PROBABILISTIC DESIGN AND RELIABILITY ANALYSIS WITH KRIGING AND ENVELOPE METHODS

 

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.