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

机译：多保真不确定性量化方法及其在非线性结构响应分析中的应用

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摘要

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. (C) 2019 Elsevier Inc. All rights reserved.
机译：不确定性量化（UQ）在复杂结构响应分析中的应用受到求解效率的限制。本文提出了一种用于UQ的多保真（MF）方法，该方法首先使用低成本低保真（LF）模型评估统计矩，然后使用少量高保真（HF）样本进行校准。仅采用LF解的误差分布以及误差与LF解之间的协方差来得出简单直接的MF公式。在带孔的C / SiC板损伤分析的UQ中证明了该方法的有效性，其中HF模型是考虑C / SiC材料损伤的非线性全局模型，而LF模型是线性全局模型驱动的非线性子模型。不确定性传播是使用稀疏多项式混沌展开方法进行的。基于四个因素对MF方法进行评估：正确性，效率，精度和可靠性。结果表明，MF方法可以无偏估计非线性应变响应的统计矩。与仅使用HF模型相比，计算成本降低了52.7％。 MF方法可以在保持精度的同时显着降低计算成本，并可以用于广泛的应用。 （C）2019 Elsevier Inc.保留所有权利。

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