A Generic Reliability Analysis and Design Framework with Random Parameter , Field , and Process Variables

Title of Document: A GENERIC RELIABILITY ANALYSIS AND DESIGN FRAMEWORK WITH RANDOM PARAMETER, FIELD, AND PROCESS VARIABLES Zhimin Xi, Doctor of Philosophy, 2010 Directed By: Professor Byeng D. Youn, Department of Mechanical Engineering This dissertation aims at developing a generic reliability analysis and design framework that enables reliability prediction and design improvement with random parameter, field, and process variables. The capability of this framework is further improved by predicting and managing reliability even with a dearth of data that can be used to characterize random variables. To accomplish the research goal, three research thrusts are set forth. First, advanced techniques are developed to characterize the random field or process. The fundamental idea of these techniques is to model the random field or process with a set of important field signatures and random variables. These techniques enable the use of random parameter, field, and process variables for reliability analysis and design even with a dearth of data. Second, a generic reliability analysis framework is proposed to accurately assess system reliability in the presence of random parameter, field, and process variables. An advanced probability analysis technique, the Eigenvector Dimension Reduction (EDR) method, is developed by integrating the Dimension Reduction (DR) method with three proposed improvements: 1) an eigenvector sampling approach to obtain statistically independent samples over a random space; 2) a Stepwise Moving Least Square (SMLS) method to accurately approximate system responses over a random space; and 3) a Probability Density Function (PDF) generation method to accurately approximate the PDF of system responses for reliability analysis. Third, a generic Reliability-Based Design Optimization (RBDO) framework is developed to solve engineering design problems with random parameter, field, and process variables. This design framework incorporates the EDR method into RBDO. To illustrate the effectiveness of the developed framework, many numerical and engineering examples are employed to conduct the reliability analysis and RBDO with random parameter, field, and process variables. This dissertation demonstrates that the developed framework is very accurate and efficient for the reliability analysis and RBDO of engineering products and processes. A GENERIC RELIABILITY ANALYSIS AND DESIGN FRAMEWORK WITH RANDOM PARAMETER, FIELD, AND PROCESS VARIABLES