Missouri University of Science and Technology, Intelligent Systems Center

Intelligent Systems Center
320 Engineering Research Lab
500 W. 16th St.
Rolla, MO 65409-0440
Phone : (573) 341-4350
Fax: (573) 341-6512

E-mail: mleu@mst.edu

Accounting for Reliability in Complex Engineering Systems Design

Investigators:	Xiaoping Du (dux@mst.edu, 573-341-7249)
Funding Source:	National Science Foundation http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0400081
Project Description:	The objective of this grant is to develop methodologies and computationally practical approaches of reliability analysis and reliability-based design for complex engineering systems. The complexities include multiple interacting disciplines, large number of design variables, the mixture of multilevel details of uncertainty information, and the extensive use of computer simulations. The complexities have hampered the wide applications of reliability-based design in real-life engineering systems design problems. This research will deal with the complexities at two complementary levels. At reliability analysis level, efficient and accurate reliability analysis methods, including Saddlepoint Approximations, will be developed. At reliability-based design level, strategies and mathematical formulations of reliability-based design models that can be solved efficiently with capabilities of dealing with the abovementioned complexities will be established. The proposed approaches will be demonstrated, verified, and validated through a reliability-based vehicle safety design problem by collaboration with industry. It is anticipated that the research results will provide industry efficient and practical tools for the implementation of reliability analysis and reliability-based design in complex engineering systems design with reduced product development times at reduced cost and risk. The research will also contribute computational methods to general engineering design under uncertainty, such as robust design and decision-based design under risk and uncertainty. In addition, the research results will contribute to education in the areas of engineering design theory and methodology, quality engineering, and systems engineering.
Publications:	1. The First Order Saddlepoint Approximation for Reliability Analysis, X. Du and A. Sudjianto, Vol. 42, No. 6, pp. 1199-1207 Abstract: In the approximation methods of reliability analysis, non-normal random variables are transformed into equivalent standard normal random variables. This transformation tends to increase the nonlinearity of a limit-state function and hence results in less accurate reliability estimation. The First Order Saddlepoint Approximation for reliability analysis is proposed to improve the accuracy of reliability analysis. By approximating a limit-state function at the Most Likelihood Point in the original random space and employing the accurate saddlepoint approximation, the proposed method reduces the chance of increasing linearity of the limit-state function and generates more accurate reliability estimation than the First Order Reliability Method without increasing the computational effort. The effectiveness of the proposed method is demonstrated by three examples in comparison with the First and Second Order Reliability Methods. 2. Sudjianto, A., Du, X., and Chen, W., Uniform Sample Saddlepoint Approximation for Probabilistic Sensitivity Analysis in Engineering Design, submitted, 2004. Sensitivity analysis plays an important role to help engineers gain knowledge of the complex model behavior and make informed decisions regarding where to spend the engineering effort. In design under uncertainty, probabilistic sensitivity analysis (PSA) is performed to quantify the impact of uncertainties in random variables on the uncertainty in the model output. One of the most challenging issues for PSA is the intensive computational demand for assessing the impact of probabilistic variations. An efficient approach to PSA is presented in this article. Our approach employs the Kolmogorov-Smirnov (KS) distance to quantify the importance of input variables. The saddlepoint approximation approach is introduced to improve the efficiency of generating cumulative distribution functions (CDFs) required for the evaluation of the KS distance, To further improve efficiency, the optimized uniform samples are used to replace the Monte Carlo simulations for determining the cumulant generating function (CGF) in saddlepoint approximation. Efficient construction of uniform design necessary to generate the “best�? samples in a mulitdimensional space is presented. Our approach is illustrated with a structural design problem. It has the potential to be the most beneficial for those high dimensional engineering design problems that involve expensive computer simulations.