Algoritmo de variável instrumental nebulosa tipo-2 no espaço de estados para identificação evolutiva de sistemas dinâmicos não-estacionários

Abstract

In this thesis, a type-2 fuzzy instrumental variable algorithm in the state space is presented for the evolving identification of non-stationary dynamic systems. The adopted interval type-2 neuro-fuzzy model has five layers: 1) The preprocessing layer applies the Singular Spectrum Analysis Recursive Algorithm to compute the unobservable components of experimental data. Amongthesecomponents,the mostsignificant are chosen to compute the noise-free signal. 2) The evolving antecedent estimation layer partitions the data space using the fuzzy clustering algorithm to define the number of rules and estimate the parameters of type-2 interval fuzzy membership functions of the proposed model. The data space partitioning uses a multiscale approach to avoid data normalization, reducing computational effort and improving performance for non-stationary problems. 3) The rules activation layer computes the activation degree of each rule, providing useful information for updating the parameters of the proposed model. 4) The recursive submodel estimation layer updates the parameters of the state observer model of the consequent. This estimation is performed by the method of estimating the Markov parameters of the observer, using type-2 fuzzy instrumental variables to obtain asymptotic non-polarization. The instruments of the algorithm are obtained from the data processed in layer 1. 5) The rule composition layer estimates the lower and upper bounds of the neuro-fuzzy model output, defining the uncertainty region of the output. This aspect is innovative in the literature of type-2 interval fuzzy systems. The thesis also addresses aspects of algorithm initialization, computational complexity, and convergence analysis. To demonstrate the applicability and efficiency of the proposed methodology, the following experiments were performed: Identification of a non-linear SISO dynamic system, identification of a non-linear SISO system with a discontinuous function in a noisy environment, Online estimation of the position of a test rocket in a noisy environment, Online estimation of the 2DOF Helicopter, and online identification of a non-linear and time-varying multivariable system in a noisy environment. The results showed that the proposed methodology is a potential approach for modeling non-linear, non-stationary, and time-varying dynamic systems.