## 4 Devised Configuration for the Integrated WT-ACO-FFANN Based ML Forecast Model
### Wavelet Transform (WT)  
The amplitude of the energy output of wind turbines alternates in each timestamp. Deeper investigation of the wind power generation data shows that it has non-stationary and non-linear behaviors. This makes the data more complex for understanding and simplification, as there might be several noise (unimportant) components superimposed. The direct use of this raw data for prediction model training input may compromise the quality of forecasts. This calls for the use of some sort of mechanism for extracting the most important and well-behaving features from the original (raw) dataset, as proposed in this work.  
Wavelet transform (WT) decomposes the forecast model target variable dataset into a group of subseries. It extracts a new set of features from the original target variable. The resulting new features provide enhanced performance compared to the original target feature. Therefore, using the new features derived from the WT decomposition instead of the original target variable (wind generation) definitely enhances the performance of the wind generation forecast.  
The main reason for the enhanced performance of the new data features obtained from the WT decomposition is due to the data filtering capability of the WT.  
There are two types of wavelet transform. They are continuous wavelet transform (C-WT) and discrete wavelet transform (D-WT). The C-WT, WT (p, q) of a signal h(x) with reference to a mother wavelet \(\Phi(x)\), is formulated below [26].  
\[\mathrm{WT}(\mathrm{p},\mathrm{q})=\frac{1}{\sqrt{\mathrm{p}}}\int\limits_{- \infty}^{+\infty}\mathrm{h}(x)\cdot\Phi\left(\frac{x-q}{p}\right)\mathrm{dx} \tag{4}\]  
Here, p is the wavelet scaling parameter that regulates the scattering of the wavelet, and q is the wavelet transformation parameter that determines the center of the wavelet. The D-WT, WT (r, s), is as precise as the C-WT but more efficiently powerful [27]. D-WT is formulated as follows.  
\[\mathrm{WT}(r,s)=2^{-(r/2)}\sum_{t=0}^{T-1}\mathrm{h}(t)\cdot\Phi\left(\frac{t -s2^{r}}{2^{r}}\right) \tag{5}\]  
Here, T is the size of h(t), p and q are functions of the integral values \(r\) and \(s\) (i.e., p = \(2^{r}\), q = s2^{r}\)), and t is a discretized time.  
[PERSON] et al. [28] developed a very quick and efficient D-WT algorithm relying on the four fundamental filter types. Multi-resolution using the Mallat decomposition and reconstruction techniques is a way to obtain \"approximation\" and \"detail\" components of a particular signal. Through sequential decomposition of the approximation, a multistep ranked decomposition is achieved. That means the initial given signal is decomposed to reduced resolution sub-signals. Figure 2 shows the flowchart of the multistep WT decomposition process.  
In this paper, a Daubechies order 4 (Db4) wavelet function is employed as the mother wavelet \(\phi(t)\). Db4 \(\phi(t)\) compromises evenness versus wavelength to provide a relevant feature for WPP. Db4 \(\phi(t)\) based WTs have been implemented by prior researchers for electricity demand prediction [26; 27], electricity price prediction [29], and solar power forecasting [30]. Moreover, three decomposition stages are employed, as in [29; 30], since this can represent the target variable (wind power) data series in a precise and sensible manner.