System Analysis and Design under Space- and Time-Dependent Uncertainty

工程系统总是受到不确定性的影响，这是由于许多地方的随机性，如环境、材料特性、制造的不精确性、知识的不完备性等。在系统设计过程中不考虑或不恰当地考虑不确定性(未知、意外)可能会导致可靠性、质量和健壮性较低；成本较高；甚至灾难。这项研究解释了最常见的不确定性类型，这种不确定性在空间和时间上都不同，有以下两个好处。首先，它使工程师能够更好地理解空间和时间相关的不确定性如何影响系统性能。其次，它使工程师能够设计出对空间和时间相关的不确定性影响最小的系统。因此，研究成果将为当前工程和系统设计的理论和方法增加新的知识，并使产品更加可靠和安全。这项研究将适用于从大型民用系统到小型集成电路系统的广泛工程应用。其他将受益的潜在领域包括运筹学、可靠性工程、统计学和概率，在这些领域，依赖空间和依赖时间的概率方法发挥着至关重要的作用。将研究成果纳入工程课程和教材将更好地培养工科学生的概率思维，使他们对公共安全和福利更加负责。本研究的目的是量化和减少空间和时间相关的不确定性对系统性能的影响。主要方法是将系统分析和设计方法与先进的随机过程和随机场理论相结合。该项目首先回答了一个问题，即系统输入(设计参数)中的空间和时间依赖的不确定性如何传播到系统输出(性能)。这有助于更好地理解不确定性的影响，并确定系统性能在空间和时间上的完全概率特征。其次，本研究回答了如何最优地确定设计变量的问题，以便以较低的成本和较低的风险最小化与空间和时间相关的不确定性的影响。所有工程系统都需要在所需的空间和时间内以稳定的性能正常工作，本项目将产生新的方法来实现这一要求。

Engineering systems are always subjected to uncertainty, which is due to the randomness in many places, such as the environment, material properties, manufacturing imprecision, and imperfect knowledge. No consideration or improper consideration of uncertainty (unknowns, surprises) during system design may result in low reliability, quality, and robustness; higher costs; and even catastrophe. This research accounts for the most common type of uncertainty that varies in space and with respect to time with the following two benefits. First, it allows engineers to better understand how the space- and time-dependent uncertainty impacts system performance. Second, it enables engineers to design systems with minimized effect of the space- and time-dependent uncertainty. As a result, the research results will add new knowledge to the current theories and methodologies of engineering and systems design, and also make products more reliable and safer. This research will be applicable to wide engineering applications, ranging from large civil systems to small integrated circuit systems. Other potential areas that will benefit include operations research, reliability engineering, statistics, and probability, where space-dependent and time-dependent probabilistic approaches play a vital role. The inclusion of research results into engineering courses and educational materials will better foster probabilistic thinking for engineering students, making them be more responsible for public safety and welfare.The objective of this research is to quantify and reduce the effect of space- and time-dependent uncertainty on system performance. The major approach is the integration of system analysis and design methodologies with advanced theories of stochastic processes and random fields. The project first answers a question about how the space- and time-dependent uncertainty in the system input (design parameters) propagates to the system output (performance). This provides a better understanding of the effect of uncertainty and identifies complete probabilistic characteristics of system performance over space and time. Second, this research answers a question of how to optimally determine design variables so that the effect of the space- and time-dependent uncertainty is minimized with a lower cost and reduced risk. All engineering systems are required to work properly with stable performance in a desired space and period of time, and this project will produce new methodologies to achieve this requirement.