Holistic Design Explorations of Building Envelopes Supported by Machine Learning

Abstract

The design of building envelopes requires a negotiation between qualitative and quantitative aspects belonging to different disciplines, such as architecture, structural design, and building physics. In contrast to hierarchical linear approaches in which various design aspects are considered and conceived sequentially, holistic frameworks allow such aspects to be taken into consideration simultaneously. However, these multi-disciplinary approaches often lead to the formulation of complex high-dimensional design spaces of solutions that are generally not easy to handle manually. Computational optimisation techniques may offer a solution to this problem; however, they mainly focus on quantitative aspects, not always guaranteeing the flexibility and interactive responsiveness designers need in the early design stage. The use of intuitive geometry-based generative tools, in combination with machine learning algorithms, is a way to overcome the issues that arise when dealing with multi-dimensional design spaces without necessarily replacing the designer with the machine. The presented research follows a human-centred design framework in which the machine assists the human designer in generating, evaluating, and clustering large sets of design options. Through a case study, this paper suggests ways of making use of interactive tools that do not overlook the performance criteria or personal preferences of the designer while preserving the simplicity and flexibility needed in the early design stage.

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031 JOURNAL OF FACADE DESIGN & ENGINEERING VOLUME 9 / NUMBER 1 / 2021
Holistic Design Explorations of
Building Envelopes Supported
by Machine Learning
Federico Bertagna1*, Pierluigi D’Acunto2, Patrick Ole Ohlbrock1, Vahid Moosavi3
* Corresponding Author
1 ETH Zurich, Institute of Technology in Architecture, Chair of Structural Design, Zurich (Switzerland). bertagna@arch.ethz.ch
2 Technical University of Munich, Department of Architecture, Munich (Germany)
3 ETH Zurich, Institute of Technology in Architecture, Chair of Digital Architectonics, Zurich (Switzerland)
Abstract
The design of building envelopes requires a negotiation between qualitative and quantitative aspects
belonging to dierent disciplines, such as architecture, structural design, and building physics.
In contrast to hierarchical linear approaches in which various design aspects are considered and
conceived sequentially, holistic frameworks allow such aspects to be taken into consideration
simultaneously. However, these multi-disciplinary approaches often lead to the formulation of
complex high-dimensional design spaces of solutions that are generally not easy to handle manually.
Computational optimisation techniques may oer a solution to this problem; however, they mainly
focus on quantitative aspects, not always guaranteeing the flexibility and interactive responsiveness
designers need in the early design stage. The use of intuitive geometry-based generative tools, in
combination with machine learning algorithms, is a way to overcome the issues that arise when dealing
with multi-dimensional design spaces without necessarily replacing the designer with the machine.
The presented research follows a human-centred design framework in which the machine assists the
human designer in generating, evaluating, and clustering large sets of design options. Through a case
study, this paper suggests ways of making use of interactive tools that do not overlook the performance
criteria or personal preferences of the designer while preserving the simplicity and flexibility needed in
the early design stage.
Keywords
holistic design approach, building envelopes, graphic statics, conceptual structural design, machine
learning, simplicity and performance
10.7480/jfde.2021.1.5423

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1 INTRODUCTION
1.1 BUILDING ENVELOPES AND THE ILL-DEFINED NATURE OF DESIGN
The building envelope is the main interface between the outdoors and the interior spaces of a
building. The design of building envelopes is an excellent example of a multi-disciplinary process
in which both qualitative and quantitative aspects must be addressed simultaneously. Conflicting
parameters belonging to diverse fields – such as architecture, structural design, and building
physics – strongly influence the performance and the outcome of the design, thus making the
building envelope a dominant system among all the subsystems in a building (Lang, 2013). Because
of the number of aspects involved, it is crucial to operate in a holistic way in order to have eective
coordination between these aspects throughout the entire design process, and especially in the
conceptual phase. Designers have to find suitable trade-os based on a cognitively complex process
of synthesis between objective and subjective evaluations. Digital tools oer adequate support to
designers in dealing with such a complexity. However, their implementation within the design
process is not always straightforward. Indeed, computers typically require a precise numerical
formulation and univocal objectives (Harding & Olsen, 2018), elements that are both generally in
conflict with the ill-defined nature of the design process itself (Rittel & Webber, 1973).
1.2 HOLISTIC DESIGN OF BUILDING ENVELOPES
When dealing with the design of building envelopes, designers have the opportunity to explore
dierent levels of integration between disciplines (Rush, 1986) and investigate the influence of
each aspect, starting from the early design stage. Definition of the architectural space, load-bearing
capacity, and mitigation of external climate conditions are all aspects that can become an integral
part of the building envelope. Despite the lack of a univocal definition (Rush, 1986), the term holistic
– or integrated – design refers here to an approach based on mutual relationships between the
dierent aspects involved in the design process.
FIG. 1 Schematic workflow of a possible sequential linear approach (left) and a holistic approach (right) for the design of building
envelopes
The present research is based on the assumption that the lack of such relationships often leads to
a linear design process (Fig. 1, left) where the outcome is conceived just as a sum of the dierent
parts (Saint, 2007), and which frequently entails the non-optimal use of material resources (Nervi,

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1965). Conversely, the ability to operate through holistic approaches (Fig. 1, right) would foster
an interdisciplinary discourse that, in addition to widening the range of possible design options,
ultimately allows for more conscious use of the available resources in the final built constructions.
This paper aims to investigate the latter strategy, regarding geometry as the mediator between
architectural qualities, structural and sun-shading performance of the building envelope.
Specifically, the research focuses on the interplay between the form of the building envelope, the
inner forces within its load-bearing structure, and its performance in terms of solar protection and
daylight modulation.
1.3 DIGITAL DESIGN FRAMEWORKS IN
ARCHITECTURE AND ENGINEERING
A design framework can be generally characterised as a process that is composed of dierent
individual operations (Brown, Jusiega, Mueller, 2020). Fig. 2 schematically shows three
characteristic frameworks that represent an adaptation of the work of Oxman (2006) and Wortmann
(2018). The main features of these three dierent frameworks will be briefly described in the
following paragraph.
FIG. 2 Three design frameworks, with their dierent operations and relationships highlighted
One typical design approach is to first generate design options and then evaluate them with respect
to a set of criteria. Designers can repeat this sequence, meaning that they can generate new
options according to the results of the evaluation in a trial-and-error fashion (Fig. 2a). Thanks to the
introduction of digital parametric tools, designers can now automatically generate a vast number
of alternative options with minimal computational eort. However, this generation is often not
directly guided by any performance criteria. Hence, such a problem-oriented approach is often
time-consuming and not very ecient when dealing with multi-dimensional design spaces that
involve a high number of design parameters. One possible way to address this challenge is to make
use of optimisation techniques such as multi-objective optimisation (MOO). These techniques allow
the evaluation step in searching for the best performing options to be simplified. More precisely,
in the case of multi-objective optimisation, they support guided explorations of the design space,
providing sub-optimal options (Brown & Mueller, 2017; Turrin, Von Buelow, & Stous, 2011; Yang Ren,
Turrin, Sariyildiz, & Sun, 2018), from which the designer has to make a selection (Fig. 2b). Although
very powerful in solving well-defined problems, optimisation techniques do not always oer the
flexibility and the responsiveness necessary in early, ill-defined design stages. In this context, the
major challenge is that all design objectives must be explicitly formulated before they are even
known (Harding & Olsen, 2018), thus making the inclusion of qualitative aspects rather complex
to achieve. The introduction of an intermediate clustering step enables the systematic integration
of such qualitative considerations (Fig. 2c). For example, clustering algorithms based on machine
learning can provide additional support by automatically organising large sets of diverse design
options according to similarities pertaining to specific criteria (Wortmann & Schroepfer, 2019).

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In combination with filtering functions, these algorithms oer the possibility to manage vast, multi-
dimensional design options and eventually allow designers to negotiate quantitative and qualitative
aspects according to personal preferences (Harding & Olsen, 2018; Fuhrimann, Moosavi, Ohlbrock,
& D'Acunto, 2018; Saldana Ochoa, Ohlbrock, D’Acunto, & Moosavi, 2020). Following this approach,
the designer is prevented from being overwhelmed (Brown & Mueller, 2017) by examining all the
options individually and at the same time is not forced to focus exclusively on quantitative aspects.
In line with the approach of Saldana Ochoa et al. (2020), the present research also implements a
design process that includes generation, evaluation, clustering, and selection steps with the scope of
considering both quantitative performance criteria and qualitative preferences of the designer while
preserving the simplicity and flexibility needed in the early design stage.
1.4 OBJECTIVES AND CONTENT OF THE PAPER
This research aims to support an eective design workflow for the multi-disciplinary design of
building envelopes, with a particular focus on the conceptual design phase. Thanks to its holistic
nature, the proposed approach fosters new design possibilities and opens up new perspectives
for the conscious use of the available resources. Following a geometry-based approach in which
the form of the building envelope is simultaneously informed by aspects related to architecture,
structure, and solar control, a set of user-defined performance criteria are taken into consideration
without necessarily overlooking the qualitative aspects involved in the design.
The paper is structured as follows. Section 2 outlines the methods that form the basis of the
research, introducing the applied geometry-based approach, the digital tools involved, and the
metrics considered. Section 3 illustrates the advantages of the proposed framework through a case
study in which several non-standard design options for a load-bearing façade are investigated and
discussed. Finally, Section 4 outlines the conclusions and presents an outlook on future work.
2 METHODOLOGY
2.1 GEOMETRY-BASED DESIGN APPROACH
Geometry plays a crucial role in the generation of architectural space. This dependency from
geometry persists in other fields, thus making geometry a common ground where aspects belonging
to diverse fields meet. For example, in structural design, geometry plays a key role in defining the
overall behaviour of a structure. Equilibrium-based methods such as graphic statics (Culmann,
1866; Maxwell, 1864; Cremona, 1872) and their contemporary digital implementations have proved
to be powerful tools for the generation of structures (Van Mele, Rippmann, Lachauer, & Block, 2012;
Rippmann, Lachauer, & Block, 2012; Beghini, Carrion, Beghini, Mazurek, & Baker, 2014; D’Acunto et
al., 2019; Konstantatou, D’Acunto, & McRobie, 2019; Ohlbrock & D’Acunto, 2020). Unlike analytical
methods, which are generally implemented through quantitative numerical approaches, geometry-
based methods provide significant support since the conceptual stages of the design, when a visual
understanding of forces is essential in order to generate creative design options (Schwartz, 2012;
Kotnik & D’Acunto, 2013). Geometry has a relevant role also in the phase of evaluation of given design
options. Digital tools for structural and energy analysis can now provide very accurate calculations
on high resolution models. However, this often comes at the price of long computation time, and

035 JOURNAL OF FACADE DESIGN & ENGINEERING VOLUME 9 / NUMBER 1 / 2021
it requires a consistent eort for the creation of the models. Since such accuracy usually is not
needed in the early stage of the design, material-independent geometry-based approaches represent
a suitable simplification for conceptual design tasks and are therefore the base for the present
research. Detailed models that take into account material properties can be then included in the
design process at a later stage.
2.2 TOOLS, PARAMETERS AND METRICS USED IN THE DESIGN PROCESS
Fig. 3 gives an overview of the various tools that are part of the proposed design framework for the
conceptual design of building envelopes. Drawing from the approach presented by Saldana Ochoa et
al. (2020), the proposed framework consists of four main steps: generation, evaluation, clustering, and
selection. The whole framework is developed using the CAD platform Rhinoceros (www.rhino3d.com,
accessed 20/11/2020) and the Grasshopper visual scripting environment (www.grasshopper3d.com,
accessed 20/11/2020).
FIG. 3 Dierent tools integrated into the proposed framework for the conceptual design of building envelopes
The generation of design options is addressed through the Combinatorial Equilibrium Modelling
(CEM) (Ohlbrock & D’Acunto, 2020). The CEM is a digital form-finding tool grounded in vector-based
3d graphic statics (D’Acunto et al., 2019), and it is used in this work to quickly generate a broad set of
form diagrams in static equilibrium as pin-jointed frameworks that represent the structures of load-
bearing building envelopes. Within the CEM, the edges of the form diagrams are subdivided into two
distinct categories: the trail edges that connect each node with a (topologically) direct load transfer
to the closest support; the deviation edges that connect nodes on dierent trail edges. Moreover, the
user can directly assign a set of metric values to the edges, and specifically the trail lengths – i.e.
the lengths of the trail edges – and the deviation force magnitudes – i.e. the force magnitudes of the
deviation edges (Ohlbrock & D’Acunto, 2020). After the definition of the topology of the structure and
the dominant load case, which in this case are kept constant, the CEM is able to generate dierent
form diagrams as alternative design options. This step is performed considering various user-defined
combinations of tension and compression forces in the edges of the form diagrams and metric
values assignments for the trail lengths and the deviation force magnitudes.
Interpreting the form diagrams generated via the CEM as framed structures, various additional
performance metrics are then assessed (evaluation) for each design option. The Finite Element
Analysis (FEA) tool Karamba3D (Preisinger, 2013) is used to evaluate the linear-elastic response
of the framed structures under lateral loads in terms of axial and bending deformation energies.
The evaluation of environmental criteria such as solar radiation and daylight availability is
performed using Ladybug Tools (Roudsari, Pak, & Smith, 2013).

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Table 1 shows all the parameters and metrics that are used to describe each design option (form
diagram and related framed structure). Note that Load Case 1 [LC1] refers to the vertical loads
considered in the generation of the form diagram and Load Case 2 [LC2] to additional unitary
horizontal forces taken into account in the FEA. For each generated design option, its geometric
characteristics and related performance values, evaluated using the parameters and metrics of Table
1, are recorded into an indexed multi-dimensional vector Dk = {dk,1,…, dk,n}. The latter is stored in a
dataset, which constitutes a numerical description of the design space.
TABLE 1 List of parameters and metrics used to characterize each design option
SOURCE PARAMETER/METRIC LABEL DESCRIPTION UNITS
CEM node position posXY position of the nodes (xi, yi) in the
form diagram
[m]
edge (trail/deviation) length edgeLen length of trail and deviation edges
in the form diagram
[m]
edge (trail/deviation) magnitude edgeMag magnitude of axial forces within
trail and deviation edges in the
form diagram
[kN]
edge load path [LC1] edgeLP product of the length li of each edge
of the form diagram by the axial
force fi acting in it
[kNm]
total load path [LC1] totLP sum of the products of the length li
of each edge of the form diagram by
the absolute value of the axial force
fi acting in it
[kNm]
max/min force [LC1] forMax,
forMin
maximum and minimum axial
forces within the edges in the form
diagram
[kN]
Karamba3D total mass totMass total mass of the structural
members of the framed structure
[kg]
axial deformation energy [LC2] defAxial sum of the products of axial forces
of the framed structure by the
corresponding displacements
parallel to their direction
[Nm]
bending deformation energy [LC2] defBend sum of the products of bending
forces of the framed structure by
the corresponding displacements
parallel to their direction
[Nm]
Ladybug solar radiation reduction SRR reduction in percentage of the total
amount of solar radiation on a test
point without shading elements
(SRi) and with shading elements
(SRf)
[%]
daylight factor DF ratio between the illuminance at
an indoor test point (E) and the
illuminance at an outdoor test
point (E0)
[%]
Hard quantitative filtering criteria can be then implemented to eliminate the relatively worst-
performing sub-set of the design space. After this filtering process, Self-Organizing Maps (Kohonen,
1982) are used for clustering the design space. Self-Organising Maps (SOMs) can be regarded as
a specific class of unsupervised artificial neural network, which allows for data dimensionality
reduction without the loss of non-linear associations between the data (Harding, 2016). Based on
user-defined clustering criteria, the SOM algorithm maps the data from a high-dimensional space

037 JOURNAL OF FACADE DESIGN & ENGINEERING VOLUME 9 / NUMBER 1 / 2021
onto a lower-dimensional one, without losing the topological features of the high-dimensional space.
That is, the design options are clustered in the low-dimensional space based on the distance of their
corresponding data points in the high-dimensional space. In this way, it is possible to conveniently
represent a multi-dimensional design space onto a 2D map, in which each node Nj (xj1, xj2) of the
map has an associated multi-dimensional vector Wj = {wj,1,…, wj,n} or Best Matching Unit (BMU).
In fact, each node of the map contains a cluster of design options that are similar with respect to
the defined clustering criteria. The SOM thus provides the designer with a quick overview of the
design space. The algorithm used in this work is implemented within the Python environment using
SOMPY (Moosavi, 2014).
Eventually, in the selection step of the design process, the designer can easily navigate within the
SOM and select the preferred design options considering both quantitative and qualitative criteria.
If necessary, design options can be filtered out according to quantitative criteria in order to reduce
the size of the design space further.
3 CASE STUDY
This section outlines an application of the proposed framework for the design of load-bearing and
shading façades based on the FAU Building designed in 1964 by the Italian architect Enrico Tedeschi
(1910-1978) for the campus of the Architecture Faculty of Mendoza, Argentina (Fig. 4).
FIG. 4 FAU Building (1964), arch. Enrico Tedeschi, Mendoza (Argentina)

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This building was chosen as a case study as its façades are not only load-bearing, but they also
provide solar protection to the glazed surfaces and create a unique architectural motif for the
building. It is, therefore, a relevant example of a holistic design approach, in which aspects related
to architecture, structure, and solar control are considered at the same time. The façades on the long
side of the FAU Building are planar diagrids made of reinforced concrete elements with a hollow
circular cross-section that support a series of post-tensioned concrete beams spanning 12.5 metres
across the façades (Codina, 2013). Thanks to these reticular façades, the architect could achieve
column-free spaces and solve the question of horizontal stability at the same time, a peculiar feature
considering the high seismicity of the zone. A critical aspect of the design was the control of natural
lighting. In this case, the objective of the architect was to obtain diuse lateral lighting, avoiding
glare and overheating issues due to direct solar radiation on the glazed surfaces.
3.1 GENERATION AND EVALUATION OF THE DESIGN OPTIONS
Taking the FAU Building as a reference, various alternative design options for its façade were
explored following the proposed design framework, based on the same design objectives that led to
the realisation of the FAU Building.
FIG. 5 Generation of various form diagrams (right) via the CEM. The topology (left), the floor heights and the load-case are kept
constant, and only the distribution of deviation force magnitudes (devMag) is varied
Fig. 5 (left) shows the topology of the structure that was used as a base for the entire generative
process via the CEM. The topology consists of 120 vertices, which are connected through 96 trail
edges and 96 deviation edges. The 96 values of the deviation force magnitudes (devMag) were
randomly generated following linear, parabolic, and sinusoidal distributions. These distinct force
distributions were then applied to groups of two, six, or eleven neighbouring edges, keeping the
central axis of the form diagram as an axis of symmetry. The values of the trail lengths (trailLen)
were controlled by the given floor heights and the necessity to ensure that all the nodes of the form
diagram belonging to the same floor were horizontally aligned. External forces [LC1] were applied
to the nodes of the form diagram according to their corresponding tributary area and assuming a
10 kN/m2 distributed load on the floor slabs (5 kN/m2 dead load + 5 kN/m2 live load). Fig. 5 (right)
shows three exemplary form diagrams that resulted from this generative set-up in which only the 96
deviation force magnitudes (devMag) were automatically varied (Fig. 6a).

039 JOURNAL OF FACADE DESIGN & ENGINEERING VOLUME 9 / NUMBER 1 / 2021
FIG. 6 Flowchart of the generation and evaluation steps showing the parameters involved, their labels (Table 1) and the number of
items for each parameter (in square brackets)
Each of the form diagrams was subsequently interpreted as a framed structure and then analysed
in relation to structural (Fig. 6b, c) and sun-shading performance (Fig. 6d) using the CEM, Karamba,
and Ladybug. These analyses were carried out in order to evaluate the quantitative metrics
introduced in Table 1. In particular, the total mass totMass of each design option was calculated
considering hollow circular cross-sections in reinforced concrete (C20/25) for the façade elements,
dimensioned according to the axial forces they had to withstand. The evaluation of the axial and
bending deformation energies – defAxial and defBend, respectively – was performed with respect to
a load case [LC2] where unitary horizontal forces were applied to the framed structure in addition to
the vertical forces of load case 1 [LC1]. The solar radiation reduction SRR was calculated on a vertical
test grid corresponding to the glazed surface of the façade, with a resolution of 0.5 x 0.5 m and an
analysis period of one year. Four daylight factors DF(0-3) were evaluated considering four horizontal
test grids, with a resolution of 1.0 m by 1.0 m, located at the four floors, at a height of 0.9 m above the
floor planes. Each generated design option (form diagram and corresponding framed structure) and
its performance was then numerically described using a 731-dimensional indexed vector Dk = {dk,1, …,
dk,731} (96 input and 635 output) (Fig. 6e). Using a 10-core 2.5 GHz CPU, the generation and evaluation
of each design option required 15 seconds, on average. By taking advantage of parallel computing, it
was possible to generate and evaluate 20’144 design options in about 20 hours.
3.2 QUANTITATIVE FILTERING AND CLUSTERING
OF THE DESIGN OPTIONS
In order to describe the peculiarities of the design options synthetically, the higher-order statistics
(mean, variance, skewness, kurtosis) (Farid, 2002) of the following parameters were additionally
calculated: position of the nodes posXY, edge length edgeLen, edge force magnitude edgeMag,
edge load path edgeLP. Before proceeding with the clustering of the generated design options, hard
filters were introduced to eliminate those design options that did not meet specific performance
levels. The filtering criteria and their sequence of application can be defined by the user based on the
task at hand. Within the analysed case study, the following filters were applied: total load path totLP
(90th percentile, 18’129 options kept), maximum edge force forMax (90th percentile, 15’944 options
kept), minimum edge force forMin (90th percentile, 14’349 options kept), and solar radiation reduction
SRR (90th percentile, 12’758 options kept). That is, from the initial set of 20’144 design options, 12’758
were kept after the filtering process.

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FIG. 7 Using the SOM algorithm, the generated and filtered design options (12’758) are clustered onto a 40x40 map (top left). Each
node Nj of the map (grey circle) contains several design options, the size of the circle being proportional to the number of design
options contained in that node. Representative design options for three nodes of the grid (N125, N1127, N1399) are shown (top
right). The designer can easily navigate within the design space and select any of the nodes to explore further the entire set of
design options contained therein. For example, N1399 (bottom) includes 15 similar design options, each one identified with its
corresponding index k and the associated 731-dimensional vector Dk.
After the filtering process, the remaining design options were clustered onto a 40 x 40 map using the
SOM algorithm (Fig. 7). The clustering was performed taking into account the following parameters:
total mass totMass, maximum edge force forMax, minimum edge force forMin, axial deformation
energy defAxial, bending energy defBend, solar radiation reduction SRR, and higher order statistics of
edge load path edgeLP, position of nodes posXY, and daylight factors per floor DF.

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3.3 SELECTION OF THE FINAL PREFERRED OPTIONS
Thanks to the SOM, the designer can navigate a complex multi-dimensional design space, having
a clear overview of the relationship between the dierent design options with respect to qualitative
and quantitative criteria. If necessary, the designer can also re-iterate the process investigating a
dierent clustering strategy, introducing new filters for the quantitative evaluation, or generating a
new pool of design options informed by the outcome of the first iteration. Within the analysed case
study, additional filters were applied to the SOM (Fig. 7) to narrow down the design space further
and proceed with the selection of three final design options. Considering the distribution maps of
Fig. 8, in the first case, only those design options whose total mass totMass was less than the 5th
percentile and the mean value of daylight factor DF_mean was greater than the 90th percentile were
considered. These filters accounted for 14 nodes in the SOM (Fig. 9). Out of this subset, node N61 (j =
61), containing 20 design options, was chosen. Among these design options, the one with index k =
16’562 was eventually selected as Option A.
FIG. 8 Distribution maps of the 18 parameters used for the SOM. Values are normalised in the range 0-100%.
Following a similar procedure, Option B (j = 969; k = 19’117) was selected among the design
options with a standard deviation value of daylight factor DF_std lower than the 10th percentile
and maximum force magnitude forMax lower than the 5th percentile. Finally, Option C (j = 1’213; k
= 1’041) was selected among the design options with a solar radiation reduction SRR higher than
the 95th percentile and a standard deviation value of the position of the nodes posXY higher than
the 70th percentile.

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FIG. 9 Selection procedure for Option A (j = 61; k = 16’562). Representative design options (right) for the 14 nodes retained from
the 40 x 40 SOM (left) after the application of hard filters on the total mass totMass (5th percentile) and the mean value of daylight
factor DF_mean (90th percentile).
FIG. 10 Axonometric views, structural diagrams, and solar radiation maps for 3 options extracted from the dataset

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3.4 DISCUSSION
The parallel coordinates plot in Fig. 10 shows the structural and sun-shading performance metrics
of the three selected design options in comparison to the original design of the FAU Building by
Enrico Tedeschi. Although illustrating very diverse geometries and patterns, all the selected design
options are characterised by similar values for the total load path totLP and its correlated total mass
totMass (Fig. 10), which are lower than those of the original design. These dierences can be mainly
explained with the high maximum axial forces forMax that is needed to redirect the accumulated
vertical forces at the height of the first floor in the original design. Since the original design defines
an overall triangulated structure, the bending deformation energy defBend is smaller than the one
calculated for the selected design options, which strongly rely on the bending capacity for resisting
lateral loads. Among the selected design options, Option B and Option C show a better performance
for the solar radiation reduction SRR in comparison to Option A and the original design. As expected,
when it comes to the daylight factor on dierent floors, the opposite can be observed.
The presented design exploration considered the FAU building as a reference case study. Several
global and local geometric parameters used for the generation of the façades were intentionally
made compliant with the original design. Indeed, introducing additional geometric parameters such
as, for example, three-dimensionality of the façade geometries, variable overhang of the floor slabs
and roof, and adjustable cross-section geometries of the façade elements, could potentially widen
the design space and possibly lead to the generation of entirely new design options. For instance, the
cross-sections of the façade elements could be materialised into dierent shapes, thus introducing
further local variations among the design options. Fig. 11 shows a possible application of such a
principle, taking Option C as a reference. The geometry of the façades in Option C1 and Option C2
are based on the form diagram of Option C, but their edges are materialised into façade elements
with rectangular cross-sections instead of the circular hollow cross-sections of the original design.
While neglecting local instability problems, the façade elements of Option C1 and Option C2 are
dimensioned to withstand the same axial forces of Option C – i.e. same cross-section areas. As a
result, these three options have the same values for total load path totLP, total mass totMass, and
maximum and minimum internal forces forMax/forMin. In particular, the façade elements in Option
C1 are thin walls perpendicular to the plane of the façade. While its width is kept constant, its
thickness is adjusted proportionally to the axial force it has to resist. The cross-section of the façade
elements in Option C2 follows a similar rule, although in this case, the elements are parallel to the
plane of the façade. The parallel coordinates plot in Fig. 11 shows that varying these local parameters
has an impact not only on the visual appearance of the design options but also on their sun-shading
performances in terms of solar radiation reduction SRR and daylight factor DF. This parallel
coordinates plot further visualises the relationships between the dierent considered metrics and
informs the negotiation process that is, in any case, necessary in multi-disciplinary design.
4 CONCLUSIONS AND FUTURE WORK
Despite allowing full control over the design process, manual design explorations often show severe
limitations due to the restricted evaluation capabilities of the designer when dealing with vast, multi-
dimensional design spaces. With the aim to couple the advantages of traditional interactive manual
explorations with the power of contemporary computational approaches, this paper presented a
holistic framework for the conceptual design of building envelopes that integrates aspects related to
architecture, structural design, and building physics.

044 JOURNAL OF FACADE DESIGN & ENGINEERING VOLUME 9 / NUMBER 1 / 2021
The proposed framework relies on a geometry-based tool (Combinatorial Equilibrium Modelling -
CEM) for the generation of design options as structures in static equilibrium, tools for the evaluation
of the structural (Karamba3d) and solar (Ladybug) performances of these options, and machine
learning (Self-Organising Map - SOM) for clustering the design space. These tools facilitate the
designer in the selection process, which is informed by sets of quantitative performance criteria
and takes into consideration the designer’s subjective preferences at the same time. The machine
eventually becomes a precious support through which the designer can easily generate, evaluate,
cluster, and finally select one or more suitable design options.
FIG. 11 Three dierent materialisations of the same form diagram. While keeping constant values for the cross-section areas,
rectangular cross-sections with dierent proportions (Option C1 and C2) are compared to the circular hollow sections of Option C.
The illustrated case study demonstrated the application of the proposed design framework to
the design of alternative solutions for an existing building façade. This example was developed
by running the dierent steps of the proposed design process in a sequence. Future work will
explore the opportunity of using the set of design options selected by the designer to inform the
re-generation of new design options, potentially through supervised machine learning algorithms

045 JOURNAL OF FACADE DESIGN & ENGINEERING VOLUME 9 / NUMBER 1 / 2021
for classification (Saldana Ochoa et al., 2020). Besides, in the proposed generative step carried out
using the CEM, the topology of the structure was kept constant. A computational implementation
that is topologically flexible would allow the number of possible design options to be significantly
enhanced, thus fostering the diversity and openness needed in the early design stage without
overlooking performance criteria or personal preferences of the designer. Future developments of
this research will thus investigate possibilities to compare and cluster design options with dierent
topologies. Moreover, further applications and extensions of the design framework to dierent
case studies and building typologies will be investigated as well as the combination with other
relevant design aspects.
When dealing with building energy simulations, long computation times may represent a significant
limitation for workflows that benefit from the interactivity in the early design phase. In the presented
case study, this issue was solved by reducing the number of aspects evaluated and by keeping the
overall resolution of the simulation on a moderate level. A possible approach to reduce computation
time could be the implementation of surrogate modelling, which has already been applied to
building energy simulation in the early design stage in several research projects (Ritter, Schubert,
Geyer, Borrmann, & Petzold,., 2014; Wortmann, Costa, Nannicini, & Schroepfer, 2015). Alternatively,
geometry-based solar design tools (Olgyay & Olgyay, 1957; Lechner, 2014) – similarly to graphic
statics in the field of structural design – could represent a possible alternative research direction.
Interpreting sun rays as vectors that interact with the building envelope, simplified solar radiation
and daylight availability studies could be embedded into a fully geometrical generative tool that
possibly allows for real-time design explorations. The designer would mostly interact with a limited
number of parameters, such as the angle and intensity of sun rays and the geometry of the building
itself. Indeed, being able to integrate environmental parameters as early as the generative phase of
the design process would greatly enhance the variability of the design space.
Acknowledgements
The authors would like to thank the student Roberto Gharib (ETH Zurich – DBAUG), whose master’s thesis has provided useful
insights for the development of the present research.
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