Engineering design of complex systems is frequently confronted with uncertainties stemming from manufacturing processes and operating environments. These uncertainties cannot be explicitly or effectively dealt with in a traditional deterministic paradigm. More often than not, heuristically acquired safety factors are used to consider the influence of uncertainties in a qualitative manner, leading to overly incompetent or unknowingly risky designs. Under this National Science Foundation award, the principal investigator and his student performed fundamental research on the design optimization of complex systems in the presence of statistically dependent uncertainty. The principal objective was to develop innovative methods to determine the best design alternative considering that the system behavior is uncertain and driven by dependent input variables. The research involved new theoretical developments and integration of state-of-the-art computational methods from engineering, mathematics, and statistics. New computer models were created to examine two principal variants of design optimization: (1) robust design optimization by propagating input uncertainties to system behavior, resulting in a reduced sensitivity of optimal design; and (2) reliability-based design optimization by fulfilling a prescribed reliability level, leading to optimal design with an acceptably low risk of failure. Depending on the objective put forward by a designer, uncertainty is deftly controlled by these design optimization methods. The novel formulations of probabilistic analysis, design sensitivity analysis, and optimization algorithms generated from this research have attained not only highly accurate but also computationally proficient design solutions. As such, the computer models developed are capable of solving industrial-scale design optimization problems with numerous design variables. The results of this research are anticipated to be applicable to a comprehensive multidisciplinary optimization methodology in the presence of uncertainty. Conceivable engineering applications include ground vehicle design for improved durability, noise-vibration-harshness, and crashworthiness; fatigue- and fracture-resistant design for civil and aerospace applications; and reliability-based design of microelectronics and interconnects, to name just a few. Beyond engineering, potential application areas include energy sciences (e.g., nuclear energy, carbon sequestration); finance and management (e.g., stock market, portfolio management); geosciences, (e.g., seismology, reservoir modeling); and transportation and logistics (e.g., freight transportation, product shipment), where optimization under uncertainty plays an important role. Therefore, this research not only advances the frontier of knowledge in engineering design but also will positively impact the U.S. economy and society.

Last Modified: 11/02/2020
Modified by: Sharif Rahman