A modified MGGP algorithm for structure selection of NARMAX models

Abstract

In the area of system identification, the input-output Nonlinear Autoregressive Moving Average with Exogenous Variables (NARMAX) models are of great interest. The most challenging task faced when working with such models is to select the appropriate model structure that best represent the underlying system in the data. This structure selection is usually made via Error Reduction Ratio (ERR)-based algorithms. These algorithms suffer from the curse of dimensionality when high degree of nonlinearity and long-term dependencies are required. Further, some nonlinearities require specific functions or terms in the model structure to be reproduced, i.e. the hysteretic behavior. The ERR-based algorithm may leave these fundamental terms out of the selected structure. Alternatively, Evolutionary Algorithms (EAs) can be used to perform the structure selection process. They are methods that evolves a population of individuals through generations (or epochs) via selection, mutation, and reproduction phenomena. In the case of system identification, each individual would be a candidate model. This dissertation proposes the hybridization of an EA called Multi-Gene Genetic Programming (MGGP) with an ERR-based algorithm to perform the identification process even for those cases in which specific functions are required. In total, four experiments are performed. The first two experiments analyse noise level and soft input problems using stochastic test systems to generate data. As result we verify that the increment of equation noise level does not interfere in the structure selection outcome and that the hybridization MGGP/ERR is beneficial in comparison with the standalone MGGP for the soft input problem. The MGGP/ERR yields more parsimonious models that perform better in free- run simulation. The third experiment is the identification of a hydraulic pumping system benchmark. It is shown that the MGGP/ERR is able to explore a wide range in search space for which the traditional ERR-based algorithm would require a very high computational power. And finally, the last experiment is the identification of a piezoelectric actuator, which is characterized by the hysteretic behavior. It is included specific functions in the search space so that the MGGP/ERR is able to identify hysteresis. A novel and easy-to-use toolbox based on Python was developed and is available under GPL.