Multi-FNN Identification Based on HCM Clustering and Evolutionary Fuzzy Granulation

In this paper, we introduce a category of Multi-FNN (Fuzzy-Neural Networks) models, analyze the underlying architectures and propose a comprehensive identification framework. The proposed Multi-FNNs dwell on a concept of fuzzy rule-based FNNs based on HCM clustering and evolutionary fuzzy granulation, and exploit linear inference being treated as a generic inference mechanism. By this nature, this FNN model is geared toward capturing relationships between information granules known as fuzzy sets. The form of the information granules themselves (in particular their distribution and a type of membership function) becomes an important design feature of the FNN model contributing to its structural as well as parametric optimization. The identification environment uses clustering techniques (Hard C - Means, HCM) and exploits genetic optimization as a vehicle of global optimization. The global optimization is augmented by more refined gradient-based learning mechanisms such as standard back-propagation. The HCM algorithm, whose role is to carry out preprocessing of the process data for system modeling, is utilized to determine the structure of Multi-FNNs. The detailed parameters of the Multi-FNN (such as apexes of membership functions, learning rates and momentum coefficients) are adjusted using genetic algorithms. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the model. To evaluate the performance of the proposed model, two numeric data sets are experimented with. One is the numerical data coming from a description of a certain nonlinear function and the other is NOx emission process data from a gas turbine power plant.