Stochastic Optimization for Design under Uncertainty with Dependent Probability Measures

具有相关概率测量的不确定性下设计的随机优化

• 批准号: 1462385
• 负责人: Sharif Rahman
• 金额: $ 28.78万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-15 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1462385&HistoricalAwards=false
• 关键词: Stochastic; Optimization; Design; under; Uncertainty

Many complex systems and engineering structures are plagued by uncertainties in manufacturing processes and operating environments. Conventional design approaches rely on heuristically derived safety factors and do not account quantitatively for the statistical variation of a system response. In this project, the principal investigator will conduct fundamental research on design optimization of complex systems in the presence of statistically dependent uncertainty. Novel methods will be developed to determine the best design alternative considering that the system behavior is uncertain and driven by dependent input variables. Potential engineering applications include 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, the results from this research will benefit the U.S. economy and society through potential application in areas such as energy, finance, management, scheduling, and transportation and logistics, where optimization under uncertainty plays a vital role. This research is multi-disciplinary, encompassing several disciplines, including engineering, computer science, mathematics, and statistics. It will help broaden participation of underrepresented groups in research and positively impact engineering education.The objectives of this project are to build a solid mathematical foundation, devise efficient numerical algorithms, and develop practical tools for design optimization subject to uncertainty characterized by dependent probability distributions. The effort will involve (1) a new theoretical development of the generalized polynomial dimensional decomposition method for a high-dimensional stochastic response; (2) new formulae and scalable algorithms for calculating the statistical moments and reliability, followed by design sensitivity analysis; and (3) new reliability-based and robust optimization algorithms for shape and topology designs. Due to innovative calculation of the expansion coefficients, the generalized decomposition method will be efficiently implemented regardless of the size of the stochastic design problem. The innovative formulation of the statistical moment and reliability analyses and design sensitivities, which requires a single or at most a few stochastic simulations for all possible designs, will markedly accelerate the optimization process, potentially producing breakthrough solutions to stochastic design problems.

许多复杂的系统和工程结构都受到制造过程和操作环境的不确定性的困扰。 传统的设计方法依赖于启发式得出的安全系数，并且没有定量地考虑系统响应的统计变化。 在该项目中，首席研究员将在存在统计相关不确定性的情况下对复杂系统的设计优化进行基础研究。 考虑到系统行为是不确定的并由相关输入变量驱动，将开发新方法来确定最佳设计方案。 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，以及恶劣环境下微电子封装的可靠设计。 除了工程之外，这项研究的结果还将通过在能源、金融、管理、调度、运输和物流等领域的潜在应用，使美国经济和社会受益，在这些领域，不确定性下的优化发挥着至关重要的作用。 这项研究是多学科的，涵盖多个学科，包括工程学、计算机科学、数学和统计学。 它将有助于扩大代表性不足的群体对研究的参与，并对工程教育产生积极影响。该项目的目标是建立坚实的数学基础，设计有效的数值算法，并开发实用工具，用于受以相关概率分布为特征的不确定性影响的设计优化。这项工作将涉及（1）高维随机响应的广义多项式维分解方法的新理论发展； （2）用于计算统计矩和可靠性的新公式和可扩展算法，然后进行设计灵敏度分析； (3) 用于形状和拓扑设计的新的基于可靠性和稳健的优化算法。由于展开系数的创新计算，无论随机设计问题的大小如何，都可以有效地实施广义分解方法。统计矩和可靠性分析以及设计敏感性的创新公式，需要对所有可能的设计进行一次或最多几次随机模拟，将显着加速优化过程，有可能为随机设计问题产生突破性的解决方案。