CIVE70086 Coursework

Inverse modelling for building retrofit

You have started work for engineers that specialise in retrofitting existing buildings to improve their environmental and energy performance. As part of your first project you have been given remote access to a building and can con-trol the total heat input to several spaces. You also have access to measurements from several temperature sensors. Unfortunately, you do not know anything about the properties of the building itself and have therefore been asked to solve the inverse problem of reconstructing a model of the building based on the available observations.

Submission

You should submit a digital copy of your report to Blackboard by 10:00 am Thursday December 12. The main report must not exceed four A4 sides in length, including diagrams, but can refer to supplementary material in appendices. The report should comprise summaries of:

1. The various load combinations used to test the building.

2. A single inferred model of the building.

3. A recommendation for how to retrofit the building to improve its environmental and energy performance.

The inferred model should consist of some or all of the following:

• The building topology and its connections with the exterior.

• The volume of individual spaces within the building.

• The sizes of the openings in the building.

• The thermal conductivity of internal/external walls and roofs of the building.

Further details

Material for the coursework can be downloaded from Blackboard. In place of measurements from a real building, you will use the ex-ecutable simulate_*.exe, which is a binary that has been compiled from Matlab code to simulate a building. Input to the program consists of a text file named input.txt, which must exist in the di-rectory from which simulate_*.exe is executed. Output from the program consists of a text file named output.txt.

The input data consist of the ambient temperature T0(n) and three heat loads f1(n), f2(n), f3(n) at each time step n. The heat loads include the heat generated by occupants, such that f1 + f2 + f3 represents the total heat input to the building from con-trolled heating/cooling, appliances and occupancy, but does not include heat transfer across the building’s envelope. You can change all of the inputs, including the duration of the simulation, by editing and running createinput.m in the same directory as simulate_*.exe. The input and output data can be read using the functions readinput.m and readoutput.m as demonstrated in main.m.

The hidden properties of the building are randomly assigned us-ing a seed generated from your email address. It is therefore impor-tant that you assign your full email address to id in createinput.m to enable your work to be fairly assessed.

>> type createinput.m % CREATEINPUT for creating temperature % and heat inputs % Enter your full email address for seeding id = '[email protected]'; % Time step dt = 1 * 60; % Select total number of hours hours = 3; n = floor( (hours * 3600) / dt ); t = linspace(0, hours, n+1); % Environment temperature T0 = zeros(1, n+1); f1 = 2000 * ones(1, n+1); f2 = 0 * ones(1, n+1); f3 = 0 * ones(1, n+1); writeinput(dt, T0, f1, f2, f3, id, 'input')

Figure 1: createinput.m

Although chosen randomly, the U-values and opening areas that are assigned to each surface and opening of the building belong to finite sets of possible values. Three bulk U-values are assigned to the building:

• one for the external walls (including windows) (Ue),

• one for the internal partitions/walls/floors (Up),

• one for the roof surfaces (Ur),

such that

Ue , Up, Ur ∈ {1.0, 2.0, 3.0, 4.0},

in Wm−2 K −1 and areas ai (which include a discharge coefficient) are assigned to each of the openings:

ai ∈ {0.1, 0.2},   i = 1, 2, . . .

in m2 .

Background

Inverse problems play a prominent role in engineering, where one is often faced with a system whose latent properties or inputs are unknown and must be inferred from observation. Examples can be found in the fields of geophysics, acoustics, oceanography, medical imaging and are closely related to questions concerning design, control and optimisation.

Figure 2: Forward problem y = G(x) in which the function f and input x are known and the output y is unknown (the network representing G is shown for illustrative purposes only).

Figure 3: Reverse or inverse problem y = G(x) in which the output y and the input x are known but the function G, representing the building, is unknown.

Suggestions

Inverse problems are difficult, if not impossible, to solve exactly and uniquely. It is therefore important that you look for the sim-plest approximate solution to the problem using logical reasoning based on physics and the available data. To do so consider:

• Simple input functions (uniform. heating, fixed environment).

• Using simple hand calculations.

• Starting with bulk models for the entire building.

• Steady states.

• The time scales associated with transients.

Marking criteria

Your report will be marked with respect to the following criteria:

Presentation and clarity of exposition [20%]

A challenging aspect of this coursework is that you need to decide the approach(es) that you will take to tackle the brief (just like prob-lems you’ll encounter in industry and/or research). After exploring several ideas and obtaining results, you will therefore need to think carefully about how to summarise your work effectively. A sim-ple and direct explanation that utilises the benefit of hindsight is likely to be more effective than a day-by-day historical account of everything that you did.

Accuracy, precision and uncertainty of calculations [20%]

Are your calculations correct? Were the correct formulae used to describe the processes? Is the level of precision you are using in calculations commensurable with the degree of uncertainty?

Accuracy of inferred model [20%]

How close is you inferred building model to the ‘actual’ building? In this regard, remember that we are looking for the simplest model that you can find (i.e. the one that invokes the fewest assumptions)

Ingenuity and lateral thinking [20%]

There are many different approaches that you could take to solv-ing this problem. Although we will give you lots of suggestions, we want you to try to develop your own approaches. How can you make best use of known physical laws to constrain your data-driven search for the optimal parameters?

Retrofit recommendation [20%]

Your recommendation for how to retrofit the building should be specific, rather than vague and general. Which particular aspect of the building’s environmental and energy performance would benefit most from improvement?