Bayesian Workflow and Hidden Markov Energy-Signature Model for Measurement and Verification

Abstract

A Bayesian data analysis workflow offers great advantages to the process of measurement and verification, including the estimation of savings uncertainty regardless of the chosen numerical model. However, it is still rarely used in practice, perhaps because practitioners are less familiar with the required tools. The present work documents a Bayesian methodology for the assessment of energy savings at the scale of a whole facility, following an energy-conservation measure. The first model, an energy signature commonly used in practice, demonstrates the steps of the Bayesian workflow and illustrates its advantages. The posterior distributions obtained by training this first model are used as prior distributions for a second, more complex model. This so-called “hidden Markov energy signature” model combines the energy signature with a hidden Markov model at an hourly resolution, and allows detection of occupancy. It has a large number of parameters and would likely not be identifiable without the Bayesian workflow. The results illustrate the advantages of the Bayesian methodology for measurement and verification: a probabilistic description of all variables, including predictions of energy use and savings; the applicability to any model structure; the ability to include prior knowledge to facilitate training complex models. Savings are estimated by the new hidden Markov energy-signature model with a much lower uncertainty than with a lower-resolution model. The highlights of the paper are twofold: it serves as a tutorial on Bayesian inference for measurement and verification; it also proposes a new flexible model structure for hourly prediction of energy use and occupancy detection.