Reliability-Based Design Optimization of Large-Scale Complex Systems

该奖项的研究目标是为复杂工程系统的大规模、基于可靠性的设计优化(RBDO)创造新的理论基础和数值算法。提出的工作包括：(1)用于一般高维随机系统可靠性分析的扩展多项式维分解(X-PDD)方法；(2)用于同时计算系统可靠性对设计变量的敏感度的X-PDD和SCORE函数；(3)基于系统级可靠性的稳健设计优化算法，使用X-PDD处理来自单个随机模拟的概率响应和灵敏度。系统可靠性分析和设计灵敏度的创新公式将极大地加速RBDO过程。因此，这项研究构成了一种新的、可能是范式转换的进步，朝着解决存在不确定性的大规模、复杂优化问题的方向发展。可交付成果包括新理论和算法的开发、建模和仿真工具的生成、研究结果的文档记录、工程学生教育以及为K-12学生提供的实践设计体验。如果成功，这项研究的结果将适用于广泛的多学科设计优化方法。潜在的工程应用包括提高耐用性和耐撞性的地面车辆设计，民用和航空航天应用的抗疲劳和抗断裂设计，以及在恶劣环境下的微电子封装的可靠设计。除了工程，潜在的应用领域包括能源、金融、管理、调度、运输和物流，其中随机优化起着至关重要的作用。该奖项创造的知识转移将通过组织与工程设计相关的研讨会、同行评议的期刊出版物、在主要会议和会议上的演讲、软件开发和学生教育来进行。教育目标包括从代表不足的少数族裔群体中招收研究生，实施软件工具来升级爱荷华州大学现有的研究生和本科课程，以及积极参与爱荷华州初中生和高中生的Lead Way项目。

The research objective of this award is to create new theoretical foundations and numerical algorithms for large-scale, reliability-based design optimization (RBDO) of complex engineering systems. The proposed effort will involve: (1) an extended polynomial dimensional decomposition (X-PDD) method for system reliability analysis of a general, high-dimensional, stochastic system; (2) integrated X-PDD and score functions for concurrently calculating sensitivities of system reliability with respect to design variables; and (3) system-level reliability-based and robust design optimization algorithms employing X-PDD for probabilistic response and sensitivities from a single stochastic simulation. The innovative formulation of system reliability analysis and design sensitivities will dramatically accelerate RBDO process. Therefore, the research constitutes a new and possibly paradigm-shifting advance towards solving large-scale, complex optimization problems in the presence of uncertainty. Deliverables include development of new theory and algorithms, generation of modeling and simulation tools, documentation of research results, engineering student education, and hands-on design experience for K-12 students.If successful, the results of this research will be applicable to a broad multidisciplinary design optimization methodology. Potential engineering applications comprise ground vehicle design for improved durability and crashworthiness, fatigue- and fracture-resistant design for civil and aerospace applications, and reliable design of microelectronic packaging under harsh environments. Beyond engineering, potential application areas include energy, finance, management, scheduling, and transportation and logistics, where stochastic optimization plays a vital role. The transfer of knowledge created by this award will take place through organization of engineering design-related symposia, peer-reviewed journal publications, presentations at major conferences and meetings, software development, and student education. Educational goals include graduate student recruitment from an underrepresented minority group, implementation of software tools to upgrade existing graduate and undergraduate courses at The University of Iowa, and active participation in Iowa's Project Lead the Way program for middle- and high-school students.