Online Simultaneous State Estimation and Parameter Adaptation for Building Predictive Control

Abstract

Model-based control of building energy offers an attractive way to minimize energy consumption in buildings. Model-based controllers require mathematical models that can accurately predict the behavior of the system. For buildings, specifically, these models are difficult to obtain due to highly time varying, and nonlinear nature of building dynamics. Also, model-based controllers often need information of all states, while not all the states of a building model are measurable. In addition, it is challenging to accurately estimate building model parameters (e.g. convective heat transfer coefficient of varying outside air). In this paper, we propose a modeling framework for “on-line estimation” of states and unknown parameters of buildings, leading to the Parameter-Adaptive Building (PAB) model. Extended Kalman filter (EKF) and unscented Kalman filter (UKF) techniques are used to design the PAB model which simultaneously tunes the parameters of the model and provides an estimate for all states of the model. The proposed PAB model is tested against experimental data collected from Lakeshore Center building at Michigan Tech University. Our results indicate that the new framework can accurately predict states and parameters of the building thermal model.

Structural observability analysis and EKF based parameter estimation of building heating models

“…Non-linear models provide a better prediction of building thermal dynamics while they are computationally intensive. Linear models are obtained following the simplification of non-linear models and tend to have limited computational intensity while restrained to the operating zones they are tuned for [Maasoumy et al (2013)]. Sometimes, it is quite tricky to assess the accuracy of the linear models owing to the inevitable idealisations and simplifications according to Madsen and Holst (1995).…”

“…Sometimes, it is quite tricky to assess the accuracy of the linear models owing to the inevitable idealisations and simplifications according to Madsen and Holst (1995). However, Maasoumy et al (2013) have stated that these linear models can be adjusted by using an adaptive parameter estimation technique such that the building parameters are updated as the inside and outside environment changes. The combination is a hybrid model and an upgraded version of the linear physical model of the building.…”

“…However, obtaining such models for buildings is difficult due to highly time-varying and non-linear nature of the weather conditions and building dynamics. Further, model-based controllers, often need information of all state variables, while not all state variables in a building model are measurable [Maasoumy et al (2013)]. According to Maasoumy et al (2013), it is also challenging to estimate the thermal parameters accurately.…”

“…Owing to the continuous ambient changes, the mathematical model describing the dynamics of the building has uncertain parameters. Therefore, the algorithms used for evaluation of these parameters should be time-varying and hence be adaptive [Maasoumy et al (2013)]. However, first principles models for the heating of buildings may present a rather large number of parameters.…”

“…When physical insight is used to propose a model for the building heat dynamics with differential equations, Maximum Likelihood method [Madsen and Holst (1995), Bacher and Madsen (2011)] and Maximum a posteriori estimation [Kristensen et al (2004)] and Kalman Filtering [Maasoumy et al (2013), Fux et al (2014), Martincevic et al (2014), Radecki and Hencey (2012)] have been used for parameter identification. They are called hybrid or grey box modelling approaches that blend the two extremes (white box and black box) in various degrees.…”