## 3 Fusion Prediction Based on Data Augmentation  
### Framework of Fusion Prediction in Data Augmentation  
Deep networks are expected to excavate the features of small-scale time series. To apply deep networks, the issue of the demand for a large data size should be solved first. In addition, a deep network cannot be regarded as an almighty tool because it can be improved in a complex environment. The novel prediction method is designed from two perspectives: the augmentation of small samples and a distributed prediction based on GRU. The framework of the proposed prediction method is shown in Figure 1.  
First, the augmentation algorithm should expand the original data based on random probability because small samples cannot satisfy the large amount of training data required by the deep learning model. Multiple augmentation sets are generated to meet the data amount requirements. Each augmentation set will be input for the multi-model prediction in the next step. The augmentation of small-scale time series will be elaborated in Section 3.2. Second, a deep prediction model based on trend decomposition is designed for the augmentation sets. For each augmentation set, the STL (seasonal and trend decomposition using loess) decomposition is applied to the set to generate three components: the trend component, the seasonal component, and the remainder component subsequence. The decomposed features are predicted with GRU models. Then, the prediction results of each GRU are fused as the prediction output of the augmentation set. The error indexes of each model are output together with the prediction results, such as with RMSE (Root Mean Square Error) and MAE (Mean Absolute Error), which provide the basis of the subsequent fusing of the outputs of multiple augmentation sets. The proposed deep prediction model based on trend decomposition will be elaborated in Section 3.3. Third, the output results of each augmentation set are fused to obtain the final output. The output of each augmentation set includes two parts: the prediction result of the deep networks based on trend decomposition and the error indexes. The covariance intersection (CI) fusion algorithm is used based on the error indexes to obtain the final output. The covariance intersection algorithm based on the prediction error index will be elaborated in Section 3.4. As mentioned above, the method consists of three major parts. Figure 1: The framework of the fusion prediction model based on the augmentation of the original data. The first part is the augmentation part, as shown in the augmentation part in Figure 1. An algorithm of augmentation based on random probability expands the original data of small-scale time series to generate augmentation sets of different sizes to train deep learning models, as shown in augmentation sets \(i,j,\) and \(k\). The augmentation results are shown in the colored blocks in the augmentation section. The green blocks represent the original data, and the blocks of other colors represent the sample data obtained via resampling based on the random probability algorithm. Each augmentation set will be used as the input of the corresponding model to learn the trend characteristics of the time series. The second major part is a deep prediction model based on trend decomposition for parallel datasets. In each augmentation set, the augmented data from the original samples obtained using a deep prediction model based on trend decomposition are nonlinear and nonstationary. Therefore, to reduce the complexity of the trend in the augmentation set, the STL algorithm is used to decompose it, and three subsequences of the trend, cycle, and fluctuation of the augmentation set are obtained. Then, the GRU is used to predict each subsequence and fuse the prediction results of the three subsequences to obtain the prediction output of a single augmentation set.