To accomplish the reliability analyses of the correlation of multi-analytical objectives,an innovative framework of Dimensional Synchronous Modeling(DSM)and correlation analysis is developed based on the stepwise mode...To accomplish the reliability analyses of the correlation of multi-analytical objectives,an innovative framework of Dimensional Synchronous Modeling(DSM)and correlation analysis is developed based on the stepwise modeling strategy,cell array operation principle,and Copula theory.Under this framework,we propose a DSM-based Enhanced Kriging(DSMEK)algorithm to synchronously derive the modeling of multi-objective,and explore an adaptive Copula function approach to analyze the correlation among multiple objectives and to assess the synthetical reliability level.In the proposed DSMEK and adaptive Copula methods,the Kriging model is treated as the basis function of DSMEK model,the Multi-Objective Snake Optimizer(MOSO)algorithm is used to search the optimal values of hyperparameters of basis functions,the cell array operation principle is adopted to establish a whole model of multiple objectives,the goodness of fit is utilized to determine the forms of Copula functions,and the determined Copula functions are employed to perform the reliability analyses of the correlation of multi-analytical objectives.Furthermore,three examples,including multi-objective complex function approximation,aeroengine turbine bladeddisc multi-failure mode reliability analyses and aircraft landing gear system brake temperature reliability analyses,are performed to verify the effectiveness of the proposed methods,from the viewpoints of mathematics and engineering.The results show that the DSMEK and adaptive Copula approaches hold obvious advantages in terms of modeling features and simulation performance.The efforts of this work provide a useful way for the modeling of multi-analytical objectives and synthetical reliability analyses of complex structure/system with multi-output responses.展开更多
Most reliability studies assume large samples or independence among components,but these assump-tions often fail in practice,leading to imprecise inference.We address this issue by constructing confidence intervals(CI...Most reliability studies assume large samples or independence among components,but these assump-tions often fail in practice,leading to imprecise inference.We address this issue by constructing confidence intervals(CIs)for the reliability of two-component systems with Weibull distributed failure times under a copula-frailty framework.Our construction integrates gamma-distributed frailties to capture unobserved heterogeneity and a copula-based dependence structure for correlated failures.The main contribution of this work is to derive adjusted CIs that explicitly incorporate the copula parameter in the variance-covariance matrix,achieving near-nominal coverage probabilities even in small samples or highly dependent settings.Through simulation studies,we show that,although traditional methods may suffice with moderate dependence and large samples,the proposed CIs offer notable benefits when dependence is strong or data are sparse.We further illustrate our construction with a synthetic example illustrating how penalized estimation can mitigate the issue of a degenerate Hessian matrix under high dependence and limited observations,so enabling uncertainty quantification despite deviations from nominal assumptions.Overall,our results fill a gap in reliability modeling for systems prone to correlated failures,and contribute to more robust inference in engineering,industrial,and biomedical applications.展开更多
基金co-supported by the National Natural Science Foundation of China(Nos.52405293,52375237)China Postdoctoral Science Foundation(No.2024M754219)Shaanxi Province Postdoctoral Research Project Funding,China。
文摘To accomplish the reliability analyses of the correlation of multi-analytical objectives,an innovative framework of Dimensional Synchronous Modeling(DSM)and correlation analysis is developed based on the stepwise modeling strategy,cell array operation principle,and Copula theory.Under this framework,we propose a DSM-based Enhanced Kriging(DSMEK)algorithm to synchronously derive the modeling of multi-objective,and explore an adaptive Copula function approach to analyze the correlation among multiple objectives and to assess the synthetical reliability level.In the proposed DSMEK and adaptive Copula methods,the Kriging model is treated as the basis function of DSMEK model,the Multi-Objective Snake Optimizer(MOSO)algorithm is used to search the optimal values of hyperparameters of basis functions,the cell array operation principle is adopted to establish a whole model of multiple objectives,the goodness of fit is utilized to determine the forms of Copula functions,and the determined Copula functions are employed to perform the reliability analyses of the correlation of multi-analytical objectives.Furthermore,three examples,including multi-objective complex function approximation,aeroengine turbine bladeddisc multi-failure mode reliability analyses and aircraft landing gear system brake temperature reliability analyses,are performed to verify the effectiveness of the proposed methods,from the viewpoints of mathematics and engineering.The results show that the DSMEK and adaptive Copula approaches hold obvious advantages in terms of modeling features and simulation performance.The efforts of this work provide a useful way for the modeling of multi-analytical objectives and synthetical reliability analyses of complex structure/system with multi-output responses.
基金supported by the Colombian government through COLCIENCIA scholarships,National Doctoral Program,Call 727 of 2015C.Castro gratefully acknowledges partial financial support from the Centro de Matematica da Universidade do Minho(CMAT/UM),through UID/00013V.Leiva acknowledges funding from the Agencia Nacional de Investigacion y Desarrollo(ANID)of the Chilean Ministry of Science,Technology,Knowledge and Innovation,through FONDECYT project grant 1200525.
文摘Most reliability studies assume large samples or independence among components,but these assump-tions often fail in practice,leading to imprecise inference.We address this issue by constructing confidence intervals(CIs)for the reliability of two-component systems with Weibull distributed failure times under a copula-frailty framework.Our construction integrates gamma-distributed frailties to capture unobserved heterogeneity and a copula-based dependence structure for correlated failures.The main contribution of this work is to derive adjusted CIs that explicitly incorporate the copula parameter in the variance-covariance matrix,achieving near-nominal coverage probabilities even in small samples or highly dependent settings.Through simulation studies,we show that,although traditional methods may suffice with moderate dependence and large samples,the proposed CIs offer notable benefits when dependence is strong or data are sparse.We further illustrate our construction with a synthetic example illustrating how penalized estimation can mitigate the issue of a degenerate Hessian matrix under high dependence and limited observations,so enabling uncertainty quantification despite deviations from nominal assumptions.Overall,our results fill a gap in reliability modeling for systems prone to correlated failures,and contribute to more robust inference in engineering,industrial,and biomedical applications.
