Research On Predictive Modeling For Multivariate Series Based On Reservoir Method

Complex systems always perform highly nonlinear and multivariable, which induces the difficult of the predictive modeling. Support vector machines and neural networks are the most common modeling method. However, the main modeling objects are often univariate series or linear systems and lack of effective methods to address complex multivariate series. The reservoir methods have a unique nonlinear processing mechanism and have achieved excellent performance in univariate series prediction. In recent years, many scholars at home and abroad have carried out extensive research on reservoir methods and made some achievements. However, reservoir methods are rarely used to predict the complex multivariable series. In addition, how to utilize the nonlinear processing mechanism of reservoirs to improve the reservoir learning algorithms is also worthy of further study. Based on the above observations, this dissertation will focus on how to predict multivariate series by reservoir method and how to improve the reservoir learning algorithms.Multivariate series are always high-dimension, nonlinear and high redundant. The directly predictive modeling always makes the prediction models complex and prediction accuracy low. Reservoir methods can translate the nonlinear features in the original space to linear features in the high-dimension reservoir state space. The troublesome nonlinear part of complex multivariate series can be addressed within the reservoir by mapping them to high-dimensional reservoir space. Then, the multivariate statistical methods are performed on mapped data in reservoir space. One hand, the strong correlation and high redundancy problems of multivariate series are settled. On the other hand, the applications of the classical multivariate statistical methods are extended from linear systems to nonlinear systems and the new nonlinear multivariate statistical methods are proposed. Moreover, the multivariate series is always high dimension and large sample size. On-line predictive methods are more practical and effective in practical applications than offline methods. A novel adaptive online prediction method is proposed based on the reservoir mechanism. It performs the KF in the high-dimension reservoir state space and the reservoir output weights could be online updated. Compared with the expanded KF (EKF) algorithm of traditional recurrent neural networks (RNN), the method here offers a convenient implementation without the computation of Jacobian matrices, which leads to an improved prediction accuracy and more broad applications. Meanwhile, the existence of outliers in training samples has the adverse effects on prediction models. Accordingly, the robust loss functions are adopted and the linear regression techniques are applied in the reservoir space to improve the robustness of the reservoir method. In order to demonstrate the validity of the proposed methods above, all methods have been used in simulation examples (multivariate chaotic time series generated by manual numerical simulation, the actual hydrological multivariate observations and the benchmark data sets). The results show that the proposed methods can effectively improve the prediction accuracy of multivariate series and reveal the dynamic characteristic of the complex system.