0
Research Papers

A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis

[+] Author and Article Information
Zhen Hu

e-mail: zh4hd@mst.edu

Xiaoping Du

e-mail: dux@mst.edu
Department of Mechanical and Aerospace Engineering,
Missouri University of Science and Technology,
290D Toomey Hall,
400 West 13th Street,
Rolla, MO 65409-0500

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received December 30, 2012; final manuscript received February 8, 2013; published online May 10, 2013. Assoc. Editor: David Gorsich.

J. Mech. Des 135(7), 071003 (May 10, 2013) (8 pages) Paper No: MD-12-1633; doi: 10.1115/1.4023925 History: Received December 30, 2012; Revised February 08, 2013

Maintaining high accuracy and efficiency is a challenging issue in time-dependent reliability analysis. In this work, an accurate and efficient method is proposed for limit-state functions with the following features: The limit-state function is implicit with respect to time. There is only one stochastic process in the input to the limit-sate function. The stochastic process could be either a general strength or a general stress variable so that the limit-state function is monotonic to the stochastic process. The new method employs a sampling approach to estimate the distributions of the extreme value of the stochastic process. The extreme value is then used to replace the corresponding stochastic process. Consequently the time-dependent reliability analysis is converted into its time-invariant counterpart. The commonly used time-invariant reliability method, the first order reliability method, is then applied to calculate the probability of failure over a given period of time. The results show that the proposed method significantly improves the accuracy and efficiency of time-dependent reliability analysis.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Singh, A., Mourelatos, Z. P., and Li, J., 2010, “Design for Lifecycle Cost Using Time-Dependent Reliability,” J. Mech. Des., Trans. ASME, 132(9), p. 0910081. [CrossRef]
Nielsen, U. D., 2010, “Calculation of Mean Outcrossing Rates of Non-Gaussian Processes With Stochastic Input Parameters-Reliability of Containers Stowed on Ships in Severe Sea,” Probab. Eng. Mech., 25(2), pp. 206–217. [CrossRef]
Sergeyev, V. I., 1974, “Methods for Mechanism Reliability Calculation,” Mech. Mach. Theory, 9(1), pp. 97–106. [CrossRef]
Singh, A., Mourelatos, Z., and Nikolaidis, E., 2011, “An importance sampling approach for time-dependent reliability,” ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE, Washington, DC, pp. 1077–1088.
Van Noortwijk, J. M., Van Der Weide, J. A. M., Kallen, M. J., and Pandey, M. D., 2007, “Gamma Processes and Peaks-Over-Threshold Distributions for Time-Dependent Reliability,” Reliab. Eng. Syst. Saf., 92(12), pp. 1651–1658. [CrossRef]
Tont, G., Vlădăreanu, L., Munteanu, M. S., and Tont, D. G., 2010, “Markov Approach of Adaptive Task Assignment for Robotic System in Non-Stationary Environments,” WSEAS Trans. Circuits Syst., 9(3), pp. 273–282. Available at: http://www.worldses.org/journals/systems/systems-2010.htm
Li, J., Chen, J. B., and Fan, W. L., 2007, “The Equivalent Extreme-Value Event and Evaluation of the Structural System Reliability,” Struct. Safety, 29(2), pp. 112–131. [CrossRef]
Chen, J. B., and Li, J., 2007, “The Extreme Value Distribution and Dynamic Reliability Analysis of Nonlinear Structures With Uncertain Parameters,” Struct. Safety, 29(2), pp. 77–93. [CrossRef]
Lutes, L. D., and Sarkani, S., 2009, “Reliability Analysis of Systems Subject to First-Passage Failure,” NASA Technical Report No. NASA/CR-2009-215782.
Sudret, B., 2008, “Analytical Derivation of the Outcrossing Rate in Time-Variant Reliability Problems,” Struct. Infrastructure Eng., 4(5), pp. 353–362. [CrossRef]
Rice, S. O., 1944, “Mathematical Analysis of Random Noise,” Bell Syst. Tech. J., 23, pp. 282–332. Available at: http://www3.alcatel-lucent.com/bstj/vol23-1944/articles/bstj23-3-282.pdf
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]
Zhang, J. F., and Du, X., 2011, “Time-Dependent Reliability Analysis for Function Generator Mechanisms,” ASME J. Mech. Des., 133(3), p. 031005. [CrossRef]
Mejri, M., Cazuguel, M., and Cognard, J. Y., 2011, “A Time-Variant Reliability Approach for Ageing Marine Structures With Non-Linear Behaviour,” Comput. Struct., 89(19–20), pp. 1743–1753. [CrossRef]
Madsen, P. H. and Krenk, S., 1984, “Integral Equation Method for the First-Passage Problem in Random Vibration,” Trans. ASME, J. Appl. Mech., 51(3), pp. 674–679. [CrossRef]
Vanmarcke, E. H., 1975, “On the Distribution of the First-Passage Time for Normal Stationary Random Processes,” Trans. ASME, J. Appl. Mech., 42(1), pp. 215–220. [CrossRef]
Preumont, A., 1985, “On the Peak Factor of Stationary Gaussian Processes,” J. Sound Vib., 100(1), pp. 15–34. [CrossRef]
Huang, B., and Du, X., 2008, “Probabilistic Uncertainty Analysis by Mean-Value First Order Saddlepoint Approximation,” Reliab. Eng. Syst. Saf., 93(2), pp. 325–336. [CrossRef]
Vennell, R., 2011, “Estimating the Power Potential of Tidal Currents and the Impact of Power Extraction on Flow Speeds,” Renewable Energy, 36(12), pp. 3558–3565. [CrossRef]
Lutes, L. D., and Sarkani, S., Random Vibrations: Analysis of Structural and Mechanical Systems ( Elsevier, New York, 2004).
Yang, H. Z., and Zheng, W., 2011, “Metamodel Approach for Reliability-Based Design Optimization of a Steel Catenary Riser,” J. Mar. Sci. Technol., 16(2), pp. 202–213. [CrossRef]
Sheu, S. H., Yeh, R. H., Lin, Y. B., and Juang, M. G., 2001, “Bayesian Approach to an Adaptive Preventive Maintenance Model,” Reliab. Eng. Syst. Saf., 71(1), pp. 33–44. [CrossRef]
Hu, Z., and Du, X., 2012, “Reliability Analysis for Hydrokinetic Turbine Blades,” Renewable Energy, 48, pp. 251–262. [CrossRef]
Li, C. C., and Kiureghian, A. D., 1993, “Optimal Discretization of Random Fields,” J. Eng. Mech., 119(6), pp. 1136–1154. [CrossRef]
Daniels, H., 1954, “Saddlepoint Approximations in Statistics,” Ann. Math. Stat., 25(4), pp. 631–650. [CrossRef]
Du, X., and Sudjianto, A., 2004, “First-Order Saddlepoint Approximation for Reliability Analysis,” AIAA J., 42(6), pp. 1199–1207. [CrossRef]
Marsh, P., 1998, “Saddlepoint Approximations for Noncentral Quadratic Forms,” Econometric Theory, 14(05), pp. 539–559. [CrossRef]
Du, X., 2010, “System Reliability Analysis with Saddlepoint Approximation,” Struct. Multidiscip. Optim., 42(2), pp. 193–208. [CrossRef]
Huang, B., and Du, X., 2006, “A Saddlepoint Approximation Based Simulation Method for Uncertainty Analysis,” Int. J. Reliab. Saf., 1(1/2), pp. 206–224. [CrossRef]
Fisher, R. A., 1928, “Moments and Product Moments of Sampling Distribution,” Proc. London Math. Soc., 30(2), pp. 199–238. [CrossRef]
Lugannani, R., and Rice, S. O., 1980, “Saddlepoint Approximation for the Distribution of the Sum of Independent Random Variables,” Adv. Appl. Probab., 12(2), pp. 475–490. [CrossRef]
Du, X., 2008, “Saddlepoint Approximation for Sequential Optimization and Reliability Analysis,” Trans. ASME, J. Mech. Des., 130(1), p. 011011. [CrossRef]
Chiralaksanakul, A., and Mahadevan, S., 2005, “First-Order Approximation Methods in Reliability-Based Design Optimization,” Trans. ASME, J. Mech. Des., 127(5), pp. 851–857. [CrossRef]
Koduru, S. D., and Haukaas, T., 2010, “Feasibility of Form in Finite Element Reliability Analysis,” Struct. Safety, 32(2), pp. 145–153. [CrossRef]
Lee, S. H., and Kwak, B. M., 2006, “Response Surface Augmented Moment Method for Efficient Reliability Analysis,” Struct. Safety, 28(3), pp. 261–272. [CrossRef]
Martin, O. L. H., 2008, Aerodynamics of Wind Turbines, 2nd ed., Earthscan, Sterling.

Figures

Grahic Jump Location
Fig. 1

Flow chart of the new time-dependent reliability method

Grahic Jump Location
Fig. 2

A Trajectory of a stochastic process

Grahic Jump Location
Fig. 3

A Beam under random loading

Grahic Jump Location
Fig. 6

Cross section at root of the turbine blade

Grahic Jump Location
Fig. 7

River flow loading on the turbine blade

Grahic Jump Location
Fig. 8

CDFs of maximum river velocity over different time intervals

Grahic Jump Location
Fig. 9

Probability of failure of the hydrokinetic turbine blade

Grahic Jump Location
Fig. 4

CDFs of maximum load over different time intervals

Grahic Jump Location
Fig. 5

Probability of failure of the beam over different time intervals

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In