Sparse Approximation of LS-SVM for LPV-ARX Model Identification: Application to a Powertrain Subsystem

Least Squares Support Vector Machine (LS-SVM) has been recently applied to non-parametric identification of Linear Parameter Varying (LPV) systems, described by the AutoRegressive with eXogenous input (ARX). However, the online application of LPV-ARX system in the LS-SVM setting requires high computational time, related to the number of training data used to compute the coefficients of the identified model, limiting the possibility to use the method to real-time applications. In this paper, the authors propose the Low-Rank (LR) matrix approximation and a pruning based approach to compute a sparse solution. In particular, the pruning algorithm is considered to compute off-line a sparse solution of Lagrangian multipliers and then speed up the testing stage, whereas the LR matrix approximation allows to speed up the training stage. The proposed approach has been tested by identifying a subsystem of a vehicle powertrain model by the input/output data collected from the simulation model. The proposed approach has been compared with respect to the standard approach based on LS-SVM. The methods are tested on the considered real-world problem and the proposed approach permits to reduce the execution time of about 77% on average in the considered identification problem, corresponding to a degradation of the identification result less than 0.2% with respect to the standard solution.