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Adaptive methods for linear dynamic systems in the frequency domain with application to global optimization.

机译：频域线性动态系统的自适应方法及其在全局优化中的应用。

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摘要

Designers often seek to improve their designs by considering several discrete modifications. These modifications may require changes in materials and geometry, as well as the addition or removal of individual components. In general, if the modifications are applied one at a time, none of them may sufficiently improve the performance. Also, the total number of modifications that may be included in the final design is often limited due to cost or other constraints. The designer must therefore determine the optimal combination of modifications in order to complete the design.;While this design challenge arises fairly commonly in practice, very little research has studied it in its full generality. This work assumes that the mathematical description of the design and its modifications are frequency dependent matrices. Such matrices typically arise due to finite element analysis as well as other modeling techniques. Computing performance metrics related to steady-state forced response, also known as performing a frequency sweep, involves factorizing these matrices many times. Additionally, determining the globally optimum design in this case involves an exhaustive search of the combinations of modifications. These factors lead to prohibitively long run times particularly as the size of the system grows. The research presented here seeks to reduce these costs, making such a search feasible. Several innovative techniques have been developed and tested over the course of the research, focused in two primary areas: adaptive frequency sweeps and efficient combinatorial optimization. The frequency sweep methods rely on an adaptive bisection of the frequency range and either a subspace approximation based on implicit interpolatory model order reduction or an elementwise approximation using piecewise multi-point Pade interpolants. Additionally, a strategy for augmenting the adaptive methods with the system's modal information is presented. For combinatorial optimization, an approximation algorithm is developed that capitalizes on any presence of dynamic uncoupling between modifications.;The net effect of this work is to allow designers and researchers to develop new dynamic systems and perform analyses faster and more efficiently than ever before.
机译：设计师经常通过考虑几种离散的修改来寻求改进他们的设计。这些修改可能需要更改材料和几何形状，以及添加或删除单个组件。通常，如果一次应用一个修改，它们都不能充分改善性能。而且，由于成本或其他限制，最终设计中可能包含的修改总数通常受到限制。因此，设计人员必须确定修改的最佳组合才能完成设计。尽管在实践中这种设计挑战相当普遍，但很少有研究能对其进行全面的研究。这项工作假设设计及其修改的数学描述是频率相关矩阵。此类矩阵通常是由于有限元分析以及其他建模技术而产生的。计算与稳态强制响应有关的性能指标（也称为执行频率扫描）涉及对这些矩阵进行多次分解。此外，在这种情况下确定全局最佳设计涉及对修改组合的详尽搜索。这些因素导致运行时间过长，尤其是随着系统大小的增长。此处提出的研究旨在降低这些成本，从而使这种搜索可行。在研究过程中已经开发并测试了几种创新技术，这些技术主要集中在两个主要领域：自适应频率扫描和有效的组合优化。扫频方法依赖于频率范围的自适应二等分和基于隐式内插模型阶数约简的子空间逼近或使用分段多点Pade插值的逐元素逼近。此外，提出了一种使用系统的模态信息来增强自适应方法的策略。对于组合优化，开发了一种近似算法，可利用修改之间任何动态解耦的存在。该工作的最终结果是使设计人员和研究人员能够比以往更快，更高效地开发新的动态系统并进行分析。

著录项

  • 作者

    Wixom, Andrew S.;

  • 作者单位

    Boston University.;

  • 授予单位 Boston University.;
  • 学科 Mechanical engineering.
  • 学位 Ph.D.
  • 年度 2016
  • 页码 206 p.
  • 总页数 206
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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