Research Papers: Design Automation

Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis

[+] Author and Article Information
Zhen Hu

Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
290D Toomey Hall,
400 West 13th Street,
Rolla, MO 65409-0500
e-mail: zh4hd@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 September 21, 2014; final manuscript received December 14, 2014; published online February 16, 2015. Assoc. Editor: Gary Wang.

J. Mech. Des 137(5), 051401 (May 01, 2015) (9 pages) Paper No: MD-14-1628; doi: 10.1115/1.4029520 History: Received September 21, 2014; Revised December 14, 2014; Online February 16, 2015

Time-dependent reliability analysis requires the use of the extreme value of a response. The extreme value function is usually highly nonlinear, and traditional reliability methods, such as the first order reliability method (FORM), may produce large errors. The solution to this problem is using a surrogate model of the extreme response. The objective of this work is to improve the efficiency of building such a surrogate model. A mixed efficient global optimization (m-EGO) method is proposed. Different from the current EGO method, which draws samples of random variables and time independently, the m-EGO method draws samples for the two types of samples simultaneously. The m-EGO method employs the adaptive Kriging–Monte Carlo simulation (AK–MCS) so that high accuracy is also achieved. Then, Monte Carlo simulation (MCS) is applied to calculate the time-dependent reliability based on the surrogate model. Good accuracy and efficiency of the m-EGO method are demonstrated by three examples.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Du, X., and Hu, Z., 2012, “First Order Reliability Method With Truncated Random Variables,” ASME J. Mech. Des., 134(9), p. 091005. [CrossRef]
Zhang, J., and Du, X., 2010, “A Second-Order Reliability Method With First-Order Efficiency,” ASME J. Mech. Des., 132(10), p. 101006. [CrossRef]
Li, J., Mourelatos, Z., and Singh, A., 2012, “Optimal Preventive Maintenance Schedule Based on Lifecycle Cost and Time-Dependent Reliability,” SAE Int. J. Mater. Manuf., 5(1), pp. 87–95. [CrossRef]
Singh, A., Mourelatos, Z. P., and Li, J., 2010, “Design for Lifecycle Cost Using Time-Dependent Reliability,” ASME J. Mech. Des., 132(9), p. 091008. [CrossRef]
Singh, A., Mourelatos, Z. P., and Nikolaidis, E., 2011, “An Importance Sampling Approach for Time-Dependent Reliability,” ASME Paper No. DETC2011-47200. [CrossRef]
Rice, S. O., 1945, “Mathematical Analysis of Random Noise,” Bell Syst.Tech. J., 24(1), pp. 146–156. [CrossRef]
Lindgren, G., 1984, “Extremal Ranks and Transformation of Variables or Extremes of Functions of Multivariate Gaussian Processes,” Stochastic Process Appl., 17(2), pp. 285–312. [CrossRef]
Breitung, K., 1984, “Asymptotic Crossing Rates for Stationary Gaussian Vector Processes,” Department of Mathematics and Statistics, University of Lund, Lund, Sweden, Technical Report No. 1.
Breitung, K., 1988, “Asymptotic Crossing Rates for Stationary Gaussian Vector Processes,” Stochastic Process Appl., 13(2), pp. 195–207. [CrossRef]
Ditlevsen, O., 1983, “Gaussian Outcrossings From Safe Convex Polyhedrons,” J. Eng. Mech., 109(1), pp. 127–148. [CrossRef]
Hagen, O., and Tvedt, L., 1991, “Vector Process Out-Crossing as Parallel System Sensitivity Measure,” J. Eng. Mech., 117(10), pp. 2201–2220. [CrossRef]
Hagen, O., and Tvedt, L., 1992, “Parallel System Approach for Vector Out-Crossing,” ASME J. Offshore Mech. Arct. Eng., 114(2), pp. 122–128. [CrossRef]
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(1), pp. 251–262. [CrossRef]
Vanmarcke, E. H., 1975, “On the Distribution of the First-Passage Time for Normal Stationary Random Processes,” ASME J. Appl. Mech., 42(1), pp. 215–220. [CrossRef]
Madsen, P. H., and Krenk, S., 1984, “Integral Equation Method for the First-Passage Problem in Random Vibration,” ASME J. Appl. Mech., 51(3), pp. 674–679. [CrossRef]
Hu, Z., and Du, X., 2013, “Time-Dependent Reliability Analysis With Joint Upcrossing Rates,” Struct. Multidiscip. Optim., 48(5), pp. 893–907. [CrossRef]
Hu, Z., Li, H., Du, X., and Chandrashekhara, K., 2012, “Simulation-Based Time-Dependent Reliability Analysis for Composite Hydrokinetic Turbine Blades,” Struct. Multidiscip. Optim., 47(5), pp. 765–781. [CrossRef]
Bichon, B. J., Eldred, M. S., Swiler, L. P., Mahadevan, S., and McFarland, J. M., 2007, “Multimodal Reliability Assessment for Complex Engineering Applications Using Efficient Global Optimization,” AIAA Paper No. AIAA-2007-1946. [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]
Jones, D. R., Schonlau, M., and Welch, W. J., 1998, “Efficient Global Optimization of Expensive Black-Box Functions,” J. Global Optim., 13(4), pp. 455–492. [CrossRef]
Chen, J. B., and Li, J., 2007, “The Extreme Value Distribution and Dynamic Reliability Analysis of Nonlinear Structures With Uncertain Parameters,” Struct. Saf., 29(2), pp. 77–93. [CrossRef]
Echard, B., Gayton, N., and Lemaire, M., 2011, “AK–MCS: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation,” Struct. Saf., 33(2), pp. 145–154. [CrossRef]
Hu, Z., and Du, X., 2013, “A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis,” ASME J. Mech. Des., 135(7), p. 071003. [CrossRef]
Hu, Z., and Du, X., 2014, “Lifetime Cost Optimization With Time-Dependent Reliability,” Eng. Optim., 46(10), pp. 1389–1410. [CrossRef]
Grogan, J. A., Leen, S. B., and Mchugh, P. E., 2013, “Optimizing the Design of a Bioabsorbable Metal Stent Using Computer Simulation Methods,” Biomaterials, 34(33), pp. 8049–8060. [CrossRef] [PubMed]
Lockwood, B., and Mavriplis, D., 2013, “Gradient-Based Methods for Uncertainty Quantification in Hypersonic Flows,” Comput. Fluids, 85(1), pp. 27–38. [CrossRef]
Raghavan, B., and Breitkopf, P., 2013, “Asynchronous Evolutionary Shape Optimization Based on High-Quality Surrogates: Application to an Air-Conditioning Duct,” Eng. Comput., 29(4), pp. 467–476. [CrossRef]
Steponaviče, I., Ruuska, S., and Miettinen, K., 2014, “A Solution Process for Simulation-Based Multiobjective Design Optimization With an Application in the Paper Industry,” Comput. Aided Des., 47, pp. 45–58. [CrossRef]
Lophaven;, S. N., Nielsen;, H. B., and Søndergaard, J., 2002, “DACE—A Matlab Kriging Toolbox,” Technical University of Denmark, Lyngby, Denmark.
Chen, W., Tsui, K.-L., Allen, J. K., and Mistree, F., 1995, “Integration of the Response Surface Methodology With the Compromise Decision Support Problem in Developing a General Robust Design Procedure,” 1995 ASME Design Engineering Technical Conference, pp. 485–492.
Hosder, S., Walters, R. W., and Balch, M., 2007, “Efficient Sampling for Non-Intrusive Polynomial Chaos Applications With Multiple Uncertain Input Variables,” 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI, Apr. 23–25, pp. 2946–2961.
Bichon, B. J., Eldred, M. S., Swiler, L. P., Mahadevan, S., and McFarland, J. M., 2008, “Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions,” AIAA J., 46(10), pp. 2459–2468. [CrossRef]
Wang, Z., and Wang, P., 2014, “A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design,” ASME J. Mech. Des., 136(2), p. 021006. [CrossRef]
Dubourg, V., Sudret, B., and Deheeger, F., 2013, “Metamodel-Based Importance Sampling for Structural Reliability Analysis,” Probab. Eng. Mech., 33, pp. 47–57. [CrossRef]
Basudhar, A., and Missoum, S., 2008, “Adaptive Explicit Decision Functions for Probabilistic Design and Optimization Using Support Vector Machines,” Comput. Struct., 86(19), pp. 1904–1917. [CrossRef]
Basudhar, A., Missoum, S., and Harrison Sanchez, A., 2008, “Limit State Function Identification Using Support Vector Machines for Discontinuous Responses and Disjoint Failure Domains,” Prob. Eng. Mech., 23(1), pp. 1–11. [CrossRef]
Basudhar, A., and Missoum, S., 2010, “An Improved Adaptive Sampling Scheme for the Construction of Explicit Boundaries,” Struct. Multidiscip. Optim., 42(4), pp. 517–529. [CrossRef]
Zhang, J., and Du, X., 2011, “Time-Dependent Reliability Analysis for Function Generator Mechanisms,” ASME J. Mech. Des., 133(3), p. 031005. [CrossRef]
Zang, C., Friswell, M. I., and Mottershead, J. E., 2005, “A Review of Robust Optimal Design and Its Application in Dynamics,” Comput. Struct., 83(4–5), pp. 315–326. [CrossRef]
Li, C.-C., and Der Kiureghian, A., 1993, “Optimal Discretization of Random Fields,” J. Eng. Mech., 119(6), pp. 1136–1154. [CrossRef]


Grahic Jump Location
Fig. 1

Ymax from independent EGO and mixed EGO and the true values

Grahic Jump Location
Fig. 2

A vibration problem

Grahic Jump Location
Fig. 3

One response Y at the mean value point of random variables

Grahic Jump Location
Fig. 4

Corroded beam subjected to stochastic loading




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