Sensor placement and parameter identi?ability in grey-box models of building thermal behaviour

Abstract

Building Energy Management systems can reduce energy consumption for space heating in existing buildings, by utilising Model Predictive Control. In such applications, good models of building thermal behaviour is important. A popular method for creating such models is creating Thermal networks, based cognitively on naive physical information about the building thermal behaviour. Such models have lumped parameters which must be calibrated from measured temperatures and weather conditions. Since the parameters are calibrated, it is important to study the identifiability of the parameters, prior to analysing them as physical constants derived from the building structure. By utilising a statistically founded parameter estimation method based on maximising the likelihood function, identifiability analysis can be performed using the Profile Likelihood method. In this paper, the effect of different sensor locations with respect to the buildings physical properties is studied by utilising likelihood profiles for identifiability analysis. The extended 2D profile likelihood method is used to compute two-dimensional profiles which allows diagnosing parameter inter-dependence, in addition to analysing the identifiability. The 2D profiles are compared with confidence regions computed based on the Hessian.

Use of Machine Learning Methods for Indoor Temperature Forecasting

“…They have been widely used in the field of predictive control [67][68][69] as well as in the area of predicting building thermal load [70,71] and indoor temperature forecasting [3]. The most common method for creating this model is applying a resistance-capacity (RC) form based on physical and statistical approaches [38,[72][73][74]. The thermal resistance R represents the component to resist the heat flux, and the thermal capacity C describes its storage capacity.…”

“…The gray box model involves both physical and black-box modeling [37]. This approach is based on the thermal modeling of buildings by analogy with an electrical resistance-capacity circuit [38]. The buildings are modeled by a set of dynamic differential equations representing the phenomenon of conduction, convection, and capacitive phenomenon.…”

Estimating uncertainty of model parameters obtained using numerical optimisation

“…Subsequently, the R3C2 model is found to be overparameterised. After some experimentation, based on previous experience with the model Brastein et al [2019b], the resistor R g is removed from the circuit model in Fig. 17, in an attempt to make the remaining parameters identifiable.…”

Metodología para el modelado y la estimación de parámetros del proceso de crecimiento de Lobesia botrana

“…De manera similar, en el trabajo desarrollado por Baulmet y Dostál en el año 2020, si bien se proponen técnicas novedosas para la estimación de parámetros en modelos matemáticos de caja gris, los autores no consideran la propiedad de identificabilidad como requisito para la implementación de algoritmos de estimación de parámetros (Bäumelt and Dostál, 2020). En el año 2019, Brastein y colaboradores, propusieron el uso de los análisis de identificabilidad práctica e identificabilidad estructural, para determinar como el diseño óptimo de experimentos afecta la información dinámica contenida en los datos utilizados para la estimación de parámetros de un modelo de caja gris (Brastein et al, 2019). En el año 2021, Hotvedt y colaboradores, propusieron el uso de la regularización de parámetros como una estrategia para conservar la interpretabilidad física de un modelo, aun cuando sus parámetros no son identificables.…”