Ontology-based mapping approach for automatic work packaging in modular construction
Xiao Li 1, Chengke Wu 2, Fan Xue 3, Zhile Yang 4, Jinfeng Lou 5, Weisheng Lu 6
This is the peer-reviewed post-print version of the paper:
Li, X., Wu, C., Xue, F., Yang, Z., Lou, J., & Lu, W. (2022). Ontology-based mapping
approach for automatic work packaging in modular construction. Automation in
Construction, 134, 104083. Doi: 10.1016/j.autcon.2021.104083
The final version of this paper is available at:
https://doi.org/10.1016/j.autcon.2021.104083. 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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Many cross-knowledge domain tasks requiring various professional backgrounds have been
transferred from construction site to factory in modular construction (MC). Forming effective
work packages in MC considering the complexity of product breakdown structure becomes
crucial for task planning and execution. However, the definition of optimal work packages in
MC is currently time-consuming and knowledge-inadequate. This study aims to develop a
dynamic ontology-based mapping (DOM) model for generating semantic-enrich work
packages. To this end, ontologies of module products, module topology, and tasks are first
established. The customized Latent Dirichlet Allocation model and weighted K-means
clustering method for mapping products to tasks and grouping tasks into work packages are
then developed. Finally, an evaluation experiment of the proposed DOM model in a real MC
case study demonstrated that it could improve the accuracy and efficiency of the dynamic
work packaging process and pave the way for collaborative planning in MC.
Keywords: Work Package; Ontology; K-means; Latent Dirichlet Allocation; Modular
Construction; Project Planning

RGC Postdoctoral Fellow, Department of Real Estate and Construction, The University of Hong
Kong, Hong Kong SAR. Email: xl1991@hku.hk, Tel.: (852) 5537 0842, ORCiD: 0000-0001-97024153;
2
School of Design and Built Environment, Curtin University, Bently 6102, Western Australia,
Australia. Email: chengke.wu@postgrad.curtin.edu.au, Tel.: (852) 5537 0842, ORCiD: 0000-00019702-4153; *: Corresponding author
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Assistant Professor, Department of Real Estate and Construction, The University of Hong Kong,
Hong Kong SAR. Email: xuef@hku.hk, Tel.: (852) 3917 4174, ORCiD: 0000-0003-2217-3693
4
Shenzhen Institue of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
5
Ph.D. student, Department of Real Estate and Construction, The University of Hong Kong, Hong
Kong SAR. Email: waseljf@connect.hku.hk, Tel.: (852) 9423 1962, ORCiD: 0000-0001-5748-0146
6
Professor, Department of Real Estate and Construction, The University of Hong Kong, Hong Kong
SAR. Email: wilsonlu@hku.hk, Tel.: (852) 3917 7981, ORCiD: 0000-0003-4674-0357
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1. Introduction

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Modular construction (MC) is an innovative construction method to manufacture the facility
(e.g., infrastructure, building) products in the factory and deliver them to the site for assembly
(Gann, 1996; Teng et al., 2017; Ekanayake et al., 2020). MC has the potentials to reach
Construction 4.0 since it has been recognized with compelling advantages over traditional
cast-in-situ construction, such as shortened construction times (Eriksson et al., 2014),
ensured quality (Goh and Goh, 2019), reduced site labor (Xu et al., 2020), and better working
environment (Hammad et al., 2019). As MC involves multi-specialty and cross-domain
knowledge in producing a facility, factories' production still requires assigning tasks to
various subcontractors, specialized work teams, or even robotics and automatic machinery
(Zhu et al., 2021; Arashpour et al., 2018). For example, a two-tower hostel residential project
needs more than 600 workers at the peak of production, and a single housing module requires
a doze of trades to work on various systems, such as structure, door/window, wall, wet, print,
mechanical, electrical and plumbing (MEP) equipment (Lawson et al., 2014). These
physically connected systems in a module are manufactured by coordinating interdependent
tasks, which need seamless project interface planning (Salama et al., 2017).
Work Breakdown Structure (WBS) is an efficient project planning tool that was jointly
developed by the U.S. Department of Defense (DoD), NASA and the U.S. aerospace industry
in 1962 (DoD and NASA, 1962). It has now been widely extended for construction project
management and planning (Siami-Irdemoosa et al., 2015; Li and Lu, 2017; Jung and Woo,
2004; Sutrisna et al., 2018). A WBS is a hierarchical decomposition of the total work scope in
a project, and a work package is the smallest element in WBS for planning one or more
executable tasks (Project Management Institute, 2021). The responsibility for executing a
work package is normally assigned to a single person or organizational unit. The benefits of
using work packages for MC project planning have also been recognized (Isaac et al., 2017;
Li et al., 2019a, 2019b; Liu et al., 2015, 2016; Wu et al., 2021b): (i) it offers the fragmented
MC project team members with clear instructions of their roles and responsibilities; (ii) it
allows concurrent tasks to be simultaneously executed on an MC project; (iii) it helps
measure the performance of schedule and cost by using techniques, such as earned value
methods; (iv) it also supports risks, constraints, and disturbances management at a task level.
The definition and formation of work packages are the very first step before conducting
efficient project planning. As work packages are mainly formed through manually
decomposing the WBS based on experience and knowledge from project managers in current
practice, it is inefficient and prone to omit critical tasks (Ramasesh et al., 2014). To address
this issue, Ibrahim et al. (2009) automatically generated the work packages using predefined
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attributes of BIM components. Isaac et al. (2017) further considered the topological relations,
sequences, and interfaces between specific BIM components to form more effective work
packages. Despite previous studies bridging object-oriented BIM components with the tasksoriented work packages, forming work packages in product-oriented MC, challenges still
exist. For example, (1) mapping rules between MC products and tasks are manually defined
rather than modeled automatically; (2) The products content (e.g., bill of material) and task
contents in work packages may vary with task execution approaching. Thus, there is a lack of
an efficient approach to automatically form semantic-rich work packages by dynamically
mapping products with tasks and then enriching the semantics of tasks for easing the
packaging process.
This study aims to develop a dynamic ontology-based mapping (DOM) model for generating
semantic-enrich work packages. It has three concrete objectives: (1) to explore and establish
the ontologies of products, topology, and tasks; (2) to investigate the mapping models among
products, tasks, and work packages; (3) to develop work packages generation method and
validate them in an MC case study. The rest of the paper is organized as follows. After this
introductory section is Section 2, which elaborates on related studies in WBS and work
package formation, ontology modeling and clustering techniques. Section 3 delineates the
research method, including the ontology models for products, topology, tasks, and the
customized mapping model of Latent Dirichlet Allocation and improved work packaging
method of weighted K-means clustering. Section 4 states the experimental evaluation in a real
MC case study to demonstrate the results of automatic work package formation processes.
Discussions are conducted in Section 5, and conclusions are drawn in Section 6.
2. Literature review

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This study mainly involves four relevant topics: WBS generation, work package formation,
ontology modeling, and data mining and clustering techniques. The review of these four
topics can help provide basics for work packaging, identify limitations of current work
packaging methods, investigate the possibility of using ontology to model the knowledge of
products, tasks, and their relations to facilitate work packaging, and justify the methods used
for product-task mapping and tasks clustering in this study. The details have been
summarized below:
The first type of relevant study is to generate WBS in project management. WBS has been
widely used to hierarchically decompose a project into manageable pieces (e.g., work
package) for reducing project complexity. Golpayegani and Emamizadeh (2007) used
neural networks to recognize the components and relationships in the project WBS. Siamiirdemoosa et al. (2015) then applied a similar method to generate WBS for the complex
underground construction project. Torkanfar and Azar (2020) further developed a similarity
measurement to conduct a semantic comparison of WBSs for achieving knowledge reuse. To
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improve the dynamic WBS generation, Lee et al. (2010) proposed a system to support bidirectional transformation between processes and WBS by using the design structure matrix.
Park and Cai (2017) also established an automated linking mechanism between tasks and
BIM objects to help generate a dynamic BIM database. In modular construction, as the
incompatibility between product-oriented off-site manufacturing and activity-oriented on-site
construction can reduce the seamless interface and integration, Sutrisna et al. (2018) proposed
a hybrid WBS-matrix to bridge the off-site PBS and on-site WBS, and each prefabricated
module is defined as a work package. Many efforts have been made to generate WBS in MC
or project management. However, previous works mainly focusing on forming the static and
dynamic structure of WBS rather than dynamically defining the smallest and executable
units, such as work packages, which is the manageable connection between planning and
execution.
The second type of relevant study is to define effective work packages in project
management. It is quite challenging because it requires decoupling and coupling the
dependencies between tasks. For example, Raz and Globerson (1998) defined the work
packages by considering the factors of cost and schedule estimation, progress control,
network construction, internal cohesion, cash flow, and risk management. Abuwarda and
Hegazy (2016) determined the work packages by selecting network paths and construction
methods. As the project scope is hard to be fully decomposed through the above dynamic
factors, recent studies utilized dynamic databases or BIM from the real project practices to
help form the work packages. For example, Isaac et al. (2017) used BIM to identify
topological relations between components and define construction sequences to generate
work packages. Wang et al. (2020) generated the work package instances using the work
package templates stored in the database and BIM. Using electrical documents, such as
workflow, bill of materials, and production schedules, is common practice for task planning
and execution in modular construction. The topic modeling approach has been investigated to
efficiently map two entities in documents. For example, Aversano et al. (2016) proposed an
approach for evaluating the alignment level between a business process and the supporting
software systems. Marcus and Maletic (2003) used latent semantic indexing to automatically
identify traceability links between system documentation and program source code. Pessiot et
al. (2010) then extended the Probabilistic Latent Semantic Analysis (PLSA) model for
document clustering. Al-Anazi et al. (2016) compared three clustering techniques: K-means,
K-means fast, and K-medoids in document clustering using measures of cosine similarity,
Jaccard similarity, and correlation coefficient. Baskara et al. (2016) used LDA to discover a
traceability link between business processes and software components. Currently, mapping
rules between BIM objects and work packages are manually defined rather than modeled
automatically. Particularly for product-oriented MC with massive components, material and
related tasks, there is a lack of an automatic mapping model to transform the MC products to
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The third type of relevant study is to develop ontology models in the construction field.
Ontology is a graphical approach to map the knowledge domain using nodes and relations
(Zhou et al. 2016). Studies related to ontology in construction could be divided into three
groups: (1) information extraction, (2) knowledge modeling, (3) reasoning and conformance
check. For example, Liu et al. (2016) developed an ontology-based semantic approach to
extract quantity take-off information for workface planning. Zhang et al. (2015) modeled
safety knowledge with an ontology model by linking tasks, methods, and job hazards. Wu et
al. (2021a) used reasoning rules to improve traditional ontology models for constraints
management. To enrich a detailed WBS for progress monitoring, Han et al. (2015) established
an ontology model for construction sequence rationale, including physical relationships
among components, path interference, code regulations, trade interaction. However, there is
lacking ontology modeling for work packages in modular construction, particularly for
mapping the relationships among products, topology and tasks.
The fourth type of relevant study is the mining and clustering of construction information.
LDA is an unsupervised probabilistic model extensively applied to analyze discrete and
unstructured data, such as texts. The LDA model first learns to identify main topics from a
large archive of text documents (i.e., the training process). In this stage, the LDA model, in
essence, clusters documents based on the topics. The number of topics can be pre-defined
according to certain criteria, e.g., perplexity and similarity. The documents used for training
the LDA model are also called a text corpus. After training, the LDA model can assign topics
to a new document (i.e., the validation or testing process) (Blei et al., 2003). In the
construction sector, LDA has been adopted by many studies for topic modeling in various
aspects, including identifying main on-site issues and their changes over time (Lin et al.,
2020), understanding the perceptions of governments towards mitigating environmental
impacts of highway construction projects (Wu et al.,2019), investigating main types of
lawsuit cases (Jallan et al., 2019), and categorizing main hazards from injury reports (Zhong
et al., 2020). Although Dirichlet topic distribution cannot capture correlations among words
(Hoffman et al., 2010), the components in MC do not require sequential correlations for
component-task mapping. Meanwhile, the LDA model is highly modular and can be easily
extended and embedded in more complicated models to improve the accuracy of componenttask mapping. For example, LDA can be enriched with topology ontology models to analyze
spatial relations among semantically related components and then cluster them based on
certain categories.
3. Research method
As the bill of material (BoM) and workflow/schedule may change with the project's progress,
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the proposed dynamic ontology-based mapping (DOM) model aims to facilitate generating
semantic-enrich work packages, as shown in Figure 1, which includes the steps of ontology
development, product-task mapping, and task-work package mapping.

Figure 1 The proposed method: DOM model
3.1.Ontology development
3.1.1. Module product ontology (MPO)
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This ontology (see Figure 2) includes two main branches to cover common classes of
components and materials in MC projects under the top class ‘Module Product’. The
ontology has a maximum of four class levels, e.g., {Module Product, Component, Beam, TBeam}. The ‘Component’ branch is built by referring to the IfcBuildingElement ontology of
buildingSmart, modified according to MC projects' features. For instance, the ‘Furniture’
class is added, as installing furniture is a critical task during producing modules. The
‘Material’ branch is built based on material classification standards (International
Organization for Standardization, 2021) for generating task2vec vectors (see Section 3.3). An
‘isMadeBy’ relation can be defined to relate classes in the two main branches. However, the
MPO is not employed for information searching (e.g., searching for spatial relations
introduced in Section 3.2.3). Thus, no semantic relations in this ontology are defined except
the ‘subclass’ relation.

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Figure 2 Conceptual structure of the MPO (not fully expanded)
3.1.2. Module topology ontology (MTO)
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The MTO defines the spatial topology of a prefabricated module. The ontology released by
the W3C, the minimal ontology for defining relationships among module products, is used to
build MTO. Figure 3 shows classes and relations in this ontology. The MTO has two main
classes, ‘Zone’ and ‘Interface’ and can be expanded to the fifth level. The ‘Interface’ class can
qualify the relationships among module products or zones, e.g., a door between two rooms.
The class has three sub-classes representing common interfaces, i.e., door, window, and MEP
(mechanical, electrical, and plumbing) openings. Instances of the classes can be linked to
instances of ‘Zone’ and MPO classes through the relation ‘interface-of’. On the other hand,
‘Zone’ defines a spatial concept that can be extended in a maximum of three dimensions.
‘Zone’ has four sub-classes: ‘Building’, ‘Story’, ‘Space’, and ‘Plane’. Their instances can be
linked using three spatial relations, i.e., ‘adjacent,’ ‘intersects’, and ‘contains’. The
‘intersects’ and ‘adjacent’ define the relationships between two zones that share an interface
while do or do not intersect with each other, respectively. The ‘contains’ defines the
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subsumption relationships among zones. A building often contains multiple stories, which
can, in turn, contain one or more spaces horizontally connected. Space has bounded 3D
spatial extent and provides certain functions (e.g., a toilet and kitchen). Finally, space
contains planes that can be either vertical (e.g., a floor or ceiling) or horizontal (e.g., a wall).

Figure 3 Conceptual structure of the MTO
3.1.3. Production task ontology (PTO)
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This ontology defines essential tasks to fabricate a module. A module is typically made of
many module products and can require different methods. The construction of the PTO is
based on these distinct methods referring to the work in An et al. (2019). Figure 4 shows the
conceptual structure of the PTO, which has a maximum of three levels. The PTO is built to
form the lexicon for disambiguation introduced in Section 3.2.2. Hence, it also only considers
one semantic relation, i.e., ‘subclass’.

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Figure 4 Conceptual structure of the PTO
3.2. Product-task mapping using LDA
3.2.1. LDA model development and training
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As mentioned, the LDA model is originally used to identify topics of text documents. It
assumes each document is described by topics, and each topic has a distribution over words.
The model is trained by simulating the process of generating documents based on topics of
documents and words. LDA relies on two Dirichlet distributions, i.e., DD1 𝑃𝑃(𝜃𝜃; 𝛼𝛼) and
DD2 (𝜙𝜙; 𝛽𝛽), and two multinominal distributions, i.e., MD1 𝑃𝑃(𝑍𝑍|𝜃𝜃) and MD2 𝑃𝑃(𝑊𝑊|𝑍𝑍).
The α and β are hyper-parameters, θ and ϕ are latent variables, and Z and W represent topics
and words, respectively. For each of the M documents to be generated, the DD1 determines
the topic of the document, from which MD1 is derived to determine the topic of each word in
the document. The MD1 is called N times (N is the number of words, i.e., the document
length). In this stage, each word only has a topic. To generate specific words, the MD2
associating topics to words is adopted to develop K DD2 (K is the number of topics), and
each DD2 determines specific words of a certain topic (Blei et al., 2003; Newman, 2007). Eq.
1 describes the document generation process, which is also shown in Figure 5.
𝐾𝐾
𝑁𝑁
∏𝑀𝑀
𝑗𝑗=1 𝑃𝑃(𝜃𝜃𝑗𝑗 ; 𝛼𝛼) ∏𝑖𝑖=1(𝜙𝜙𝑖𝑖 ; 𝛽𝛽) ∏𝑛𝑛=1 𝑃𝑃�𝑍𝑍𝑗𝑗,𝑛𝑛 |𝜃𝜃𝑗𝑗 �𝑃𝑃(𝑊𝑊𝑗𝑗,𝑛𝑛 |𝑍𝑍𝑗𝑗,𝑛𝑛 )

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Eq. 1

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Figure 5. LDA document (TAs) generation process
This study borrows the above ideas, except that: 1) task assignments (TAs) (more details are
introduced below) are generated to replace the role of documents; and 2) the task types and
products are treated as topics and words, respectively. The DD1 decides probabilities that a
TA belongs to each task type, and the DD2 decides the probabilities of building products used
in a task given the task type. In other words, in this study, the M, K, and N in Eq. 1 represent
the number of TAs, task types, and products in a TA, respectively. Figure 5 shows the flow of
the LDA model. The training data come from two sources: 1) the MC production workflow,
where each task is extracted as a unique task type, and 2) the BoM, where each item is taken
as a product. Then, the products are manually associated with task types, generating task
assignments (TAs) as inputs to train the LDA model. Each TA includes one task type and a set
of building products, and Table 1 lists several examples.
Training the LDA model requires estimating the parameters α and β so that the model can
maximize the probability of generating similar TAs in the training data. This can be realized
by Gibbs sampling. The method works as follows: 1) randomly assigns a task type to a
building product in the training data, 2) summarizes the number of products belonging to
each task type in each TA and the number of products belonging to each task type in the
entire dataset, 3) for each product, recalculates the MD2 based on statistics obtained in the
last step, 4) reassigns a new task type to each product using the newly obtained MD2, 5)
repeats the process until parameters in the MD1 and MD2 converge (Gelfand, 2000). The
maximum number of iterations is usually defined to save time and computation power. After
training, each task type can be represented by key building products ranked by MD2
distributions (see examples in Section 4). The aim is to map building products to tasks, which
does not consider TA generation, only the DD2 produced by training the LDA model is
employed in model testing.
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3.2.2. Data disambiguation

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A challenge to implement the proposed model is that the names of tasks and products in the
MC workflow and BoM are often freely written by engineers. This can cause ambiguity, e.g.,
different words are used to describe the same task. Thus, as suggested in Wu et al. (2021b), a
heuristic method is proposed to 1) generate standard expressions (SEs) for products and tasks
during training; and 2) match new products and tasks to the SEs during testing.

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Given that the number of unique products for fabricating modules is not very large, the
ambiguity of products’ names often comes from their variations (e.g., studs and stud) and
different orders of words when the name includes multiple words. Hence, pre-processing is
applied (See example in Figure 6), which includes four steps: normalization (e.g.,
lowercasing), tokenization (i.e., separating a name into words), stop words removal (i.e.,
removing meaningless words), and stemming (i.e., converting a word to its basic form). The
process is similar to text pre-processing, and more details can be found in Denny and Spirling
(2016). The processed products during training form a large corpus covering SEs of common
MC products. However, it is difficult to distinguish tasks in this way as their names contain
many variations. For instance, a task can be carried out in different locations (e.g., installing
studs at the wall or ceiling) or with different products/materials (e.g., installing cabinets or
conduits). Therefore, based on practical experience, relevant literature, and the three
ontologies, a lexicon is manually defined to cover tasks for fabricating MC modules. Each
item in the lexicon is formed by ontology classes in the MPO, MTO, and PTO, which can
unambiguously define a task type. Examples in the lexicon are shown in Table 2.

Figure 6 Example of four steps in data pre-processing
A similarity matching mechanism is carried out in the testing stage to find a standard
expression for new products and tasks. The four-step mechanism is based on word
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embeddings, where a new product: 1) undergoes the pre-processing steps introduced; 2)
traverses the corpus or lexicon; 2) computes similarity value among the pre-processed new
tasks/products, each SE in the corpus, and lexicon following Eq. 2, where 𝒆𝒆𝒄𝒄 and 𝒆𝒆𝒆𝒆 are
word embeddings of a token of the SE and new products/tasks, respectively; 3) obtains an
average similarity s; 4) replaces the new products and tasks using the SE with the maximum
s. Word embeddings are employed as they are low-dimension real-valued vectors that can
capture meanings of words despite different expressions (Church, 2017). Word embeddings
should be learned by machine learning models (e.g., word2vec). However, training such
models is very data demanding. Thus, it is common to utilize word embeddings trained by
others. Table 1 lists several examples to show the effect of disambiguation.
𝒔𝒔 =

𝑐𝑐
𝑒𝑒
∑𝑛𝑛
𝑖𝑖=1 𝑒𝑒𝑖𝑖 ×𝑒𝑒𝑖𝑖
2

𝑐𝑐
𝑒𝑒
� 𝑛𝑛
�∑𝑛𝑛
𝑖𝑖=1�𝑒𝑒𝑖𝑖 � × ∑𝑖𝑖=1�𝑒𝑒𝑖𝑖 �

2

(n=the dimension of the word embedding) Eq. 2

3.2.3. Data enriching based on spatial relations

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Following the conventional approach to develop LDA models, a TA only consists of
associated products. However, such simple data cannot suit situations in practical MC
projects. One common problem is that when producing a room module, a product is required
in multiple tasks thus should be included in multiple TAs. For instance, a gypsum board
simultaneously belongs to the tasks ‘board pre-treatment and punching’ and ‘installation of
the board at wall surface’. Therefore, the conventional LDA model cannot distinguish such
differences and can only make a random guess when mapping a new ‘gypsum board’ product.
To address this issue, spatial relations of module products are identified by referring to the
BIM model and MTO to enrich TA data. The process has three steps: 1) as the BoM is
derived from the BIM model, associated spatial instances (i.e., instances of MTO classes) of
each product can be extracted from the BIM model (e.g., a gypsum board is related to a ‘wall’
instance in BIM); 2) a ‘contains’ spatial relation is set up between the spatial instance and
product; and 3) the triple taking the form (i.e., ‘spatial instance contains product’) is added to
the TA data. If no spatial relation is found, for instance, the product is used in pre-installation
tasks (e.g., board punching), a triple ‘non contains product’ is added. As such, the same
products can be distinguished by different spatial relations with a spatial instance. Figure 7
illustrates the process and difference between TA data before and after enriching.
Moreover, after investigating the workflow charts and schedules of MC projects in Hong
Kong, it is found that 1) the unit for managing MC projects is individual rooms (e.g., house
modules); 2) distinct spatial instances are considered as one system, and tasks performed on
these instances are managed as one package (e.g., installing studs in all walls of a room is
treated as a single package). Therefore, it is unlikely that the same triple (e.g., ‘wall contains
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Figure 7 TA data enriching process

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Table 1 Examples of TA data (before enriching)
Task
(before Product
(before
disambiguation) disambiguation)
Metal skeletons, Shear
Studs, RUnner, the panel
Stud installation
of
wall,
TRACK,
at wall
channels, wall Tiles, some
noggins, braces
2D
Panels,
Corner
Casting, Steel COLUMN,
Steel
Angles,
Shear
3D assembly
StuDS,
CandleLoc
System, ceiling beam,
Purlins, FLOOR beam
Ironmongery of DOOR
Door
aluminium window, FRP
ironmongery
Timber
door,
glass
and
windows
PANEL,
Hinges,
installation
hanDLes, latches

Task
(after Product
disambiguation) disambiguation)
{stud
wall}

(after

metal skeleton, shear
instal stud, runner, panel wall,
track, channel, wall tile,
noggin, brace

{3d assembl}

2D panel, corner cast,
steel column, steel angle,
shear stud, candleloc
system, ceiling beam,
purlins, floor beam

{door,
ironmongeri,
window, instal}

ironmongery
door,
aluminum window, frp
timber door, glass panel,
hinge, handle, latch

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Table 2 Examples in the standard task lexicon
Task
preTask
Product lexicon
processed
2D
panel {2d
{Panel,
assembly
assembl}
Assembling}
Stud
{stud instal {Wall,
Stud,
installation at
wall}
Installing}
wall
{Door,
Door
and {door
Window, Door
window
window
Interface,
frame
frame
Window
installation
instal}
Interface,
Installing}

320

14

MTO

MPO

PTO

N/A

Panel

Assembling

Wall

Stud

Installing

{Door
Interface,
Window
Interface}

{Door,
Window}

Installing

3.3. Task-work package mapping using weighted K-means clustering
3.3.1. Ontology-based task numerical presentation – Task2vec

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The automated task-package mapping depends on clustering MC tasks, which requires
transforming tasks to numerical vectors according to their attributes. Based on literature
review and discussion with engineers in MC projects, three critical attributes are identified
when packaging tasks: task relations, spatial relations, and resource demands (Li and Hall,
2019).
Task relationships concern sequential (preceding and succeeding), parallel, and coupled
relations between two tasks. Figure 8 illustrates the three relationships. In particular, the
coupled relation indicates that two tasks are interchangeably performed, such as ‘2D panel
assembly’ and ‘butt and fillet welding’. When packaging tasks, planned schedules are often
available. Thus, tasks for fabricating a module can be indexed from 1 to T based on their
dependencies. Then, the dependency vector 𝑣𝑣 𝑑𝑑 ∈ ℝ3 can be generated, where each entry is
the index of another task holding the preceding, succeeding, and parallel relation with it (the
value is -1 if no parallel task is found). It should be noted that the coupled relation is not
explicitly covered in 𝑣𝑣 𝑑𝑑 , since it can be modeled if two tasks are indexed as predecessors and
successors of one another simultaneously.

Figure 8 Tasks relations
340

345

The spatial attributes of a task are determined by the spatial instances and module products
mapped to the task. Hence, a spatial vector 𝑣𝑣 𝑠𝑠 is generated using a one-hot encoding
approach as follows: 1) for each task, 𝑣𝑣 𝑠𝑠 is initialized as a zero vector of shape ∈ ℝ𝐶𝐶 , where
each entry corresponds to one of the C classes in the MTO; 2) the bottom-level spatial
instance of each product belong to the task is extracted by referring to spatial triples
introduced previously (e.g., ‘ceiling’ is extracted from the triple ‘ceiling contains rockwool’);
2) a spatial class list is constructed by searching for superclasses in the MTO, e.g., the list
{Zone, Space, Room-Level Space, Horizontal Plane, Ceiling} can be formed given the
15

350

355

360

instance ‘ceiling’, while the list {Interface, MEP Opening} can be formed given ‘conduits’;
3) a complete list is generated by integrating information from lists of all products of the task;
4) 𝑣𝑣 𝑠𝑠 is re-evaluated, where the entry value is set as one if the corresponding ontological
class exists in the complete list. Locations (i.e., local coordinates) of all products assigned to
the same task should be the same in an MC module (e.g., studs and tiles consumed in one
task ‘wall stud installation’ are located in the same place). Thus, generating 𝑣𝑣 𝑠𝑠 needs to only
consider one product, but the above process considers all products to avoid missing
information (Salama et al., 2017). On the other hand, many MC tasks require distinct material
resources, e.g., painting materials for painting and coating tasks and welding materials for
assembling tasks. As such, the resource vector 𝑣𝑣 𝑟𝑟 ∈ ℝ𝐷𝐷 can be formed following a similar
procedure to generating spatial vectors, where D is the number of classes in the MPO. The
three vectors (i.e., 𝑣𝑣 𝑑𝑑 , 𝑣𝑣 𝑠𝑠 , 𝑣𝑣 𝑟𝑟 ) are concatenated into a single long vector 𝑣𝑣 𝑡𝑡 ∈ ℝ3+𝐶𝐶+𝐷𝐷 to
convert an MC task into a numerical vector. Figure 9 presents the pseudo-code of the process.

Figure 9 The pseudo-code of task2vec process

16

3.3.2. K-means clustering with heuristic weighting

365

370

K-means clustering is a simple but effective unsupervised algorithm to automatically partition
m data samples into L clusters. It works as an iterative refinement process: 1) randomly select
L samples as initial centroids, 2) compute the distance (e.g., Euclidean distance) between the
cluster centroids and all other samples; 3) assign each sample to the cluster with the nearest
distance; 3) recalculate cluster centroids using all samples it contains then reassign all
samples. The process converges when the assignments no longer change or after a certain
number of iterations (Tsai and Chiu, 2008). Steps 2-3 are shown in Eq. 3, which determines
the cluster of the 𝑖𝑖 𝑡𝑡ℎ task according to centroids 𝑢𝑢𝑗𝑗 {𝑗𝑗 = 1,2 … 𝑳𝑳}.
𝑐𝑐 (𝑖𝑖) ∶= argmin�𝑥𝑥 𝑖𝑖 − 𝑢𝑢𝑗𝑗 � Eq. 4
𝑗𝑗

375

380

385

However, K-means clustering can cause many errors if it is directly applied to task vectors.
For instance, the two tasks ‘door frame installation’ and ‘door ironmongery installation’ will
be grouped in one cluster (i.e., one package) despite that in practice, they are separated by a
dozen tasks and managed in two packages. Most parts of the vectors (i.e., 𝑣𝑣 𝑠𝑠 , 𝑣𝑣 𝑟𝑟 ) of the two
tasks are similar owing to similar class lists. Therefore, the differences between 𝑣𝑣 𝑑𝑑 cannot
impose its impact. On the other hand, it is critical to ensure enough classes are covered in 𝑣𝑣 𝑠𝑠
and 𝑣𝑣 𝑟𝑟 , otherwise closely related tasks can be grouped in different packages. To address this
problem, before clustering, vectors 𝑣𝑣 𝑠𝑠 , 𝑣𝑣 𝑟𝑟 are normalized (i.e., each sample subtracts the
mean and is divided by the standard deviation of all samples), while 𝑣𝑣 𝑑𝑑 remains unchanged.
In this way, the K-means algorithm can pay more attention (in other words, assigns more
weights) to the dependency attributes of data. In addition, parallel tasks should not be
packaged, to consider this rule in the clustering process, a penalty 𝜆𝜆 is added when
computing the distance between tasks, where a large value (e.g., 10) is assigned to 𝜆𝜆 if a
parallel task of the current task 𝑥𝑥 (𝑖𝑖) is found to exist in a cluster.

390

395

Another issue is that the one-hot encoding can result in similar vectors where most entries are
0, making clustering difficult. Therefore, a heuristic weighting method is proposed. It is
reasonable to assign more weights to more abstract classes while fewer weights to more
specific classes. For instance, installing windows and doors should be packaged together
because they are instances of installing ‘Furniture’, although they have different bottom-level
classes (i.e., ‘Window’ and ‘Door’) in the class lists. As such, descending integer weights are
assigned based on class levels in the MPO and MTO, e.g., weights {4, 3, 2, 1} are assigned to
the level 1 to 4 classes in the MPO, which results in a weight vector w. Task vectors are
multiplied with w through Hadamard production before being fed to K-means, making
differences among vectors more distinct. The pseudo-code of the weighted K-means
17

clustering is shown in Figure 10.

Figure 10 The pseudo-code of weighted K-means clustering
400

405

Finally, the number of clusters L (i.e., the number of packages) must be determined, and this
study uses one of the most popular methods, i.e., the gap statistic (GP) method, to find the
optimal L. The K-means model can be evaluated by the distortion value, i.e., the sum squared
error (SSE) of the distance between each data sample and its assigned centroid (see Eq. 5).
The GP method could find L automatically, which works as follows: 1) generates random
data samples using uniform distribution; 2) applies K-means to the generated samples and
compute SSE; 3) repeats above two steps multiple times (often through Monte Carlo
simulation) and obtain the SSE; 5) computes the GP value using Eq. 6; 4) determines the
optimal L as the one obtaining the largest GP value. More details of the GP method can be
found in Yan and Ye (2007).
𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆 = ∑𝑚𝑚
𝑖𝑖 �𝑥𝑥 − 𝑢𝑢𝑖𝑖 �

410

4. Experiments

415

Eq. 5

𝐺𝐺𝐺𝐺𝐺𝐺(𝐾𝐾) = 𝐸𝐸(log 𝑆𝑆𝑆𝑆𝑆𝑆𝑘𝑘 ) − log 𝑆𝑆𝑆𝑆𝑆𝑆𝑘𝑘

Eq. 6

In this section, experiments are conducted to evaluate the performance of the DOM model for
work package generation in a real MC project in Hong Kong. This project is a student
residence with two 17-floor towers comprising 1224 prefabricated hostel rooms and other
18

420

425

supporting facilities (e.g., prefabricated toilet, kitchen). The graphical details of the project
are shown in Figure 11. All the prefabricated modules are produced at an off-shore factory in
Mainland China, and this project is currently under the mock-up stage. As this factory will
simultaneously produce around 400 modules with a peak of 600 workers at the mass
production stage, automatically generating semantic-enrich work packages under the complex
production environments for each worker or team are urgently needed. DOM proposed in this
study has the potentials to facilitate collaborative and dynamic planning in the mass
production stage of MC.

Figure 11 Overview of the MC project for this experiment
4.1.Data preparation

430

As the project went on, more than ten versions of workflow/schedule and BIM model (i.e.,
can generate BoM) had been generated and updated for producing module M1. The number
of products in BoM and tasks in the workflow increased as the schedule went on. The initial
version (T-10) and the one for the latest mock-up stage (T-23) are selected for this
experiment, which includes 10 tasks and 23 tasks, respectively. The changes in these two
versions of workflow and BoM can lead to changes in work package content. Thus it can not
only help test the dynamic performance of the DOM model in work packaging but also prove
that the proposed method can be repeatable in varied datasets.
19

435

4.2.Results Analysis
4.2.1. Product-task mapping results

440

Figure 12 compares the effect of disambiguation and data enriching for both T-10 and T-23.
More errors occur if without enriching. After running the model 100 times, the average
accuracy is 0.904 and 0.938 for T-10, 0.883 and 0.968 for T-23, respectively. The results
show that the spatial relation enriching could significantly improve the mapping accuracy
between products and tasks.

(a) T-10

(b) T-23

Figure 12 Accuracy of product-task mapping
445

450

The errors mainly come from the lack of information for the LDA model to classify products.
Figure 13 shows a few distinct examples, where the counts are obtained by running the naive
LDA model 100 times while counting the task assignments of the products in the T-23
situation. Some products can only be used in a particular task (e.g., electrodes for the welding
task), which can be handled by the navie LDA model. However, several products (e.g.,
‘promatect h-board’ and ‘ceiling panel’) can belong to two or more tasks. The same
ambiguation happened when mapping products ‘shear stud’ and ‘gypsum board’ in the T-10
situation. The navie LDA model cannot distinguish such product-task relations, thus make
wrong assignments.

20

455

460

465

Figure 13 Examples of errors that occurred without data enriching
The confusion matrices in Figure 14 present the differences between products with data
enriching and without data enriching. For instance, for T-23, the product ‘steel column beam’
can belong to either ‘3D assembly’ (task 5) or ‘installing ceiling studs’ (task 1). The matrix in
Fig.14 (c) shows that seven ‘steel column beam’ products are wrongly assigned to task ID-1.
The situation is much better in the second matrix, and all ‘steel column beam’ products can be
correctly assigned to task 1.
However, errors still occur for a few products that cannot be distinguished even when spatial
relations are utilized. For instance, for T-23, the product ‘ceiling panel’ should be used in task
9, ‘installing studs at the ceiling’, as stated in the workflow. However, the LDA model
wrongly assigns it to task 15‘layer and coat painting ceiling’ because the product has the
same spatial relations in both tasks. Nevertheless, the accuracy for T-23 is still increased by
more than 7%.

21

470

Figure 14 Confusion matrix of product-task mapping (both x and y-axis are task ID, see Table
3 & 4 for specific task names, the tasks are not arranged in sequence in the product-task
mapping stage)
4.2.2. Task-package mapping results

475

In this section, the weighted K-means model is demonstrated when packaging tasks for
producing module M1. Task vectors are multiplied with weight vector w through Hadamard
production before being fed to K-means, making differences among vectors more distinct.
The optimal number of packages is determined using the GP method, automatically selecting
L, thus minimizing subjective judgment. As shown in Figure 15, the method suggests six and
ten work packages as the good choice for T-10 and T-23, respectively.
22

480

Figure 15 Determining the optimal number of clusters (work packages)

485

490

495

500

Tables 3 & 4 compare the manual assignment results (based on the project manager's
experience) and three K-means mapping results for T-10 and T-23, respectively. MA and KM
mean assigning MC tasks manually and through k-means clustering, respectively. KM-1 does
not implement heuristic weighting as introduced in Section 3.2.3. In Table 3, the proposed
clustering method perfectly packages the tasks, the same as manual packaging results.
However, KM-1 wrongly packages tasks 7-9, where tasks 7 and 9 are separated by task 8,
which is impractical given their close dependencies. It is because they have similar spatial
and resource attributes, which outweigh the impact of task relationships when heuristic
weighting is not applied. In Table 4, KM-1 for T-23 does not separate tasks 2-4 as attribute
vectors (one-hot encoding without heuristic weighting and normalization), including many 0
and a few 1, which are not distinct enough to be separated. Moreover, similar to the issue in
Table 3, the two tasks (i.e., tasks 8 and 23) are packaged together in KM-1, despite being
separated by many tasks. The packaging results for tasks 12-14 have a similar problem.
In contrast, when handling the 23 tasks, the proposed K-means model can address both issues
and produce the most practical packaging results, which are also very similar to the manual
packaging results. The only difference is that fabricating the wall and ceiling is separated into
two packages instead of one. It is because the manual packaging suggests nine packages,
while the K-means model suggests ten. It is also reasonable as tasks for wall and ceiling can
be separated by the spatial relations, and they can also be executed concurrently and
combined as the wall work package in practice.
Table 3 Comparison of task-package mapping results
ID Task

MA

KM-1

Proposed KM

0
1
2

1
2
2

1
2
2

1
2
2

Board pretreatment and punching
2D panel assembly
Butt weld and fillet weld
23

3
4
5
6
7
8
9

3D assembly
Apply fire paint at strucutral member
Rebar Fixing
Pouring and curing Concrete
Door and window frame installation
Stud installation at the ceiling
Stud installation at wall

3
3
4
4
5
6
6

3
3
4
4
5
6
5

3
3
4
4
5
6
6

ID Task

MA

KM-1

Proposed KM

0
1
2
3
4
5
6
7
8
9
10

1
2
2
3
3
4
4
5
6
6

1
2
2
2
2
3
3
4
6
5

1
2
2
3
3
4
4
5
6
6

6

5

6

6

5

7

6

5

7

6

6

7

6

5

7

7
7
8
8
9
9
9
9

7
7
8
8
9
9
10
4

8
8
9
9
10
10
10
10

Table 4 Comparison of task-package mapping results

11
12
13
14
15
16
17
18
19
20
21
22

Board pretreatment and punching
2D panel assembly
Butt weld and fillet weld
3D assembly
Apply fire paint at strucutral member
Rebar Fixing
Pouring and curing Concrete
Door and window frame installation
Installation of MEP at the ceiling
Stud installation at the ceiling
Rockwool in-fill and fire board installation
at the ceiling
Stud installation at wall
Rockwool in-fill and fire board installation
at wall
Installation of MEP at the wall surface
Installation of gypsum board at the wall
surface
Layer and coat painting ceiling
Layer and coat painting wall
Installation of pipes
Electrical cable wiring
Window type AC installation
Installation of lighting system
Cabinets installation
Door and window ironmongery

505

Finally, the proposed K-means model was applied to all 368 tasks in this case project. The
24

510

model was evaluated using two important metrics (See Table 3 & 4), i.e., the Silhouette
Coefficient and Calinski-Harabaz index. The two metrics evaluate the SEE and data covariance within each cluster (work package) and between clusters (work packages), and both
favor the large values. It can be argued that the proposed weighting method can significantly
improve the model performance. In addition, the improvement is more evident with more
tasks (i.e., when the situation is more complex).
Table 4 Comparison between K-means clustering metrics
Task
Silhouette Corfficient (T-10)
Calinski-Harabaz index (T-10)
Silhouette Corfficient (T-23)
Calinski-Harabaz index (T-23)

515

520

KM-1
0.582
307.057
0.440
97.196

KM (proposed)
0.855
548.161
0.569
487.660

Figure 16 demonstrates the clusters (i.e., packaging results). Task ID in Fig.16 could be well
matched with Tables 3 & 4. Each rectangular area with the same color suggests rows
correlated with the corresponding columns. Tasks in both T-10 and T-23 can be separated into
distinct clusters (i.e., working packages). The right two columns for both T-10 and T-23 have
lighter colors. Because vectors 𝑣𝑣 𝑠𝑠 , 𝑣𝑣 𝑟𝑟 are normalized, while 𝑣𝑣 𝑑𝑑 remains unchanged in these
two samples. In this way, the K-means algorithm can assign more weights to the dependency
attributes of data.

(a) T-10

25

(b) T-23

525

Figure 16 Overview of K-means clustering results
5. Discussion

530

The proposed DOM model is a brand new approach to enrich the semantics of tasks and
generate the work packages more accurately and automatically. Compared with the previous
studies, three aspects of the DOM model’s novelty are summarized as follows.


Firstly, three ontology models, namely, MPO, MTO, and PTO, are established as the
knowledge base in MC, which facilitates extracting information in product, topology,
and tasks. These ontology models represent not only the knowledge of product
breakdown structure, products’ spatial topology, and work breakdown structure but
also form relationships between these knowledge domains. Previous works, such as
An et al. (2019), have built the knowledge domains in MC's resource, operation, and
product. However, they only modeled knowledge for wood frames rather than an
entire prefabricated module and considered less knowledge in the product topology.



Secondly, the improved LDA model enriches products with spatial topology relations
to improve the mapping accuracy between products and tasks. LDA is a kind of
unsupervised machine learning technique that does not consider the relations of
different retrieved words, and it may confuse the model when the same product name
under different statuses should be mapped to more than two tasks (See Fig.7). MTO
can enrich the product data to improve the efficiency and accuracy of product-task
mapping, and these enriched product data can play an important role as the resource
attributes in the work packaging process.



Thirdly, the approach for forming a semantic-rich task by transforming a task’s
attributes of dependency, topology, and resources into a vector is first developed. A

535

540

545

26

heuristic weighting method is then designed to improve the clustering accuracy of Kmeans, which help finally packaging the semantic-rich tasks and get the practical
work packages. The previous studies used the design structure matrix to generate final
work packages. However, it only considers the task dependency and works manually
(Lee et al., 2017).

550

Despite these contributions, our study still has several limitations.
555



Firstly, As the ontology modeling process is extremely time-consuming, this study
adopted the “transferred modeling” strategy by customizing and modifying existing
ontology models (e.g., IfcBuildingElement, W3C building topology). Although it
would be easy to expand the proposed ontology models to other MC projects, to make
DOM more practical, it still requires sufficient knowledge to involve all relevant
knowledge domains regarding module production and the more well-defined
relationships among the three ontology models.



Secondly, the modified LDA model in this study still requires a proper level of details
(LoD) for products and tasks to maximize mapping accuracy. Compared with the
naïve LDA model embracing Dirichlet distributions' inability to capture correlations,
the proposed model can to-some-extent distinguish module products accurately by
leveraging spatial relationships. However, ambiguity issues still arise if the LoD is too
high. For instance, if the task ‘stud installation’ is divided into first- and second-layer
stud installation, the LDA model cannot correctly assign the product ‘stud’. The
underlying reason could be twofold. (1) the length of BoM is short, leading to the
scattering of document-level word co-occurrences. It could be further improved by
extending the BoM document with more semantics (e.g., spatial relationships,
attributes). (2) Some task compositions are overlapping, meaning that the same
product can be in multiple tasks. Therefore, the generated tasks are not independent
and orthogonal. It may consider the hierarchical LDA by combing tasks in a hierarchy
using a Nested Chinese Restaurant Process (NCRP).



Thirdly, the work packaging process in this study only considers some critical
attributes of products and tasks. However, this study did not determine the optimal
work package size in clustering tasks into packages by linking with project
performance (e.g., schedule, cost). Many factors influence work package sizes, such
as workload, schedule estimation, economies of scale, cost of monitoring and control.

560

565

570

575

580

6. Conclusion
Modular construction (MC) has the great potential to put the construction industry forward to
Construction 4.0 since it follows industrialized principles that could provide a collaborative
27

585

590

595

600

605

610

615

working environment among workers, robotics, and machines. However, current practice
indicates that cross knowledge domain tasks in the MC factory still require dynamic and
collaborative planning, particularly in the mass production stage. Thus, this study proposed a
dynamic ontology-based mapping (DOM) model to help generate work packages
dynamically and automatically. Firstly, three ontology models, namely, MPO, MTO, PTO, are
established as the knowledge base to facilitate extracting the information of products, spatial
relations, and tasks. Then, the customized LDA model is developed to accurately map module
products (enriched by the spatial topology) to relevant tasks, where these products can serve
as the resource attributes for tasks. Finally, semantic-enrich tasks with dependency, topology,
and resources could be converted into vectors, where the weighted K-means clustering
method is developed to combine these tasks into optimal work packages. The experiment is
conducted on two versions of datasets (i.e., workflow with 23 tasks and 33 tasks), the results
show that the DOM model can help dynamically generate the optimal work packages when
schedule and BoM changed.
Modular construction companies can benefit from our work in several ways. First, they can
better understand the mechanism by which various knowledge related to modular products,
tasks, and work package generation. Second, work packages can be generated efficiently in
the mass production stage to instruct the workers, machines, or robotics’ tasks execution in a
complex MC production environment. Third, they can use this proposed solution to generate
work packages that significantly reduce their planning costs.
Several topics remain open for future research. First, more MC tasks related ontology models
(e.g., production tools and machines, durations, costs) can be further established to enrich the
knowledge base for more accurate work packaging; Second, the factors (e.g., level of details
in products) that affect the accuracy of the LDA model for product-task mapping should be
further investigated to improve LDA model with more semantic features, or other supervised
learning model can be developed for product-task mapping; Third, we note that our work
focuses on work package formation, rather on the work package sizing. Developing a more
complicated model that simultaneously generates work packages and optimizes the work
package sizes may be possible. In conclusion, we hope our work will encourage further
research on this topic, potentially enhancing the collaborative planning and performance of
MC projects.
Acknowledgment
This research was financially supported by the Hong Kong Innovation and Technology Fund
(ITF) (No. ITP/029/20LP) and the Fellowship of China Postdoctoral Science Foundation (No.
2021M692169).
28

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