Genetically optimized BP-ANN for parameter estimation of Time Varying Autoregressive process

Abstract

An optimal intelligent technique to estimate Time Varying Autoregressive (TVAR) model coefficients is proposed in this thesis. Conventionally, three methods may be used to estimate the TVAR coefficients which are Direct Method (DM), Adaptive Methods (AM) and Basis Function Methods (BFM). All of these methods are built on complex mathematics and recursive in nature which increases the computation time. Although the BFM approach is preferred for few reasons such as (1) they are able to track both slow and fast changing dynamics, (2) BFM does not suffer from convergence problem as in AM. However, it is complex to compute their parameters. In addition to that a type of Basis Function (BF) is able to detect Nonstationary Signals (NSS) with similar characteristics with the BF only. Therefore, limiting the use of AM and BFM in broader NSS processing as naturally they have signal dependent characteristics. In this thesis, a hybrid framework of Artificial Neural Network (ANN) and Genetic Algorithm (GA) known as BP-ANN-GA is proposed to estimate TVAR coefficients. Superior performances of ANN in prediction and its ability to learn complex mapping of input to output is combined with optimization ability of GA to perform this task. Two different ANN architectures are proposed, one to represent TVAR and another one for TVAR BF. These ANN architectures consist of three layers. The number of nodes in input layer is determined by model orders with one hidden layer which consists of an artificial neuron. The third layer has a single node which computes the estimation error which is used to update e the synaptic weight using Backpropagation (BP) learning algorithm. Estimated TVAR coefficients are then fed into GA for further optimization by allowing the TVAR coefficient to be changed within certain limits to ensure the stability. Finally, the TVAR coefficients estimated from proposed method are used to reconstruct various NSS and compared with other methods such as AR, TVAR and BF. It is shown that proposed method yields better accuracy than BP-ANN, AR, TVAR and BF methods. It is also found that the GA optimization produces stable TVAR coefficients when the TVAR coefficients are allowed to be optimized in limits of .Interestingly the BP-ANN-GA also exhibits signal independence characteristics such as independence from model orders and BF, therefore allowing its application to be extended to analyze various types of NSS.