Tree-Based Response Surface Analysis

Abstract

Computer-simulated experiments have become a cost effective way for engineers to replace real experiments in the area of product development. However, one single computer-simulated experiment can still take a significant amount of time. Hence, in order to minimize the amount of simulations needed to investigate a certain design space, different approaches within the design of experiments area are used. One of the used approaches is to minimize the time consumption and simulations for design space exploration through response surface modeling. The traditional methods used for this purpose are linear regression, quadratic curve fitting and support vector machines. This paper analyses and compares the performance of four machine learning methods for the regression problem of response surface modeling. The four methods are linear regression, support vector machines, M5P and random forests. Experiments are conducted to compare the performance of tree models (M5P and random forests) with the performance of non-tree models (support vector machines and linear regression) on data that is typical for concept evaluation within the aerospace industry. The main finding is that comprehensible models (the tree models) perform at least as well as or better than traditional black-box models (the non-tree models). The first observation of this study is that engineers understand the functional behavior, and the relationship between inputs and outputs, for the concept selection tasks by using comprehensible models. The second observation is that engineers can also increase their knowledge about design concepts, and they can reduce the time for planning and conducting future experiments.