Novel Computational Methods for Design Under Uncertainty with Arbitrary Dependent Probability Distributions

具有任意相关概率分布的不确定性设计的新颖计算方法

• 批准号: 2317172
• 负责人: Sharif Rahman
• 金额: $ 43.1万
• 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: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2317172&HistoricalAwards=false
• 关键词: Novel; Computational; Methods; Design; Under

Design of complex systems and engineered artifacts is often confronted with uncertainties in manufacturing processes, material properties, and operating environments. Traditional design approaches often rely on heuristically derived safety factors and do not quantitatively address the statistical variation of a system response. This project will promote scientific progress through foundational research on the design optimization of complex engineering systems and structures in the presence of statistically dependent uncertainty. Novel methods will be created to determine the best design alternative, considering uncertain system behavior, influenced by dependent input variables. Potential engineering applications include ground vehicle design for improved durability and crashworthiness, fatigue- and fracture-resistant design for aerospace applications, and design of microelectronic packaging under harsh environments. The results from this research will contribute to national prosperity through the development of complex systems and products that are more durable, robust, and reliable. Beyond engineering, the results from this research will benefit the U.S. economy and society through potential application in areas such as energy, finance and management, and transportation and logistics, where optimization under uncertainty plays a vital role. This research is multi-disciplinary, spanning several fields, including engineering design, applied mathematics, and probability and statistics. It will foster broad participation of underrepresented groups in research and positively impact engineering education.The chief goal of this project is to conduct research in the creation of efficient computational algorithms and practical computational tools for robust and reliability-based design optimization (RDO and RBDO) of high-dimensional complex systems subject to random input resulting from an arbitrary dependent probability distribution. The research plan comprises three scientific objectives: (1) novel mathematical developments of a generalized analysis-of-variance expansion, leading to a generalized spline dimensional decomposition (GSDD) for tackling dependent random variables directly; (2) new scalable algorithms of the GSDD method for calculating relevant probabilistic response characteristics and design sensitivities of a high-dimensional, complex mechanical system; and (3) innovative GSDD-driven optimization algorithms for efficiently solving high-dimensional RDO and RBDO problems, including stochastic shape and topology designs. This research is innovative for several reasons. First, the GSDD method will account for truly arbitrary, dependent probability distributions of random input, heretofore unavailable to the scientific community. Second, it will address discontinuous or non-smooth performance functions, if they exist, using hundreds of random/design variables, thereby diminishing the curse of dimensionality to a great extent. Third, the synchronous formulation of the statistical moment, reliability, and design sensitivity analyses, which requires a single or at most a few stochastic simulation(s) for all possible designs, will markedly accelerate the design optimization process, potentially producing breakthrough solutions to RDO/RBDO problems. The implementation of the probabilistic methods will lead to next-generation computational tools, bridging stress analysis, stochastic simulation, and optimization to form a seamless design pipeline of the future.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

复杂系统和工程制品的设计经常面临制造工艺、材料特性和操作环境的不确定性。传统的设计方法通常依赖于启发式得出的安全系数，并且不能定量地解决系统响应的统计变化。该项目将通过在存在统计相关不确定性的情况下对复杂工程系统和结构的设计优化进行基础研究来促进科学进步。考虑到受相关输入变量影响的不确定系统行为，将创建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、航空航天应用的抗疲劳和抗断裂设计以及恶劣环境下的微电子封装设计。 这项研究的结果将通过开发更耐用、稳健和可靠的复杂系统和产品，为国家繁荣做出贡献。除了工程之外，这项研究的结果还将通过在能源、金融和管理、运输和物流等领域的潜在应用而造福美国经济和社会，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，跨越多个领域，包括工程设计、应用数学、概率与统计。它将促进代表性不足的群体广泛参与研究，并对工程教育产生积极影响。该项目的主要目标是开展研究，创建高效的计算算法和实用的计算工具，以实现稳健和基于可靠性的设计优化（RDO 和 RBDO）受任意相关概率分布产生的随机输入影响的高维复杂系统。该研究计划包括三个科学目标：（1）广义方差分析展开的新颖数学发展，产生用于直接处理相关随机变量的广义样条维分解（GSDD）； (2) GSDD方法的新可扩展算法，用于计算高维、复杂机械系统的相关概率响应特性和设计灵敏度； (3) 创新的 GSDD 驱动优化算法，用于有效解决高维 RDO 和 RBDO 问题，包括随机形状和拓扑设计。这项研究具有创新性有几个原因。首先，GSDD 方法将解释随机输入的真正任意的、相关的概率分布，这是科学界迄今为止无法获得的。其次，它将使用数百个随机/设计变量来解决不连续或非平滑的性能函数（如果存在），从而在很大程度上减少维数灾难。第三，同步制定统计矩、可靠性和设计灵敏度分析，需要对所有可能的设计进行一次或最多几次随机仿真，将显着加速设计优化过程，有可能为 RDO 带来突破性的解决方案/RBDO 问题。概率方法的实施将带来下一代计算工具、桥接应力分析、随机模拟和优化，以形成未来的无缝设计流程。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准。