Doctoral Dissertations


Xinpeng Wei

Keywords and Phrases

Adaptive Training; Machine Learning; Mean Time To Failure; Reliability Analysis; Robustness Analysis; Uncertainty Quantification


”During an engineering system design, engineers usually encounter uncertainties that ubiquitously exist, such as material properties, dimensions of components, and random loads. Some of these parameters do not change with time or space and hence are time- and space-independent. However, in many engineering applications, the more general time- and space-dependent uncertainty is frequently encountered. Consequently, the system exhibits random time- and space-dependent behaviors, which may result in a higher probability of failure, lower average lifetime, and/or worse robustness. Therefore, it is critical to quantify uncertainty and predict how the system behaves under time- and space- dependent uncertainty. The objective of this study is to develop accurate and efficient methods for uncertainty analysis. This study contains five works. In the first work, an accurate method based on the series expansion, Gauss-Hermite quadrature, and saddle point approximation is developed to calculate high-dimensional normal probabilities. Then the method is applied to estimate time-dependent reliability. In the second work, we develop an adaptive Kriging method to estimate product average lifetime. In the third work, a time- and space-dependent reliability analysis method based on the first-order and second-order methods is proposed. In the fourth work, we extend the existing robustness analysis to time- and space-dependent problems and develop an adaptive Kriging method to evaluate the time- and space-dependent robustness. In the fifth work, we develop an adaptive Kriging method to efficiently estimate the lower and upper bounds of the electric potentials of the photoelectron sheaths near the lunar surface”--Abstract, page iv.


Han, Daoru Frank

Committee Member(s)

Du, Xiaoping
Chandrashekhara, K.
Hosder, Serhat
He, Xiaoming


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Mechanical Engineering


This dissertation was supported by the National Science Foundation under Grant No. 1923799 (formerly 1727329) and the Intelligent System Center, which are gratefully acknowledged.

Research Center/Lab(s)

Intelligent Systems Center


Missouri University of Science and Technology

Publication Date

Fall 2020

Journal article titles appearing in thesis/dissertation

  • Approximation to multivariate normal integral and its application in time-dependent reliability analysis
  • Physics-based Gaussian process method for predicting average product lifetime in design stage
  • Uncertainty analysis for time- and space-dependent responses with random variables
  • Robustness metric for robust design optimization under time- and space-dependent uncertainty through modeling
  • Adaptive Kriging method for uncertainty quantification of the photoelectron sheath and dust levitation on the lunar surface


xvi, 188 pages

Note about bibliography

Includes bibliographic references.


© 2020 Xinpeng Wei, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11802

Electronic OCLC #