Stochastic structural optimization using particle swarm optimization, surrogate models and Bayesian statistics

Abstract This paper focuses on a method to solve structural optimization problems using particle swarm optimization (PSO), surrogate models and Bayesian statistics. PSO is a random/stochastic search algorithm designed to find the global optimum. However, PSO needs many evaluations compared to gradient-based optimization. This means PSO increases the analysis costs of structural optimization. One of the methods to reduce computing costs in stochastic optimization is to use approximation techniques. In this work, surrogate models are used, including the response surface method (RSM) and Kriging. When surrogate models are used, there are some errors between exact values and approximated values. These errors decrease the reliability of the optimum values and discard the realistic approximation of using surrogate models. In this paper, Bayesian statistics is used to obtain more reliable results. To verify and confirm the efficiency of the proposed method using surrogate models and Bayesian statistics for stochastic structural optimization, two numerical examples are optimized, and the optimization of a hub sleeve is demonstrated as a practical problem.

[1]  Ehl Emile Aarts,et al.  Simulated annealing and Boltzmann machines , 2003 .

[2]  Yuxin Zhao,et al.  A modified particle swarm optimization via particle visual modeling analysis , 2009, Comput. Math. Appl..

[3]  David Maxwell Chickering,et al.  Learning Bayesian Networks: The Combination of Knowledge and Statistical Data , 1994, Machine Learning.

[4]  Bilal M. Ayyub,et al.  Probability, Statistics, and Reliability for Engineers and Scientists , 2003 .

[5]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[6]  F. Vahabzadeh,et al.  Application of the central composite design and response surface methodology to the advanced treatment of olive oil processing wastewater using Fenton's peroxidation. , 2005, Journal of hazardous materials.

[7]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[8]  Chongzhao Han,et al.  Knowledge-based cooperative particle swarm optimization , 2008, Appl. Math. Comput..

[9]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[10]  T. Simpson,et al.  Use of Kriging Models to Approximate Deterministic Computer Models , 2005 .

[11]  T. W. Layne,et al.  A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models , 1998 .

[12]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[13]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .