Uncertainty Analysis for Time- and Space-Dependent Responses with Random Variables


The performance of a product varies with respect to time and space if the associated limit-state function involves time and space. This study develops an uncertainty analysis method that quantifies the effect of random input variables on the performance (response) over time and space. The combination of the first order reliability method (FORM) and the second-order reliability method (SORM) is used to approximate the extreme value of the response with respect to space at discretized instants of time. Then the response becomes a Gaussian stochastic process that is fully defined by the mean, variance, and autocorrelation functions obtained from FORM and SORM, and a sequential single loop procedure is performed for spatial and random variables. The method is successfully applied to the reliability analysis of a crank-slider mechanism, which operates in a specified period of time and space.


Mechanical and Aerospace Engineering

Research Center/Lab(s)

Intelligent Systems Center


Directorate for Engineering, National Science Foundation under grant CMMI 1727329. The support from the Intelligent Systems Center at the Missouri University of Science and Technology is also acknowledged.

Keywords and Phrases

Random processes; Random variables; Reliability analysis; Stochastic systems, Autocorrelation functions; Crank slider mechanisms; Extreme value; First order reliability methods; Gaussian stochastic process; Limit state functions; Random input; Second-order reliability methods, Uncertainty analysis

International Standard Serial Number (ISSN)

1050-0472; 1528-9001

Document Type

Article - Journal

Document Version


File Type





© 2019 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Feb 2019