# A Short-Term Wind Speed Forecasting Model Based on EMD/CEEMD and ARIMA-SVM Algorithms
## 2 Methodology  
### Modal Decomposition Technique  
In order to effectively deal with nonlinear and non-stationary data, [PERSON] et al. [23; 24] proposed the empirical mode decomposition (EMD) method.  
EMD decomposes the original time series into a finite number of intrinsic mode functions (IMFs) and a residual component. IMFs must satisfy two conditions: (1) The number of the extremums and zeros of all IMF datasets must be the same or with a maximal difference of one; and (2) The average value of the upper and lower envelopes composed of the local maximums and local minimums at any point is zero.  
The IMF extracts the local variation characteristics of the signal, which reflects the internal change of the signal. Therefore, the EMD method has a strong adaptability to the decomposing signal. It actually decomposes the signal into different scales of fluctuations or trend terms step by step, which eliminates the influence between the components. Therefore, the impact of the non-stationarity of signals could be diminished.  
In terms of time series \(y(t)\), it rewrites it as the following expression, processed by EMD. It gets:  
\[y(t)=\sum\limits_{j=1}^{m}c_{j}(t)+r(t) \tag{1}\]  
where \(c_{j}(t)\) is the \(j\)th IMF component; it represents the \(j\)th separated signal component from the original signals, which present different characteristic scales of the signals; \(r(t)\) is the residual component reflecting the trend term of the original signal.  
However, one of the major drawbacks of the original EMD is the frequent appearance of modal mixing, which makes the physical meaning of individual IMF unclear. In order to relieve the influence of the mode mixing, the complementary ensemble empirical mode decomposition (CEEMD) is proposed by [PERSON], [PERSON] et al. [25]. The CEEMD is achieved through the following steps: firstly, the original time series is reconstructed by adding a series of pairs of Gaussian white noises with equal size and opposite direction; subsequently, with the applying of the EMD to each pair of the reconstructed time series, the final IMFs are obtained by means of averaging all of the EMD results of the IMFs. On the one hand, this improved method suppresses the defect of modal mixing of the original EMD algorithm; on the other hand, the auxiliary white noise signals will produce a mutual cancellation effect after decomposition and superposition, and the original signal will not be greatly affected by the addition of white noise. The detailed steps of the CEEMD algorithm are as follows:  
1. The original signal \(y(t)\) is added with a pair of Gaussian white noises \(\varepsilon_{j}(t)\) to form a new set of signals \(G(t)\), namely \[\begin{array}{l}G_{1}(t)=y(t)+\varepsilon_{i}(t)\\ G_{2}(t)=y(t)-\varepsilon_{i}(t)\end{array}\] (2)
2. The EMD is applied to the reconstructed signal of Equation (2) to obtain m IMF components: \[\begin{array}{l}G_{1}(t)=\sum\limits_{j=1}^{m}C_{ij\cdot 1}(t)\ +r_{i,1}(t)\\ G_{2}(t)=\sum\limits_{j=1}^{m}C_{ij,2}(t)\ +r_{i,2}(t)\end{array}\] (3) where, \(G_{ij\cdot}(t)\) indicates the \(j\)th IMF of the EMD decomposition after the adding of the \(i\)th white noise; \(r_{i,\cdot}(t)\) represents the trend term of the EMD decomposition.
3. Different white noises \(\varepsilon_{i}(t)\) (\(i=1,2,\,\ldots,\,n\)), are added, repeating steps 1 and 2, getting \(n\) sets of IMFs and trend terms.  
The mean of all IMFs are calculated to obtain the final IMF \(c_{j}(t)\):  
\[c_{j}(t)=\frac{1}{2n}\sum_{i=1}^{n}\left(C_{ij,1}(t)+C_{ij,2}(t)\right)\ \ \ (j=1,\;2,\;\cdots,m) \tag{4}\]