## 4 Experimental Results and Discussion
### Generality Experiment  
To better evaluate the generality of LR-TCN and GRU-LR-TCN, the datasets of monitoring station 1002, monitoring station 1003, and monitoring station 1023 were selected for experiments. The estimation performance of different improved TCNs, different gated networks, and the proposed integrated model is experimentally analyzed and compared with seven metrics and time. To make the conclusions more convincing, comparisons were also made with some integrated algorithms Spatiotemporal causal convolutional network (ST-TCN) [46], dual memory scale network (DMSnet) [47], and the experimental results are shown in Table 5. As shown in Table 5, on the same dataset, the estimation performance of LR-TCN outperforms the other improved TCN models in most metrics, while GRU outperforms the other models based on the gating mechanism in most metrics. The integrated GRU-LR-TCN further improves the performance of GRU and LR-TCN models. On different datasets, combining all the metrics, LR-TCN can be applied more generally than other improved TCN models. However, on datasets with higher complexity and severe data loss, its estimation performance is not satisfactory. This requires a detailed analysis of the spatial relationships between monitoring stations and the specific conditions during data collection. Combining datasets from correlated monitoring stations for model training can improve the accuracy of the evaluation results. Compared with other gating-based models, GRU has better generalization ability, while GRU-LR-TCN effectively compensates for the limitations of LR-TCN, combining the advantages of the two models to achieve better generalization. In addition, the experimental comparisons of GRU-LR-TCN over other combined models on different datasets all demonstrate better estimation performance and generalization ability of the proposed model. For station 1002, the RMSE of GRU-LR-TCN improved by 1.3% and 4% compared to GRU and LR-TCN, respectively. For station 1003,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **RMSE** & **MSE** & **MAE** & **SMAPE** & **NAE** & **R\({}^{2}\)** & **IA** & **Time** \\ \hline LSTM-TCN & 17.951 & 322.265 & 11.771 & 21.864 & 0.037 & 0.874 & 0.964 & 97.09 s \\ GRU-TCN & 16.862 & 284.340 & 10.561 & 19.192 & 0.033 & 0.889 & 0.969 & 91.47 s \\ SRU-TCN & 17.364 & 301.542 & 11.475 & 21.171 & 0.036 & 0.882 & 0.967 & 90.09 s \\ LSTM-Gaussian-TCN & 18.019 & 324.693 & 11.723 & 21.881 & 0.037 & 0.873 & 0.967 & 116.38 s \\ GRU-Gaussian-TCN & 16.954 & 287.445 & 10.620 & 20.046 & 0.034 & 0.888 & 0.970 & 117.46 s \\ SRU-GaussianTCN & 17.144 & 293.943 & 10.869 & 20.533 & 0.034 & 0.885 & 0.970 & 104.47 s \\ LSTM-GL-TCN & 17.855 & 318.835 & 11.477 & 21.693 & 0.036 & 0.875 & 0.966 & 95.38 s \\ GRU-GL-TCN & 17.038 & 290.294 & 10.724 & 20.514 & 0.034 & 0.887 & 0.969 & 95.49 s \\ SRU-GL-TCN & 16.848 & 283.867 & 10.626 & 19.737 & 0.034 & 0.889 & 0.970 & 92.94 s \\ LSTM-DD-TCN & 17.351 & 301.066 & 10.921 & 20.597 & 0.035 & 0.882 & 0.969 & 143.65 s \\ DDTCN-GRU & 17.040 & 290.375 & 10.704 & 20.480 & 0.034 & 0.886 & 0.970 & 144.91 s \\ SRU-DD-TCN & 17.119 & 293.062 & 10.719 & 19.613 & 0.034 & 0.885 & 0.970 & 133.45 s \\ LSTM-D-TCN & 17.754 & 315.232 & 11.495 & 21.512 & 0.036 & 0.877 & 0.967 & 112.55 s \\ GRU-D-TCN & 17.333 & 300.458 & 10.822 & 20.069 & 0.034 & 0.883 & 0.969 & 112.46 s \\ SRU-D-TCN & 17.063 & 291.179 & 10.573 & 19.508 & 0.034 & 0.886 & 0.970 & 100.72 s \\ LSTM-LR-TCN & 17.001 & 289.021 & 10.816 & 20.184 & 0.034 & 0.887 & 0.970 & 84.68 s \\ GRU-LR-TCN & 16.261 & 264.444 & 10.138 & 18.978 & 0.032 & 0.897 & 0.972 & 78.54 s \\ SRU-LR-TCN & 16.369 & 267.969 & 10.348 & 19.476 & 0.033 & 0.897 & 0.895 & 80.01 s \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison experiments of estimation integrated models for PM\({}_{2.5}\) concentration in monitoring station 1001.  
the RMSE of GRU-LR-TCN improved by 1% compared to GRU. For station 1023, the RMSE of GRU-LR-TCN improved by 1.7% compared to LR-TCN.