CDS&E: Theoretical Foundation and Computational Tools for Complex Nonlinear Stochastic Dynamical Engineering Systems - A New Paradigm

工程结构在动态荷载作用下，包括地震等自然事件，会造成巨大的生命损失、财产损失和经济活动损失。由于这些事件的不可预测性，激发时间历史不能预先知道。在这种激励下设计结构的成本是巨大的，在预测结构在这些条件下的响应方面，目前的知识状况有相当大的改进空间。本文的研究将为结构分析提供理论基础和计算工具，从而提高工程设计的效率和整体安全性。预计这项研究的影响将是多学科的。然而，直接的主要受益者将是对设计耐地震损害和风险一致的结构感兴趣的工程专业人员。由于根本风险无法完全消除，因此需要对其进行管理，研究将提供必要的工具。这种多学科方法将有助于扩大代表性不足的群体对研究的参与，并将影响工程教育。一个多学科的变革性理论概念将解决上述知识差距。与经典的随机振动方法不同，不确定动态载荷将应用于时间域，并将明确地包含有关主要非线性来源、改进的建模和最近引入的几个能量耗散特征的信息，以及相关的不确定性，因为随机系统在故障前经历了几个阶段。一些基本的挑战是理解输入不确定性，在大型非线性动态系统中将它们从参数传播到满足基本物理条件的系统级别，获得可靠的概率响应特征/度量/统计，并使用有限的数据对其进行验证。研究目标将通过考虑敏感度分析、模型简化技术、智能抽样方案和几个产生有益的复合效应的高级因子方案来实现，从而在不牺牲精度的情况下获得效率。它们将在利用最先进的计算能力的多尺度环境中实施。该公式将只使用数十个智能分析而不是数千个基于模拟的分析来提取随机动态行为。从本质上讲，这是一种智能的多重确定性分析。总体努力将有效地整合教育、外展、研究和培训。

Engineered structures excited by dynamic loadings, including natural events like earthquakes, cause enormous damage in terms of loss of life, property damage, and lost economic activity. Because of the unpredictability of these events, the excitation time histories cannot be known in advance. The cost of designing structures against such excitation is enormous, and there is considerable room for improvement in the current state of knowledge in predicting the response of structures under these conditions. This study will provide a theoretical foundation and computational tools to analyze structures, and thus to improve the efficiency and overall safety of engineering designs. The impact of the study is expected to be multi-disciplinary in nature. However, the immediate major beneficiary will be the engineering profession interested in designing seismic damage-tolerant and risk-consistent structures. Since the underlying risk cannot completely be eliminated, it needs to be managed and the study will provide the necessary tools. This multi-disciplinary approach will help broaden the participation of underrepresented groups in research and will impact engineering education. A multi-disciplinary transformational theoretical concept will address the knowledge gap mentioned above. Instead of using the classical random vibration approach, the uncertain dynamic loadings will be applied in the time domain and will explicitly incorporate information on major sources of nonlinearity, improved modeling and several recently introduced energy dissipation features, and associated uncertainties, as the stochastic system goes through several phases just before failure. Some of the basic challenges are the understanding of input uncertainties, propagating them in large nonlinear dynamic systems from the parameter to the system level satisfying the underlying physics, obtaining reliable probabilistic response characteristics/metrics/statistics, and validating them using limited data. The research objectives will be achieved by taking into account sensitivity analysis, model reduction techniques, intelligent sampling schemes, and several advanced factorial schemes producing a beneficial compounding effect to obtain efficiency without sacrificing accuracy. They will be implemented in a multi-scale environment exploiting state-of-the-art computational power. The formulation will extract stochastic dynamical behavior using only tens of intelligent analyses instead of thousands of simulation-based analyses. Essentially, this is intelligent multiple deterministic analyses. The overall effort will effectively integrate education, outreach, research, and training.