A general two-phase Markov chain Monte Carlo approach for constrained design optimization: Application to stochastic structural optimization

Jensen, H, Jerez, D and Beer, M ORCID: 0000-0002-0611-0345 (2021) A general two-phase Markov chain Monte Carlo approach for constrained design optimization: Application to stochastic structural optimization. Computer Methods in Applied Mechanics and Engineering, 373. p. 113487.

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Official URL: http://dx.doi.org/10.1016/j.cma.2020.113487

Abstract

This contribution presents a general approach for solving structural design problems formulated as a class of nonlinear constrained optimization problems. A Two-Phase approach based on Bayesian model updating is considered for obtaining the optimal designs. Phase I generates samples (designs) uniformly distributed over the feasible design space, while Phase II obtains a set of designs lying in the vicinity of the optimal solution set. The equivalent model updating problem is solved by the transitional Markov chain Monte Carlo method. The proposed constraint-handling approach is direct and does not require special constraint-handling techniques. The population-based stochastic optimization algorithm generates a set of nearly optimal solutions uniformly distributed over the vicinity of the optimal solution set. The set of optimal solutions provides valuable sensitivity information. In addition, the proposed scheme is a useful tool for exploration of complex feasible design spaces. The general approach is applied to an important class of problems. Specifically, reliability-based design optimization of structural dynamical systems under stochastic excitation. Numerical examples are presented to evaluate the effectiveness of the proposed design scheme.

Item Type:	Article
Uncontrolled Keywords:	Constrained optimization, Feasible design space, Meta-models, Markov sampling method, Reliability-based design, Stochastic optimization
Depositing User:	Symplectic Admin
Date Deposited:	03 Nov 2020 09:44
Last Modified:	18 Jan 2023 23:23
DOI:	10.1016/j.cma.2020.113487
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3105935