Impact of feature selection on system identification by means of NARX-SVM

Abstract

Support Vector Machines (SVM) are widely used in many fields of science, including system identification. The selection of feature vector plays a crucial role in SVM-based model building process. In this paper, we investigate the influence of the selection of feature vector on model’s quality. We have built an SVM model with a non-linear ARX (NARX) structure. The modelled system had a SISO structure, i.e. one input signal and one output signal. The output signal was temperature, which was controlled by a Peltier module. The supply voltage of the Peltier module was the input signal. The system had a non-linear characteristic. We have evaluated the model’s quality by the fit index. The classical feature selection of SVM with NARX structure comes down to a choice of the length of the regressor vector. For SISO models, this vector is determined by two parameters: nu and ny. These parameters determine the number of past samples of input and output signals of the system used to form the vector of regressors. In the present research we have tested two methods of building the vector of regressors, one classic and one using custom regressors. The results show that the vector of regressors obtained by the classical method can be shortened while maintaining the acceptable quality of the model. By using custom regressors, the feature vector of SVM can be reduced, which means also the reduction in calculation time.