Confidence statistical inference method for life data of mixed weibull distribution with uncertain prior knowledge
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TAIHANG NATIONAL LABORATORY
- Filing Date
- 2026-05-07
- Publication Date
- 2026-06-02
Smart Images
Figure CN122133825A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of reliability assessment and life prediction technology for key components of aero-engines, specifically to a confidence statistical inference method for life data based on hybrid Weibull distribution that integrates uncertain prior knowledge. Background Technology
[0002] Reliability assessment and life prediction of key aero-engine components are core bases for overall aircraft design and condition-based maintenance strategies. Comprehensive collection and analysis of failure data enables accurate identification of failure modes and mechanisms during the R&D and verification phases, providing a basis for the scientific selection of life distribution models. For high-reliability, long-life products, the amount of data generated in actual use is often insufficient for analysis needs. Therefore, truncated life tests are frequently used to shorten test time and accelerate data collection to obtain a sufficient number of truncated samples. In practical engineering, the probability density function of life data for key aero-engine components often exhibits a significant bimodal or multimodal shape due to the combined effects of multiple failure mechanisms. Hybrid Weibull distributions, by linearly superimposing multiple Weibull distributions with different parameters, can effectively characterize such complex failure processes dominated by multiple physical mechanisms due to their highly flexible distribution shape, thus providing a crucial theoretical tool for component reliability modeling and life assessment.
[0003] The statistical inference method for mixed Weibull distributions under traditional truncated lifetime experiments is mainly based on the classical probability and statistics framework. Its core idea is to iteratively optimize the truncated lifetime data containing missing information by using algorithms such as expectation maximization (EM). That is, by continuously maximizing the conditional expectation of the full likelihood function under the current observation data and parameter settings, the method gradually approaches the maximum value of the observation likelihood function, thereby achieving the estimation of lifetime distribution parameters.
[0004] However, in the actual engineering analysis of aero-engine components, life analysis of progressively truncated mixed Weibull distribution data faces severe challenges due to multiple uncertainties. Traditional statistical inference methods have the following limitations:
[0005] (1) Incomplete data and difficulty in identifying latent variables: In stepwise truncation experiments, the failure time of some samples is truncated and cannot be observed, resulting in a lack of information; at the same time, it is also impossible to directly observe which Weibull sub-distribution in the mixture distribution each sample belongs to. Although the traditional EM algorithm can estimate parameters through iterative expectation maximization, it cannot utilize the information of latent variables, which reduces the estimation accuracy, and the posterior probability estimation of latent variables is prone to getting trapped in local optima.
[0006] (2) Cognitive uncertainty is difficult to quantify and integrate: In practical engineering, prior knowledge such as sample category attribution and distribution parameters can be formed by relying on expert experience or historical data. However, such knowledge has significant cognitive uncertainty due to limited information sources and subjective judgment differences. Traditional probabilistic methods rely on the precise setting of prior distributions, which cannot effectively express and integrate this uncertainty caused by incomplete cognition. As a result, the estimation results in data-scarce scenarios rely too much on subjective assumptions and lack robustness.
[0007] (3) Insufficient ability to model multi-source uncertainty coupling: In the modeling of progressively truncated mixed distribution lifetime data, there are both objective uncertainties caused by the inherent randomness of the system (such as the randomness of sample failure) and subjective uncertainties caused by cognitive limitations. Traditional probabilistic frameworks treat the two together and can only describe randomness through probability distributions. They lack independent modeling and propagation mechanisms for cognitive uncertainty, making it difficult to separate, identify and comprehensively measure the two types of uncertainty sources, thus limiting the inference accuracy and decision reliability of the model in the context of multiple uncertainty coupling.
[0008] In summary, existing methods generally suffer from limitations such as being confined to traditional probabilistic frameworks, only being able to handle incomplete truncated lifetime data, and failing to effectively utilize uncertain prior knowledge that may exist in reality. This, to some extent, restricts the accuracy and generalization ability of model estimation. Therefore, there is currently a lack of a statistical inference method that can systematically integrate uncertain prior information, that is, fully utilize uncertain information about failure mechanisms in actual engineering, to improve the accuracy and robustness of inference. Summary of the Invention
[0009] In view of this, the embodiments of this application aim to address the problems existing in traditional statistical inference methods for mixed Weibull distribution data under progressive truncation, such as insufficient utilization of prior information, lack of uncertain knowledge fusion mechanisms, and limited estimation accuracy. This method provides a confidence statistical inference method for mixed Weibull distribution lifetime data that integrates uncertain prior knowledge. This method constructs a unified quantitative representation method for uncertain information in lifetime data and failure mechanism types, establishes a statistical modeling and parameter estimation mechanism based on multi-source information fusion, and effectively integrates uncertain prior information in failure mechanisms with observed truncation sample data. This significantly improves the parameter estimation accuracy and robustness of statistical inference for mixed Weibull distribution data under progressive truncation, and constructs a novel confidence statistical inference framework for lifetime assessment and failure mechanism analysis of high-reliability products such as aero-engines.
[0010] This application provides the following technical solution: a method for confidence statistical inference of lifetime data from a hybrid Weibull distribution that integrates uncertain prior knowledge, comprising the following steps: Step S1: Obtain the observed life data of key components of the aero-engine during the step-down life test, and obtain uncertain prior knowledge about the failure mechanism category and / or distribution parameters of the samples based on expert experience and / or historical data. Step S2: Construct a mixed Weibull distribution statistical model to fit the observed lifetime data, and make initial estimates of the key parameters of the model to obtain initial parameters for characterizing the lifetime distribution characteristics; Step S3: Based on the confidence function theory, perform a unified mathematical representation on the uncertain information in the observed lifetime data and the uncertain prior knowledge, and construct a confidence likelihood function to quantify the consistency between the model and the uncertain information; Step S4: Using the initial parameters as the starting point of the iteration, the confidence likelihood function is iteratively optimized using the framework of the expectation-maximization algorithm to solve for the maximum confidence likelihood estimate of the parameters of the mixed Weibull distribution statistical model. Step S5: Based on the maximum confidence likelihood estimate, construct the reliability function of the key components of the aero-engine and perform a reliability assessment.
[0011] According to one embodiment of this application, in step S3, based on confidence function theory, a unified mathematical representation is performed on the uncertain information in the observed lifetime data and the uncertain prior knowledge, specifically including: A profile function is introduced to quantify the uncertainty of missing lifetime information for unobserved samples, as well as the uncertainty of the failure mechanism category to which the sample belongs. Based on cognitive independence, the various profile functions are fused to obtain a unified profile function that represents the uncertainty of the total sample. The confidence likelihood function is constructed based on the unified profile function.
[0012] According to one embodiment of this application, step S4, which involves solving for the maximum confidence likelihood estimate of the parameters of the mixed Weibull distribution statistical model, specifically includes: E-step: Based on the current parameter estimates, calculate the conditional expectation of the complete data likelihood function to obtain the Q function; M-step: Update the parameter estimates by maximizing the Q-function; Repeat the E-step and M-step iteratively until the change in the parameter estimate is less than the preset convergence threshold, and output the current parameter estimate as the maximum confidence likelihood estimate.
[0013] According to one embodiment of this application, step S5, which involves constructing a reliability function for the key components of the aero-engine and performing a reliability assessment, further includes: Based on the asymptotic normality of the maximum confidence likelihood estimator, the Delta method is used to construct the confidence interval of the reliability function according to the covariance matrix of the parameter estimates, so as to quantify the statistical error of key life indicators.
[0014] According to one embodiment of this application, the hybrid Weibull distribution statistical model is constructed by linearly superimposing multiple Weibull distributions with different parameters, and is used to characterize complex failure processes dominated by multiple physical mechanisms.
[0015] According to one embodiment of this application, in step S2, the maximum likelihood estimation method or the moment estimation method is used to initially estimate the model parameters.
[0016] According to one embodiment of this application, step S5 further includes: identifying the main failure mechanism that dominates the failure of the key components of the aero-engine and the relative contribution of the mechanism by analyzing the mixed weight distribution in the maximum confidence likelihood estimator.
[0017] According to one embodiment of this application, in step S2, the key parameters include shape parameters, scale parameters, and mixing weights.
[0018] Compared with the prior art, the beneficial effects that at least one technical solution adopted in the embodiments of this specification can achieve include at least: (1) Achieving the fusion of prior knowledge: Traditional methods are limited by strict probability assumptions and are difficult to effectively utilize the uncertain prior information (such as expert experience, historical data, failure physics analysis results, etc.) that are widely present in engineering practice. This invention establishes a unified mathematical representation and fusion mechanism for uncertain prior information by introducing confidence function theory, realizing the systematic integration and effective utilization of multi-source uncertain knowledge, and significantly improving the information utilization efficiency and engineering applicability of the model.
[0019] (2) Enhanced processing capability of progressively truncated lifetime data: Due to the lack of information in progressively truncated lifetime data, the likelihood function construction of traditional methods often faces the problem of insufficient information utilization. The confidence likelihood inference criterion proposed in this invention enhances the model's adaptability to truncated data structures by extending the traditional likelihood function, and improves the accuracy and robustness of parameter estimation while maintaining statistical consistency.
[0020] (3) Improve the accuracy of identifying hybrid failure mechanisms: Traditional hybrid Weibull distribution parameter estimation methods are sensitive to initial values and are prone to large estimation biases in the overlapping areas of failure mechanisms. This invention effectively improves the identification accuracy of weights and hybrid distribution shape parameters and scale parameters by fusing uncertain prior information of failure mechanisms and combining them with an improved EM algorithm optimization strategy, especially enhancing the ability to analyze complex failure mechanisms.
[0021] (4) Enhanced interpretability of reliability inference results: This invention not only provides point estimates of parameters, but also quantifies the uncertainty in statistical inference by constructing interval estimates of reliability functions, providing a more complete statistical basis for lifetime prediction and reliability assessment, and significantly improving the reliability of engineering decision support.
[0022] In summary, this invention establishes a confidence statistical inference framework that integrates uncertain prior knowledge. While maintaining statistical rigor and model interpretability, it achieves more accurate and robust estimation of mixed Weibull distribution parameters under progressively truncated data, providing new theoretical tools to support the reliability assessment and life prediction of key components of aero-engines. Attached Figure Description
[0023] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0024] Figure 1 This is a schematic diagram of the confidence statistical inference process for hybrid Weibull distribution lifetime data that incorporates uncertain prior knowledge according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the solution of the maximum confidence likelihood estimator in an embodiment of the present invention. Detailed Implementation
[0025] The embodiments of this application will now be described in detail with reference to the accompanying drawings.
[0026] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0027] This invention provides a confidence statistical inference method for hybrid Weibull distribution lifetime data that integrates uncertain prior knowledge. This method achieves robust estimation and efficient solution of lifetime distribution parameters under progressively truncated conditions by constructing a quantitative expression model of uncertain information and a fusion mechanism of multi-source failure data. The main steps include: Step S1: Acquisition of lifetime data and prior knowledge Acquire observed lifetime data of key components (such as turbine blades, disks, shafts, etc.) of aero-engines during truncated lifetime tests, and based on expert experience and / or historical data, obtain the expression form and fusion rules of uncertain prior information about the failure mechanism category and / or distribution parameters of the samples.
[0028] Step S2: Construction and Fitting of the Hybrid Weibull Model A mixed Weibull distribution statistical model is constructed to fit the observed lifetime data, and the key parameters of the model are initially estimated to obtain initial parameters for characterizing the lifetime distribution characteristics. Specifically, a parameterized statistical model is constructed based on a hybrid Weibull distribution to fit the life observation dataset of key aero-engine components obtained through stepwise truncation, thereby acquiring key parameters characterizing the life distribution (including shape parameters, scale parameters, and hybrid weights). The obtained parameter estimation results are used as the initial values for subsequent iterative optimization algorithms, providing a stable computational basis for parameter convergence.
[0029] Step S3: Construction of the Uncertainty Characterization Framework and Confidence Likelihood Criterion Based on the confidence function theory, a unified mathematical representation is made of the uncertain information in the observed lifetime data and the uncertain prior knowledge, and a confidence likelihood function is constructed to quantify the consistency between the model and the uncertain information. Specifically, based on confidence function theory, a unified mathematical representation framework is constructed for uncertain lifetime information and prior knowledge of failure mechanisms. On this basis, a confidence likelihood inference criterion applicable to hybrid Weibull distribution lifetime data under progressively truncated conditions is proposed. The likelihood function is extended to... This criterion extends the traditional likelihood function by introducing a confidence function, establishing a statistical inference mechanism that includes uncertain prior information, thereby enabling the effective fusion and statistical utilization of multi-source uncertain knowledge.
[0030] Step S4: Solving the maximum confidence likelihood estimation Using the initial parameters as the starting point of the iteration, the confidence likelihood function is iteratively optimized using the framework of the expectation-maximization algorithm to solve for the maximum confidence likelihood estimate of the parameters of the mixed Weibull distribution statistical model. Specifically, based on the constructed confidence likelihood function of the progressively truncated mixed Weibull distribution lifetime data, the corresponding parameter estimates are obtained by maximizing this function. The EM algorithm framework is adopted, and the optimization process is implemented by alternately executing the expectation step (E-step) and the maximization step (M-step): in the E-step, the conditional expectation of the complete data likelihood function based on the current parameter values is calculated to obtain the Q function. In M steps, the expected function is maximized to find the update parameters at each iteration. , making By iterating multiple times until the convergence condition is met, robust estimates of the shape parameters, scale parameters, and mixing weights of the mixed Weibull distribution are finally obtained.
[0031] Step S5: Statistical property verification and reliability assessment Based on the maximum confidence likelihood estimate, a reliability function for the key components of the aero-engine is constructed, and a reliability assessment is performed.
[0032] Specifically, the proposed maximum confidence likelihood estimator is subjected to theoretical analysis and verification of its statistical properties, with a focus on examining its consistency and asymptotic normality. Based on the obtained parameter estimation results, interval estimates of the corresponding parameters are further constructed to provide uncertainty quantification support for statistical inference. On this basis, requirements for the use and maintenance strategies of key components are formulated, and system reliability analysis is carried out: utilizing the parameter estimation results and their statistical properties such as invariance, point estimation and interval estimation models of the reliability function are established to achieve a complete statistical description and reliability assessment of product life characteristics.
[0033] Through the above technical solutions, this invention constructs a confidence statistical inference framework that integrates uncertain prior knowledge and observed lifetime data, realizing robust parameter estimation and reliability analysis of hybrid Weibull distribution lifetime data under progressive truncation. It significantly improves the accuracy and robustness of lifetime data statistical inference, providing effective theoretical tools and engineering application support for lifetime prediction, reliability assessment and design optimization of key components of aero-engines.
[0034] like Figure 1 As shown, Figure 1 This invention demonstrates the overall process of confidence statistical inference for hybrid Weibull distribution lifetime data that integrates uncertain prior knowledge, including the main steps of lifetime data and prior knowledge acquisition, construction of a unified uncertainty characterization framework and confidence likelihood criterion, maximum confidence likelihood estimation solution, and verification of statistical properties and reliability assessment.
[0035] like Figure 2 As shown, Figure 2This paper presents a stepwise truncated mixed Weibull distribution confidence likelihood function constructed based on a contour function to uniformly represent two types of uncertainty. In confidence function theory, a series of confidence functions are defined, among which the two most commonly used functions are the confidence degree functions. and likelihood function , representing the total direct support and potential support of the current evidence for the proposition, respectively. The profile function: It is the value of the likelihood function at a single point.
[0036] Employing the EM algorithm framework, the expected step and maximization step are iteratively executed until convergence, maximizing the likelihood function of the complete data, and then approximately maximizing the confidence likelihood function, ultimately obtaining the maximum confidence likelihood estimate of the distribution parameters. This figure fully presents the complete solution process from representing uncertain information to parameter estimation. It demonstrates the core advantage of this invention in achieving a synergistic improvement in statistical inference accuracy and robustness in complex scenarios with uncertain prior information and incomplete lifetime data.
[0037] In specific implementation, the method and system architecture of this invention mainly include the following: (I) Overall System Structure like Figure 1 and Figure 2 As shown in this embodiment of the invention, the hybrid Weibull distribution lifetime data statistical inference system based on confidence function theory mainly consists of a lifetime data acquisition and preprocessing layer, an uncertainty information representation layer, a maximum confidence likelihood estimator solution module, and a reliability assessment module. The lifetime data acquisition and preprocessing layer is responsible for processing multi-source data such as failure time and failure mechanism type in stepwise truncated lifetime tests, and completing preprocessing such as data cleaning and standardization. The uncertainty information representation layer constructs a unified mathematical representation framework for uncertainty information in expert experience, historical information, and sample lifetime data using confidence function theory. The maximum confidence likelihood estimator solution module, based on the constructed confidence likelihood function, uses an improved EM algorithm to alternately execute expectation calculation and maximization steps until convergence, obtaining robust estimation results of the distribution parameters. The reliability assessment module uses the parameter estimation results to generate key indicators such as reliability function and failure probability density, completing the statistical description and uncertainty quantification of component lifetime characteristics. This system achieves multi-source information fusion through the uncertainty information representation layer, optimizes statistical inference through the maximum confidence likelihood estimation module, and forms a robust reliability analysis architecture under the reliability assessment module.
[0038] (II) Implementation of the Uncertain Information Representation Layer The uncertainty information representation layer, based on confidence function theory, provides a unified mathematical model for the multi-source uncertainties present in progressively truncated life tests. The experimental data includes two types of samples: one is a complete sample where the failure time was precisely observed. Secondly, truncated samples that were removed during the experiment and for which the specific failure time could not be observed. The uncertainties that the system needs to handle mainly cover two aspects: the uncertainty due to the lack of lifetime information for unobserved samples, and the uncertainty regarding the failure mechanism category to which the sample belongs. (Profile function) As a core tool in confidence function theory, it can quantify the degree of support for a specific proposition. The profile function is introduced to mathematically represent the two types of uncertain information mentioned above, based on cognitive independence—that is, new evidence about one variable does not change or affect existing knowledge of another independent variable. If we believe... and Having cognitive independence, then Based on this, the various contour functions are merged into a unified contour function that characterizes the uncertainty of the total sample: .
[0039] Furthermore, a confidence likelihood function is constructed as a measure of consistency between the statistical model and uncertain observed data. In subsequent inference, an optimization algorithm is used to find the parameter combination that maximizes the confidence likelihood function, which is then used as the final estimate of the distribution parameters, completing the entire inference process from the representation of uncertain information to parameter estimation.
[0040] (III) Implementation of the module for solving the maximum confidence likelihood estimator The core task of the maximum confidence likelihood estimator module is to find the parameter combination that maximizes the confidence likelihood function through an optimization algorithm. Since the confidence likelihood function contains latent variables and has a complex form, directly maximizing this function is very difficult. Therefore, based on the idea of the EM algorithm, the estimated parameters are updated through two iterative steps: E-step expectation calculation and M-step maximization, until the difference between the estimates of two iterations is less than a preset convergence threshold. In this algorithm, the threshold can be set to 10. -6 Alternatively, if the value is other sufficiently small and acceptable, the algorithm is considered convergent, and the output parameter value is used as the algorithm's estimate. This method approximates the maximization of the confidence likelihood function by calculating the expectation of the full likelihood function and iteratively optimizing it, given the current observations and parameters. Notably, the result obtained by calculating the expectation of the Q function in the E-step can be viewed as a combination of the probabilistic model of the observed data and the contour function of uncertain prior information under a synthesis rule within the theoretical framework of the confidence function. Using this synthesis rule, the estimation algorithm can effectively fuse information from the data and prior information.
[0041] (iv) Implementation of the reliability assessment module Based on parameter estimation results, the reliability assessment module constructs a complete probabilistic model with a mixed Weibull distribution to achieve statistical description and engineering interpretation of product life characteristics. First, based on converged shape parameters, scale parameters, and mixed weights, the module establishes a comprehensive life model including a probability density function, cumulative distribution function, and reliability function, forming a complete mathematical representation of multimodal failure characteristics. On this basis, through numerical integration and probabilistic calculations, it generates key reliability indicators such as reliability curves, failure rate functions, percentage lifetime, and mean lifetime, comprehensively describing the product's life characteristics at different service stages. Considering the uncertainty of parameter estimation, the module employs the Delta method. Uncertainty propagation analysis is conducted, and confidence intervals for the reliability function are constructed based on the parametric covariance matrix to quantify the statistical errors of key life indicators. Simultaneously, by analyzing the mixed weight distribution, the dominant failure mechanisms and their relative contributions are identified, revealing the impact patterns of different failure modes on overall reliability. Finally, the module outputs a comprehensive reliability assessment report through a visualization system, including a life distribution probability map, a failure mode analysis map, and a maintenance strategy recommendation map. This transforms statistical inference results into decision-making basis with clear engineering significance, providing comprehensive quantitative support for product design improvement, maintenance strategy optimization, and service safety assessment.
[0042] (V) Algorithm and Working Steps Step S1 (Acquisition of Lifetime Data and Prior Knowledge): Acquire lifetime data of key components of aero-engines under progressively truncated lifetime tests, acquire uncertain prior knowledge based on expert experience or historical data, and construct a dataset that integrates observational data and prior information.
[0043] Step S2 (Construction and Fitting of Mixed Weibull Distribution Model): Construct a mixed Weibull distribution statistical model, and use maximum likelihood estimation or moment estimation methods to fit the initial parameters to obtain preliminary estimates of shape parameters, scale parameters and mixing weights, providing initial values for subsequent confidence inference.
[0044] Step S3 (Unified Uncertainty Characterization and Confidence Likelihood Criterion Construction): Based on confidence function theory, construct profile functions for the uncertainties of unobserved lifetime data and failure mechanism categories. This is done using synthesis rules from confidence function theory, such as Dempster's synthesis rule. ; in By fusing uncertain information from multiple sources, a confidence likelihood function suitable for progressively truncated data is constructed.
[0045] Step S4 (Solving the Maximum Confidence Likelihood Estimation): The improved EM algorithm is used to iteratively optimize the confidence likelihood function: In the E-step, the conditional expectation of the complete data likelihood function is calculated based on the current parameters; in the M-step, the expectation function is maximized to update the parameter estimate. The maximum confidence likelihood estimate is output when the parameter change is less than the convergence threshold.
[0046] Step S5 (Statistical Property Verification and Reliability Assessment): Verify the statistical properties of the maximum confidence likelihood estimator, such as consistency and asymptotic normality. Based on the parameter estimation results, construct indicators such as reliability functions and failure probability densities. Combine uncertainty quantification to complete lifetime distribution modeling and comprehensive reliability assessment, providing statistical basis for engineering decisions.
[0047] This invention establishes a statistical modeling and parameter estimation mechanism based on multi-source information fusion, effectively integrating uncertain prior information and truncated observational sample data in failure mechanisms. This significantly improves the accuracy of parameter estimation and the robustness of statistical inference for mixed Weibull distribution data under progressive truncation, constructing a novel confidence-based statistical inference framework for life assessment and failure mechanism analysis of high-reliability products such as aero-engines. This invention is particularly applicable to reliability modeling and analysis of key components such as fuel metering valves, integrated drive generators, and hydraulic mechanical components of aero-engines under complex failure mechanisms and multiple uncertainties. It can be widely applied to life reliability verification, condition-based maintenance, and health management strategy formulation for key aero-engine components.
[0048] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for confidence statistical inference of lifetime data from a hybrid Weibull distribution that integrates uncertain prior knowledge, characterized in that, Includes the following steps: Step S1: Obtain the observed life data of key components of the aero-engine during the step-down life test, and obtain uncertain prior knowledge about the failure mechanism category and / or distribution parameters of the samples based on expert experience and / or historical data. Step S2: Construct a mixed Weibull distribution statistical model to fit the observed lifetime data, and make initial estimates of the key parameters of the model to obtain initial parameters for characterizing the lifetime distribution characteristics; Step S3: Based on the confidence function theory, perform a unified mathematical representation on the uncertain information in the observed lifetime data and the uncertain prior knowledge, and construct a confidence likelihood function to quantify the consistency between the model and the uncertain information; Step S4: Using the initial parameters as the starting point of the iteration, the confidence likelihood function is iteratively optimized using the framework of the expectation-maximization algorithm to solve for the maximum confidence likelihood estimate of the parameters of the mixed Weibull distribution statistical model. Step S5: Based on the maximum confidence likelihood estimate, construct the reliability function of the key components of the aero-engine and perform a reliability assessment.
2. The method according to claim 1, characterized in that, In step S3, based on confidence function theory, a unified mathematical representation is performed on the uncertain information in the observed lifetime data and the uncertain prior knowledge, specifically including: A profile function is introduced to quantify the uncertainty of missing lifetime information for unobserved samples, as well as the uncertainty of the failure mechanism category to which the sample belongs. Based on cognitive independence, the various profile functions are fused to obtain a unified profile function that represents the uncertainty of the total sample. The confidence likelihood function is constructed based on the unified profile function.
3. The method according to claim 1, characterized in that, In step S4, solving for the maximum confidence likelihood estimate of the parameters of the mixed Weibull distribution statistical model specifically includes: E-step: Based on the current parameter estimates, calculate the conditional expectation of the complete data likelihood function to obtain the Q function; M-step: Update the parameter estimates by maximizing the Q-function; Repeat the E-step and M-step iteratively until the change in the parameter estimate is less than the preset convergence threshold, and output the current parameter estimate as the maximum confidence likelihood estimate.
4. The method according to claim 1, characterized in that, Step S5, which involves constructing reliability functions for key components of the aero-engine and performing reliability assessments, also includes: Based on the asymptotic normality of the maximum confidence likelihood estimator, the Delta method is used to construct the confidence interval of the reliability function according to the covariance matrix of the parameter estimates, so as to quantify the statistical error of key life indicators.
5. The method according to claim 1, characterized in that, The hybrid Weibull distribution statistical model is constructed by linearly superimposing multiple Weibull distributions with different parameters, and is used to characterize complex failure processes dominated by multiple physical mechanisms.
6. The method according to claim 1, characterized in that, In step S2, the maximum likelihood estimation method or the method of moments is used to make initial estimates of the model parameters.
7. The method according to claim 1, characterized in that, Step S5 further includes: analyzing the mixed weight distribution in the maximum confidence likelihood estimator to identify the main failure mechanism that dominates the failure of the key components of the aero-engine and the relative contribution of the mechanism.
8. The method according to claim 1, characterized in that, In step S2, the key parameters include shape parameters, scale parameters, and mixing weights.