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，材料属性，制造的不精确性和不完善的知识。在系统设计过程中，不考虑或不适当地考虑不确定性（未知数、意外）可能会导致可靠性、质量和鲁棒性降低;成本增加;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有变化，有以下两个好处。首先，它使工程师能够更好地了解空间和时间相关的不确定性如何影响系统性能。第二，它使工程师能够设计系统，最大限度地减少空间和时间相关的不确定性的影响。因此，研究成果将为当前的工程和系统设计理论和方法增添新的知识，并使产品更加可靠和安全。这项研究将适用于广泛的工程应用，从大型民用系统到小型集成电路系统。其他可能受益的领域包括运筹学、可靠性工程、统计学和概率学，其中空间相关和时间相关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程专业学生的概率思维，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随机过程和随机场的先进理论相结合。该项目首先回答了一个关于系统输入（设计参数）中的空间和时间相关的不确定性如何传播到系统输出（性能）的问题。这提供了一个更好的理解不确定性的影响，并确定完整的概率特性的系统性能在空间和时间。其次，本研究回答了一个问题，如何最佳地确定设计变量，使空间和时间相关的不确定性的影响最小化，以较低的成本和降低的风险。所有的工程系统都需要在所需的空间和时间内正常工作，并具有稳定的性能，该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.