## 2 Knowledge and Tools of Model Preparation
For the sake of removing the noise and further collect helpful information from the power load sequence, we use ICEEMDAN technology to disintegrate the original sequence, and rebuild the smooth time series. Specifically, the original sequence is decomposed into some IMFs. IMFs with higher frequency are eliminated to filter the time series. Here we remove IMF\({}_{1}\), and the remaining IMFs are rebuilt to get the final series. **Step 2:** Single model predicting. In this study, we first use single models to predict the points to obtain a preliminary impression of each model. Then the higher prediction accuracy model, RBF, ELM, ENN and ARIMA, are chosen as member prediction models to build the combination model. RBF, ELM and ENN are used to handle the non-linear features of load, while ARIMA has a good effect on discerning linear characteristics of load data. Say concretely, we divide 1488 load data into training set _train_ and testing set _test_, where _train_ includes 1152 data and _test_ includes 336 data. The rolling forecasting strategy is employed, which adopts the original data of the previous five periods to forecast the next period. The input and output structure of _train_ is shown in Equations (14) and (15). Using the RBF, ELM and ENN which trained by _train_ to predict the load of the testing set, the prediction sequences _predict\({}_{1}\)_, _predict\({}_{2}\)_ and _predict\({}_{3}\)_ are obtained, respectively. Similarly, ARIMA is used to obtain the prediction sequence. _predict\({}_{i}\)_ (_i_ = 1,... _A_), including 336 forecasting values are taken as the input datasets, which are inputted into the BP model. \[input_{1}=\left[ \begin{array}{cccc}x(1)&x(2)&\cdots&x(l)\\ x(2)&x(3)&\cdots&x(l+1)\\ \vdots&\vdots&\ddots&\vdots\\ x(n-l)&x(n-l+1)&\cdots&x(n-1)\end{array} \right] \tag{14}\]

\[output_{1}=\left[ \begin{array}{c}x(l+1)\\ x(l+2)\\ \vdots\\ x(n)\end{array} \right] \tag{15}\]

In the Equations (14) and (15), \(n\) is the number of _train_ and \(l\) is look-back time lag, and \(x(k)\) is the power load value at time \(k\). For example, take \(x(1)\) to \(x(l)\) as input and \(x(l+1)\) as output; next, take \(x(2)\) to \(x(l+1)\) as input and \(x(l+2)\) as output, to train the structure of RBF, ELM and ENN. Here, we set \(l\) = 5. **Step 3:** Nonlinear combination model constructing. For the sake of obtaining the combination model, a nonlinear decision-making method on the basis of BP neural network optimized by MOEA/D is proposed to achieve the best result. Before introducing the nonlinear integration, the linear integration method is first introduced. Linear integration is to sum up the prediction results by linear weighting the prediction results of \(n\) single prediction models. Suppose \(y_{t}\) is the actual value, _predict\({}_{it}\)_ (i = 1, 2,..., \(n\)) is the prediction result at time \(t\), and \(n\) is the number of prediction models. \(w_{i}\) represents the weight of the \(i\)-th prediction model, and \(\sum_{i=1}^{n}w_{i}=1\). Therefore, the final prediction results can be calculated as follows

\[\hat{y}_{t}=\sum\
olimits_{i=1}^{n}w_{i}predict_{it},\quad t=1,2,\ldots,m \tag{16}\]

Considering the complexity of power load and the characteristic of different single models, we choose nonlinear weight combination forecasting to compensate for the shortage of linear integration. In this study, as an important application of nonlinear integration, BP is applied to the integration of a single prediction component for final prediction. Specially, BP neural network is a complex nonlinear black box operation, and a large number of internal nodes in it are connected with each other, which can be used as an arbitrary function approximation mechanism. We regard the trained BP neural network as the weight integration of each single model, so this combination weight can also be regarded as nonlinear integration. However, BP parameters have an important impact on the prediction results and it is difficult to determine.