# Hierarchical System of Digital Twins: A Holistic Architecture for Swarm System Analysis

Mouhamadou Ball, Jannik Laval, Loïc Lagadec

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Mouhamadou Ball, Jannik Laval, Loïc Lagadec. Hierarchical System of Digital Twins: A Holistic Architecture for Swarm System Analysis. 2025. hal-04932447

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# Hierarchical System of Digital Twins: A Holistic Architecture for Swarm System Analysis

Mouhamadou F. BALL¹ IDª, Jannik LAVAL² IDᵇ, and Loïc LAGADEC¹ IDᶜ

¹Lab-STICC UMR 6285, ENSTA Bretagne, Brest, France

²DISP-UR4570, Univ Lyon, Univ Lyon 2, Lyon, France

**Keywords:** Digital Twin, Swarm System, Modeling, Holistic Architecture

**Abstract:** Swarm systems are being increasingly adopted for their operational capabilities and are now assigned more sensitive missions, often in unpredictable environments. Therefore, it is crucial to evaluate their performance in the face of natural or human-induced uncertainties before deployment and enhance their resilience during missions. To enable a comprehensive analysis of this system, a multi-level analysis must be conducted to capture the dynamics at the component, cluster, and swarm levels. Digital Twin (DT) offers a promising solution to address this challenge. While there are existing approaches that use digital twins to analyze complex systems, they do not take into account the specific requirements introduced by swarm configuration. This paper presents a holistic reference architecture, the Hierarchical System of Digital Twins (HSDT), which lays the groundwork for creating digital twins of swarm systems. To support this framework, we introduce the concepts of functional and aggregation hierarchies and propose a goal-oriented method for instantiating DT with a specific level of sophistication. Additionally, we present a metamodel that integrates elements of the Asset Administration Shell (AAS) data model to ensure interoperability with external standards. A prototype of HSDT was developed, and a case study was presented, focusing on analyzing spatial parameters within a swarm of Unmanned Vehicles (UVs).

## 1 INTRODUCTION

The swarm configuration of systems is an emerging approach, adopted for its numerous advantages, such as enhanced performance through load distribution, easier scalability, and increased robustness (Liu and Passino, 2000). Systems in swarm configuration can be compared to systems of systems (SoS), as they meet the properties presented by (Maier, 1998). This configuration is beginning to be concretely adopted for unmanned vehicles (UVs). For instance, the European Union's SCAF project for the future air force is based on this configuration. Given the increasingly critical missions assigned to this type of system and its evolution in uncertain environments, it becomes essential to analyze it, study its behavior, and implement strategies for performance enhancement. Furthermore given the specifics of these systems, the analysis must be conducted at different levels of abstraction (component, cluster, swarm) and from various perspectives. The Digital Twin (DT) represents a

promising technology for addressing the challenges of analyzing such systems. The literature presents various approaches that leverage digital twins for analyzing complex systems (e.g., Cyber Physical System, SoS). However, after defining the requirements for a digital twin in the context of swarm systems, we observe that current architectures do not fully address all of these requirements. This position paper aims to address the research question: **How can we design a digital twin architecture that fulfills the fundamental requirements of swarm systems?**

In fact, to enable the full use of digital twins in the analysis of swarm systems we need an architecture that accommodates these types of systems. Therefore, we propose an architecture for designing a hierarchical system of digital twins. We start by defining the requirements of such digital twins based on the specifications of swarm systems, then propose a digital twin structure rooted in a service-oriented approach, and finally, the holistic architecture that leverages the use of several digital twins in a hierarchy. Two types of Digital Twins are introduced in this architecture, forming its core: the Instance DT, which is directly connected to reality, and the Aggregate DT, which is a composition of multiple Digital Twins. Furthermore,

<footnote>a ID https://orcid.org/0009-0005-9245-2892</footnote>

<footnote>b ID https://orcid.org/0000-0002-7155-5762</footnote>

<footnote>c ID https://orcid.org/0000-0003-3778-3144</footnote>
we introduce a goal-driven method for the instantia-
tion of DTs. An event-based services synchroniza-
tion is also introduced to connect services between
DTs. To ensure interoperability with external tech-
nologies and integrate our architecture with current
DT standards, we propose a metamodel based on the
Asset Administration Shell (AAS) data model (Bader
and Maleshkova, 2019). So the architecture does not
only meet the requirements of swarm systems but also
enables the seamless integration of third-party com-
ponents, including emerging technologies in industry
4.0.

The paper is structured as follows: Section 2 pro-
vides a review of the existing literature on design-
ing digital twins for the analysis of complex systems.
Section 3 outlines the key requirements for designing
a digital twin system specifically for swarm systems.
Section 4 provides an overview of our implementation
approach, with Section 5 detailing the implementa-
tion and Section 6 presenting a basic case study. Fi-
nally, Section 7 concludes the paper.

## 2 BACKGROUND AND PROBLEMATIC

Recent interest has grown in applying digital twins
to complex systems. In our review, we examine sev-
eral of these applications. The article (Human et al.,
2023) presents a six-step design framework that facil-
itates decision-making in the creation of a system of
digital twins with aggregation capabilities. It presents
a reference architecture as the foundation for these
systems, comprising three modules: an aggregation
hierarchy, a service network, and management ser-
vices. Inspired by SLADTA's work (Redelinghuys
et al., 2020), It introduces two types of digital twins:
the DTI, representing digital twins directly linked to
the physical, and the DTA, which aggregates data
from multiple DTs. The data-based aggregation pro-
posed in the paper does not provide a reliable means
to capture emerging behaviors in the DTA, as it re-
lies solely on data. In (Reiche et al., 2021) the inte-
gration of multiple digital twins and the management
of their network are examined. This study proposes
an approach to merge multiple digital twins under the
governance of a single point of truth called the Dig-
ital Twin of a System (DTS). It presents a vision of
the digital twin as a composition of Digital Models
(DM) and an aggregation of Digital Shadow (DS).
However, the connection possibilities through DTS
do not include direct communications between what
they call subordinate digital twins, which is crucial in
swarm systems. Additionally, the combinations are

only made with DTs of the same level. The article
(Moyne et al., 2020) presents the concept of digital
twins by adopting an object-oriented approach. It en-
visions the digital twin as consisting of models with
a computational engine, connected through an associ-
ation with a cardinality of (1,*). They introduce the
notion of classes of digital twins and, using object-
oriented concepts such as generalization hierarchy, in-
heritance, and aggregation, they define possible com-
binations between different digital twins. This ap-
proach, based on object-oriented concepts, is quite
original and interesting. However, since multiple in-
heritance is not supported by default in the object-
oriented concept, it is impossible to have an entity
that allows for the abstract representation of a digi-
tal twin resulting from the aggregation of lower-level
digital twins from different classes. Thus with the
proposed framework, aggregation can only occur with
digital twins of the same type and level. The articles
(Zhou et al., 2023b; Zhou et al., 2023a) discuss the
implementation of a digital twin network for satellite
communication. They propose a hierarchical archi-
tecture, but it is limited to two levels: the edge-DT
and the central-DT. This restricted hierarchy does not
accurately reflect the configuration of swarm systems,
which can include multiple levels of hierarchy.

So far, the review indicates that while there are
existing architectures and methodologies for the use
of digital twins in complex systems, they generally
lack certain specifications and features necessary for
application in the context of swarm systems analysis.

## 3 REQUIREMENTS OF DIGITAL TWIN ARCHITECTURE FOR SWARM SYSTEMS

In this section, we will present the specific character-
istics and properties of swarm systems, along with an
example. Additionally, we will outline the design re-
quirements imposed by such systems for developing
a digital twin.

### 3.1 Specifications of Swarm Systems

Swarm system represent a paradigm in how au-
tonomous entities collaborate to achieve complex
tasks. Unlike traditional single-agent systems,
swarms operate as decentralized networks where indi-
vidual components, often equipped with sensors, ac-
tuators, and communication capabilities, interact lo-
cally to accomplish shared objectives. The following
figure 1 illustrates a simple configuration of a swarm
of 2 thrusters surface drones during an escort mission. Swarm systems have a unique configuration with significant spatial and temporal dynamics, encompassing some properties developed by (Maier, 1998) for a system of systems (SoS). Below, we outline five key characteristics of swarm systems that will guide our vision for the digital twins of swarm systems.

*   **Managerial Independence:** The components are separately acquired and integrated but maintain a continuing operational existence independent of the swarm;
*   **Operational Independence:** If the swarm is disassembled into its components the components must be able to usefully operate independently;
*   **Hierarchy:** In the swarm, the concept of responsibility suggests that the components might function at different levels and offer varying services;
*   **Geographic Distribution:** The components of swarm systems are often distributed within a given space and exhibit a high spatiotemporal dynamic;
*   **Components Interaction:** The components of a swarm are subject to intense interactions, enabling the emergence of collective behaviors.

<figure><img src="image_3.png" /><figcaption>Figure 1: A formation of surface marine drones performing escort mission.</figcaption></figure>

## 3.2 Requirements Definition

As presented by (Human et al., 2023) in their design process of DT, a key step is the needs analysis, which results in the creation of a list of requirements. In their paper (Michael et al., 2022) authors list several challenges related to the integration of digital twins in a SoS context. These systems are similar to swarm configurations, as, highlighted in the introduction, the properties described in SoS are also present in swarm configurations. They identify 15 key points to consider for the integration of digital twins into a SoS. We have identified and included key points essential to our objectives, along with additional aspects

based on the swarm specifications outlined in the previous section. Relevant requirements definition ensure that our architecture will be able to achieve the expected abstraction. The following list outlines the key requirements, emphasizing the design considerations our system must fulfill as well as addressing specific DT user concerns.

*   **Synchronization:** The system must ensure data synchronization between physical entities and their corresponding digital twins, as well as between the digital twins deployed service;
*   **Hierarchical Structure:** The different levels of the physical world imply different levels of abstraction of functionality within the corresponding DTs;
*   **Aggregation:** The system should aggregate information from lower-level digital twins to provide a digital twin that offers a comprehensive view at higher levels for advanced analysis;
*   **Interoperability:** Achieving both syntactic and semantic interoperability is essential for the digital twins within this architecture and following the existing standards;
*   **HMI (Human Machine Interface):** Given the different levels of granularity, advanced views will be necessary, allowing the user to perform either a deep exploration of a component or the abstraction of a group of components.

## 4 HIERARCHICAL SYSTEM OF DIGITAL TWINS (HSDT)

Based on the defined requirements outlined above, this section presents the proposed architecture and vision for digital twins specifically tailored to the analysis of swarm systems. Several definitions of Digital Twins (DT) have been proposed (LaGrange, 2019; Glaessgen and Stargel, 2012; Singh et al., 2021), with most being predominantly domain-specific. Among them, the definition provided by the AIF committee stands out with its comprehensive approach, describing a DT as an organized set of digital models representing a real-world entity to address specific problems and use cases. While this definition is particularly interesting, we believe it would be valuable to incorporate the nature of the services rendered and to clearly specify that the reality being represented is not limited to the physical domain. Therefore, from a service-oriented perspective, we define the digital twin as a virtual system that represents a reality whether physical or not and connected to it through
a data flow; capable of delivering a range of ser-
vices, including simulation, debugging, formal verifi-
cation, monitoring, and system control, by leveraging
dynamic numerical models.

Regarding the composition of a digital twin, vari-
ous proposals are presented in the literature. We will
focus specifically on the proposal of (Kruger et al.,
2021), which the author presents in a hybrid service-
oriented approach where services can be hosted ei-
ther within the digital twin or in a Service-Oriented
Architecture (SOA). The services requiring data from
the physical system are provided by the digital twin,
while other services that need different types of data
are delivered through the SOA. This approach aligns
with our needs, as it allows for a level of functional
abstraction, which is one of the requirements outlined
in the previous section. According to the work of
(Human et al., 2023), which partially builds on the
research of (Kruger et al., 2021), the digital twin is
considered to consist of three layers: a model layer,
a services layer, and a data layer. Real-time bidirec-
tional communication is a crucial element in the life
cycle of digital twins, as presented in (Vaezi et al.,
2022). Therefore, we will also align with the work
(Chen et al., 2024) by integrating an interface layer.
This layer will define the interaction between the rep-
resented reality and the digital twin and between the
services provided by the DTs in the global architec-
ture.

Figure 2 illustrates the structure of DT and its
physical system (PS). Our digital twin structure incor-
porates a control data flow originating from the digi-
tal twin, unlike (Human et al., 2023) proposal, which
does not account for this level of sophistication in the
 workflow of DT.

<figure><img src="image_4.png" /><figcaption>Figure 2: The structure of a digital twin and its physical counterpart.</figcaption></figure>

Based on the proposed DT structure above, we de-
fine the HSDT architecture with the purpose of en-
hancing the development and deployment of multiple
digital twins in hierarchical configuration for analyz-
ing swarm system. The requirements outlined in Sec-
tion 3 serve as foundation for the development of this
architecture. Two types of Digital Twins are intro-
duced in this architecture, forming its core: the In-

stance DT, which is directly connected to reality, and
the **Aggregate** DT, which is a composition of multi-
ple Digital Twins. Figure 3 presents the overview of
the hierarchical system of digital twins. In the follow-
ing subsections, we detail the key aspects introduced
by the architecture.

<figure><img src="image_5.png" /><figcaption>Figure 3: Holistic reference architecture of the hierarchical system of digital twins.</figcaption></figure>

## 4.1 HSDT Metamodel and Interoperability

We define a metamodel (see Figure 4) based on the
Meta-Object Facility (MOF) standard. The meta-
model is designed to represent the domain structure
of the hierarchical digital twin (DT) system and to
ensure interoperability. The two defined types of DTs
are structured using a composite design pattern. Each
type of DT is associated with one or more goals, such
as monitoring, formal verification, simulation, or de-
bugging. However, the debugging and control capa-
bilities of a DT are specialized for the Instance DT, as
it is the only type of DT directly connected to reality.
Each DT includes embedded models utilized by var-
ious services. The Aggregate DT class, in contrast,
is not associated with an atomic Asset because it is
generated through the composition of DTs.

The notion of a goal is introduced to guide the ap-
propriate instantiation and level of sophistication of
DTs. Depending on the goal, certain elements of the
DTs may not be utilized. For example, for monitoring
purposes, only the data layer may be required, as no
computation is involved.

Interoperability within the HSDT architecture
refers to the ability of its entities to exchange data
(syntactic interoperability) and understand each other
(semantic interoperability). This property is critical,
as a DT may provide or depend on a service of-
fered by another DT, necessitating seamless data ex-
change. The proposed metamodel supports interop-
erability not only within the architecture but also se-
mantic interoperability with the AAS (Asset Admin-
istration Shell) standard, a cornerstone of Industry
4.0. To align with the AAS standard, we incorporate
two key elements into the AAS data model (Bader and
Maleshkova, 2019): **Asset** and **Submodel**, as high-
lighted in yellow in Figure 4.

<figure><img src="image_6.png" /><figcaption>Figure 4: The metamodel of the Hierarchical System of Digital Twin coupled with elements of AAS data model.</figcaption></figure>

## 4.2 Instance/Aggregate DT

As previously explained, the Instance DT is directly
connected to reality and possesses specific capabili-
ties such as debugging and control of the represented
reality, in addition to analytical functions. However,
achieving higher-level analysis requires a DT operat-
ing at a level above the Instance DT. To address this
need, we introduced the Aggregate DT (ADT) and a
method for its instantiation. The ADT enhances the
HSDT by enabling analysis at various levels of sys-
tem granularity. This aggregation of Digital Twins is,
therefore, a key feature for the advanced analytical
capabilities within the HSDT architecture. (Redel-
inghuys et al., 2020) introduced the concept of Digital
Twin Aggregation (DTA) for combining digital twins,
but their approach relies exclusively on data from
other digital twins. In contrast, we believe that ag-
gregating digital twins should be driven by a defined
analysis goals, allowing for a more selective choice of
elements involved in the aggregation. Therefore, in
the goal-oriented method presented here, ADT is cre-
ated based on a specific analysis problem (e.g., visu-
alization, prediction, anomaly detection), which helps
determine the appropriate goal. This approach con-
siders both data and/or models, depending on the se-
lected goal. The interest in introducing model aggre-
gation lies in the ability to capture, beyond the data,

the paradigm of each digital twin composing the new
twin. The model's aggregation could be achieved us-
ing model federation techniques, such as those pre-
sented in (Guérin, 2023) or for more formal model
by using composition operation such as parallel com-
position for automata. The goal-based aggregation
strategy enables the right choice of the sophistication
level of the new DT. For instance, if the aggregation
aims to provide an overview of a cluster's metrics, it
is not necessary to include model aggregation; data
from low-level DTs alone is sufficient. The synopsis
in Figure 5 illustrates the steps for instantiating a Dig-
ital Twin, in the case of Instance DT and Aggregate
DT.

<figure><img src="image_7.png" /><figcaption>Figure 5: The workflow of DT instantiation based on the goal-driven method.</figcaption></figure>

## 4.3 Hierarchical Structure

Given the hierarchy of responsibilities within swarm
systems, the digital twin system must reflect this orga-
nization. Therefore, with HSDT, we present two types
of hierarchies: a functional hierarchy and an aggrega-
tion hierarchy.

**Functional hierarchy:** The digital twins may dif-
fer in the range or complexity of services they pro-
vide. The functional hierarchy is based on the ca-
pabilities of each digital twin. For example, in the
HSDT, some digital twins might have more special-
ized functions or greater capabilities than others. So,
in this hierarchy, each digital twin's level is deter-
mined by the number of services it offers. Essentially,
DTs offering more or critical services are considered
higher in the hierarchy, reflecting their greater func-
tional role within the swarm.
**Aggregation hierarchy:** The aggregation hierar-
chy is distinct and is specifically designed for Aggre-
gate DTs. This type of hierarchy considers the struc-
tural relationships among digital twins that are com-
posed of multiple components. An important con-
cept here is **aggregation depth**, which corresponds to
the level within the hierarchy. Digital twins that are
directly connected to physical systems or real-world
data have an aggregation depth of 0. When these
individual twins are combined to form an aggregate
DT, the aggregation depth of the composite twin is
defined as one level higher than the maximum depth
of its components. This concept of aggregation depth
provides a standardized way to understand and orga-
nize complex digital twins built from multiple layers
of other twins. Equation 1 defined the way to calcu-
late the aggregation depth of an ADT composed of
n instances of DT and/or ADT. The process of ADT
creation will be explained in the following subsection.
This method enables the HSDT to organize and nav-
igate complex structures efficiently, helping to distin-
guish between different levels of aggregation in the
swarm system.

$$
d_{\text{ADT}} = \max(d_1, d_2, \dots, d_n) + 1 \quad (1)
$$

4.4 Synchronization: PS to DT and DT
to DT

The synchronization is essential to ensure that decisions made based on the digital twin are reliable and relevant. A failure in synchronization can lead to inconsistencies, errors in data analysis, and inappropriate actions. As highlighted by the authors in (Coviello et al., 2020), who emphasize the importance of a synchronization mechanism in a multi-sensor system, the digital twin directly connected to a physical system has similar requirements. Indeed, it can be fed by various data sources from the different sensors of the system entity it represents. Synchronization must occur in real-time, and for the twin to remain up-to-date, the latency with the data generated by the physical system must be low. In our context, where the components of the swarm system are considered to be equipped with sensors and the data is accessible, synchronization involves establishing communication capable of transmitting this data with minimal latency. Certain protocols enable fast and reliable message handling between two application entities. The authors (Uy and Nam, 2019) compare two widely used protocols in the context of IoT and M2M communication: Message Queuing Telemetry Transport (MQTT) and Advanced Message Queuing Protocol (AMQP). The conclusions of their study show that AMQP is the better choice when designing a link with a continuous

data stream. Therefore, in the architecture, we recom-
mend using the Advanced Message Queuing Proto-
col (AMQP). Implementing this protocol will ensure
a low-latency level in data exchanges.

In addition to synchronizing the digital twin with
the reality it represents, it is essential to ensure syn-
chronization between the digital twins, especially be-
tween the services provided by each DT. This is es-
sential to ensure effective and coordinated commu-
nication between the various services. To synchro-
nize these services, several solutions are available to
us, including the use of an orchestrator or an event-
based coordination. In the HSDT architecture we use
an event-based synchronization. This later involves
services communicating through a service bus. Ser-
vices act as both event consumers and/or event pro-
ducers. Figure 6 illustrates the synchronization be-
tween DTs services; service_y of DT_j can publish an
event on Topic 2, while service_x of DT_i subscribes
to this event.

<figure><img src="image_8.png" /><figcaption>Figure 6: Service synchronization in HSDT, an Event-Based approach.</figcaption></figure>

5 HSDT PLATFORM PROTOTYPE

We propose to implement our architecture using
Pharo, a purely object-oriented programming lan-
guage and a powerful environment focused on sim-
plicity and immediate feedback. The HSDT platform
called *DTwinSync* will be deployed within instances
of the Pharo 12 Image. The platform offers all the
tools and APIs needed to develop and interact with
an HSDT architecture. This allows us to create dig-
ital twins, associate them with physical components.
This implementation offers several advantages, such
as ease of deployment, with all dependencies included
in the image, as well as re-usability. In this implemen-
tation, we will use multi-threading concepts to meet
real-time constraints. Specifically, communication-
related functions will be executed in separate threads.
The communication between the digital twin inside
the Pharo image and the physical system is done us-
ing the MQTT protocol (for seek of simplicity). The development platform's source code is available in a public repository<fnref n="1" />.

# 6 Case Study: UVs Target Search

In this section, we present a simple case study to demonstrate the ability of our approach to analyze in different levels of granularity in a swarm of UVs. The case study is as follows: marine UVs are deployed over a body of water and organized into a swarm formation, divided into two groups, the identifiers and the actuators. The identifiers are equipped with devices to detect a target in a specific location, while the actuators are responsible for carrying out the necessary action. The success of the mission depends on the cooperation between the UVs from both groups, with each fulfilling its designated tasks. The target is located within the water body, and its position is known. The DTs directly linked to the UVs will be fed with data such as position and status. Due to difficulties in accessing physical infrastructure, we will use a Python program to simulate the physical swarm. The objective of the analysis in this case study is to have an idea of the spatial distribution of our swarm at a specific point in time.

## Instance DT

The following code snippet shows the script in Pharo that declare the instance DT and link them to their physical counterparts. Once this instantiation is complete, the data flow shared by the physical system will be available in real time on the digital twin (DT).

```pharo
1 dt := OrderedCollection new.
2 0 to: 3 do: [ :i |
3     dt add: (DTwin new start:
4         (PhysicalCounterpart new id: i))
5     $].
```

## Aggregate DT

The goal now is to analyze a very simple parameter: entropy, which can provide information about the geographic distribution of our robots. These metrics cannot be calculated by the local digital twins of the UVs, highlighting the need for high-level analysis. Subsequently, we will instantiate different digital twins and use aggregation to create ADT that will allow us to calculate the entropy of our group of marine UVs.

### 1. Related DTs: The digital twins of the 4 UVs

### 2. Goals: Monitoring (Analyze the entropy)

### 3. Data Aggregation: Location attribute of each UV, thus the data layer of the affiliated DTs

The following code snippet shows the syntax for instantiating an ADT. The model that will be loaded onto the ADT is *EntropyModel*. The principle of this method is straightforward: it calculates entropy by dividing the area into cells and counting the number of points in each cell. Next, it computes the probabilities of having a point in each specific cell. Finally, the total entropy is calculated using the equation 2. To achieve this, after instantiating the ADT, we loaded the *EntropyModel*, which calculates the entropy, along with the *EntropyVisualisation* service, which displays a plot of the entropy evolution. The figure illustrates this evolution.

1. ADT := DTwinHL new.
2. ADT aggregationType
3. add: (AggType dataAggregation).
4. ADT aggregate: dt;
5. load: EntropyModel;
6. load: EntropyVisualisation.

$$H(X) = - \sum_{i=1}^{n} p_i \log_b(p_i) \quad (2)$$

In the following figure 7, after running the computation in the ADT, the model is executed, and the results are passed to the visualizer, which then plots them. The closer the entropy gets to zero, the more concentrated the points become. Thus, as the mission progresses, the expected behavior is observed: the UVs move closer to the target point and become less dispersed.

<figure><img src="image_9.png" /><figcaption>Figure 7: Plot showing the Entropy of the UVs swarm through ADT.</figcaption></figure>

# 7 CONCLUSION

In this article, we present our vision to design a hierarchical system of digital twins, aimed at analyzing systems in a swarm configuration. After defining the requirements we proposed a holistic architecture

<footnote n="1">¹https://github.com/Cracen26/DTwinSync-beta</footnote>
that emphasizes organizing DTs within a hierarchical configuration. This architecture is holistic because it considers all levels of granularity within the swarm and accounts for the relationships between them. We introduce a new method called goal-driven to instan- tiate DT. Furthermore, the proposed metamodel is built upon the standard AAS, aiming to enhance the openness of our architecture to Industry 4.0. Finally, we present a simple case study to apply the theoreti- cal concepts of HSDT, particularly by conducting an analysis through the creation of an Aggregate DT. However, this case study does not fully validate all elements of the architecture and should be further de- veloped to encompass all the aspects discussed in this paper. Some areas require further development, such as the reconfiguration loop between the digital twin and the represented reality. Established engineering approaches, like MAPE-K (Arcaini et al., 2015), can be leveraged to design this connection.

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