Sistemas neuro-fuzzy evolutivos : novos algoritmos de aprendizado e aplicações

Abstract

This work introduces incremental learning algorithms for evolving fuzzy models with applications in real-time systems with fast dynamics and algorithms with adaptive feature selection. The focus is on efficient and low computational cost algorithms. Four incremental learning algorithms were developed using the Neo-Fuzzy-Neuron (NFN) neuro-fuzzy network. Basically, the NFN is a set of n decoupled zero-order Takagi-Sugeno models, one for each input variable, each one containing m rules. The network structure favors the use of efficient recursive algorithms for parameter update and the inclusion/exclusion of fuzzy rules and input variables during incremental learning. The first algorithm (eNFN) uses an incremental learning approach that simultaneously granulates the input space and updates the weights of output models. Initially, two fuzzy rules are defined for each input and, depending on an error measure computed based on a data stream, rules can be added, deleted and/or have their parameters adjusted. The second algorithm (NFN-AFS) is an incremental mechanism for adaptive feature selection that allows inclusion/exclusion of input variables using a statistical test that considers the accuracy and complexity of the model, computed recursively. The third (eNFN-AFS) and fourth (X-eNFN-AFS) algorithms use an approach to evolve the network structure introduced in the eNFN and the mechanism to adaptive feature selection of the NFN-AFS. In eNFN-AFS the granulation of the domain of the input variables and the computation of the degree of activation of the membership functions are performed only once at each step, i.e. there is a unique set of membership functions for each input variable. Unlike of the eNFN-AFS, in X-eNFN-AFS granulation the domain of the input variables and computation of the degree of activation of the membership functions are performed for the current model and for each candidate model, i.e. each model (current and candidate) has a set of membership functions for each one of its input variable, at each step. The performance of the algorithms is evaluated considering nonlinear processes identification and times series forecasting problems. Computational experiments and comparisons against alternative evolving models show that the approaches introduced here are accurate and fast, characteristics suitable for adaptive systems modeling, especially in realtime, on-line environments. Furthermore, the eNFN was evaluated experimentally in real-time to model two actual systems (Magnetic Levitation System (MagLev) and Twin Rotor MIMO System (TRMS)) using high sampling rate. Experimental results show that the eNFN is capable to quickly capture the behavior of the system dynamics, and to model the system with precision and low computational complexity. Experimental results also show that the eNFN attains good accuracy, and suggest the neuro-fuzzy network as an effective approach to estimate state variables of fast nonlinear dynamic processes in real-time.