Mathematical Problems in Engineering

Volume 2017, Article ID 3513980, 7 pages

https://doi.org/10.1155/2017/3513980

## Sunspots Time-Series Prediction Based on Complementary Ensemble Empirical Mode Decomposition and Wavelet Neural Network

School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi 710121, China

Correspondence should be addressed to Guohui Li; moc.361@dchgl

Received 25 January 2017; Accepted 2 March 2017; Published 16 March 2017

Academic Editor: Tomasz Kapitaniak

Copyright © 2017 Guohui Li and Siliang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The sunspot numbers are the major target which describes the solar activity level. Long-term prediction of sunspot activity is of great importance for aerospace, communication, disaster prevention, and so on. To improve the prediction accuracy of sunspot time series, the prediction model based on complementary ensemble empirical mode decomposition (CEEMD) and wavelet neural network (WNN) is proposed. First, the sunspot time series are decomposed by CEEMD to obtain a set of intrinsic modal functions (IMFs). Then, the IMFs and residuals are reconstructed to obtain the training samples and the prediction samples, and these samples are trained and predicted by WNN. Finally, the reconstructed IMFs and residuals are the final prediction results. Five kinds of prediction models are compared, which are BP neural network prediction model, WNN prediction model, empirical mode decomposition and WNN hybrid prediction model, ensemble empirical mode decomposition and WNN hybrid prediction model, and the proposed method in this paper. The same sunspot time series are predicted with five kinds of prediction models. The experimental results show that the proposed model has better prediction accuracy and smaller error.

#### 1. Introduction

The sunspot numbers are the major targets which describes the solar activity level. The solar activity influences the human health and living environment on earth. Long-term prediction of sunspot activity can provide important reference information for aerospace, communication, disaster prevention, and so on [1]. Therefore, the research of sunspot number time-series prediction method has been an important and hot topic in this field [2]. The data of annual and monthly sunspot activity is considered as typical nonlinear, non-Gaussian, and nonstationary time series, which has obvious characteristics of chaotic sequences [3, 4]. The accurate prediction of sunspot numbers has great research significance [5, 6]. It is difficult to predict using the traditional method and the accuracy is not high.

Currently, BP neural network, wavelet neural network, and empirical mode decomposition (EMD) [7] are widely used in nonlinear, nonstationary time-series prediction [8]. BP neural network has some advantages such as simple structure, strong learning ability, and nonlinear mapping ability. But the predict model of BP neural network is easy to fall into the local minimum problem, and the convergence rate is slow [9]. Wavelet neural network is combined with the characteristics of artificial neural network and wavelet analysis. It has the advantages of self-learning ability and localization of wavelet transform, so it can effectively solve the local minimum problem [10]. In [11], tight wavelet neural network is used to predict sunspot number. Wavelet neural network is used to predict the charge load in [12]. It is shown that wavelet neural network obviously improves the prediction accuracy compared with BP neural network model. In [13], EMD is used to extract a signal which is more stable, and then the wavelet analysis method is used to get key features of sunspot data time series. However, the mode mixing effect will happen in the process of decomposing signal by the EMD, which leads to unsatisfactory decomposition. Wu and Huang [14] proposes ensemble empirical mode decomposition (EEMD) which is a noise-assisted data analysis method, and the mode mixing can be avoided during the empirical mode decomposition [15]. In [16], the mix model with EEMD and wavelet neural network is proposed. Although the reconstruction error is reduced, the cost of computing is increased [17]. Yeh et al. [18] propose complementary ensemble empirical mode decomposition. The method adds different Gaussian white noise to the remaining components of each intrinsic mode functions to reduce the mode mixing and decrease false component.

Therefore, the prediction model based on complementary ensemble empirical mode decomposition and wavelet neural network is proposed, which is combined with the advantages of CEEMD and wavelet neural network and adopts the idea of a combined model.

#### 2. Basic Principle

##### 2.1. Complementary Ensemble Empirical Mode Decomposition

CEEMD is a noise-assisted analysis method [19]. Two opposite white noise signals are added to the time series signal, and th mode is obtained by the EMD. represents the th intrinsic modal function of the EMD. represents zero mean Gaussian white noise with unit variance, that is, . represents the signal-to-noise ratio which is selected for each stage. is set as target signal, and then the signal added to white noise is . The concrete steps of the CEEMD algorithm [20] are as follows:(1)Decompose by the EMD for times, then is obtained:(2)Calculate the first-order residual :(3)Decompose , . The first intrinsic modal function is used as the of the CEEMD:(4)In the same way, the th residual is obtained:(5)Decompose . The first intrinsic modal function is used as the of the CEEMD:(6)Repeat steps () and (), until the residual can no longer be decomposed, and then the final residuals is

Therefore, the target signal can be expressed aswhere is the sum of . The complete CEEMD decomposition signal may be obtained through the above formula, and the original signal can be precisely reconstructed.

##### 2.2. Wavelet Neural Network

Wavelet neural network is a multilayer feedforward neural network which is based on BP neural network and wavelet theory, and it takes the wavelet basis function as the hidden layer excitation function [10]. So WNN has better generalization ability than neural network [21]. WNN is a good predictive method that can process nonlinear data, and it has characteristic of wavelet analysis and neural network.

The structure of the wavelet neural network is similar to a feedforward neural network [10]. The input node layer has one or more inputs. There is an implicit layer in the middle of the network. The function of basis wavelet is used as the activation function of the hidden layer. The output layer consists of one or more linear combiners. The structure of wavelet neural network is shown in Figure 1.