Abstract
Reliability theory is the core basis of engineering design, mainly including forward reliability theory and inverse reliability theory. Forward reliability theory is used to obtain the reliability index using the known design parameters, that is, it is a mapping function that translates the design parameters to the reliability index. Inverse reliability theory is used to obtain the design parameters using the known reliability index, that is, it is a mapping function that translates the reliability index to the design parameters. In other words, forward reliability theory and inverse reliability theory together constitute a method of dual mapping, which is the specific application of symmetry theory in the reliability field. In this paper, a new inverse reliability analysis method is proposed, which can satisfy the requirements of the target reliability index while obtaining the design parameters, without additional calculation and verification of reliability. The method simplifies the reliability inverse problem to the problem of the nonlinear equation, which is solved by identifying the design parameters, and finally obtains the design parameters by iterating the reliability index for each design parameter to gradually approach the target reliability index. For high-dimension and complex problems, the Levenberg–Marquardt method is introduced to avoid the problem of sensitivity to initial values and iterative divergence when identifying the design parameters. The implicit limit state function problem is solved by the interactive operation between ANSYS software and MATLAB software using finite element theory. The accuracy of the proposed method in this paper is verified by several numerical examples, the applicability of the implicit limit state function is verified by a single-story frame structure, and the engineering applicability of the proposed method is demonstrated with a bamboo bridge.
Highlights
In the current structural design specifications for structures with different safety levels, structural safety can be ensured by satisfying target reliability indices
The existing design parameter evaluation methods cannot solve the problem of considering the randomness of parameters, where the forward reliability index is checked after the design parameters are determined, which leads to low efficiency
In order to solve the above three problems, this paper proposes a hybrid algorithm for the inverse reliability analysis based on the first-order reliability method (FORM), Newton–Raphson and Levenberg– Marquardt methods
Summary
Fenghui Dong * , Jie Gao, Aijin Hao, Yang Wei * , Xin Huang, Feng Shi and Kaiqi Zheng. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
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