A Modified Conjugate Gradient Approach for Reliability-Based Design Optimization

Zhiming Wang,Yalong Song,Yafei Zhang

doi:10.1109/access.2020.2966661

Abstract

To improve the efficiency of structural reliability-based design optimization (RBDO) based on the performance measure approach (PMA), a modified conjugate gradient approach (MCGA) is proposed for RBDO with nonlinear performance function. In PMA, the advanced mean value (AMV) approach is widely used in engineering because its simplicity and efficiency. However, the AMV method shows the inefficient and unstable results for structural performance function with high nonlinearity in RBDO. To overcome this shortcoming, the proposed MCGA method improves the efficiency of solution by modifying the relevant parameters of conjugate gradient approach (CGA) and the direction of conjugate gradient algorithm for searching the optimal design point. Finally, three numerical examples with highly nonlinear performance function and an optimization design example of speed reducer are presented. Compared with different methods, the results show that the MCGA method exhibited the better efficiency and robustness in structural reliability and RBDO analyses.

Highlights

In the structural optimization design, the traditional optimization methods are often used to solve the deterministic optimization problem, which means that the design variables are deterministic variables
New design parameters are obtained through the optimization loop, and the reliability analysis method is used to evaluate the feasibility of the design parameters for the probability constraint
In reliability-based design optimization (RBDO), double loop method based on the reliability index approach (RIA) and performance measure approach (PMA) is widely used [5]–[8]

Summary

INTRODUCTION

In the structural optimization design, the traditional optimization methods are often used to solve the deterministic optimization problem, which means that the design variables are deterministic variables. There are certain uncertainties in the dimensional parameters, material properties and external loads of the structure owing to machining errors, internal dispersion of materials and accidental factors, etc [1], [2] To solve this problem, the reliability-based design optimization (RBDO) has been proposed. An external optimization loop and an internal reliability constraint loop are usually used to solve the RBDO problem. In RBDO, double loop method based on the reliability index approach (RIA) and performance measure approach (PMA) is widely used [5]–[8]. In RBDO, the PMA of the double loop method transforms the probability constraint problem into an optimization problem with the constraint function of target reliability index, the minimum performance target point (MPTP) can be obtained through continuously searching in PMA. They are called reliability index approach (RIA) and performance measurement approach (PMA) respectively

EXISTING RELIABILITY ANALYSIS TOOLS IN RBDO

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CONCLUSION