PROBABILISTIC DESIGN AND RELIABILITY ANALYSIS WITH KRIGING AND ENVELOPE METHODS

<p> </p> <p>In the mechanical design stage, engineers always meet with uncertainty, such as random</p> <p>variables, stochastic processes, and random processes. Due to the uncertainty, products may</p> <p>behave randomly with respect to time and space, and this may result in a high probability of failure,</p> <p>low lifetime, and low robustness. Although extensive research has been conducted on the</p> <p>component reliability methods, time- and space-dependent system reliability methods are still</p> <p>limited. This dissertation is motivated by the need of efficient and accurate methods for addressing</p> <p>time- and space-dependent system reliability and probabilistic design problems.</p> <p>The objective of this dissertation is to develop efficient and accurate methods for reliability</p> <p>analysis and design. There are five research tasks for this objective. The first research task develops</p> <p>a surrogate model with an active learning method to predict the time- and space-independent</p> <p>system reliability. In the second research task, the time- and space-independent system reliability</p> <p>is estimated by the second order saddlepoint approximation method. In the third research task, the</p> <p>time-dependent system reliability is addressed by an envelope method with efficient global</p> <p>optimization. In the fourth research task, a general time- and space-dependent problem is</p> <p>investigated. The envelope method converts the time- and space-dependent problem into time- and</p> <p>space-independent one, and the second order approximation is used to predict results. The last task</p> <p>proposes a new sequential reliability-based design with the envelope method for time- and spacedependent</p> <p>reliability. The accuracy and efficiency of our proposed methods are demonstrated</p> <p>through a wide range of mathematics problems and engineering problems.</p>