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Investigation of the Effects of the Classification of Building Stock Geometries Determined Using Clustering Techniques on the Vulnerability of Galvanized Iron Roof Covers Against Severe Wind Loading

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In the risk assessment of buildings against severe wind loading, the vulnerability component of risk is highly affected by the geometry of the structure. Parameters such as the height, width, length, aspect ratio, eaves length, and roof slope, affect the pressure distribution around the structure, which in turn affects the response of galvanized iron (GI) roof covers to wind loadings. In developing countries, there is a large variation in the building geometric parameters which poses a challenge in determining the archetypes that would best represent the building population for risk assessment. This paper aims to develop and propose a method in determining the building archetypes based on its geometry. The hierarchy for grouping of geometries started with the roof type. These were gable type roofs, mono-slope type roofs and hip type roofs. The building datasets per roofing type were then clustered using a two-stage approach involving Hierarchical and K-means clustering which were based on the aforementioned geometric parameters. These algorithms will aggregate buildings having similar sets of geometric parameters but the number of clusters must be specified. In order to determine the optimal number of clusters, this study employs various validation tools or measures namely – dendrograms, variation of the variance ratio criterion (VRC) across number of clusters, validity indices such as, Davies Bouldin, Silhouette and Calinski Harabasz, and the elbow method. Although guided by these validation methods, the final selection of the number of clusters were determined considering computational time and resources. To define an archetype, the mean values of each parameter per cluster were selected. Resulting to 5, 3, and 3, archetypes for gable, hip, and mono-slope roof buildings, respectively. The selection of the archetype was further evaluated by investigating its effects on the vulnerability of GI roof covers in order to see how distinct each archetype would behave. A Kruskal Wallis test on the vulnerability curves of the different building archetypes showed that there is a significant difference between vulnerability curves under a roof shape category, which reinforces the distinction between the selected building archetypes.
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Investigation of the Effects of the Classification of Building Stock
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ICMSET 2021
IOP Conf. Series: Materials Science and Engineering 1150 (2021) 012024
IOP Publishing
doi:10.1088/1757-899X/1150/1/012024
1
Investigation of the Effects of the Classification of Building
Stock Geometries Determined Using Clustering Techniques
on the Vulnerability of Galvanized Iron Roof Covers Against
Severe Wind Loading
Tan, Liezl Raissa E., Acosta, Timothy John S.*, Gumaro, Joshua Joseph C.,
Agar, Joshua C., Tingatinga, Eric Augustus J., Plamenco, Dean Ashton D.,
Ereno, Mary Nathalie C., Musico, John Kenneth B., Pacer, Jihan S., Baniqued,
Julius Rey D., Hernandez, Jaime Jr. Y., Villalba, Imee Bren O.
1Insitute of Civil Engineering, University of the Philippines Diliman, Philippines
E-mail: tsacosta@up.edu.ph
Abstract.In the risk assessment of buildings against severe wind loading, the vulnerability
component of risk is highly affected by the geometry of the structure. Parameters such as the
height, width, length, aspect ratio, eaves length, and roof slope, affect the pressure distribution
around the structure, which in turn affects the response of galvanized iron (GI) roof covers to
wind loadings. In developing countries, there is a large variation in the building geometric
parameters which poses a challenge in determining the archetypes that would best represent the
building population for risk assessment. This paper aims to develop and propose a method in
determining the building archetypes based on its geometry. The hierarchy for grouping of
geometries started with the roof type. These were gable type roofs, mono-slope type roofs and
hip type roofs. The building datasets per roofing type were then clustered using a two-stage
approach involving Hierarchical and K-means clustering which were based on the
aforementioned geometric parameters. These algorithms will aggregate buildings having similar
sets of geometric parameters but the number of clusters must be specified. In order to determine
the optimal number of clusters, this study employs various validation tools or measures namely
dendrograms, variation of the variance ratio criterion (VRC) across number of clusters,
validity indices such as, Davies Bouldin, Silhouette and Calinski Harabasz, and the elbow
method. Although guided by these validation methods, the final selection of the number of
clusters were determined considering computational time and resources. To define an archetype,
the mean values of each parameter per cluster were selected. Resulting to 5, 3, and 3, archetypes
for gable, hip, and mono-slope roof buildings, respectively. The selection of the archetype was
further evaluated by investigating its effects on the vulnerability of GI roof covers in order to see
how distinct each archetype would behave. A Kruskal Wallis test on the vulnerability curves of
the different building archetypes showed that there is a significant difference between
vulnerability curves under a roof shape category, which reinforces the distinction between the
selected building archetypes.
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IOP Conf. Series: Materials Science and Engineering 1150 (2021) 012024
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doi:10.1088/1757-899X/1150/1/012024
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1. Introduction
The determination of the building stock is a key parameter in the field of risk analysis. Albayrak et. al
(2015) were able to classify buildings into existing building stock for rapid seismic risk assessment [1].
The classification of building stock helps most especially in the classification of local housing
construction wherein these are non-engineered buildings. Parameters such as the main structural frame,
load-bearing systems, connections between structural elements among others, are used to identify basic
typologies for certain countries [2]. One classification system was developed for the Prompt Assessment
of Global Earthquakes for Response (PAGER) system. This system is used to estimate an earthquake’s
impact in order to guide governments, insurance agencies and relief organizations in post-disaster relief
operations and strategies [3]. This system made use of a global building inventory that was developed
through the use of different inventory data sources worldwide [4]. Databases such as the UN statistical
database on global housing [4], the United Nations Human Settlement Program (UN-HABITAT)
database [4], World Housing Encyclopedia (WHE) database [5] have information on the housing
dwelling type, construction materials for wall, roof or floors, structural systems and other parameters
that contribute to the vulnerability of building to seismic activity [4]. Aside from these databases, FEMA
was able to develop HAZUS standard model building classification schemes. These building stock
classifications were not only used for seismic risk assessment but were used for multi-hazard loss
estimations.
One of the hazards which HAZUS assesses is severe wind events. For their methodology, two building
stock classification methods were used. The first method was through the inspection of aerial
photography samples of Dade, Broward and Palm Beach of Southeast Florida. It was concluded that,
for commercial building stocks, simple rectangular-shaped building models were adequate for damage
simulation which came from random sampling from the aerial photographs wherein they observed that
80% of the samples accounted for rectangular or L shaped plan areas. For the residential building stock,
they used three simple default classifications which were the single-story gable, single story hip and
two-story gable. It was also noted that no attempt was made to quantify the plan shapes. The other
method made use of contractor surveys to determine the distribution of GI roof cover types. The method
was able to come up with 13 building stock classifications [6]. Each building stock classification had
multiple combinations of building envelope components that contributed to the vulnerability against
wind loadings. For the building geometries used to determine the wind loads were based on expert
opinion for each building stock classification [6,7]. The different building geometries which were
derived using expert opinion may also affect the determination of the wind loads which in turn will
affect the resulting vulnerability of the building stock.
With the advancement of computational fluid dynamics (CFD), many researches have been done to
explore the effects of geometric parameters on the wind loads of a building [8,13,14,15]. In the
application of risk assessment, the use of CFD to individually analyze the configuration of the population
of buildings is very complicated and computationally heavy. Thus, there is a need to explore the use of
a building geometry that would statistically best represent the population of buildings being assessed
and will also improve the risk assessment of the population of buildings being considered. One method
is to use clustering techniques on diverse data to come up with a representative ensemble for the
population of buildings. Since the wind pressures on the building will be computed using computational
fluid dynamics, the objective of determining the building geometry archetypes, instead of individual
buildings of the population, will significantly reduce the computational cost.
The use of clustering techniques in the classification of building stock for different applications has been
prominent in the past decade. The technique has been applied to cluster buildings; based on their
sensitivity to retrofitting measures [16], in the context of air conditioning electricity demand flexibility
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[17], performance in energy savings [18], energy efficiency and emission reduction [19], and many other
areas. With this in mind, this paper seeks to investigate the use of clustering techniques to develop
building stock geometries for risk assessment of low-rise buildings against severe wind loadings.
This proposed methodology was implemented in a pilot study to assess the risk of the province of Cebu,
Philippines against severe wind loadings. The pilot study is part of the Philippine government’s national
effort to produce scientifically based vulnerability profiles which would help in disaster risk and
reduction strategies. The greater metro manila area risk analysis project (GMMA-RAP) [20] is a
precedent of the current pilot study wherein key government agencies and institutions such as the
Philippine Atmospheric, Geophysical and Astronomical Services Administration (PAG-ASA),
Philippine Institute of Volcanology and Seismology (PHIVOLCS) and Institute of Civil Engineering,
University of the Philippines Diliman (UPD-ICE) were involved. And given a lack of a high-resolution
exposure database, this study was performed to improve the risk analysis methodology.
2. Methodology
2.1. Parameter Identification.
Various researches have shown that the roof shape, slope, length, width, height [9,10,11,12] have
significant effect on the pressures for low-rise structures. The hierarchy of the parameters was patterned
after the aerodynamic database developed by Tokyo Polytechnic University (TPU) [21]. The dataset
was then classified by the roof shapes.
2.2. Clustering Analysis.
Clustering techniques group data points into clusters in a way that the data points in the same cluster are
similar to one another compared to data points in another cluster [22]. This paper employed a two-stage
approach involving Hierarchical and K-means clustering algorithms employed in MatLAB. The two
algorithms complemented each other in a way that k-means clustering, known for its efficiency in large
datasets, works best when a non-random starting point is specified, which is provided by the cluster
centroids obtained from the hierarchical clustering. A series of the number of clusters were run using
the k-means approach where each building data point was assigned to the nearest cluster. The cluster
centroids were recomputed and data points reassigned to minimize the variability within clusters whilst
maximizing the variability between clusters. This approach is similar to the ones employed in the study
on electricity usage for consumer archetypes [22].
2.3. Evaluation of the results.
In order to assess the optimum number of clusters, various validation methods were utilized. Visual
methods such as the use of dendrograms and the elbow method, were used to roughly assess the
distinction across clusters. The elbow method plots the within-cluster-sum-of-squared error (WSS), for
every number of clusters considered. The number of clusters corresponding to the elbow of the graph is
regarded as the optimum number of clusters. WSS is computed as follows,
 =∑ ∑ ()
(1)
Where is an element within the  cluster with mean value equal to .Thus  takes the
summation of the summation of the sum-of-square error (SSE) within the cluster which is then summed
across all clusters C.
Internal validity indices were also used to evaluate the clustering performance. These are the Silhouette
index, Davies Bouldin Index and the Calinski Harabasz Index. The silhouette width indicates the
belongingness of a datapoint in a cluster it was assigned. Values ranges from -1 to 1 wherein a value
close to 1 means that the “within” dissimilarity is much smaller than the “between” dissimilarity, hence
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it is said to be well-clustered. Davies Bouldin index is a ratio of the total scatter within the cluster to the
separation between clusters, and hence a smaller value is regarded as good clustering. Calinski Harabasz
is the ratio of the overall between-cluster variance to the overall within-cluster variance multiplied by
the factor ratio between the difference of the total data points and the number of clusters to the number
of clusters minus 1. There is no acceptable cut-off value, but the higher the index the better.
Another validation method makes use of the variance ratio criterion (VRC) [24,25]. F value were
determined for each parameter, , per number of clusters, . The F value,
, measures the ratio of
variability of each parameter, , between clusters, , given by the Between-Group-Sum-of-Square Error
(BGSS) and the variability within a cluster or WGSS. [23].
=




(2)
 =
(3)
 =∑ ∑
(4)
Where ,represents the centroid of all the number of datapoints,, while represents the centroid
within clusters of datapoints.
The F value of each parameter can be used to identify which parameter greatly affects the distinction
between clusters. So, for a number of clusters considered, the higher the F value of a parameter the
higher its influence to the clustering process, and therefore can be regarded as a critical clustering
parameter. In relation to determining the optimum number of clusters, the F values were totaled to get
the VRC for every number of clusters. The higher the value of the VRC implies that either clusters are
highly distinct from each other or that the data points within each cluster is highly similar with each
other, and thus a high value of VRC is preferable in the selection of the number of clusters. However,
the VRC value generally increases as the number of clusters approaches the total number of datapoints.
To aid in selecting an efficient number of clusters, the VRC values were then compared to its
neighboring number of clusters using the equation for , which quantifies the difference between the
deviations of VRC from the current cluster to the succeeding and preceding clusters.
=( )()(5)
A positive value for the first term indicates that the current cluster performs worse than the succeeding
cluster while a positive value for the second term indicates that the current cluster performs better than
the previous cluster. Therefore, the more negative the value of the indicates a more efficient selection
of the number of clusters.
2.4. Roofing Vulnerability Analysis.
In order to illustrate the use of the above geometries, the vulnerability curves for the roof sheeting were
determined in this paper. The framework was patterned after the GMMA-RAP simulation methodology
[20]. The archetypes developed in the clustering analysis served as the representative geometries that
would be subjected to computational fluid dynamics. The damage ratio was finally derived by
determining the percent area of the roofing sheets that exceeded the threshold capacity and dividing this
by the total area. The vulnerability curve for each building archetype was then derived by getting the
mean of the models accounting for different wind directions and plotting by the corresponding wind
speed.
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3. Results: Case Study of Cebu, Philippines
3.1. Clustering Analysis.
For the pilot study area, which is Cebu, Province, the parameters of interest were surveyed by a team
coming from the Institute of Civil Engineering, University of the Philippines Diliman. The target areas
in Cebu were chosen based on the analysis of the construction material typology per municipality
wherein the data on the construction materials came from the housing tables of the Philippine Statistic
Authority (PSA) [26]. A total of 179 buildings from 15 municipalities of the province were gathered.
The prominent roof shapes were gable roofs, mono-slope roofs, and hip roofs which comprised 50.8%,
24.58%, and 12.89% of the data, respectively. Hence these were selected as the three main groups used
for the cluster analysis.
The figure below shows the dendrograms produced by the hierarchical clustering algorithm. The
centroids of these results were used as the input cluster centroids for the k-means clustering algorithm.
Each number in the horizontal axis represents the building ID number and hence represents one building
data point. While the vertical axis represents the mean values of the parameters or also termed as cluster
centroid. The height of the links in a dendrogram is indicative of the distinction between clusters. Each
color represents a cluster in a group of a particular roof shape, and consequently shows how big of the
building population a cluster represents.
Figure. 1 Dendrograms from Hierarchical Clustering of different roof shapes using Ward’s Method.
Figure. 2 Plots of the a) elbow method, b) Davies-Bouldin Indices, c) Silhouette indices, and d)
Calinksi-Harabasz indices against the number of clusters for gable, mono-slope and hip roof types.
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The validation indices from various methods provided the team a range of number of clusters to select
from and also gives a measure of how distinct these clusters are from each other yet contains data points
that are similar within each cluster. Consideration of the computational time and resources were also a
major influence in the selection of the final number of clusters.
The values were obtained for 3 to 10 clusters for all roof shapes and are shown in the following
figure.
Figure. 3 Variation in VRC between neighboring clusters ()for every number of clusters.
A selection between 2 to 7, 4 to 8 and 3 to 10 number of clusters were considered for gable, mono-slope
and hip roof types, respectively. Considering the roof type composition in the building and
computational time and resources the author’s settled at 5, 3 and 3 number of clusters for gable, mono-
slope and hip roof types, respectively. In order to understand the characteristics of the population of
buildings, the relative contribution of each clustering parameter to the development of the clusters was
investigated. The F values of each parameter were ranked to see the importance of each parameter to
the clustering algorithm.
Table 1. Rank, F,VRC and values for parameters of the cluster solutions of different roof shapes
Parameter
Gable Clusters
k =5
Hip Clusters
k = 3
Mono
slope Clusters
k = 3
Rank
F
Rank
F
F
Height
3
12.79
3
6.66
3
14.32
Length
1
263.88
1
108.93
1
71.38
Width
2
142.69
2
50.65
2
45.51
Slope
6
0.77
6
2.84
4
4.44
Eaves
-
L
5
1.16
5
4.36
5
1.48
Eaves
S
4
5.91
4
4.76
6
1.31
VRC
427.22
178.19
138.43
wk
139.094
83.80
276.87
The table above shows us that the primary parameters that affected the formation of clusters are the
length (ranked 1st) and width (ranked 2nd) of the building geometries. This implies that the building
population can be categorized more by their plan area rather than their roof shape parameters. This also
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tells us that the construction practice for the roof slope, eaves and length has a low variability in the pilot
study area.
The final geometry clusters produced through the clustering techniques are now considered as the
archetypes which will be used to determine the wind loads on the roofing sheets. The building archetypes
for the different roof shapes can be found in table 2 to 4. The illustration in figure 4 gives a reference on
how the different parameters are measured.
Figure. 4 Illustration of parameter measurements for gable roof archetypes
Table 2. Centroids for Gable K-means clusters
ARCHETYPE LABEL HEIGHT LENGTH WIDTH ROOF SLOPE EAVES-L EAVES-S
G1
4.08
10.50
5.07
15.33
1.01
0.50
G2
8.50
41.67
27.00
19.00
1.10
1.90
G3
4.26
5.97
4.62
19.00
0.85
0.58
G4
8.75
22.00
16.35
19.00
1.22
0.25
G5
5.84
11.6
8.76
19.5
0.68
0.58
Table 3. Centroids for Hip K-means clusters
ARCHETYPE
LABEL HEIGHT LENGTH WIDTH ROOF SLOPE EAVES-L EAVES-S
H1
3.95
7.37
5.70
24.20
0.83
0.70
H2
8.90
24.95
17.45
38.31
1.45
1.45
H3
5.90
13.42
8.75
21.03
1.03
0.875
Table 4. Centroids for Mono-slope K-means clusters
ARCHETYPE
LABEL HEIGHT LENGTH WIDTH ROOF SLOPE EAVES-L EAVES-S
M1
5.42
6.92
4.78
8.83
0.70
0.20
M2
9.00
18.23
11.00
2.50
0.50
0.10
M3
20.00
50.00
30.00
0.00
0.00
0.00
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3.2. Vulnerability Results.
The simulations were done for wind speeds from 10 m/s to 100 m/s and considered different orientations
of the wind relative to the building surfaces. Due to the symmetry of the archetypes, only angles between
0 degrees to 90 degrees at increments of 15 degrees were considered. The various combinations gave a
total of 770 models that were simulated with 350 models for the 5 gable roof archetypes, 210 models
for the 3 hip roof archetypes and 210 for the 3 mono-slope roof archetypes. All CFD simulations were
implemented through the software ANSYS CFX. The GI roof cover failure which was primarily
characterized by pullout strength of 4.3 kPa [27] was compared to the positive and negative wind
pressures developed on the building archetypes. The simulated data points were then fitted into a
lognormal cumulative distribution function (CDF) using a nonlinear regression analysis that minimized
the sum of squared estimate of errors (SSE) to represent the final vulnerability curves. The final
vulnerability curves are then shown in figure 5.
Table 5. Lognormal cumulative distribution function parameters
CDF
Paramete
rs
BUILDING ARCHETYPES
G1 G2 G3 G4 G5 H1 H2 H3 M1 M2 M3
Mean 4.92 4.86 4.87 4.67 4.69 4.92 4.89 4.83 4.65 4.54 4.38
Std 0.31 0.37 0.30 0.23 0.21 0.29 0.29 0.32 0.22 0.21 0.36
Figure. 5 Roof Sheeting Vulnerability for different building archetypes
A Kruskal-Wallis test was used to determine if the vulnerability curves for each building archetype were
significantly different from one another. For gable, hip and mono-slope roof building archetypes, it was
observed that for wind speeds from 60 m/s – 100 m/s, there was a significant difference (p= .001) for
the vulnerability curves between the 5 building archetypes at a level of significance of 5%. For hip roof
building archetypes, the same conclusion of a significant difference (p= .001) was also observed
between the three building archetypes. And for the mono-slope building archetypes, the vulnerability
curves were also significantly (p< .0001) different from each other. These results show that the use of
building archetypes developed from the two-stage clustering algorithm has a significant effect on the
vulnerability analysis of roof sheeting against severe wind loadings. The use of multiple building
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archetypes that best represent the population of buildings considers the variability of the geometric
parameters of the area being assessed. The analysis can be extended to investigate the vulnerability
curves that also consider other building envelope components aside from the roofing sheets that are also
vulnerable to severe wind loadings.
4. Conclusion
This paper presents the application of clustering techniques in determining the building geometry
archetypes which will be used for vulnerability and risk assessments. Specifically, the vulnerability
assessment for galvanized iron roof covers against severe wind loading was evaluated. The paper
implemented a two-stage clustering approach wherein Hierarchical and K-means clustering algorithms
were used to develop clusters for the population of buildings in Cebu, Philippines. A total of 179
buildings were considered and subdivided into 3 main categories based on roof shape namely the gable,
mono-slope and hip. Cluster analysis was employed on buildings in each roof shape category
considering the parameters, length, width, height, roof slope, and eaves lengths. The analysis considers
various numbers of clusters where cluster centroids and cluster assignments were obtained. The clusters
were then evaluated using validation scores for cluster analysis namely the elbow method, silhouette
index, Davies-Bouldin, Calinski Harabasz and the variation in VRC between neighboring clusters ().
The validation scores were used to serve as a guide in the selection of the number of clusters to define
the archetypes per roof type. Considering the composition of building population and the computational
time and resources, the final number of clusters were selected for each roof shape. These are 5, 3, and 3
for gable, mono-slope and hip roof type, respectively. The cluster centroids for the selected number of
clusters per roof type were then used as the dimensions for the building archetypes to be subjected to
vulnerability analysis. For each building archetype, the simulated damage ratios for every wind speed
data were fitted with lognormal cumulative distribution functions in obtaining the vulnerability curves.
The vulnerability curves for the gable, hip and mono-slope building archetypes were observed to have
a significant difference within each respective roof category at a level of significance of 5%. This shows
that the consideration of the building archetypes from a sample population will significantly affect the
results of the vulnerability analysis for wind speeds greater than 60 m/s. Further studies can be done to
investigate the effect on vulnerability curves that also consider different building components that are
vulnerable to severe wind loadings.
Acknowledgements
This work is part of the project entitled “Enhanced Vulnerability Curves for Different Building Types
in the Philippines” under the program “Severe Wind Risk Assessment of Cebu City” wherein this project
received funding from the Department of Science and Technology (DOST) through the Grants-In-Aid
(GIA) program. The program was implemented in collaboration with the Philippine Atmospheric,
Geophysical and Astronomical Services Administration (PAG-ASA) and Philippine Institute of
Volcanology and Seismology (PHIVOLCS).
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... Figure 3 shows the sample structural models used for different roof shapes. The representative geometries were identified through the clustering analysis of the building stock geometry of the surveyed buildings, where statistical geometric similarity identified clusters in the building population [7]. The representative geometries shown in Table 1 were then derived from the identified clusters in the building population. ...
... Also, shown in Figure 5, the failure of the supports will also lead to the propagation of failure to the other building components, as it signifies structural collapse as observed in the field surveys. As a consequence, the failure of the supports will attribute to most of the building damage ratio, with the slope of the vulnerability curve expected to increase along with the increase of the probability of exceedance of the failure of the supports, which is classified as Damage State 4 based on the fragility curves proposed by the GMMA-RAP report [7]. ...
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