Dynamic modeling of presence of occupants using inhomogeneous Markov chains

• Presence profiles in an office environment are successfully modeled using inhomogeneous Markov chains.
• As inputs to the Markov chain polynomials and splines of time of day are used to model diurnal dependence.
• Exponential smoothing of observations is used to model per-sequence dynamics.
• Simulations using the fitted model show same key features as collected data.

Occupancy modeling is a necessary step towards reliable simulation of energy consumption in buildings. This paper outlines a method for fitting recordings of presence of occupants and simulation of single-person to multiple-persons office environments. The method includes modeling of dependence on time of day, and by use of a filter of the observations it is able to capture per-employee sequence dynamics. Simulations using this method are compared with simulations using homogeneous Markov chains and show far better ability to reproduce key properties of the data.The method is based on inhomogeneous Markov chains with where the transition probabilities are estimated using generalized linear models with polynomials, B-splines, and a filter of passed observations as inputs. For treating the dispersion of the data series, a hierarchical model structure is used where one model is for low presence rate, and another is for high presence rate.