Building feature-based machine learning regression to quantify urban material stocks: A Hong
Kong study
Liang YUAN1, Weisheng LU1*, Fan XUE1, and Maosu LI2
Department of Real Estate and Construction, Faculty of Architecture, the University of Hong Kong.
* Corresponding email: wilsonlu@hku.hk
2
Department of Urban Planning and Design, Faculty of Architecture, the University of Hong Kong.
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This is the post-print version of the paper:
Yuan, L., Lu, W., Xue, F., & Li, M. (2023). Building feature-based machine
learning regression to quantify urban material stocks: A Hong Kong study.
Journal of Industrial Ecology, to appear. Doi: 10.1111/jiec.13348
The final version is available here: https://doi.org/10.1111/jiec.13348

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Abstract
Urban material stock (UMS) represents an elegant thinking by perceiving cities as a repository
of construction materials that can be reused in the future, rather than a burdensome generator
of construction and demolition waste. Many studies have attempted to quantify UMS but they
often fall short in accuracy, primarily owing to the lack of proper quantification methods or
good data available at a micro level. This research aims to develop a simple but satisfactory
model for UMS quantification by focusing on individual buildings. Generally, it is a ‘bottomup’ approach that uses building features to proximate the material stocks of individual buildings.
The research benefits from a set of valuable, ‘post-mortem’ ground truth data related to 71
buildings that have been demolished in Hong Kong. By comparing a series of machine
learning-based models, a multiple linear regression model with six building features, namely
building type, building year, height, perimeter, total floor area, and total floor number, is found
to yield a satisfactory estimate of building material stocks with a mean absolute percentage
error of 9.1%, root-mean-square error of 474.13, and R-square of 0.93. The major contribution
of this research is to predict a building’s material stock based on several easy-to-obtain building
features. The methodology of machine learning regression is novel. The model provides a
useful reference for quantifying UMS in other regions. Future explorations are recommended
to calibrate the model when data in these regions is available.
Keywords
Urban material stocks; Sustainable development; Circular economy; Construction materials;
Machine learning regression; Industrial ecology

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1. Introduction
An urban material stock (UMS) is the accumulation of construction materials (e.g., bricks,
concrete, timber, or steel) used in buildings and infrastructure within the urban area (Manelius
et al., 2019; Tanikawa & Hashimoto, 2009). UMS plays a crucial but underappreciated role in
shaping the use of material and energy resources (Krausmann et al., 2017). Research interest
in UMS has grown in recent years. The UMS changes can be used as a proxy for understanding
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urban metabolism (Schandl et al., 2020; Tanikawa & Hashimoto, 2009), and as an indicator for
calculating embodied greenhouse gas emissions. UMS is considered a precursor for predicting
future material demand and supply, and (Gassner et al., 2020; Huang et al., 2013). In this
perception, urban material is a future anthropogenic resource deposit temporarily stocked in
cities that can be reused or recycled in the future (Mesta et al., 2019; Nasir et al., 2021), rather
than passively treating cities as material and energy consumers, or construction and demolition
(C&D) waste generators (Marcellus‐Zamora et al., 2016). The UMS is thus considered a
proactive approach aligning with the global pursuit of sustainable development and a circular
economy (Gontia et al., 2020; Haas et al., 2015).
Given the significant role of UMS, researchers have proposed various methods to measure it.
For instance, Müller (2006) developed a demand-driven approach to quantify the concrete
stock of the Netherlands’ dwelling buildings. Tanikawa and Hashimoto (2009) proposed a
spatial material stock analysis approach based on 4-dimensional geographic information
system (4D-GIS) data. Fishman et al. (2014) proposed a novel method to quantify national
material stock based on historical material flow data. Several recent studies have also tried to
use a building component inventory-based approach to estimate material stock (de Tudela et
al., 2020; Heeren & Hellweg, 2019; Heisel et al., 2022). Notably, studies have emerged to
review and categorize UMS quantification methods. For example, Augiseau and Barles (2017)
identify two main methodological approaches: bottom-up stock analysis and top-down
retrospective stock analysis using a flow-driven model. Wiedenhofer et al. (2019) suggested a
new classification: stock-driven vs. inflow-driven. More reviews and categorizations on UMS
quantification methods can refer to Lanau et al. (2019) and Nasir et al. (2021).

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Whilst existing methods have made important contributions to UMS quantification, they also
suffer from shortcomings, mainly related to estimation accuracy. For both bottom-up and topdown approaches, the crux seems to lie in the accurate estimate of building material stock
(BMS) or infrastructure material stock (IMS) at an individual level. By summing up the BMS
and IMS in the urban area, a UMS can be derived. Nevertheless, the data to verify the BMS or
IMS is often not available unless a building or an infrastructure is demolished, and its embodied
materials are segregated and weighed. Such ‘post-mortem’ analyses are simply unrealistic. It
is thus not surprising to see previous studies giving a possible error range for the estimate based
on experience (Guo et al., 2019), or indirectly calibrating the accuracy level against studies in
other regions (Mastrucci et al., 2017; Nasiri et al., 2021). The research on UMS quantification
will see a breakthrough if a method is found to estimate the BMS or IMS with reasonable
accuracy based on visible, easy-to-obtain building or infrastructure features.
This research aims to develop a novel UMS quantification approach based on easy-to-obtain
building features (e.g., explicit building geometries, floor areas, and so on). As mentioned
earlier, the repository of construction materials in the urban built environment comprises two
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sectors: buildings and infrastructure. As the first step, this research focuses on buildings. The
research benefits from a valuable data set related to waste generation and features of 71
buildings demolished in Hong Kong. The remainder of the paper is organized as follows.
Subsequent to this introductory section, Section 2 reviews studies on UMS quantification.
Section 3 introduces the research methodology and Section 4 describes model development
and validation. Section 5 discusses the research contributions and shortcomings, and
conclusions are drawn in Section 6.

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2. Urban material stock quantification
A wealth of research has been conducted to quantify UMS. Following the widespread
categorizations as adopted in the literature (see Table 1), we classified previous approaches
into two types, namely top-down approaches and bottom-up approaches.

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Table 1. Approaches for quantifying urban material stock
Type and
principle

basic

Top-down
approaches:
MS = I−O

Variable

Material
inflow
(I,
unit: tonne)

Material
outflow (O,
unit: tonne)

Number
of
cohorts
(N,
unit: cohort)

Bottom-up
approaches:
MS = ∑𝑁𝑁
𝑖𝑖=1 𝐺𝐺𝐺𝐺𝐺𝐺 ×
MI

Gross floor
area
(GFA,
2
unit: m )

Variable gauging solution
Directly extracting from material flow
statistic reports
Multiplying construction activity amount
(construction floor area or construction
expense) by material input rate (material
weight per floor area or expense)
Multiplying material inflows by assumed
stock survival probability distributions
(e.g., normal distribution)
Summing up C&D waste estimated based
on waste generation rates
Summing all building clusters divided by
one or multiple criteria (e.g., usage type,
building year, structure type).
Multiplying population by floor area per
capita (exclusive for residential buildings)
Directly extracting from governmental
building area statistic reports
Extracting data from digital databases
(e.g., GIS database, land-use database,
Google
Maps
database,
aerial
photographs, earth-observation raster
data) and then transforming them to the
gross floor area
Multiplying night-time light radiance by
transformation coefficients

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Representative study
Fishman et al. (2014)

Hashimoto et al. (2009))

Bergsdal et al. (2007)
Wang et al. (2019)
Bergsdal et al. (2007);
Ergun and Gorgolewski
(2015); Mao et al.
(2020); Miatto et al.
(2019)
Müller (2006)
Ortlepp et al. (2016)
Haberl et al. (2021);
Marcellus‐Zamora et al.
(2016); Tanikawa and
Hashimoto
(2009);
Wang et al. (2019)
Peled and
(2021)

Fishman

Material
intensity (MI,
unit:
tonne/m2)

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Directly extracted from public data (e.g.,
statistics reports, building specifications,
design codes; or construction handbooks)
Interviewing experts
Calculating based on building documents
(e.g., drawings and bill of quantities) and
sample measuring

Hashimoto et al. (2007);
Mesta et al. (2019);
Tanikawa et al. (2015)
Bergsdal et al. (2007)
Ergun and Gorgolewski
(2015)

2.1 Top-down approaches
Top-down approaches estimate construction material stock by calculating the difference
between material inflows and outflows; that is, construction materials input and output from
in-use buildings, respectively. There are two ways to estimate material inflows: 1) directly
extracting them from material inflow statistics, and then, 2) multiplying the quantity of
construction activities by a material input rate. Material outflows can be obtained by: 1)
multiplying material inflows by an assumed stock survival probability distribution; or 2) adding
up the construction waste quantity from new C&D activities. These approaches are mainly used
to derive the material stock of countries or regions, and uncover the evolution of construction
material stocks over a period by combining temporal material flows.
2.2 Bottom-up approaches
Bottom-up approaches mean to sum up the total material bank building by building. It involves
three variables: 1) number of building cohorts, 2) gross floor area (GFA) of each building
cohort, and 3) typical material intensity of each building cohort. Since no two buildings in a
building cohort have the same material stock, ideally this would be quantified building by
building. However, the cost to do so would be prohibitively high. In a trade-off between
accuracy and cost, previous studies chose to classify buildings into multiple cohorts according
to certain criteria such as building age, usage type, and structure type (Kleemann et al., 2017;
Mesta et al., 2019).
Researchers have proposed various methods to calculate GFA. Müller (2006) proposed to
multiply the population by floor area per capita to estimate the GFA of residential buildings.
Increasingly, governments start to issue building area statistical reports, from which researchers
can directly extract GFA data for their uses (Han & Xiang, 2013; Ortlepp et al., 2016). Urban
digital databases (e.g., GIS, building footprint databases) also enable researchers to aggregate
GFA via simple data extraction and transformation (Haberl et al., 2021; Marcellus‐Zamora et
al., 2016). Peled and Fishman (2021) innovatively used night-time light radiance data to
calculate GFA in Europe.
Material intensity, or ‘building material composition’, describes the construction material
weight per GFA. It represents the typical material composition of each building cohort. One
method used to obtain material intensities is to estimate based on public data, including
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building specifications (Tanikawa & Hashimoto, 2009), design codes (Han & Xiang, 2013),
and construction handbooks (Gao et al., 2020). When these public data sets are unavailable or
incomplete, researchers tended to interview local experts (Bergsdal et al., 2007; Mesta et al.,
2019). The third method is to calculate material intensities based on building documents
gathered, such as drawings (Kleemann et al., 2017; Nasiri et al., 2021) and bill of quantities
(Mao et al., 2020), with site visits to collect supplementary data (Surahman et al., 2017). Since
cost and time limits, researchers usually sampled one or several representative buildings from
different cohorts, and then applied the abovementioned methods to derive representative
material intensities.
2.3 Strengths and weaknesses of existing approaches
Top-down approaches are convenient and efficient. However, they involve simplified building
lifespan assumptions (Fishman et al., 2014), and estimated coefficients, e.g., material input rate
(Hashimoto et al., 2009), or waste generation rate (Wang et al., 2019), which may lead to large
deviations in the final estimate. Also, they rely heavily on the availability of statistical data
about material inflows or construction activities. Therefore, they are mainly applicable for
national or regional material stock quantification.
By comparison, bottom-up approaches can quantify material stocks at a micro spatial scale.
However, it also has two weaknesses. The typical material intensity of each building cohort is
usually derived based on one or several sampled building representatives. Sampling
representative buildings inevitably leads to bias in the quantification result due to building
heterogeneity (Mollaei et al., 2021; Stephan & Athanassiadis, 2017). Furthermore, no research
explains why a building is representative (Brøgger & Wittchen, 2018). Inappropriate selection
of representative buildings will also cause inaccurate UMS quantification. Therefore, in short,
the crux is the quantification of BMS. Another weakness of the bottom-up approaches is that
little research has derived material intensities by using real-life material stock data. This may
be due to the difficulty of weighing all construction materials in a building.
3. Methodology
3.1 The rationale
The rationale of our BMS quantification approach is intuitive: there should be a correlation
between building material stock and building features. Generally, for the geometrical features
(i.e., building height, floor area, perimeter, and storeys), any increase will naturally result in a
rise in BMS. Some semantic features also impact BMS. For instance, Mao et al. (2020) and
Kleemann et al. (2017) demonstrated that building age is related to BMS, as different building
materials and codes may have been adopted in different eras. Mastrucci et al. (2017) and Lanau
and Liu (2020) showed that BMS also depends on building usage (e.g., residential or
commercial). Usually, these visible building features are easy to obtain, e.g., by referring to
drawings, building approvals, or simple surveys. If a reliable correlation between a building’s
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features and its embodied material stock can be ascertained, the BMS can be accurately
estimated rather than waiting for the building to be demolished and its materials to be
segregated and weighed.
3.2 Research methods
Figure 1 illustrates our proposed BMS quantification approach. At the core of the approach is
machine learning (ML) regression. According to Ij (2018), traditional statistical regression
mainly infers and interprets the relationships between the dependent variable (e.g., the BMS)
and one or more independent variables (e.g., building features). In the end, a human
interpretable model like 𝑦𝑦 = 𝑎𝑎𝑖𝑖 𝑥𝑥𝑖𝑖 + 𝑏𝑏 or non-linear relationships will be derived. Unlike
traditional statistical regression, ML regression aims to construct a generalizable model that
can accurately predict the unobserved output (Ij, 2018). It is largely a data-driven approach by
choosing a regression algorithm and harnessing the power of data. In other words, it may lead
to a satisfactory predicting model that can be applied for specific objectives such as BMS
estimation, although the model itself may not be human-interpretable. Given the primary aim
of the research, ML regression is chosen.

Figure 1. Framework of the proposed UMS quantification approach
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3.3 Data collection
Two data sets from the same batch of buildings are needed: construction material stocks (by
weight) and building features. For the former, in 2005 the Hong Kong Environmental
Protection Department (HKEPD) established a Construction Waste Disposal Charge Scheme
to manage C&D waste. According to the Scheme, any building demolition project with a
contract sum of more than HK$ 1 million must apply for a sole disposal account from the
HKEPD. This account records the features of the demolition project (e.g., location, client, and
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contract sum) and the details (e.g., weight-in, weight-out) of every truckload of demolition
waste material disposed of at government facilities.
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Figure 2 illustrates the C&D waste disposal and recording system in Hong Kong. Because the
Scheme adopts a closed-loop management approach, any piece of demolished waste, unless
properly reused or recycled, must be disposed of at government facilities and use the account
opened with the HKEPD (Yuan et al., 2013). We thus consider that the total waste materials
derived from an account accurately represent the material stock of that building, with a caveat
that a few materials might have been reused or recycled elsewhere and hence not been properly
recorded in the system. We obtained the accounts of 433 demolition projects implemented
between 2011 and 2020 with a contract sum larger than HK$1 million. We then derived the
weight of waste materials for individual buildings.

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Figure 2. The construction and demolition waste disposal and recording system in Hong Kong

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Then, we acquired the building feature data. Based on the building location recorded in the
accounts, we first used Google Earth 3D views to count total floor number (above ground) of
the building. Building height, floor area, and perimeter were then derived by using iB1000
(HKLD, 2022a), which is a 1:1,000 digital topographic map issued by the Lands Department
providing address, hydrography, land coverage, place of interest, relief, transportation, and
utility information of all buildings in Hong Kong. For those buildings that had been wiped from
the iB1000 database, their heights, floor areas, and perimeters were obtained from Google
Earth and Google Maps. To derive building usage types (i.e., residential or non-residential),
we referred to the Planning Department’s land utilization type database (HKPD, 2021).
Building ages were gathered via housing agencies’ websites.
Figure 3 shows the data collection process. We finally collected a data set of 71 buildings.
Figure 4(a) visualizes the structure of collected data. The data set contains the building stocks
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and six easy-to-obtain building features: (1) building year, (2) total floor number, (3) building
height, (4) total floor area, (5) building perimeter, and (6) building usage type. Given Hong
Kong’s hilly terrain and steep slopes, it is a common practice to build a podium and then
construct multiple high-rise towers on it. Therefore, this study further divides a building into
two parts: building blocks and podium. When a building has no podium, the value of the
podium variable is set to zero.

Figure 3. An illustration of the data collection processes
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Figure 4. (a) The structure of collected data; (b) The data distribution under four common
building categorization features (underlying data for Figure 4b are available in Table S2 of
Supporting Information S1)
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At a glimpse, the 71 buildings consist of 44 residential and 27 non-residential buildings. Their
building years range from 1930 to 1999 with most between 1950 and 1980. 65 out of the 71
buildings have no podium. Building heights range from 4.0m to 88.8m and the total floor
numbers range from 1 to 26. The building material stocks range from 299 to 9,967 tonnes with
most concentrating between 840 and 2,800 tonnes. It is noticed that the material stocks have
no detailed composition information, e.g., inert or non-inert; concrete, copper, steel, etc.).
Figure (4)b presents the data distribution in line with four building features.
4. Model development
4.1 Selecting building features
Building features are independent variables. Previous studies indicate that BMS is correlated
with building geometrical features such as GFA (Nasiri et al., 2021), building height
(Kleemann et al., 2017), and perimeter-area ratio (i.e., perimeter per unit floor area) (Stephan
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& Athanassiadis, 2017); as well as semantic features such as building type (e.g., residential,
non-residential) (Gontia et al., 2019). We also referred to the building features used in other
research domains, such as building energy consumption prediction (Fan et al., 2014;
Seyedzadeh et al., 2018) and C&D waste estimation (Lu et al., 2021; Maués et al., 2020),
particularly on demolition waste generation (Chen & Lu, 2017; Lu et al., 2016). By combining
the previous literature with the data presented in Figure 4, we sourced 33 building features that
might be relevant to BMS quantification (see Table 2). In addition, we were aware of the
presence of other potential features, such as roof type, façade material, and so on. However,
this research does not consider them due to the data availability limitation.
Table 2. The 33 building features relevant to BMS quantification
Type

Data

collection

or

Name

Symbol

Building block height

Hblock

Building block floor area

FAblock

The number of building block floors

FNblock

Building block perimeter

Pblock

Original

Building podium height

Hpodium

Collecting

variables

Building podium floor area

FApodium

sources

The number of building podium floors

FNpodium

Building podium perimeter

Ppodium

Building year

Ybuilt

Building type (residential vs. non-residential)

UT

Building block floor height

FHblock

Building block façade area

FCAblock

Gross volume of building block

GVblock

Gross floor area of building block

GFAblock

Height-floor area ratio of building block

H/FAblock

FAblock×FNblock

Envelope-gross volume ratio of building block

E/GVblock

(FCAblock+FAblock)÷GVblock

Perimeter-floor area ratio of building block

P/FAblock

Composite

Building podium floor height

FHpodium

variables

Building podium façade area

FCApodium

Gross volume of building podium

GVpodium

Gross floor area of building podium

GFApodium

Height-floor area ratio of building podium

H/FApodium

FApodium×FNpodium

Envelope-gross volume ratio of building podium

E/GVpodium

(FCApodium+FApodium)÷GVpodium

Perimeter-floor area ratio of building podium

P/FApodium

Total building height

Htotal

Total number of floors

FNtotal

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calculation methods

from

the

first

Hblock÷FNblock
Pblock×Hblock

FAblock×Hblock

Hblock÷FAblock
Pblock÷FAblock

Hpodium÷FNpodium
Ppodium×Hpodium

FApodium×Hpodium

Hpodium÷FApodium
Ppodium÷FApodium
Hblock+Hpodium

FNblock+FNpodium

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Total façade area

FCAtotal

FCAblock+FCApodium

Gross floor area

GFAtotal

GFAblock+GVpodium

Gross building volume

GVtotal

GVblock+ GVpodium

Mean floor height

FHmean

(FHblock+FHpodium)÷2

Mean height-floor area ratio

H/FAmean

(H/FAblock+ H/FApodium)÷2

Mean envelope-gross volume ratio

E/GVmean

(E/GVblock+ E/GVpodium)÷2

Mean perimeter-floor area ratio

P/FAmean

(P/FAblock+ P/FApodium)÷2

Notes: (1) For the definition of features such as block, and podium; as well as the calculation method of building
height, perimeter, and floor area, please refer to HKLD (2022b); (2) We have conducted a preliminary regression
prediction experiment, which demonstrated that re-categorizing the original six building types into two categories
is optimal.

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Of the features, 10 are original variables derived from original data collection while the other
23 features are composite variables, which means they are made up of two or more variables
or measures that are highly related to one another. Using composite variables is a common
practice for organizing multiple highly correlated variables into more concise yet meaningful
ones (Song et al., 2013). Among the 33 feature variables, some of them are cross-correlated
(e.g., Hblock and FNblock). In statistical regression, the cross-correlation may result in the
multicollinearity problem, affecting the coefficient estimation of independent variables. For
regression prediction performance, however, one does not need to worry about the specific role
of independent variables and their multicollinearity. According to Kutner et al. (2004),
multicollinearity would not change regression prediction performance.

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It is not necessarily a case of the more variables, the better a model performs (Guyon &
Elisseeff, 2006). It is thus critical to choose appropriate variables for an ML regression. There
are three methods for variable selection. The Filter method uses variable ranking techniques
for variable selection (Chandrashekar and Sahin (2014). A suitable ranking criterion (e.g.,
Pearson’s r) is used to score variables and a threshold is used to remove variables below the
threshold. Its drawbacks are that the selected variables might not be optimal, and a redundant
subset might be obtained. The Wrapper method decides the best variable subset by comparing
the real model performance when inputting different variable combinations. Its shortcoming is
the huge computation cost to exhaust all feature combinations. Finally, the Embedded method
also compares the real model performance, but it integrates feature ranking techniques to
optimize the computation cost. In this study, we adopt the Embedded method to investigate the
best combination of variables (i.e., building features). The general procedure of the Embedded
method can refer to the work by Lal et al. (2006) and Chandrashekar and Sahin (2014).
4.2 Choosing machine learning regression algorithms
To determine an appropriate ML regression algorithm, the types of output variables must be
considered. For a categorical variable with different logistic values, logistic regression
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algorithms are recommended (Nasteski, 2017). When the variables are continuous, there are
six types of ML regression algorithms: multiple linear regression, support vector machine
regression, tree regression, Gaussian process regression, tree regression ensemble, and
regression neural network algorithms (Fahrmeir et al., 2021). In this study, the dependent
variable (i.e., material stock of buildings) is continuous. However, it is unknown which one of
the six algorithms is better. Therefore, we compared these regression algorithms to ascertain
the one with the best predicting performance.

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The comparison requires one or more model evaluation criteria. Five criteria, namely mean
squared error (MSE), root-mean-squared error (RMSE), mean absolute error (MAE), mean
absolute percentage error (MAPE), and R-square, are usually used to evaluate the predicting
performance of regression models (Emmert-Streib & Dehmer, 2019). In this study, the ML
regression model is expected to estimate the BMS with high accuracy. Thus, MAPE, which
indicates the regression model accuracy (accuracy=100% − MAPE), is the top choice. RMSE
and R-square are also selected for evaluating the accuracy of the estimate.
4.3 Data preparation

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Prior to ML regression model training and validation, it is necessary to conduct data
normalization and division. Data normalization, which means scaling data to a defined interval
(Luor, 2015), is needed due to the big magnitude order difference of different feature data. For
example, the GFA ranges from 219.77 to 41,077.04 (unit: m2) whereas the total floor number
only ranges from 1 to 26 (unit: floor). The range difference has negative impacts on the
performance of regression models that leverage the relative weight of features (Gal &
Rubinfeld, 2019). Among the multiple applicable data normalization methods, this study used
𝑧𝑧-score scaling to normalize feature data. 𝑧𝑧-score scaling transforms a data sample into a new
set with a mean value of 0 and a standard deviation of 1, by using Equation (1):
z-score value=

𝑋𝑋𝑖𝑖 −𝜇𝜇

𝜎𝜎

(1)

where 𝑋𝑋𝑖𝑖 is an observation value of a feature. 𝜇𝜇 and 𝜎𝜎 are the mean and standard deviation of
all observation values of the feature, respectively.
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Data division aims to split all sample data into two datasets, one for model training and the
other for model validation. When the collected data sample is big enough, the popular method
is to randomly split 70~80% of the sample for model training, while using the rest 20~30% for
model validation. When sample data is not abundant, like in this case, k-fold cross-validation
is recommended. Cross-validation is a resampling technique that uses different portions of the
data to train and test a model on different iterations (Browne, 2000). However, for a small
training data sample, the probability of model overfitting would be high (Karystinos & Pados,
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2000). Overfitting means a model performs well on the small data sample in model training
but badly in predicting based on new, unseen input data (Mohri et al., 2018). Under this
circumstance, a recommended solution is to synthesize the new data based on the original data
to expand the training dataset for model training (Karystinos & Pados, 2000; Ying, 2019). Data
synthesis is akin to transferring the training data insufficiency problem to the classical data
imbalance problem, and then solving it using oversampling techniques (Sharma et al., 2021).
With 33 determined building features, the data size of the 71 buildings is actually rather small.
This study thus used the data synthesis technique to prepare datasets for model training and
validation. Following the comparative analysis conducted by Aborujilah et al. (2020), this
study chose the Bootstrap algorithm to synthesize new data. The specific data preparation
process is as follows:
1) Shuffling the 71 samples and randomly extracting 50 of them as model training data
and the remaining 21 for model testing;
2) Based on the training sample of 50 buildings, using the Bootstrap algorithm to
synthesize new data until the sample is expanded to 1000;
3) Training an ML regression model based on the 1000 samples;
4) Testing the trained model by using the remained 21 samples and recording model
performance; and
5) Repeating steps 1–4 ten times and then calculating the average model performance.
This is equivalent to 10-fold cross-validation.
4.4 Model training and validation
Based on the Embedded feature selection method, we first conducted experiments to find out
the best feature combination for every determined ML regression algorithm. The experiments
were implemented in the MATLAB platform. Specifically, we used the F-test to calculate the
importance score of each feature and ranked them based on the score (MathWorks, 2022) (See
Figure 5(a)). Round by round, the feature with the lowest importance score was removed while
the rest features were used as the model input. With 33 building features and six types of
regression algorithms, 198 rounds of experiments were conducted to obtain the best
combination of building features for each type of regression algorithm.

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Figure 5. (a) Feature importance score ranking by using the F-test algorithm; (b) The change
of MAPE when inputting different feature subsets and using different ML regression
algorithms (MLR: multiple linear regression, SVMR: support vector machine regression, TR:
tree regression, GPR: Gaussian process regression, TRE: tree regression ensemble, RNN:
regression neural network; underlying data for Figure 5a&b are respectively available in Table
S2&S3 of Supporting Information S2)

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The feature selection experiment results are shown in Figure 5(b), which presents how the
MAPE changes in line with the number of selected features. The feature number that
corresponds to the lowest MAPE represents the optimal result. As shown in filled dots in Figure
5(b), the optimal building feature numbers are 19 for multiple linear regression algorithm, 18
for support vector machine regression algorithm, 16 for tree regression algorithm, 10 for
Gaussian process regression algorithm, 7 for tree regression ensemble algorithm, and 5 for
regression neural network algorithm. In addition, under a certain optimal feature number, the
specific features, which constitute the best feature combination, were identified and then
extracted from the full feature set (see Table 2) for further experiments.

380
Based on the best feature combination of each regression algorithm, we conducted experiments
to explore the regression model that has the best performance in estimating material stocks. Six
different models were trained and tested. Table 3 summarizes the experimental results. When
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measured by MAPE, the multiple linear regression model is the best because of showing the
smallest MAPE (9.1%). This value means the model estimation accuracy reaches 90.9%.
Meanwhile, the regression tree model is also acceptable, with a MAPE of 27.5% which is
equivalent to an accuracy of 72.5%. If only considering RMSE, the regression tree ensemble
model performs better than the multiple linear models. However, both of them are excellent.
When focusing on the R-square metric, both the multiple linear regression model and the
regression tree ensemble model perform well, respectively being 0.93 and 0.78. In this study,
the best model is determined by considering the MAPE, RMSE, and R-square together.
Therefore, the trained multiple linear regression model with 19 building features is
recommended for estimating BMS.
Table 3. The performance of models using different ML regression algorithms
Regression model algorithm
Multiple linear regression
Support vector machine regression
Regression tree
Gaussian process regression
Regression tree ensemble
Regression neural network

400

Model’s MAPE
9.1%
48.1%
27.5%
44.8%
34.2%
32.3%

Model’s RMSE
474.13
1325.70
1,050.50
1,904.41
448.25
1,302.44

Model’s R-square
0.93
0.21
0.46
0.28
0.78
0.33

Referring to existing regression prediction studies, a consensus is that both MAPE<10% and
R-square>0.9 represent a good model performance. Thus, the multiple linear regression model
developed by using the data of the 71 buildings is sufficient for BMS estimation. Besides,
unlike traditional statistical regression models, the trained multiple linear regression model is
an ML model that consists of 121 function terms. It is therefore difficult to express it in
mathematical forms or interpret it by a human. We can treat the model as a ‘black box’
considering the primary concern is its estimation performance. Equation (2) outlines the ML
regression model:

405
� = ℱ(Htotal, GFAtotal, GVtotal, P/FAblock, FNtotal, Ybuilt, FAblock, Pblock, FNblock, UT,
𝑀𝑀𝑀𝑀
P/FAmean, FCAblock, FHblock, FHmean, H/FAblock, H/FAmean, GVblock, E/GVblock,
E/GVmean)

(2)

� refers to the estimated material stock of buildings, and the building features are
where 𝑀𝑀𝑀𝑀
defined in Table 2.
410

4.5 Model application
When applying the model to estimate the BMS, one needs to firstly collect six types of building
features, including building type, building year, height, perimeter, floor area, and total floor
number. Generally, benefiting from various urban digitalization initiatives, acquiring these data
is no longer difficult. Building height, floor area, perimeter, and total floor number can be
15

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obtained from Google Maps, Google Earth, and other available map databases like the iB1000
used in this research. The building type can be derived from land-use databases issued by the
Land Department. The building year can be gathered by browsing the website of real estate
agencies, calculating the average age of surrounding buildings (Aksözen et al., 2017), or
making inferences based on some features (Biljecki & Sindram, 2017).

420

425

With the six types of data and the formulas shown in Table 2, the value of the 19 input variables
can be smoothly derived and then combined into a matrix, which will be further normalized by
using the z-score algorithm (see Equation [1] above). The input variable sequence in the matrix
refers to Equation (2). The MATLAB code for calling the model is EMS =
predict(MSmodel_multipleLinearRegression, matrix). Here EMS is ‘estimated material stock’.
It represents the output of material stock estimation by weight. Predict is a common MATLAB
program language for calling trained models, and MSmodel_multipleLinearRegression is the
name of the multiple linear regression model developed by this research. We have encoded and
shared the BMS quantification model through a GitHub link (Yuan et al., 2022).

430

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445

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5. Discussion
The key to UMS quantification, whether bottom-up or top-down, lies in the accurate estimation
of material stocks at the individual building or infrastructure level. The biggest challenge faced
by current studies of this kind is the lack of ground-truth data to verify their results, as the data
are only available if the building is demolished and its embodied materials are properly
measured. Benefiting from a valuable dataset related to 71 demolished buildings in Hong Kong,
this research developed a BMS estimation model by using simple and easy-to-obtain building
features.
This research makes two contributions. Firstly, it contributes a novel approach to UMS
quantification by dealing with it at the building level. With reliable BMS being quantified, it is
possible to scale up the estimate to neighbourhood, city, region, and even national scales for
applications such as modelling urban metabolism, urban mining, and national resource
planning. However, information on overall material stocks is also desired in multiple
application scenarios such as stock-enabled socio-economic metabolism analysis (Fishman et
al., 2015; Guo et al., 2019), spatiotemporal stock dynamic analysis (Marcellus‐Zamora et al.,
2016; Mastrucci et al., 2017; Mollaei et al., 2021), and so on. The approach is also able to
support microscopic material stock management, e.g., proper deconstruction for cross-project
waste material sharing or cross-jurisdiction construction waste material trading. Secondly, the
research makes a methodological contribution to the UMS quantification domain. Unlike
previous top-down and bottom-up approaches, this research successfully demonstrated that
BMS can be accurately estimated by using six easy-to-obtain building features and ML
regression algorithms. This provides a novel UMS quantification perspective and, more
importantly, contributes a methodology that can be used in other regions.
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460

465

470

475

480

485

This study is not free from shortcomings. Firstly, it might be difficult for other interested
researchers to obtain similar ground truth data in other cities. Nevertheless, this difficulty is
increasingly relieved. More and more cities have started to implement construction waste
disposal levy schemes. These schemes may help capture and record various data in a central
place. The demolition data like Hong Kong’s may just stay with these related government
departments without being harnessed. Our research is thus inspiring for researchers to tap into
these data sets as “buried assets”. Moreover, demolition data sets can also be obtained from
demolition companies. We noticed this from previous studies, such as Kleemann et al. (2016)
and Sprecher et al. (2021). Secondly, this study does not measure the detailed material
composition of the BMS. This is attributable to the fact that the demolition data recorded inert
and non-inert portions only. Notably, several leading construction companies in town have
started to delve into the detailed compositions for internal material management. There are also
research teams trying to use computer vision or other machine learning means to obtain the
detailed waste compositions (Chen et al., 2021; Dong et al., 2022). Furthermore, with the
accurate overall stock estimate, the specific material stock can also be derived through the
following steps: 1) grouping the overall stock according to building cohort classifications, 2)
obtaining the typical material composition of each building cohort, and 3) multiplying each
group of stocks by corresponding typical material composition to obtain stock by material
categories. Lastly, the research did not cover urban infrastructure as another component of
UMS. Future studies can expand to this important sector.
6. Conclusion
Previous studies have successfully introduced many urban material stock (UMS) quantification
approaches. However, their common crux is to have a relatively accurate estimate of a building
material stock (BMS). One cannot ascertain whether his/her estimate of a BMS is accurate
before the building is demolished and its embodied materials are separated and weighed. This
research aimed to develop a BMS quantification model based on some easy-to-obtain building
features without necessarily demolishing and weighing the building. Using 71 demolished
buildings in Hong Kong as a valuable sample and machine learning regression techniques, we
discovered that six building features, namely (1) building type, (2) building year, (3) height,
(4) perimeter, (5) total floor area, and (6) total floor number can satisfactorily predict the BMS
of individual buildings. A trained multiple linear regression model has a performance of mean
absolute percentage error (MAPE) of 9.1%, root-mean-square error (RMSE) of 474.13, and Rsquare of 0.93. By summing up the BMS, a reasonably accurate UMS estimate can be derived.

490
This research provides an innovative solution to UMS quantification, BMS in particular, by
using several simple and visible building features. The research is data-driven and rigorous.
However, the data-driven approach is like a ‘black box’ that is not readily accessible to us.
Future research is recommended to verify the model in other urban areas when data is available.
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Efforts should also be paid to make the BMS quantification model explainable to humans. In
addition, it would provide more valuable decision-making information if the BMS covers
detailed material compositions. Finally, similar research can be expanded to quantify IMS so
as to derive a complete UMS. Further studies are encouraged to cover these limitations in the
future.

500
Acknowledgement
This research is jointly supported by the Strategic Public Policy Research (SPPR) (Project No.:
S2018.A8.010.18S) Funding Schemes and the Environmental Conservation Fund (ECF)
(Project No.: ECF Project 111/2019) of the Hong Kong SAR Government.
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Conflict of Interest Statement
The authors declare no conflict of interest.
Data Availability Statement

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The building material stock data is available on request from the corresponding author. The
data is not publicly available due to privacy or ethical restrictions. The building feature-related
data were derived from the following resources available in the public domain:
(1) iB1000 Digital Map [https://www.hkmapservice.gov.hk/OneStopSystem/mapsearch?product=OSSCatB&series=iB1000];
(2) Land utilization type database of Hong Long

725

[https://www.pland.gov.hk/pland_en/info_serv/open_data/landu/];
(3) Google Earth [https://earth.google.com/]; and
(4) Housing agency websites such as SPACIOUS [https://www.spacious.hk/en/hongkong].

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Supporting information
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Supporting information can be found in the online version of the article at the publisher’s
website.

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