Research Papers: Design Automation

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

[+] Author and Article Information
Xinpeng Wei

Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
258A Toomey Hall 400 West 13th Street,
Rolla, MO 65409-0500
e-mail: weixinp@mst.edu

Xiaoping Du

Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
272 Toomey Hall, 400 West 13th Street,
Rolla, MO 65409-0500
e-mail: dux@mst.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 25, 2018; final manuscript received August 31, 2018; published online December 20, 2018. Assoc. Editor: Nam H. Kim.

J. Mech. Des 141(2), 021402 (Dec 20, 2018) (6 pages) Paper No: MD-18-1486; doi: 10.1115/1.4041429 History: Received June 25, 2018; Revised August 31, 2018

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.

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Grahic Jump Location
Fig. 2

The procedure of updating β(t) using SORM

Grahic Jump Location
Fig. 3

Flow chart of the complete procedure

Grahic Jump Location
Fig. 4

Probability of failure over different time intervals

Grahic Jump Location
Fig. 5

A slider mechanism

Grahic Jump Location
Fig. 6

Probability of failure over different time intervals



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