Kriging Models: An Extensive Analysis of their Current State, Applicability, Advantages and Limitations

Abstract

In recent decades, surrogate models have become an essential tool for optimizing complex systems, particularly within the framework of Design and Analysis of Computer Experiments (DoCE). These models have become increasingly popular due to their ability to reduce the computational time and costs associated with simulation models. This thesis explores the application of surrogate models in predicting the performance of complex systems, with a specific focus on a case study involving the simulation of a shaving machine developed by Philips. The simulation model evaluates the cut length of individual hairs based on multidimensional input data, but it is computationally expensive and time-consuming. The complex nature of the output, where approximately half of the cases have a zero evaluation, presents unique challenges that this thesis addresses through the application of various surrogate models. We provide a comprehensive review of surrogate models for both binary and continuous responses, including logistic regression, random forests, linear regression, and Kriging. Each model, along with its mathematical framework, training processes, and potential extensions, is discussed. Additionally, to asses the models, various performance metrics are explained. A novel methodology is introduced to handle the complex output structure of the Philips simulation model, which combines surrogate models for binary and continuous responses. Our findings show promising results as this new methodology produces results comparable to ordinary surrogate models while significantly reducing time complexity. This thesis contributes to the broader understanding of surrogate models and their applicability in complex industrial simulations.