Matlab codes of Subset Simulation for reliability analysis and structural optimization

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/.

[1]  James L. Beck,et al.  SUBSET SIMULATION AND ITS APPLICATION TO SEISMIC RISK BASED ON DYNAMIC ANALYSIS , 2003 .

[2]  James L. Beck,et al.  Hybrid Subset Simulation method for reliability estimation of dynamical systems subject to stochastic excitation , 2005 .

[3]  Lambros S. Katafygiotis,et al.  A two-stage Subset Simulation-based approach for calculating the reliability of inelastic structural systems subjected to Gaussian random excitations , 2005 .

[4]  Hong-shuang Li.  Subset simulation for unconstrained global optimization , 2011 .

[5]  James L. Beck,et al.  Reliability Estimation for Dynamical Systems Subject to Stochastic Excitation using Subset Simulation with Splitting , 2005 .

[6]  Maurice Lemaire,et al.  Assessing small failure probabilities by combined subset simulation and Support Vector Machines , 2011 .

[7]  Zhenzhou Lu,et al.  Subset simulation for structural reliability sensitivity analysis , 2009, Reliab. Eng. Syst. Saf..

[8]  Yu Wang,et al.  Efficient Monte Carlo Simulation of parameter sensitivity in probabilistic slope stability analysis , 2010 .

[9]  Jin Jiang,et al.  Efficient functional reliability estimation for a passive residual heat removal system with subset simulation based on importance sampling , 2015 .

[10]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[11]  Siu-Kui Au,et al.  Reliability-based design sensitivity by efficient simulation , 2005 .

[12]  Enrico Zio,et al.  Monte Carlo simulation-based sensitivity analysis of the model of a thermal-hydraulic passive system , 2012, Reliab. Eng. Syst. Saf..

[13]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[14]  Siu-Kui Au,et al.  Engineering Risk Assessment with Subset Simulation , 2014 .

[15]  Lambros S. Katafygiotis,et al.  Modified Metropolis–Hastings algorithm with delayed rejection , 2011 .

[16]  Lambros S. Katafygiotis,et al.  Bayesian post-processor and other enhancements of Subset Simulation for estimating failure probabilities in high dimensions , 2011 .

[17]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[18]  Dian-Qing Li,et al.  Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation , 2016, Landslides.

[19]  Sanjay R. Arwade,et al.  Computational Analysis of Randomness in Structural Mechanics , 2011 .

[20]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[21]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[22]  Helmut J. Pradlwarter,et al.  Chair of Engineering Mechanics Ifm-publication 2-402 Reliability Analysis of Spacecraft Structures under Static and Dynamic Loading , 2022 .

[23]  Siu-Kui Au,et al.  Application of subset simulation methods to reliability benchmark problems , 2007 .

[24]  Guillermo Rus-Carlborg,et al.  Approximate Bayesian Computation by Subset Simulation , 2014, SIAM J. Sci. Comput..

[25]  Kong Fah Tee,et al.  Application of subset simulation in reliability estimation of underground pipelines , 2014, Reliab. Eng. Syst. Saf..

[26]  Manolis Papadrakakis,et al.  Accelerated subset simulation with neural networks for reliability analysis , 2012 .

[27]  Hong-Shuang Li,et al.  Discrete Optimum Design for Truss Structures by Subset Simulation Algorithm , 2015 .

[28]  Lambros S. Katafygiotis,et al.  Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study , 2007 .

[29]  Yu WangY. Wang,et al.  Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet , 2011 .

[30]  Hong-shuang Li,et al.  Design optimization using Subset Simulation algorithm , 2010 .

[31]  Dian-Qing Li,et al.  Efficient and consistent reliability analysis of soil slope stability using both limit equilibrium analysis and finite element analysis , 2016 .

[32]  K. Phoon,et al.  Modified Metropolis–Hastings algorithm with reduced chain correlation for efficient subset simulation , 2011 .