Solving inverse problems in building physics: An overview of guidelines for a careful and optimal use of data

Abstract

Building physics researchers have benefitted from elements of statistical learning and time series analysis to improve their ability to construct knowledge from data. What is referred to here as inverse problems are actually a very broad field that encompasses any study where data is gathered and mined for information. The purpose of the present article is twofold. First, it is a tutorial on the formalism of inverse problems in building physics and the most common ways to solve them. Then, it provides an overview of tools and methods that can either be used to assess or the reliability of inverse problem results, prevent erroneous interpretation of data, and optimise information gained by experiments. It provides an introduction, along with useful references, to the topics of estimation error assessment, regularisation, identifiability analysis, residual analysis, model selection and optimal experiment design. These concepts are presented in the context of building simulation and energy performance assessment: a simple RC model is used as a running example to illustrate each chapter.

Integrating physics-based models with sensor data: An inverse modeling approach

“…It is used widely in the field of data assimilation where it serves as a method for estimating the state of a system and for determining optimal values of uncertain model parameters [34,35]. Many inverse modeling techniques are explored in building physics research to estimate the target parameters of complex problems, and the importance of the optimal use of data and algorithms was addressed when solving inverse problems [36]. Zhang et al [37] addressed the limitations of physics-based thermodynamics and heat transfer in understanding building systems and environmental problems and introduced inverse modeling approaches to solve uncertain or unknown parameters using measured data.…”

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

“…Model selection is a frequently advocated approach, for example, by Bacher and Madsen [8], Raillon and Ghiaus [10], Rouchier [43]. The strongly regulating prior used for the air infiltration parameter C in f can be viewed as model selection.…”

Sequential Monte Carlo for on-line estimation of the heat loss coefficient

“…where x t denotes the vector of states at the time coordinate t, and y t denotes the observations. The reader is referred to (Madsen and Holst, 1995) and (Rouchier 2018) for more details regarding the discretization steps.…”

“…4), filtering produces p ( x t ∨ y 1 : T , θ ), the probability distribution function of each state given measurements and parameter values, and the marginal likelihood function L y ( θ)= p ( y 1 :T ∨θ ). The Kalman filter algorithm is not described here for the sake of concision, but has been described by many authors including (Madsen and Holst, 1995;Rouchier 2018).…”

“…The calibration of simplified building energy models using in-situ measurements is now a widespread research topic (Rouchier, 2018). It is commonly performed for two general types of applications: the characterisation of intrinsic building performance (Heo et al 2012;Bauwens and Roels, 2014), and the identification of a model for predictive purposes, for instance in the aim of model predictive control.…”