Hierarchical System of Digital Twins: A Holistic Architecture for Swarm

System Analysis

Mouhamadou F. Ball

1 a

, Jannik Laval

2 b

and Lo

ıc Lagadec

1 c

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

DISP-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 solu-

tion 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 Eu-

ropean Union’s SCAF project for the future air force

is based on this conﬁguration. Given the increas-

ingly critical missions assigned to this type of sys-

tem and its evolution in uncertain environments, it be-

comes 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 ab-

straction (component, cluster, swarm) and from vari-

ous perspectives. The Digital Twin (DT) represents a

https://orcid.org/0009-0005-9245-2892

https://orcid.org/0000-0002-7155-5762

https://orcid.org/0000-0003-3778-3144

promising technology for addressing the challenges

of analyzing such systems. The literature presents

various approaches that leverage digital twins for ana-

lyzing complex systems (e.g., Cyber Physical System,

SoS). However, after deﬁning the requirements for a

digital twin in the context of swarm systems, we ob-

serve 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 funda-

mental 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 hierarchi-

cal system of digital twins. We start by deﬁning the

requirements of such digital twins based on the spec-

iﬁcations 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,

280

Ball, M. F., Laval, J. and Lagadec, L.

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

DOI: 10.5220/0013258900003896

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Model-Based Software and Systems Engineering (MODELSWARD 2025), pages 280-287

ISBN: 978-989-758-729-0; ISSN: 2184-4348

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

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

281

of 2 thrusters surface drones during an escort mission.

Swarm systems have a unique conﬁguration with sig-

niﬁcant spatial and temporal dynamics, encompass-

ing 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 disas-

sembled into its components the components must

be able to usefully operate independently;

• Hierarchy: In the swarm, the concept of respon-

sibility suggests that the components might func-

tion 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 dy-

namic;

• Components Interaction: The components of a

swarm are subject to intense interactions, enabling

the emergence of collective behaviors.

Figure 1: A formation of surface marine drones performing

escort mission.

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 con-

sider for the integration of digital twins into a SoS.

We have identiﬁed and included key points essen-

tial to our objectives, along with additional aspects

based on the swarm speciﬁcations outlined in the pre-

vious section. Relevant requirements deﬁnition en-

sure that our architecture will be able to achieve the

expected abstraction. The following list outlines the

key requirements, emphasizing the design consider-

ations 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 be-

tween the digital twins deployed service;

• Hierarchical Structure: The different levels of

the physical world imply different levels of ab-

straction of functionality within the corresponding

DTs;

• Aggregation: The system should aggregate infor-

mation 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 se-

mantic interoperability is essential for the digital

twins within this architecture and following the

existing standards;

• HMI (Human Machine Interface): Given the dif-

ferent levels of granularity, advanced views will

be necessary, allowing the user to perform either

a deep exploration of a component or the abstrac-

tion 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 vi-

sion for digital twins speciﬁcally tailored to the anal-

ysis of swarm systems. Several deﬁnitions of Digi-

tal 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, describ-

ing a DT as an organized set of digital models repre-

senting a real-world entity to address speciﬁc prob-

lems and use cases. While this deﬁnition is particu-

larly 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 digi-

tal twin as a virtual system that represents a reality

whether physical or not and connected to it through

MODELSWARD 2025 - 13th International Conference on Model-Based Software and Systems Engineering

282

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 2: The structure of a digital twin and its physical

counterpart.

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 3: Holistic reference architecture of the hierarchical

system of digital twins.

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-

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

283

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 4: The metamodel of the Hierarchical System of

Digital Twin coupled with elements of AAS data model.

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 (Gu

erin, 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 5: The workﬂow of DT instantiation based on the

goal-driven method.

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 differ

in the range or complexity of services they provide.

The functional hierarchy is based on the capabilities

of each digital twin. For example, in the HSDT, some

digital twins might have more specialized functions

or greater capabilities than others. So, in this hier-

archy, each digital twin’s level is determined by the

number of services it offers. Essentially, DTs offer-

ing more or critical services are considered higher in

the hierarchy, reﬂecting their greater functional role

within the swarm.

Aggregation Hierarchy. The aggregation hierarchy

is distinct and is speciﬁcally designed for Aggregate

DTs. This type of hierarchy considers the structural

MODELSWARD 2025 - 13th International Conference on Model-Based Software and Systems Engineering

284

relationships among digital twins that are composed

of multiple components. An important concept 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 ag-

gregation depth of the composite twin is deﬁned as

one level higher than the maximum depth of its com-

ponents. This concept of aggregation depth provides a

standardized way to understand and organize complex

digital twins built from multiple layers of other twins.

Equation 1 deﬁned the way to calculate the aggrega-

tion 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 navigate complex

structures efﬁciently, helping to distinguish between

different levels of aggregation in the swarm system.

ADT

= max(d

, d

, . . . , d

) + 1 (1)

4.4 Synchronization: PS to DT and DT

to DT

The synchronization is essential to ensure that deci-

sions made based on the digital twin are reliable and

relevant. A failure in synchronization can lead to in-

consistencies, errors in data analysis, and inappropri-

ate actions. As highlighted by the authors in (Coviello

et al., 2020), who emphasize the importance of a syn-

chronization 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 oc-

cur 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 com-

ponents of the swarm system are considered to be

equipped with sensors and the data is accessible, syn-

chronization involves establishing communication ca-

pable of transmitting this data with minimal latency.

Certain protocols enable fast and reliable message

handling between two application entities. The au-

thors (Uy and Nam, 2019) compare two widely used

protocols in the context of IoT and M2M communica-

tion: 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 6: Service synchronization in HSDT, an Event-

Based approach.

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

https://github.com/Cracen26/DTwinSync-beta

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

285

6 CASE STUDY: UVs TARGET

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 for-

mation, divided into two groups, the identiﬁers and

the actuators. The identiﬁers are equipped with de-

vices to detect a target in a speciﬁc location, while the

actuators are responsible for carrying out the neces-

sary 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 dif-

ﬁculties 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 com-

plete, the data ﬂow shared by the physical system will

be available in real time on the digital twin (DT).

1 dt := OrderedCollection new.

2 0 to: 3 do: [ :i |

3 dt add: (DTwin new start:

4 (PhysicalCounterpart new id: i))

].→

Aggregate DT

The goal now is to analyze a very simple parame-

ter: entropy, which can provide information about

the geographic distribution of our robots. These met-

rics cannot be calculated by the local digital twins of

the UVs, highlighting the need for high-level analy-

sis. Subsequently, we will instantiate different digital

twins and use aggregation to create ADT that will al-

low 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 in-

stantiating an ADT. The model that will be loaded

onto the ADT is EntropyModel. The principle of this

method is straightforward: it calculates entropy by di-

viding the area into cells and counting the number

of points in each cell. Next, it computes the prob-

abilities of having a point in each speciﬁc cell. Fi-

nally, the total entropy is calculated using the equa-

tion 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) = −

∑

i=1

log

) (2)

In the following ﬁgure 7, after running the computa-

tion 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 concen-

trated the points become. Thus, as the mission pro-

gresses, the expected behavior is observed: the UVs

move closer to the target point and become less dis-

persed.

Figure 7: Plot showing the Entropy of the UVs swarm

through ADT.

7 CONCLUSION

In this article, we present our vision to design a hi-

erarchical system of digital twins, aimed at analyz-

ing systems in a swarm conﬁguration. After deﬁning

the requirements we proposed a holistic architecture

that emphasizes organizing DTs within a hierarchical

conﬁguration. This architecture is holistic because it

considers all levels of granularity within the swarm

MODELSWARD 2025 - 13th International Conference on Model-Based Software and Systems Engineering

286

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.

REFERENCES

Arcaini, P., Riccobene, E., and Scandurra, P. (2015). Mod-

eling and analyzing mape-k feedback loops for self-

adaptation. In 2015 IEEE/ACM 10th International

Symposium on Software Engineering for Adaptive and

Self-Managing Systems, pages 13–23. IEEE.

Bader, S. R. and Maleshkova, M. (2019). The seman-

tic asset administration shell. In Semantic Systems.

The Power of AI and Knowledge Graphs: 15th Inter-

national Conference, SEMANTiCS 2019, Karlsruhe,

Germany, September 9–12, 2019, Proceedings 15,

pages 159–174. Springer.

Chen, Z., Surendraarcharyagie, K., Granland, K., Chen, C.,

Xu, X., Xiong, Y., Davies, C., and Tang, Y. (2024).

Service oriented digital twin for additive manufac-

turing process. Journal of Manufacturing Systems,

74:762–776.

Coviello, G., Avitabile, G., and Florio, A. (2020). The

importance of data synchronization in multiboard ac-

quisition systems. In 2020 IEEE 20th Mediter-

ranean Electrotechnical Conference (MELECON),

pages 293–297. IEEE.

Glaessgen, E. and Stargel, D. (2012). The digital twin

paradigm for future nasa and us air force vehi-

cles. In 53rd AIAA/ASME/ASCE/AHS/ASC structures,

structural dynamics and materials conference 20th

AIAA/ASME/AHS adaptive structures conference 14th

AIAA, page 1818.

erin, S. (2023). FML: un langage de f

eration de

mod

eles pour l’interop

erabilit

e s

emantique de sources

d’information h

erog

enes. PhD thesis, ENSTA

Bretagne-

Ecole nationale sup

erieure de techniques

avanc

ees Bretagne.

Human, C., Basson, A., and Kruger, K. (2023). A design

framework for a system of digital twins and services.

Computers in Industry, 144:103796.

Kruger, K., Human, C., and Basson, A. (2021). Towards the

integration of digital twins and service-oriented archi-

tectures. In International Workshop on Service Ori-

entation in Holonic and Multi-Agent Manufacturing,

pages 131–143. Springer.

LaGrange, E. (2019). Developing a digital twin: The

roadmap for oil and gas optimization. In SPE

Offshore Europe Conference and Exhibition, page

D011S003R001. SPE.

Liu, Y. and Passino, K. M. (2000). Swarm intelligence: Lit-

erature overview. Department of electrical engineer-

ing, the Ohio State University.

Maier, M. W. (1998). Architecting principles for systems-

of-systems. Systems Engineering: The Journal of

the International Council on Systems Engineering,

1(4):267–284.

Michael, J., Pfeiffer, J., Rumpe, B., and Wortmann,

A. (2022). Integration challenges for digital twin

systems-of-systems. In Proceedings of the 10th

IEEE/ACM International Workshop on Software Engi-

neering for Systems-of-Systems and Software Ecosys-

tems, pages 9–12.

Moyne, J., Qamsane, Y., Balta, E. C., Kovalenko, I., Faris,

J., Barton, K., and Tilbury, D. M. (2020). A require-

ments driven digital twin framework: Speciﬁcation

and opportunities. Ieee Access, 8:107781–107801.

Redelinghuys, A., Kruger, K., and Basson, A. (2020). A

six-layer architecture for digital twins with aggrega-

tion. In Service Oriented, Holonic and Multi-agent

Manufacturing Systems for Industry of the Future:

Proceedings of SOHOMA 2019 9, pages 171–182.

Springer.

Reiche, L.-T., Gundlach, C. S., Mewes, G. F., and Fay, A.

(2021). The digital twin of a system: A structure for

networks of digital twins. In 2021 26th IEEE interna-

tional conference on emerging technologies and fac-

tory automation (ETFA), pages 1–8. IEEE.

Singh, M., Fuenmayor, E., Hinchy, E. P., Qiao, Y., Murray,

N., and Devine, D. (2021). Digital twin: Origin to

future. Applied System Innovation, 4(2):36.

Uy, N. Q. and Nam, V. H. (2019). A comparison of amqp

and mqtt protocols for internet of things. In 2019

6th NAFOSTED Conference on Information and Com-

puter Science (NICS), pages 292–297. IEEE.

Vaezi, M., Noroozi, K., Todd, T. D., Zhao, D., Karakostas,

G., Wu, H., and Shen, X. (2022). Digital twins from a

networking perspective. IEEE Internet of Things Jour-

nal, 9(23):23525–23544.

Zhou, L., Leng, S., and Wang, Q. (2023a). A federated dig-

ital twin framework for uavs-based mobile scenarios.

IEEE Transactions on Mobile Computing.

Zhou, Y., Zhang, R., Liu, J., Huang, T., Tang, Q., and Yu,

F. R. (2023b). A hierarchical digital twin network for

satellite communication networks. IEEE Communica-

tions Magazine.

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

287