Multi-fidelity uncertainty quantification method with application to nonlinear structural response analysis

Abstract

• A multi-fidelity method is proposed for statistical moment calculations of nonlinear structural responses. • The proposed formulation requires only small numbers of high fidelity solution and simple statistical techniques. • High-cost material damage analysis can be limited in local areas without biasing results of uncertainty quantification . • A computational cost reduction of 52.7% has been achieved in the numerical example. The application of uncertainty quantification (UQ) in complex structural response analysis is limited by solution efficiency. A multi-fidelity (MF) method for UQ is proposed in this paper, in which statistical moments are first evaluated using low cost low-fidelity (LF) model first, and then calibrated with a small number of high-fidelity (HF) samples. Only the error distribution of LF solutions and the covariance between the errors and the LF solutions are employed to derive a simple and straight forward MF formulation. The proposed method is demonstrated in the UQ of damage analysis of a C/SiC plate with a hole, where the HF model is a nonlinear global model considering C/SiC material damage, and the LF model is a linear global model driven nonlinear sub model. Uncertainty propagation is carried out using a sparse polynomial chaos expansion method. Evaluations of the MF method based on four factors: correctness, efficiency, precision and reliability, are carried out. The results show that the MF method can estimate the statistical moments of nonlinear strain responses unbiasedly. Computational cost is reduced by 52.7% compared to that utilizing HF model alone. MF methods can reduce computational cost significantly while maintaining accuracy and can be used for wide range of applications.