## 2 Knowledge and Tools of Model Preparation  
In constructing our model, several methods are chosen as the best choice, and they are combined to improve the ability of the model. Here we introduce three main methods named improved complete ensemble empirical mode decomposition (ICEEMDAN), multi-objective evolutionary algorithm based on decomposition (MOEA/D) and Fuzzy C-Means (FCM) clustering algorithm in detail. The first is improved complete ensemble empirical mode decomposition (ICEEMDAN). Being an effective data processing method, ICEEMDAN is proposed by [PERSON], [PERSON] and [PERSON] [39] in 2014. It disintegrates the actual series into some intrinsic mode functions (IMF) and a residual from high frequency to low frequency. CEEMDAN has been proposed to restore the integrity property of EMD. Nevertheless, CEEMDAN is still worthy of improvement in mode and signal decomposition. In ICEEMDAN, \(F_{k}(\cdot)\) represents the operator figures out the \(k\)-th mode achieved by EMD, \(\mathbf{\omega}^{(i)}\) is the formation of Gaussian white noise that has zero mean and unit variance, and \(\mathbf{x}^{(i)}=\mathbf{x}+\mathbf{\omega}^{(i)}\). \(\mathbf{M}(\cdot)\) is the operator and it can produce the local average of the signal. Then \(E_{1}(z)=z-\mathbf{M}(z)\) can be obtained. The general steps of ICEEMDAN are as follows:  
**Step 1. ** The first residue is obtained by calculating the local averages of \(I\) formations \(\mathbf{x}^{(i)}=\mathbf{x}+\beta_{0}E_{1}(\mathbf{\omega}^{(i)})\) (\(i=1,\ldots,I\)) using EMD:  
\[\mathbf{r}_{1}=\left\langle\mathbf{M}(\mathbf{x}^{(i)})\right\rangle,\ (i=1,\ldots,I) \tag{1}\]  
In the formula, \(\beta_{0}=\varepsilon_{0}\cdot\mathbf{S}(\mathbf{x})/\mathbf{S}(E_{1}(\mathbf{\omega}^{(i)}))\), and \(\varepsilon_{0}\) is the reciprocal of the expected signal-to-noise ratio between the first additional noise and the analytical signal. \(\mathbf{S}(\cdot)\) is the operator which can calculate the standard deviation of the signal. **Step 2. ** The first mode is calculated at the first stage (\(k=1\)):  
\[\overline{\mathbf{d}}_{1}=\mathbf{x}-\mathbf{r}_{1} \tag{2}\]  
**Step 3. ** Calculate the \(k\)-th residual (\(k=2,\ldots,K\)):  
\[\mathbf{r}_{k}=\left\langle\mathbf{M}(\mathbf{r}_{k-1}+\beta_{k-1}\mathbf{E}_{k}(\mathbf{\omega}^{ (i)}))\right\rangle \tag{3}\]  
\[\beta_{k}=\varepsilon_{0}\cdot\mathbf{S}(\mathbf{\tau}_{k}) \tag{4}\]  
**Step 4. ** The second mode is defined, where the local average of the formations \(r_{1}+\beta_{1}\mathbf{E}_{2}(\mathbf{\omega}^{(i)})\) is obtained by estimating the second residue. The second mode is  
\[\overline{\mathbf{d}}_{2}=\mathbf{r}_{1}-\mathbf{r}_{2}=\mathbf{r}_{1}-\left\langle\mathbf{M}(\bm {r}_{1}+\beta_{1}\mathbf{E}_{2}(\mathbf{\omega}^{(i)}))\right\rangle \tag{5}\]  
**Step 5. ** Computing the \(k\)-th mode  
\[\overline{\mathbf{d}}_{k}=\mathbf{r}_{k-1}-\mathbf{r}_{k} \tag{6}\]  
**Step 6. ** Return back to **Step 3** and prepare for the next \(k\). The second is **Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D)**. Recently, decomposition-based multi-objective evolutionary algorithm (MOEA/D) proposed by [PERSON] et al. [40] has attracted more and more researchers' interest because of its concise and effective characteristics, and many theoretical and practical achievements have emerged. The MOEA/D algorithm is introduced below. A multi-objective optimization problem (MOP) with \(M\) objectives and \(N\) decision variables can be expressed as follows:  
\[ \begin{array}{ll}\text{Mininize}&F(x)=\left(f_{1}(x),f_{2}(x),\cdots,f_{m} (x)\right)\\ \text{Subject}&\text{to}\quad x\in\Omega\end{array}  \tag{7}\]  
In the formula, \(\Omega\in\mathbb{R}^{n}\) is decision space, and the decision vector \(x=\{x_{1},x_{2},\cdots,x_{n}\}\in\Omega\) is a candidate solution of MOP.