An Echo State Network With Improved Topology for Time Series Prediction

An echo state network with improved topology (IESN) is proposed for accurate and efficient time series prediction. In this approach, a tighter bound of the echo state property related to the Lipshitz constant of reservoir activation function and the maximum structured singular value of reservoir is firstly researched to run the model at the edge of chaos. A smooth composite reservoir activation function is then designed to enhance the ESN. The exact echo state property bound is solved by computing the Lipshitz constant of the composite function. Finally, a decoupling matrix with eigenvalues distributing uniformly in the complex plane is built as the reservoir for abundant dynamic characteristics. Six classical benchmarks are employed to test the IESN. Besides, combined with amplitude-frequency separation based on the Hilbert transform, the IESN predicts a set of engine vibration signals in knock. Compared with several popular models, the proposed IESN shows the best performance.