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1. High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

   https://doi.org/10.1115/DETC2021-70067  

   Yin, Jianhua; Du, Xiaoping (August 2021, Proceedings of the ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference)

   Abstract Reliability analysis is usually a core element in engineering design, during which reliability is predicted with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high dimensional reliability analysis method by a new dimension reduction strategy so that the contributions of both important and unimportant input variables are accommodated by the proposed dimension reduction method. The consideration of the contributions of unimportant input variables can certainly improve the accuracy of the reliability prediction, especially where many unimportant input variables are involved. The dimension reduction is performed with the first iteration of the first order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis, such as the second order reliability analysis and metamodeling method, is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method, which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples. 

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2. Active learning with generalized sliced inverse regression for high-dimensional reliability analysis

   https://doi.org/10.1016/j.strusafe.2021.102151  

   Jianhua Yin, Xiaoping Du (October 2021, Structural safety)

   It is computationally expensive to predict reliability using physical models at the design stage if many random input variables exist. This work introduces a dimension reduction technique based on generalized sliced inverse regression (GSIR) to mitigate the curse of dimensionality. The proposed high dimensional reliability method enables active learning to integrate GSIR, Gaussian Process (GP) modeling, and Importance Sampling (IS), resulting in an accurate reliability prediction at a reduced computational cost. The new method consists of three core steps, 1) identification of the importance sampling region, 2) dimension reduction by GSIR to produce a sufficient predictor, and 3) construction of a GP model for the true response with respect to the sufficient predictor in the reduced-dimension space. High accuracy and efficiency are achieved with active learning that is iteratively executed with the above three steps by adding new training points one by one in the region with a high chance of failure. 

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3. A Safety Factor Method for Reliability-Based Component Design

   https://doi.org/10.1115/1.4049881  

   Yin, Jianhua; Du, Xiaoping (September 2021, Journal of Mechanical Design)

   null (Ed.)

   Abstract Reliability-based design (RBD) employs optimization to identify design variables that satisfy the reliability requirement. For many routine component design jobs that do not need optimization, however, RBD may not be applicable, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a modified RBD approach to component design so that the reliability target can be achieved by conducting traditional component design repeatedly using a deterministic safety factor. The new component design is based on the first-order reliability method (FORM), which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to several iterations of deterministic component design, the other additional work is the calculation of the derivatives of the design margin with respect to the random input variables. The proposed method can be used for a wide range of component design applications. For example, if a deterministic component design is performed manually or with a spreadsheet, so is the reliability-based component design. Three examples are used to demonstrate the practicality of the new design method. 

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4. 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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5. Time-Dependent System Reliability Analysis With Second Order Reliability Method

   https://doi.org/10.1115/DETC2020-22214  

   Wu, Hao; Du, Xiaoping (August 2020, 2020 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE))

   null (Ed.)

   Abstract System reliability is quantified by the probability that a system performs its intended function in a period of time without failure. 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 that uses the envelop 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 existing second order component reliability method, which produces component reliability indexes. The covariance between components responses are estimated with the first order approximations, which are available from the second order approximations of the component reliability analysis. Then the joint probability 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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