σ}}_k^2,{\mathrm{\λ}}_k,{\mathrm{\ξ}}_k)$

Wherein

According to the four steps, the relation between the degradation degree prediction and the historical degradation data is established, and the hidden state can be updated in an iterative and real-time manner.

And step 3: estimating the performance degradation model parameters on line, which comprises the following steps:

step 3.1: according to the degradation data obtained by sampling, a log-likelihood function is constructed

$\ln f_{{\mathrm{\Δ}}_{2:k}|{\mathrm{\Δ}}_1}\left({\mathrm{\δ}}_{2:k}\right|{\mathrm{\δ}}_1)=\underset{i=2}{\overset{k}{\Σ}}\ln f_{{\mathrm{\Δ}}_i|{\mathrm{\Δ}}_{1:i-1}}\left({\mathrm{\δ}}_i\right|{\mathrm{\δ}}_{1:i-1})$

Step 3.2: after obtaining a new measurement, i.e. obtaining a conditional probability density function of the degree of degradation, the above equation is expanded to:

$\begin{array}{c}\ln f_{{\mathrm{\Δ}}_{2:k}|{\mathrm{\Δ}}_1}\left({\mathrm{\δ}}_{2:k}\right|{\mathrm{\δ}}_1)=\underset{i=2}{\overset{k}{\Σ}}\{-\frac{1}{2}\ln \[2\mathrm{\π}({\mathrm{\τ}}_i^2{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2{\mathrm{\τ}}_i)\]-\frac{{({\mathrm{\δ}}_i-{\mathrm{\τ}}_i{\mathrm{\μ}}_{i-2})}^2}{2({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2{\mathrm{\τ}}_i)}\}\\ +\underset{i=2}{\overset{k}{\Σ}}\ln \mathrm{\Φ}\left\{\frac{{\mathrm{\λ}}_{i-2}{\mathrm{\σ}}_{i-2}({\mathrm{\δ}}_i-{\mathrm{\τ}}_i{\mathrm{\μ}}_{i-2})+{\mathrm{\ξ}}_{i-2}({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2)}{\sqrt{({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2)\[{\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+(1+{\mathrm{\λ}}_{i-2}^2)({\mathrm{\τ}}_i{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2)\]}}\right\}\\ -\underset{i=2}{\overset{k}{\Σ}}\ln \mathrm{\Φ}\left(\frac{{\mathrm{\ξ}}_{i-2}}{\sqrt{1+{\mathrm{\λ}}_{i-2}^2}}\right)\end{array}$

step 3.3: maximization by searching using numerical methodsThe parameter (c) of (c).

And 4, step 4: obtaining a probability distribution expression of the residual service life of the equipment, wherein the specific steps are as follows:

step 4.1: the first-pass time is used as a link for connecting the prediction of the degradation degree and the prediction of the residual life, namely, the random variable of the residual life is defined as L ═ inf { L: x (L + t)_k)>ω|X_1:kWhere l is the implementation of a random variable for remaining life, ω is a predefined threshold, X_1:kIs a historical measurement.

Step 4.2: the remaining lifetime distribution probability density function at the kth sampling instant is,

$f_{L|X_{1:k}}\left(l\right|X_{1:k})=\frac{\mathrm{\ω}-x_k}{\sqrt{2{\mathrm{\πl}}^3({\mathrm{l\σ}}_k^2+{\mathrm{\α}}^2)}}\exp \[-\frac{{(\mathrm{\ω}-x_k-{\mathrm{\μ}}_{k}l)}^2}{2l({\mathrm{l\σ}}_k^2+{\mathrm{\α}}^2)}\]\frac{\mathrm{\Φ}(\mathrm{\ζ}/\sqrt{1+{\mathrm{\γ}}^2})}{\mathrm{\Φ}({\mathrm{\ξ}}_k/\sqrt{1+{\mathrm{\λ}}_k^2})}$

wherein,

therefore, a probability density function accurate expression of the online prediction of the residual life of the equipment is obtained and is used for online prediction of the residual life of the electromechanical equipment.

In the formula of the method of the invention, the undefined parameter with a subscript indicates the value of the parameter at the sampling instant corresponding to the subscript, e.g. mu_k,σ_kRespectively, the position parameter and the scale parameter at the kth sampling instant.

The online residual life prediction method under the condition of two-stage degradation can be applied to online life prediction of mechanical equipment and power electronic devices. By constructing the oblique Gaussian model capable of reasonably describing the characteristics of the degradation process, a more accurate prediction effect can be obtained. The method provides powerful data support for subsequent equipment health management, is particularly valuable for high-reliability equipment maintenance management, and has wide prospects in the aspect of practical engineering application.

Drawings

FIG. 1 is vibration data of a bearing in an embodiment;

fig. 2 is a comparison of performance of remaining life prediction in the examples.

Detailed Description

The embodiments of the present invention will now be further described with reference to the accompanying drawings.

The following example illustrates the specific operational steps and the effectiveness of the verification method by a set of actual bearing degradation data from the PRONOSTIA experimental platform.

In the data acquisition of this degradation experiment, the experimenter collected 2560 vibration data per sampling time, and the sampling time interval was 10 seconds. At each sampling instant, the root mean square value of 2560 vibration data is calculated as a characteristic value at each sampling instant, so that a new time series data is formed for each bearing. The sampling time interval of the root mean square eigenvalue is 10 seconds. Since the model of the present invention is inspired by the adaptive gaussian-wiener process model, the present example compares the performance differences between the two in this example.

Step 1: establishing a performance degradation model depicting equipment conforming to two-stage degradation characteristics

Step 1.1: the bearing degradation model is expressed as follows:

η_k＝η_k-1+ν_k

_k＝η_k-1τ_k+αΒ(τ_k)

_k＝x_k-x_k-1

wherein, t_kAt the kth sampling instant, η_kIs t_kIs used for characterizing the degradation speed and satisfies a closed oblique gaussian distribution, and the probability density function f (η) is:

$f\left(\mathrm{\η}\right)=\mathrm{\φ}\left(\frac{\mathrm{\η}-\mathrm{\μ}}{\mathrm{\σ}}\right)\mathrm{\Φ}\[\mathrm{\λ}\left(\frac{\mathrm{\η}-\mathrm{\μ}}{\mathrm{\σ}}\right)+\mathrm{\ξ}\]/\[\mathrm{\σ}\mathrm{\Φ}\left(\frac{\mathrm{\ξ}}{\sqrt{1+{\mathrm{\λ}}^2}}\right)\]$

in the above formula, phi (DEG) is a probability density function of the standard Gaussian distribution, phi (DEG) is a cumulative distribution function of the standard Gaussian distribution, mu and sigma are a position parameter and a scale parameter respectively, ξ is a general parameter, lambda is a shape parameter, and v_kIs system white noise, and v_k～N(0,²) α is the diffusion coefficient, and α>0，τ_kIs the sampling time interval, and_k＝t_k-t_k-1，Β(τ_k) Is a standard brownian motion, andx_kthe degree of degradation of the device, i.e. the vibration signal strength, is characterized at the kth sampling instant. (ii) a_kThe degradation degree of two adjacent sampling moments is increased.

Step 1.2: the monitoring system is in t ═ t { [ t₁,...,t_kMonitoring it to detect the number of degraded state of bearingAccording to the degree of equipment degradationThis example defines the historical degradation increment from product commissioning to the kth sampling time as_1:k＝{₁,...,_k}，₁＝x₁。

Step 2: estimating a degraded hidden state using an iterative filtering algorithm

Step 2.1: the degradation speed of the electromechanical device, i.e. the hidden degradation drift coefficient of the model, and the initial state of the model satisfies the closed oblique Gaussian distribution, i.e.Further, the initial state of the apparatus is (₁|η₀)～N(η₀τ₁,α²τ₁)

In this example, bearings #1-4, #2-6 and #3-1 were first selected randomly as training data. Using the training data, initial values of unknown parameters of the oblique wiener process model and the gaussian-wiener process model are estimated to be μ 0 ═ 0.088, σ 0 ═ 0.155, λ 0 ═ 1.393, ξ 0 ═ 1.105, ═ 0.003, α ═ 0.009 μ ' 0 ═ 0.0015, σ ' 0 ═ 0.1265, ' -0.0005, and α ═ 0.012, respectively.

Step 2.2: at the kth sampling instant, there is a degenerate hidden state satisfying the distribution

$\left({\mathrm{\η}}_{k-1}\right|{\mathrm{\δ}}_{1:k-1})~CSN({\mathrm{\μ}}_{k-1},{\mathrm{\σ}}_{k-1}^2,{\mathrm{\λ}}_{k-1},{\mathrm{\ξ}}_{k-1})$

With a degree of deterioration (_k|η_k-1,_1:k-1)～N(η_k-1τ_k,α²τ_k)。

Step 2.3: according to the obtained new measurement quantity, the degradation hidden state of the equipment satisfies a closed oblique Gaussian distribution

$\left({\mathrm{\η}}_{k-1}\right|{\mathrm{\δ}}_{1:k})~CSN({\widehat{\mathrm{\μ}}}_{k-1},{\widehat{\mathrm{\σ}}}_{k-1}^2,{\widehat{\mathrm{\λ}}}_{k-1},{\widehat{\mathrm{\ξ}}}_{k-1})$

Wherein,

step 2.4: the posterior distribution of degenerate hidden states is obeyed according to the result of step 2.3

$\left({\mathrm{\η}}_k\right|{\mathrm{\δ}}_{1:k})~CSN({\mathrm{\μ}}_k,{\mathrm{\σ}}_k^2,{\mathrm{\λ}}_k,{\mathrm{\ξ}}_k)$

Wherein

According to the four steps, the relation between the degradation degree prediction and the historical degradation data is established, and the hidden state can be updated in an iterative and real-time manner.

And step 3: on-line estimation of model parameters

Step 3.1: according to the degradation data obtained by sampling, constructing a log-likelihood function:

$\ln f_{{\mathrm{\Δ}}_{2:k}|{\mathrm{\Δ}}_1}\left({\mathrm{\δ}}_{2:k}\right|{\mathrm{\δ}}_1)=\underset{i=2}{\overset{k}{\Σ}}\ln f_{{\mathrm{\Δ}}_i|{\mathrm{\Δ}}_{1:i-1}}\left({\mathrm{\δ}}_i\right|{\mathrm{\δ}}_{1:i-1})$

step 3.2: after obtaining a conditional probability density function for a new measurement, i.e. for the degree of degradation, the above equation is expanded to:

$\begin{array}{c}\ln f_{{\mathrm{\Δ}}_{2:k}|{\mathrm{\Δ}}_1}\left({\mathrm{\δ}}_{2:k}\right|{\mathrm{\δ}}_1)=\underset{i=2}{\overset{k}{\Σ}}\{-\frac{1}{2}\ln \[2\mathrm{\π}({\mathrm{\τ}}_i^2{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2{\mathrm{\τ}}_i)\]-\frac{{({\mathrm{\δ}}_i-{\mathrm{\τ}}_i{\mathrm{\μ}}_{i-2})}^2}{2({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2{\mathrm{\τ}}_i)}\}\\ +\underset{i=2}{\overset{k}{\Σ}}\ln \mathrm{\Φ}\left\{\frac{{\mathrm{\λ}}_{i-2}{\mathrm{\σ}}_{i-2}({\mathrm{\δ}}_i-{\mathrm{\τ}}_i{\mathrm{\μ}}_{i-2})+{\mathrm{\ξ}}_{i-2}({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2)}{\sqrt{({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2)\[{\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+(1+{\mathrm{\λ}}_{i-2}^2)({\mathrm{\τ}}_i{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2)\]}}\right\}\\ -\underset{i=2}{\overset{k}{\Σ}}\ln \mathrm{\Φ}\left(\frac{{\mathrm{\ξ}}_{i-2}}{\sqrt{1+{\mathrm{\λ}}_{i-2}^2}}\right)\end{array}$

step 3.3: parameters maximizing the above formula are obtained by searching with a numerical method, and the parameter estimation results of the two models are obtained according to the bearing #1-3 as shown in the following table.

TABLE 1 estimation of unknown parameters in oblique wiener Process models and Gaussian-wiener Process models

	Oblique wiener process model	Gauss-wiener process model
			α	3.91×10-2	7.275×10-2
ε	8.30×10-4	3.207×10-4

And 4, step 4: obtaining distribution expression of residual life of equipment

Step 4.1: the first-pass time is used as a link for connecting the prediction of the degradation degree and the prediction of the residual life, namely, the random variable of the residual life is defined as L ═ inf { L: x (L + t)_k)>ω|X_1:kWhere in italics l is the implementation of the residual lifetime random variable, ω is a predefined threshold, X_1:kIs a historical measurement. In the experiment, the failure threshold of the original vibration signal was 20g, where g represents the acceleration of gravity. The present example defines the rms eigenvalue threshold as the rms eigenvalue at the sampling instant that contains the first more than 20g of the original vibration signal. Taking bearing #1-3 as an example, at 2342 th sampling time, the original vibration data exceeds 20g for the first time, and therefore, the threshold of the root mean square eigenvalue is 2342 th root mean square eigenvalue, namely 4, 7145.

$f_{L|X_{1:k}}\left(l\right|X_{1:k})=\frac{\mathrm{\ω}-x_k}{\sqrt{2{\mathrm{\πl}}^3({\mathrm{l\σ}}_k^2+{\mathrm{\α}}^2)}}\exp \[-\frac{{(\mathrm{\ω}-x_k-{\mathrm{\μ}}_{k}l)}^2}{2l({\mathrm{l\σ}}_k^2+{\mathrm{\α}}^2)}\]\frac{\mathrm{\Φ}(\mathrm{\ζ}/\sqrt{1+{\mathrm{\γ}}^2})}{\mathrm{\Φ}({\mathrm{\ξ}}_k/\sqrt{1+{\mathrm{\λ}}_k^2})}$

Wherein,

figure 1 gives vibration data for a bearing. Fig. 2 shows a comparison of the performance of the remaining life prediction of the two models from the 1800 th sampling instant to the 2300 th sampling instant, every 100 sampling instants. It is clear that the true remaining life value is covered by the remaining life distributions of both models. Also, with the increase in measurement data, some common phenomena can be observed for the two models: 1. the residual life distributions of the two models move to the direction of less residual life; 2. the peak values of the remaining life distributions of the two models become gradually higher; 3. the uncertainty of the remaining life prediction becomes gradually smaller. The results verify the effectiveness of the model, and in addition, the residual service life distribution obtained by the oblique wiener process model is more compact than that obtained by the Gaussian-wiener process model, which shows that the oblique wiener process model can provide more reliable information for the subsequent formulation of management decisions.

Claims (5)

1. An online prediction method for the residual life of electromechanical equipment under the condition of two-stage degradation is characterized in that: the actual degradation of the equipment is divided into two stages of normal degradation and accelerated degradation, the performance degradation process conforms to a self-adaptive oblique wiener process model, a two-stage parameter estimation algorithm is adopted for the parameters of the model, an iterative filtering algorithm is adopted to obtain the degradation state in real time, and after the degradation state estimation and the parameter estimation are finished, the residual life of the equipment is predicted by using the updated degradation drift state, the estimated parameters and the measured quantity; the method comprises the following specific steps:

step 1: establishing a performance degradation model describing equipment conforming to the two-stage degradation characteristics;

step 2: estimating a degraded hidden state by adopting an iterative filtering algorithm;

and step 3: estimating performance degradation model parameters on line;

and 4, step 4: and obtaining a probability distribution expression of the residual service life of the equipment.

2. The method for predicting the residual life of the electromechanical device under the condition of two-stage degradation according to claim 1, wherein: the specific steps of establishing a performance degradation model characterizing the equipment conforming to the two-stage degradation characteristics in the step 1 are as follows:

step 1.1: a device degradation model satisfying the two-stage degradation characteristic is expressed as follows:

η_k＝η_k-1+ν_k

_k＝η_k-1τ_k+αΒ(τ_k)

_k＝x_k-x_k-1

wherein, t_kAt the kth sampling instant, η_kIs t_kIs used for characterizing the degradation speed and satisfies a closed oblique gaussian distribution, and the probability density function f (η) is:

$f\left(\mathrm{\η}\right)=\mathrm{\φ}\left(\frac{\mathrm{\η}-\mathrm{\μ}}{\mathrm{\σ}}\right)\mathrm{\Φ}\[\mathrm{\λ}\left(\frac{\mathrm{\η}-\mathrm{\μ}}{\mathrm{\σ}}\right)+\mathrm{\ξ}\]/\[\mathrm{\σ}\mathrm{\Φ}\left(\frac{\mathrm{\ξ}}{\sqrt{1+{\mathrm{\λ}}^2}}\right)\]$

in the above formula, phi (DEG) is a probability density function of the standard Gaussian distribution, phi (DEG) is a cumulative distribution function of the standard Gaussian distribution, mu and sigma are a position parameter and a scale parameter respectively, ξ is a general parameter, lambda is a shape parameter, and v_kIs system white noise, and v_k～N(0,²) α is the diffusion coefficient, and α>0，τ_kIs the sampling time interval, and_k＝t_k-t_k-1，Β(τ_k) Is a standard brownian motion, andx_kcharacterizing the degradation degree of the device at the kth sampling moment;_kthe degradation degree increment of two adjacent sampling moments is obtained;

step 1.2: once the product starts to run, the monitoring system will start to run at t ═ { t ═ t₁,...,t_kIt is monitored for equipment state data, i.e. equipment degradation degree is Defining the historical degradation increment from the product to the kth sampling time as_1:k＝{₁,...,_k}，₁＝x₁。

3. The online prediction method of the remaining life of the electromechanical device under the condition of two-stage degradation according to claim 1, characterized in that: the specific steps of "estimating the degraded hidden state by using the iterative filtering algorithm" described in step 2 are as follows:

step 2.1: the degradation speed of the electromechanical equipment, namely the hidden degradation drift coefficient of the oblique wiener process model, and the initial state of the model satisfies the closed oblique Gaussian distribution, namelyCSN is closed oblique Gaussian distribution, and unknown parameters of an initial degradation drift state are obtained by fitting initial degradation data of similar products; further, the initial state of the apparatus is (₁|η₀)～N(η₀τ₁,α²τ₁) The unknown parameters are obtained by a maximum likelihood estimation method through historical degradation data and an initial degradation drift state obtained through estimation;

step 2.2: at the kth sampling instant, there is a degenerate hidden state satisfying the distribution

$\left({\mathrm{\η}}_{k-1}\right|{\mathrm{\δ}}_{1:k-1})~CSN({\mathrm{\μ}}_{k-1},{\mathrm{\σ}}_{k-1}^2,{\mathrm{\λ}}_{k-1},{\mathrm{\ξ}}_{k-1})$

With a degree of deterioration (_k|η_k-1,_1:k-1)～N(η_k-1τ_k,α²τ_k)。

Step 2.3: according to the obtained new measurement quantity, the degradation hidden state of the equipment satisfies a closed oblique Gaussian distribution

$\left({\mathrm{\η}}_{k-1}\right|{\mathrm{\δ}}_{1:k})~CSN({\widehat{\mathrm{\μ}}}_{k-1},{\widehat{\mathrm{\σ}}}_{k-1}^2,{\widehat{\mathrm{\λ}}}_{k-1},{\widehat{\mathrm{\ξ}}}_{k-1})$

Wherein,

step 2.4: the posterior distribution of degenerate hidden states is obeyed according to the result of step 2.3

$\left({\mathrm{\η}}_k\right|{\mathrm{\δ}}_{1:k})~CSN({\mathrm{\μ}}_k,{\mathrm{\σ}}_k^2,{\mathrm{\λ}}_k,{\mathrm{\ξ}}_k)$

Wherein

According to the four steps, the relation between the degradation degree prediction and the historical degradation data is established, and the hidden state can be updated in an iterative and real-time manner.

4. The method for predicting the residual life of the electromechanical device under the condition of two-stage degradation according to claim 1, wherein: the specific steps of the online estimation of the performance degradation model parameters in the step 3 are as follows:

step 3.1: according to the degradation data obtained by sampling, a log-likelihood function is constructed

$\ln f_{{\mathrm{\Δ}}_{2:k}|{\mathrm{\Δ}}_1}\left({\mathrm{\δ}}_{2:k}\right|{\mathrm{\δ}}_1)=\underset{i=2}{\overset{k}{\Σ}}{\mathrm{lnf}}_{{\mathrm{\Δ}}_i|{\mathrm{\Δ}}_{1:i-1}}\left({\mathrm{\δ}}_i\right|{\mathrm{\δ}}_{1:i-1})$

Step 3.2: after obtaining a new measurement, i.e. obtaining a conditional probability density function of the degree of degradation, the above equation is expanded to:

$\begin{array}{c}\ln f_{{\mathrm{\Δ}}_{2:k}|{\mathrm{\Δ}}_1}\left({\mathrm{\δ}}_{2:k}|{\mathrm{\δ}}_1\right)=\underset{i=2}{\overset{k}{\mathrm{\Σ}}}\left\{-\frac{1}{2}\ln \[2\mathrm{\π}\left({\mathrm{\τ}}_i^2{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2{\mathrm{\τ}}_i\right)\]-\frac{{\left({\mathrm{\δ}}_i-{\mathrm{\τ}}_i{\mathrm{\μ}}_{i-2}\right)}^2}{2\left({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2{\mathrm{\τ}}_i\right)}\right\}\\ +\underset{i=2}{\overset{k}{\mathrm{\Σ}}}\ln \mathrm{\Φ}\left\{\frac{{\mathrm{\λ}}_{i-2}{\mathrm{\σ}}_{i-2}\left({\mathrm{\δ}}_i-{\mathrm{\τ}}_i{\mathrm{\μ}}_{i-2}\right)+{\mathrm{\ξ}}_{i-2}\left({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2\right)}{\sqrt{\left({\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+{\mathrm{\τ}}_i^2{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2\right)\[{\mathrm{\τ}}_i{\mathrm{\σ}}_{i-2}^2+\left(1+{\mathrm{\λ}}_{i-2}^2\right)\left({\mathrm{\τ}}_i{\mathrm{\ϵ}}^2+{\mathrm{\α}}^2\right)\]}}\right\}\\ -\underset{i=2}{\overset{k}{\mathrm{\Σ}}}\ln \mathrm{\Φ}\left(\frac{{\mathrm{\ξ}}_{i-2}}{\sqrt{1+{\mathrm{\λ}}_{i-2}^2}}\right)\end{array}$

step 3.3: maximization by searching using numerical methodsThe parameter (c) of (c).

5. The online prediction method of the remaining life of the electromechanical device under the condition of two-stage degradation according to claim 1, characterized in that: the specific steps of obtaining the distribution expression of the remaining life of the equipment in the step 4 are as follows:

step 4.1: the first-pass time is used as a link for connecting the prediction of the degradation degree and the prediction of the residual life, namely, the random variable of the residual life is defined as L ═ inf { L: x (L + t)_k)>ω|X_1:kWhere l is the implementation of a random variable for remaining life, ω is a predefined threshold, X_1:kIs a historical measurement.

Step 4.2: the remaining lifetime distribution probability density function at the kth sampling instant is,

$f_{L|X_{1:k}}\left(l|X_{1:k}\right)=\frac{\mathrm{\ω}-x_k}{\sqrt{2{\mathrm{\πl}}^3({\mathrm{l\σ}}_k^2+{\mathrm{\α}}^2)}}\exp \[-\frac{{(\mathrm{\ω}-x_k-{\mathrm{\μ}}_{k}l)}^2}{2l({\mathrm{l\σ}}_k^2+{\mathrm{\α}}^2)}\]\frac{\mathrm{\Φ}(\mathrm{\ζ}/\sqrt{1+{\mathrm{\γ}}^2})}{\mathrm{\Φ}({\mathrm{\ξ}}_k/\sqrt{1+{\mathrm{\λ}}_k^2})}$

wherein,

therefore, a probability density function accurate expression of the online prediction of the residual life of the equipment is obtained and is used for online prediction of the residual life of the electromechanical equipment.