A stochastic approach to modeling the dynamics of natural ventilation systems

• Explore and formulate a stochastic approach to analyze the dynamics of natural ventilation systems.
• Illustrate the emergence of bi-stable behavior under stochastic conditions, which is not seen in the deterministic case.
• Construct the sensitivity of the systems to stochastic inputs.

Heating ventilation and air conditioning (HVAC) systems in residential and commercial buildings make up 16% of the United States energy consumption. Utilizing natural ventilation strategies is a low energy solution to reduce the energy used by building environmental control systems. Design of effective natural ventilation strategies is challenging because of inherent stochasticity in interior (machine loads, number of people) and exterior conditions (wind load, outside temperature). However, by exploiting the natural dynamics of building systems, efficient design and control seems possible. We explore this idea by introducing a stochastic approach to analyze the natural dynamics of building systems (under natural ventilation) by explicitly incorporating the effects of stochastic wind speeds and stochastic internal loads. We show that complex dynamics in the form of bi-stable behavior emerges when considering a single zone building with stochastic inputs. We show that neglecting these complex stochastic dynamics leads to inaccurate predictions in the thermal response, especially for natural ventilation. We compute the sensitivity of the system with respect to various system parameters which provide insight into developing robust design guidelines. The techniques presented aid in the design process, and are a step toward adaptive, efficient, robust control of natural ventilation systems.