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Research Papers

Time-Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals

[+] Author and Article Information
Zhonglai Wang

University of Electronic Science and Technology of China,
Chengdu, Sichuan 611731, China

Zissimos P. Mourelatos

Mechanical Engineering Department,
Oakland University,
Rochester, MI 48309
e-mail: mourelat@oakland.edu

Jing Li

Mechanical Engineering Department,
Oakland University,
Rochester, MI 48309

Igor Baseski, Amandeep Singh

U.S. Army TARDEC,
Warren, MI 48397

1Visiting Scholar from Mechanical Engineering Department, Oakland University, Rochester, MI 48309.

2Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 1, 2013; final manuscript received March 9, 2014; published online April 21, 2014. Assoc. Editor: Xiaoping Du.

J. Mech. Des 136(6), 061008 (Apr 21, 2014) (12 pages) Paper No: MD-13-1385; doi: 10.1115/1.4027162 History: Received September 01, 2013; Revised March 09, 2014

Time-dependent reliability is the probability that a system will perform its intended function successfully for a specified time. Unless many and often unrealistic assumptions are made, the accuracy and efficiency of time-dependent reliability estimation are major issues which may limit its practicality. Monte Carlo simulation (MCS) is accurate and easy to use, but it is computationally prohibitive for high dimensional, long duration, time-dependent (dynamic) systems with a low failure probability. This work is relevant to systems with random parameters excited by stochastic processes. Their response is calculated by time integrating a set of differential equations at discrete times. The limit state functions are, therefore, explicit in time and depend on time-invariant random variables and time-dependent stochastic processes. We present an improved subset simulation with splitting approach by partitioning the original high dimensional random process into a series of correlated, short duration, low dimensional random processes. Subset simulation reduces the computational cost by introducing appropriate intermediate failure sub-domains to express the low failure probability as a product of larger conditional failure probabilities. Splitting is an efficient sampling method to estimate the conditional probabilities. The proposed subset simulation with splitting not only estimates the time-dependent probability of failure at a given time but also estimates the cumulative distribution function up to that time with approximately the same cost. A vibration example involving a vehicle on a stochastic road demonstrates the advantages of the proposed approach.

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Figures

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Fig. 4

Schematic of basic features of the SS/SPT method

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Fig. 3

Sample functions generated by splitting

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Fig. 2

Accepted and rejected sample functions generated by MCMC

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Fig. 1

Pictorial representation of failure subdomains

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Fig. 5

Quarter vehicle model

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Fig. 6

Failure rate (a) and probability of failure (b) from SS/SPT method calculated at 2 s intervals

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Fig. 7

Failure rate (a) and probability of failure (b) from SS/SPT method calculated at 4 s intervals

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Fig. 8

Failure rate (a) and probability of failure (b) from SS/SPT method calculated at 8 s intervals

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Fig. 9

(a) C.O.V. of failure rate versus time, (b) C.O.V. of probability of failure in time interval [Tn-1,Tn] versus Nsn, and (c) C.O.V. of probability of failure in time period [0, T]

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