applied
sciences
Article
Performance Evaluation of Artificial Neural Networks (ANN)
Predicting Heat Transfer through Masonry Walls Exposed
to Fire
Iasonas Bakas *
and Karolos J. Kontoleon
Laboratory of Building Construction & Building Physics, Department of Civil Engineering, Faculty of
Engineering, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece; kontoleon@civil.auth.gr
* Correspondence: iasompak@civil.auth.gr
Featured Application: The use of Artificial Neural Networks for the prediction of heat transfer
through a variety of masonry wall build-ups exposed to elevated temperatures on one side.
Citation: Bakas, I.; Kontoleon, K.J.
Performance Evaluation of Artificial
Neural Networks (ANN) Predicting
Heat Transfer through Masonry Walls
Exposed to Fire. Appl. Sci. 2021, 11,
Abstract: The multiple benefits Artificial Neural Networks (ANNs) bring in terms of time expediency
and reduction in required resources establish them as an extremely useful tool for engineering
researchers and field practitioners. However, the blind acceptance of their predicted results needs to
be avoided, and a thorough review and assessment of the output are necessary prior to adopting
them in further research or field operations. This study explores the use of ANNs on a heat transfer
application. It features masonry wall assemblies exposed to elevated temperatures on one side,
as generated by the standard fire curve proposed by Eurocode EN1991-1-2. A juxtaposition with
previously published ANN development processes and protocols is attempted, while the end results
of the developed algorithms are evaluated in terms of accuracy and reliability. The significance of the
careful consideration of the density and quality of input data offered to the model, in conjunction
with an appropriate algorithm architecture, is highlighted. The risk of misleading metric results is
also brought to attention, while useful steps for mitigating such risks are discussed. Finally, proposals
for the further integration of ANNs in heat transfer research and applications are made.
11435. https://doi.org/10.3390/
app112311435
Keywords: Machine Learning; Artificial Neural Networks; ANN performance; fire action; masonry
wall heat transfer; prediction evaluation; input data quality; performance index
Academic Editor: Francesco
Salamone
Received: 24 October 2021
Accepted: 27 November 2021
Published: 2 December 2021
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1. Introduction
1.1. Purpose and Innovation of This Work
Machine Learning and Artificial Neural Networks, in particular, are increasingly becoming the scientific method of choice for several engineering researchers and practitioners
alike. Although the notion was introduced in 1956 [1], its practical adoption was delayed
until the early 1990s [2] mainly due to the inadequate computational power available.
Arguably, the benefits Artificial Neural Networks (ANNs) can bring to a scientific
project make them an attractive method for analysing data. Enabling researchers to make
predictions regarding the phenomenon they study without the need for computationally
heavy numerical models or expensive testing facilities, in conjunction with Finite Element
or BIM model analysis [3], significantly reduces the cost of their research. In the same direction, the reduction in resources used for experiments and the ability to draw information
from previous experimental work could put the use of ANNs at the forefront of efforts for
sustainability within the scientific community. In terms of reliability and performance, it
has been shown that, usually, ANNs outperform or are of equivalent accuracy to traditional
linear and nonlinear statistical analysis methods [4]. Despite these apparent advantages,
the adoption of ANNs in certain research fields, such as heat transfer and fire engineering
in the context of civil engineering, is still slow [5].
Appl. Sci. 2021, 11, 11435. https://doi.org/10.3390/app112311435
https://www.mdpi.com/journal/applsci
Appl. Sci. 2021, 11, 11435
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This study’s contribution is twofold; it aims to fill part of the ANN utilisation gap in
heat transfer research, on one hand, while stimulating a constructive dialogue regarding
the evaluation and significance of input selection for ANNs on the other. The first aim is
achieved through the development of an ANN architecture able to make predictions on
the thermal performance of masonry wall assemblies exposed to elevated temperatures. It
specifically proposes a neural network algorithm capable of predicting the temperature
development on the non-exposed face of the wall assemblies over time, when the standard
fire curve (as described in Eurocode EN1991-1-2) is applied to the other face of the wall.
Although there are a number of studies exploring the use of Machine Learning and Neural
Networks in applications such as structural health monitoring [6] and the residual capacity
of structural members [7], the adoption of these methods is still not as widespread within
the field of fire engineering as in other scientific domains [5]. Equally, there are studies
exploring the optimisation of the internal environment for user comfort through the use
of Artificial Intelligence [8]; the main focus, though, largely deviates from heat transfer
through structural members. The first part of this study’s unique contribution is that
it combines aspects of fire engineering (exposure to fire and the change of phase of the
components of the structural member) with the transient movement of heat through a
masonry wall. This work paves the way for a range of practical applications of heat transfer
through the composite, non-uniform, and perforated elements of varying material thermal
properties with prospects in the field of civil engineering and materials science.
The latter is approached with a systematic evaluation of the aforementioned algorithm’s performance in terms of accuracy and reliability. Different metrics are used to
measure the credibility of the ANN in this specific application and an intuitive comparison
to the “ground truth” data is also employed to evaluate the final predictions. To ensure a
robust model development and evaluation process, a step by step approach is adopted,
closely following previously published ANN development protocols as a guideline [9]. The
developed evaluation methodology constitutes an initial step towards the establishment of
a standardised process of quantifying the input data impact on the ANN’s performance. A
parallel investigation of a wide range of research facets (other ML techniques, optimisation
algorithms, the integration of other scientific fields beyond fire engineering, and heat transfer, to name a few) could provide additional value to the current proposal. Nonetheless,
this initial attempt already contributes towards building confidence around the accuracy
and reliability of ANN results, and it sets an initial foundation for developing a filter and
evaluation process during the selection of input datasets through a quantitative and visual
assessment of ANN predictive performance.
Several scientific efforts have focused on optimising and assessing the impact of
alternative algorithm architectures and the choice of hyperparameters on the performance
of ANNs [10]; on the other hand, this study explores the impact of varying degrees of
input data quantity and quality. The initially developed ANN architecture is maintained
identically throughout the study, while portions of the input data are gradually withheld,
with the intention to observe the degradation of the ANN’s predictive capabilities. This
results in four different regressor models with identical structures but significantly different
ultimate performance. The predictions of each model are assessed and the risk of receiving
misleading results is commented upon. Eventually, conclusions and recommendations on
how to mitigate such risks arising from specific ANN metrics are made.
Arguably, the field of Machine Learning is constantly evolving and expanding to
incorporate new bodies of theoretical study and practical applications. An extensive and
analytical review of such works would undeniably be fruitful and beneficial. Nevertheless,
the nature of such a thorough investigation does not align directly with the objectives of
the current study. Cutting edge research currently attempts to optimise the architecture
and performance of Machine Learning algorithms by exploring solutions ranging from the
use of genetic algorithms [11] and dispersing the computational and data processing load
to peripheral computers (the Edge) [12], to developing state of the art spatial accelerators to
expedite big data processing [13]. Despite the utmost significance of these advancements,
Appl. Sci. 2021, 11, 11435
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this study aims to establish an evaluation regime for the more conventional form of ANNs,
which are still in the early stages of their implementation within the field of fire engineering
and built-environment heat transfer applications.
1.2. Advantages and Disadvantages of the Proposed Evaluation Method
Artificial Neural Networks are progressively used more extensively both in the context
of scientific research and industrial applications. Despite the multifaceted benefits their use
can bring to the research and industrial processes, careful consideration needs to be given
to achieve a balanced assessment of their advantages and drawbacks. The following list
outlines some of the main advantages of using ANNs within the context of heat transfer
and fire engineering and highlights the benefits of the methodology proposed herein in
terms of enhancing these favourable attributes:
•
•
•
•
•
The use of ANNs can lead to a reduction in the cost and resources associated with
further fire and heat transfer testing. This also contributes towards achieving the
sustainability targets of research institutions and academic organisations by removing
the need for the unnecessary use of fuel, test samples, and the construction of testing
facilities. The proposed methodology provides an opportunity for a more efficient
and accurate assessment of the ANN’s results.
Artificial Neural Networks can also help reduce the required time for developing
and analysing computationally heavy 3D Finite Element heat transfer models. This
further reduces the cost associated with acquiring powerful computers to support the
aforementioned models. Despite this powerful feature, the use of ANNs needs to be
regulated and evaluated; the methodology developed herein sets the foundation for
such an evaluation framework.
ANNs can increase and simplify the reproducibility of heat transfer and fire performance experiments. ANNs introduce efficiency in the exploratory amendment
of experiment parameters. Previously recorded figures can feed in and help construct the ANN model, providing the ability to then tweak and replicate the parameters to explore variations of the original experimental arrangements. As this
process involves the amendment and adjustment of the input data of ANNs, the
workflow introduced in this study can highlight the potential pitfalls arising from this
retrospective processing.
The methodology for input data review proposed herein aims to contribute towards
the prevention of misleading or not adequately precise results generated by the ANN,
for integration into further research or field applications.
This body of work also raises awareness regarding the need for a standardised methodology for assessing ANN performance and ANN model development.
On the other hand, some of the main disadvantages and limitations that need to be
addressed before ANNs and the proposed assessment methodology are fully integrated
into the scientific and industrial workflow include:
•
•
•
The development of ANNs usually requires a large amount of input data, which
are not always easy or affordable to obtain. The proposed methodology essentially
introduces additional filters and methods for stricter input data quality assessment,
which can make the above process even more involved.
The interpretation of the ANN output is not always straightforward, and its precision
can be difficult to judge unless a solid understanding of the expected results has been
developed beforehand. The following sections of this study touch on this specific
matter and make recommendations.
To extend the scope of the scientific and industrial application of the proposed model
within the context of the heat transfer and fire performance of wall assemblies, further
research is needed to incorporate a wider range of material properties, fire loadings,
and geometrical wall configurations.
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•
There are a plethora of proposed model architectures and ML approaches that could
potentially enhance the performance of the proposed model. Although the detailed
review and integration of such methodologies fall outside the scope of the present
study, it would be beneficial for those to be reviewed and compared against the
proposed model structure and topology.
1.3. Scope Limitations and Extended Application
The evaluation process presented in the following paragraphs focuses on a specific
application (heat transfer through masonry wall elements exposed to fire on one side) and,
as such, it is optimised for the parameters describing this particular case. The parameters
used as part of this study could be extended to capture additional features of the experimental and/or modelling data. This would provide a wider scope for the application
of the evaluation methodology within the context of heat transfer and fire engineering.
The additional parameters could include, but not be limited to, the moisture content of
the wall assembly materials, the different types and positions of insulation, a range of
different fire loads, ventilation parameters, the different compositions of masonry units
with the associated variations in their thermal properties, and the different qualities of
bedding and render mortar. The inclusion of a wider array of material properties, geometries, and thermal loading could greatly increase the scope of the modelling process and
evaluation method.
Another aspect that could enhance the flexibility of the current proposal would
be the integration of other Machine Learning (ML) techniques. Although an extensive
comparative study is beyond the scope of the present work, a replication of the proposed
process on the output generated by other ML algorithms and models would help build a
more holistic understanding of the method’s transferability.
Although there is wide scope for the further expansion of the proposed methodology,
a conscious effort has been made to primarily focus on its underpinning principles. This
provides an overview of the cornerstones of the evaluation concept and enables a straightforward transfer of its universally applicable values. The aim of the final conclusions and
recommendations is to furnish fellow researchers with a guideline on how to assess their
ANN output regardless of their specific scientific field and practical application.
1.4. Intuition of Artificial Neural Networks
Artificial Neural Networks (ANN) belong to the sphere of supervised Machine Learning (ML), which in turn falls under the wider concept of Artificial Intelligence (AI) [14].
The cornerstones of ANNs are their architecture and training data. In terms of architecture,
each ANN comprises multiple layers of interconnected nodes. These include the input
layer (input nodes), responsible for receiving and offering the input data to the network;
the output layer (output node), which represents the final prediction of the network; and
the hidden layer(s) in between, which capture and factor the various features present in the
available dataset. In the case of Deep Learning, the ANN category that the present study
falls under, the networks involve more than one hidden layer. These are fully connected;
all nodes of one layer are connected to all nodes of the previous and following layers.
The structure of ANNs resembles the structure of the human brain. Each node,
mentioned above, represents a neuron, and the connections between those perform similar
functions to brain synapses, as seen in Figure 1. Each neuron represents a feature of the
training data and can be outlined by Equation (1), where f(x) is an appropriately selected
activation function [15,16]:
!
n
P=f
∑ wi x i + b
(1)
i =1
where P is the output figure of the neuron, wi is the weights applied to each feature of the
data that are fed to the neuron, xi is the features of the input data themselves, and b is the
applied bias.
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Figure 1. Graphical representation of the neurons the ANN consists of. The illustrated activation function is indicative only
and represents the one used as part of this study.
Each neuron is initially assigned a random weight, quantifying the significance of the
represented feature to the value of the dependent variable. These weights are constantly
updated and ultimately optimised through an iterative training process (epoch). In each
training loop, the contribution of each neuron to the dependent variable and the overall
accuracy of the ANN algorithm prediction against a known value is evaluated. The process
of comparing the network predictions against known values (the ground truth) is the
founding principle of supervised learning [17]. To enable this internal assessment and
feedback process, the use of a loss function at the end of each epoch is necessary. This
feedforward, backpropagation training process is illustrated schematically in Figure 2.
Figure 2. Graphical representation of the feedforward and backpropagation process of a
typical ANN.
Similar to the architecture of the network, the choice of an appropriate loss function,
along with parameters including, but not limited to, the activation function, number of
epochs, learning rate, and batch size, is dependent on the type, quantity, and quality of the
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input data and type of expected predictions [18]. These are called hyperparameters, and
in conjunction with the ANN structure (number of hidden layers and number of neurons
on each hidden layer) turn an ANN algorithm into a trainable and functioning predictive
model. There is no prescriptive method for standardising the process of ANN development
at the moment, in terms of hyperparameters and architecture selection [19]. However,
previous scientific studies summarise useful conclusions that provide some guidance in
this respect.
Apart from developing an effective architecture and choosing appropriate hyperparameters, an aspect that requires attention is network overfitting [1]. Although an algorithm
can perform extremely well in making predictions on the given training and test set, there
is the risk of excessive focus on the provided observations, leading to the reduced general
applicability of the model. Overfitting limits the scope of use of an artificial neural network
and can potentially lead to misleading prediction results. The impact of input data quality
and quantity on the overfitting of the ANN is discussed in subsequent sections.
Fundamental details regarding the architecture of the ANN built and utilised for this
study are presented in the following paragraphs, allowing for a more holistic understanding
of the factors impacting the performance of the model. Similarly, the structure of the
input and ground truth data is thoroughly explained in the relevant chapter of this paper,
provoking thought on the relationship between input and output precision.
1.5. Input Data Reference
The development, implementation, and evaluation of the ANN algorithm constitute
the focal point of this work. The basis of the heat transfer input data, used to train the
ANN algorithm, became available after adjusting and interrogating finite element analysis
models developed as part of previous scientific research. Specifically, Kanellopoulos and
Koutsomarkos [20] set the foundation with their research on heat transfer through clay
brick walls, focusing on the contribution of radiation through the voids of the masonry
units. This was further developed by Kontoleon et al. [20,21] and their work on heat transfer
through insulated and non-insulated masonry wall assemblies. The various amendments
and pre-processing routines imposed on this foundation dataset are described in the
following paragraphs.
1.6. Software and Hardware Utilised for This Research
The analysis of the physical phenomenon of heat transfer was undertaken using
COMSOL Multiphysics® simulation software (v 5.3a). The development, training, and
review of the ANN algorithm were carried out using the programming language Python
and the application programming interface Keras along with its associated libraries. Other
libraries used include Pandas, NumPy, Statistics, Scikit-learn [22], Matplotlib, and Seaborn
(the last two for visualisation purposes). Finally, the ANN predictions were exported to
MS Excel for ease of diagram formatting and presentation.
The finite element analysis and the development and training of the ANN were
performed using a 64-bit operating system, running on an Intel Core i7-920 processor at
2.67 MHz, and with 24GB of RAM installed.
2. Modelling and Methods
2.1. Masonry Wall Assembly Finite Element (FE) Models
2.1.1. Geometrical Features of Models’ Components
The training of the ANN algorithm was based on data extracted from 30 different
wall assembly FE models. Despite having a core model onto which the structure of
the wall samples was founded, a range of variables was incorporated to enable a more
accurate representation of the phenomenon of heat transfer through the wall samples. This
pluralism also enhanced the understanding of the impact of various parameters on the
process, through the use of ANNs in the following stages of the study.
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The foundation model involved the use of a single skin of perforated clay bricks
stacked with cement bedding mortar. In the simplest modelling case, either face of this
brick core was covered with a single layer of cement render before it was exposed to fire
on one side (details regarding the boundary conditions and fire load applied to the model
are included in the following paragraphs). Specifically, the masonry core consisted of
250 mm wd × 140 mm dp × 330 mm lg clay bricks incorporating an array of 18 full-length
holes (12 holes of 26 mm × 34.7 mm and 6 more elongated holes of 26 mm × 56 mm), as
indicated by the following sections in Figure 3. The bedding mortar and cement render
were consistently 10 mm thick.
Figure 3. Sections of typical masonry wall assemblies modelled as part of this study. (a) Wall section insulated externally,
(b) non-insulated wall section, (c) wall section insulated internally.
Two variations of this basic matrix model were then developed and analysed; namely,
a brick wall insulated with EPS internally (exposed to fire) and a brick wall insulated with
EPS externally (non-exposed face of the wall). For each case, two EPS layer thicknesses
were analysed: 50 mm and 100 mm.
2.1.2. Model Material Properties and Combinations
The range of material properties incorporated into the FE models enriched the available analysis cases and consequently provided a wide variety of output data. The properties
and their values considered as part of the FE analysis included:
•
•
•
•
Clay brick density (ρ): 2000 kg/m3 and 1000 kg/m3 .
Clay brick thermal conductivity coefficient (λ): 0.8 W/(m·K) and 0.4 W/(m·K).
Clay brick thermal emissivity coefficient (ε): 0.1, 0.5, 0.9.
Insulation thickness (d): 0 mm, 50 mm, 100 mm.
The above range of variables and material property values allowed for the formation
of the following combinations. Each combination appearing in Table 1 represents a separate
FE model whose analysis output subsequently offered portions of the overall input data
for training, testing, and evaluating the ANN model.
The development of a complete finite element analysis model required the definition
of some additional parameters (which were not explicitly used for the development of the
ANN). The specific heat capacity (Cp ) of all components needed to be specified, along with
the density (ρ) and thermal conductivity coefficient (λ) of the cement mortar and insulation
panels. Table 2 summarises this additional information.
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Table 1. Material property combinations defining the various FE models analysed.
Insulation Position and
Thickness
Brick Density
Thermal Conductivity
Coefficient
Thermal Emissivity
Coefficient
Sample Reference 1
No insulation
1000
1000
1000
0.4
0.4
0.4
0.1
0.5
0.9
Smpl1-1
Smpl1-2
Smpl1-3
No insulation
2000
2000
2000
0.8
0.8
0.8
0.1
0.5
0.9
Smpl2-1
Smpl2-2
Smpl2-3
Non-exposed EPS (50 mm)
1000
1000
1000
0.4
0.4
0.4
0.1
0.5
0.9
Smpl3-1
Smpl3-2
Smpl3-3
Non-exposed EPS (50 mm)
2000
2000
2000
0.8
0.8
0.8
0.1
0.5
0.9
Smpl4-1
Smpl4-2
Smpl4-3
EPS exposed to fire (50 mm)
1000
1000
1000
0.4
0.4
0.4
0.1
0.5
0.9
Smpl5-1
Smpl5-2
Smpl5-3
EPS exposed to fire (50 mm)
2000
2000
2000
0.8
0.8
0.8
0.1
0.5
0.9
Smpl6-1
Smpl6-2
Smpl6-3
Non-exposed EPS (100 mm)
1000
1000
1000
0.4
0.4
0.4
0.1
0.5
0.9
Smpl7-1
Smpl7-2
Smpl7-3
Non-exposed EPS (100 mm)
2000
2000
2000
0.8
0.8
0.8
0.1
0.5
0.9
Smpl8-1
Smpl8-2
Smpl8-3
EPS exposed to fire (100 mm)
1000
1000
1000
0.4
0.4
0.4
0.1
0.5
0.9
Smpl9-1
Smpl9-2
Smpl9-3
EPS exposed to fire (100 mm)
2000
2000
2000
0.8
0.8
0.8
0.1
0.5
0.9
Smpl10-1
Smpl10-2
Smpl10-3
1
Only used for ease of reference in the following sections of this study and for cross-referencing with model analysis files by the
research team.
Table 2. Other material properties used for the development of the FE models.
Material
Density
kg/m3
Thermal Conductivity Coefficient
W/(m·K)
Specific Heat Capacity
J/kg·K
Clay bricks
Insulation (EPS)
Cement mortar
As above
30
2000
As above
0.035
1.400
1000
1500
1000
It is worth highlighting that although most of the thermophysical and mechanical
properties of the masonry structure fluctuate depending on the temperature of the components [23], for the needs of this study they have all been assumed to remain constant
throughout the development of the phenomenon. It has also been shown that clay brick
spalling affects the thermal performance of the masonry wall when exposed to fire [24,25];
this parameter has not been considered in the finite element models. The dramatic impact
on the insulation’s performance, due to phase change when exposed to high temperatures,
could not be ignored. The modelling convention used to reflect this characteristic behaviour
is explained in the following paragraphs.
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2.2. Heat Transfer Analysis, Fire Load, Assumptions, and Conventions
To effectively assess the performance of the ANN and evaluate the accuracy of its
predictions, a basic description and understanding of the physical phenomenon under
consideration are deemed necessary. The founding principles and equations of heat transfer
are presented herein, in conjunction with the various assumptions, simplifications, and
conventions used when constructing the relevant finite element analysis model.
2.2.1. Heat Transfer Fundamentals
Although the aim of this study is not to review and present the fundamental principles
of heat transfer, it is worth briefly presenting the basic mechanisms operating on the finite
element analysis model. The analysis commences with the wall samples in thermal balance,
with an ambient room temperature applied on either side. At time t = 0 sec, an increasing
fire load (as described in the following paragraph) is applied on one side (hereon referred
to as “exposed”), initiating the combined heat transfer mechanism of convection and
radiation. The fundamental Equations (2) and (3) govern the convective and radiation heat
transfers, respectively [26], from the fire front towards the exposed wall surface:
00
qconv = h ( TS − T∞ )
00
4
qrad = ε·σ Ts4 − Tsur
00
(2)
(3)
00
where qconv and qrad are the resulting heat flux due to convection and radiation, respectively,
h is the convection heat transfer coefficient (W/(m2 ·K)), Ts is the surface temperature, T ∞ is
the surrounding fluid temperature (for convection), Tsur is the surrounding environment
temperature (for radiation), ε is the emissivity coefficient, and σ is the Stefan–Boltzmann
constant (σ = 5.67 × 10−8 W/(m2 ·K4 )).
The heat transfer mechanism of conduction is also activated as heat progressively
travels through the solid parts of the wall assembly. Equation (4) is the governing relationship for heat conduction, and it was used to replicate the phenomenon on the finite
element analysis model. The clay brick cavities play an integral part in the transfer of heat
through the sample [27], and thus attention was paid to modelling them accurately. Heat
transfer through radiation between the cavity walls and convection through air movement
within the cavities has been considered. The previously described convection and radiation
formulas apply:
00
qcond,x = −λ
∂T
∂x
(4)
00
where qcond,x is the resulting heat flux due to conduction, λ is the thermal conductivity, and
∂T
∂x
is the temperature gradient in the direction of the heat’s transient movement.
The final stage of the transient movement of heat through the wall sample is its release
to the environment through the non-exposed face of the section. The applicable heat
transfer mechanisms are convection, through the surrounding air, and radiation.
2.2.2. Boundary Conditions and Fire Load
A definition of the applicable boundary conditions is necessary before the solution of
the differential equations can be attempted. The analysis initiates assuming an ambient
room temperature of 20 ◦ C on both faces of the wall assembly. This condition is adhered to
throughout the analysis for the non-exposed wall face.
At time t = 0 sec, the “exposed” wall face becomes subject to the increasing fire load
represented by the standard fire curve ISO 834 as present in Eurocode EN1991-1-2 [28].
Although scientific research is being carried out to identify and compile new, more accurate
fire curves and loading regimes [29], it was considered that the well-established methodology proposed by the Eurocodes currently fulfils the needs of this study. Equation (5)
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mathematically describes the relationship of temperature increase due to the applied fire
load over time, while Figure 4 is the corresponding visual representation:
Qg = 20 + 345 log10 (8 t + 1)
(5)
where t is the time in seconds and Qg is the developed temperature in ◦ C.
Figure 4. Typical fire curve (ISO 834) applied to finite element analysis models as seen in EN1991-1-2.
The boundaries between the various layers of the wall assembly follow the fundamental heat transfer equations, as described in the previous paragraph.
2.2.3. Modeling Heat Transfer Assumptions and Conventions
An element that required special attention was the behaviour of EPS when exposed to
significantly high temperatures. The material is a combustible thermoplastic that remains
stable when exposed to temperatures up to 100 ◦ C. Its thermal properties start to rapidly
degrade shortly after that, while temperatures upwards of 160 ◦ C lead to the complete loss
of the inflated bead structure and the liquefaction of the insulation boards. Approaching
temperatures of 278 ◦ C leads to the gasification of the material [30]. Provided that the wall
samples were subject to temperatures significantly higher than 100 ◦ C, the above behaviour
had to be stimulated.
Conventionally, and accepting that no material can be removed from the finite element
analysis model once the analysis has commenced, a temperature-dependent variable was
utilised to reproduce the reduced performance and ultimate collapse of EPS. The thermal
conductivity coefficient (λEPS ) of the insulating material was artificially increased when
temperatures beyond 150 ◦ C were encountered. That allowed for the unhindered transfer
of heat through the melting EPS boards, resembling the gradual removal of the physical
barrier. The coefficient was linearly increased from a value of λEPS = 0.035 W/(m·K) at
150 ◦ C to λEPS = 20 W/(m·K) at 200 ◦ C (practically no heat transfer resistance). Similarly,
its density (ρEPS ) and special heat capacity (CpEPS ) were reduced to negligible figures.
Figure 5 demonstrates the steep material property changes for the melting EPS layer.
It is worth highlighting that the failure of the EPS material would naturally result in
the detachment and collapse of the attached render. To ensure the removal of the render’s
beneficial insulating function, a similar approach was adopted, wherein all associated
thermophysical properties were altered to reproduce its collapse. To ensure the change was
introduced in a timely manner, an exploratory analysis was performed to identify the time
for the interface between render and EPS to reach the critical temperature of 150 ◦ C. This
threshold temperature was achieved at t = 240 sec. The thermal conductivity coefficient
(λrender ) was increased from λrender = 1.40 W/(m·K) to λrender = 2000 W/(m·K), while its
density (ρrender ) and specific heat capacity (Cprender ) were reduced to negligible values.
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Although the same process would normally apply to both faces of the wall (exposed
to fire and non-exposed), only the properties of the exposed insulation and render were
altered within the scope of the present study. Similarly, no allowance has been made for
the ignition of EPS volatiles.
Figure 5. Artificial steep modification of insulation material properties to emulate its degradation
until complete destruction due to fire exposure.
2.3. ANN Complete Input Dataset (CID)
Since part of the algorithm’s structure (the size of the input layer) depends on the
structure of the input dataset, it was considered important to conclude the data format
prior to commencing the development of the ANN itself. A brief outline of the parameters
used has been given in the description of the FE models; these were further refined and
structured in an appropriate CSV file format ready for reading by the algorithm.
The file incorporated columns representing the independent variables defining the FE
models described in previous paragraphs. A “timestamp” column was also added to allow
for the observation and correlation of the temperature magnitude on the non-exposed
face of the wall over time as the phenomenon developed. The last column of the dataset
included the output of the FE model analysis, the temperature observed on the non-exposed
face of the wall at a 30 sec time step when the standard Eurocode fire curve was applied
to the other face. Table 3 provides a typical section of the dataset file offered to the ANN
algorithm; the example reflects the values used for an internally insulated wall panel.
Table 3. Representative example of the dataset structure and contents.
Index
Sample
Ref
Brick
Density
Thermal
Conductivity
Coef.
Thermal
Emissivity
Coef.
Insulation
Thickness
...
11,449
11,450
11,451
11,452
11,453
...
...
Smpl6-1
Smpl6-1
Smpl6-1
Smpl6-1
Smpl6-1
...
...
2000
2000
2000
2000
2000
...
...
0.8
0.8
0.8
0.8
0.8
...
...
0.1
0.1
0.1
0.1
0.1
...
...
50
50
50
50
50
...
Insulation Insulation
Type
Position
...
EPS
EPS
EPS
EPS
EPS
...
...
Int
Int
Int
Int
Int
...
Time
Temperature of
Non-Exposed Face
...
18,990
19,020
19,050
19,080
19,110
...
...
41.77246
41.85622
41.94014
42.02421
42.10843
...
It is apparent that not all columns were necessary for the training, testing, and evaluation of the algorithm, thus the input data was further modified and stripped into a
more appropriate format as part of the “preprocessing” phase (see following paragraphs).
Nevertheless, these variables and references are useful for an intuitive understanding of the
Appl. Sci. 2021, 11, 11435
12 of 26
input data content and structure. Variables referring to material properties were discussed
in detail in previous paragraphs. Other columns include:
•
•
•
•
•
•
Index—variable purely counting the number of unique observations included in
the data. Each temperature measurement generated by the FE model analysis (time
step of 30 s) is used as a separate observation. The complete dataset includes a
total of 21,630 observations. The index was excluded from any training or testing of
the algorithm.
Sample reference—this variable enabled the research team to easily cross-reference
between the dataset tables and the analysis files. Similarly, it was excluded from any
training or testing of the neural network.
Insulation type—the data structure and ANN algorithm were developed with the
intention of incorporating and analysing various insulation materials. Although the
present study only considers EPS, it was considered useful to build some flexibility in
the algorithm, enabling the further expansion of the scope of work in the future. It
takes the values “EPS” and “NoIns”, representing the insulated and non-insulated
wall samples, respectively. This categorical variable was encoded into a numerical one
as part of the pre-processing phase.
Insulation position—this variable represents the position of the insulation. It takes
three values; “Int”, “Ext”, and “AbsIns”, representing insulation exposed to fire
(internal insulation), insulation not exposed to fire (external insulation), and noninsulated wall samples, respectively. As a categorical variable, this was also encoded
as part of the pre-processing phase.
Time—to enable the close observation of the temperature development on the nonexposed face of the wall over time, it was considered necessary to include a “timestamp” variable. This was obtained directly from the FE model analysis output, where
time and temperature are given as two separate columns. The temperature is measured every 30 s for a duration of 6 h and a total of 720 observations for each of the
30 models.
Temperature of the non-exposed face—this is the output of the finite element analysis
models in ◦ C as generated by COMSOL Multiphysics® simulation software. It reflects
the temperature developed gradually within a reference area on the non-exposed face
of the wall panels. This constitutes the dependent variable of the dataset and ultimately
is the figure that the ANN algorithm will be trying to predict in the following steps.
It is apparent that the above set of parameters and values are relevant only to the
specific masonry wall heat transfer application presented in this study. However, the
process of compiling a group of independent variables and organising them into a dataset
structure appropriate for analysis in Python is universal. Depending on the number of the
recorded independent variables, the architecture of the network might need to be adapted
(more or fewer input neurons), different hyperparameters might generate better results, or
slightly different preprocessing methods might be applicable (scaling might/might not be
necessary, encoding of categoric variables might be needed or not, etc). The list of used
variables, and their range of values given in the preceding Tables 1 and 3, should provide
a guide for understanding the form of the dataset and possibly substituting it with other
data available to interested research parties. Similarly, the list of hyperparameters included
in the following sections of the study, along with the values used for this research, should
provide adequate detail for understanding and replicating the structure of the ANN itself,
if desired.
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pred
score
y
t
good
was
ct
(s
ve
nce
pred
a
score
ready
t
was
ct
(s
ve
nce
a
score
ready
t
was
(s
nce
a
re
Smpl1-2
Smpl1-2
Smpl1-2
Smpl1-2
kg/m
,
λ:
0.4
kg/m
W/(m·K),
,
λ:
0.4
kg/m
W/(m·K),
0.5
,
λ:
0.4
kg/m
W/(m·K),
0.5
,
λ:
0.4
W/(m·K),
0.5
0.5
3
tra
ned
w
tra
th
fu
ned
data)
w
tra
th
fu
ned
t
was
data)
w
tra
th
nc
fu
ned
uded
t
was
data)
w
n
th
nc
the
fu
uded
t
was
resu
data)
n
nc
t
the
ng
uded
t
graphs
was
resu
n
nc
t
the
ng
for
uded
graphs
resu
comparat
n
t
the
ng
for
graphs
resu
comparat
ve
reasons
t
ng
for
graphs
comparat
ve
reasons
for
comparat
ve
reason
0.9
0.9
Smpl1-3
Smpl1-3






 hm 


32000
Smpl2-1
ρρ
ρ=y
ρymm,
=or
0.8
0.8
εs50
=W/(m·K),
0.1
0.8
=ou
0.8
=ou
0.1
= 0.1
Tab eSmpl2-1
4 =L1000
sTab
o kg/m
wa
eSmpl2-1
assemb
Tab
o0.4
wa
eW/(m·K),
y
4 ==ana
L,2000
assemb
sTab
ys
o kg/m
swa
ou
4 =0.1,
ana
Lpu
assemb
oused
wa
ou
ana
pu
assemb
ys
used
nεsεng
or
ana
each
pura
used
a=nεgor
s50
ng
or
each
hm
pura
used
anεgor
ng
or
each
hmraa
ngor
ng
each
hmagor
Smpl2-2
Smpl2-2
λ:
0.5
,2000
λ:ra
W/(m·K),
0.5
0.9
Smpl2-3
ρ4 =L32000
kg/m

Smpl3-1 Smpl2-1
Smpl3-1
ρ
1000
,3 sλ:
εeW/(m·K),
, sλ:dys
0.4
=kg/m
External
=y0.1
0.1,
dys
mm,
External
featur
ng
m
featur
d-range
ng
m
featur
va
d-range
ues
ng
(
m
featur
e
va
d-range
50
ues
mm
ng
(
m
e
of
va
d-range
50
ues
nsu
mm
(
at
e
of
on
va
50
ues
nsu
or
mm
ε
(
at
=
e
0
of
on
5)
50
nsu
or
A
mm
ε
though
at
=
0
of
on
5)
nsu
or
A
t
ε
though
was
at
=
0
on
5)
ant
or
A
t
c
ε
though
was
=
0
5)
ant
A
t
c
though
was
an
Smp
8
2
SampSmp
e
Reference
Samp
e
Reference
Samp
e
Reference
Samp
e
Reference
Proper
es
Proper
of
Wa
Samp
es
Proper
of
Wa
e
Samp
es
Proper
of
Wa
e
Samp
es
of
Wa
e
ANN
Samp
1
ANN
e
ANN
2
1
ANN
ANN
ANN
3
2
ANN
1
ANN
ANN
4
ANN
3
2
ANN
1
ANN
ANN
4
3
2
AN
A
ρ
=
2000
kg/m
λ
0
8
W/
m
K
ε
=
0
5
d
=
100
mm
Ex
erna
33,1000
33an
33an
33ng








1
1
Smp
1
1
ρ
=
1000
kg
ρ
m
=
λ
0
kg
4
W
m
m
λ
K
0
4
ε
W
=
0
m
1
K
ε
=
0
1
pated
that
pated
ANN
that
1
wou
ANN
d
have
1
wou
d
extreme
have
y
extreme
good
pred
y
good
ct
ve
pred
score
ct
(s
ve
nce
score
t
was
(s
nce
a
ready
t
was
a
ready




2
2
Smp
1
2
Smp
1
2
ρ
=
1000
kg
ρ
m
=
5
1000
λ
0
kg
4
W
m
m
5
λ
K
0
4
ε
W
=
0
m
5
K
ε
=
0
5


tra
ned
w
tra
th
fu
ned
data)
w
tra
th
fu
ned
t
was
data)
w
tra
th
nc
fu
ned
uded
t
was
data)
w
n
th
nc
the
fu
uded
t
was
resu
data)
n
nc
t
the
uded
t
graphs
was
resu
n
nc
t
the
ng
for
uded
graphs
resu
comparat
n
t
the
ng
for
graphs
resu
comparat
ve
reasons
t
ng
for
graphs
comparat
ve
reasons
for
comparat
ve
reason
λ:
0.4
W/(m·K),
,
λ:
0.4
W/(m·K),
0.9
,
λ:
0.4
W/(m·K),
0.9
,
λ:
0.4
W/(m·K),
0.9
0.9
Smpl1-3
Smpl1-3
Smpl1-3
Smpl1-3
kg/m
kg/m
kg/m
kg/m








3
Smpl2-1
ρy=ana
0.8
0.1
= 0.1
Tab eSmpl2-3
4 =L1000
sTab
o kg/m
wa
eSmpl2-2
assemb
wa
assemb
ou
ana
pu
used
pu
used
nεng
or
each
ra0.8
anεgor
ng
each
hm a εgor
hm  

Smpl2-2 Smpl2-1
Smpl2-2
Smpl2-2
ρ mm,
=or
0.5
0.5
0.5
= 0.5


,2000
λ:ys
0.8sεW/(m·K),
εs50=ou
0.9
,2000
λ:ra
0.8
W/(m·K),
= 0.9
Smpl2-3
ρ4 =L2000
kg/m
ρ=y=0.1,
2000

Smpl3-1
ρ
,3 sλ: o0.4
W/(m·K),
dys
=kg/m
External
Smp
8
3
SampSmp
e
Reference
Samp
e
Reference
Samp
e
Reference
Samp
e
Reference
Proper
es
Proper
of
Wa
Samp
es
Proper
of
Wa
e
Samp
es
Proper
of
Wa
e
Samp
es
of
Wa
e
ANN
Samp
1
ANN
e
ANN
2
1
ANN
ANN
ANN
3
2
ANN
1
ANN
ANN
4
ANN
3
2
ANN
1
ANN
ANN
4
3
2
AN
A
ρ
=
2000
kg/m
λ
0
8
W/
m
K
ε
=
0
9
d
=
100
mm
Ex
erna














33L
33L
33an
33an
1
1
Smp
1
1
Smp
1
1
Smp
ρ
=
1000
1
1
kg
ρ
m
=
1000
λ
0
kg
4
W
ρ
m
=
m
1000
λ
K
0
kg
4
ε
W
=
ρ
m
0
=
m
1
1000
λ
K
0
kg
4
ε
W
=
m
0
m
1
λ
K
0
4
ε
W
=
0
m
1
K
ε
=
0
1
pated
that
pated
ANN
that
1
wou
pated
ANN
d
have
that
1
wou
pated
ANN
an
d
extreme
have
that
1
wou
ANN
y
d
extreme
good
have
1
wou
pred
y
d
extreme
good
have
ct
ve
pred
an
score
y
extreme
good
ct
(s
ve
nce
pred
score
y
t
good
was
ct
(s
ve
nce
pred
a
score
ready
t
was
ct
(s
ve
nce
a
score
ready
t
was
(s
nce
a
re
2
2
5
5
tra
ned
w
tra
th
fu
ned
data)
w
th
fu
t
was
data)
nc
uded
t
was
n
nc
the
uded
resu
n
t
the
ng
graphs
resu
t
ng
for
graphs
comparat
for
comparat
ve
reasons
ve
reasons
9
9
9
9
3
3
3
3














3
3
Smpl2-1
Smpl2-1
Smpl2-1
Smpl2-1
ρ
=
2000
kg/m
ρ
=
2000
kg/m
ρ
=
2000
kg/m
ρ
=
2000
kg/m
,
λ:
0.8
W/(m·K),
,
λ:
0.8
ε
W/(m·K),
=
0.1
,
λ:
0.8
ε
W/(m·K),
=
0.1
,
λ:
0.8
ε
W/(m·K),
=
0.1
ε
=
0.1
Tab
e
4
L
s
Tab
o
wa
e
4
L
assemb
s
Tab
o
wa
e
y
4
ana
assemb
s
Tab
ys
o
s
wa
e
ou
y
4
ana
pu
assemb
s
ys
o
used
s
wa
ou
y
or
ana
pu
assemb
ra
ys
used
n
s
ng
ou
y
or
ana
each
pu
ra
ys
used
a
n
gor
s
ng
ou
or
each
hm
pu
ra
used
a
n
gor
ng
or
each
hm
ra
a
n
gor
ng
each
hm
a
gor
hm
Smpl2-2
Smpl2-2 Smpl2-3
0.5
0.9 External
0.9
0.9
0.9
Smpl2-3
Smpl2-3
 External
 

Smpl3-1 Smpl2-3
Smpl3-1
ρ = 1000 kg/m
ρ = 1000 kg/m
,3 λ: 0.4 W/(m·K),
ε = 0.1,
, λ:d 0.4
= 50W/(m·K),
mm,
ε =0.5
0.1, d = 50 mm,
Smp
9e1Reference
SampSmp
e Reference
Samp
Proper
es
Proper
ofwas
Wa
Samp
es
of
Wa
eεεw
Samp
eεεsIn
ANN
1K
ANN
ANN
2hm
1ANN
ANN
3t
2hm
ANN
ANN
4gor
3
ANN
4
ρ4tra
=L1000
kg/m
λ1
0kg
4ρ
W/
m
K
εy
=ana
0fu
1K
d
=W
100
mm
erna











1
1
Smp
1
1
Smp
1
1
Smp
ρ
=
1000
1
m
=
1000
λ
0
kg
4
W
ρ
m
=
m
1000
λ
0
kg
4
=
ρ
m
0
=
1
1000
λ
K
0
kg
4
W
=
m
0
m
1
λ
K
0
4
ε
W
=
0
m
1
ε
=
0
1
3L
3L
3m
3ng
2
2
2
2
5
5
5
5
ned
w
tra
th
fu
ned
data)
w
tra
th
fu
ned
t
data)
w
tra
th
nc
ned
uded
t
was
data)
n
th
nc
the
fu
uded
t
was
resu
data)
n
nc
t
the
uded
t
graphs
was
resu
n
nc
t
the
ng
for
uded
graphs
resu
comparat
n
t
the
ng
for
graphs
resu
comparat
ve
reasons
ng
for
graphs
comparat
ve
reasons
for
comparat
ve
reason
9
9
3
3














3
3
3
3
Smp
2
1
Smp
2
1
Smp
2
1
Smp
ρ
=
2000
2
1
kg
ρ
m
=
2000
kg
ρ
m
=
2000
kg
ρ
m
=
2000
kg
m
λ
0
8
W
m
λ
K
0
8
W
=
0
m
1
λ
K
0
8
W
=
0
m
1
λ
K
0
8
ε
W
=
0
m
1
K
ε
=
0
1
Tab
e
s
Tab
o
wa
e
4
L
assemb
s
Tab
o
wa
e
y
4
ana
assemb
s
Tab
ys
o
s
wa
e
ou
4
pu
assemb
s
ys
o
used
s
wa
ou
y
or
ana
pu
assemb
ra
ys
used
n
ng
ou
y
or
ana
each
pu
ra
ys
used
a
n
gor
s
ng
ou
or
each
hm
pu
ra
used
a
n
gor
ng
or
each
ra
a
n
gor
ng
each
a
hm
Smpl2-2
Smpl2-2
Smpl2-2
Smpl2-2
kg/m
kg/m
kg/m
kg/m
,
λ:
0.8
W/(m·K),
,
λ:
0.8
W/(m·K),
0.5
,
λ:
0.8
W/(m·K),
0.5
,
λ:
0.8
W/(m·K),
0.5
0.5
0.9
0.9
Smpl2-3
 dExternal
 External
 
 

Smpl3-1 Smpl2-3
Smpl3-1 Smpl3-1
ρ = 1000 kg/m
Smpl3-1
ρ = ,1000
kg/m
ρ = ,1000
kg/m
= ,1000
λ: 0.4
W/(m·K),
λ: 0.4
ε W/(m·K),
=ρ 0.1,
λ:d 0.4
=kg/m
50
ε W/(m·K),
=mm,
0.1,
, λ:dExternal
0.4
= 50
ε W/(m·K),
=mm,
0.1, dExternal
= 50
ε =mm,
0.1,
= 50 mm,
3 Proper
Smp
9e2Reference
SampSmp
e Reference
Samp
Samp
es
Proper
of00K
Wa
Samp
es
Proper
of
Wa
Samp
es
Proper
of
Wa
Samp
es
of
ANN
Samp
eεεgor
ANN
ANN
1ANN
1ANN
4 3 2AN
A
ρ4e =Reference
1000
kg/m
0kg
4ρym
W/
m
εm==ana
0λ
5Kys
d
100
mm
In
erna








12Samp
12312 Smp
12Tab
12312 eSmp
ρ
λ
kg
4
0used
48eεεs=W
==ou
000.9
==m
000.9

12sTab
232o kg/m
12sλ:λ232o0.4
ρ
ρ
==0.1,
λ
000.8
48eεε50
W
000.8
W
== 000.9
m
== 000.9


33,1000
3m
3m
3m


2hm
 ANN
3 
 ANN
4 ANN
 ANN
Smp
Smp
kg
kg
8sεW
W
m
λ
m
15159pu
K
15159, λ
wa
eSmp
4e===Reference
L31000
assemb
wa
assemb
ou
pu
or
ra
used
ng
or
each
ra
aWa
n48eεεgor
ng
each
hm
2ANN
3 
2ANN
Smp
Smp
kg
m
kg
m
λ
W
m
λ
K
W
m
559 1K
K aANN
559 1ANN


λ:
0.8
W/(m·K),
,1000
λ:K
W/(m·K),
,1000
λ:K
W/(m·K),
λ:K
W/(m·K),
Smpl2-3
Smpl2-3
Smpl2-3
Smpl2-3
ρρ
2000
kg/m
ρm==ana
2000
kg/m
ρ=ym
=0.1,
2000
kg/m
ρ=m
2000
kg/m




Smpl3-1
Smpl3-1
ρ =L1000
kg/m
W/(m·K),
,λ
λ:ys
0.4
W/(m·K),
d00.8
=kg
50
εW
mm,
dExternal
=nkg
mm,
External
3,1000
Smp
9
3
SampSmp
e Reference
Samp
e
Reference
Samp
e
Reference
Samp
e
Reference
Proper
es
Proper
of
Wa
Samp
es
Proper
of
Wa
e
Samp
es
Proper
of
Wa
e
Samp
es
of
Wa
e
ANN
Samp
1
ANN
e
ANN
2
1
ANN
ANN
ANN
3
2
ANN
1
ANN
ANN
4
ANN
3
2
ANN
1
ANN
ANN
4
3
2
AN
A
ρ
=
1000
kg/m
λ
0
4
W/
m
K
ε
=
0
9
d
=
100
mm
In
erna














1
1
Smp
1
1
Smp
1
1
Smp
ρ
=
1000
1
1
kg
ρ
m
=
1000
λ
0
kg
4
W
ρ
m
=
m
1000
λ
K
0
kg
4
ε
W
=
ρ
m
0
=
m
1
1000
λ
K
0
kg
4
ε
W
=
m
0
m
1
λ
K
0
4
ε
W
=
0
m
1
K
ε
=
0
1
2
2
5
5
3312 eSmp
331o kg/m
331o0.4






gor

hm 


32000
32000
λsλ:
0o0.4
8kg/m
λsλ:
K
0oused
8kg/m
εs50
=W/(m·K),
0=0.1,
m
1599pu
K
0used
8εs50
W
=W/(m·K),
00.1,
m
1599pu
λK
0used
W
=ou
00.1,
m
199puK
= mm,
0
199 ra
4 =L1000
wa
eSmp
4 ==L32000
assemb
Tab
wa
eW/(m·K),
y
4m==ana
L32000
assemb
Tab
ys
swa
ou
y
4m=0.1,
Lm
pu
assemb
wa
ou
or
ana
assemb
ra
ys
ou
or
ana
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ra
ys
a=n8εgor
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or
each
hm
ra
used
a=nεgor
ng
or
each
hm
a
ngor
ng
each
hma
Smp
2 3312 Smp
2Tab
2sTab
ρρ
2sλ:
kg
ρρ
kg
ρ=ρ
ρ=ym

Smpl3-1
Smpl3-1
Smpl3-1
ρ
Smpl3-1
kg/m
=ana
,31000
,1000
εeW
W/(m·K),
,1000
dys
0.4
=kg
εW
mm,
, λλ:
dExternal
0.4
=nkg
εng
=ym
mm,
dExternal
εng
=mm,
dExternal
50
External
Smp
10
1
SampSmp
e Reference
Samp
e
Reference
Proper
es
Proper
of
Wa
Samp
es
of
Wa
e
Samp
e
ANN
1
ANN
ANN
2
1
ANN
ANN
3
2
ANN
ANN
4
3
ANN
4
ρ
=
2000
kg/m
λ
0
8
W/
m
K
ε
=
0
1
d
=
100
mm
In
erna














1
1
Smp
1
1
Smp
1
1
Smp
ρ
=
1000
1
1
kg
ρ
m
=
1000
λ
0
kg
4
W
ρ
m
=
m
1000
λ
K
0
kg
4
ε
W
=
ρ
m
0
=
m
1
1000
λ
K
0
kg
4
ε
W
=
m
0
m
1
λ
K
0
4
ε
W
=
0
m
1
K
ε
=
0
1
2
2
2
2
5
5
5
5
m
15 Ex
erna
 

 


23 121 kg
Smp
23λ1210kg
ρ=ρm
=0=m
2000
ρ=m
m
λλK00kg
8kg
W
λλK
00=kg
8kg
ε450
W
=W
0=0m
15992000
λλK
00=kg
8ε450
W
=W
00m
1599m
λK
0=8ε50
W
==mm
00
151 K
ε50
= mm
0


Smp 23 33121 Smp 23 33121 Smp
ρρm
==2000
ρ
m
=
2000

Smp
ρ = 1000
Smp
1000
kg
ρ
m
=
1000
m
1000
m
4
W
m
4
ε
W
m
1
d
K
ε
mm
m
1
d
K
Ex
ε
erna
=
mm
1
d
K
Ex
ε
erna
d
Ex
=
erna
3 Proper
Smp
10
2
SampSmp
e Reference
Samp
e
Reference
Samp
e
Reference
Samp
e
Reference
es
Proper
of
Wa
Samp
es
Proper
of
Wa
e
Samp
es
Proper
of
Wa
e
Samp
es
of
Wa
e
ANN
Samp
1
ANN
e
ANN
2
1
ANN
ANN
ANN
3
2
ANN
1
ANN
ANN
4
ANN
3
2
ANN
1
ANN
ANN
4
3
2
AN
A
ρ
=
2000
kg/m
λ
0
8
W/
m
K
ε
=
0
5
d
=
100
mm
In
erna








1
1
Smp
1
1
ρ
=
1000
kg
ρ
m
=
1000
λ
0
kg
4
W
m
m
λ
K
0
4
ε
W
=
0
m
1
K
ε
=
0
1




2
2
Smp
1
2
Smp
1
2
ρ
=
1000
kg
ρ
m
=
5
1000
λ
0
kg
4
W
m
m
5
λ
K
0
4
ε
W
=
0
m
5
K
ε
=
0
5


9
9
9
9
3
3
3
3
m

59
 
 
λλK00kg
84εW
m
λK
0=kg
8ε50
W
=ρ=m
0=0m
1592000
K
ε50
=m
0m
159 λKEx
2
λ
0
8
W
0
8
ε
W
=
0
5
K
ε
=
0

9
Smp 23 3112 Smp 23 3112 Smp
2 32 kg
Smp
ρρm
==2000
2
3
kg
ρ
m
=
2000
ρ
m
=
2000
kg



ρ = 1000
1000
kg
m
λ
0
4
W
m
W
=
0
m
1
d
K
ε
mm
1
d
Ex
=
erna
mm
erna
3 λ 0 8 W/ m K ε = 0 9 d = 100 mm In erna
3 1
ρ = 2000














Smp
12Smp
123312 10
Smp
123312 Smp
12 1331 kg/m
Smp
ρ
== 1000
12 1331 kg
ρ
m
== 1000
λ
00 kg
4
W
ρ
m
== m
1000
λ
K
00 kg
48εε W
==ρ
m
00== m
1
1000
λ
K
0
kg
4
ε
W
=
m
0
m
1
λ
K
0
4
ε
W
=
0
m
1
K
ε
=
0
1
5
5
9
9
9
9














Smp
Smp
2
Smp
Smp
ρ
2000
kg
ρ
m
2000
kg
ρ
m
2000
kg
ρ
m
2000
kg
m
λ
8
W
m
λ
K
W
m
1
λ
K
0
8
ε
W
=
0
m
1
λ
K
0
8
ε
W
=
0
m
1
K
ε
=
0
1
9 Exerna

 

Smp 3 1 Smp 3 1 Smp
ρ = 1000
3 1 kg
Smp
ρm= 1000
3λ10 kg
ρm= m
1000
4W
λK0 kg
4ε W
=ρm
0= m
11000
λd
K0=kg
450
εW
=m
mm
059m
1 λd
K
Ex
0= 450
εerna
W
=mm
059m
1 d
K
Ex
= 50
εerna
=mm
091 dEx
= 50
erna
mm








Smp
1
2
Smp
ρ
=
1000
1
2
kg
ρ
m
=
1000
λ
0
kg
4
W
ρ
m
=
m
1000
λ
K
0
kg
4
ε
W
=
ρ
m
0
=
m
5
1000
λ
K
0
kg
4
ε
W
=
m
0
m
5
λ
K
0
4
ε
W
=
0
m
5
K
ε
=
0
5




9
9


2
1
2000
2
1
2000
2000
2000
8
8
1
8
1
8
1
1








Smp 123 233121 Smp
Smp 123 233121 Smp
Smp
2
Smp
ρ
=
2
kg
ρ
m
=
kg
ρ
m
=
kg
ρ
m
=
kg
m
λ
0
W
m
λ
K
0
ε
W
=
0
m
5
λ
K
0
ε
W
=
0
m
5
λ
K
0
ε
W
=
0
m
5
K
ε
=
0
5

ρ = 1000
3 1 kgρm= 1000
3λ10 kg
ρm= m
1000
4W
λK0 kg
4ε W
=ρm
0= m
11000
λd
K0=kg
450
εW
=m
mm
09m
1 λd
K
Ex
0= 450
εerna
W
=mm
09m
1 d
K
Ex
= 50
εerna
=mm
0 1 dEx
= 50
erna
mm Exerna  














λ
0
4
W
m
λ
K
0
4
ε
W
=
0
m
9
λ
K
0
4
ε
W
=
0
m
9
λ
K
0
4
ε
W
=
0
m
9
K
ε
=
0
9
Smp
1
3
Smp
ρ
=
1000
1
3
kg
ρ
m
=
1000
kg
ρ
m
=
1000
kg
ρ
m
=
1000
kg
m
8
8
1
1
2
2
5
8
5
8
5
5














λ
0
W
m
λ
K
0
ε
W
=
0
m
9
λ
K
0
ε
W
=
0
m
9
λ
K
0
ε
W
=
0
m
9
K
ε
=
0
9
Smp 123 33121 Smp
Smp 123 33121 Smp
Smp
2
3
Smp
ρ
=
2000
2
3
kg
ρ
m
=
2000
kg
ρ
m
=
2000
kg
ρ
m
=
2000
kg
m
ρ = 1000 kgρm= Each
1000
m mλthm
λ 0 kg
4aW
K0 4ε W
=0m
1 eventua
d
K= 50
ε =mm
0 1ydEx
= 50
erna
mm Extoerna
gor
was
compared
the va ues nc uded n the fu set of














1
1
λ
0
8
W
m
λ
K
0
8
ε
W
=
0
m
1
λ
K
0
8
ε
W
=
0
m
1
λ
K
0
8
ε
W
=
0
m
1
K
ε
=
0
1
5
5
9
9
9
9
Smp 23 3121 Smp 23 3121 Smp
2
3
Smp
ρ
=
2000
2
3
kg
ρ
m
=
2000
kg
ρ
m
=
2000
kg
ρ
m
=
2000
kg
m







ρ = 1000
3 1 kg
ρm= 1000
3λ10on
kg
ρm
=m
1000
=m
kg
4W
λKthe
0 kg
4ε W
0m
11000
λd
K0=dent
450
εW
=m
mm
0fy
m
1 λng
d
K
Ex
0= 4the
50
εerna
W
=mm
0eve
m
1 d
K
Ex
=of50
εerna
=naccuracy
mm
0 1 dEx
= 50
erna
mm
Ex ernaby w thho d ng
nformat
w
th
a=ρm
of
ntroduced

  
23 21 kg
Smp
23λ210kg
ρ=ρm
=0=m
2000
ρ=m
λλK00kg
8kg
λλK
8kg
ε450
=W
0=0m
592000
00=kg
8ε450
W
=W
00m
59m
0=8ε50
W
==mm
00m
51 K
= mm
05 Exerna
Smp 23 321 Smp 23 321 Smp
ρρm
==2000
ρρm
==2000
ρ = 1000
1000
kg
m
1000
m
m
4W
m
4εW
W
m
11000
d
K00=kg
εW
mm
m
1λλK
d
K
Ex
εerna
=m
mm
1λK
d
K
Ex
εerna
dEx
= ε50
erna

84εW
8ε50
=ρ=m
0=0m
92000
0=kg
8ε50
W
=m
0m
9 λKEx
0 8εerna
W
= 0m
9 K ε
= 09
Smp 23 31 Smp 23 31 Smp
2 3 kg
Smp
ρρm
==2000
2λ30kg
ρm
= 2000
ρ=m=0m
2000
  
ρ = 1000
1000
kg
m
4W
mλλK00kg
W
m
1λK
d
K0=kg
εW
mm
1λK
dEx
erna
mm
 Exerna

 

Smp 3 1 Smp 3 1 Smp
ρ = 1000
3 1 kg
Smp
ρm= 1000
3λ10 kg
ρm= m
1000
4W
λK0 kg
4ε W
=ρm
0= m
11000
λd
K0=kg
450
εW
=m
mm
0m
1 λd
K
Ex
0= 450
εerna
W
=mm
0m
1 d
K
Ex
= 50
εerna
=mm
01 dEx
= 50
erna
mm
Appl. Sci. 2021, 11, 11435
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part of the input data. The comparison was carefully made against the wall assemblies
incorporating the variable values that the algorithms were deprived of. Since the regressor
models were generally trained using extreme values of insulation (with the exception of
ANN 1, which utilised the full dataset), the comparison was made against wall assemblies
featuring mid-range values (i.e., 50 mm of insulation or ε = 0.5). Although it was anticipated
that ANN 1 would have an extremely good predictive score (since it was already trained
with full data), it was included in the resulting graphs for comparative reasons.
In addition to assessing each algorithm’s performance, it was important to ensure
that overfitting was avoided. Once the most accurate regressor was identified, it was
considered necessary to evaluate its applicability on wall assemblies that had not been
offered to the algorithm at any stage of its development and were, as such, completely
unknown to the model. The variable values and basic structure of these new models had to
be within the range of the algorithm’s training space, as shown on Table 5; however, they
featured completely new parameter value combinations. To enable the comparison of the
ANN predictions with actual ground truth values, six new FE models were developed and
analysed. Their output was finally compared to the regressor predictions, as shown in the
results section of this study. The six new models included the following:
Table 5. Additional FE model parameters.
Sample Ref
Brick Density
Thermal
Conductivity
Coef.
Thermal
Emissivity
Coef.
Insulation
Thickness
Insulation
Type
Insulation
Position
Test Sample 1
Test Sample 2
Test Sample 3
Test Sample 4
Test Sample 5
Test Sample 6
2000
2000
2000
2000
1500
1500
0.8
0.8
0.8
0.8
0.6
0.6
0.9
0.9
0.7
0.3
0.9
0.7
25
25
0
0
0
75
EPS
EPS
NoIns
NoIns
NoIns
EPS
Ext
Int
AbsIns
AbsIns
AbsIns
Int
2.5. ANN Development Protocol
It is a common realisation of the scientific community (at least, the parts working
with Machine Learning and Artificial Neural Networks, in particular) that no formal
standards, guidance or commonly accepted scientific methods of developing an ANN are
available at the moment [9]. Efforts to establish such methods have indeed been made,
providing the first step towards standardisation and a defined set of criteria for choosing
the algorithm input data, architecture, training parameters, and evaluation metrics. The
following paragraphs are dedicated to a step-by-step description of the ANN development
process, following relevant, recently proposed protocols [9,31].
2.5.1. Input Data Selection and Organisation
As mentioned previously, data selection and organisation are the first steps towards
the development of a functional and effective ANN. The importance of careful input
selection is underlined, with a particular focus on data significance and independence.
Although there are various statistical ways of determining the significance of data, the use
of previous experience and domain knowledge is deemed acceptable and valid [9]. In this
case, the independent variables selected are all known to have a considerable contribution
to the development of the final values of the dependent variable.
Data filtering and clustering can reduce the number of input parameters, enabling the
development of a more efficient and computationally manageable algorithm [32]. Such
techniques ensure that any interdependence present in input variables is identified and
either removed or merged, reducing the dimensionality of the necessary analysis. The
number of independent variables used in the present study is considered small. Although,
at present, some dependency between variables is known to exist (i.e., brick density with
its thermal conductivity coefficient), the data is structured in a way that allows for the
Appl. Sci. 2021, 11, 11435
15 of 26
introduction of further test cases able to remove such issues (i.e., varying combinations of
brick density and thermal conductivity that are not proportionally related).
2.5.2. Input Data Preprocessing
Although data preprocessing does not appear explicitly as a separate step in the
ANN development protocol, it was considered necessary to be mentioned here; it did
form an integral part of the work method followed for this study. From the input data
presentation, it became apparent that categorical variables have also been included in
the dataset (i.e., insulation type, insulation position, etc.). These variables were encoded
to ensure that, ultimately, the input offered to the ANN was consistently numerical. To
prevent the negative effect of a “dummy trap” [33], some of the resulting encoded numerical
variables were removed.
Acknowledging that the range of the variable values was quite wide, taking values
from 1 for the encoded variables to 21,600 sec for the timestamps, a scaling of the data
was considered appropriate [34]. To prevent an implicit bias of the algorithm towards the
higher values of the dataset, standardisation was applied throughout the dataset values.
The default values of the “StandardScaler” function from the library sklearn.preprocessing
were utilised [35]. Equation (6) describes the scaling method followed for both the input
and output data. Once the predictions were made, the same scaling tool was used to
reverse the scaling and allow for the inspection of the actual predicted temperature figures
generated by the algorithm.
( x − u)
(6)
s
where z is the standard score of the sample being converted, x is the feature being converted,
u is the mean, and s is the standard deviation.
z=
2.5.3. Data Splitting
Splitting the dataset into training and testing sets is a fundamental part of the ANN
algorithm development process. To avoid introducing figure selection bias, the use
of automatic random selection was opted for: the “train_test_split” function from the
“sklearn.model_selection” library, under the Scikit Learn API [35]. Random selection is
currently the most-used unsupervised splitting technique [9]. Following the example of
several other research studies, a ratio of 80–20% of the available observations was allocated
to training and testing the algorithm, respectively [14,36].
2.5.4. Model Architecture and Structure Selection
The feedforward multilayer perceptron (MLP), the ANN setup that was utilised for
this study, is one of the most popular artificial neural network architectures [31]. The number of input and output nodes was defined by the number of input and output variables,
respectively. The input layer features 8 nodes, reflecting the number of input variables.
This incorporates the dummy variables introduced due to encoding the categorical features, as mentioned previously. The output layer includes a single node representing
the dependent variable, which the ANN has to make predictions against (non-exposed
wall-face temperature through time). To achieve a Deep Learning model, a minimum of
two hidden layers had to be constructed. The number of nodes on each layer was based on
previous experience of ANNs achieving satisfactory prediction results. Figure 6 represents
the structure of the ANN used as part of this study.
Appl. Sci. 2021, 11, 11435
16 of 26
Figure 6. Graphical representation of the employed ANN architecture.
Although methods of optimising the architecture and hyperparameters of the model
do exist, achieving the optimum model was beyond the scope of this study, which instead
focused on the impact of the quality and quantity of input data. Given that an identical
model architecture was utilised for all 4 different models, the final comparison was undertaken on a level plain. Since the activation function has an impact on the performance of
the model [37], it is worth mentioning that the rectified linear unit activation function was
used in both hidden layers of all models. For clarity, the other hyperparameters used for
the development of the ANN are presented in Table 6.
Table 6. Hyperparameters used for the development of the ANN.
Hyper Parameter
Value
Comments
Number of epochs
Learning rate
Batch size
Activation function
Optimiser
Loss function
50
0.001
10
ReLU
Adam
MSE
Following ad hoc experimentation with various values.
Default value of Adam optimiser.
To allow more efficient processing of the large dataset.
Used the default values of the rectified linear unit activation function.
Default values of Adam [38] optimiser were used.
Mean squared error loss function.
2.5.5. Model Calibration
Through training, the ANN converges to the optimum values of the initial random
weights assigned to its neurons; this enables an accurate prediction of the dependent
variable to eventually be made. One of the most computationally efficient algorithms for
achieving such optimisation is backpropagation [39]. A loss function is used at the end
of every epoch to calculate the difference between the ANN prediction and the ground
truth. This study utilises the Mean Squared Error (MSE) loss function, since the physical
phenomenon under consideration was not linear and the final predictions were not distinct
categories (i.e., aiming for the regression of a range of values). With the level of inaccuracy
now quantified, an optimisation function, in this instance Gradient Descent, calculates the
local minimum (optimum) and feeds back to the network, updating the neuron weights
accordingly to reduce the difference between the prediction and the truth (loss). Although
other methodologies for optimising the performance of the model are available [40], they
are beyond the scope of this study.
Appl. Sci. 2021, 11, 11435
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2.5.6. Model Validation
Once the ANN is constructed, trained, and functional, it is necessary to evaluate its
performance before deploying it in field operations or using it for further scientific research.
The evaluation process of the ANN constitutes the focal point of this study, and although it
will be explained thoroughly in the results section, it is worth briefly mentioning the three
core evaluation aspects, along with the various metrics to be considered. An outline of
the implementation method of the above, within the context of this research effort, will
also be given, with the intention of gradually introducing the structure of the upcoming
results section.
There are three main steps in validating the functionality and reliability of an artificial
neural network [9]. The “replicative validity” is the first thing to check to ensure that the
ANN is functional and captures the underlying mechanisms of the physical phenomenon.
Essentially, the algorithm needs to be able to replicate the known data observations that
were offered as input (including the training and testing sets). This process yields “obvious”
results, but it does also provide a sanity check that the algorithm has captured at least
the minimum relationship between the independent and dependent variables. The use
of fitness metrics or visual observation of comparative graphs between predictions and
provided data can aid in this direction. In this study, both methods, metrics and visual
inspection of the algorithm’s ability to replicate the data, have been employed.
The validation of the predictive capacity of the algorithm is the second stage in
building confidence before its implementation in real applications. In this step, the ability
of the algorithm to make accurate predictions, when provided with unknown (not included
in the original training data set) input observations, is assessed by the use of specific
efficiency indices. The impact of training some models with progressively fewer input data
becomes apparent at this stage. An observation of the diminishing scores of the various
metrics and also the deviation of the graphical representation of the predictions from the
ground truth values elucidates the major contribution that appropriately rich and diverse
input data can have on the development of an effective ANN.
Finally, the “structural validity” of the model needs to be confirmed. As part of this
step, the neural network is checked against “a priori knowledge” of how the physical
system under consideration works [9]. Apart from making correct predictions on specific
values, the ANN needs to prove a holistic understanding of the underlying mechanisms
that define the phenomenon that is being studied. In this study, instead of generating
only individual predictions, the ANN is requested to predict the whole time series of the
phenomenon. Thus, the structural validity of the ANN is evaluated through a comparison
of the predicted physical behaviour against the known development of the heat transfer
process through the various wall samples.
In the previous paragraphs, reference was made to the metrics used to assess the
performance of the ANN in terms of accuracy and reliability. Table 7 presents the main
indices used as part of this work [41].
2.5.7. From Evaluation Methodology to Structured Results
The above outlines the main steps and methods for the performance and validity evaluation of the developed artificial neural network algorithms; it also informs the structure
of the investigation and results of this study. Instead of exploring methods of algorithm optimisation, the research interest, in this case, focuses on the impact of quality and quantity
of the provided input data. As such, a single algorithm was developed, adhering to the
requirements of the “Architecture and Structure” section above. Then, the same algorithm
was trained with varying numbers of input data (as presented in Section 2.4 Test Cases)
and was thereon treated as 4 separate predictive models. Each model was subsequently
evaluated, using the aforementioned indices and metrics, to reach a conclusion regarding
the most effective regressor. As a final step, the dominant model was tested and evaluated again, against completely unknown data combinations. A brief outline of the work
sequence followed so far and leading to the following results would include:
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•
•
•
•
•
•
An initial review of the existing bibliography proposing a protocol for the development
of ANNs.
The development of one ANN algorithm based on the peer-reviewed protocol.
The training of the ANN algorithm with varying degrees of input data (ending up
with 4 regressors of the same architecture but different levels of input data).
A comparison of the performance of the 4 regressor models (same architecture/different
input data) and an evaluation of the impact of the quality of offered input data on
each model’s predictive capability.
The identification of the best-performing ANN and validation against a completely
new set of data.
An outline of observations, conclusions, and recommendations regarding the impact
of input data quality and ways of mitigating the problem.
Table 7. Metrics used for the evaluations of the performance of the ANN.
Metric
Reference
Formula 1
Absolute maximum error
AME
AME = max(|Qi − Q̂i |)
Mean absolute error
MAE
Relative absolute error
RAE
Peak difference
Per cent error in peak
PDIFF
PEP
Root mean squared error
RMSE
Coefficient of
determination
R2
MAE =
1
n
RAE =
n
∑ Qi − Q̂i
i =1
n
∑i=1 | Qi − Q̂i |
n
∑ i =1 | Q i − Q |
PDIFF = max(Qi ) − max(Q̂i )
max( Qi )−max( Q̂i )
PEP =
× 100
max( Q̂i )
q n
∑i=1 ( Qi − Q̂i )
RMSE =
n
"
#2
n
e)
Q
−
Q̂
Q̂
−
Q
∑
(
)(
i
i
=
0
R2 = q
2 n
n
e )2
∑i=1 ( Qi − Q) ∑i=1 ( Q̂i − Q
Perfect Score
0.0
0.0
0.0
0.0
0.0
0.0
1.0
1
Nomenclature of the above formulas: n = number of data points; Qi = observed value; Q̂i = ANN value prediction; Q = mean of the
e = mean of the values predicted by the ANN.
observed data points; Q
3. Results
A rigorous testing procedure, following the development and training of the various
ANN models, enabled the assessment of the input data contribution. The graphs included
below allow for a visual interpretation of the impact that varying degrees of input quality
have on the performance of the ANN, while the accompanying metrics help quantify the
same more accurately. For ease of reference, the results are organised in accordance with
the structure and nomenclature of the test cases presented earlier herein.
3.1. Impact of Data Quality on ANN Performance
An observation of the following graphs (Figure 7) highlights the excellent fit of the
network trained with the full training data (ANN 1). The thick grey line on all graphs
represents the ground truth—that is, the actual temperature development on the nonexposed face of the wall through time. The dotted line representing the predictions made
by ANN 1 coincides almost entirely with the ground truth line. The above observation is
very well recorded and reinforced by the metric results.
The indices used to evaluate the performance of the fully trained network (ANN 1)
when tested against the ground truth are summarised in Table 8. The algorithm manages
to predict the final temperature with a maximum error of 2.55 ◦ C, which translates to 2.2%
(test on Wall Assembly 3) of the scale of the overall developed temperatures throughout the
analysis. The good fit is evident not only on the final temperature prediction but throughout
the process, where the maximum error appears to be 3.03 ◦ C. The overall agreement
between the trained algorithm and the ground truth is demonstrated by the Mean Absolute
Error, which on average is 0.73 ◦ C (or a 2.62% difference between the observed values and
their mean). An average of 0.9992 coefficient of determination provides robust evidence of
the agreement between the observed and predicted data.
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Figure 7. Graphical representation of the predictive performance of the 4 ANN models (same algorithm, varying quality of
input data).
The training data offered to ANN 2 was deprived of any middle values of insulation
thickness (removed observations incorporating 50 mm insulation externally or internally).
The graphical representation of the network’s predictions reveals that the algorithm, despite
the reduced data, still captures the “essence” of the physical phenomenon and follows the
route of the ground truth curve. Clearly, a perfect fit is not achieved; the prediction lines
generally run close but parallel to the ground truth curve. Wall Assembly 4 (WA4) is an
exception, where the two lines cross at timestamp 15,300 s; the temperature predictions
decline from there onwards.
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Table 8. Metric scores for ANN 1 in the testing phase.
Wall Assembly
AME
MAE
RAE
PDIFF
PEP
RMSE
R2
WA1
WA2
WA3
WA4
WA5
WA6
Average
1.80
1.63
3.03
2.48
1.69
1.67
2.05
0.56
0.78
1.10
0.83
0.45
0.64
0.73
2.33%
2.78%
4.62%
2.60%
1.42%
1.97%
2.62%
1.80
1.55
2.55
1.39
−0.65
0.70
1.22
1.7%
1.4%
2.2%
1.2%
−0.5%
0.6%
1.1%
0.75
0.88
1.29
1.05
0.55
0.78
0.88
0.9993
0.9992
0.9981
0.9991
0.9998
0.9995
0.9992
The above is reflected in the performance indices in Table 9. The predictions of the
final temperature are generally within −0.30 ◦ C and 6.76 ◦ C (−0.24% and 6.27% of the
observed values, respectively) of the actual values. As observed graphically, the final
prediction error for WA4 lies at 11.85 ◦ C (10.37% error compared to the actual temperature
value), slightly beyond the range seen on the other tests. Although the prediction and
ground truth lines are generally parallel, indicating a good capture of the heat transfer
mechanisms, the absolute maximum error of 32.04 ◦ C observed in Wall Assembly 3 is a
reminder of the inferior performance of this ANN. This is not an outlier, as on average there
is a 16.82% error in all observations made by this network. The degraded performance
of this network is also reflected by the lower coefficient of determination and higher root
mean square error, which on average are 0.9540 (compared to ANN 1’s score: 0.9992) and
6.65 (compared to ANN 1’s excellent fit score of 0.88), respectively.
Table 9. Metric scores for ANN 2 in the testing phase.
Wall Assembly
AME
MAE
RAE
PDIFF
PEP
RMSE
R2
WA1
WA2
WA3
WA4
WA5
WA6
Average
8.45
11.44
32.04
22.88
13.09
9.96
16.31
2.69
3.85
5.06
6.87
4.86
5.73
4.85
11.3%
13.7%
21.3%
21.6%
15.3%
17.7%
16.82%
6.76
2.83
2.34
11.85
3.90
−0.30
4.56
6.27%
2.51%
2.03%
10.37%
2.97%
−0.24%
4.0%
3.45
5.07
9.74
8.84
6.25
6.57
6.65
0.9844
0.9741
0.8921
0.9363
0.9702
0.9668
0.9540
A graphical observation of the third network’s (ANN 3) performance reveals similar
trends to ANN 2. The predictive capacity of the model is clearly inferior to ANN 1. However, the general mechanism of the heat transfer process has been captured, as indicated
by the fact that the ground truth and prediction curves are approximately parallel. The
distance between the two lines is larger than observed in the case of ANN 2. It is also
worth noting that the curves generated by the ANN 3 predictions appear to be smoother
compared to the ones resulting from plotting the predictions of ANN 2.
In a similar fashion, the indices in Table 10 reflect the reduced performance of ANN 3.
The degradation from the removal of the middle values of the emissivity coefficient appears
to be more severe, with absolute maximum error values in the range of 28.46 ◦ C to 48.84 ◦ C.
Throughout the six tests, algorithm ANN 3 generates a relative absolute error of 45.60%
on average, with a maximum of 57.80% for the values predicted for Wall Assembly 2. The
overall performance reduction is reflected by the low average coefficient of determination
(R2 ) and root mean square error (RMSE) of 0.6723 and 18.37, respectively.
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Table 10. Metric scores for ANN 3 in the testing phase.
Wall Assembly
AME
MAE
RAE
PDIFF
PEP
RMSE
R2
WA1
WA2
WA3
WA4
WA5
WA6
Average
28.46
45.00
41.09
48.84
28.77
30.34
37.08
10.87
16.21
9.64
15.12
11.37
14.99
13.03
45.59%
57.80%
40.57%
47.49%
35.85%
46.29%
45.60%
22.58
45.00
27.81
27.71
14.56
24.19
26.98
20.95%
39.93%
24.18%
24.25%
11.07%
19.55%
23.3%
15.05
22.55
16.01
22.35
15.06
19.18
18.37
0.7023
0.4870
0.7081
0.5922
0.8271
0.7171
0.6723
The most data-deprived network, ANN 4, presents an irregular graphic form of
prediction results. In all tests, there is an approximate agreement between predictions and
observed values in the lower range of temperatures. However, when the impact of heat
transfer becomes more evident on the finite element analysis model (i.e., ground truth
values), ANN 4 fails to react accordingly.
The indices describing the performance of ANN 4 are presented in Table 11. The
average coefficient of determination for ANN 4 between the six tests is 0.8321 and the
network’s average maximum error is 26.20 ◦ C. ANN 4 generates ultimate temperature
predictions that have an error of 14.55 ◦ C to 31.65 ◦ C (12.92% and 24.06% deviation from the
actual ultimate temperature). Between the six wall assembly tests, the ANN 4 predictions
constitute a mean absolute error of 10.04 ◦ C (35.44% relative absolute error).
Table 11. Metric scores for ANN 4 in the testing phase.
Wall Assembly
AME
MAE
RAE
PDIFF
PEP
RMSE
R2
WA1
WA2
WA3
WA4
WA5
WA6
Average
18.13
22.03
29.39
33.29
31.66
22.70
26.20
8.36
10.46
9.82
15.44
8.25
7.91
10.04
35.08%
37.30%
41.35%
48.49%
26.01%
24.42%
35.44%
18.13
14.55
28.83
29.33
31.65
22.70
24.20
16.82%
12.92%
25.06%
25.66%
24.06%
18.34%
20.5%
10.18
12.39
13.25
19.49
12.56
10.58
13.07
0.8639
0.8451
0.8002
0.6898
0.8797
0.9140
0.8321
Although the above results give an indication of the performance each ANN achieves,
depending on the quality and completeness of the offered training data, it is worth presenting the coefficients of determination obtained after training each algorithm. The figures in
Table 12 indicate the goodness of fit between the predictions made by the algorithms and the
corresponding observed values on the test set. They all appear to be performing extremely
well; this contrasting behaviour is reflected upon further in the discussion section.
Table 12. Final metric scores for each ANN following the completion of their training with their
respective training dataset.
Neural Network
Loss
ANN 1
ANN 2
ANN 3
ANN 4
5.0840 × 10−4
5.0721 × 10−4
2.1836 × 10−4
2.4811 × 10−4
3.2. Performance of the Dominant ANN Model
Following the review of the results presented in the previous paragraphs, the superiority of ANN 1 became apparent. To assess the “dominant” model’s performance
against completely unknown data, 6 more tests were carried out. Figure 8 is the visual
representation of the results of these additional tests. The goodness of fit between the
ground truth (data obtained from finite element model analysis) and the predictions made
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by the ANN is easy to observe. This is further founded and reinforced by the metrics
included in Table 13.
Figure 8. Graphical representation of the predictive performance of the dominant ANN model against completely unknown
wall assembly combinations.
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Table 13. Metric scores for ANN 1, as the dominant network, on unknown data sets
(wall test samples).
Test Sample
AME
MAE
RAE
PDIFF
PEP
RMSE
R2
TS1
TS 2
TS 3
TS 4
TS 5
TS 6
Average
3.83
4.26
6.06
11.42
12.43
4.13
7.02
0.90
1.93
2.08
3.80
4.16
1.92
2.47
1.89%
3.72%
6.37%
26.50%
10.32%
4.64%
8.91%
−0.44
3.72
4.42
11.42
−4.02
4.03
3.19
−0.28%
2.03%
3.30%
15.04%
−2.70%
2.66%
3.3%
1.20
2.48
2.73
5.36
5.81
2.25
3.31
0.9995
0.9981
0.9946
0.8990
0.9832
0.9976
0.9787
The ANN manages to predict the ultimate temperature developed on the non-exposed
surface of the wall test samples with a relatively low error, 3.3% on average. Although
on one occasion (Test Sample 4) the prediction of peak temperature differs from the
observed value by 11.42 ◦ C (15.04% deviation from the actual temperature), on average,
the predictions lie within 3.19 ◦ C of the ground truth. This high predictive performance is
observed not only on the peak temperature, as an isolated success, but also by the overall
low mean absolute error that ranges from 0.90 ◦ C to 4.16 ◦ C.
Tests TS4 and TS5 appear to have more onerous metric results. The absolute maximum
errors are 11.42 ◦ C (in peak temperature, as explained above) and 12.43 ◦ C, respectively.
These can be observed in the graphic representation of the results as deviations of the
prediction curve from the ground truth curve. Despite these local inconsistencies with the
observed figures, the overall high coefficient of determination (0.9787 on average between
tests) and low root mean squared error (3.31 on average) indicate a high-performing model.
4. Discussion
Although an algorithm capable of predicting the temperature developed on the wall
samples’ non-exposed face was eventually constructed, a few items worth highlighting
and discussing further appeared during the development and evaluation process. These
are listed in the following paragraphs, with the intention to evoke thoughts and discussion
regarding potential pitfalls and respective solutions when the ANNs are employed on heat
transfer through masonry wall applications.
The perfect fit of ANN 1 with the ground truth is not a surprising result. The network
was trained with the full training data, which means that its comparison with the ground
truth merely verifies whether its predictions can replicate already-known patterns and
figures. Despite its obvious results, however, this step is far from unnecessary, as it ensures
the replicative validity of the developed algorithm. It helps in building confidence that the
network is not only functional but that it is also able to identify and capture the underlying
patterns in the provided dataset.
After achieving this first level of validation, the research could proceed by exploring
the limits of the algorithm architecture by varying the quality and quantity of the provided
training data. ANN 2, deprived of mid-range insulation thickness values, and ANN 3,
deprived of mid-range emissivity coefficient values, both had difficulty in achieving equally
high predictive rates as ANN 1, which was trained with the full range of data. It is worth
highlighting that the predictions of ANN 2 lay closer to the ground truth but demonstrated
some local irregularities. On the contrary, the predictions generated by ANN 3 lay further
from the ground truth curve (as reflected by the more onerous performance indices);
however, these were largely offset from the observed figures, following their smooth
curvature. This raises questions as to the impact different variables may have on the
performance of ANNs, depending on their contribution to the physical phenomenon under
consideration. The emissivity coefficient is a constant value throughout the finite element
analysis, while properties relating to the EPS are time-dependent (within the context of this
study). The physical importance of the independent variables needs to be well understood
before they are incorporated into an ANN structure.
Appl. Sci. 2021, 11, 11435
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The most data-deprived network, ANN 4, presents the most irregular graphic form
of prediction results. The comparison between the performance indices for ANN 4 and
ANN 3 show that the former performed better. However, a visual observation shows
clearly that the prediction line of ANN 4 is more erratic compared to ANN 3, whose line is
just “offset” (i.e., consistently overestimating or underestimating compared to the ground
truth). Although networks ANN 2 and ANN 3 failed to make accurate predictions (at least
to the degree ANN 1 did), they appeared to capture the underlying principles and function
of the physical phenomenon. On the other hand, the lack of resemblance to the ground
truth curve demonstrates that the capture of the underlying mechanisms of the physical
phenomenon by ANN 4 is poor, despite its better metrics.
At the training stage, all algorithms returned high indices of fitness to the test data.
However, their performance on predicting values beyond their training sets varied greatly
depending on the amount and quality of data that was offered at that initial stage. This
underlines the need for the validation of the algorithms and a multifaceted evaluation of
their performance prior to their application in further research or field operations. It also
shows that, despite developing a functioning and potentially effective ANN architecture,
the ultimate performance might be compromised by a lack of representative observations
in the training set.
5. Conclusions and Further Research
This paper contributes towards the further integration of ANNs in the field of heat
transfer through building materials and assemblies. Arguably, there is a wide scope for
further development of this research in directions such as the use of different algorithm
types and structures, an extended range of building assemblies and materials, and different
thermal loadings. Nevertheless, some first conclusions can be drawn from this initial
effort, informing future scientific work aiming to employ Artificial Neural Networks for
the description of heat transfer phenomena. Although good metric results quantifying
the replicative validity of the algorithm offer an indication of a functional ANN, they
do not necessarily constitute evidence of a fully operational and reliable network. As
such, the use of further validation techniques is of paramount importance. A comparison
against unknown data (methodology followed in this study) is an objective way of ensuring
the constructed model behaves and performs as expected. When “external” data is not
available or difficult to obtain, k-fold cross validation could provide a route for building
some confidence in the performance of the model. To mitigate the risk of overfitting,
neuron “dropout” can be introduced as part of the algorithm’s hyperparameters. This
would artificially weaken the fitting of each neuron to the supplied training data.
As seen in the previous paragraphs, metrics and indices can sometimes be misleading.
An intuitive understanding of the predictions and their relevance to factual data is necessary to mitigate the impact of the “black box” phenomenon of blindly accepting output
generated by an AI model. Outlining the expectations of the models’ output in advance
could provide a measure against which a preliminary assessment of the ANN’s predictions
can be undertaken. In the same direction, producing visual representations of the output at
every stage can enhance the understanding of the relationship between the ground truth
and the predictions and can imminently highlight subtle inaccuracies or major errors.
Depending on the nature and contribution of each parameter to the physical phenomenon, the impact of its loss from the training data can have a more severe impact on
the predictive capability of the Neural Network. It is worth researching this relationship
by quantifying the contribution of various parameters on the development of a physical
phenomenon and then training ANNs with a gradual deprivation of the variables in question. This could provide an opportunity for quantifying the correlation of various physical
parameters with the performance of the artificial neural model.
The ANN’s development, analysis, and interrogation need to be considered within the
wider context of a specific scientific study or practical application. This contextualisation
can have a significant effect on the specification of required accuracy levels for the chosen
Appl. Sci. 2021, 11, 11435
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evaluation methodology. Different scientific applications have different required levels
of accuracy in their produced results. As such, it is prudent to avoid trying to establish
ill-defined accuracy thresholds without specific application requirements to hand.
This study presented the underpinning principles of an assessment methodology
for the evaluation of ANN predictions and highlighted potential pitfalls arising from
the use of ANNs within a masonry wall heat transfer context. The focus of the present
work is to identify the impact of varying quantities and qualities of input data on the
accuracy of a specific ANN architecture and to propose a methodology for demonstrating
this relationship. This objective has been accomplished by presenting the inferior results
generated by the models trained with reduced amounts of data. Ultimately, the proposed
methodology for the assessment and validation of the ANN’s performance was proposed
not as a panacea for all ML evaluation problems, or as an optimum precision benchmark,
but as a first step towards preventing (or at least enabling the quantification of) accuracy
deficiencies in models developed using the data each research team has available.
It is hoped by the authors that future work can feed into the existing proposed
protocols for the development of ANNs while aligning such documentation to the needs
of heat transfer and building fire research. Expanding the existing understanding of the
factors impacting the performance of ANNs and incorporating elements specific to fire
engineering and heat transfer through building elements could help safeguard future
research in this field from misleading results or discrepancies caused by different ANN
models and parameters.
Author Contributions: Conceptualisation, methodology, code writing, data curating, original draft
preparation, illustrations: I.B.; review, supervision, heat transfer theoretical background, thermal
simulations, foundation input data: K.J.K. All authors have read and agreed to the published version
of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data utilised for the development of the ANN algorithms is not
currently available as it forms part of ongoing research.
Conflicts of Interest: The authors declare no conflict of interest.
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