Efficient optimization of composite structures using multi-fidelity models

Abstract

Composite structures are receiving increasing interest in the last few decades. These often require the use of numerical analysis methods, such as the Finite Element Method (FEM) or the Isogeometric Analysis (IGA). Due to their high design flexibility, the optimization of composites is very promising, as it may provide more efficient structures. This work uses Surrogate Based Optimization (SBO) to make the process more efficient. Examples of robust surrogate modeling techniques are Radial Basis Functions (RBF) and Kriging. For an efficient optimization process, one may use the model to locate promising regions in the design space and add new data points. This way, the approximation quality in the regions of interest is improved. Another way of improving the model quality is to consider information from low-fidelity sampling points, which are often cheaper and easier to assess. Here, a low-fidelity point refers to data evaluated using lower fidelity sources, such as using a coarser mesh or a simplified theory. If low-fidelity and high-fidelity sources are well-correlated, the low-fidelity sample may capture the general behavior of the function in the design space, thus greatly improving the model prediction while also allowing for a lower computational cost. These are denominated Multi-Fidelity Models (MFMs). This work aims at employing these techniques in the optimization of laminated composites and functionally graded structures, mainly plates and shells. The use of adaptive sampling is integrated into MFMs, where error-based exploration is employed to further improve the model. Different surrogate modeling approaches and adaptive sampling criteria are tested. Different aspects of multi-fidelity modeling are discussed, such as importance of correlation between sources, analyses cost, and ratio between low and high-fidelity samples. Our proposed methodology is able to solve both functionally graded and laminate problems, and very good results are also obtained when expensive constraints are considered. Results show that MFMs are able to significantly reduce the number of expensive analyses required to find the optimum in most optimization problems. Accuracy is also improved, especially in complex multi-modal optimization problems. At the same time, as MFMs present higher model complexity, model building and evaluation costs are more restrictive than those found for usual single-fidelity models.