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

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.

Performance Assessment of Repair and Reinforcement of Concrete Cable-Stayed Bridges in Service Based on Time-Dependent Reliability under Environmental Sustainability Development

“…In order to solve the Equations ( 19), we can use the symmetry reliability method [18]. The equation 𝛽(𝑿, 𝑑, 𝑟) = 𝛽 𝑇 can be rewritten as a general nonlinear equation…”

“…𝒕 𝒊 𝒕=𝒕 𝟎 𝒕 𝒊 𝒕=𝒕 𝟎 (18) where, 𝐼 𝑡 is the normal operation benefit of the concrete cable-stayed bridge in the t year; h (t) is the failure risk of the concrete cable-stayed bridge after T-Year normal operation; 𝑟 𝑡 is the first T-year the discount rate of funds; 𝑆 𝑡 is the loss caused by the failure in the t year; 𝐶 𝐼𝑁𝑆 is the cost for the periodic inspection of concrete cable-stayed bridges; and 𝐶 𝑅𝐸𝑆 is the cost for the maintenance and reinforcement of concrete cable-stayed bridges using this scheme.…”

Novel Analysis between Two-Unit Hot and Cold Standby Redundant Systems with Varied Demand

“…Many reliability issues were then examined by several researchers under the assumptions of multi-level observation sequences [27], preventive maintenance [28], algorithms [29,30], and predictive group maintenance [31], respectively. Further, Dong et al [32] discussed a new approach to symmetry reliability by taking the concept of the inverse reliability principle. Meanwhile, Gao and Wang [33] examined the implications of unreliable repair facilities and predictive group maintenance on reliability.…”

Study on the Nonlinear Stability and Parametric Analysis of a Tensile–Beam Cable Dome

“…Stability capacity refers to the ability of a structure to hold its form or undergo deformation in a loading state [9,10]. By utilizing the meshless generalized finite difference method (GFDM), Wang et al [11] proposed a system for 3D composite elastic materials.…”