Bayesian Calibration with Augmented Stochastic State-Space Models of District-Heated Multifamily Buildings

Reliable energy models are needed to determine building energy performance. Relatively detailed energy models can be auto-generated based on 3D shape representations of existing buildings. However, parameters describing thermal performance of the building fabric, the technical systems, and occupant behavior are usually not readily available. Calibration with on-site measurements is needed to obtain reliable energy models that can offer insight into buildings’ actual energy performances. Here, we present an energy model that is suitable for district-heated multifamily buildings, based on a 14-node thermal network implementation of the ISO 52016-1:2017 standard. To better account for modeling approximations and noisy inputs, the model is converted to a stochastic state-space model and augmented with four additional disturbance state variables. Uncertainty models are developed for the inputs solar heat gains, internal heat gains, and domestic hot water use. An iterated extended Kalman filtering algorithm is employed to enable nonlinear state estimation. A Bayesian calibration procedure is employed to enable assessment of parameter uncertainty and incorporation of regulating prior knowledge. A case study is presented to evaluate the performance of the developed framework: parameter estimation with both dynamic Hamiltonian Monte Carlo sampling and penalized maximum likelihood estimation, the behavior of the filtering algorithm, the impact of different commonly occurring data sources for domestic hot water use, and the impact of indoor air temperature readings.