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1. Time-Dependent System Reliability Analysis With Second-Order Reliability Method

   https://doi.org/10.1115/1.4048732  

   Wu, Hao; Hu, Zhangli; Du, Xiaoping (March 2021, Journal of Mechanical Design)

   null (Ed.)

   Abstract System reliability is quantified by the probability that a system performs its intended function in a period of time without failures. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method using the envelope method and second-order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the second-order component reliability method with an improve envelope approach, which produces a component reliability index. The covariance between component responses is estimated with the first-order approximations, which are available from the second-order approximations of the component reliability analysis. Then, the joint distribution of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples. 

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2. System Reliability Analysis With Second Order Saddlepoint Approximation

   https://doi.org/10.1115/DETC2019-97561  

   Wu, Hao (January 2019, The ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   The second order saddlepoint approximation (SPA) has been used for component reliability analysis for higher accuracy than the traditional second order reliability method. This work extends the second order SPA to system reliability analysis. The joint distribution of all the component responses is approximated by a multivariate normal distribution. To maintain high accuracy of the approximation, the proposed method employs the second order SPA to accurately generate the marginal distributions of component responses; to simplify computations and achieve high efficiency, the proposed method estimates the covariance matrix of the multivariate normal distribution with the first order approximation to component responses. Examples demonstrate the high effectiveness of the second order SPA method for system reliability analysis. 

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3. System Reliability Analysis With Second-Order Saddlepoint Approximation

   https://doi.org/10.1115/1.4047217  

   Wu, Hao; Du, Xiaoping (December 2020, ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg)

   Abstract The second-order saddlepoint approximation (SOSPA) has been used for component reliability analysis for higher accuracy than the traditional second-order reliability method (SORM). This work extends the second-order saddlepoint approximation (SPA) to system reliability analysis. The joint distribution of all the component responses is approximated by a multivariate normal distribution. To maintain high accuracy of the approximation, the proposed method employs the second-order SPA to accurately generate the marginal distributions of the component responses; to simplify computations and achieve high efficiency, the proposed method estimates the covariance matrix of the multivariate normal distribution with the first-order approximation to the component responses. Examples demonstrate the high effectiveness of the second-order SPA method for system reliability analysis. 

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4. Recovering Missing Component Dependence for System Reliability Prediction via Synergy Between Physics and Data

   https://doi.org/10.1115/1.4052624  

   Li, Huiru; Du, Xiaoping (April 2022, Journal of Mechanical Design)

   Abstract Predicting system reliability is often a core task in systems design. System reliability depends on component reliability and dependence of components. Component reliability can be predicted with a physics-based approach if the associated physical models are available. If the models do not exist, component reliability may be estimated from data. When both types of components coexist, their dependence is often unknown, and therefore, the component states are assumed independent by the traditional method, which can result in a large error. This study proposes a new system reliability method to recover the missing component dependence, thereby leading to a more accurate estimate of the joint probability density function (PDF) of all the component states. The method works for series systems whose load is shared by its components that may fail due to excessive loading. For components without physical models available, the load data are recorded upon failure, and equivalent physical models are created; the model parameters are estimated by the proposed Bayesian approach. Then models of all component states become available, and the dependence of component states, as well as their joint PDF, can be estimated. Four examples are used to evaluate the proposed method, and the results indicate that the method can produce more accurate predictions of system reliability than the traditional method that assumes independent component states. 

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5. Envelope Method for Time- and Space-Dependent Reliability Prediction

   https://doi.org/10.1115/1.4054171  

   Wu, Hao; Du, Xiaoping (December 2022, ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg)

   Abstract Reliability can be predicted by a limit-state function, which may vary with time and space. This work extends the envelope method for a time-dependent limit-state function to a time- and space-dependent limit-state function. The proposed method uses the envelope function of time- and space-dependent limit-state function. It at first searches for the most probable point (MPP) of the envelope function using the sequential efficient global optimization in the domain of the space and time under consideration. Then the envelope function is approximated by a quadratic function at the MPP for which analytic gradient and Hessian matrix of the envelope function are derived. Subsequently, the second-order saddlepoint approximation method is employed to estimate the probability of failure. Three examples demonstrate the effectiveness of the proposed method. The method can efficiently produce an accurate reliability prediction when the MPP is within the domain of the space and time under consideration. 

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