Thermal Bridge Modeling According to Time-Varying Indoor Temperature for Dynamic Building Energy Simulation Using System Identification
Abstract
:1. Introduction
2. Methods
2.1. Building Envelope Analysis and Thermal Bridge Modeling Concept
2.2. Indoor Temperature and Thermal Bridge Modeling
2.2.1. Indoor Temperature: Constant
2.2.2. Indoor Temperature: Variable
- Step 1: Disaggregation stageDetermine the dimensional system.
- Step 2: Dynamic simulation stagePerform the dynamic simulation of the entire wall and the clear wall.
- Step 3: Model construction stageChoose the LTI system order of the TB region and construct the TB transfer function.
- Step 4: System identification stageObtain the parameters of TB transfer function using the system identification process.
2.3. Model Construction and System Identification for Thermal Bridge
2.3.1. Linear Time-Invariant System
2.3.2. Thermal Bridge Transfer Function for the Indoor Temperature
3. Explanatory Example
3.1. Geometry and Materials
3.2. System Identification and Validation Process
4. System Identification Results and Step Response Validation
5. Annual Simulation Validation
6. Discussion
7. Conclusions
- In the same way as in steady-state thermal bridge analysis, the thermal bridge model explains the remaining heat flow after subtracting the heat flow that enters the room through the clear wall that can be analyzed in one dimension from the heat flow that enters the room through the entire building envelope.
- The heat flow that enters the room is divided into the heat flow according to the indoor temperature and the heat flow according to the outdoor temperature, and is obtained by adding these values together.
- The thermal bridge model appears in the form of a transfer function, and is divided into the following two types: a transfer function for indoor temperature and a transfer function for outdoor temperature.
- Each thermal bridge model is estimated through system identification using data. At this time, the data are obtained using a precise dynamic analysis program and the transfer function form is determined using the number of poles and zeros by analyzing the thermal network model and considering the relationship between input (indoor temperature and outdoor temperature) and output (heat flow that enters the room) as a linear, time-invariant system.
- The first step: the validation of the model itself.
- -
- Validation of whether the thermal bridge model can explain the data used for system identification.
- The second step: the validation of the annual simulation.
- -
- Validation of whether the thermal bridge model can explain the random annual data.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Thermal Network Model and Transfer Function
- [1]
- 2R1C model
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# 1 | Material | Lx 2 (mm) | Ly 3 (mm) | 4 (W/mK) | 5 (kg/m3) | 6 (J/kgK) |
---|---|---|---|---|---|---|
1 | Brick | 135 | 1500 | 0.700 | 1600.0 | 850.0 |
2 | 135 | 1500 | 0.700 | 1600.0 | 850.0 | |
3 | Extruded polystyrene | 100 | 1500 | 0.035 | 25.0 | 1470.0 |
4 | 100 | 1500 | 0.035 | 25.0 | 1470.0 | |
5 | Air gap | 65 | 1500 | 0.560 | 1.185 | 1004.4 |
6 | 65 | 1500 | 0.560 | 1.185 | 1004.4 | |
7 | Plasterboard | 10 | 1500 | 0.500 | 1300.0 | 840.0 |
8 | 10 | 1500 | 0.500 | 1300.0 | 840.0 | |
9 | Concrete | 1810 | 300 | 2.600 | 2300.0 | 930.0 |
Dimensional System | Thermal Transmittance | Heat Flow | ||||
---|---|---|---|---|---|---|
Entire Wall (W/m2K) | Clear Wall (W/m2K) | TB Region (W/mK) | Entire Wall (W) | Clear Wall (W) | TB Region (W) | |
External | 0.6945 | 0.2980 | 1.3086 | 45.8376 | 19.6657 | 26.1719 |
Time Step | Duration | Initial Condition | Boundary Condition |
---|---|---|---|
(20 days) | All structures and | (1 day) (1 day) |
Model # 1 | Description |
---|---|
Model 0 | FDM model as exact solution |
Model 1 | Steady-state model (T) |
Model 2 | Only 3rd order TB transfer function |
Model 3 | Only 3rd order TF with arithmetic correction of |
Model 4 | 3rd order TB transfer function + 1st order TB transfer function |
Model 5 | 3rd order TB transfer function + 2nd order TB transfer function |
Model 6 | 3rd order TB transfer function + 3rd order TB transfer function |
System Order | First-Order | Second-Order | Third-Order | |
---|---|---|---|---|
Transfer Function | ||||
# 1 of poles | 1 | 2 | 3 | |
# 1 of zeros | 1 | 2 | 3 | |
−9.1193 × 10−6 | −1.8796 × 10−9 | −1.7402 × 10−12 | ||
−8.9426 | −1.8304 × 10−3 | −1.6960 × 10−6 | ||
- | −8.0620 | −8.0498 × 10−3 | ||
- | - | −8.2158 | ||
9.6066 × 10−6 | 1.9727 × 10−9 | 1.8266 × 10−12 | ||
- | 2.1032 × 10−4 | 1.9551 × 10−7 | ||
- | - | 9.9425 × 10−4 | ||
NRMSE 2 | 0.0254 | 0.0024 | 0.0008 | |
FPE 3 | 0.4573 | 0.0041 | 3.5690 × 10−4 | |
MSE 4 | 0.4572 | 0.0041 | 3.5665 × 10−4 |
Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | |
---|---|---|---|---|---|---|
RMSE | 13.3204 | 24.9975 | 12.8481 | 1.8147 | 1.6967 | 1.6951 |
NRMSE | 0.8772 | 1.6424 | 0.8461 | 0.1195 | 0.1117 | 0.1116 |
R2 | 0.2396 | 0.2996 | 0.2845 | 0.9857 | 0.9875 | 0.9875 |
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Kim, H.; Kim, J.; Yeo, M. Thermal Bridge Modeling According to Time-Varying Indoor Temperature for Dynamic Building Energy Simulation Using System Identification. Buildings 2022, 12, 2178. https://doi.org/10.3390/buildings12122178
Kim H, Kim J, Yeo M. Thermal Bridge Modeling According to Time-Varying Indoor Temperature for Dynamic Building Energy Simulation Using System Identification. Buildings. 2022; 12(12):2178. https://doi.org/10.3390/buildings12122178
Chicago/Turabian StyleKim, Heegang, Jihye Kim, and Myoungsouk Yeo. 2022. "Thermal Bridge Modeling According to Time-Varying Indoor Temperature for Dynamic Building Energy Simulation Using System Identification" Buildings 12, no. 12: 2178. https://doi.org/10.3390/buildings12122178