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Multiscale design under uncertainty.

机译：不确定性下的多尺度设计。

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摘要

With the advances in physical, biological and material sciences, multiscale theories and models have been developed to gain a holistic understanding of physical phenomena at a system level by intelligently and efficiently combining the underlying physical mechanisms at multiple scales across the atomic, molecular, microscopic, and macroscopic scales. Building upon the advancements of multiscale modeling, Multiscale design is an emerging research paradigm that aims for achieving exceptional system performance through concurrent design of materials and product across multiple scales. However, challenges remain in the design of multiscale systems due to the complexity of multiscale analysis, coupled information exchanges, various uncertainty sources (especially those due to the random nature of materials), and the complexity of multiscale/multidisciplinary decision making. The objective in this dissertation is to develop formulations and efficient solution strategies for multiscale design under uncertainty, with a special emphasis on designing integrated hierarchical material and product systems.;To meet the challenges and facilitate multiscale design under uncertainty, design formulations and methods are first developed for generic research topics including the enhancement of probabilistic design optimization and statistical sensitivity analysis for hierarchical systems. In particular, new formulations that take into account the non-fixed variances are developed and integrated into the Sequential Optimization and Reliability Assessment (SORA) method. The developed formulations are generic enough to be extended and utilized in other probabilistic optimization strategies that involve the Most Probable Point (MPP) estimations. To facilitate the application of Statistical Sensitivity Analysis (SSA) to complex engineering systems with a hierarchical structure, a Hierarchical Statistical Sensitivity Analysis (HSSA) method is developed to manage the complexity of designing hierarchical engineering systems. A top-down strategy is introduced to invoke the SSA of critical submodels and later the SSA results at each individual scale are aggregated to measure the global impact of local submodel parameters without using additional samples.;For multiscale design under uncertainty involving hierarchical materials and product design, efforts have been made to first develop computational methods for identifying critical material microstructure parameters with respect to material properties. A predictive stochastic volume element method is developed for studying material microstructure-property relations considering material random microstructure configurations. A comprehensive statistical cause-effect analysis approach is presented for determining critical microstructure parameters.;Statistical upscaling methods are then proposed to quantify uncertainty propagated from a fine scale to a coarse scale in a multiscale context. To quantify the uncertainty propagated from material microstructure to material property, a statistical calibration process is employed to calibrate probabilistic material constitutive models based on the simulations of random microstructure configurations. An efficient random field uncertainty propagation technique is proposed to estimate the uncertainty in product performances using advanced dimension reduction techniques for both uncertainty representation and propagation.;Design methodologies and strategies are finally developed for designing multiscale systems under uncertainty. Based on the generalized hierarchical multiscale decomposition pattern in multiscale modeling, a set of computational techniques are developed to manage the complexity of multiscale design under uncertainty. Novel design of experiments and metamodeling strategies are proposed to manage the complexity of propagating random field uncertainty through three generalized levels of transformation: the material microstructure random field, the material property random field, and the probabilistic product performance. Multilevel optimization techniques are employed to find optimal design solutions at individual scales.;The benefits of the proposed techniques are illustrated through a variety of mathematical examples and multiscale design problems. It is shown that the research developments in this dissertation are generally applicable to multiscale design under uncertainty with high effectiveness and efficiency, and thus provide intelligent computational techniques for designing innovative, multiscale engineered systems.
机译：随着物理，生物和材料科学的进步，已经开发了多尺度的理论和模型，以通过智能，高效地组合原子，分子，微观，和宏观尺度。基于多尺度建模的进步，多尺度设计是一种新兴的研究范式，旨在通过跨多个尺度的材料和产品的并行设计来实现出色的系统性能。但是，由于多尺度分析的复杂性，耦合的信息交换，各种不确定性源（尤其是由于材料的随机性而导致的不确定性）以及多尺度/多学科决策的复杂性，在多尺度系统的设计中仍然存在挑战。本文的目的是为不确定性下的多尺度设计开发公式和有效的解决方案策略，特别着重于设计集成的分层材料和产品系统。为了应对挑战并在不确定性下促进多尺度设计，首先是设计公式和方法针对通用研究主题而开发，包括增强概率设计优化和分层系统的统计敏感性分析。特别是，开发了考虑非固定方差的新公式，并将其整合到顺序优化和可靠性评估（SORA）方法中。所开发的公式具有足够的通用性，可以扩展并用于涉及最高概率点（MPP）估计的其他概率优化策略。为了促进统计敏感性分析（SSA）在具有层次结构的复杂工程系统中的应用，开发了一种分层统计敏感性分析（HSSA）方法来管理设计层次工程系统的复杂性。引入了自上而下的策略来调用关键子模型的SSA，然后将每个单独规模的SSA结果汇总起来，以在不使用额外样本的情况下测量局部子模型参数的全局影响。;对于涉及层次结构材料和产品的不确定性下的多尺度设计在设计上，已经做出努力来首先开发用于识别关于材料特性的关键材料微观结构参数的计算方法。提出了一种预测随机体积元方法，用于研究考虑材料随机组织结构的材料组织与性能的关系。提出了一种综合的统计因果分析方法来确定关键的微观结构参数。然后提出了统计上规模化方法，以量化在多尺度情况下从细尺度到粗尺度传播的不确定性。为了量化从材料微观结构传播到材料性能的不确定性，基于随机微观结构配置的模拟，采用统计校准过程来校准概率材料本构模型。提出了一种有效的随机场不确定性传播技术，通过先进的降维技术对不确定性表示和传播进行估计，以评估产品性能中的不确定性。最后，开发了设计方法和策略来设计不确定性下的多尺度系统。基于多尺度建模中的广义层次化多尺度分解模式，开发了一套计算技术来管理不确定性下的多尺度设计的复杂性。提出了新颖的实验设计和元建模策略，以通过三个广义的转换级别来管理传播随机场不确定性的复杂性：材料微观结构随机场，材料属性随机场和概率产品性能。采用多级优化技术来找到各个规模的最佳设计解决方案。通过各种数学示例和多级设计问题来说明所提出技术的好处。结果表明，本文的研究进展普遍适用于不确定性下的多尺度设计，具有较高的效率和效率，为设计创新的多尺度工程系统提供了智能的计算技术。

著录项

  • 作者

    Yin, Xiaolei.;

  • 作者单位

    Northwestern University.;

  • 授予单位 Northwestern University.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 297 p.
  • 总页数 297
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

  • 入库时间 2022-08-17 11:38:30

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