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Abstract
The dynamic hygrothermal behaviour of existing buildings can be characterized using data-driven models that are established via system identification techniques. However, most of the time the identification problem is difficult to solve for multi-zone buildings due to high dimensionality of the model and poor excitation in the training data. In addition, building thermal and moisture dynamics are coupled and simultaneous identification of the coupled model is challenging. This paper presents a simplified one-way coupled inverse model to capture the building thermal and moisture dynamics where the impact of space moisture on the building thermal response is neglected. This simplification enables the thermal and moisture sub-models to be estimated sequentially which reduces the computation complexity and improves model identifiability. Both thermal and moisture sub-models adopt a physically based approach in which moisture interactions between different zones are neglected while the inter-zonal thermal interactions are captured. A 3-step procedure is developed to reduce the problem dimension in identifying the thermal sub-model. As a case study, the overall approach was applied to model a medium-size commercial building with nine thermal zones from measured data and the estimated models were validated for different periods of time during a cooling season.
Disclosure statement
No potential conflict of interest was reported by the authors.
Nomenclature
| Awall | = | total wall area within a zone (m2 or ft2) |
| C | = | thermal/moisture capacitance (kJ/K or Btu/°F/kg or lb) |
| cp,air | = | air specific heat (kJ/kg-K or Btu/lb- °F) |
| CS | = | coupling matrix for the zones |
| J | = | sensitivity matrix |
| M | = | information matrix |
| msup | = | supply air mass flow rate (kg/s or lb/hr) |
| Occup | = | number of occupants within a zone |
| Pwhole,bui | = | whole building power (kW or Btu/hr) |
| PHVAC | = | HVAC system power (kW or Btu/hr) |
| Qsol,ext | = | solar radiation absorbed on the external walls (kW or Btu/hr) |
| Qsol,trans | = | solar radiation transmitted through the windows (kW or Btu/hr) |
| Qgain,rad | = | radiative internal heat gains (kW or Btu/hr) |
| Qgain,conv | = | convective internal heat gains (kW or Btu/hr) |
| Qsen | = | sensible cooling/heating to the space (kW or Btu/hr) |
| R | = | thermal/moisture resistance (K-s/kJ or °F-hr/Btu / s/kg or hr/lb) |
| RH | = | relative humidity (%) |
| Tgrd | = | ground temperature (°C or °F) |
| Tsup | = | supply air temperature (°C or °F) |
| Tzone,adj | = | air temperature of the adjacent zone (°C or °F) |
| u | = | input vector |
| U | = | excitation data |
| w | = | disturbance vector |
| w | = | water content (kg water/kg air or lb water/lb air) |
| wwall | = | wall water content (kg water/kg material or lb water/lb material) |
| woccup | = | moisture generation rate per occupant (kg water/s or lb water/hr) |
| x | = | state vector |
| y | = | output vector |
| δ | = | parameter perturbation level |
| σ | = | model error standard deviation |
| θ | = | estimate parameters |
| ξ | = | slope of the wall material sorption curve |
| ψ | = | slope of the air relative humidity to humidity ratio curve |
| Δwgen | = | zone internal moisture gain (kg/s or lb/hr) |
| Δwvent | = | moisture gain/removal due to mechanical cooling (kg/s or lb/hr) |
| Subscripts/superscripts | = | |
| amb | = | ambient condition |
| avgd | = | averaged value |
| cal | = | calculated/estimated matrix |
| d | = | discrete version of the state-space matrices |
| deep | = | deep layer in the EMPD method |
| GA | = | generated points in global analysis |
| inf | = | infiltration |
| moi | = | moisture-related variables/matrices |
| norm | = | normalized matrix |
| surf | = | surface layer in the EMPD method |
| wall | = | wall-related variables |
| zone | = | zone air condition |
| σ | = | switching mode in the moisture model |