TY - JOUR

T1 - Structural synthesis considering mixed discrete–continuous design variables

T2 - A Bayesian framework

AU - Jensen, H. A.

AU - Jerez, D. J.

AU - Beer, M.

N1 - Funding Information: The research reported here was supported in part by CONICYT, Chile (National Commission for Scientific and Technological Research) under grant number 1200087 . Also, this research has been supported by CONICYT, Chile and DAAD, Germany 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 - 2022/1/1

Y1 - 2022/1/1

N2 - In this work attention is directed to general structural optimization problems considering discrete–continuous design variables. The optimization problem is formulated as the minimization of an objective function subject to multiple design requirements. The mathematical programming statement is set into the framework of a Bayesian model updating problem. Constraints are handled directly within the proposed scheme, generating designs distributed over the feasible design space. Based on these samples, a set of designs lying in the vicinity of the optimal solution set is obtained. The Bayesian model updating problem is solved by an effective Markov chain Monte Carlo simulation scheme, where appropriate proposal distributions are introduced for the continuous and discrete design variables. The approach can efficiently estimate the sensitivity of the final design and constraints with respect to the design variables. In addition, the numerical implementation of the optimization algorithm depends on few control parameters. For illustration purposes, the general formulation is applied to an important class of problems, specifically, reliability-based design optimization of structural systems under stochastic excitation. Three numerical examples showing the effectiveness and potentiality of the approach reported herein are presented.

AB - In this work attention is directed to general structural optimization problems considering discrete–continuous design variables. The optimization problem is formulated as the minimization of an objective function subject to multiple design requirements. The mathematical programming statement is set into the framework of a Bayesian model updating problem. Constraints are handled directly within the proposed scheme, generating designs distributed over the feasible design space. Based on these samples, a set of designs lying in the vicinity of the optimal solution set is obtained. The Bayesian model updating problem is solved by an effective Markov chain Monte Carlo simulation scheme, where appropriate proposal distributions are introduced for the continuous and discrete design variables. The approach can efficiently estimate the sensitivity of the final design and constraints with respect to the design variables. In addition, the numerical implementation of the optimization algorithm depends on few control parameters. For illustration purposes, the general formulation is applied to an important class of problems, specifically, reliability-based design optimization of structural systems under stochastic excitation. Three numerical examples showing the effectiveness and potentiality of the approach reported herein are presented.

KW - Bayesian updating

KW - Discrete–continuous optimization

KW - Feasible design space

KW - Markov sampling method

KW - Reliability-based optimization

KW - Stochastic optimization

UR - http://www.scopus.com/inward/record.url?scp=85110307848&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2021.108042

DO - 10.1016/j.ymssp.2021.108042

M3 - Article

AN - SCOPUS:85110307848

VL - 162

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 108042

ER -