Device residual life prediction method and system based on dynamic calibration of degradation model

Abstract

The application relates to a device residual life prediction method and system based on dynamic calibration of a degradation model, and relates to the technical field of complexity engineering. The method comprises the following steps: updating model parameters of a degradation model by using a Bayesian theory and an EM algorithm to obtain a degradation model after parameter updating; predicting by using the degradation model after parameter updating according to monitoring data of device operation to obtain a degradation prediction value; constructing a degradation prediction error model according to the degradation prediction value and the monitoring data of device operation; calibrating the degradation model after updating according to the monitoring data of device operation and the degradation prediction error model to obtain multiple calibration degradation models; and determining a residual life prediction model by using the AIC (Akaike Information Criterion) according to the multiple calibration degradation models and predicting the residual life by using the residual life prediction model according to the monitoring data of device operation. The application considers individual differences of devices, dynamically calibrates the degradation model, and improves the accuracy of device residual life prediction.

Description

Technical Field

[0001] This invention relates to the field of complex engineering technology, and in particular to a method and system for predicting the remaining life of equipment based on dynamic calibration of a degradation model. Background Technology

[0002] With the continuous advancement of science and technology, increasingly complex, automated, and intelligent equipment has emerged in fields such as aerospace and military. Accurate lifespan determination for this equipment is a crucial prerequisite for maintaining its performance and conducting preventative maintenance. Traditional methods based on failure data are ineffective in predicting the lifespan of such equipment and struggle to characterize individual differences between devices. Therefore, lifespan prediction methods that employ different degradation models and real-time updates to model parameters are widely used.

[0003] Degradation models built based on historical degradation data for lifetime estimation cannot accurately describe the lifetime status of individual devices. To address this issue, Bayesian-based remaining lifetime prediction methods have been extensively studied. These methods typically use data from batch degradation tests of equipment as prior information and data from individual equipment operation or periodic testing as sample information. They utilize the Bayesian method to obtain posterior information for the parameters in the remaining lifetime prediction model of individual equipment, enabling accurate and real-time prediction of its remaining lifetime. Currently, there is a lack of research on establishing degradation prediction error models to compensate for degradation models and simultaneously dynamically calibrate the functional form and parameters of random degradation models of equipment, considering individual equipment differences. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for predicting the remaining life of equipment based on dynamic calibration of a degradation model. This method considers individual differences in equipment, dynamically calibrates the degradation model, and improves the accuracy of the remaining life prediction.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for predicting the remaining life of equipment based on dynamic calibration of a degradation model includes:

[0007] Acquire monitoring data of equipment operation and construct a degradation model based on the monitoring data and drift coefficient;

[0008] The model parameters of the degenerate model are updated using Bayesian theory and the EM algorithm to obtain the degenerate model with updated parameters.

[0009] Based on the monitoring data of the equipment operation, the degradation model updated with the parameters is used to make predictions and obtain the degradation prediction value;

[0010] A degradation prediction error model is constructed based on the degradation prediction value and the monitoring data of the equipment operation; the degradation prediction error model includes a multinomial regression model, a sine function model, and a nonlinear model;

[0011] The updated degradation model is calibrated based on the monitoring data of the equipment operation and the degradation prediction error model to obtain multiple calibrated degradation models;

[0012] Based on multiple calibration degradation models, the remaining lifetime prediction model is determined using the Akaike Information Criterion, and the remaining lifetime is predicted using the remaining lifetime prediction model based on the monitoring data of the equipment operation.

[0013] Optionally, updating the model parameters of the degenerate model using Bayesian theory and the EM algorithm to obtain the parameter-updated degenerate model specifically includes:

[0014] Based on the monitoring data of the equipment operation, the prior distribution is determined using Bayesian theory, and the log-likelihood function is determined based on the prior distribution.

[0015] Based on the monitoring data of the equipment operation and the log-likelihood function, the model parameters are estimated offline using the EM algorithm;

[0016] Based on the model parameters and the degradation model, the parameter-updated degradation model is obtained.

[0017] Optionally, the step of calibrating the parameter-updated degradation model based on the monitoring data of the device operation and the degradation prediction error model to obtain multiple calibrated degradation models specifically includes:

[0018] The degradation model updated with the parameters is compensated according to the degradation prediction error model to obtain the model calibrated in the form of a model function.

[0019] Based on the monitoring data of the equipment operation, the model parameters after calibration in the functional form are updated using Bayesian theory and EM algorithm to obtain multiple calibration degradation models.

[0020] Optionally, determining the remaining lifetime prediction model based on the Akaike information criterion using multiple calibration degradation models specifically includes:

[0021] The AIC values ​​of multiple calibration degradation models are calculated using the Akaike Information Criterion.

[0022] The calibration degradation model with the smallest AIC value is selected as the remaining lifetime prediction model.

[0023] A system for predicting the remaining life of equipment based on dynamic calibration of a degradation model includes:

[0024] The acquisition module is used to acquire monitoring data of equipment operation and construct a degradation model based on the monitoring data of equipment operation and the drift coefficient;

[0025] The update module is used to update the model parameters of the degenerate model using Bayesian theory and EM algorithm to obtain the degenerate model with updated parameters.

[0026] The degradation prediction value determination module is used to make predictions based on the monitoring data of the equipment operation and the degradation model updated by the parameters, so as to obtain the degradation prediction value.

[0027] A construction module is used to construct a degradation prediction error model based on the degradation prediction value and the monitoring data of the equipment operation; the degradation prediction error model includes a multinomial regression model, a sine function model, and a nonlinear model;

[0028] The calibration module is used to calibrate the parameter-updated degradation model based on the monitoring data of the device operation and the degradation prediction error model, so as to obtain multiple calibrated degradation models.

[0029] The remaining lifetime prediction module is used to determine the remaining lifetime prediction model based on the Akaike Information Criterion using multiple calibration degradation models, and to predict the remaining lifetime using the remaining lifetime prediction model based on the monitoring data of the equipment operation.

[0030] Optionally, the update module specifically includes:

[0031] The prior distribution and log-likelihood function determination unit is used to determine the prior distribution based on the monitoring data of the equipment operation using Bayesian theory and to determine the log-likelihood function based on the prior distribution.

[0032] The offline estimation model unit is used to estimate model parameters offline using the EM algorithm based on the monitoring data of the device operation and the log-likelihood function;

[0033] The updated degradation model determination unit is used to obtain a parameter-updated degradation model based on the model parameters and the degradation model.

[0034] Optionally, the calibration module specifically includes:

[0035] The compensation unit is used to compensate the parameter-updated degradation model according to the degradation prediction error model to obtain the model after calibration in the form of model function.

[0036] The update unit is used to update the parameters of the model after calibration in the model function form based on the monitoring data of the device operation using Bayesian theory and EM algorithm, so as to obtain multiple calibration degradation models.

[0037] Optionally, the remaining lifetime prediction module specifically includes:

[0038] A calculation unit is used to calculate the AIC values ​​of multiple calibration degradation models using the Akaike information criterion;

[0039] The selection unit is used to select the calibration degradation model with the smallest AIC value as the remaining lifetime prediction model.

[0040] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0041] This invention acquires monitoring data of equipment operation and constructs a degradation model based on the monitoring data and drift coefficients. The model parameters of the degradation model are updated using Bayesian theory and the EM algorithm to obtain an updated degradation model. A degradation prediction value is obtained by using the updated degradation model based on the monitoring data of equipment operation. A degradation prediction error model is constructed based on the predicted value and the monitoring data of equipment operation. The updated degradation model is calibrated based on the monitoring data of equipment operation and the degradation prediction error model to obtain multiple calibrated degradation models. A remaining lifetime prediction model is determined using the Akaike Information Criterion based on the multiple calibrated degradation models, and the remaining lifetime is predicted using the remaining lifetime prediction model based on the monitoring data of equipment operation. By considering the drift coefficient, which characterizes the individual differences of the equipment, in constructing the degradation model, and selecting the calibrated degradation model according to the Akaike Information Criterion, the remaining lifetime prediction is performed, thereby improving the accuracy of the remaining lifetime prediction. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 A schematic diagram illustrating the effect of charge-discharge cycles on lithium battery capacity provided by the present invention;

[0044] Figure 2 A schematic diagram illustrating the actual degradation trajectory and predicted degradation trajectory of lithium battery capacity provided by this invention;

[0045] Figure 3 A schematic diagram of the remaining lifetime results of the first model calibration provided by this invention;

[0046] Figure 4 A schematic diagram of the remaining lifetime results of the second model calibration provided by the present invention;

[0047] Figure 5 The flowchart of the device remaining life prediction method based on dynamic calibration of degradation model provided by the present invention is shown. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] The purpose of this invention is to provide a method and system for predicting the remaining life of equipment based on dynamic calibration of a degradation model. This method considers individual differences in equipment, dynamically calibrates the degradation model, and improves the accuracy of the remaining life prediction.

[0050] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] like Figure 5 As shown, the present invention provides a method for predicting the remaining life of equipment based on dynamic calibration of a degradation model, comprising:

[0052] Step 101: Obtain monitoring data of equipment operation and construct a degradation model based on the monitoring data of equipment operation and the drift coefficient.

[0053] Step 102: Update the model parameters of the degenerate model using Bayesian theory and the EM algorithm to obtain the degenerate model with updated parameters.

[0054] Step 102 specifically includes:

[0055] Based on the monitoring data of the equipment operation, the prior distribution is determined using Bayesian theory, and the log-likelihood function is determined based on the prior distribution; based on the monitoring data of the equipment operation and the log-likelihood function, the model parameters are estimated offline using the EM algorithm; based on the model parameters and the degradation model, the parameter-updated degradation model is obtained.

[0056] Step 103: Based on the monitoring data of the equipment operation, use the updated degradation model with the parameters to make a prediction and obtain the degradation prediction value.

[0057] Step 104: Construct a degradation prediction error model based on the degradation prediction value and the monitoring data of the equipment operation; the degradation prediction error model includes a multinomial regression model, a sine function model, and a nonlinear model.

[0058] Step 105: Based on the monitoring data of the equipment operation and the degradation prediction error model, calibrate the degradation model after parameter update to obtain multiple calibrated degradation models.

[0059] Step 105 specifically includes:

[0060] The degradation model updated with the parameters is compensated according to the degradation prediction error model to obtain the model calibrated in the form of a model function; the parameters of the model calibrated in the form of a model function are updated according to the monitoring data of the equipment operation using Bayesian theory and EM algorithm to obtain multiple calibrated degradation models.

[0061] Step 106: Determine the remaining lifetime prediction model using the Akaike Information Criterion based on multiple calibration degradation models, and predict the remaining lifetime using the remaining lifetime prediction model based on the monitoring data of the equipment operation. Specifically, determining the remaining lifetime prediction model using the Akaike Information Criterion based on multiple calibration degradation models includes: calculating the AIC value of multiple calibration degradation models using the Akaike Information Criterion; and selecting the calibration degradation model with the smallest AIC value as the remaining lifetime prediction model.

[0062] This invention also provides a specific processing flow for a method of predicting the remaining life of equipment based on dynamic calibration of a degradation model in practical applications. Utilizing current equipment degradation data and predicted degradation trends, and fully considering individual differences among equipment, the degradation model function is dynamically calibrated to solve for the remaining life distribution of the equipment. The steps are as follows:

[0063] (1) Establish a linear degradation model and use the degradation data of the current equipment to estimate and update the model parameters through Bayesian theory and EM algorithm.

[0064] Establishment of a degradation model

[0065] Let X(t) represent the device at time t. k The performance degradation at time t is based on the degradation process {X(t),t} of the diffusion process. k ≥0} can be represented as

[0066] X(t) = x0 + θt + σB(t) 0 < t ≤ t k (1)

[0067] In the formula, x0 represents the initial performance degradation of the equipment. To simplify the problem, we can assume x0 = 0, t is the equipment's operating time, and t0 = 0; θ is the drift coefficient, characterizing the individual variability of the equipment. We assume θ follows a mean of μ0 and a variance of... The normal distribution; σ is called the diffusion coefficient, σ>0; B(t) is the standard Brownian motion, and B(t)~N(0,t).

[0068] For the stochastic degradation model given in equation (1), the lifetime T of the equipment can be defined as follows in the sense of first arrival time:

[0069] T=inf{t:X(t)≥ωX(0)<ω}(2)

[0070] In the formula, lifespan T is a random variable; ω is the failure threshold of the equipment, which is usually determined by industry standards and expert experience.

[0071] So, for the device at the current monitoring time t k The degradation data obtained from monitoring is X(t) k )=x k Then X0: k ={x0,x1,x2,…,x k} represents the monitoring time t0, t1, t2, ..., t k The obtained equipment monitoring data, then the equipment at t k The remaining lifetime at time t is

[0072] L k =inf{l k :X(t k +l k )≥ω|X(t k )≤ω} (3)

[0073] In the formula, L k Indicates the device at t k The remaining lifetime at time t, the PDF representation of the remaining lifetime is as follows: The remaining lifespan PDF during equipment operation is estimated as follows:

[0074]

[0075] Where ω is the failure threshold of the device; x k For the equipment at t k The amount of degradation at any given time; l k For the equipment at t k The remaining time until the device fails; μ θ,k and The drift coefficient θ at monitoring time t are respectively k Expectation and variance.

[0076] Parameter estimation of degradation model

[0077] Online updating of random parameters based on Bayesian theory. Assume the drift coefficient θ follows a prior distribution p(θ) with the following distribution parameters: According to the properties of standard BM, for a given θ, X0: k ={x0,x1,x2,...,x k The sampling distribution of} is a multivariate normal distribution. According to Bayesian theory, in t k The posterior distribution of the time drift coefficient can be expressed as:

[0078]

[0079] Where p(X) 0:k |θ) represents the endpoint up to t k The joint distribution of real-time degradation information. According to the model description, X 0:k θ is a multivariate normal distribution, x j-1 For the equipment at monitoring time t j-1 The amount of degradation, t j Let J be the monitoring time of the device, where j = 1, 2, ..., k, and k is a non-zero positive integer. Therefore, according to the conjugate property, the posterior distribution of the drift coefficient θ still follows a normal distribution, expressed as p(θX). 0:k Its relevant parameters can be denoted as: The posterior estimation results can be obtained:

[0080]

[0081]

[0082] According to the normal distribution θX 0:k From its properties, we can know

[0083]

[0084] According to the above formula, we can obtain

[0085]

[0086] The posterior estimate of the drift coefficient θ can be updated when new observation data becomes available.

[0087] Offline estimation of model parameters is based on the EM algorithm. Using monitoring data from equipment operation, the hyperparameter μ in the prior distribution of the drift coefficient θ in the model is estimated. θ , And the diffusion coefficient σ is estimated. To understand the update characteristics of the model parameters over time, let... Indicates based on X0:k The model parameters mentioned above need to be estimated. This indicates the estimated result.

[0088] In order to monitor data X based on equipment operation 0:k Estimate Θ k First, calculate the complete log-likelihood function lnp(X). 0:k ,θΘ k ),Right now

[0089]

[0090] Given Indicates according to X 0:k The estimated value obtained at step i, lnp(X) 0:k ,θΘ k Expected value The following formula can be used for calculation:

[0091]

[0092] make achievable for:

[0093]

[0094]

[0095] The results obtained from equations (12) and (13) It is the only certainty, and in Place To obtain the maximum value.

[0096] (2) Based on the established linear degradation model, the degradation trend of the equipment is predicted. A degradation prediction error model driven by predicted and actual values ​​is proposed to be established and the function form of the degradation model is dynamically calibrated.

[0097] (3) Using the degradation data of the equipment, the model parameters are estimated and updated through Bayesian theory and EM algorithm. The optimal error model is selected using the AIC criterion, and the degradation model function form is calibrated. By repeating the above process, the function form and parameters of the random degradation model of the equipment are simultaneously dynamically calibrated.

[0098] Degradation prediction and dynamic model calibration

[0099] Using the model to monitor the operating equipment at future s monitoring times t k+1 ,t k+2 ,…,t k+s Degenerate state x k+1 ,x k+2 ,...,x k+sTo make predictions, that is At the same time, the equipment was obtained from t k+1 Time runs to t k+s The actual value of degradation at time X k+1 : k+s ={x k+1 ,x k+2 ,...,x k+s After that, it is proposed to base the degradation prediction error data e k+1:k+s ={e k+1 ,e k+2 ,...,e k+s},in A data-driven parameterized model of prediction error is established, and the functional form of the degenerate model is calibrated. The choice of the specific functional form depends on the characteristics of the error data. In practical applications, three commonly used error models are selected as follows.

[0100]

[0101] Where model M1 is a multinomial regression model, ε represents the randomness of the error data, and let... a0, a1, ..., a p Let p be a fixed parameter, and e0 be the initial error value. Model M2 is a sine function and model, where ε represents the randomness of the error data. Let... a i ,b i ,c i All parameters are fixed; e0 is the initial degradation value. Model M3 is a nonlinear model, where λ(t; β) is a nonlinear function of time t, used to characterize the nonlinearity of the error model, specifically expressed as λ(t; β) = bt. b-1 ; 'a' represents the randomness of the error data, which is assumed to follow an expectation of μ. a The variance is It follows a normal distribution.

[0102] Based on the above error model, the degradation model at t k+s Compensation is performed continuously to achieve dynamic calibration of the model function form of the random evolution process of the equipment, specifically expressed as:

[0103] X(t)=x k +θt-e(t)+σB(t),t k <t≤t k+s (15)

[0104] After calibration in the form of the model function, it is proposed to base the device on t k+1 Time to t k+s Time-degradation data X k+1:k+s ={x k+1 ,xk+2 ,...,x k+s The model parameters after functional calibration are estimated and updated using Bayesian theory and the EM algorithm.

[0105] Degradation model parameter estimation based on error model M1 and M2 compensation. The prior distributions of ε and θ in the model are normal distributions, and are expressed as... Where ρ k For parameters ε and θ in t k Correlation coefficient at time points.

[0106] Using the conjugate property of the normal distribution, we know that the joint posterior distribution of ε and θ is a normal distribution, which can be expressed as: Where ρ k+s For parameters ε and θ in t k+s The correlation coefficient at time points is then:

[0107]

[0108] Among them, e j For the operating equipment at monitoring time t j The prediction error between the predicted and actual degradation values; e j-1 For the operating equipment at monitoring time t j-1 The prediction error between the predicted and actual values ​​of degradation is denoted as j = k+1, k+2, ..., k+s.

[0109] We can obtain:

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] The EM algorithm is used to estimate the deterministic unknown parameters, and the unknown parameters σ after calibration of the degradation model are then used. 2 ,μ θ,k , μ ε,k , An estimate is made. This is to reflect the impact of monitoring data X. k+1:k+s Dependence and monitored data X k+1:k+s The essential characteristic of updating is that... Indicates t k+s Time based on X k+1:k+s The parameters that need to be estimated are... This indicates the final estimated result.

[0116] make Let represent the parameter estimate at step i in the EM algorithm. First, the complete likelihood function is expressed as:

[0117]

[0118] Furthermore, according to achievable

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] make achievable as follows:

[0125]

[0126]

[0127] Parameter estimation of the degradation model based on error model M3 compensation. The joint posterior distribution of the drift coefficient θ and the random error parameter a in the degradation model is updated using Bayesian theory. It is known that θ and a follow a bivariate Gaussian distribution. The device t is monitored. k+s After degenerate data at time t, the posterior distributions of θ and a can be obtained from the previous t. k+s Degradation data X at time point k+1:k+s ={x k+1 ,x k+2 ,...,x k+s The calculation yields the following result:

[0128] p(θ,a|X k+1:k+s )∝p(X k+1:k+s |θ,a)π k (θ,a) (26)

[0129] Where p(θ,a|X) k+1:k+s Given θ and a, the degenerate data X k+1:k+s ={x k+1 ,x k+2 ,...,x k+s The joint posterior distribution of}, and the prior distributions of θ and a are: Where ρ kFor parameters a and θ in t k Correlation coefficient at time points.

[0130] According to the derivation, we can obtain:

[0131]

[0132] in

[0133] Since we assume that the prior distributions of random parameters θ and a follow a bivariate Gaussian distribution, according to the conjugate property of the Gaussian distribution, the joint posterior distribution of θ and a is also a bivariate Gaussian distribution, denoted as θ = θa + ... Where ρ k+s For parameters a and θ in t k+s The correlation coefficient at time t, i.e.:

[0134]

[0135] Comparative expression and t k+s The parameters in the posterior distributions at times θ and a can be calculated using the following formula:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] in:

[0142]

[0143]

[0144] Based on the EM algorithm, deterministic parameter estimation of the error model M3 calibration degradation model is performed, which will estimate the unknown parameter σ of the model. 2 ,μ θ,k , μ a,k , The fixed parameter b in the error model is estimated. This reflects the effect of the monitoring data X... k+1:k+s Dependence and being X k+1:k+s The essential characteristic of updating is that... Indicates t k+s Time based on X k+1:k+s The parameters that need to be estimated are... This indicates the final estimated result.

[0145] make Let represent the parameter estimate at step i in the EM algorithm. First, the complete likelihood function is expressed as:

[0146]

[0147] Furthermore, according to We can obtain:

[0148]

[0149] make achievable as follows:

[0150]

[0151]

[0152] The maximum likelihood estimate based on the fixed parameter b in the error model can be obtained by maximizing the likelihood function using a two-dimensional search method.

[0153] For the three error models mentioned above, this paper uses the Akaike Information Criterion (AIC) to evaluate their performance and selects the optimal error model to compensate for the degradation model.

[0154] In general, AIC can be represented as:

[0155] AIC=2N-2ln(L) (38)

[0156] Where N is the number of model parameters and L is the likelihood function. Assuming the model error follows an independent normal distribution, let n be the number of observations and SSR (Sum Square of Residue) be the sum of squared residuals. Then AIC becomes: AIC = 2N + nln(SSR / n). The residuals are the differences between the actual observed values ​​and the estimated values. The model with the smallest AIC value is preferred to compensate for degenerate models.

[0157] (4) By obtaining the calibrated degradation model in the form of model function, solve for the remaining lifetime distribution and uncertainty quantification characterization.

[0158] Remaining life prediction

[0159] Based on the concept of first-arrival time, the remaining lifetime distribution of the equipment under dynamic calibration of the degradation model is solved. For the calibrated stochastic degradation model, based on the current time t... k+s Corresponding equipment degradation amount x k+s The stochastic degradation model can be further expressed as:

[0160] X(t)=x k+s +θ(tt k+s )-(e(t)-e(t k+s ))+σ(B(t)-B(t k+s ),t≥t k+s (39)

[0161] Furthermore, the time scale of this model is transformed into the residual time l k That is, remaining lifespan.

[0162] X(l k+s +t k+s )=x k+s +θl k+s -(e(l k+s +t k+s )-e(t k+s ))+σ(B(l k+s +t k+s )-B(t k+s ),t≥t k+s (40)

[0163] Based on the concept of first arrival time, the device t is defined. k+s The remaining lifetime at time L k+s =inf{l k+s :X(t k+s |l k+s )≥ω|X(t k+s )<ω}, L k+s The cumulative distribution function is expressed as This is to solve for the remaining lifetime distribution. The problem can be transformed into a degenerate process {X(t), t≥0} from x k+s The problem of solving for the time distribution of the first arrival at the time-varying boundary is expressed as:

[0164]

[0165] Among them l k+s =tt k+s ,W(l k+s )=B(l k+s +t k+s )-B(t k+s ),ν(l k+s )=θl k+s -(e(t k+s +l k+s )-e(t k+s )) is a time-varying function.

[0166] Remaining lifetime prediction based on the degradation model compensated for by error models M1 and M2. The posterior distribution p(θ,ε|X) estimated using the aforementioned Bayesian method is... k+1:k+s The updated remaining lifetime probability density function can be obtained using the law of total probability. They can be calculated using the following formulas respectively:

[0167]

[0168]

[0169]

[0170] After updating the parameters, X is obtained. k+1:k+s The PDF and CDF for the remaining lifetime estimate are as follows:

[0171]

[0172]

[0173] Remaining lifetime prediction of the degradation model based on error model M3 compensation. The PDF of the remaining lifetime estimate of the degradation model is as follows:

[0174]

[0175] Among them, the failure threshold ω describes the degradation process. k+s =ω-x k+s According to the formula, the analytical expression for the remaining lifetime PDF of the degradation model after calibration based on the error model M3 is as follows:

[0176]

[0177] in, In the final experimental verification of this invention, the error model M3 was selected only through the AIC criterion.

[0178] This invention starts with monitoring data from the start of equipment operation to the present moment. First, it establishes a linear stochastic process-based equipment degradation model, predicting degradation information for any future moment based on this model. Then, it establishes a data-driven degradation prediction error model based on predicted and actual data, calibrating the functional form of the degradation model. Next, based on the concept of first-arrival time, it derives the remaining lifetime distribution after the degradation model calibration. Finally, using lithium batteries as an example, experiments are conducted to verify the effectiveness of the proposed method.

[0179] The effectiveness of the proposed method is verified using capacity degradation data of lithium-ion batteries from NASA's Ames Prediction Center. This invention presents a degradation model-based remaining lifetime prediction method based on model calibration. The method records changes in battery state information, including capacity, over cycling. Due to complex aging mechanisms, the capacity of lithium-ion batteries decreases with charge-discharge cycles. Figure 1 The data presents the capacity degradation trends of four NASA lithium-ion batteries (sizes 5, 6, 7, and 18), showing a decrease in capacity with each cycle. Furthermore, significant fluctuations in the degradation process indicate that the degradation rate may vary.

[0180] Discharge data from battery No. 7 was randomly selected, and after appropriate transformations, the discharge process was calibrated twice using a model. First, battery capacity degradation data X from the initial monitoring point to the 81st monitoring point was selected. 0:81 ={x0,x1,x2,...,x 81 A linear stochastic degradation model was established, and the drift and diffusion coefficients in the model were estimated using Bayesian theory and the EM algorithm. Then, based on the parameter-updated degradation model, the degradation capacity of the lithium battery from the 82nd to the 142nd monitoring point was predicted. like Figure 1 As shown.

[0181] An error model between predicted and actual values ​​is established. Using the AIC criterion, the model with the smallest AIC value among the three degradation models is selected to calibrate the degradation model. Comparing Tables 1, 2, and 3, it can be seen that error model M3 has the smallest AIC value. Therefore, it is selected to compensate for the degradation model, and a new first degradation trajectory prediction is obtained, as shown below. Figure 1 As shown, it is closer to the actual degradation trajectory.

[0182] Table 1 Comparison results of error model M1

[0183]

[0184] Table 2 Comparison results of error model M2

[0185]

[0186] Table 3 Comparison results of error model M3

[0187]

[0188] Where SSE is the sum of squared errors; the smaller the SSE, the smaller the model fitting error and the better the model performance; R 2 To determine the coefficients, R 2 The larger the value, the better the model fit.

[0189] The lifetime prediction results are obtained based on the calibrated degradation model, such as Figure 2 and Figure 3 As shown, the PDF predicted by RUL gradually narrows over time, indicating that the uncertainty of the prediction is decreasing, which shows that the proposed method can achieve better prediction results in lifetime prediction.

[0190] Similarly, to further improve the accuracy of the degradation model, the degradation model was dynamically calibrated again using the same method as the first model calibration, and the remaining lifetime prediction results were obtained. Figure 2 As shown, after recalibrating the model, the predicted degradation trajectory is closer to the actual degradation trajectory. From Figure 4 As can be seen, the PDF of RUL after the second model calibration gradually becomes sharper, indicating that the uncertainty of RUL prediction for lithium batteries is gradually decreasing and the accuracy is getting higher and higher, indicating that further accurate prediction results have been achieved in terms of life prediction.

[0191] This invention relates to a method for predicting the remaining useful life (LUV) of complex equipment based on dynamic calibration of a degradation model. By utilizing equipment condition monitoring data and equipment prediction information, the method solves the problem of predicting the LUV of complex equipment. First, a model based on a linear stochastic process is used to characterize the equipment degradation process, and the model parameters are updated using Bayesian theory and the EM algorithm. Then, the established degradation model is used to predict the degradation trend at any future time. A degradation characteristic prediction error model driven by equipment prediction information and actual value data is proposed to calibrate the functional form of the degradation model. After the functional form of the degradation model is calibrated, the model parameters are estimated and updated using Bayesian theory and the EM algorithm. This process is repeated to achieve simultaneous dynamic calibration of the functional form and parameters of the stochastic degradation model of in-service equipment. Finally, based on the concept of first arrival time, the distribution of LUV and the uncertainty quantification characterization based on the dynamically calibrated degradation model are solved. A practical case study of lithium batteries demonstrates the superiority of this method. The results show that this method has higher LUV estimation accuracy and certain engineering practical value.

[0192] The present invention also provides a device remaining life prediction system based on dynamic calibration of a degradation model, comprising:

[0193] The acquisition module is used to acquire monitoring data of equipment operation and construct a degradation model based on the monitoring data of equipment operation and the drift coefficient.

[0194] The update module is used to update the model parameters of the degenerate model using Bayesian theory and the EM algorithm to obtain the degenerate model with updated parameters.

[0195] The degradation prediction value determination module is used to make predictions based on the monitoring data of the equipment operation and the degradation model updated by the parameters, so as to obtain the degradation prediction value.

[0196] A construction module is used to construct a degradation prediction error model based on the degradation prediction value and the monitoring data of the equipment operation; the degradation prediction error model includes a multinomial regression model, a sine function model, and a nonlinear model.

[0197] The calibration module is used to calibrate the parameter-updated degradation model based on the monitoring data of the device operation and the degradation prediction error model, so as to obtain multiple calibrated degradation models.

[0198] The remaining lifetime prediction module is used to determine the remaining lifetime prediction model based on the Akaike Information Criterion using multiple calibration degradation models, and to predict the remaining lifetime using the remaining lifetime prediction model based on the monitoring data of the equipment operation.

[0199] As an optional implementation, the update module specifically includes:

[0200] The prior distribution and log-likelihood function determination unit is used to determine the prior distribution based on the monitoring data of the equipment operation using Bayesian theory and to determine the log-likelihood function based on the prior distribution.

[0201] The offline estimation model unit is used to estimate model parameters offline using the EM algorithm based on the monitoring data of the device operation and the log-likelihood function.

[0202] The updated degradation model determination unit is used to obtain a parameter-updated degradation model based on the model parameters and the degradation model.

[0203] As an optional implementation, the calibration module specifically includes:

[0204] The compensation unit is used to compensate the parameter-updated degradation model according to the degradation prediction error model to obtain the model after calibration in the form of model function.

[0205] The update unit is used to update the parameters of the model after calibration in the model function form based on the monitoring data of the device operation using Bayesian theory and EM algorithm, so as to obtain multiple calibration degradation models.

[0206] As an optional implementation, the remaining lifetime prediction module specifically includes:

[0207] A calculation unit is used to calculate the AIC values ​​of multiple calibration degradation models using the Akaike Information Criterion.

[0208] The selection unit is used to select the calibration degradation model with the smallest AIC value as the remaining lifetime prediction model.

[0209] This invention focuses on complex and precision equipment and designs a method for predicting the remaining life of equipment based on dynamic calibration of a degradation model. First, a degradation model based on a linear stochastic process is established to predict the equipment's value at any future moment. Then, a data-driven parameterized model of the degradation prediction error is established based on predicted and actual information. The functional form of the degradation model is calibrated, and the model parameters are estimated based on Bayesian theory and the EM algorithm. The optimal error model is selected according to the AIC criterion. Finally, based on the concept of first-arrival time, the remaining life distribution based on dynamic calibration of the degradation model is obtained.

[0210] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0211] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for predicting the remaining life of equipment based on dynamic calibration of a degradation model, characterized in that, include: Acquire monitoring data of equipment operation and construct a degradation model based on the monitoring data and drift coefficient; The model parameters of the degenerate model are updated using Bayesian theory and the EM algorithm to obtain the degenerate model with updated parameters. Based on the monitoring data of the equipment operation, the degradation model updated with the parameters is used to make predictions and obtain the degradation prediction value; A degradation prediction error model is constructed based on the degradation prediction value and the monitoring data of the equipment operation; the degradation prediction error model includes a multinomial regression model, a sine function model, and a nonlinear model; The process of calibrating the parameter-updated degradation model based on the monitoring data of the equipment operation and the degradation prediction error model to obtain multiple calibrated degradation models specifically includes: compensating the parameter-updated degradation model based on the degradation prediction error model to obtain a model calibrated in model function form; and updating the parameters of the model calibrated in model function form using Bayesian theory and the EM algorithm based on the monitoring data of the equipment operation to obtain multiple calibrated degradation models. Based on multiple calibration degradation models, the remaining lifetime prediction model is determined using the Akaike Information Criterion, and the remaining lifetime is predicted using the remaining lifetime prediction model based on the monitoring data of the equipment operation.

2. The method for predicting remaining equipment life based on dynamic calibration of a degradation model according to claim 1, characterized in that, The process of updating the model parameters of the degenerate model using Bayesian theory and the EM algorithm to obtain the parameter-updated degenerate model specifically includes: Based on the monitoring data of the equipment operation, the prior distribution is determined using Bayesian theory, and the log-likelihood function is determined based on the prior distribution. Based on the monitoring data of the equipment operation and the log-likelihood function, the model parameters are estimated offline using the EM algorithm; Based on the model parameters and the degradation model, the parameter-updated degradation model is obtained.

3. The method for predicting remaining equipment life based on dynamic calibration of a degradation model according to claim 1, characterized in that, The step of determining the remaining lifetime prediction model based on multiple calibration degradation models using the Akaike information criterion specifically includes: The AIC values ​​of multiple calibration degradation models are calculated using the Akaike Information Criterion. The calibration degradation model with the smallest AIC value is selected as the remaining lifetime prediction model.

4. A system for predicting the remaining life of equipment based on dynamic calibration of a degradation model, characterized in that, include: The acquisition module is used to acquire monitoring data of equipment operation and construct a degradation model based on the monitoring data of equipment operation and the drift coefficient; The update module is used to update the model parameters of the degenerate model using Bayesian theory and EM algorithm to obtain the degenerate model with updated parameters. The degradation prediction value determination module is used to make predictions based on the monitoring data of the equipment operation and the degradation model updated by the parameters, so as to obtain the degradation prediction value. A construction module is used to construct a degradation prediction error model based on the degradation prediction value and the monitoring data of the equipment operation; the degradation prediction error model includes a multinomial regression model, a sine function model, and a nonlinear model; The calibration module is used to calibrate the parameter-updated degradation model based on the monitoring data of the device operation and the degradation prediction error model, so as to obtain multiple calibrated degradation models. The calibration module specifically includes: a compensation unit, used to compensate the parameter-updated degradation model according to the degradation prediction error model to obtain a model calibrated in model function form; and an update unit, used to update the parameters of the model calibrated in model function form according to the monitoring data of the equipment operation using Bayesian theory and EM algorithm to obtain multiple calibration degradation models. The remaining lifetime prediction module is used to determine the remaining lifetime prediction model based on the Akaike Information Criterion using multiple calibration degradation models, and to predict the remaining lifetime using the remaining lifetime prediction model based on the monitoring data of the equipment operation.

5. The equipment remaining life prediction system based on dynamic calibration of a degradation model according to claim 4, characterized in that, The update module specifically includes: The prior distribution and log-likelihood function determination unit is used to determine the prior distribution based on the monitoring data of the equipment operation using Bayesian theory and to determine the log-likelihood function based on the prior distribution. The offline estimation model unit is used to estimate model parameters offline using the EM algorithm based on the monitoring data of the device operation and the log-likelihood function; The updated degradation model determination unit is used to obtain a parameter-updated degradation model based on the model parameters and the degradation model.

6. The equipment remaining life prediction system based on dynamic calibration of a degradation model according to claim 4, characterized in that, The remaining lifetime prediction module specifically includes: A calculation unit is used to calculate the AIC values ​​of multiple calibration degradation models using the Akaike information criterion; The selection unit is used to select the calibration degradation model with the smallest AIC value as the remaining lifetime prediction model.

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