On efficient multistep non-linear time series prediction in chaotic diode resonator circuits by optimizing the combination of non-linear time series analysis and neural networks

Abstract

An improved novel non-linear time series prediction method is presented based on optimizing the combination of non-linear signal analysis and deterministic chaos techniques with Artificial Neural Networks of the Multilayer Perceptron (MLP) type. The proposed methodology has been applied to the non-linear time series produced by a diode resonator chaotic circuit. Multisim is used to simulate the circuit and show the presence of chaos. The first stage of the proposed approach employs a non-linear time series analysis module applying the method proposed by Grasberger and Procaccia, involving estimation of the correlation and minimum embedding dimension as well as of the corresponding largest Lyapunov exponent in combination with a nearest neighbour-based non-linear signal predictor. The two previously mentioned modules are used to construct the first stage of a one-step/multistep predictor while a back-propagation MLP is involved in the second stage to enhance prediction results. The novelty of the proposed two-stage predictor lies on that the back-propagation MLP is employed as an error predictor of the nearest neighbour-based first-stage non-linear signal forecasting application following an efficient strategy for optimizing the combination of nearest neighbour prediction based on deterministic chaos techniques and MLP neural networks. This novel two-stage predictor is evaluated through an extensive experimental study and is favourably compared with rival approaches.