Study On Probabilistic Structural Design Optimization Based On Inverse Reliability Analysis

Traditional structural optimization methods fail to fully consider uncertainties in material properties,geometric dimensions,external loads and so on,which may lead to waste of resources due to high reliability or failure of the structure due to low reliability.The probabilistic structural design optimization(PSDO)is more rational and attracting more and more attention.However,the reliability analysis and design variables optimization in the PSDO need to be solved iteratively,the prohibitive computation cost of PSDO limits its application in engineering.Therefore,it is imperative to study efficient,stable and reliable approach for PSDO.The main contents of this paper are generalized as follows:1.This paper first introduces the common methods of PSDO,including performance measure approach(PMA),reliability index approach(RIA),sequential optimization and reliability assessment(SORA)and single loop approach(SLA).Then,the common methods of solving probabilistic performance measure(PPM)in PMA are further introduced,including advanced mean value method(AMV),hybrid mean value method(HMV),chaos control method(CC)and modified chaos control method(MCC).Compared with RIA,PMA is more stable and efficient.This paper is mainly based on PMA,which is also called the inverse reliability analysis.2.In this paper,a new method,conjugate gradient step length adjustment method(CGS),is presented to perform the inverse reliability analysis.This method is based on the RMIL conjugate search direction and the self-adaptive step length strategy.The new conjugate search direction accelerates the iterative process under the premise of ensuring the convergence.The self-adaptive step length strategy makes it unnecessary for CGS to obtain the prior information such as convexity or concavity and non-linearity of the performance function.The step length is first selected by initial step length criterion and is automatically adjusted during the iteration process until the final convergence.Multiple examples show that the proposed CGS method is more efficient and robust than other methods.Moreover,CGS is embedded in SORA for probabilistic structural design optimization.Several numerical examples also show that the SORA-CGS is more stable and efficient than the SORA-AMV,SORA-CC and other methods.3.Based on the concept of single-loop approach(SLA),an enhanced single-loop approach(ESLA)is proposed.ESLA utilizes evaluation control strategy and approximate strategy.In each cycle,the evaluation control strategy evaluates the current approximate most probable target point(MPTP).If it is feasible,the approximate MPTP and the sensitivity of performance function at this point is reserved.Otherwise,the conjugate gradient approach(CGA)is used to obtain accurate MPTP.The new point will replace the original approximate point and the gradient information is accordingly renewed.Although the evaluation control strategy may increase the computation cost of the performance function,it ensures the effectiveness and robustness of the ESLA method.The approximate strategy is to use the information of MPTP and the sensitivity of performance function at this point to build the linear Taylor expansion of the constraint functions.In this way the performance functions are not calculated again in the deterministic optimization,which will greatly reduce the number of performance function evaluations and improve efficiency.Multiple numerical examples illustrate the high efficiency and robustness of ESLA.