Prediction of Mackey-Glass Chaotic Time Series with Effect of Superimposed Noise using FTLRNN Model

S.L. Badjate and S.V. Dudul (India)


Chaotic, focused time lagged recurrent neural network (FTLRNN), Multilayer perceptron, neural network, Multi step prediction, Noise.


In this paper, a focused time lagged recurrent neural network (FTLRNN) model with gamma memory is developed for multi step ahead (k=1,5,10.20,50,100) prediction of typical Mackey-glass Chaotic time series. It has been used as a model for white blood cell production and subsequently popularized in Neural network field due to its richness in chaotic behavior. It is observed that Mackey glass equation for τ =17 exhibit a rich chaotic behavior. This paper compares the performance of two neural network configurations namely a Multilayer Perceptron (MLP) and proposed FTLRNN with gamma memory. The standard back propagation algorithm with momentum term has been used for both the models. It is seen that estimated dynamic FTLRNN based model with gamma memory filter clearly outperforms the MLP NN in various performance matrices such as Mean square error (MSE), Normalized mean square error (NMSE) and correlation coefficient on testing as well as training data set for Multi step prediction (K=1,5,10,20,50,100).In addition, the output of proposed neural network model closely follows the desired output for multi step prediction. Also the proposed model robustness is tested by superimposing Uniform & Gaussion noise at the input and output in a network with a variance of 1% to 20%.

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