On-the-fly mathematical formulation for estimating people flow from elevator load data in smart building virtual sensing platforms

This paper considers a new approach for people flow estimation in buildings from elevator trip records and corresponding load data, and the resulting model is used on the virtual sensing platform we have developed. People flow data can be used to improve elevator performance through optimal car assignments to hall calls by a group controller and are useful for estimating occupant distributions as heat loads allowing for optimized air-conditioning control to realize energy savings. Available data from an elevator controller is insufficient for exact people flow estimation and therefore this problem becomes under-defined. Our virtual sensing platform adopts equation-based modeling and optimization-based parameter estimation, which estimates application-related parameters from available sensor data, allowing for over- or under-defined situations among sensory information, but better mathematical formulation is essential for accurate parameter estimation on this virtual sensing platform. Accordingly, we propose a new method to define an elevator trip-wise mathematical formulation by modifying pre-defined base equations or defining additional equations. The key idea is that each elevator trip has different features, including sparsity, that are useful for improving accuracy and can be successfully formulated as simultaneous equations that our virtual sensing platform accepts. The procedure for defining a mathematical formulation is invoked after trip data are obtained and we refer this procedure as “on-the-fly mathematical formulation.” The formulated trip-wise equations are combined as simultaneous equations for estimating people flow over a given period on the virtual sensing platform by mathematical optimization.