Multi-point Extended Reduced Order Modeling For Design Optimization and Uncertainty Analysis
Multi-point Extended Reduced Order Modeling For Design Optimization and Uncertainty Analysis
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用于设计优化和不确定性分析的多点扩展降阶建模
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
K. Maute
中科院分区：
文献类型：
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作者：
G. Weickum;Mike Eldred;K. Maute
对于大型计算模型，由于需要重复评估模型，标准的确定性优化方法可能非常昂贵。这种困难被放大时，随机方面的模型包括在内，如在基于可靠性的设计优化。这项工作旨在减轻计算成本分析动态系统，通过采用替代模型代替完整的模型分析。感兴趣的代理模型是一个降阶模型（ROM），它采用Galerkin投影的系统响应使用一组计算的基函数，以显着减少系统中的自由度的数量。ROM技术将不仅能够近似响应准确地在标称设计，在计算成本显着降低，但也将估计由于设计或不确定的可变参数的变化的响应。将探讨两种概念方法：扩展降阶建模（EROM）和跨越降阶建模（SROM）。这些方法之间的区别是EROM近似更新的基础（本征模，奇异向量）的每个参数的变化，而SROM使用一个完整的参数空间的单一生成基础。EROM和SROM基地的计算不同的技术进行了探讨，并将这些方法中最好的纳入结构问题的优化和随机分析，证明ROM的好处。
For large computational models, standard deterministic optimization approaches can be prohibitively expensive due to the need to repeatedly evaluate the model. This difficulty is amplified when stochastic aspects of the model are included, such as in reliability based design optimization. This work seeks to alleviate the computational costs of analyzing dynamic systems through employing a surrogate model in place of the full model analysis. The surrogate model of interest is a reduced-order model (ROM), which employs a Galerkin projection of the system response using a computed set of basis functions in order to significantly reduce the number of degrees of freedom in the system. The ROM techniques presented will not only be able to approximate the response accurately at the nominal design, with a significant reduction in computation cost, but will also estimate the response due to a change in design or uncertain variable parameters. Two conceptual approaches will be explored: extended reduced order modeling (EROM) and spanning reduced order modeling (SROM). The difference between these methods is an EROM approximates an updated basis (eigenmodes, singular vectors) for each change in parameters while an SROM uses a single spanning basis for the full parameter space. Different techniques for the computation of the EROM and SROM bases are explored, and the best of these methods are incorporated into the optimization and stochastic analysis of a structural problem, demonstrating the benefit of ROMs.