Gradient-Enhanced Universal Kriging with Polynomial Chaos Expansion for Design Exploration

• Main Author: Zakaria, Kemas
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/42009
• Institution: Institut Teknologi Bandung

Kriging has been well-known as a surrogate model used in many engineering design exploration problem. Surrogate models is quick to evaluate and gives accurate approximation for design exploration purpose. In this thesis, a new surrogate model is proposed and is categorized as a gradient-enhanced universal Kriging by utilizing polynomial chaos expansion as the trend function. The polynomial term will be chosen based on the least angle regression (LARS) method, along with the training of hyperparameters in the surrogate model through maximizing the likelihood estimate. The performance of the proposed gradient-enhanced polynomial chaos Kriging (GEPCK) in both analytical and real test cases is presented and then compare it with other common types of surrogate models, such as ordinary Kriging (OK), ordinary gradientenhanced Kriging (GEK), polynomial chaos expansion (PCE), and gradientenhanced polynomial chaos expansion (GEPCE). The results are presented in the normalized root-mean-squared-error (NRMSE) metric as a boxplot, with 50 dierent initial sample position, hence producing 50 data in each boxplots, in order to see the robustness of the proposed surrogate models and then the number of samples in each cases is varied to see the in uence of increasing the number of samples in the proposed surrogate models. The test cases involve analytical functions and real cases such as drag coecient of an arifoil and a wing, and aerostructural problem. From all of the results, GEPCK consistently outperforms other surrogate models, either in terms of accuracy or robustness, for both in analytical and real test cases.