# A Sensor Drift Compensation Method with a Masked Autoencoder Module
## 3 Experiment and Results
### Results  
We calculated the root mean squared error (RMSE) of concentration estimations for each model with the test set of each gas type listed in Table 1. The resulting RMSEs are plotted in Figure 5, where \(n\) denotes the latent space dimension and was set to 3. In Figure 5, the RMSE generally increases with time due to sensor drift. The top three models with the lowest RMSE for the test set of dataset-C are MLP-tuned, MLP-CFE, and MLP-AE for every gas. For the test set of dataset-B, except for ammonia and toluene, the top three models with the lowest RMSEs are MLP-tuned, MLP-CFE, and MLP-AE. For the six gases, the mean RMSE and the standard deviation of the RMSE, which represent the average accuracy of gas concentration estimations and robustness to gas type, respectively, were compared for MLP-tuned, MLP-CFE, and MLP-AE (Figure 6 and Table 3). For this comparison, latent layer dimensions of two, three, and four are also used for  
Figure 4: A schematic diagram of training process of MLP-tuned. MLP-tuned undergoes training at each step using the dataset of that step, with the parameters of the model initialized based on the parameters from the previous step. Figure 5: RMSE graphs of (**a**) Ethanol, (**b**) Ethylene, (**c**) Ammonia, (**d**) Acetaldehyde, (**e**) Acetone, and (**f**) Toluene for each models. MLP-CFE and MLP-AE. MLP-CFE (\(n=3\)) shows the lowest mean RMSE on dataset-A and -C test samples. On dataset-B test samples, it shows the second lowest mean RMSE, with a small difference of 1.33 compared to MLP-AE (\(n=3\)). For the standard deviation of the RMSE, MLP-CFE (\(n=3\)) shows the lowest RMSE on dataset-A and -C test samples, while for dataset-B test samples, it shows the second lowest RMSE, with a small difference of 1.38 compared to MLP-AE (\(n=3\)). When the mean RMSEs for 0-20 months, 21-23 months, and 24-36 months are averaged for each of the models, MLP-CFE (\(n=3\)) exhibits the lowest value of 6.63. In addition, when the standard deviations of the RMSE for these three periods were averaged in the same way, MLP-CFE (\(n=3\)) exhibits the lowest value of 2.79. Notably, the MLP-CFE (\(n=3\)) model, which is our proposed model, exhibits a superior performance over the other models with regard to the mean and the standard deviation of the RMSE for all test sets. In particular, for the dataset-C test set, the best performing model is MLP-CFE (\(n=3\)), which means that our method for compensating sensor drift is efficient for long-term sensor drift and also robust to different types of gases. The training times per epoch, averaged for six gases, were compared for each model and are shown in Table 4. The results for the MLP-CFE and MLP-AE models with latent vector dimensions of \(n=2,3,4\) were averaged to represent the time complexity of MLP-CFE and MLP-AE. MLP-PLS has the longest training time per epoch, at an average of 0.239 s, followed by MLP and MLP-tuned at 0.1592 s and 0.132 s, respectively. The average training time per epoch is 0.0912 s and 0.0084 s for MLP-CFE and MLP-AE, respectively, both below 0.1 s, which is lower than training times for MLP, MLP-PLS, and MLP-tuned. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**0–20 Months**} & \multicolumn{2}{c}{**21–23 Months**} & \multicolumn{2}{c}{**24–36 Months**} \\ \cline{2-7}  & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** \\ \hline MLP & 21.12 & 15.14 & 62.4 & 45.47 & 107.9 & 44.71 \\ PLS & 23.1 & 20.51 & 48.55 & 17.19 & 97.83 & 37.89 \\ MLP-PLS & 18.09 & 14.08 & 64.43 & 44.76 & 105.5 & 43.09 \\ MLP-AE (\(n=2\)) & 8.4 & 7.64 & 7.89 & 3.77 & 21.52 & 17.39 \\ MLP-AE (\(n=3\)) & 4.63 & 2.12 & 5.79 & 1.73 & 10.04 & 6.14 \\ MLP-AE (\(n=4\)) & 7.77 & 8.76 & 7.84 & 7.33 & 10.22 & 8.27 \\ MLP-CFE (\(n=2\)) & 8.26 & 4.66 & 8.6 & 4.22 & 15.17 & 8.35 \\ MLP-CFE (\(n=3\)) & 3.73 & 1.65 & 7.12 & 3.11 & 9.05 & 3.62 \\ MLP-CFE (\(n=4\)) & 9.51 & 8.23 & 9.85 & 7.44 & 14.69 & 8.6 \\ MLP-tuned & 21.12 & 15.14 & 51.759 & 54.83 & 21.99 & 22.03 \\ \hline \hline \end{tabular}
\end{table}