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Uncertainty and multi-criteria global sensitivity analysis of structural systems using acceleration algorithm and sparse polynomial chaos expansion

机译:使用加速算法和稀疏多项式混沌扩展结构系统的不确定性和多标准全局敏感性分析

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摘要

Sparse polynomial chaos expansion (PCE) can be used to emulate the stochastic model output where the original model is computationally expensive. It is a powerful tool in efficient uncertainty quantification and sensitivity analysis. Structural systems are usually associated with high dimensional and probabilistic input. The number of candidate basis functions increases significantly with input dimension, resulting in high computational burden for establishing sparse PCE. In this study, acceleration techniques are integrated to formulate an algorithm for efficient computation of sparse PCE (ASPCE). The integrated algorithm can improve efficiency of computational process compared with conventional greedy algorithm while ensuring the satisfying predictive performance. Once the sparse PCE model is obtained, the statistic moments, probability density function of stochastic output, and global sensitivity index could be computed efficiently. Traditional PCE based global sensitivity analysis only assesses the sensitivity on individual structural performance criterion. Assessing the global sensitivity considering multiple criteria is challenging as the sensitive parameters may not be consistent for different performance criteria. To address this issue, a two-stage multi-criteria global sensitivity analysis algorithm is proposed by coupling ASPCE and the technique for order preference by similarity to ideal solution (TOPSIS). A holistic global sensitivity index is proposed to identify the sensitive parameters incorporating multiple performance criteria. In order to illustrate the efficiency, accuracy, and applicability of the proposed approach, two illustrative cases are presented.
机译:稀疏多项式混沌扩展(PCE)可用于模拟原始模型计算昂贵的随机模型输出。它是一个有效的不确定性量化和敏感性分析的强大工具。结构系统通常与高维和概率输入相关联。候选基函数的数量随着输入尺寸而显着增加,导致建立稀疏PCE的高计算负担。在该研究中,集成了加速技术以制定用于稀疏PCE(Aspce)的有效计算的算法。与传统的贪婪算法相比,集成算法可以提高计算过程的效率,同时确保满足预测性能。一旦获得了稀疏的PCE模型,可以有效地计算统计瞬间,随机输出的概率密度函数和全局灵敏度指数。基于传统的PCE全局敏感性分析只评估个人结构性能标准的敏感性。考虑多个标准的全局敏感性是挑战,因为敏感参数可能不具有不同的性能标准。为了解决这个问题,通过将Aspce和技术耦合到理想解决方案(TOPSIS)来提出两阶段的多标准全局敏感性分析算法。建议全局全局敏感指数识别包含多种性能标准的敏感参数。为了说明所提出的方法的效率,准确性和适用性,提出了两个说明性情况。

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