Doctoral Dissertations


Zhangli Hu

Keywords and Phrases

Design under uncertainty; Optimization; Reliability; Simulation-based design; Uncertainty; Uncertainty quantification


"Engineers always encounter time-dependent uncertainties that ubiquitously exist, such as the random deterioration of material properties and time-variant loads. Therefore the reliability of engineering systems becomes time-dependent. It is crucial to predict the time-dependent reliability in the design stage, given possible catastrophic consequences of a failure. Although extensive research has been conducted on reliability analysis, estimating the reliability accurately and efficiently is still challenging. The objective of this work is to develop accurate and efficient reliability methodologies for engineering design. The basic idea is the integration of traditional reliability methods with saddlepoint approximation (SPA), which can accurately approximate the tail distribution of a random variable. Four methods are proposed in this work. The first three methods deal with time-independent reliability while the last one estimates the time-dependent reliability. The first method combines SPA with first-order approximation and achieves higher accuracy over the traditional first-order reliability method when bimodal distributions are involved. The second method further improves the accuracy of reliability estimation by integrating SPA with the second-order approximation. The third method extends the second method into the reliability-based design for higher accuracy, and the high efficiency is maintained by an efficient algorithm for searching for an equivalent reliability index. The fourth method uses sequential efficient global optimization to convert a time-dependent problem into a time-independent counterpart. Then the second method is utilized to estimate the time-independent reliability after the conversion. The accuracy and effectiveness of the above methods are demonstrated by both numerical examples and engineering applications"--Abstract, page iv.


Han, Daoru Frank
Du, Xiaoping

Committee Member(s)

Hosder, Serhat
Midha, A. (Ashok)
Okafor, A. Chukwujekwu (Anthony Chukwujekwu)
Qin, Ruwen


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Mechanical Engineering


National Science Foundation (U.S.)
Missouri University of Science and Technology. Intelligent Systems Center


The author greatly appreciates the financial support from the National Science Foundation through Grants CMMI 1562593 and CMMI 1727329

Research Center/Lab(s)

Intelligent Systems Center


Missouri University of Science and Technology

Publication Date

Spring 2019

Journal article titles appearing in thesis/dissertation

  • Reliability methods for bimodal distribution with first order approximation
  • Saddlepoint approximation reliability method for quadratic functions in normal variables
  • Efficient reliability-based design with second order approximations
  • Second order reliability method for time-dependent reliability analysis using sequential efficient global optimization


xiv, 152 pages

Note about bibliography

Includes bibliographic references.


© 2019 Zhangli Hu, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11532

Electronic OCLC #