Hybrid sampling applied to machine learning for modeling multivariable engineering problems

Purpose The purpose of this work is to present a new sampling method to improve the computational time and accuracy of metamodels applied to multivariable engineering problems. Design/methodology/approach This method combines a geostatistical approach based on adaptive kriging (AK) with a genetic algorithm (GA) based on Non-dominated Sorting Genetic Algorithm II (NSGA II) operating on a dedicated mesh. An initial set of random designs is selected by Latin hypercube sampling (LHS). The machine learning technique based on k-means groups them into clusters. From each cluster, the best design is selected using the coupled AK and GA algorithms, with the maximum mean squared error (MSE) and its minimum derivative (dMSE) as selection criteria. Findings The results indicate that the metamodel generated by the proposed method reaches a 2% error and is 2,700 s faster than conventional kriging (CK) in the cantilever problem with 10 variables and 350 s faster in the underwater explosion problem with 6 variables. Those results suggest that the proposed method produces metamodels that achieve higher fidelity faster than CK, particularly in high-dimensional and/or complex problems. Research limitations/implications Problems with few variables and simple complexity are better suited to CK rather than the proposed method, due to the shorter computational time required by CK. Originality/value This proposed procedure optimizes the sampling process by identifying specific locations in the design space with relatively few samples using AK, GA, LHS and K-means algorithms all together, adopting MSE and dMSE as metric selection for the best sample.