Nonlinear Model Order Selection: A GMM Clustering Approach Based on a Genetic Version of EM Algorithm

Choosing an accurate model order is one of the important sections in system identification. Traditionally, the model order selection of a nonlinear system depends on a predetermined model. However, it requires excess calculation and is impossible to get rid of the trouble of the structural design of the model, once the specific model was determined. A false nearest neighbor (FNN) algorithm that only relies on input-output data to estimate the model order is proposed here. Due to the FNN algorithm is sensitive to its own threshold which is a crucial constant for evaluating the model structure, Gaussian mixture model (GMM) clustering based on a genetic version of the expectation-maximization (EM) algorithm and minimum description length (MDL) criterion is developed in this paper, where the order can be determined without relying on a specific model. The GMM clustering is proposed to calculate the threshold of the FNN. Then, the genetic algorithm and MDL criteria are embedded to optimize the calculation of the EM algorithm as reduce the influence of initial values and not prone to fall into local extreme values as well. Three examples are given here to indicate the superiority of this technique: simulation of a strongly nonlinear system, isothermal polymerization process, and Van der Vusse reaction in relevant reference. Finally, some typical modeling methods are conducted to confirm the validity of this approach.