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

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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Andrieu-Renaud, C. , Sudret, B. , and Lemaire, M. , 2004, “ The PHI2 Method: A Way to Compute Time-Variant Reliability,” Reliab. Eng. Syst. Saf., 84(1), pp. 75–86. [CrossRef]
Hu, Z. , and Du, X. , 2012, “ Reliability Analysis for Hydrokinetic Turbine Blades,” Renewable Energy, 48, pp. 251–262. [CrossRef]
Hu, Z. , and Du, X. , 2013, “ Time-Dependent Reliability Analysis With Joint Upcrossing Rates,” Struct. Multidiscip. Optim., 48(5), pp. 893–907. [CrossRef]
Preumont, A. , 1985, “ On the Peak Factor of Stationary Gaussian Processes,” J. Sound Vib., 100(1), pp. 15–34. [CrossRef]
Singh, A. , and Mourelatos, Z. P. , 2010, “ On the Time-Dependent Reliability of Non-Monotonic, Non-Repairable Systems,” SAE Int. J. Mater. Manuf., 3(1), pp. 425–444. [CrossRef]
Wang, Z. , and Wang, P. , 2012, “ A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization,” ASME J. Mech. Des., 134(12), p. 121007. [CrossRef]
Hu, Z. , and Du, X. , 2015, “ Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis,” ASME J. Mech. Des., 137(5), p. 051401. [CrossRef]
Li, J. , Chen, J.-b. , and Fan, W.-l. , 2007, “ The Equivalent Extreme-Value Event and Evaluation of the Structural System Reliability,” Struct. Saf., 29(2), pp. 112–131. [CrossRef]
Jiang, C. , Huang, X. , Han, X. , and Zhang, D. , 2014, “ A Time-Variant Reliability Analysis Method Based on Stochastic Process Discretization,” ASME J. Mech. Des., 136(9), p. 091009. [CrossRef]
Du, X. , 2014, “ Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation,” ASME J. Mech. Des., 136(8), p. 081010. [CrossRef]
Singh, A. , Mourelatos, Z. , and Nikolaidis, E. , 2011, “ Time-Dependent Reliability of Random Dynamic Systems Using Time-Series Modeling and Importance Sampling,” SAE Int. J. Mater. Manuf., 4(1), pp. 929–946. [CrossRef]
Wang, Z. , Mourelatos, Z. P. , Li, J. , Baseski, I. , and Singh, A. , 2014, “ Time-Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals,” ASME J. Mech. Des., 136(6), p. 061008. [CrossRef]
Hu, Z. , and Du, X. , 2015, “ First Order Reliability Method for Time-Variant Problems Using Series Expansions,” Struct. Multidiscip. Optim., 51(1), pp. 1–21. [CrossRef]
Hagen, Ø. , and Tvedt, L. , 1991, “ Vector Process Out-Crossing as Parallel System Sensitivity Measure,” J. Eng. Mech., 117(10), pp. 2201–2220. [CrossRef]
Song, J. , and Der Kiureghian, A. , 2006, “ Joint First-Passage Probability and Reliability of Systems Under Stochastic Excitation,” J. Eng. Mech., 132(1), pp. 65–77. [CrossRef]
Radhika, B. , Panda, S. , and Manohar, C. , 2008, “ Time Variant Reliability Analysis of Nonlinear Structural Dynamical Systems Using Combined Monte Carlo Simulations and Asymptotic Extreme Value Theory,” Comput. Model. Eng. Sci., 27(1–2), pp. 79–110.
Dey, A. , and Mahadevan, S. , 2000, “ Reliability Estimation With Time-Variant Loads and Resistances,” J. Struct. Eng., 126(5), pp. 612–620. [CrossRef]
Ditlevsen, O. , 1979, “ Narrow Reliability Bounds for Structural Systems,” J. Struct. Mech., 7(4), pp. 453–472. [CrossRef]
Hohenbichler, M. , and Rackwitz, R. , 1983, “ First-Order Concepts in System Reliability,” Struct. Saf., 1(3), pp. 177–188. [CrossRef]
Dey, A. , and Mahadevan, S. , 1998, “ Ductile Structural System Reliability Analysis Using Adaptive Importance Sampling,” Struct. Saf., 20(2), pp. 137–154. [CrossRef]
Youn, B. D. , and Wang, P. , 2009, “ Complementary Intersection Method for System Reliability Analysis,” ASME J. Mech. Des., 131(4), p. 041004. [CrossRef]
Wang, Z. , and Wang, P. , 2015, “ An Integrated Performance Measure Approach for System Reliability Analysis,” ASME J. Mech. Des., 137(2), p. 021406. [CrossRef]
Sudret, B. , and Der Kiureghian, A. , 2000, “ Stochastic Finite Element Methods and Reliability: A State-of-the-Art Report,” Department of Civil and Environmental Engineering, University of California, Berkeley, CA, Technical Report No. UCB/SEMM-2000/08.
Amsallem, D. , and Farhat, C. , 2012, “ Stabilization of Projection-Based Reduced-Order Models,” Int. J. Numer. Methods Eng., 91(4), pp. 358–377. [CrossRef]
Xi, Z. , Youn, B. D. , and Hu, C. , 2010, “ Random Field Characterization Considering Statistical Dependence for Probability Analysis and Design,” ASME J. Mech. Des., 132(10), p. 101008. [CrossRef]
Santner, T. J. , Williams, B. J. , and Notz, W. , 2003, The Design and Analysis of Computer Experiments, Springer, New York.
Swiler, L. P. , Hough, P. D. , Qian, P. , Xu, X. , Storlie, C. , and Lee, H. , 2014, “ Surrogate Models for Mixed Discrete-Continuous Variables,” Constraint Programming and Decision Making, Springer, Cham, Switzerland, pp. 181–202.
Wang, P. , Hu, C. , and Youn, B. D. , 2011, “ A Generalized Complementary Intersection Method (GCIM) for System Reliability Analysis,” ASME J. Mech. Des., 133(7), p. 071003. [CrossRef]
Zhang, J. , and Du, X. , 2011, “ Time-Dependent Reliability Analysis for Function Generator Mechanisms,” ASME J. Mech. Des., 133(3), p. 031005. [CrossRef]
McDonald, M. , and Mahadevan, S. , 2008, “ Design Optimization With System-Level Reliability Constraints,” ASME J. Mech. Des., 130(2), p. 021403. [CrossRef]


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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. 3

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

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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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