A Comparative Study of CO2 Forecasting Strategies in School Classrooms: A Step Toward Improving Indoor Air Quality
Abstract
:1. Introduction
- Use of Real-World Datasets: Many studies rely on publicly available or simulated datasets, which may not accurately reflect real-world conditions, thereby introducing noise and potentially biasing models.
- Validation Techniques: Inadequate validation strategies can affect model performance and generalization. Many studies provide limited details on the validation methods used or apply traditional ML techniques that do not account for temporal dependencies in the TS data. Adopting specialized TS validation techniques would provide more robust insights.
- Prediction Horizons: Although model performance varies across different prediction horizons, systematic comparisons are rare. In IAQ forecasting, earlier predictions allow more time for corrective actions such as activating ventilation systems. Without systematic comparisons, it is difficult to understand how the effectiveness of the model changes over time and how timing impacts decision-making.
- Comparison with Simple Models: Complex DL architectures are often assumed to outperform simpler models. However, in short-term predictions, simpler models with lower computational costs can achieve similar accuracy. Whether or not complex ML models consistently outperform simpler methods in TS forecasting remains an open question [33,34].
- Statistical Techniques for Reliability: Statistical methods that enhance the reliability and validity of forecasting results are underutilized in the literature. The absence of rigorous statistical validation can undermine the credibility of model performance and its generalization to real-world scenarios.
- Scale-Independent Performance Metrics: Many studies rely on traditional ML performance metrics that are scale-dependent, which complicates the comparison of forecasting models across different TS datasets. The use of scale-independent metrics is essential for more reliable and comparable evaluations.
- Real-World Data Collection: CO2 levels were continuously monitored in fifteen schools located in Navarra, Spain using IoT devices from 10 January 2022 to 3 April 2022.
- Forecasting Methodologies: Three distinct strategies were implemented: simplistic methods (Shifted Model and Moving Average Model), a statistical approach (ARIMA), and ML-based models (XGBoost, Random Forest, N-HiTS, and TCN), allowing for a comprehensive evaluation of forecasting effectiveness and complexity.
- Prediction Horizons: The forecasting models were tested across six different horizons ranging from 10 min to 4 h in order to systematically assess how model performance varies over different temporal windows.
- Validation and Statistical Testing: A rolling cross-validation scheme was employed to account for temporal dependencies, ensuring robust and unbiased performance evaluation. Additionally, statistical tests were conducted to validate the results, enhancing the reliability and credibility of the findings. Scale-independent performance metrics were used to enable consistent and fair comparisons across models.
2. Materials and Methods
2.1. Data Collection
2.1.1. Study Area
2.1.2. Devices
2.2. Data Analysis and Preprocessing
Preprocessing
2.3. Data Partitioning for Validation
2.4. Model Training
2.5. Model Evaluation
2.6. Implementation Tools
3. Results and Discussion
Statistical Test
4. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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School | Non-Occupation | Occupation | Global | |||||
---|---|---|---|---|---|---|---|---|
Mean | Std | Max | Mean | Std | Max | Mean | Std | |
408.31 | 9.46 | 438.00 | 432.54 | 49.57 | 849.00 | 430.26 | 47.79 | |
409.30 | 11.29 | 447.00 | 462.74 | 92.42 | 1016.00 | 457.72 | 89.41 | |
405.23 | 7.69 | 436.00 | 450.12 | 101.97 | 1262.00 | 445.90 | 97.97 | |
401.81 | 3.66 | 419.00 | 431.77 | 59.91 | 924.00 | 428.95 | 57.70 | |
404.82 | 7.37 | 429.00 | 497.35 | 139.44 | 1954.00 | 488.65 | 135.46 | |
404.70 | 7.54 | 446.00 | 455.03 | 86.88 | 1137.00 | 450.30 | 84.02 | |
409.86 | 9.62 | 445.00 | 453.20 | 122.30 | 1971.00 | 449.12 | 117.12 | |
410.30 | 11.37 | 463.00 | 457.38 | 115.82 | 1599.00 | 452.93 | 111.12 | |
404.38 | 6.85 | 443.00 | 431.34 | 63.54 | 1081.00 | 428.81 | 61.02 | |
405.15 | 6.94 | 444.00 | 436.79 | 49.99 | 734.00 | 433.81 | 48.51 | |
417.11 | 24.84 | 515.00 | 478.23 | 118.44 | 1639.00 | 472.48 | 114.39 | |
401.53 | 3.79 | 425.00 | 441.62 | 55.82 | 977.00 | 437.84 | 54.41 | |
403.92 | 6.83 | 431.00 | 468.97 | 119.93 | 1562.00 | 462.84 | 115.73 | |
409.35 | 10.19 | 446.00 | 458.75 | 109.62 | 1125.00 | 454.11 | 105.37 | |
404.44 | 6.61 | 434.00 | 432.71 | 45.17 | 827.00 | 430.05 | 43.82 | |
AVG | 406.68 | 8.94 | 444.07 | 452.57 | 88.72 | 1243.80 | 448.25 | 85.59 |
TRAIN | VAL | |||
---|---|---|---|---|
#Fold | Start-Date | End-Date | Start-Date | End-Date |
1 | 10-Jan-2022 | 6-Feb-2022 | 7-Feb-2022 | 13-Feb-2022 |
2 | 17-Jan-2022 | 13-Feb-2022 | 14-Feb-2022 | 20-Feb-2022 |
3 | 24-Jan-2022 | 20-Feb-2022 | 21-Feb-2022 | 27-Feb-2022 |
4 | 31-Jan-2022 | 27-Feb-2022 | 28-Feb-2022 | 6-Mar-2022 |
5 | 7-Feb-2022 | 6-Mar-2022 | 7-Mar-2022 | 13-Mar-2022 |
6 | 14-Feb-2022 | 13-Mar-2022 | 14-Mar-2022 | 20-Mar-2022 |
7 | 21-Feb-2022 | 20-Mar-2022 | 21-Mar-2022 | 27-Mar-2022 |
8 | 28-Feb-2022 | 27-Mar-2022 | 28-Mar-2022 | 3-Apr-2022 |
Prediction Instant (t) | Metric | SH | MA | ARIMA | RF | XGB | N-HiTS | TCN |
---|---|---|---|---|---|---|---|---|
1 | MAPE | 1.452 | 2.887 | 1.518 | 1.700 | 1.877 | 2.357 | 1.473 |
MAE | 8.126 | 16.183 | 8.389 | 9.472 | 10.595 | 12.599 | 8.176 | |
MSE | 730.4 | 2319.3 | 750.8 | 871.6 | 1082.9 | 1083.7 | 693.6 | |
SMAPE | 1.441 | 2.837 | 1.504 | 1.690 | 1.880 | 2.359 | 1.465 | |
3 | MAPE | 2.995 | 3.688 | 3.154 | 3.337 | 3.494 | 4.447 | 2.935 |
MAE | 16.851 | 20.638 | 17.569 | 18.088 | 19.245 | 22.971 | 16.160 | |
MSE | 2820.0 | 3685.6 | 2961.9 | 2402.8 | 2850.8 | 3875.4 | 2189.2 | |
SMAPE | 2.937 | 3.614 | 3.081 | 3.274 | 3.451 | 4.180 | 2.903 | |
6 | MAPE | 4.532 | 4.814 | 4.769 | 4.624 | 4.687 | 4.619 | 4.144 |
MAE | 25.276 | 26.666 | 26.458 | 24.616 | 25.272 | 24.858 | 22.452 | |
MSE | 5378.7 | 5376.7 | 6242.7 | 3815.0 | 4104.4 | 3991.2 | 3524.2 | |
SMAPE | 4.419 | 4.721 | 4.594 | 4.510 | 4.618 | 4.574 | 4.091 | |
9 | MAPE | 5.546 | 5.738 | 5.905 | 5.368 | 5.539 | 5.607 | 4.696 |
MAE | 30.570 | 31.420 | 32.454 | 28.254 | 29.345 | 29.458 | 25.490 | |
MSE | 6822.2 | 6641.8 | 8900.1 | 4488.3 | 4910.8 | 4698.9 | 4221.5 | |
SMAPE | 5.414 | 5.636 | 5.642 | 5.246 | 5.438 | 5.538 | 4.683 | |
12 | MAPE | 6.292 | 6.506 | 6.806 | 5.918 | 6.092 | 6.177 | 5.499 |
MAE | 34.301 | 35.248 | 37.047 | 30.895 | 31.929 | 32.208 | 29.190 | |
MSE | 7797.5 | 7669.0 | 12183.4 | 4997.6 | 5351.3 | 5199.1 | 4629.9 | |
SMAPE | 6.144 | 6.388 | 6.435 | 5.794 | 5.985 | 6.108 | 5.481 | |
24 | MAPE | 8.985 | 9.197 | 9.941 | 7.334 | 7.659 | 7.029 | 7.902 |
MAE | 47.554 | 48.519 | 52.729 | 37.513 | 39.215 | 36.719 | 39.848 | |
MSE | 11574.3 | 11436.8 | 26829.3 | 6226.0 | 6824.1 | 6307.2 | 5960.7 | |
SMAPE | 8.721 | 8.970 | 9.121 | 7.206 | 7.514 | 7.041 | 7.817 |
Prediction Instant (t) | Fr | p-Value | SH | MA | ARIMA | RF | XGB | N-HiTS | TCN |
---|---|---|---|---|---|---|---|---|---|
1 | 12.748 | 0.047 | 23.8 | 95.467 | 29.8 | 48.333 | 64.267 | 84.933 | 24.4 |
3 | 12.742 | 0.047 | 29.4 | 75.2 | 40.067 | 52.2 | 64.4 | 83.333 | 26.4 |
6 | 13.411 | 0.037 | 48.667 | 68.733 | 63.133 | 52.867 | 58.867 | 54.2 | 24.533 |
9 | 13.330 | 0.038 | 58.0 | 66.6 | 71.133 | 44.467 | 53.333 | 61.0 | 16.467 |
12 | 13.298 | 0.039 | 59.933 | 70.4 | 76.933 | 38.933 | 48.4 | 53.933 | 22.467 |
24 | 13.100 | 0.041 | 71.133 | 77.133 | 88.733 | 28.933 | 37.667 | 22.333 | 28.933 |
Prediction Instant (t) | Best Model | SH | MA | ARIMA | RF | XGB | N-HiTS | TCN |
---|---|---|---|---|---|---|---|---|
1 | SH | - | 1.179 | 0.082 | 0.001 | 1.179 | ||
3 | TCN | 0.787 | 0.438 | 0.061 | 0.003 | - | ||
6 | TCN | 0.030 | 0.003 | 0.023 | 0.008 | 0.023 | - | |
9 | TCN | 0.012 | 0.002 | - | ||||
12 | TCN | 0.003 | 0.139 | 0.039 | 0.014 | - | ||
24 | N-HiTS | 0.553 | 0.336 | - | 0.123 |
Prediction Instant (t) | Best Methods |
---|---|
1 | SH, ARIMA, RF, TCN |
3 | SH, ARIMA, RF, TCN |
6 | TCN |
9 | TCN |
12 | RF, TCN |
24 | RF, XGB, N-HiTS, TCN |
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Garcia-Pinilla, P.; Jurio, A.; Paternain, D. A Comparative Study of CO2 Forecasting Strategies in School Classrooms: A Step Toward Improving Indoor Air Quality. Sensors 2025, 25, 2173. https://doi.org/10.3390/s25072173
Garcia-Pinilla P, Jurio A, Paternain D. A Comparative Study of CO2 Forecasting Strategies in School Classrooms: A Step Toward Improving Indoor Air Quality. Sensors. 2025; 25(7):2173. https://doi.org/10.3390/s25072173
Chicago/Turabian StyleGarcia-Pinilla, Peio, Aranzazu Jurio, and Daniel Paternain. 2025. "A Comparative Study of CO2 Forecasting Strategies in School Classrooms: A Step Toward Improving Indoor Air Quality" Sensors 25, no. 7: 2173. https://doi.org/10.3390/s25072173
APA StyleGarcia-Pinilla, P., Jurio, A., & Paternain, D. (2025). A Comparative Study of CO2 Forecasting Strategies in School Classrooms: A Step Toward Improving Indoor Air Quality. Sensors, 25(7), 2173. https://doi.org/10.3390/s25072173