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.
