# Sensorless Air Flow Control in an HVAC System through Deep Learning
## 4 Experimental Evaluation
### Static Pressure Prediction in Normal and Test Operations  
In order to validate our claim that DNN-based prediction of the static pressure in the duct is viable without installing and operating a pressure sensor, we performed the prediction using the LSTM network presented above and measured its accuracy by comparing its predictions with the sensor data. For training and testing, we used all three data sets from different floors of the target building. In Experiment 4.1 in Table 3, we divided each data set of three floors into training, validation, and test data by month. The total number of data entries in the 4 th floor data set was 172,206 after removing faulty or lost data entries. Among these data points, 125,120 were used for the training and validation, and 47,086 were used to test the model. In the 5 th floor data set, the total number was 172,186, of which 126,656 were used for training and validation, and 45,530 were used for testing. In the 6 th floor data set, the total was 171,933, with 126,470 used as the training and validation data, and 45,463 used as the test data. The result of the test on the 4 th floor data set is encouraging, with MAE = 0.139 mmAq, MAPE = 1.064%, and RMSE = 0.398. This error is safely within the 5-10% error margin recommended by the ASHREA standard [26]. Figure 14 graphically shows how close the predicted values are to the sensed values. In the figures, the left column is for May, during which the system was in regular operation. The right column corresponds to the test operation during August, which is in the summer vacation season. In Figure 14a, the set-point was constant at 8 mmAq, and we can see that the prediction closely matches the sensed static pressure. For the 5 th floor, the target static pressure \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment** & **Training Data** & **Validation Data** & **Test Data** \\ \hline \multirow{4}{*}{4.1 (4F, 5F, 6F)} & 01/05–17/05 (17 days) & 18/05–22/05 (5 days) & 23/05–31/05 (9 days) \\  & 01/06–18/06 (18 days) & 19/06–22/06 (4 days) & 23/06–30/06 (8 days) \\  & 01/07–17/07 (18 days) & 18/07–22/07 (5 days) & 23/07–31/07 (9 days) \\ \cline{2-3}  & 01/08–17/08 (17 days) & 18/08–20/08 (3 days) & 21/08–29/08 (9 days): 4F \\ \cline{2-3}  & 01/08–25/05 (25 days) & 26/05–31/05 (6 days) & 01/07–29/08 (60 days) \\ \hline \multirow{4}{*}{4.3} & 01/05–25/05 (25 days) & 26/05–31/05 (6 days) & \\  & 01/06–24/06 (24 days) & 25/06–30/06 (6 days) & \\ \cline{1-1}  & 01/07–25/07 (25 days) & 26/07–31/07 (6 days) & 01/05–28/08 (120 days): 5F, 6F \\ \cline{1-1}  & 01/08–24/08 (24 days) & 25/08–29/08 (5 days) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Training, validation and test data period for each experiment. In Figure 14b, however, the static pressure significantly fluctuates because the system was operated at the extremes of the designed operating range. In the designed operating ranges, the static pressure should be kept under 15 mmAq for the 4 th floor, 20 mmAq for the 5 th floor, and 30 mmAq for the 6 th floor. In any condition, the static pressures for these floors should never exceed 40 mmAq. Even for the recalibration operation that pushes the system to this limit, the prediction by the LSTM network trained with the values produced from August 1 to 22 matches the real values relatively well. The error figures for the 4 th floor during the recalibration period are MAE = 0.317 mmAq, MAPE = 2.941%, and RMSE = 0.968. Again, we obtained similar error values to those from the other floors. For the 5 th floor, the static pressure fluctuates wildly (Figure 14d), which leads to slightly larger errors: MAE = 0.409 mmAq, MAPE = 3.284%, and RMSE = 1.391. For the 6 th floor, MAE = 0.398 mmAq, MAPE = 4.319%, and RMSE = 1.173 (Figure 14f). The test results for each floor clearly show that the proposed model produces values that are close to the sensor-measured ones.