## 4 Simulation and Experiment
### Test on Time Series in Practical Systems  
#### 4.2.1 Dataset  
The food safety check data were collected from the websites of the Chinese General Administration of Quality Supervision, Inspection, and Quarantine. The data are from 26 provinces of China from 2013 to 2018. The sampling area and scope consider the production and consumption conditions. The food safety attributes of rice are measured and integrated as a comprehensive index, namely, the fraction ratio, to present its safety degree. The data are organized as a time series by value per day.  
For the atmospheric quality data, the concentration of SO2 is set as the main index. It was measured at an industrial park in Hebei Province, China. A segment of data from December 2017 is used in the experiment.  
As mentioned in the introductory section, many practical systems generate data at a low frequency according to monitoring demands and the manual sampling approach. Therefore, practical data are tested except for the simulation systems above. The data from the spot check system of food safety are recorded once a day. The data from the atmospheric quality monitoring system are the typical time series. Then, parts of the data are shown in Figure 11 for an intuitional observation. The two categories of data are tested with our proposed and contrast methods in the same mode as a simulation experiment. The data size is set as 1000 sets in training, 300 in the validation, and 200 in the test.  
Similarly, the original practical data used in the experiments is decomposed using the STL algorithm to obtain seasonal subsequences, and the enhancement set obtained through the sample enhancement algorithm is decomposed using STL to obtain seasonal subsequences, as shown in Figures 12 and 13. Although practical data have more complex characteristic trends and more severe volatility, the seasonal subsequences decomposed from the augmented practical data in Figures 12 and 13 still have a high similarity in the same trend as the original practical data.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & \multicolumn{3}{c}{**MG System**} & \multicolumn{3}{c}{**MSO System**} \\  & & **5** & **10** & **15** & **5** & **10** & **15** \\ \hline \multirow{6}{*}{RMSE} & ARIMA & 0.0860 & 0.1210 & 0.1109 & 1.2327 & 1.3584 & 1.5893 \\  & LSTM & 0.0577 & 0.0712 & 0.0832 & 0.6205 & 0.8289 & 0.8938 \\  & GRU & 0.0472 & 0.0689 & 0.0789 & 0.2444 & 0.3589 & 0.3623 \\  & Transformer & 0.1379 & 0.1590 & 0.1642 & 0.4485 & 0.6149 & 0.7211 \\  & CI-GRUs & 0.0356 & 0.0412 & 0.0634 & 0.3623 & 0.4012 & 0.4265 \\  & A-CI-GRUs & 0.0269 & 0.0313 & 0.0529 & 0.2343 & 0.2783 & 0.3074 \\ \hline \multirow{6}{*}{MAE} & ARIMA & 0.1889 & 0.2034 & 0.2101 & 1.0061 & 1.3342 & 1.3983 \\  & LSTM & 0.1223 & 0.1324 & 0.1423 & 0.4955 & 0.5253 & 0.5321 \\ \cline{1-1}  & GRU & 0.1070 & 0.1132 & 0.1198 & 0.2160 & 0.3129 & 0.3983 \\ \cline{1-1}  & Transformer & 0.1093 & 0.1268 & 0.1286 & 0.3600 & 0.4863 & 0.5880 \\ \cline{1-1}  & CI-GRUs & 0.0729 & 0.0805 & 0.0894 & 0.2817 & 0.3029 & 0.3182 \\ \cline{1-1}  & A-CI-GRUs & 0.0583 & 0.0612 & 0.0669 & 0.2054 & 0.2983 & 0.3056 \\ \hline \end{tabular}
\end{table}
Table 4: Errors in the prediction result in different steps in the MG system and MSO system.