Modelling and Analysis of Simple Pendulum Computer Experiments using a Support Vector Regression Model with B-Splines Kernel Function
Computer experimentation technique has been commonly applied as an alternative approach to physical experiment in engineering, science and technology in the recent time. It is more accepted than the classical physical experiments due to its flexibility when developing computer experiments and building metamodels of computer models. Sometimes, it is used to complement or serve as a proxy to real life or physical experiments. Experimental design is rapidly growing since it is useful to both physical processes and computer or simulation models. In this study, an Orthogonal Array Latin Hypercube Design, OA (N, k ) LHD was used to develop simple pendulum computer experiments. The OA (49, 3) LHD was adopted in the development of simple pendulum computer experiments using a simple pendulum model. This model was used to simulate a simple pendulum experiment that is conventionally performed in the laboratory. A Support Vector Regression (SVR) model was employed as a computer based metamodel to mimic the simple pendulum computer model in order to reduce the required computational efforts in running the computer codes and predict the stoppage time of pendulum at untried inputs. The SVR algorithm was used for modelling and analysing simple pendulum computer experiments. MATLAB 2016 software was used to implement the SVR algorithm with B-Splines kernel function so that the SVR model adequately captures non-linearities in the simple pendulum computer model. The e-insensitive loss function was set at e=0.05 and C=8 in order to control the support vector regression model. Results obtained using the SVR model with B-Splines function trained with only 85.7% of the experimental runs with zero bias. The fitted SVR model predicted values that were close to the test data as shown in Figure 1.
Index Terms - Computer Experiments, B-splines Kernel Function, SVR Model, Orthogonal Array Latin Hypercube Design, Simple Pendulum Computer Model.