Prediction on the static response of structures with large-scale uncertain-but-bounded parameters based on the adjoint sensitivity analysis

Abstract

The number of uncertain parameters increases sharply with structures becoming more complex, which leads to huge computational consuming. Two approaches are presented to efficiently predict the static response bounds of structures with large-scale uncertain-but-bounded parameters. These two methods can solve the problem efficiently because the sensitivity information of structural response with respect to uncertain parameters is used. Since the number of the uncertain parameters is so large, it leads to the expansive computational cost issue due to calculating much gradient information. To deal with this issue, the adjoint method is employed to efficiently generate the partial derivative of the structural response with respect to uncertain parameters by fewer number of finite element analysis. Based on the sensitivity information, the adjoint-based Taylor series Expansion Method (ATEM) is proposed to approximate the structural response when the uncertain range is small. The ATEM has high efficiency because only the value and partial derivatives of one point are required. Moreover, the partial derivatives required in ATEM are efficiently calculated by the adjoint method. Alternatively, an adjoint-based optimization method (AOM) is constructed to find the max/min value of the response bound, which is a method with high accuracy even the uncertain range is large. It provides two choices to address the uncertainty propagation problems under different circumstances. Numerical examples are provided to illustrate the accuracy and efficiency of the proposed approaches.