Residual life prediction method considering prior credibility

Abstract

The invention relates to the technical field of reliability engineering, in particular to a residual life prediction method considering prior credibility, which comprises the following steps: S1, constructing conjugate prior distribution: modeling a degradation model parameter by adopting the conjugate prior distribution, and determining a hyper-parameter value of the prior distribution; s2, posterior weighted representation: representing posterior parameters of the degradation model as a weighted combination form of field observation information and prior information; s3, weight calibration based on credibility: the weight of the prior information in posterior distribution is calibrated; s4, posterior distribution updating: based on the calibrated weight, updating parameter posterior distribution in the degradation model to reflect actual characteristics of individual degradation behaviors, and performing residual life prediction by using the updated posterior distribution; according to the method, the prior credibility factor is introduced to carry out weighted updating on the degradation model parameters, so that the service life prediction accuracy and the modeling robustness under the condition that prior information is not completely reliable are improved.

Description

Technical Field

[0001] This invention relates to the field of reliability engineering technology, and in particular to a method for predicting remaining lifetime that takes into account prior confidence. Background Technology

[0002] With the rapid development of science and technology and the increasing complexity of industrial product structures, the degradation behavior of products during service is becoming more and more diversified, which puts forward higher requirements for their reliability modeling and life prediction. In order to improve the prediction accuracy, traditional reliability modeling methods usually rely on a large amount of prior information, such as accelerated degradation data, historical degradation data of the same model of products, etc., and use this prior information as the basis for modeling.

[0003] However, in practical applications, prior information may be inaccurate, incomplete, or have inconsistent data sources, which can easily lead to distortion of the prior model. In addition, when integrating prior and observational information, the classic Bayesian modeling method does not consider the credibility of the prior information itself. Regardless of the quality of the prior data, its influence weight on the posterior distribution is fixed. In scenarios where prior information is unreliable, this can easily lead to prediction bias and reduce the model's ability to characterize the real degradation process. Summary of the Invention

[0004] This invention provides a remaining lifetime prediction method that considers prior confidence. By introducing a confidence factor to weight and calibrate prior information, and combining it with field observation data to dynamically adjust the distribution of posterior parameters, it can more accurately reflect the actual degradation behavior of products and improve the accuracy and engineering applicability of reliability analysis and lifetime prediction.

[0005] A method for predicting remaining lifetime that considers prior confidence levels includes the following steps: S1, Constructing a conjugate prior distribution: To address the degradation differences between individual products, a conjugate prior distribution is used to model the degradation model parameters, and the hyperparameter values ​​of the prior distribution are determined. S2, Posterior weighted representation: The posterior parameters of the degradation model are represented as a weighted combination of field observation information and prior information; S3, Credibility Calibration Weight: Introducing a prior credibility coefficient to calibrate the weight of prior information in the posterior distribution; S4, Posterior Distribution Update: Based on the calibrated weights, update the posterior distribution of parameters in the degradation model to reflect the actual characteristics of individual degradation behavior, and use the updated posterior distribution to predict remaining lifespan.

[0006] Optionally, the construction of the conjugate prior distribution in S1 includes: S11, Determine the prior distribution form: Due to manufacturing and storage factors, products in the same batch vary. The differences in degradation parameters between individuals are described by the gamma distribution. The prior distribution is set as follows: ; in, a For shape parameters, b For drift parameters, β For the scale parameters in the gamma process. It is a gamma function; S12, Define the prior probability density function: Based on the gamma distribution, the prior probability density function is expressed as: ; in, This is the prior distribution function; S13, Construct the full likelihood function: The full likelihood function is used to estimate the hyperparameters of the prior distribution, expressed as: ; in, L Let the target likelihood function be defined. To estimate the prior hyperparameter values, These are the hyperparameter values ​​during each iteration. For the first i The measurement interval between each sample and the previous sample. For the first i Under the stress level, the first j The increment of a product performance measurement value N For the set number N One level of accelerating stress, n The first set at each stress level i One sample, It is a gamma function; S14, take the logarithm of the likelihood function: take the logarithm of the likelihood function to obtain the log-likelihood function; S15, Differentiation of the log-likelihood function: Perform differentiation; S16, gives the maximum likelihood estimate of the hyperparameters: the maximum likelihood estimate of the hyperparameters is calculated by taking the derivative; S17, Establish iterative update conditions: for Set a set of initial values ​​and iteratively update them, setting the current... The iteration stops when the difference between the new iteration value and the previous iteration value reaches the predetermined precision, and the final iteration value is set to the hyperparameter value of the prior distribution.

[0007] Optionally, the iterative update condition is expressed as: .

[0008] Optionally, the posterior weighted representation in S2 includes: S21, Define field observation data and measurement interval: Set the field-measured data and measurement interval time, where the field-measured data is... The measurement interval is Define the measurement interval and increment as follows: ; ; in, and For on-site data; S22, Bayesian derivation and parameter update of the posterior distribution: By combining field observation data with the gamma distribution using the Bayesian derivation method, the posterior distribution is derived, expressed as: in, Let be the posterior distribution function. and Let be the hyperparameter in the posterior distribution. This is prior information; S23, Update the posterior distribution parameters: Since the prior and posterior are conjugate, the updated posterior distribution parameters are expressed as follows: ; .

[0009] Optionally, the confidence calibration weights in S3 include: S31, Clarify the weighted composition of the posterior parameters: In the update of the posterior distribution parameters, the parameters... and All are obtained by weighted superposition of prior information and field-measured data, among which, In the calculation, For data measured on site, It is a priori hyperparameter estimation. In the calculation, For data measured on site, It is a priori hyperparameter estimation; S32, Introducing a credibility factor and reconstructing the weighting: Introducing a credibility factor B, and by adjusting the prior weights, suppressing unreliable prior information, resulting in a calibrated update of the posterior parameters, expressed as: ; .

[0010] Optionally, the posterior distribution update in S4 includes: S41, Calculate the posterior expectation as the distribution parameter: Let the degenerate parameter be... Combined with posterior parameters after confidence calibration and Calculate the posterior expectation, expressed as: ; in, It is the expected value of the assumed distribution; S42, Construct the probability density function of the degradation process: Substitute the expected value Given the probability density function, construct the probability density function of the product under degradation state; S43, Update the reliability function and lifetime expression: Based on the calibrated posterior parameters, derive and update the product's reliability function, lifetime distribution function, and expected lifetime function to achieve quantitative prediction of remaining lifetime.

[0011] Optionally, the probability density function of the product in the degradation state is expressed as: ; in, It is the probability density function after introducing prior confidence.

[0012] Optionally, the updated reliability function and lifetime expression in S43 include: Reliability function update: ; Where D is the product's failure threshold. It is the reliability function after introducing prior confidence; Lifetime distribution function update: ; in, It is the cumulative fault distribution function after introducing prior confidence; Expected lifetime function update: ; in, It is the product lifetime expression of the BS distribution after introducing prior confidence.

[0013] The beneficial effects of this invention are: This invention constructs a conjugate prior distribution and introduces a credibility factor to calibrate prior information. It can dynamically adjust the degree of influence of prior information based on the quality of the prior information source, overcoming the defect of traditional Bayesian modeling that cannot distinguish prior reliability. It improves the robustness and flexibility of parameter estimation in degenerate models and is suitable for reliability analysis scenarios with strong product heterogeneity and incompletely reliable priors.

[0014] This invention, by fusing field observation data with prior information weighted by reliability, updates the posterior distribution parameters of the degradation model and further derives the reliability function, lifetime distribution function, and lifetime expectation expression. This enables quantitative prediction of the remaining lifespan of a product, effectively improving prediction accuracy and providing important decision-making basis for product maintenance strategy formulation and lifecycle management. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the modeling method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the carbon film resistivity degradation data under accelerated stress at 83°C in Embodiment 8 of the present invention; Figure 3 This is a schematic diagram of the carbon film resistivity degradation data under accelerated stress at 133°C in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the carbon film resistivity degradation data under accelerated stress at 173°C in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the remaining lifetime without considering prior confidence in an embodiment of the present invention. Figure 6 This is a schematic diagram of the remaining lifetime considering prior confidence level in an embodiment of the present invention. Detailed Implementation

[0017] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Those skilled in the art may employ other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0018] like Figures 1-6 As shown, a method for predicting remaining lifetime considering prior confidence includes the following steps: 1. Construct the conjugate prior distribution of the products. Due to various factors such as manufacturing process and storage conditions, the degradation of different individuals within the same batch of products can vary slightly. A random parameter is often introduced to describe these individual differences. The conjugate prior distribution has good statistical properties in Bayesian statistical inference; therefore, the Gamma process assumes... ( β (The scale parameter in the gamma process) follows a gamma distribution, i.e.: ; in, a >0 represents the shape parameter. b >0 is a scale parameter. This is a gamma function.

[0019] Therefore, the prior probability density function can be obtained as follows: ; in, Let be the prior distribution function. and is the hyperparameter in the prior distribution.

[0020] To find the hyperparameter values ​​of the prior distribution, a total likelihood function is established: ; in, N For the set number N One level of accelerating stress, n The first set at each stress level i One sample, L Let the target likelihood function be defined. To estimate the prior hyperparameter values, These are the hyperparameter values ​​during each iteration. For the first i The measurement interval between each sample and the previous sample. For the first i Under the stress level, the first j The increment of a product performance measurement value This is a gamma function.

[0021] Take the logarithm of the total likelihood function: ; in, This is a gamma function.

[0022] Regarding the logarithmic expression Differentiate: ; in, It is the reciprocal of the gamma function multiplied by the derivative of the gamma function.

[0023] The maximum likelihood estimates of the hyperparameters are: ; ; ; for Set an initial set of values, and iteratively update them according to the above procedure. Set the current... The iteration stops when the difference between the new iteration value and the previous iteration value reaches a certain precision, and the final iteration value is set to the hyperparameter value of the prior distribution.

[0024] 2. Solving for the posterior distribution parameter update method. Assume... The data was measured on-site. It is the measurement interval time. , The posterior probability density can be obtained from Bayes' theorem: in, Let be the posterior distribution function. and Let be the hyperparameter in the posterior distribution. and For on-site data, α For shape parameters.

[0025] The prior probability density is: ; in, Let be the prior distribution function. and is the hyperparameter in the prior distribution.

[0026] Since the conjugate prior and posterior distributions do not change in form but only in parameters, the update method for the posterior distribution parameters can be obtained as follows: ; ; in, and is the hyperparameter in the posterior distribution.

[0027] 3. The weighted sum of posterior and prior information, through the update method of the posterior parameters, reveals the relationship between the parameters. The update formula is obtained by weighted addition of two parts, where These are prior hyperparameter estimates. This is on-site information; similarly, in parameters The updated formula is also obtained by weighted addition of two parts, where These are prior hyperparameter estimates. This is on-site information. The advantage of organizing the posterior distribution into a weighted sum of on-site and prior information is that the posterior information can be modified accordingly as the reliability of the prior information changes.

[0028] In classic Bayesian modeling, the reliability of prior data is not considered; regardless of the reliability level, the contribution of prior data to the posterior model is consistent. This invention addresses this shortcoming. Assuming the prior reliability is B, the posterior information update incorporating the prior data reliability is as follows: ; ; 4. Distribution update. As assumed previously... ,but The expectation is: ; in, It is the expected value of the distribution calculated in each iteration of the EM algorithm.

[0029] Will Substitute the expected value From the probability density function, we get: ; in, It is the probability density function after introducing prior confidence.

[0030] The reliability function is updated as follows: ; Where D is the product's failure threshold. It is the reliability function after introducing prior confidence.

[0031] Product lifespan The distribution function is updated as follows: ; in, It is the cumulative fault distribution function after introducing prior confidence.

[0032] ; in, It is the average lifespan of the product.

[0033] Product lifespan The expression is updated to: ; in, This is the product lifetime expression for the Black-Scholes distribution after introducing prior confidence. It is a function of time.

[0034] Case Study: The following will provide a case analysis of this invention. This case is merely to aid in understanding the invention and should not be construed as limiting its scope of application. It should be noted that any modifications and improvements made to the invention without actually departing from its concept are within the protection scope of this invention.

[0035] The parameters in the gamma process are set to random parameters to describe the differences between individuals, and when the model is a conjugate prior distribution, there is only a change in parameter values ​​between the posterior and the prior.

[0036] Based on the above, establish The degradation model, and .

[0037] in, a >0 represents the shape parameter. b >0 is a scale parameter. This is a gamma function.

[0038] The EM algorithm is used to estimate the hyperparameter values ​​in the prior distribution, and the total likelihood function is established: ; in, N For the set number N One level of accelerating stress, n The first set at each stress level i One sample, L Let the target likelihood function be defined. To estimate the prior hyperparameter values, These are the hyperparameter values ​​during each iteration. For the first i The measurement interval between each sample and the previous sample. For the first i Under the stress level, the first j The increment of each product performance measurement value.

[0039] ; in, This is a gamma function.

[0040] Obtain the estimator: ; ; ; in, It is the reciprocal of the gamma function multiplied by the derivative of the gamma function.

[0041] The update method for posterior parameters obtained through Bayesian inference is as follows: ; ; in, and is the hyperparameter in the posterior distribution.

[0042] Assumption a , b , α The initial value is a (0) , b (0) , α (0) ,go through k The value after the nth iteration is represented as a (k) , b (k) , α (k) E-step algorithm (solving) and (Expectations) ; ; in, It is the expected value of the assumed distribution. It is the expected value of the assumed logarithm of the distribution.

[0043] In step M, using Replacing the three estimators respectively Assuming that after k+1 After rounds of iteration, the hyperparameter values ​​reach convergence accuracy. , , As estimates of the hyperparameters of the prior distribution: ; ; ; The case study will use experimental data on a certain type of carbon film resistor in CSADT provided by Meeker et al. Figure 2 , Figure 3 , Figure 4 The data shown are the test data under three accelerated stresses: 83℃, 133℃, and 173℃.

[0044] The EM algorithm was used to analyze accelerated data at 83℃, and the results were obtained. The values ​​were 2.605, 0.118, 0.534, and 0.466, respectively. .

[0045] The degradation data of a single resistor obtained through simulation are shown in Table 1: Table 1 Simulation degradation data for a single resistor like Figure 5 The diagram shows the remaining lifetime without considering prior confidence. Assuming the product's failure threshold is 5, and without considering prior confidence, the parameters are estimated posteriorly. The parameter update process is shown in Table 2. Table 2. Posterior parameter estimation process without considering prior confidence level. like Figure 6 The diagram illustrates the remaining lifetime considering prior confidence level. Assuming the product's failure threshold is 5 and the prior data confidence level is 0.87, the parameters are estimated posteriorly, and the parameter update process is shown in Table 3. Table 3. Posterior parameter estimation process considering prior confidence level. Simulation results show that the time required for the resistance value to increase by 5% is 118,225 hours. The predicted lifetime results considering and not considering prior confidence are listed in Table 4.

[0046] Table 4. Predicted lifetimes before and after considering prior confidence level The accuracy of lifetime prediction without considering prior confidence is %. The accuracy of lifetime prediction considering prior confidence is [percentage missing]. .

[0047] Table 5. Accuracy and error before and after considering prior confidence. Based on experimental results, introducing prior confidence significantly improves the prediction accuracy in predicting the accelerated degradation lifetime of carbon film resistors. Without considering prior confidence, the predicted lifetime of parameter estimation is severely overestimated (e.g., the predicted value at the 25,000-hour observation point is 2.013 × 10⁻⁶). 6 The accuracy was only 5.91%, with an error rate as high as 94.09%, due to the lack of prior information with a confidence level of 0.87. However, after adding prior information with a confidence level of 0.87, the predicted value (e.g., 0.946 × 10⁻⁶) improved significantly. 5 The time to failure (in hours) is closer to the actual failure time of 118,225 hours, with the accuracy improved to 80.03% and the error reduced to 19.97%. Experiments have shown that the reasonable use of prior confidence can effectively correct the bias of posterior parameter estimation, greatly improve the reliability of lifetime prediction, and provide an important reference for the modeling and optimization of accelerated degradation tests in engineering.

[0048] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0049] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for predicting remaining lifetime considering prior confidence, characterized in that, Includes the following steps: S1, Constructing a conjugate prior distribution: To address the degradation differences between individual products, a conjugate prior distribution is used to model the degradation model parameters, and the hyperparameter values ​​of the prior distribution are determined. S2, Posterior weighted representation: The posterior parameters of the degradation model are represented as a weighted combination of field observation information and prior information; S3, Credibility Calibration Weight: Introducing a prior credibility coefficient to calibrate the weight of prior information in the posterior distribution; S4, Posterior Distribution Update: Based on the calibrated weights, update the posterior distribution of parameters in the degradation model to reflect the actual characteristics of individual degradation behavior, and use the updated posterior distribution to predict remaining lifespan.

2. The remaining lifetime prediction method considering prior confidence level according to claim 1, characterized in that, The construction conjugate prior distribution in S1 includes: S11, Determine the prior distribution form: Due to manufacturing and storage factors, products in the same batch vary. The differences in degradation parameters between individuals are described by the gamma distribution. The prior distribution is set as follows: ； in, a For shape parameters, b For drift parameters, β For the scale parameters in the gamma process. It is a gamma function; S12, Define the prior probability density function: Based on the gamma distribution, the prior probability density function is expressed as: ； in, This is the prior distribution function; S13, Construct the full likelihood function: The full likelihood function is used to estimate the hyperparameters of the prior distribution, expressed as: ； in, L Let the target likelihood function be defined. To estimate the prior hyperparameter values, These are the hyperparameter values ​​during each iteration. For the first i The measurement interval between each sample and the previous sample. For the first i Under the stress level, the first j The increment of a product performance measurement value N For the set number N One level of accelerating stress, n The first set at each stress level i One sample, It is a gamma function; S14, take the logarithm of the likelihood function: take the logarithm of the likelihood function to obtain the log-likelihood function; S15, Differentiation of the log-likelihood function: Perform differentiation; S16, gives the maximum likelihood estimate of the hyperparameters: the maximum likelihood estimate of the hyperparameters is calculated by taking the derivative; S17, Establish iterative update conditions: for Set a set of initial values ​​and iteratively update them, setting the current... The iteration stops when the difference between the new iteration value and the previous iteration value reaches the predetermined precision, and the final iteration value is set to the hyperparameter value of the prior distribution.

3. The remaining lifetime prediction method considering prior confidence level according to claim 2, characterized in that, The iterative update condition is expressed as follows: 。 4. The remaining lifetime prediction method considering prior confidence level according to claim 3, characterized in that, The posterior weighted representation in S2 includes: S21, Define field observation data and measurement interval: Set the field-measured data and measurement interval time, where the field-measured data is... The measurement interval is Define the measurement interval and increment as follows: ； ； in, and For on-site data; S22, Bayesian derivation and parameter update of the posterior distribution: By combining field observation data with the gamma distribution using the Bayesian derivation method, the posterior distribution is derived, expressed as: in, Let be the posterior distribution function. and Let be the hyperparameter in the posterior distribution. This is prior information; S23, Update the posterior distribution parameters: Since the prior and posterior are conjugate, the updated posterior distribution parameters are expressed as follows: ； 。 5. The remaining lifetime prediction method considering prior confidence level according to claim 4, characterized in that, The confidence calibration weights in S3 include: S31, Clarify the weighted composition of the posterior parameters: In the update of the posterior distribution parameters, the parameters... and All are obtained by weighted superposition of prior information and field-measured data, among which, In the calculation, For data measured on site, It is a priori hyperparameter estimation. In the calculation, For data measured on site, It is a priori hyperparameter estimation; S32, Introducing a credibility factor and reconstructing the weighting: Introducing a credibility factor B, and by adjusting the prior weights, suppressing unreliable prior information, resulting in a calibrated update of the posterior parameters, expressed as: ； 。 6. The remaining lifetime prediction method considering prior confidence level according to claim 5, characterized in that, The posterior distribution update in S4 includes: S41, Calculate the posterior expectation as the distribution parameter: Let the degenerate parameter be... Combined with posterior parameters after confidence calibration and Calculate the posterior expectation, expressed as: ； in, It is the expected value of the assumed distribution; S42, Construct the probability density function of the degradation process: Substitute the expected value Given the probability density function, construct the probability density function of the product under degradation state; S43, Update the reliability function and lifetime expression: Based on the calibrated posterior parameters, derive and update the product's reliability function, lifetime distribution function, and expected lifetime function to achieve quantitative prediction of remaining lifetime.

7. The remaining lifetime prediction method considering prior confidence level according to claim 6, characterized in that, The probability density function of the product in its degraded state is expressed as: ； in, It is the probability density function after introducing prior confidence.

8. The remaining lifetime prediction method considering prior confidence level according to claim 7, characterized in that, The updated reliability function and lifetime expression in S43 include: Reliability function update: ; Where D is the product's failure threshold. It is the reliability function after introducing prior confidence; Lifetime distribution function update: ; in, It is the cumulative fault distribution function after introducing prior confidence; Expected lifetime function update: ; in, It is the product lifetime expression of the BS distribution after introducing prior confidence.

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