The Optimization Of Leaky-ESN And Its Application In Time Series Prediction

Time series prediction was proposed in 1970 s, which is based on historical data to predict future problems. It develops quickly and is used for many fields, like engineering, economy, military and so on, which has been a research field of great practical value. In this article, the research is that the optimization of leaky integrator echo state network(Leaky-ESN)and its application in time series prediction.The optimization of Leaky-ESN is that we optimize the state space or parameters of its reservoir based on standard Leaky-ESN to improve its prediction accuracy. Firstly, we propose a various leaky-integrator echo state network(VLeaky-ESN) model, which has different leaky rates corresponding to different state components. The model increases the flexibility of parameter selection and the adaptation for multiple inputs. To further improve the prediction ability of VLeaky-ESN model, we use extend kalman filtering(EKF) to optimize the parameters of the model.Secondly, using state update equations of EKF replace the reservoir state update equations to improve prediction accuracy and accelerate convergence. Because the merit of state update equations of EKF can remedy the deficiency of reservoir state equation which ignores output feedback for the purely input-driven application. Thirdly, to solve the influence of echo state property which is an inequality constraint condition concerning the key parameters of leaky rate and spectral radius when using stochastic gradient descent method optimizes parameters, penaltyfunction interior point method transforms constrained optimization problem into unconstrained optimization problem to search for optimal parameter values and improve the prediction accuracy. Finally, we use the optimized Leaky-ESN model predicts the output power of photovoltaic system.