Inverse Reliability Task: Artificial Neural Networks and Reliability-Based Optimization Approaches

Lehký, David; Slowik, Ondřej; Novák, Drahomı́r

doi:10.1007/978-3-662-44654-6_34

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“…For high-dimensional nonlinear problems, Lee et al [17,18] proposed a dimension reduction method (DRM) based on the most probable point (MPP) to solve the inverse reliability analysis problem. Lehký et al [19,20] used neural networks to make the relationship between reliability indices and random variables explicit, and then identified the unknown parameters in the nonlinear equations (sets) to identify the design parameters in the inverse reliability analysis problem. Cheng and Li [21] combined the response surface with the FORM method to solve the inverse reliability analysis problem of the implicit limit state function.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Symmetry Reliability: Combination of Forward and Inverse Reliability Principle and Its Application to Frame Structures and Bamboo Bridges

et al. 2022

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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.

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