A reliability-based robust design for structural components with a variable cross section under limited probabilistic information

Abstract

In engineering design, structural components with variable cross sections are extensively employed due to their excellent mechanical properties. From a strength and stiffness perspective, structural components with a uniform cross section are not always ideal. Therefore, to effectively utilize material, variable cross section structural components with excellent properties such as high strength and stiffness are employed in many practical engineering applications. As a multi-dimensional function is required to describe the state of a variable cross section structural component, determining the locations of its dangerous cross sections is very difficult. As a result, the development of a reliability-based design for a variable cross section structural component is a complex process. Therefore, strict theoretical derivations and reasonable quantitative research are required to understand the variation pattern of the reliability of the variable cross section structural component with the coordinates to determine the locations of its dangerous cross sections. This article presents a reliability sensitivity analysis with limited probabilistic information and a reliability-based robust design variable cross section structural component. Mathematical models for reliability sensitivity analysis and reliability-based robust design of variable cross section structural components with incomplete probabilistic information are established. Reliability sensitivity analysis and reliability-based robust design methods for variable cross section structural components with non-normally distributed parameters are proposed. The article provides the changing condition of the reliability with respect to the variable cross section, describes the change rule of reliability with respect to design parameters, and provides the multi-objective optimal design model based on reliability sensitivity. The reliability index obtained using the presented method is insensitive and therefore robust. Using a numerical example, the variation curves of the reliability index and reliability of a variable cross section structural component with coordinates of variable cross section are obtained. A reliability-based robust optimal design approach for variable cross section structural components for given design reliability index conditions is provided.

A reliability‐based robust optimization design for the drum brake using adaptive Kriging surrogate model

“…The basic idea of the RBROD method is to consider the reliability of mechanical products and its reliability sensitivity in the optimization model, and the general mathematical model is described as below 5 :…”

“…The basic idea of the RBROD method is to consider the reliability of mechanical products and its reliability sensitivity in the optimization model, and the general mathematical model is described as below 5 : $$$$\begin{equation} \left. \def\eqcellsep{&}\begin{array}{c}\displaystyle\min f\left(X\right)=\sum _{i=1}^{{m}_{1}}{\lambda}_{i}{f}_{i}(X)\\[10pt]\displaystyle s.t.$$…”

“…In the presented approach, in order to avoid repeated executions of finite element analysis (FEA) code in an optimization loop, the dual RSM is adopted to acquire the response surface. Zhang and He 5 present the reliability sensitivity analysis and RBROD for the structural components with non‐normal distributed parameters, the accuracy of which is proved by the proposed numerical example. Wang et al 6 .…”

Structure Optimization of Guide Vane on Combustion Performance of Premixed H2/Air in Micro Cavity-Combustor

“…where f1 and f2 are the functions of total pressure loss and combustion efficiency established by the BP neural network in section 4.1, 𝜆 1 and 𝜆 2 are the weighting factors of f1 and f2, 𝜆 1 = 0.00286 and 𝜆 2 = 0.99714 by Eq. ( 14) [26]. where 𝑿 * 1 and 𝑿 * 2 are the optimum solution of f1 and f2.…”