TY - JOUR

T1 - A general two-phase Markov chain Monte Carlo approach for constrained design optimization

T2 - Application to stochastic structural optimization

AU - Jensen, H.

AU - Jerez, D.

AU - Beer, M.

N1 - Funding Information: The research reported here was supported in part by CONICYT (National Commission for Scientific and Technological Research) under grant number 1200087 . Also, this research has been supported by CONICYT and DAAD under CONICYT-PFCHA/Doctorado Acuerdo Bilateral DAAD Becas Chile/ 2018-62180007 . In addition, this research has been implemented under the PAC (Programa Asistente Cientifico 2017)-UTFSM program. These supports are gratefully acknowledged by the authors.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - 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.

AB - 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.

KW - Constrained optimization

KW - Feasible design space

KW - Markov sampling method

KW - Meta-models

KW - Reliability-based design

KW - Stochastic optimization

UR - http://www.scopus.com/inward/record.url?scp=85093679937&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2020.113487

DO - 10.1016/j.cma.2020.113487

M3 - Article

AN - SCOPUS:85093679937

VL - 373

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 113487

ER -