Kriging-based optimization of functionally graded structures

Abstract

This work presents an efficient methodology for the optimum design of functionally graded structures using a Krigingbased approach. The method combines an adaptive Kriging framework with a hybrid particle swarm optimization (PSO) algorithm to improve the computational efficiency of the optimization process. In this approach, the surrogate model is used to replace the high-fidelity structural responses obtained by a NURBS-based isogeometric analysis. In addition, the impact of key factors on surrogate modelling, as the correlation function, the infill criterion used to update the surrogate model, and the constraint handling is assessed for accuracy, efficiency, and robustness. The design variables are related to the volume fraction distribution and the thickness. Displacement, fundamental frequency, buckling load, mass, and ceramic volume fraction are used as objective functions or constraints. The effectiveness and accuracy of the proposed algorithm are illustrated through a set of numerical examples. Results show a significant reduction in the computational effort over the conventional approach.

BIOS: an object-oriented framework for Surrogate-Based Optimization using bio-inspired algorithms

“…In fact, p l is often set at 2 to ease out the model fitting. Another way to describe the correlation between data points is the Matérn 5/2 function (Maia et al 2021):…”

“…In optimization problems, however, it might be wise to improve accuracy in promising regions of the design space, which corresponds to the Sequential Approximate Optimization (SAO) (Schmit and Farshi 1974;Kitayama and Yamazaki 2011;Ribeiro et al 2020;Maia et al 2021). In this approach, the surrogate model is continuously updated by the addition of new sampling points.…”

“…To this day, there are still important open issues in SAO design (Queipo et al 2005;Stork et al 2020b), e.g., what is the best approach to perform the selection of new data points, or how to deal with constrained optimization and discrete variables. Thus, further experimentation, testing, and comparison are required to establish SAO as a reliable technique for global optimization of real-world engineering problems (Simpson et al 2002;Wang and Shan 2007;Steponavičė et al 2016;Liu et al 2018;Ribeiro et al 2020;Maia et al 2021). For that purpose, the availability of a framework that allows further development and comparison between different methods is essential.…”

“…The SBO approach allows the use of more complex analysis procedures and enables the solution of practical composite design problems, which is a field that demands further study (Luersen et al 2015;Jaiswal et al 2018). BIOS implements SAO for different sampling methods, surrogate models, and infill criteria and proved to be highly efficient in this type of problem (Ribeiro et al 2020;Maia et al 2021).…”

“…Just as in the case of the MLE maximization, the maximization of the acquisition function is carried out by instantiating heuristic algorithms in BIOS and solving it as an optimization problem. This is interesting due to the multimodal nature of these functions (Maia et al 2021).…”