An Evolving Fuzzy Clustering Algorithm Based on Multivariable Potential Function for Data Modeling

In this paper, an evolving fuzzy clustering algorithm for time series is proposed, in which the clustering is performed based on computing the potential of the data, adopting the rate of variation and the density as variables within a multivariable Gaussian potential function criterion. The algorithm identifies clusters with time-varying prototypes using fuzzy covariance matrices and an exponential distance metric. Additionally, a sensitivity factor is employed to select centers of clusters from the potential of the data, a mutation-like mechanism is used for updating the clusters, and a crossover-like mechanism is used for merging the clusters. Computational results consider the implementation of the algorithm for evolving fuzzy clustering of data applied to the identification of SISO and MIMO Hammerstein dynamic systems, where the algorithm is employed in the data fuzzification process and in the creation of fuzzy rules in a fuzzy inference system that represents the static nonlinearity of the Hammerstein dynamic system. Experimental results consider the implementation of the algorithm for evolving fuzzy clustering of data applied to online identification of real-world dynamic systems (Thermal System and 2DOF Helicopter), where the algorithm is employed in the data fuzzification process and in the creation/updating of evolving fuzzy rules in an evolving fuzzy inference system. The identified fuzzy models present state-space submodels in the consequent propositions of the fuzzy rules, and their parametric identification is performed through OKID (Observer/Kalman Filter Identification), which computes the Markov parameters of the model from experimental data, and ERA (Eigensystem Realization Algorithm), which computes the matrices of the state-space submodels from the Markov parameters. In general, the results indicate that the proposed algorithm identifies clusters which are representative of the behavior of dynamic systems and obtains competitive performance compared to clustering algorithms in the literature.