EFFICIENT METHODS FOR ENGINEERING DESIGN UNDER UNCERTAINTY
Author: Du, Xiaoping
Supervisor: Chen, Wei
Institution: Graduate College, University of Illinois at Chicago
With today's increasing and global competition, the probabilistic design method with consideration of uncertainty has been getting much attention. The consideration of uncertainty enables engineers to make reliable decisions, to lessen quality loss, to manage risk, and to avoid conservative designs. However, a probabilistic design is extremely computationally expensive compared to a deterministic design. To address the engineering needs for affordable design methods under uncertainty, methods are developed in this dissertation to improve the computational efficiency of uncertainty analysis with the consideration of uncertainty in design from three aspects, namely, analysis, modeling, and synthesis. These methods emphasize and address the needs in quality engineering and the design of complex engineering systems. In the area of uncertainty analysis, the Modified Advanced Mean Value (MAMV) method is developed based the technique of reliability analysis for the purpose of percentile evaluation of system performance with high computational efficiency and robustness in dealing with various function and distribution types. The method is also extended to evaluate the system reliability and to generate the distribution of system performance. All of developed uncertainty analysis methods serve as the fundamental methods for other developments in design feasibility assessment and synthesis under uncertainty in this dissertation. Associated with modeling design feasibility under uncertainty, commonly used feasibility modeling techniques are investigated extensively in terms of capability, accuracy, efficiency, and ease of use. Constructive guidelines are formulated for engineers to choose appropriate techniques to model the design feasibility robustness under various circumstances. Based on the techniques developed for uncertainty analysis and uncertainty modeling, a new method for synthesis under uncertainty, the Sequential Optimization and Reliability Assessment (SORA) method, is developed. Different from the traditional double-loop method, the SORA method adopts a single-loop strategy and separates the reliability assessments from the optimization. The design is conducted in sequential cycles of isolated optimization and reliability assessments. As a result, the design solution can be identified much more quickly than the traditional double-loop method. The SORA method has the capability for performing reliability-based design, robust design, and other forms of probabilistic optimization. To meet the need of multidisciplinary systems design, a multidisciplinary robust design procedure is developed. Different from the existing uncertainty analysis techniques, the proposed techniques, the system uncertainty analysis (SUA) method and the concurrent subsystem uncertainty analysis (CSSUA) method, bring the features of multidisciplinary design optimization (MDO) framework into consideration. Compared to the Monte Carlo simulation approach, the proposed techniques significantly reduce the number of design evaluations at the system level, and therefore improve the efficiency of robust design in the domain of MDO. Through both example problems adopted from literature and industrial applications such as the Pratt & Witney engine design and the reliability-based design for vehicle crashworthiness of side impact, it is illustrated that the proposed methods have resulted in significant computational savings. The methods are applicable to the general class of engineering systems, with a great impact on systems that require computationally expensive analyses.