# Hierarchical Modelling for CO\({}_{2}\) Variation Prediction for HVAC System Operation
## 5 Experimental Setup
### Experimental Parameters  
The analysis of HMCOVP commences by applying it to a large conference room, referred to as room00 and then later the models are evaluated on a smaller conference room, referred to as room01. Room00 can fit 12 people, with an area comprising 28.0 m\({}^{2}\) and a volume of 89.6 m\({}^{3}\) while room1 is of area 14.2 m\({}^{2}\) and a volume of 38.3 m\({}^{3}\)[25]. This process is followed to evaluate the transferability of the developed models to a room of different capacities. The hierarchical structure of HMCOVP promotes its transferability, which addresses a common concern in the IAQ-related literature. The following paragraphs explain the parameters involved in the experimental procedure summarized in Figure 3.  
**History and Future Time Windows**: The EDA highlighted the relationship between lagged environmental features and the CO\({}_{2}\) concentrations to infer a reasonable prediction time window. This EDA showed that a prediction horizon of 20 min is viable for the available dataset. The analysis includes the results of applying HMCOVP with the same time window for history and future time horizons. These parameters are subsets of the ones evaluated in FECOP. The remainder of the possible combinations will be considered in future work, given that the current formulation is not concerned with the memory constraints of the deployment environment. The history and the future time horizon will be referred to as \"h-[\(w\)]_f-[\(w\)]\", whereby \(w\) represents the time window. Time windows of 5, 10, 15, and 20 min were considered. The combinations of the history and future time windows experimented with are h-5.f-5, h-10.f-10, h-15.f-15, and h-20. f-20. The time series to image transformation step yielded several datasets that vary depending on the historical and future time windows. A 1-minute sliding window is implemented to produce larger datasets. For example, for h-5.f-5, a single row is formed by predictors representing GAF images from \(t=0\) to \(t=5\) and the CO\({}_{2}\) variations from \(t=5\) to \(t=10\)  
Figure 3: Summary of Experimental Parameters. The next row would represent the GAF images from \(t=1\) to \(t=6\) and the CO\({}_{2}\) variations from \(t=6\) to \(t=11\). The resulting process yields datasets of different sizes that range between 328,647 to 334,677 data points for training data and 74,085 to 74,730 data points for testing data for different history and future time horizons. The training and testing data points for different history and future time windows are summarized in Table 1.  
**Experimental Features**: The original dataset consists of five environmental features: pressure, temperature, humidity, CO\({}_{2}\) concentration, and activity levels. The activity level or PIR is a categorical variable formed of 0.5 increments from 0 to 12, amounting to 25 variables. The PIR feature space is first reduced to four categories, each representing eight contiguous activity levels, except 0, which is a category on its own. The one-hot encoding schema would create many 0-1 variables, which cannot be transformed into an image representation. Therefore, the PIR feature is transformed into two features, denoted by temperature_PIR and CO\({}_{2}\)_PIR. These two features are chosen because they exhibit the highest correlation with the PIR feature. The quantities are obtained by calculating the ratio of CO\({}_{2}\) and temperature to the PIR feature. Six environmental features are obtained following this feature engineering step that includes CO\({}_{2}\), temperature, pressure, humidity, CO\({}_{2}\)_PIR, and temperature_PIR. **GAF Representation**: Normalization is a fundamental step in the time series to image transformation. Two main methods can branch out from this step, referred to as \"local\" and \"holistic\" approaches. Each of these methods targets a specific angle of the studied phenomenon. On the one hand, the \"local\" method calculates the minimum and the maximum in a defined \(w\).