Reliability-based Design Optimization Based On Augmented Step Size Adjustment Method

Reliability-based design optimization is an important development direction of structural optimization.With the increasing requirements for structural reliability in engineering practice,especially in the aerospace field,reliability-based design optimization method has received more and more attention.The reliability analysis method based on probabilistic uncertainty can quantitatively consider various uncertain factors existing in the structure,making up for the defect that deterministic optimization can only roughly cover all uncertain factors with one safety factor.However,the problems of poor robustness and low efficiency faced by reliabilitybased design optimization have greatly restricted its application in engineering practice.Therefore,the study of efficient and robust reliability-based design optimization is of great significance.This paper first proposes an augmented step size adjustment(ASSA)method based on performance measure approach to improve the robustness of the iterative solution process.The ASSA method aims to improve the efficiency and robustness of the reliability analysis.The ASSA method can accurately identify the situation where the minimum performance target point(MPTP)is missed during the search process by using a brand-new oscillation recognition mechanism,locate interval where the MPTP is located,limit the search interval,and enhance the iterative robustness.At the same time,the step size adjustment mechanism of ASSA method can efficiently approximate the MPTP.During each step size adjustment,the MPTP is approximately approached,which greatly improves the convergence efficiency.In addition,there is no prior parameter that needs to be preset in the ASSA method,which ensures the applicability and stability of the algorithm.The calculation results of many different types of calculation examples show that the ASSA method can efficiently and robustly solve various types of problems.In view of the effective application in the performance measure approach,through the adaptive adjustment,the ASSA method is successfully applied to the reliability index approach.When the ASSA method is applied to the reliability index approach,it also has excellent calculation efficiency and convergence stability,which greatly improves the performance of the reliability index approach.Since the reliability-based design optimization is essentially a double loop optimization problem,the complete reliability analysis must be performed at each design iteration point,which brings huge computation costs.In this paper,the reliability-based design optimization based on the improved two-point adaptive nonlinear approximation(TANA-2)function is proposed.When the target reliability index hypersphere is far from the limit state surface through the set criterion.Based on the TANA-2 approximation function,the ASSA method is used to solve the MPTP to improve the calculation efficiency.In contrast,when the target reliability index hypersphere is close enough to the limit state surface,based on the real constraint function,the ASSA method is used to solve the MPTP to ensure the calculation accuracy at the critical point.In this way,the calculation efficiency of the entire process of reliability-based design optimization is improved,and at the same time,the accuracy of the solution is effectively guaranteed.In addition,at two adjacent design iteration points,the MPTPs direction vector of each constraint function at the previous design point is retained as the initial direction of the MPTPs searching at the next design point.This strategy greatly reduces the early invalid search range of MPTP searching to further effectively improve the efficiency of reliability-based design optimization.Several classic examples of reliability-based design optimization show that the reliability-based design optimization method based on TANA-2 function can further improve the solution efficiency.