# Multi-Model Identification of HVAC System
## 4 Simulation and Validation  
### Simulation Results  
The proposed method in identifying a nonlinear system using a multi-mode approach is tested on a building ventilation system. In this example, the air volume inside the building is divided into three zones. The ventilation unit blows cool air into Zone 1 and exhausts air from Zone 3. The vented air can be optionally recycled back into Zone 1. A door in Zone 2 can be opened to vent air out to the atmosphere. The schematic of the ventilation system is shown in Figure 2.  
Figure 2: The building ventilation schematic [15]. There are five different types of disturbances in this example, including outdoor and indoor temperature, fan speed, door state and recycling periods. The daily average temperature of Edmonton, Canada, for the last 3 years [16] was used as the simulated outdoor temperature. The NaN (not-a-number) values in outdoor temperature are replaced with the last observed values. The ventilation system's outdoor and indoor air characteristics are mixed and blown into the zones are illustrated in Figure 3. In this test, the fan is operated at a fixed speed. The heating resistance of the building is shown in Figure 4. In this test, for each zone, conductive heat transfers from above ground and below the foundation are considered, which are the heat transfers between insides and outsides through windows, doors and walls. The convective heat losses are ignored at this stage phase, which will be addressed in the near future. To test the performance of the proposed method, the building ventilation system has been operated in three different operation modes. As seen in Figure 5, the outdoor temperature changes in the range [\(-25\)\({}^{\circ}\)C, \(25\)\({}^{\circ}\)C]. This test aims to assess the performance of the proposed identification method in classifying these operation modes and building a  
Figure 4: The thermal resistance schematic of the test ventilation system. Figure 3: The fan control block [15]. multi-mode model for this system. The temperatures at all three zones are illustrated in Figure 5. In this test, the ventilation system does not have pre-heating coils, so the outdoor temperature directly affects the zones temperature. This is why the zones' temperatures are varying significantly. Therefore, utilizing a pre-heating system before blowing the outdoor air into the zone, especially in cold regions, will produce smoother temperature trends. The following ARX model structure with 10 models is used in this test. \[ \begin{array}{rl}\text{\em Model }i:y(t+1)&=a_{1}^{i}y(t)+a_{2}^{i}y(t-1)+a_{3}^{i}y (t-2)+b_{1}^{i}u(t-3)\\ &\quad+b_{2}^{i}u(t-4)+b_{3}^{i}u(t-5)\quad i=1.\cdots.10\end{array}  \tag{10}\]  
where \(y(t)\) denotes indoor temperature at Zone 1, and \(u(t)\) denotes the fan temperature, which is almost the same as the outdoor temperature. This model identifies the ventilation behavior with respect to the outdoor temperature changes. The temperature range is divided into 10 equal regions, then the 10 linear models in the form (10) are identified for each region. After identifying the 10 models, the gap-metric method is utilized to remove the unnecessary models (models have similar responses) and decrease the local model numbers. The similarity between models is decided based on the gap metric and threshold level. If the distance between models is less than the threshold level, one of the models will be discarded. Therefore, we can decide the number of models and the accuracy of the multi-model by determining a proper threshold level. A higher value will result in lower accuracy but a less complex model. In this test, to assess the impact of different threshold values, we have selected two different threshold levels \(\tau=0.2\) and \(\tau=0.5\), which results in five and three local models, respectively. The estimated values for these two models' parameters are given in Tables 1 and 2. Figure 5: Temperatures at all three zones.