Probabilistic Design and Reliability Analysis with Kriging and Envelope Methods
Abstract
In the mechanical design stage, engineers always meet with uncertainty, such as random variables, stochastic processes, and random processes. Due to the uncertainty, products may behave randomly with respect to time and space, and this may result in a high probability of failure, low lifetime, and low robustness. Although extensive research has been conducted on the component reliability methods, time- and space-dependent system reliability methods are still limited. This dissertation is motivated by the need of efficient and accurate methods for addressing time- and space-dependent system reliability and probabilistic design problems. The objective of this dissertation is to develop efficient and accurate methods for reliability analysis and design. There are five research tasks for this objective. The first research task develops a surrogate model with an active learning method to predict the time- and space-independent system reliability. In the second research task, the time- and space-independent system reliability is estimated by the second order saddlepoint approximation method. In the third research task, the time-dependent system reliability is addressed by an envelope method with efficient global optimization. In the fourth research task, a general time- and space-dependent problem is investigated. The envelope method converts the time- and space-dependent problem into time- and space-independent one, and the second order approximation is used to predict results. The last task proposes a new sequential reliability-based design with the envelope method for time- and spacedependent reliability. The accuracy and efficiency of our proposed methods are demonstrated through a wide range of mathematics problems and engineering problems.
Degree
Ph.D.
Advisors
Du, Purdue University.
Subject Area
Engineering|Artificial intelligence|Computer science|Design|Labor relations|Marketing|Pedagogy
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