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Research Papers: Design Automation

Time-Dependent System Reliability Analysis Using Random Field Discretization

[+] Author and Article Information
Zhen Hu

Department of Civil and
Environmental Engineering,
Vanderbilt University,
279 Jacobs Hall,
VU Mailbox: PMB 351831,
Nashville, TN 37235
e-mail: zhen.hu@vanderbilt.edu

Sankaran Mahadevan

Professor
Department of Civil and
Environmental Engineering,
Vanderbilt University,
272 Jacobs Hall,
VU Mailbox: PMB 351831,
Nashville, TN 37235
e-mail: sankaran.mahadevan@vanderbilt.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 29, 2015; final manuscript received August 11, 2015; published online September 2, 2015. Assoc. Editor: Xiaoping Du.

J. Mech. Des 137(10), 101404 (Sep 02, 2015) (10 pages) Paper No: MD-15-1334; doi: 10.1115/1.4031337 History: Received April 29, 2015; Revised August 11, 2015

This paper proposes a novel and efficient methodology for time-dependent system reliability analysis of systems with multiple limit-state functions of random variables, stochastic processes, and time. Since there are correlations and variations between components and over time, the overall system is formulated as a random field with two dimensions: component index and time. To overcome the difficulties in modeling the two-dimensional random field, an equivalent Gaussian random field is constructed based on the probability equivalency between the two random fields. The first-order reliability method (FORM) is employed to obtain important features of the equivalent random field. By generating samples from the equivalent random field, the time-dependent system reliability is estimated from Boolean functions defined according to the system topology. Using one system reliability analysis, the proposed method can get not only the entire time-dependent system probability of failure curve up to a time interval of interest but also two other important outputs, namely, the time-dependent probability of failure of individual components and dominant failure sequences. Three examples featuring series, parallel, and combined systems are used to demonstrate the effectiveness of the proposed method.

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Figures

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Fig. 1

Three-level illustration of time-dependent system reliability analysis

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Fig. 2

Flowchart for surrogate modeling of β̂(d) and ρ̂L(di, dj)

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Fig. 4

A function generator mechanism system

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Fig. 5

Time-dependent system probability of failure and failure sequences: (a) component 1, (b) component 2, (c) system, and (d) failure sequences

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Fig. 6

A Daniels system with two components

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Fig. 7

Time-dependent system probability of failure and failure sequences of example 2: (a) component 1, (b) component 2, (c) system, and (d) failure sequences

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Fig. 8

(a) A six-bar indeterminate truss and (b) system configuration

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Fig. 9

Time-dependent component probability of failure: (a) component 1, (b) component 2, (c) component 3, (d) component 4, (e) component 5, and (f) component 6

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Fig. 10

Time-dependent system probability of failure

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Fig. 3

An example of a network system: (a) Wheatstone bridge system, (b) I3 = 1, and (c) I3 = 0

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