CO2-based grey-box model to estimate airflow rate and room occupancy

In the existing building stock, heating, cooling and ventilation often run on fixed schedules assuming maximal occupancy. However, fitting the control of the HVAC system to the building's real demand offers large potential for energy savings over the status quo. Building occupants' presence as well as mechanically supplied and infiltrated airflow rates provide information that enables to define tailored strategies for demand-controlled ventilation.

Hence, real-time estimations of these quantities are a valuable input to demand-controlled built environments. In this work, the use of stochastic differential equations (SDE) to estimate the room occupancy, infiltration air-rate and ventilation air-rate is investigated. In particular, a grey-box model based on a carbon dioxide (CO2) mass balance equation is presented.

The model combines knowledge about the physical system with statistical, data-driven parameter estimation. Furthermore, the proposed model contains uncertainty parameters. This is in contrast to purely deterministic models based on ordinary differential equations, where uncertainty is usually disregarded.

The suggested model has been tested in a naturally ventilated and in a mechanically ventilated environment; the performance in these two cases has been compared. We show that the ability to address measurement errors and non-homogeneous conditions in the room air implies that the suggested SDE-based grey-box approach is suitable in the context of demand-controlled ventilation.