## 5 Discussion  
A fusion prediction model is proposed considering small samples in some practical systems. The fusion model extracts the features by augmenting the sample and utilizing the  
Figure 16: Errors in prediction methods for the food fraction ratio. Figure 17: Errors in the prediction methods for the SO\({}_{2}\) concentration. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Food Safety Fraction Ratio**} & \multicolumn{3}{c}{**SO\({}_{2}\) Concentration**} \\  & & **5** & **10** & **15** & **5** & **10** & **15** \\ \hline \multirow{8}{*}{RMSE} & ARIMA & 7.0300 & 9.3423 & 10.3224 & 4.7846 & 5.8321 & 6.1232 \\  & LSTM & 8.0841 & 8.4562 & 8.9342 & 5.3669 & 5.9832 & 6.1233 \\  & GRU & 6.6246 & 7.3452 & 7.8923 & 4.5867 & 5.3422 & 5.9653 \\  & Transformer & 5.6369 & 7.0029 & 8.3610 & 8.6905 & 10.2021 & 10.5355 \\  & CI-GRUs & 5.9455 & 6.2345 & 7.1234 & 4.0821 & 5.3983 & 5.7834 \\  & A-CI-GRUs & 5.4012 & 5.9839 & 6.2532 & 2.8743 & 3.5683 & 3.9834 \\ \hline \multirow{8}{*}{MAE} & ARIMA & 4.5877 & 5.8965 & 6.2312 & 3.7824 & 4.5834 & 6.0123 \\  & LSTM & 4.8356 & 4.9342 & 4.9834 & 4.0112 & 4.2342 & 5.2736 \\ \cline{1-1}  & GRU & 4.2812 & 5.0745 & 4.8912 & 3.7135 & 4.2453 & 4.9832 \\ \cline{1-1}  & Transformer & 4.4159 & 5.4351 & 6.2418 & 5.7427 & 7.1292 & 7.4242 \\ \cline{1-1}  & CI-GRU & 3.9939 & 4.0234 & 4.1235 & 3.1694 & 4.2341 & 4.0231 \\ \cline{1-1}  & A-CI-GRUs & 3.5680 & 3.9834 & 4.2371 & 2.1708 & 2.9843 & 3.7532 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Errors in the prediction result in different steps of the food safety fraction ratio and SO\({}_{2}\) concentration. multiple models parallelly. It was tested with simulation and practical data and compared with other relative methods. This can be discussed in the context of the experimental results to analyze the characteristics of the proposed method. On the one hand, the situation mainly considers that many systems and activities generate data at a low frequency, and historical datasets are often small. Thus, an augmentation method is designed in this paper for the training demands of deep models. The proposed method is compared with CI-GRUs, which lack the augmentation part. For MG and MSO simulation data, the RMSE values of our method are 75.56% and 64.67% of those in the CI-GRUs. Similarly, in the practical prediction of the food fraction ratio and SO\({}_{2}\) concentration, the RMSE decreases by 9.15% and 31.51% compared with the CI-GRUs. The other methods, LSTM, GRU, and transformer, which are trained on the original small sample, perform poorly in accurately fitting the true value. This proves that augmentation can enlarge the sample size with the inherent data feature and can help improve the model's prediction performance. On the other hand, the proposed method realizes the fusion of multiple methods. Finite samples limit single models such as ARIMA, LSTM, GRU, and transformer. Although the deep models of LSTM, GRU, and transformer can trace the general trend in the experiment, their precision is low in predicting the concrete values of each point. When facing data prediction tasks with more complex trend characteristics, the transformer cannot exert its ability to fit data trends when the number of samples is small. Furthermore, a covariance intersection is introduced to fuse the models instead of using the traditional addition method. In the covariance intersection fusion, the performance of each model is evaluated with the error degree in the validation set. Then, the fusion weight can be obtained quantificationally rather than using the weight of the artificial experience or a random value. The proposed method guarantees the sample size for deep models. It also realizes reliable predictions by integrating multiple models. In this paper, the type and number of models used in the fusion framework are determined with common sense. Future work can deeply explore how to choose concrete models considering the calculation speed and computing resources.