CN107480440B - Residual life prediction method based on two-stage random degradation modeling - Google Patents

Abstract

The invention discloses a residual life prediction method based on two-stage random degradation modeling, which belongs to the field of industrial monitoring and fault diagnosis and mainly comprises the following steps: performing off-line modeling, updating on-line parameters and predicting the residual life; wherein the offline modeling process comprises: collecting historical degradation data; obtaining a variable point estimation value of each group of degradation by utilizing maximum likelihood estimation, and obtaining the distribution characteristic of the variable point by utilizing statistical analysis; identifying two-stage degradation model parameters off line based on an expected maximization algorithm; taking the parameter estimation value obtained offline and the statistical characteristics of the variable point distribution as the prior information of online parameter updating; the online parameter estimation and the residual life prediction comprise the following steps: collecting degradation data on line; updating on line based on Bayesian theory model parameters; and estimating the residual life of the current operation equipment based on the updated parameters. The invention can model the degradation data with two-stage characteristics and accurately predict the residual life.

Description

A Remaining Life Prediction Method Based on Two-Stage Stochastic Degradation Modeling

technical field

The invention belongs to the field of industrial monitoring and fault diagnosis, and in particular relates to a remaining life prediction method based on two-stage stochastic degradation modeling.

Background technique

The remaining life prediction method refers to the use of historical and current operating data to estimate and predict the remaining operating time of equipment. Because this method can provide a theoretical basis for maintenance decisions and ensure the safe and reliable operation of equipment, it is a key issue in forecasting and health management technology, and has received extensive attention and in-depth research in recent years.

Due to the switching of external environmental stress and the change of the internal degradation mechanism, the degradation rate and fluctuation range of the equipment during operation are difficult to keep consistent. Therefore, the existing single-stage method is no longer applicable, and it is necessary to predict the remaining life of the equipment through a two-stage degradation model. In engineering practice, the degradation data are often non-monotonic, so the degradation model based on the two-stage Wiener process is more reasonable. However, in the existing two-order Wiener process degradation model, the analytical life probability density function and remaining life probability density function in the first sense have not been given, so that it is difficult to predict the remaining life online.

SUMMARY OF THE INVENTION

Aiming at the above technical problems existing in the prior art, the present invention proposes a remaining life prediction method based on two-stage degradation modeling, which has a reasonable design, overcomes the deficiencies of the prior art, and has good effects.

In order to achieve the above object, the present invention adopts the following technical solutions:

A remaining life prediction method based on two-stage stochastic degradation modeling, the method includes two parts: offline modeling, online parameter update and remaining life prediction, and specifically includes the following steps:

Step 1: Offline modeling process, including the following steps:

处共有m_i个退化数据；假设所有监测为等间隔监测，令Δt＝t_i,j-t_i,j-1；Step 1.1: Collect n battery historical degradation data, and establish a training data set X={X ₁ , X ₂ ,...,X _n }, where Indicates that the i-th battery is at time

There are m _i degradation data at the place; assuming that all monitoring is monitored at equal intervals, let Δt=t _i,j -t _i,j-1 ;

Step 1.2: Define the two-stage degradation model as follows:

以及

和

为正态分布的期望与方差，但对于每个单独样本，μ₁与μ₂为固定常数；Among them, μ ₁ and μ ₂ are the drift coefficients of the two-stage Wiener process model, and σ ₁ and σ ₂ are the diffusion parameters. In order to describe the differences between different samples, let

as well as

and

are the expectation and variance of the normal distribution, but μ ₁ and μ ₂ are fixed constants for each individual sample;

Step 1.3: Construct the log-likelihood function shown in formula (2) for each set of degraded data X={X ₁ , X ₂ ,...,X _n }, and obtain each The estimated value of the change point τ _i of the group degraded data, as shown in formula (3):

Among them, μ _i ,σ _i represent the drift and diffusion coefficients of the ith group of degradation models, X _i ∈{X ₁ ,X ₂ ,...,X _n }, x _i,j represent the jth in the ith group of degradation models degenerate value,

表示τ_i的估计值，并且通过统计分析得到变点的概率分布函数p(τ)；in,

Represents the estimated value of τ _i , and obtains the probability distribution function p(τ) of the change point through statistical analysis;

Step 1.4: Based on the discrete estimation parameters of the EM algorithm, the relationship between the iterative update of the parameters in the k+1 step and the estimated value in the k-th step is obtained as follows:

分别表示μ_1p，σ_1p，μ_2p，σ_2p，σ₁，σ₂在第k+1次迭代的估计值， in,

respectively represent the estimated values of μ _1p , σ _1p , μ _2p , σ _2p , σ ₁ , and σ ₂ at the k+1th iteration,

in

表示对中括号内取期望；in,

Indicates that expectations are taken within the square brackets;

Step 1.5: Iterate formula (4) and formula (5) continuously until all parameters converge, and the estimated parameter value at the time of convergence is the estimated value of the model parameter obtained offline, and the estimated value is used as the prior for subsequent online update. information;

Step 2: Online model update and remaining life prediction, including the following steps:

Step 2.1: Collect online degradation data of operating equipment, assuming that the current moment is t _κ , the corresponding degradation data is X _0:κ ={x ₀ ,x ₁ ,...,x _κ }, a total of κ+1 data;

Step 2.2: Change point detection based on maximum likelihood estimation, the method is as follows:

为变点时间τ的估计值；where x _i ∈{x ₀ ,x ₁ ,...,x _κ },

is the estimated value of the change point time τ;

那么说明到t_κ时刻为止变点尚未出现，则执行步骤2.3；反之，则说明变点出现了且变点为

则执行步骤2.5；If estimated

Then it means that the change point has not appeared until the time t _κ , and then go to step 2.3; otherwise, it means that the change point has occurred and the change point is

Then go to step 2.5;

Step 2.3: Based on Bayesian theory, use prior information to update the first-stage model parameters and change point probability distribution, as follows:

Among them, Pr( ) represents the occurrence probability of the event in parentheses, μ _1p,0 represents the expectation of the μ ₁ prior distribution, σ _{1p, 0} represents the standard deviation of the μ ₁ prior distribution;

Step 2.4: The online prediction results of the remaining life based on the two-stage degradation model under the random change point are as follows:

in, represents the probability density function of the remaining life at t _κ as _lκ , and p(τ) represents the probability distribution function of the change point;

in,

μ _a4 = μ _2p (l _κ -τ+t _κ ), μ _b4 =ξ-x _κ -μ _1p (τ-t _κ ),

Step 2.5: Based on Bayesian theory, use prior information to update the second-stage model parameters, as follows:

Among them, μ _2p,0 represents the expectation of the μ ₂ prior distribution, and σ _2p,0 represents the standard deviation of the μ ₂ prior distribution;

Step 2.6: Obtain the remaining life prediction results according to the single-stage degradation modeling method, as follows:

The core idea and principle of the present invention are:

The invention proposes a degradation model based on a two-stage Wiener process, and obtains the analytical representation of life and remaining life based on the first meaning of the model. Method for online parameter update.

Beneficial technical effects brought by the present invention:

Compared with the traditional single-stage degradation model, the two-stage model proposed in the present invention can better describe the degradation data of the two-stage degradation characteristics; secondly, compared with the existing two-stage Wiener process degradation model, the analytical remaining life is obtained in this paper. The prediction expression is more convenient for online calculation; thirdly, based on the EM algorithm and Bayesian theory, the offline model identification and online parameter estimation methods are respectively given, which can make full use of historical information and ensure online parameter update, reducing the calculation. complexity, improving the efficiency of online computing.

Description of drawings

FIG. 1 is a flowchart of offline model identification.

Figure 2 is a flow chart of online parameter update and remaining life prediction.

Figure 3 is a schematic diagram of the actual data of battery degradation.

Figure 4 is a schematic diagram of the parameter update result.

Figure 5 is a schematic diagram of remaining life prediction.

FIG. 6 is a schematic diagram showing the comparison between the predicted expected remaining life and the actual remaining life.

Detailed ways

The present invention is described in further detail below in conjunction with the accompanying drawings and specific embodiments:

In order to help understand the present invention and demonstrate its fault detection effect, an example is described in detail below. This example is based on the MATLAB tool, uses the actual battery degradation data to illustrate the present invention, and shows the effect of the present invention in conjunction with the accompanying drawings.

1. The flow of the offline modeling process is shown in Figure 1. The specific steps in this example are as follows:

Step 1.1: Collect four groups of battery degradation data as shown in Figure 3, and select three groups (CS2-35, CS2-37, CS2-38) for offline model identification;

Step 1.2: Define the two-stage degradation model as follows:

但对于每个单独样本而已，μ₁与μ₂为固定常数。Among them, in order to describe the differences between different samples, let as well as

But for each individual sample only, μ ₁ and μ ₂ are fixed constants.

Step 1.3: Construct the log-likelihood function shown in formula (2) for each set of degraded data X={X ₁ , X ₂ ,...,X _n }, and obtain each The estimated value of the change point τ _i of the group degraded data, as shown in formula (3):

然后最大化似然函数如下：in

Then the maximized likelihood function is as follows:

In this way, the estimated values of the change points are 623, 736, 753 (times), respectively. Assuming that the change point obeys the Poisson distribution, then the density parameter λ=704 of the Poisson distribution is obtained according to statistical analysis;

Step 1.4: Based on the EM algorithm, iterate repeatedly until the parameter estimates converge, and the final result is:

This result is used as prior information for subsequent online methods.

2. Online model update and remaining life prediction, the process is shown in Figure 2;

Step 2.1: Collect battery degradation data CS2-36;

Step 2.2: The change point detection method based on maximum likelihood estimation is as follows:

为变点时间τ的估计值。where x _i ∈{x ₀ ,x ₁ ,...,x _κ },

is the estimated value of the change point time τ.

那么说明到t_κ时刻为止变点尚未出现，则执行步骤2.3；反之，则说明变点出现了且变点为则执行步骤2.5；If estimated

Then it means that the change point has not appeared until the time t _κ , and then go to step 2.3; otherwise, it means that the change point has occurred and the change point is Then go to step 2.5;

Step 2.3: Update the first stage model parameters and change point probability distribution based on Bayesian theory as follows:

Among them, Pr(·) represents the probability of occurrence of the event in parentheses. μ _1p,0 represents the expectation of the μ ₁ prior distribution, and σ _{1p, 0} represents the standard deviation of the μ ₁ prior distribution.

Step 2.4: Online prediction of remaining life based on the two-stage degradation model under random change points. The results are as follows:

表示在t_κ剩余寿命为l_κ的概率密度函数，p(τ)表示变点的概率分布函数。in,

Represents the probability density function of the remaining life at t _κ as _lκ , and p(τ) represents the probability distribution function of the change point.

in

μ _a4 = μ _2p (l _κ -τ+t _κ ), μ _b4 =ξ-x _κ -μ _1p (τ-t _κ ),

Step 2.5: Update the model parameters of the second stage as follows:

where μ _2p,0 represents the expectation of the μ ₂ prior distribution, and σ _{2p, 0} represents the standard deviation of the μ ₂ prior distribution.

Step 2.6: According to the single-stage degradation modeling method, the remaining life prediction results are as follows:

According to the change point detection method described in step 2.2 and the parameter update algorithm described in steps 2.3 and 2.5, the parameter update result obtained when the change point discovery time is 681 (times) is shown in Figure 4;

Given that the failure prediction is 45% of the initial value, combining the parameter update results and the remaining life prediction methods described in steps 2.4 and 2.6, the remaining life prediction probability density function is obtained as shown in Figure 5, and Figure 6 is the residual life obtained by the method of the present invention. The life prediction expectation is compared with the actual life and the results based on the single-stage linear degradation model and the exponential degradation model.

It can be seen from the results of life prediction that the method of the present invention can accurately predict the remaining life of the battery.

Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the essential scope of the present invention should also belong to the present invention. the scope of protection of the invention.

Claims (1)

1. A residual life prediction method based on two-stage random degradation modeling is characterized in that: the method comprises two parts of off-line modeling, on-line parameter updating and residual life prediction, and specifically comprises the following steps:

step 1: the off-line modeling process specifically comprises the following steps:

step 1.1: collecting n battery historical degradation data, wherein the degradation data refers to the electric capacity of the battery, and establishing a training data set X ═ X₁,X₂,...,X_nTherein of

Indicates the ith battery at the moment

Has m at all_iA plurality of degradation data; let Δ t be t, assuming all monitoring is at equal intervals_i,j-t_i,j-1；

Step 1.2: the two-stage degradation model is defined as follows:

wherein, mu₁And mu₂The drift coefficient, σ, for a two-stage Wiener process model₁And σ₂For diffusion parameters, to describe the differences between different samples, let

And

and

is normally distributed expectation and variance, but for each individual sample, mu₁And mu₂Is a fixed constant;

step 1.3: for each set of degraded data X ═ X₁,X₂,...,X_nRespectively constructing log-likelihood functions shown in formula (2), and obtaining a variable point tau of each group of degradation data through maximum likelihood estimation_iAs shown in equation (3):

wherein, mu_i,σ_iRepresenting the drift and diffusion coefficients of the i-th degradation model, X_i∈{X₁,X₂,...,X_n}，x_i,jRepresenting the jth degradation value in the ith set of degradations,

wherein,

denotes τ_iAnd obtaining a probability distribution function p (tau) of the change point by statistical analysis;

step 1.4: based on the discrete estimation parameters of the EM algorithm, the relationship between the iterative update of the parameters in the (k + 1) th step and the estimated value in the k < th > step is obtained as follows:

wherein,

respectively represent mu_1p，σ_1p，μ_2p，σ_2p，σ₁，σ₂At the estimate of the (k + 1) th iteration,

wherein

Wherein,

indicates that the centering brackets are expected;

step 1.5: continuously iterating the formula (4) and the formula (5) until all parameters are converged, wherein the parameter estimation value during convergence is the model parameter estimation value obtained offline, and the estimation value is used as the prior information updated online later;

step 2: updating an online model and predicting the residual life, specifically comprising the following steps:

step 2.1: collecting the online degradation data of the battery, and assuming that the current time is t_κWith corresponding degraded data of X_0:κ＝{x₀,x₁,...,x_κA total of κ +1 datum;

step 2.2: the method for detecting the change point based on the maximum likelihood estimation comprises the following steps:

wherein x is_i∈{x₀,x₁,...,x_κ}，

Is an estimated value of the time of the change point tau;

if estimated to beThen explain to t_κExecuting step 2.3 if the change point does not appear until the moment; otherwise, the change point appears and is

Then step 2.5 is executed;

step 2.3: updating the first-stage model parameters and the variable point probability distribution by using prior information based on the Bayesian theory as follows:

wherein Pr (. cndot.) represents the probability of occurrence of an event in parentheses,. mu._1p,0Represents μ₁Expectation of a priori distribution, σ_1p,0Represents μ₁Standard deviation of prior distribution;

step 2.4: the online residual life prediction result based on the two-stage degradation model under the random change point is as follows:

wherein,

is shown at t_κResidual life of l_κP (τ) represents a probability distribution function of the change point;

wherein,

μ_a4＝μ_2p(l_κ-τ+t_κ),μ_b4＝ξ-x_κ-μ_1p(τ-t_κ),

step 2.5: updating the second-stage model parameters by using prior information based on Bayesian theory as follows:

wherein, mu_2p,0Represents μ₂Expectation of a priori distribution, σ_2p,0Represents μ₂Standard deviation of prior distribution;

step 2.6: obtaining a residual life prediction result according to a single-stage degradation modeling method, as follows:

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