Skip to main content
SpringerLink
Log in

Matlab codes of Subset Simulation for reliability analysis and structural optimization

  • EDUCATIONAL ARTICLE
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This paper presents two efficient and compact Matlab codes of Subset Simulation for reliability analysis and structural optimization. The codes for reliability analysis and structural optimization comprise of the direct Monte Carlo and Markov Chain Monte Carlo. The theoretical and numerical elements of Subset Simulation are briefly presented in this paper, as well as the detailed instructions to implement the standard codes for solving reliability analysis and structural optimization problems. The paper also discusses simple extensions of argument check, post-processing, alternative stop criterion and constraint-handling. Four examples are presented to demonstrate these codes, two for reliability analysis and two for structural optimization. This paper will be helpful for the students and newcomers both in reliability analysis and structural optimization to understand and use Subset Simulation. The complete codes are included in Appendixes 1 and 2, and they can be downloaded from https://sites.google.com/site/rasosubsim/.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  • Au SK (2005) Reliability-based design sensitivity by efficient simulation. Comput Struct 83(14):1048–1061

    Article  Google Scholar 

  • Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4):263–277

    Article  Google Scholar 

  • Au SK, Beck JL (2003) Subset simulation and its application to seismic risk based on dynamic analysis. J Eng Mech ASCE 129(8):901–917

    Article  Google Scholar 

  • Au SK, Wang Y (2014) Engineering risk assessment with subset simulation. John Wiley & Sons

  • Au SK, Ching J, Beck JL (2007) Application of subset simulation methods to reliability benchmark problems. Struct Saf 29(3):183–193

    Article  Google Scholar 

  • Bourinet JM, Deheeger F, Lemaire M (2011) Assessing small failure probabilities by combined subset simulation and support vector machines. Struct Saf 33(6):343–353

    Article  Google Scholar 

  • Bucher C (2009) Computational analysis of randomness in structural mechanics. CRC Press

  • Chiachío M et al (2014a) Approximate Bayesian computation by subset simulation. SIAM J Sci Comput 36(3):A1339–A1358

    Article  MathSciNet  MATH  Google Scholar 

  • Chiachío M, et al (2014) An efficient simulation framework for prognostics of asymptotic processes-a case study in composite materials. in Proceedings of the European conference of the prognostics and health management society

  • Ching J, Au SK, Beck JL (2005a) Reliability estimation for dynamical systems subject to stochastic excitation using subset simulation with splitting. Comput Methods Appl Mech Eng 194(12-16):1557–1579

    Article  MathSciNet  MATH  Google Scholar 

  • Ching J, Beck JL, Au SK (2005b) Hybrid Subset Simulation method for reliability estimation of dynamical systems subject to stochastic excitation. Probab Eng Mech 20(3):199–214

    Article  MATH  Google Scholar 

  • Coello Coello CA (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    Article  MATH  Google Scholar 

  • Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109

    Article  MathSciNet  MATH  Google Scholar 

  • Katafygiotis L, Cheung SH (2005) A two-stage subset simulation-based approach for calculating the reliability of inelastic structural systems subjected to gaussian random excitations. Comput Methods Appl Mech Eng 194(12-16):1581–1595

    Article  MATH  Google Scholar 

  • Katafygiotis LS, Cheung SH (2007) Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study. Struct Saf 29(3):194–207

    Article  Google Scholar 

  • Li HS (2011) Subset simulation for unconstrained global optimization. Appl Math Model 35(10):5108–5120

    Article  MathSciNet  MATH  Google Scholar 

  • Li HS, Au SK (2010) Design optimization using subset simulation algorithm. Struct Saf 32(6):384–392

    Article  Google Scholar 

  • Li HS, Ma YZ (2015) Discrete optimum design for truss structures by subset simulation algorithm. J Aerosp Eng 28(4):04014091

    Article  Google Scholar 

  • Li DQ, Xiao T, Cao Z, Zhou C B, and Zhang LM (2015). Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation. Landslides, p. 1-11.

  • Li DQ, Xiao T, Cao Z, Phoon KK and Zhou CB (2016). Efficient and Consistent Reliability Analysis of Soil Slope Stability Using both Limit Equilibrium Analysis and Finite Element Analysis. Applied Mathematical Modelling, in press.

  • Metropolis N et al (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092

    Article  Google Scholar 

  • Papadopoulos V et al (2012) Accelerated subset simulation with neural networks for reliability analysis. Comput Methods Appl Mech Eng 223-224:70–80

    Article  MathSciNet  MATH  Google Scholar 

  • Pellissetti MF et al (2006) Reliability analysis of spacecraft structures under static and dynamic loading. Comput Struct 84(21):1313–1325

    Article  Google Scholar 

  • Robert CP, Casella G (2004) Monte Carlo statistical methods, 2nd edn. Springer, New York

    Book  MATH  Google Scholar 

  • Santoso AM, Phoon KK, Quek ST (2011) Modified metropolis–hastings algorithm with reduced chain correlation for efficient subset simulation. Probab Eng Mech 26(2):331–341

    Article  Google Scholar 

  • Song S, Lu Z, Qiao H (2009) Subset simulation for structural reliability sensitivity analysis. Reliab Eng Syst Saf 94(2):658–665

    Article  Google Scholar 

  • Tee KF, Khan LR, Li H (2014) Application of subset simulation in reliability estimation of underground pipelines. Reliab Eng Syst Saf 130:125–131

    Article  Google Scholar 

  • Wang Y, Cao Z, Au S-K (2010) Efficient Monte Carlo simulation of parameter sensitivity in probabilistic slope stability analysis. Comput Geotech 37(7–8):1015–1022

    Article  Google Scholar 

  • Wang Y, Cao Z, Au S-K (2011) Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Can Geotech J 48(1):162–172

    Article  Google Scholar 

  • Wang B et al (2015) Efficient functional reliability estimation for a passive residual heat removal system with subset simulation based on importance sampling. Prog Nucl Energy 78:36–46

    Article  Google Scholar 

  • Zio E, Pedroni N (2012) Monte Carlo simulation-based sensitivity analysis of the model of a thermal–hydraulic passive system. Reliab Eng Syst Saf 107:90–106

    Article  Google Scholar 

  • Zuev KM, Katafygiotis LS (2011) Modified metropolis–hastings algorithm with delayed rejection. Probab Eng Mech 26(3):405–412

    Article  Google Scholar 

  • Zuev KM et al (2012) Bayesian post-processor and other enhancements of subset simulation for estimating failure probabilities in high dimensions. Comput Struct 92–93:283–296

    Article  Google Scholar 

Download references

Acknowledgments

The authors are grateful for the support by Fundamental Research Funds for the Central Universities (Project No.3082015NS2015007).

Author information

Authors and Affiliations

  1. Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicles, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Hong-Shuang Li

  2. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, China

    Zi-Jun Cao

Authors
  1. Hong-Shuang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zi-Jun Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hong-Shuang Li.

Appendices

Appendix 1: subset simulation for reliability analysis

Appendix 2: subset simulation for structural optimization

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, HS., Cao, ZJ. Matlab codes of Subset Simulation for reliability analysis and structural optimization. Struct Multidisc Optim 54, 391–410 (2016). https://doi.org/10.1007/s00158-016-1414-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-016-1414-5

Keywords

Search

Navigation