Reliability-based Design Optimization Using Decoupling Methods

The reliability-based design optimization can reasonably characterize the influence of uncertainty on structural reliability.Double-loop method is a traditional method to solve the reliability-based design optimization,which the structure reliability analysis is nested in optimal loops.However,for complex engineering structures,the most obvious shortcoming of double-loop method is time-consuming resulting in high cost.In order to solve this problem,this paper does some studies,as follows:(1)Improved response surface method based on the sub-region of interestBased on the theory of structural reliability,the region around the most possible point has the main effect to the failure probability.In this paper,the region around the most probable point is defined as sub-region of interest,and an improved response surface method based on sub-region of interest is proposed.The region,in where the response function should have good approximate accuracy,can be clearly given.Numerical examples show that although this method is less efficient than first order reliability method,it is better than first order reliability method in assessment accuracy in terms of the failure probability.(2)Reliability-based design optimization using reliability mapping functionsBased on the theory of structural reliability,for a given limit state function,the reliability indices and failure probabilities obtained by different methods should be correlated.This correlated relationship is called reliability mapping functions that is constructed by the mean first order reliability method and an improved response surface method.This method not only retains the high efficiency of the mean first order reliability method,but also overcomes the disadvantage of low precision.This method can transform the double-loop optimization into single-loop optimization,and the optimization efficiency can be improved.Numerical examples show that this method does not depend on the selection of sample points.This method can obtain the consistent optimization solutions for different limit state functions,and has good robustness.(3)Three-stage decoupling method of reliability-based design optimizationIn the first stage,the deterministic optimization based on reliability safety factor is used to find an optimal design,and the optimal design is chosen as the initial sample point.In the second stage,sample points are adjusted by using reliability sensitivities and weight factor,and data sets of the objective function and the failure probability can be obtained.In the third stage,the objective function corresponding to the acceptable failure probability is obtained by using the relationship curve between the objective function and the failure probability,and the final optimization design variables are obtained.The deterministic optimization is used only one time in the proposed method,and all classical algorithms of structural reliability can be used for the proposed method.The adaptability of the proposed method is strong.The numerical results show that the proposed method can obviously reduce the number of evaluation of failure probability,and results are not sensitive to reliability safety factor and weight factor.