Buildings’ Thermal Behaviour: Black, White and Grey Boxes

If an engineer wants to model a building to solve problems in the energy realm, there is not a single, unique way to go about it. There are many methods to choose from to predict a building’s energetic performance. The most important aspect of this practice is typically thermal characterisation. Indoor well being and comfort depend, for the most part, on what goes on with indoor spaces thermally. But the virtually infinite combination of location, orientation, shape, window-opening patterns, materials and other variables makes this characterisation complex.

But what is an engineer really doing when they characterise a building thermally? In very simple terms, they are calculating a building’s thermal inertia. This physical concept is defined as the “capacity of a material to store heat and to delay its transmission” [1]. In the field of buildings, it defines the rate and readiness with which a building’s thermal mass cools or heats itself. For example, a thick stone wall has high inertia: it stores heat energy when exposed to direct sun and releases it during hours after the sun sets.

Normally, the key associated physical properties are:

● Heat Capacity “C”: how much energy a building can store per unit of temperature difference — the “store heat” part of the definition above.

● Heat Transfer Coefficient “HTC”: the speed at which heat exits a building when it’s colder outdoors (and the opposite flow) — the “delay its transmission” part.

Initially, one could believe that having great knowledge of the materials that a building is made of could be enough to predict how heat enters and leaves the indoor spaces along a day, week or year. This is true for simple buildings. Think of a simple house in Alentejo: it could be practically a shoebox made of adobe and ceramic roof-tiles, with a single glass window and wooden door. The thermal values of adobe, ceramic, glass, and wood are readily available. An engineer would just compile these into the simple design, account for some air-loss rate since no construction is nor should be air-tight (e.g. airflow between the door and the doorframe), and the physical model of the building could be done with fairly accurate results. The method used in this shoebox case is an example of what is known as a “white-box” modelling method. Meaning we know everything we need to know about the physics of the building’s components and develop our model forward from there.

Now think of an old, 2-storey house Porto’s Baixa neighbourhood with asymmetric design, a renovated kitchen, big sliding glass doors to the back garden, and irregular window-opening patterns (carried out by the occupants). The number of different materials and internal gains result in irregular heat flows that make predicting its thermal behaviour from scratch a big challenge. This is where other methods come in, other than pure white-box. For instance: real, historical measured data may be used to understand how the building behaves along the year, and how this affects indoor temperature and thus occupant’s wellbeing. With enough time and resources, this data can be compiled and a predictive model may be developed. This is called a “black-box” model. The result: we do not understand why, but we know very accurately what temperatures we can expect in each indoor space. But you might have already thought of the main issue: engineers don’t usually have enough time and resources to put this work into a simple family house.

However, measured data over short periods of time (e.g. a week) may be combined with a good understanding of the physics of the construction to reach a midpoint in which a model is based on both some empirical data and some physical aspects of the building, mediated by simplified but accurate equations. The name of these methods is naturally “grey-box”. These innovative methods have lately been proven to be quite powerful, and more importantly, to serve engineers’ and human occupants’ needs. Take a look at the graph below. It shows the results of a case study conducted by Hollick et al[2]., where the measured temperature of a room (black line) was compared against the results of 2 grey-box models (dotted blue and red lines). For most applications, it’s safe to say the results are excellent.

February temperature predictions from a grey-box model against real data from a case study conducted in a house[2].

But technology use in modelling doesn’t stop at these grey-box models. Neural networks are being used by engineers to model even more accurately the dynamic nature of a building’s heat flows, and are showing promising results for widespread application[3]. We might soon be seeing a Portuguese rammed-earth, rural, single-family house being modelled on an adaptive neural network model.

Mateo Barbero

Co-founder

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[1] J. Sala-Lizarraga, Exergy analysis and thermoeconomics of buildings, 1st ed. Waltham: Elsevier, 2019.

[2] F. P. Hollick, V. Gori, and C. A. Elwell, ‘Thermal performance of occupied homes: A dynamic grey-box method accounting for solar gains’, Energy Build., vol. 208, Feb. 2020

[3]R. Baccoli, L. Di Pilla, A. Frattolillo, C.C. Mastino, An Adaptive Neural Network model for thermal characterization of building components, Energy Procedia, Volume 140, 2017.

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