Structural synthesis considering mixed discrete–continuous design variables: A Bayesian framework

• Published in: Mechanical systems and signal processing Vol. 162; p. 108042
• Main Authors: Jensen, H.A., Jerez, D.J., Beer, M.
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01.01.2022; Elsevier BV
• Subjects: Algorithms; Bayesian analysis; Bayesian updating; Constraint modelling; Continuity (mathematics); Design optimization; Discrete–continuous optimization; Feasible design space; Markov chains; Markov sampling method; Mathematical programming; Model updating; Monte Carlo simulation; Reliability-based optimization; Stochastic optimization; System effectiveness; Bayesian updating; Reliability-based optimization; Markov sampling method; Feasible design space; Stochastic optimization; Discrete–continuous optimization
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2021.108042

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. •Structural optimization considering discrete–continuous design variables is considered.•The optimal design is set into the framework of a Bayesian model updating problem.•The formulation is applied to the reliability-based optimization of stochastic systems.•The algorithm generates a set of nearly optimal designs.•Proposed scheme is a useful tool for exploration of complex design spaces.