Estimation of construction waste composition based on bulk density: A big data-probability (BD-P) model
Liang Yuan, Weisheng Lu*, and Fan Xue
Department of Real Estate and Construction, Faculty of Architecture, the University of Hong
Kong, Hong Kong, China (*: corresponding author email: wilsonlu@hku.hk)
This is the peer-reviewed post-print version of the paper:
Yuan, L., Lu, W., & Xue, F. (2021). Estimation of construction waste composition
based on bulk density: a big data-probability (BD-P) model. Journal of Environmental
Management, 292, Article ID 112822. Doi: 10.1016/j.jenvman.2021.112822.
The final version of this paper is available at: https://doi.org/10.1016/j.jenvman.2021.112822.
The use of this file must follow the Creative Commons Attribution Non-Commercial No
Derivatives License, as required by Elsevier’s policy.
Abstract

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Estimating the composition of construction waste is crucial to the efficient operation of various
waste management facilities, such as landfills, public fills, and sorting plants. However, this
estimating task is often challenged by the desire of quickness and accuracy in real-life scenarios.
By harnessing a valuable data set in Hong Kong, this research develops a big data-probability
(BD-P) model to estimate construction waste composition based on bulk density. Using a
saturated data set of 4.27 million truckloads of construction waste, the probability distribution
of construction waste bulk density is derived, and then, based on the Law of Joint Probability,
the BD-P model is developed. A validation experiment using 604 ground truth data entries
indicates a model accuracy of 90.2%, Area Under Curve (AUC) of 0.8775, and speed of around
52 seconds per load in estimating the composition of each incoming construction waste load.
The BD-P model also informed a linear model which can perform the estimation with an
accuracy of 88.8% but consuming 0.4 seconds per case. The major novelty of this research is
to harmonize big data analytics and traditional probability theories in improving the classic
challenge of predictive analyses. In the practical sphere, it satisfactorily solves the construction
waste estimation problem faced by many waste management facility operators. In the academic
sphere, this research provides a vivid example that big data and theories are not adversaries, but
allies.
Keywords: Big Data; Probability; Big Data Enabled Probabilistic Analysis; Construction
Waste; Composition Estimation
1. Introduction

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Construction waste, sometimes also called construction and demolition (C&D) waste, is the
solid waste generated from site clearance, soil excavation, new building, refurbishment,
renovation, demolition, and other construction activities (HKEPD, 2019; Lu et al., 2020). It is
often composed of both inert and non-inert construction materials (UK DEFRA, 2020;
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Australian Government, 2011; HKEPD, 2008). The former includes clay, earth, concrete,
rubble, and bitumen, while the latter includes wood, bamboo, paper, plastics, and vegetation
(Aslam et al., 2020; EPA, 1997; EU, 2018). Prevalent construction waste management (CWM)
systems normally stipulate different disposal destinations of C&D waste depending on its
composition. For example, in the U.S., most C&D waste is lawfully destined for disposal in
landfills regulated under Title 40 of the Code of Federal Regulations (CFR) (Allegri, 1986). In
Hong Kong, non-inert waste goes to landfills or incinerators, inert waste to public fills or
recycling plants, and mixed waste to sorting facilities (HKEPD, 2008). It is common that the
facilities will have to determine admissibility or chargeable waste disposal levy, depending on
waste composition. For example, in the Australian state of New South Wales, the Protection of
the Environment Operations (Waste) Regulation (NSWEPA, 2020) and the Waste Levy
Guidelines (NSWEPA, 2014) set out waste composition calculations and waste levy details.
Recognition of waste composition also needs to be done swiftly, since many users are queuing
outside the facilities. Therefore, quick and accurate estimation of construction waste
composition is key to these CWM facilities or even the entire CWM system.
Previous methods for estimating waste composition can be roughly classified into three
categories: statistical sampling, photogrammetry, and other non-invasive approaches. The
statistical sampling approach classifies, weighs, and calculates the percentage of each type of
waste material in a sample. It is widely used to analyze construction waste component
characteristics in a specific region (Asgari et al., 2017; Cochran et al., 2007; Hoang et al., 2020),
different project types (Villoria Sáez et al., 2012), or different construction stages (Wu et al.,
2019). However, a drawback of the approach is its inefficiency due to requiring onerous manual
operation. The photogrammetry-based approach uses algorithms to deal with the collected
visual imagery of construction waste for recognizing its composition. Visual features recorded,
measured and interpreted in photogrammetry include shape, pattern, gradation, and size (Chen
et al., 2021; Califice et al., 2013; Paine & Kiser, 2012). The photogrammetry-based approach
had received attention around ten years ago (Wagland et al., 2012) and is still topical nowadays
(Davis et al., 2021) for academic studies and practical applications. The advantage of such
approach is to reduce the onerous manual operation (Peddireddy et al., 2015; Wagland et al.,
2012), but the downside is that construction waste must be spread evenly to a depth (generally
no greater than 30 cm) for waste components to be visually recognised (Wagland et al., 2012).
Based on an assumption that the visible surface composition reflects the total one, Chen et al.,
(2021) proposed a depth-controlling-free photogrammetry approach to gauge the composition
by looking at the surface of truck-loaded construction waste dumps. However, more proofs are
needed to prove the reliability and universality of the assumed condition. Other non-invasive
approaches to waste composition estimation have also been explored, e.g., using fluorescence
presence, microwave frequency measurement, and X-ray imaging (Vrancken et al., 2017).
While these approaches can capture component type information, they lack accuracy in
recording component weight and volume.
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This research aims to develop a quick and accurate approach to estimating construction waste
composition. It is a direct response to a real-life challenge as faced by the HKEPD
(Environmental Protection Department of Hong Kong), but we found parallels in many other
places such as India, Taiwan, and the UK wherein their CWM facilities also need to estimate
the composition of incoming waste bulks/loads quickly and accurately (see Figure 1).
Particularly, HKEPD is responsible for managing all C&D waste in the territory. It uses a tiered
system whereby all construction waste must be disposed of at governmental waste disposal
facilities, unless it is properly reused or recycled. A truckload of construction waste is sent to
public fills or a recycling plant if it contains purely inert materials, to a sorting plant if it contains
more than 50% inert materials by weight, or otherwise to landfill (Lu et al., 2016). Waste
producers are charged a landfill disposal fee of HK$200 per tonne, a sorting plant fee of
HK$175 per tonne, and HK$71 per tonne at public fills. Different levies and disposal
destinations generate the need for construction waste composition estimation. Based on the
empirical knowledge about the relationship between waste weight and composition, the
HKEPD uses a ‘quick and dirty’ approach to screen waste loads at its CWM facilities,
translating the weight and height of each load into a single index similar to a body mass index
(BMI). This approach, however, has been found problematic by a Hong Kong Audit
Commission review report (HKAC, 2016). It only had an accuracy of around 60%.

Figure 1. Equipment used to measure incoming waste loads (Sources: a: made by authors; b:
https://bit.ly/2MgdREa; c: https://bit.ly/399WQoh; d: https://bit.ly/3c2Jqfs;)

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Recent advancements in big data analytics suggest the potential for a solution to the waste
composition recognition problem. The promise of big data has been widely documented. For
example, it reveals that construction waste in a region is not entirely random in terms of its
composition (Lu et al., 2021). Constrained by the prevailing construction materials,
technologies, and waste recycling practices, the bulk density of different types of construction
waste should converge into an interval and follow a certain probability distribution pattern. If
we know the pattern, we should be able to tell the composition of an incoming truckload of
construction waste by its bulk density. A strength of big data is its ability to reach a closer truth
on the ground (LaValle et al., 2011; Lu et al., 2015). Having acquired a set of data concerning
millions of truckloads of construction waste disposed of in Hong Kong over the past ten years,
we are able to leverage this strength. The rest of the paper is organized as follows. Section 2
introduces bulk density and its probability distribution as informed by big data. Section 3
introduces the research methodology including the theoretical foundation and research methods.
The composition estimation model is explained in Section 4. Section 5 describes the model
validation experiment. Section 6 discusses the strengths, novelty, prospects, and challenges of
the approach, and conclusions are drawn in Section 7.
2. Bulk density and its probability distribution
Bulk density is the mass of material divided by the total volume it occupies, where the total
volume can include particle volume, inter-particle void volume, and internal pore volume (Lyon
& Buckman, 1922). True density, apparent density, and bulk density are the three kinds of
density in materials science. Figure 2 shows their differences and how they are calculated. Bulk
density is not an intrinsic material property. Rather, it is changeable in line with constitutional
material, pore, and inter-particle volume. Because of this, the bulk densities of construction
waste appear to be totally random since the constitutional materials could be any combination
of construction materials (e.g., concrete, clay, soil, rocks, paper, wood, vegetation), with any
size of pore voids and inter-particle voids. Nevertheless, our hypothesis is that bulk density in
a specific region should converge into an interval and follow a certain probability distribution
pattern, as it is determined by prevailing regional construction materials, technologies, and
waste recycling practices.

Figure 2. The three types of material densities and their calculation methods
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In practice, many CWM facilities have devised methods to measure the mass and volume of
waste loads on arrival. Figure 1 illustrates some equipment used. Specifically, at HKEPD’s
facilities (Figure 1a), the (net) weight of a load of C&D waste is calculated by weighing the
vehicle at the in- and out-weighbridges and subtracting the two. Waste volume is captured and
calculated using sensors above the in-weighbridge. Bulk density is then calculated using
Equation (1):
𝜌𝜌 =

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𝑊𝑊
𝑉𝑉

(1)

where ρ is the bulk density of a load of construction waste, W is the net weight, and V is the
total volume. As mentioned above, the concept is similar to that of BMI, which divides body
mass by the square of height. Despite having its critics, BMI is an easy-to-obtain and
comprehend indicator to measure whether a person is underweight, normal weight, overweight
or obese.
Using a big data set of 4.27 million truckloads of construction waste recorded by the HKEPD
from 2017 to 2020, the convergent bulk density intervals of inert and non-inert C&D waste
materials, and their probability distributions are derived as shown in Figure 3. The bulk density
of inert construction waste ranges from 0.207 tonnes/m3 to 2.435 tonnes/m3, and highly
concentrates at around 1.300 tonnes/m3 and 1.800 tonnes/m3. The bulk density of non-inert
construction waste is between around 0.045 tonnes/m3 and 2.434 tonnes/m3, and highly
concentrates at around 0.300 tonnes/m3. Although the exact cause of multiple crests is yet to be
fully understood, the big data paints a clear distribution pattern of bulk densities of construction
waste. This can be harnessed to estimate the composition of a new incoming waste load.

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Figure 3. The bulk density probability distributions of inert and non-inert construction waste
(Source: Adapted from Lu et al., 2021)
3. Research methodology
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3.1 Big data-enabled statistical probability
The theoretical underpinning of the methodology here is a novel combination of traditional
statistical probability theories with modern big data analytics. The classical statistical
probability theories define an event’s probability as the limit of its relative frequency in many
repeated trials (Neyman, 1937). Conducting sufficient repeated trials to derive the frequencies
and to ensure the trials are representative enough of the whole population is often too onerous
to accomplish. Monte Carlo simulation and similar methods can be used to circumvent this
problem, but such methods need to know the intervention of random variables. Modern
analytics of big data, which is accumulated unintentionally as the business is done, offer a
convenient means to this end. Big data can get researchers as close as possible to obtaining an
event’s probability, or even its totality. This has triggered a series of intellectual debate on the
relationship between big data and scientific methods. Succi and Coveney (2019), for example,
report that many researchers draw upon the Law of Large Numbers and foresee that with big
enough data, errors (uncertainty) are bound to surrender to certainty. Big data-enabled
correlation supersedes causation and science can advance even without coherent models,
unified theories, or any mechanistic explanations (Anderson, 2008). This has even prompted
the pronouncement that big data is the end of scientific theory.
Statistics and big data analytics are combined mainly in support of more accurate event
prediction. Using big data-enabled probability distribution for prediction or estimation is a
nascent field normally referred to as predictive analytics. Specifically, predictive analytics
refers to using current and historical data to predict future or unknown events (Waller & Fawcett,
2013). Emerging studies have adopted it in several domains. Zuccolotto et al. (2018) analyzed
the shooting performance of basketball players in high-pressure game situations by using the
big data on Olympic Basketball Tournament. Zhang et al. (2015) estimated the probability
distributions of safety distance of different-sized ships by using automatic identification system
data collected in Singapore’s port waters. Fu et al. (2018) proposed a big data-driven probability
model to estimate the probability of insufficient gas supply incidents due to weather uncertainty.
Li et al. (2017) developed a new method for tackling the problem of inaccurate disease
probability prediction in the field of big health. These studies demonstrate the promise of using
the big data-enabled probability distribution for predictive analysis. The key is to derive the
probability distribution of the target event from the big data set, and then use a proper theoretical
probability model (e.g., normal, lognormal, or Poisson distribution) to fit the distribution.
Finally, the fitted probability model is used for predicting or estimating future events.

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3.2 Harmonizing big data analytics and probability theories for waste composition
estimation
The bulk density probability distributions of inert and non-inert construction waste are complex,
showing two significant crests for non-inert waste and seven for inert waste (see Figure 3).
Finding a theoretical probability model to fit these two distributions is not easy. In the end,
inspired by Ross (2020), Scott (2018), and Torrecilla (2018), we decide not to fit theoretical
probability models but to use the unfitted probability distribution directly. The Law of Joint
Probability and Cumulative Distribution Function are adopted to build the core link of the
composition estimation model. Firstly, we need to derive the joint probabilities of all possible
composition forms (inert vs. non-inert composition) in a construction waste load. Then, we
adopt the cumulative distribution function to calculate the cumulative probability of the
composition belonging to a specific composition range or not.
The composition form of a construction waste load can be quantitatively expressed by the inert
component weight proportion in the total weight, denoted as 𝐼𝐼𝐼𝐼𝐼𝐼 (inert waste proportion).
With a known 𝐼𝐼𝐼𝐼𝐼𝐼, the non-inert component weight can be easily derived because a waste
bulk only consists of inert and non-inert parts. In this study, the output of construction waste
composition estimation is defined as the range of 𝐼𝐼𝐼𝐼𝐼𝐼, such as 𝐼𝐼𝐼𝐼𝐼𝐼 > 80%.
The two bulk density probability distributions presented in Figure 3 can be expressed in
Equation (2) and (3) as follows:
𝑃𝑃�𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝜌𝜌𝑗𝑗 � = 𝑃𝑃𝑗𝑗 ; 𝑗𝑗=1, 2, 3, …, 𝑛𝑛

𝑃𝑃(𝜌𝜌𝑛𝑛𝑛𝑛𝑛𝑛−𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝜌𝜌𝑘𝑘 ) = 𝑃𝑃𝑘𝑘 ; 𝑘𝑘=1, 2, 3, …, 𝑚𝑚

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(2)
(3)

where 𝜌𝜌𝑗𝑗 is one of the inert waste bulk densities (𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ), and 𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ∈ [0.207, 2.435] tonne/m3.

𝜌𝜌𝑘𝑘 is one of the non-inert waste bulk densities (𝜌𝜌𝑛𝑛𝑛𝑛𝑛𝑛−𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ), and 𝜌𝜌𝑛𝑛𝑛𝑛𝑛𝑛−𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ∈ [0.045, 2.434]
tonne/m3. 𝑛𝑛 and 𝑚𝑚 refer to the finite number of inert and non-inert composition bulk density
values respectively, and they depend on the decimal place determination of weight and volume.
Both the sum of all 𝑃𝑃𝑗𝑗 and the sum of all 𝑃𝑃𝑘𝑘 are 100%.

We know that a bulk of incoming construction waste contains inert and non-inert materials with
an unknown weight ratio. The total waste weight and volume can be obtained by using
measuring equipment as shown in Figure 1. The possible inert composition weight ranges from
zero to the total waste weight, and possible inert composition volume ranges from zero to the
total waste volume. Randomly selecting a value from the weight interval to be the weight of the
inert component of the construction waste load, and a value from the volume interval to be the
volume of the inert component, we can calculate an inert composition bulk density value (𝜌𝜌𝑗𝑗 )

by using the selected weight divided by the selected volume. The selected inert composition
weight and volume naturally determine non-inert composition weight and volume, because the
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waste load consists of inert and non-inert components only. We can thus calculate a non-inert
composition bulk density value (𝜌𝜌𝑘𝑘 ) by the same method. In this way, we can assume a possible
ratio of inert and non-inert composition in a waste load and calculate their respective bulk
densities by having a pair of weight and volume values.
If the derived 𝜌𝜌𝑗𝑗 belongs to 𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 interval and the derived 𝜌𝜌𝑘𝑘 belongs to 𝜌𝜌𝑛𝑛𝑛𝑛𝑛𝑛−𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 interval,

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the combination of 𝜌𝜌𝑗𝑗 and 𝜌𝜌𝑘𝑘 exactly represents one possible composition of the new incoming

waste load, denoted as 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 . We can obtain the probability of 𝜌𝜌𝑗𝑗 according to Equation (2) and
the probability of 𝜌𝜌𝑘𝑘 according to Equation (3). The joint probability of 𝜌𝜌𝑗𝑗 and 𝜌𝜌𝑘𝑘 can be

calculated using the law of joint probability (Kelley, 1994), as Equation (4):

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𝑃𝑃𝑖𝑖 = 𝑃𝑃�𝜌𝜌𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑃𝑃𝑗𝑗 ∩ 𝜌𝜌𝑛𝑛𝑛𝑛𝑛𝑛−𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑃𝑃𝑘𝑘 � = 𝑃𝑃𝑗𝑗 × 𝑃𝑃𝑘𝑘

where 𝑃𝑃𝑖𝑖 represents the probability of 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 . In other words, 𝑃𝑃𝑖𝑖 is the probability of one possible
composition.
Traversing all possible inert composition weight values in the interval between zero and the
total waste weight of the construction waste load, and all possible inert composition volume
values in the interval between zero and the total volume, we can obtain a data set of 𝐼𝐼𝐼𝐼𝐼𝐼 and
a data set of joint probabilities. Each 𝐼𝐼𝐼𝐼𝐼𝐼 value solely corresponds to one joint probability, the
two data sets thus form a new probability distribution regarding construction waste composition
𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 and corresponding joint probability 𝑃𝑃𝑖𝑖 , as shown in Equation (5):
𝑃𝑃(𝐼𝐼𝐼𝐼𝐼𝐼 = 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 ) = 𝑃𝑃𝑖𝑖 ; 𝑖𝑖=1, 2, 3, …, ℎ

(5)

𝐹𝐹(𝐶𝐶𝐶𝐶) = 𝑃𝑃(𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 > 𝑅𝑅) = � 𝑃𝑃𝑖𝑖

(6)

where ℎ refers to the finite number of 𝐼𝐼𝐼𝐼𝐼𝐼 values. Its finiteness results from manual operations
or the precision limitation of measuring equipment. The sum of all 𝑃𝑃𝑖𝑖 is 100%. As the
probability of 𝐼𝐼𝐼𝐼𝐼𝐼 belonging to a specific inert composition range is a cumulative probability,
and the probability distribution of all 𝐼𝐼𝐼𝐼𝐼𝐼 values has been derived as Equation (5), we can
calculate the probability of 𝐼𝐼𝐼𝐼𝐼𝐼 belonging to the specific inert composition range by using the
cumulative distribution function (Park & Park, 2018), as in Equation (6):

𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 >𝑅𝑅

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(4)

where 𝐶𝐶𝐶𝐶 is a specific inert composition range. 𝐹𝐹(𝐶𝐶𝐶𝐶) is the cumulative distribution function
of 𝑅𝑅.
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Figure 4 illustrates how the cumulative distribution function works. The inert composition
range 𝐶𝐶𝑅𝑅 in the example is arbitrarily set as 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 >53%. When a truckload of construction
waste is incoming (a) with the different possible composition of inert and non-inert materials,
the individual probabilities of inert and non-inert composition (b) will be calculated by referring
to the probability distribution patterns from the big data analytics. Then, the joint probability of
each possible composition state will be calculated (c). The combination of the joint probabilities
of all possible composition states is visualized in (d). Finally, the cumulative probability of the
composition states belonging to the set 𝐶𝐶𝑅𝑅 is calculated, as shown in the blue area of Figure 4
(e). Another part (namely, the orange area) represents the cumulative probability of the
composition states not belonging to the set 𝐶𝐶𝑅𝑅. The orange and blue areas in Figure 4 (e)
together present the probability distribution of all possible composition forms in the new
incoming construction waste load, and their sum is equal to 100%. By comparing the two
cumulative probabilities, if ‘𝐹𝐹(𝐶𝐶𝐶𝐶)’ is greater than ‘1- 𝐹𝐹(𝐶𝐶𝐶𝐶)’, the composition of the newly
incoming construction waste load belongs to the composition range of 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 ; otherwise, not
belongs. The estimation of waste composition is completed.

Figure 4. An example of cumulative probability calculations under a specific inert composition
range
4. Development of the BD-P Model

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Based on the research methodology as explained above, this section goes further to develop the
construction waste composition estimation model. Given that the model is the bulk density
probability distribution enabled by big data analytics, it is referred to as a big data-enabled
probability model (BD-P model). As shown in Figure 5, the model consists of three parts: 1)
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input collection to obtain the weight and volume of a construction waste load; 2) probability
calculation to calculate the probability of each possible composition state; and 3) composition
estimation to ascertain the composition of the construction waste load.
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Using the BD-P model for composition estimation mainly includes two steps. The first step is
measuring the weight and volume of construction waste. When there is an incoming truckload
of construction waste, the volume and weight of construction waste can be easily obtained by
using some on-site measuring equipment (see Figure 1) and combining pre-registered truck
body specifications. According to a site observation for industrial practice, the collection of
weight and volume generally takes one minute when using currently popular technologies and
equipment. The second step is feeding the obtained weight and volume into the BD-P model
for calculating construction waste composition.

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Figure 5. The architecture of the construction waste composition estimation model (BD-P
model)
5. Model Validation
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This section describes the experiments conducted to validate the BD-P model. It includes
constructing ground truth data set, determining evaluation criteria for model performance, and
analyzing experimental results.
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5.1 Constructing the “ground truth”
Performance testing of the BD-P model requires multiple composition-known construction
waste loads as ground truth data. In this study, raw ground truth data is collected from a
construction waste sorting facility (TKO137SF) in Hong Kong. This facility is designated to
receive and sort construction waste loads containing more than 50% inert composition by
weight (HKEPD, 2008). The admission system installed at the entrance of the facility captures
information about an incoming waste load to judge whether it contains more than 50% inert
composition by weight, and therefore whether to accept or reject the waste load. The admission
system will integrate all information regarding the waste load into a disposal record no matter
the waste load being rejected or accepted. A complete record contains 37 variables, including
total weight when the truck enters, weight when the truck exits, vehicle number, final decision
about acceptance or rejection, waste bulk height, waste load photos, permitted gross vehicle
weight (PGVW) of the hauling truck, facility name, date, and so on. We collected 22,800 such
records, covering all construction waste load disposal data at TKO137SF from September to
November 2019. The data set comprises 2,278 records for rejected waste loads (i.e., inert
composition weight less than 50% of total waste weight), and 20,522 records for accepted waste
loads (i.e., inert composition weight more than 50% of total waste weight). It is important to
note that the compositions of 251 loads among the accepted construction waste loads were
manually checked at the facility by experienced inspectors.
The collected data is used to construct a ground truth data set including positive and negative
data. In this study, the positive data refers to waste loads containing more than 50% inert
material by weight (i.e., 𝐼𝐼𝐼𝐼𝐼𝐼 >50%), and the negative data refers to waste loads containing
not more than 50% inert material by weight (i.e., 𝐼𝐼𝐼𝐼𝐼𝐼 ≤50%). In general, a larger size of the
ground truth dataset can promise a more reliable model accuracy (Krig, 2016), but collecting
more ground truth data is usually limited by time and cost viability, e.g., the manual separation
and inspection as at TKO137SF. A proper size is thus more feasible than a large size. Referring
to the method proposed by Sharma et al. (2017), this study determines the proper ground truth
dataset size when the model accuracy no longer changes significantly, i.e. stabilized or saturated.
Our preliminary experimental analyses found that the model accuracy starts to be stable when
the ground truth dataset size increases to around 600 data points with balanced positive and
negative data. Therefore, this study decided to construct a ground truth dataset containing
around 300 positive data and 300 negative data.
We can confidently adopt the 251 manually checked loads as positive ground truth data. For
the negative data, we selected 450 construction loads from the chronological 2,278 rejected
loads by the Equidistant Sampling method. However, we cannot directly use them as negative
ground truth data due to the auditing report finding that the admission system is not 100%
accurate. Therefore, using the admission system judgement as a reference, we combine the
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waste weight, waste bulk height, waste load photos, and domain knowledge to manually check
each rejected waste load’s state, and correct it when finding the admission system’s judgment
wrong (see Figure 7 for an example). Through these, 339 raw positive data records and 362 raw
negative data records are included in the ground truth data set. Finally, the data is further
cleansed and a ground truth dataset containing 604 records is generated for model validation
(see Figure 8).

Figure 7. An example of the manual check and correction (Note: for this truck type, the HKEPD
admission system makes the >50% inert composition decision on the basis of waste height
<1.6m and waste weight ratio >18% [HKEPD, 2019])

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365

370

375

380

Figure 8. The weight and volume distribution of 604 ground truth data
5.2 Determining evaluation criteria for model performance
Accuracy, speed, complexity, and receiver operating characteristic (ROC) curve are widely
used criteria for prediction model performance evaluation (Alpaydin, 2020; Yuan et al., 2020).
For construction waste composition estimation, a model with higher estimation accuracy and
speed is preferred for practical applications. Therefore, three indicators, namely accuracy, ROC
curve, and speed are chosen as the BD-P model performance evaluation metrics in this study.
Estimation accuracy has two calculation methods. Mean absolute percentage error (De
Myttenaere et al., 2016) is used when the estimated result is numerical, while Confusion Matrix
method (Alpaydin, 2020) is suitable when the estimated result is not numerical. The estimation
output in this study is not numerical, as shown in Figure 5 (Part III). Thus, the confusion matrix
method as shown in Equation (7) is adopted to calculate accuracy:
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 =

𝐴𝐴𝐴𝐴 + 𝑅𝑅𝑅𝑅
× 100%
𝐴𝐴𝐴𝐴 + 𝑅𝑅𝑅𝑅 + 𝑅𝑅𝑅𝑅 + 𝐴𝐴𝐴𝐴

(7)

where AP is the number of accepted positive ground truth data. RN is the number of rejected
negative ground truth data. RP is the number of rejected positive ground truth data. AN is the
number of accepted negative ground truth data. Acceptance means the model-estimated inert
waste composition is in the > 50% by weight range, while rejection means it is not. AP and RN
are correct estimation results. RP and AN are incorrect estimation results.
The ROC curve is a graphical plot that illustrates the diagnostic ability of a classification model
at all classification thresholds (Fawcett, 2006). This curve presents two parameters: 1) the true
positive rate, which is equivalent to the accepted positive rate (APR) in this study; and 2) the
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false positive rate, which is equivalent to the accepted negative rate (ANR) in this study. APR
reflects the model’s sensitivity (or detectable rate) while ANR reflects the model’s fall-out rate
(Metz, 1978). Equation (8) illustrates their calculation methods. Additionally, the index Area
Under Curve (AUC) derived from the ROC curve is usually used to quantitatively evaluate the
model’s diagnostic ability. The AUC value is equivalent to the probability that a randomly
chosen positive sample is ranked higher than a randomly chosen negative sample (Fawcett,
2006).
𝐴𝐴𝐴𝐴
𝐴𝐴𝐴𝐴 + 𝑅𝑅𝑅𝑅
𝐴𝐴𝐴𝐴
𝐴𝐴𝐴𝐴𝐴𝐴 =
𝐴𝐴𝐴𝐴 + 𝑅𝑅𝑅𝑅
𝐴𝐴𝑃𝑃𝑃𝑃 =

395

400

405

(8)

Model speed refers to the time consumption of conducting one complete computation for waste
composition estimation. It mainly depends on the model’s complexity, the computation power
of used computers, and the weight and volume of construction waste loads. This study uses the
consumed time for completing the computation of one construction waste load (namely, second
per load) to represent model speed.
5.3 Conducting experiments and analyzing results
The BD-P model is coded into a computer program using MATLAB. The constructed 604
ground truth data are fed into the program one by one for experimental composition estimation.
During the procedure for exploring the possible inert and non-inert composition ratio (Figure
5, Part I), the decimal places of the randomly selected inert composition weight and volume are
set as three, usually the maximum for practical weight and volume measuring when using
tonnes and cubic meters as units. The input composition range 𝐶𝐶𝐶𝐶 (Figure 5, Part III) is
𝐼𝐼𝐼𝐼𝐼𝐼 >50% according to the classification of ground truth data. It means that the BD-P model
will accept or reject a construction waste load if it estimates the inert composition weight range
as more or less than 50%, respectively.

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415

420

Figure 9 presents the experimental results of using the BD-P model to estimate the 604 waste
loads. Figure 9 (a) shows that 252 of 294 positive data are accepted by the BD-P model and
293 of 310 negative data are rejected. These are correct estimations. However, the model
incorrectly rejected 39 construction waste loads which actually meet the composition range 𝐶𝐶𝐶𝐶,
and incorrectly accepted 20 loads which actually do not meet the composition range 𝐶𝐶𝐶𝐶. To
sum up, of the 604 construction waste loads, the BD-P model correctly estimated 545 loads and
incorrectly estimated 59. The model’s estimation accuracy is 90.2%. Figure 9 (b) is the ROC
curve of the BD-P model. An AUC of 0.8775 demonstrates the good diagnostic ability of the
model. Figure 9 (c) indicates the median of the BD-P model’s estimation speed is 52 seconds
per construction waste load.
15

Figure 9. The experimental results of using the BD-P model to estimate the composition of the
604 waste loads
425

430

Furthermore, Figure 10 visualizes the estimated results of the 604 construction waste loads by
using the BD-P model, where the input composition range 𝐶𝐶𝑅𝑅 is 𝐼𝐼𝐼𝐼𝐼𝐼 >50%. Of particular
interest is that there has an obvious division line in the estimated results. It implies a linear
boundary. Generally, using a linear function would have a significantly smaller computation
burden than using the BD-P model. Therefore, the research goes on to investigate the feasibility
of using the linear function of this division line to substitute the BD-P model for composition
estimation. Based on the output results by the BD-P model, we first use the Perceptron Learning
algorithm (Stephen, 1990) to derive the optimal linear decision boundary function, as Equation
(9):

435

�

440

𝑊𝑊 − 0.4152𝑉𝑉 − 0.2944 > 0
𝑊𝑊 − 0.4152𝑉𝑉 − 0.2944 < 0,

𝑌𝑌𝑌𝑌𝑌𝑌;
𝑁𝑁𝑁𝑁.

(9)

where 𝑊𝑊 is the total weight of a construction waste load. 𝑉𝑉 is its total volume. Yes means its
estimated inert waste composition weight exceeds 50%. No means it does not. Then, we use the
function to re-estimate the 604 constructed ground truth data. The experimental result indicates
an estimation accuracy of 88.8%, slightly lower than the BD-P model’s 90.2% but still
acceptable. However, the computation speed of the linear function is about 130 times faster
than that of the BD-P model, changing from an average of 52 seconds to 0.4 seconds per case.
Therefore, it is recommendable to use the linear decision boundary function informed by the
BD-P model to estimate construction waste composition.

445

16

Figure 10. Composition estimation model results (accuracy: 90.2%)

450

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460

465

470

6. Discussion
The strengths of the BD-P model are multifold. Firstly, it is easy to use. One can simply measure
the weight and volume of a load of waste to calculate its bulk density, just like we measure
one’s body weight and height to calculate the BMI. Secondly, the BD-P model is easy to adjust
for different criteria. The criterion for inert component waste proportion adopted in the
experiments of this study is set at 50%, but it can be adjusted to other real-life criteria without
necessarily changing the underlying BD-P modelling method. Thirdly, the accuracy of the BDP model is at an acceptable level: 90.2% using the original BD-P model and 88.8% using the
linear model generated from the BD-P model. The accuracies are slightly lower than the
currently highest accuracy of construction waste composition estimation. Davis et al. (2021)
achieved an accuracy of 94% by using a deep learning-enabled photogrammetry approach.
Nevertheless, the BD-P model only requires two easy-to-obtain inputs: the weight and volume
of construction waste loads. This saves much manual operation required by previous
approaches, e.g., spreading waste to an even and thin depth for photogrammetry-based
approaches, or pre-sorting construction waste into different composition categories for
statistical sampling approaches. Meanwhile, the BD-P model can complete the computation at
a speed of around 52s per construction waste load. Taking the time of measuring the waste
weight and volume by using currently popular technologies and equipment (i.e., around one
minute) into consideration, the BD-P model is expected to estimate the composition of a
truckload of construction waste in two minutes.
The accuracy and speed achieved by the BD-P model make it highly applicable for real-life
applications. In February 2021, we conducted a workshop with governmental officials, site
inspectors, and system operators who are managing the CWM facilities in Hong Kong. The
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490

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500

BD-P model was generally accepted by the experts and stakeholders, who support us with more
ground truth data to fine-tune the model towards 100% accuracy. This research has practical
value to not only CWM facility managers but also construction contractors and waste hauliers.
These latter stakeholders also face the difficulty of reasonably estimating the composition of
their waste loads and deciding proper disposal destinations.
The biggest novelty of this research is the harmonization of traditional probability theories and
modern big data analytics. There is a popular debate that big data is able to paint a fuller picture
of a subject matter, therefore, undermine the necessity of traditional theories built upon
probability. This research proves that big data is indeed able to inform a fuller spectrum of
something but goes further to show that big data analytics and probability theories are allies
instead of adversaries. The research also provides a compelling case of using probability
distribution obtained from big data for predictive analysis. Traditional statistical approaches
tend to find an existing theoretical probability distribution model (e.g., normal, lognormal, or
Poisson distribution model) to fit the given data, and then use the fitted model for predictive
analyses. However, in the real world, it is not often feasible to fit a theoretical distribution model.
Instead, this study uses the raw probability distribution for predictive analysis without fitting
the underlying theoretical probability model. The key is that the saturated big data set reveals
the total spectrum of the probability distributions.
Nevertheless, the BD-P model also has several shortcomings. Firstly, it can only classify the
construction waste into inert and non-inert portions. It is unable to identify specific construction
materials (e.g., concrete, wood, vegetation, etc.) in a load of construction waste. Further
research can select a more detailed composition classification or add extra information (e.g.,
images) to improve the estimation. Secondly, the BD-P model is not simply transferable to
other economies with different construction techniques and waste composition characteristics.
Necessary adjustments are needed in line with different data sets and admissibility criteria.
However, as mentioned above, the underlying modelling is the same.
7. Conclusions

505

510

With an aim to solve a real-life conundrum as faced by many construction waste management
facilities, this research developed a big data-probability (BD-P) model to quickly and accurately
estimate the composition of construction waste for these facilities. The yardstick of the BD-P
model is the convergent interval and stable probability distribution of construction waste bulk
density, which are derived from big data analytics using 4.27 million truckloads of construction
waste. Just two easy-to-obtain inputs, waste weight and waste volume, are required when
applying the BD-P model to estimate construction waste composition. Experimental tests were
conducted to validate the BD-P model. A ground truth data set consisting of 604 construction
waste loads was constructed in-house and fed into the BD-P model to test its estimation

18

performance. Results revealed a model accuracy of 90.2%, Area Under Curve (AUC) of 0.8775,
and speed of around 52 seconds per construction waste load.
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520

525

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535

Furthermore, to optimize the efficiency of composition estimation, this study proposes using
the fitted linear function of the decision boundary generated by the BD-P model to substitute
the BD-P model for composition estimation. An additional experiment was conducted to
validate the proposal. Experimental results showed an accuracy of 88.8%, slightly lower than
the BD-P model’s 90.2% but still acceptable. However, the model speed is about 130 times
faster than that of the BD-P model, changing from around 52s to 0.4s per construction waste
load, proving the feasibility of the proposal. Therefore, both the BD-P model and the linear
model have great promise for improving the operations of CWM facilities through rapid and
accurate waste composition estimation.
The major novelty of this research is not only to showcase the power of big data to reach a more
comprehensive truth of a subject, but also to illustrate that combining traditional probability
theories and big data analytics can catalyse many powerful applications that cannot be done
before. This study makes a methodological contribution in the context of data science. The
developed BD-P model provides a method case of harnessing the unfitted probability
distribution derived from big data analytics for predictive analysis. With big enough data to plot
the probability distribution of a target event, it is not necessary to deduce the underlying
theoretical probability model for an event’s probability. Instead, the unfitted probability
distribution can be used for predictive analysis directly. Moreover, future studies are
recommended to strengthen the estimation model so that it can accurately estimate the
quantities of specific construction waste materials (e.g., concrete, bricks, rocks, and timber).
Acknowledgement

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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.: ECS Project 111/2019) of the Hong Kong SAR Government.
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