Towards a Domain-Neutral Platform for Sustainable Digital Twin Development

Abstract

In this paper, we propose an abstract domain-neutral architecture for a cognitive digital twin (CDT) and a software platform to develop such CDTs, including machine reasoning capabilities. Sustainable development refers here to an abstract model that enables a holistic view of limiting resources and has an ability to adapt to different application domains while reusing existing resources. The proposed solution allows for a unified abstract representation and the development of a wide range of diverse digital twins, as well as facilitating their interoperability. The abstract architecture consists of a four-layer structure (observation/actuation layer, data management layer, reasoning layer, and simulation layer) with an upper ontology to which the domain ontology of the specific CDT is mapped. The architecture relies on semantic web technologies, including ontology-based reasoning using OWL, and a loosely coupled, component-based service-oriented software architecture. The platform utilizes a microservice architecture that enables separate, loosely coupled services on each layer, message queues to provide asynchronous communication, and possesses cloud technologies to achieve scalability. The proposed approach was validated by implementing a software platform prototype and demonstrating its key features through two dissimilar scenarios. The first scenario demonstrates simple sustainable energy management through IoT systems inside smart buildings, while the second one demonstrates knowledge quality management based on knowledge space theory.

1. Introduction

Sustainability can be understood in various ways, as different communities and interest groups perceive it differently. Nevertheless, they all strive for a common objective: securing a sustainable future for the coming generations. In this work, we have embraced the definition put forth by the University of Alberta [1], which reads: “Sustainability is the process of living within the limits of available physical, natural, and social resources in ways that allow the living systems in which humans are embedded to thrive in perpetuity”.

Digital twins (DTs) are virtual representations of real physical systems, enabled by a combination of technologies such as the Internet of Things (IoT), cloud, etc. [2]. The concept of DTs has a significant capacity to improve sustainability due to the ability to expand the boundaries of available physical, natural, and social resources. This expansion is achieved by representing real resources through their digital equivalents, thereby minimizing the irreversible consumption of real resources. The source [3] examines DTs benefits in promoting the sustainable development goals, specifically the role of inclusive, reliable, and responsible computer simulations for achieving sustainable development.

In modern society, the concept of a DT applies to most domains, from commodity production to complex social interactions, and therefore, its implementation requires an extremely complex apparatus, often highly dependent on the specific domain. Nevertheless, the starting point in developing such systems is the construction of a digital model of an individual (not necessarily physical) entity. Subsequently, the next step is to build a digital model of a complex system by composing individual entities that interact with each other and with the external environment.

Platforms intended to support DT systems are still in the infancy stage of development. They are currently limited to specialized application domains, mostly different industries, and therefore have both semantic and syntactic limitations, allowing modeling only for specific domains and according to a pre-defined set of rules.

This research should help resolve the problem by providing unified support (conceptual and technical) to facilitate the development of digital twins for a wide range of complex systems.

One characteristic of DTs is that they essentially depend on interoperability due to the wide range of applications, the scale, and heterogeneity of the technologies used and, finally, the presence of the phenomenon of silos in industries. There are vivid activities in this area. The results are, in addition to scientific papers, numerous international standards concerning interoperability of DTs, such as the family of IEEE 1451 standards that deal with communication interfaces for connecting sensors or actuators to other devices and networks, the ISO 23247-1:2021 standard that defines interoperability of DTs through a reference architecture for DTs in manufacturing, and the ISO/IEC/IEEE 42010:2022 standard that deals with the creation, analysis, and maintenance of system architecture in the field of system and software engineering. In addition to scientific works and standards, there are also publications of professional associations, among which the document “Digital Twin System Interoperability Framework” [4], a white paper of the Digital Twins Consortium stands out. This document provides a broader, domain-neutral framework for interpreting and implementing the interoperability of DTs. The document proposes a DT interoperability framework based on seven interoperability concepts: system-centric design, model-based approach, holistic information flow, state-based interactions, federated repositories, actionable information, scalable mechanisms. Blockchain combined with semantic technologies is currently popular in achieving interoperability [5,6]. Despite the clearly identified need for the interoperability of DTs, there is still no generally accepted framework, i.e., the issue of interoperability of DTs is solved individually, most often in close connection with the application domain.

As for the abstract architectures of DTs, the situation is similar to that of interoperability. There are attempts to define reference architectures in scientific papers, and the mentioned proposal of reference architecture from the ISO 23247-1:2021 standard. Among the architectures proposed in scientific papers, most are strictly domain-dependent, but there are also proposals for architectures that are applicable to multiple domains, such as the architectures C2PS digital twin architecture reference model for the cloud-based cyber-physical systems [7] and three-dimensional CDT reference architecture [8]. As for platforms to support DTs, it can be said that they are in the initial stage of development and also domain-limited. An interesting proposal of a DT software platform is published in [9]. The platform is characterized, first of all, by its pragmatic nature, but it also contains elements that form a good basis for utilization in different domains. Here again, the need for some kind of commonly accepted reference framework to support DTs in different domains is clearly identified, but such a framework still does not exist.

To ensure sustainable management of limited resources, a cross-domain view of the system is needed. From this requirement, the research question in this paper arises: Is it possible to create a domain-independent platform of digital twins and how would specific application domains be represented in such a platform? We tried to answer that question by developing an abstract domain-neutral architecture of a CDT, and a software platform that enables the development and operation of such CDTs, including machine reasoning capabilities.

The rest of the paper is organized as follows: Section 2 presents the materials and methods by analyzing related work and investigating their suitability to meet the platform’s requirements. In Section 3, which contains the main scientific contribution, we present the conceptual model of the CDT-enabling platform and describe its implementation architecture. Section 4 validates the proposed approach through two usage scenarios. Finally, Section 5 provides conclusions about the presented research and outlines future work.

2. Materials and Methods

This paper investigates a software platform aimed at representing physical entities through their digital immaterial equivalents. The materials used in this platform consist of immaterial digital equivalents of all physically materialized entities. The research employs two basic methodological approaches: systems engineering and software engineering.

This section is divided into two subsections. The first subsection provides an overview of the related work conducted so far in the field. The second subsection outlines how these relevant results are applied in the research presented in this paper.

2.1. Related Work

Research in the domain of DTs dates back to the end of the last century. It is widely acknowledged that the concept of a DT was first introduced in 1997 in the work [10]. The term, as it is understood today as a “digital equivalent to a physical product”, was introduced by Michael Grieves in his Executive Course on product lifecycle management (PLM) at the University of Michigan in 2003.

The concept of DTs continues to evolve in the context of digital transformation, occupying a prominent place in the integration of human–machine systems. As a result, several extensions of the DT concept have emerged, among which CDT and symbiotic autonomous systems (SAS) are particularly relevant for the platform researched in this paper.

The remainder of this section will focus on analyzing results related to DT, CDT, SASs, and DT platform implementations. The primary goal is to investigate how these results can contribute to the development of our platform.

Several publications review the state-of-the-art in DTs. Paper [11] stands as one of the first review papers about DTs. The authors present the state-of-the-art in the field, covering the concept and a brief history of DTs, the current development of DTs (theoretical foundations, DT modeling and simulation, data fusion, interaction and collaboration, and services), and industrial applications of DTs reported through publications, patents, and the best practices of leading companies. The paper concludes with observations and recommendations outlining two promising DT application areas: dispatching optimization and operational control. Although the paper’s focus is primarily on industrial applications, the authors mention that Gartner’s 2017 Report considered facilities and environments as well as people, businesses, and processes. Furthermore, Gartner’s 2022 Report introduced the concept of the “digital twin of the customer” (DToC), which represents a dynamic virtual representation of a customer, capable of simulating, learning, emulating, and anticipating behavior. In their publication [12], Liu et al. selected and classified 240 academic publications about DTs and conducted a review to analyze DTs from the perspective of concepts, technologies, and industrial applications. They demonstrated the research status, the evolution of the concept, and the key enabling technologies in three aspects: data, modeling, and model-based simulation. The paper also presents fifteen kinds of industrial applications of DTs in respective lifecycle phases. Based on their findings, the authors offer observations and future work recommendations for DT research, organized into four lifecycle phases: design, manufacturing, service, and retire phase. In the publication [13], Semeraro et al. present a systematic literature review approach, resulting in a multi-perspective picture of the DT concept emerging from the scientific literature. The review covers six main aspects: the definition of DTs, application contexts, life cycle phases, functions, architecture, and components, as well as research challenges. To serve that purpose, the authors applied text mining analysis for extracting DT features and formal concept analysis (FCA) to gain a deeper understanding of the definition of DT life cycle phases, functions, architecture, and components. The source [14] reviews technologies and discusses the sustainability of intelligent manufacturing. The relevant content of intelligent manufacturing (equipment, systems, and services) is analyzed, and the sustainability of intelligent manufacturing is discussed emphasizing the role of DTs.

Without any doubt, the most numerous works in the field of DTs are those that deal with solving specific practical tasks in different domains by applying the idea of a DT. In this context, we will only mention some results that are directly related to the topic of research in this paper, specifically referring to the management of sustainable infrastructure, such as buildings and energy [15,16,17], and learning and education [18,19].

The term cognitive DT appeared in the literature in the second decade of the 21st century, in the publications of authors Ahmed El Adl [20] in 2016 and Fariz Saračević [21] in 2017. This concept was inspired by the basic requirements set by the vision of Industry 4.0 and the emergence of various technologies needed for its implementation. Essentially, the concept represents an expansion of the DT concept, incorporating elements that enable a certain level of autonomous behavior during the life cycle of a system. The paper authored by Xiaochen Zheng, Jinzhi Lu, and Dimitris Kiritsis [8] stands out for its comprehensive presentation of research and results concerning CDTs. It identifies the vision, challenges, and possibilities of the CDT concept. In our research, we adopted the definition of the term CDT from this source: “Cognitive Digital Twin (CDT) is a digital representation of a physical system that is augmented with certain cognitive capabilities and support to execute autonomous activities. It comprises a set of semantically interlinked digital models related to different lifecycle phases of the physical system, including its subsystems and components. Furthermore, it evolves continuously with the physical system across the entire lifecycle”.

The analyzed publications can be further divided into works that predominantly deal with theoretical issues and those that are primarily dedicated to creating solutions for specific engineering tasks. In the paper [22], Kharlamov and co-authors report preliminary results on developing a system that would support semantic-based DTs. They argue that semantic technologies, particularly ontologies, constitute a promising modeling paradigm for DTs. They perceive a semantic model as an instrument that can help address the data and application-dependency challenges that exist with asset models. By using semantic models, they can abstractly represent an industrial asset and ‘connect’ it to the actual data about the asset, its sensors, and signals with the help of declarative mapping specifications. Boschert, Heinrich, and Rosen [23] introduced the term “next generation digital twin (nextDT)” paradigm, which refers to a comprehensive networking of all information shared between partners, connecting design, production, and usage. The concept involves a collection of relevant digital artifacts (DTs), where a DT refers to a description of a component, product, system, or process using a set of well-aligned, descriptive, and semantically linked executable models. These models evolve with the real system throughout the entire life cycle and integrate the currently available and commonly required data and knowledge. Starting with the presumption that the choice of DT’s characteristics depends on its purpose, Fernández, Sánchez, Vélez, and Belén Moreno coined the term “associative cognitive digital twin” for “a real-time goal-oriented augmented virtual description, which explicitly includes the associated external relationships of the considered entity for the considered purpose” [24]. The corresponding graph data model of the involved world supports artificial consciousness, enabling the understanding of involved ecosystems and related higher-level cognitive activities. The cognitive architecture for SAS is defined based on the “consciousness framework”. As a specific application example, an architecture for critical safety systems is shown. In the paper [25], the authors attempted to cope with probably the most difficult challenge that arises in the application of CDT—how to improve the management of complexity and support decision making during the entire life cycle of the system. The paper explores the CDT concept and its key elements using a system engineering approach. It defines an ISO 42010 standard-compliant conceptual architecture to support the development of CDT, provides an application framework for the implementation of CDT applications based on a knowledge graph, proposes a set of tools for the application framework to facilitate the implementation of CDT, and presents a case study based on simulation experiments as proof of concept. In [26], a novel modeling method for a complex DT is proposed, considering the total elements, variable scale of working environments, and changeable processes. The complex model of a DT is divided into simple 4C architecture models (composition, context, component, and code). Complex models of DTs are constructed by assembling the simple models through information fusion, multi-scale association, and multi-scenarios iterations. Semantic technologies are employed to establish a comprehensive information library of entities on different DTs (ontology) and bridge the structural relationship between different scales of DTs (knowledge graph). The iterative scenario approach leads to an implementable method for constructing complex models of DTs. In [27], the authors propose a conceptual framework for implementing CDTs to support resilience in production. Through analyzing five real-life production cases in different industries the corresponding needs are identified, and a connection between resilience and cognition is established. Furthermore, a conceptual architecture is proposed, mapping the tools materializing cognition within the DT core, along with a cognitive process that enables resilience in production through the utilization of CDTs. Papers [26,27,28,29,30,31,32,33,34,35,36,37,38,39] are included in this analysis to illustrate that the CDT concept is utilized in various industrial domains, such as process industry [28], manufacturing [29,30,31], maintenance management [32], construction [33,34,35,36,37] where works [36,37] propose ML models suitable for the design of DTs in the construction industry, and health care [38,39]. Additionally, publication [40] with its thematic focus on DTs in learning and education attracted the attention of the authors of this paper. The publication includes a total of 54 titles, with 22 of them primarily dealing with learning and learning management, and an additional 8 titles specifically targeting the topic of sports training.

Although the concept of a cognitive DT captures key elements in the subject of our research, the role of humans in such a system deserves special attention, as addressed in the field of SAS. The idea of symbiosis between humans and machines has drawn interest from researchers across various domains and has resulted in practical solutions with concrete value. We will now list the most significant results [37,38,39,40,41,42,43,44,45,46,47,48] in our opinion and briefly analyze those that form the foundation of the field and address issues relevant to our platform. Three white papers [41,42,43] were published in 2017, 2018, and 2019, respectively, as part of the IEEE SAS Initiative. These publications provide in-depth elaboration on SAS. White Paper I [41] examines current and emerging technologies, as well as their ethical, socioeconomic, legal, and technology policy impacts. It outlines an interdisciplinary path from the past to the present and envisions possible futures through 2050. The paper identifies primary technologies categorized into advanced interaction capabilities, self-evolving capabilities, and autonomous decision making capabilities. Additionally, it presents a roadmap to the most likely technological futures, discussing their sociocultural implications and narrative scenarios in various fields. The conclusion emphasizes that SAS holds significant potential and, therefore, is associated challenges that require attention to educational, sociocultural, and legal aspects. White Paper II [42] and White Paper III [43] further delve into the subject of SAS. White Paper II expands on the technology overview provided in the first white paper, focusing on the evolution of artificial general intelligence and supporting technologies, sentiment and mood analysis, human augmentation technologies, and the growing prevalence of DTs. These technological developments are then contextualized within society and economics, exploring mutual implications, how technology influences society, culture, and economics, and how societal, economic, cultural, legal, and political circumstances influence technology evolution. The paper also delves into philosophical and societal aspects, such as the concept of selves, ethics, the evolution of the law, and the changing meaning of democracy, considering the expanding notion of a citizen to encompass symbiotic citizens with blurred boundaries between humans and machines. White Paper II also emphasizes the impact on the market and education. In the realm of education, DTs are recognized as essential for managing the knowledge gap through personal knowledge DTs. The concept of SAS is envisioned to lead us into an era of symbiotic shared education, where the education protocol undergoes significant changes to focus on educating machines rather than just humans. On the other hand, White Paper III discusses the evolution of the market, including technology market trends and the adoption of SAS in various industrial sectors such as manufacturing, health care, retail, finance, transport, telecommunications, and security. The paper also explores the societal impacts at personal, city, and community levels, as well as the effects on jobs and ethical considerations associated with the adoption of these systems. The Special Issue “Towards Symbiotic Autonomous Systems” published in the Philosophical Transactions of The Royal Society includes results from papers [40,41,42,43,44,45,46], which are categorized into research, review, discussion, and opinion pieces. The papers were selected to cover a wide range of topics and were classified into fundamentals-related, methodology-related, and application-related articles. The fundamentals-related articles [44,45,46] address ethical issues [44], the philosophical, cognitive, and mathematical foundations of SAS [45], and the development of symbiotic relationships [46]. The methodology-related articles are [47,48]. In [47], the potential of combining semantics and data analysis in the context of DTs is explored, while [48] focuses on the engineering of human-focused systems in the context of Industry 4.0. The application-related articles [49,50] showcase examples of applications in the domains of cyber security and production, respectively. Paper [51] presents an application in the field of health care, specifically in the diagnostics and rehabilitation of multiple sclerosis. The results of [52,53] specifically deal with entities and the process of learning phenomena. They are linked by the authors and the topic as they explore the possibilities of the evolution of education (in engineering and symbiotics) based on the DT as a common denominator. Regarding the quality of knowledge gained through a learning process, the knowledge space theory (KST) [54] is widely used. The KST provides a theoretical framework for assessing the quality of learners’ knowledge by representing it with states rather than a single quantitative or qualitative value. The key issue in the KST is the construction of knowledge spaces (KSs), and two classes of methods apply: theory driven and data driven [55]. Theory-driven methods are based on experts’ theoretical knowledge about the domain, while data-driven methods construct KSs by analyzing learners’ responses without requiring theoretical assumptions about the domain problems or relationships among them. Paper [56] presents promising research on data-driven methods, establishing analogies between artificial neural networks (ANNs) and KSs and using deep learning techniques for KS construction.

The range of technologies needed to implement CDTs is quite wide. Among other sources, papers [14,18] stand out for elaborating on technologies that precisely and sufficiently connect them to the concept of a DT. Source [8] identifies the following key technologies: semantic technologies (ontology engineering, knowledge graphs), model-based systems engineering technologies, PLM technologies, and industrial data management technologies (including IoT technologies, cloud computing with its extensions, natural language processing, and distributed ledger technologies). On the other hand, source [25] provides a deep elaboration on the use of a model-based systems engineering approach with accompanying technologies such as architecture modeling, simulation, semantic modeling tools, and machine learning. Virtually all the literature sources, whether explicitly or implicitly, identify semantic technologies and IoT technologies as key components for DCT implementation. Sheth, Henson, and Sahoo [57] observe that the lack of integration and communication between sensor networks isolates important data streams, resulting in an abundance of data but insufficient knowledge. To address this problem, they propose the Semantic Sensor Web, which achieves increased interoperability and contextual information essential for situational knowledge through semantic metadata annotating sensor data. Bermudez-Edo and co-authors [58] propose a lightweight semantic model for the IoT, known as IoT-Lite. They introduce a set of rules for scalable semantic model design, intended for creating a semantic sensor network ontology. Nikolić, Penca, Segedinac, and Konjović [59] suggest the use of semantic web technologies for managing hardware heterogeneity in wireless sensor networks. Additionally, papers [46,47,48] offer different ontologies and related technologies for the Web of Things and IoT. For example, in [60], Steinmetz and co-authors propose an ontology for the DT in cyber-physical systems, while Reda et al. in [61] discuss the use of OWL and SWRL rules for smart home scenarios. Antoniazzi and Viola [62] propose a shared ontology for describing devices, which includes patterns for dynamic interactions between devices, defining it as a dynamic ontology.

Nowadays, physical environments equipped with IoT systems are being enhanced with sophisticated data analysis and data management software. The scalability of virtual systems, in terms of intelligence, storage, and processing power, can be significantly increased by leveraging cloud technologies. One notable proposal in this direction is the cloud-based cyber-physical system architecture called C2PS, as introduced in source [7]. In the C2PS architecture, each physical thing within the system has a separate virtual representation stored in the cloud’s data store. Whenever an interaction is received through the cyber layer, the corresponding virtual representation is updated to reflect the current state of the affected physical sensor. Similarly, any changes made to the virtual representation are also propagated to the physical layer, and interactions received through the physical layer are transmitted to the cyber layer.

We conclude this section with our perspective on the current state of software platforms for DT and CDT utilization. Our view is based on the analysis of 49 commercial solutions listed in [63] and insights from three scientific sources: [64,65,66]: (1) concepts and general requirements that are recognized and specified verbally in [46], and (2) operational solutions. The latter, as discussed in [65], partly implement these concepts to address specific domain tasks using common technologies, yet they exhibited shallow standardization. Nevertheless, it is noteworthy that some operational solutions profoundly explore new modeling approaches, like category theory, as presented in [47].

2.2. Methodology

To meet the research question stated in the introduction of the paper, our general goal is aimed at the development and operation of a wide class of digital twins representing highly complex, dynamic physical systems that interact with multiple external systems. Such digital twins are required to enable two things: (1) To ensure a reasonable degree of automation in the operational work of the system. (2) To enable a reasonable integration of people and machines into a coherent and consistent whole.

From this general goal, more specific objectives emerge. First, DTs built and operating on such platforms should offer a logical view of the system tailored to diverse tasks and user groups. The diversity and changeable structures of systems the platform deals with require support for “pluggable” modeling approaches and reasoning over the models, as well as extensible DTs and the platform itself. Since the platform is supposed to support a system that interacts with other systems, it must enable easy integration. Finally, due to the heterogeneity of the components that make up the systems under consideration and the heterogeneity of corresponding DTs, the platform must support syntactic and semantic interoperability. In summary, both the platform and DTs must be dynamic and open, rather than static and closed.

In our paper, we have chosen CDT as a key concept because a properly defined CDT is sufficient to represent all system entities that the platform should support, i.e., it enables representation of holistic models of heterogeneous systems. To fulfill the requirement for the reasonable integration of people and machines into a coherent and consistent whole, a kind of CDT characterized by an ability to learn and utilize acquired knowledge is necessary. For this purpose, we introduce a CDT relying upon KST, where acquired knowledge is represented by the corresponding KS, and the knowledge acquisition process is represented by the corresponding learning space (LS). Finally, we map the core specific goals/requirements of the platform to the challenges and opportunities of CDT identified in [14] (knowledge management, integration of DT models, standardization, and implementation of CDT), annotated with key technologies.

Table 1. Mapping key platform goals/requirements to cognitive digital twin (CDT) challenges and opportunities.

Platform Goal/Requirement	CDT Challenge/Opportunity
A logical view of the system tailored to diverse tasks and user groups	Knowledge management relies upon ontology-driven modeling and Semantic Web technologies (RDF, OWL).
Extensibility and easy integration with external systems	Integration of CDT models, where the development of CDTs is based on model-based system engineering, ontology-driven models’ integration, and standards (ISO 42010, OWL, SPARQL); implementation of CDT viewed as a component of a loosely coupled component-based software architecture (REST, JSON).
Support for diverse modeling approaches and reasoning over models	Knowledge management and Integration of CDT models governed by a semantic approach and Semantic Web technologies (RDF, OWL, SPARQL, and SWRL).
Interoperability	Ontology-based Integration of CDT models; standards-based syntactic and semantic interoperability (JSON, ISO 23247)
Scalability	Implementation of CDT as a cloud-based digital twin (WolkAbout, Novi Sad, Serbia).

shows the mapping.

As shown in Table 1, the technologies planned for the platform implementation align with the core CDT technologies recognized by other researchers. In addition, we have conducted a thorough analysis of several influential framework models in the current academic community to assess their suitability for our platform implementation.

One such framework is IoTLite [58], which offers a lightweight semantic model for the IoT. IoTLite employs a set of rules for scalable semantic model design, specifically intended for creating a semantic sensor network ontology. This adoption of IoTLite could help us address complexity and reduce processing time in IoT environments. To tackle the scalability issue, we have chosen to adopt the reference architecture C2PS, as proposed in [7], and the associated platform [67].

3. Results

3.1. The CDT-Enabling Platform Architecture

The CDT platform is structured with loosely coupled services that facilitate data exchange, processing, and reasoning derived from physical devices. The architecture is divided into four distinct layers, as illustrated in Figure 1:

• Observation/actuation layer
• Data layer
• Inference layer
• Simulation layer

In the proposed architecture, the DT is not only a digital reflection of a real entity but also an active element that can influence the real system it represents. In the inference layer, there exists a model of some phenomenon or behavior that is mapped to the digital world through simulation. Additionally, it can translate the information generated in the simulation process back to the physical world, enabling real entities (such as configurable devices) to replicate that model.

The observation/actuation layer serves as the interface through which a DT interacts with the physical world. It comprises entities capable of observation and subsequent action. These entities can be physical objects equipped with sensors and actuators or digital objects directly involved in the physical system. Examples of entities from this layer include temperature sensors, air-conditioning devices, and knowledge assessment tests. The data observed in this layer can be classified as passive, having no direct impact on the observing entity’s behavior, or active, causing a change in the observing entity’s behavior. Therefore, the data produced in this layer can be context-dependent, for example, measured temperature becoming active data when it triggers an actuation in some device.

The data layer is responsible for the syntactic integration of all data in the system. It acts as a data hub, connecting the observation/actuation layer (the interface with the physical world) with the cognitive aspect of the DT. At this layer, data received from and sent to other layers are transformed to enable the platform to handle syntactically heterogeneous data sources. For instance, a simple query solved at this layer might involve finding all sensors that have measured a temperature within a given range, without the reporting application having to be concerned about the data formats supplied by each temperature sensor.

The inference layer and simulation layer together form the cognitive part of the DT.

The inference layer facilitates the semantic integration of information from the data layer and performs reasoning over the data. The architecture supports multiple inference approaches, encapsulating them into inference services. An example of a query handled at this level could be finding rooms in a building where the heating is unnecessarily turned on. Answering such a query requires a mechanism to enable contextual semantics, considering the purpose of the room and the influence of its temperature on surrounding rooms with shared walls and floors/ceilings. Currently, the models are represented as OWL ontologies, and reasoning is performed over them. However, the models in this layer do not have to be explicitly specified in human-readable form; they can be represented using large language models that are queried from the simulation layer, enabling reasoning over simulation results and models.

The simulation layer provides model-based simulations of the processes in the system. Similar to the inference layer, the simulation layer encapsulates functionalities into separate services, allowing easy integration of different modeling approaches into the platform. An example of a query requiring processing at this layer could involve finding clogging in a fire evacuation corridor and efficiently managing fire evacuation.

Even though DTs are primarily designed for specific domains, it is essential for them to be interoperable, allowing them to be combined to create more complex DTs. To achieve interoperability, a formal, machine-readable representation of the platform is necessary, encompassing both domain-specific and domain-neutral aspects of DTs. This requirement leads to the need for formal models representing the application domains. Additionally, a formal model representing the domain-neutral aspects of DTs should also be developed. To address these needs, we have created an upper ontology of CDT architecture, as illustrated in Figure 2.

3.2. Example Domains Model

We have developed ontologies for two distinct domains to validate the generalized architecture of CDT: an energy-efficient university and knowledge quality management.

The ontology for the energy-efficient university covers the virtual representation of an IoT system within a smart building, incorporating fundamental individuals such as devices and sensors relevant to the case study. The ontology revolves around three main entities: space, device, and sensor. Relationships between these entities are defined as object properties. All pertinent attributes, including sensor values, units, and identifiers, are represented as data properties. Figure 3 illustrates the proposed ontology. Each device is located within a specific space inside the building and contains sensors and actuators. In this particular case study, the focus is on measuring temperature and motion detection inside the building, leading to the creation of two sensor individuals accordingly.

This ontology has been integrated with the CDT architecture’s upper ontology by aligning the sensors and actuators in both of them.

Figure 4 shows the domain ontology developed for knowledge quality management, representing the fundamental concepts of KST [54,55].

In that ontology, the key concept is KS, which consists of Knowledge States, each representing the quality of the learner’s current knowledge. It includes a set of problems that a learner can solve.

The learning instructions are represented by the concept of a learning path, with the assumption that the learning path is unique for a study group. The learning path consists of a totally ordered set of learning path steps, each suitable for a particular learning state.

This ontology integrates with the upper ontology of CDT architecture by subclassifying Learning_Path_Step from Learning_Instruction and Question from Knowledge_Test.

4. Platform Validation

4.1. Platform Prototype Implementation

One implementation of the proposed abstract architecture is an IoT platform proposed in the paper [68], as shown in Figure 5. The components of this platform directly align with the proposed abstract architecture.

The software platform prototype was implemented following the proposed architecture. The data layer is implemented using WolkAbout. The inference layer is implemented as a separate web service which utilizes Apache Jena. The simulation layer is also implemented as a separate web service. It consists of a Spring application, a simulator, and data storage.

The observation/actuation layer comprises a series of IoT devices equipped with sensors for observation and actuators for actuation. Sensors detect and measure changes in the physical environment, and their data is transmitted either to central nodes or directly to the next layer. Actuators manipulate the physical environment based on data generated by sensors or received from the upper layers of the architecture. In many cases, sensors and actuators are integrated into the same physical devices.

The data layer is implemented using WolkAbout [67], an IoT application enablement platform facilitating the connection, management, and analysis of IoT devices and data integration. The key features of this platform include:

• Device connectivity: supporting various IoT devices, protocols, and standards to facilitate easy device connection and management.
• Data management: providing powerful tools for handling and processing IoT data, including data visualization, analytics, and storage.
• Application development: offering a robust application development framework for rapid deployment of custom IoT applications.
• Security and reliability: ensuring the safety and integrity of IoT data through robust security features like device authentication, data encryption, and access control.
• Scalability: designed to handle large volumes of IoT data from thousands of devices efficiently.

The inference layer, responsible for supporting reasoning over OWL ontologies, is implemented as a separate web service. It utilizes Apache Jena, which provides a range of tools and APIs for creating, manipulating, and querying OWL ontologies in Java. The key features used in this solution include:

• OWL parsing and serialization: the library supports reading and writing OWL ontologies in various formats, such as RDF/XML, Turtle, and OWL/XML.
• Utilizing models through imperative programming code: the library provides Java classes and interfaces for modeling OWL ontologies, including those representing OWL classes, properties, individuals, and axioms.
• Ontology reasoning: the library includes an inference engine capable of reasoning about OWL ontologies and deducing new knowledge based on ontological axioms.
• SPARQL querying: the library supports SPARQL queries, enabling the querying of OWL ontologies to retrieve specific information.

The simulation layer is also implemented as a separate web service. It consists of a spring application, a simulator, and data storage. The simulator is a custom software component that generates a random sequence of events by simulating random transitions between states. Starting from a specified initial state, the simulator randomly selects the next state based on the probabilities of available transitions from the current state. This process continues until a stopping condition is met, such as a specified number of iterations or reaching a specified final state. The primary purpose of this service is predictive modeling, although it can be utilized for various other applications.

4.2. Validation Scenarios

In our validation, we present two cases to demonstrate the effectiveness of the platform.

The first case illustrates the use of a platform for developing conventional DTs (smart buildings). However, there are practical tasks that require multifaceted modeling and corresponding DTs. The second case presented in the paper represents an example where three DTs were used to represent learning processes (Knowledge Space).

The validation in both cases was performed on simulated data. In the case of smart buildings, Markov Chain simulation was used to generate the data. In the case of Knowledge Space, BLIM was used to generate the data. The data as well as source code are available on request.

4.2.1. Simple Sustainable Energy Management on the University Campus

The proposed approach is validated by applying the prototype platform to the task of managing electric energy consumption for heating and cooling inside a smart building equipped with motion and temperature detection sensors. The management is based on the predicted agents’ behavior (motion from one room to another), enriched by considering the fact that the period of the day (for instance, early morning or lunchtime) which drastically affects agents’ motions around the building, and consequently, the data acquired by motion detection sensors. In this example, we have assumed that temperature sensors are not affected by agents’ motions.

For this purpose, the IoT ontology is used as a domain model, and two separate microservices are implemented. The first service is the simulator of motions and interactions inside the building, while the second one plans actuation for corresponding physical devices and, eventually, generates control signals.

The simulator loads seed data and a graph that represents the topology of the building and simulates the motions of agents throughout the rooms. As the agent moves from one room to another, soft sensors are triggered, and the simulated data is generated. The changes in the system are recorded as system states modeled by a state machine.

Seed data consists of the meta-data, name, and id of specific periods of a day. Each period of the day is represented separately, in the form of a connected graph. In this example, the graph nodes represent rooms inside a building, more precisely states. For every node, it is important to note that the agent has a certain dwell time inside a room, represented by its dwell function. The dwell time is computed based on the minimum and maximum time measured in minutes for each state. These times are loosely defined, based on experience and the type of room. The time spent in each room is modeled empirically using a uniform distribution. Nodes and states can be considered interchangeable terms in this context. The edges in the graph represent the movement from one room to another. A building with a set $N=\left\{N_1, N_2, \dots , N_K\right\}$ of $K$ rooms and a set $A=\left\{A_1, A_2, \dots , A_L\right\}$ of $L$ agents is represented by a set $G=\left\{G_{A_1}, G_{A_2}, \dots , G_{A_L}\right\}$ of 4-tuples $G_{A_i}=\left(N, E_{A_i}, T_{A_i},F_{A_i}\right), i=1,L$ where $E_{A_i}$ stands for edges in the graph for the agent $A_i$, $T_{A_i}$ stands for probability for agent $A_i$ to move from one room to another, and $F_{A_i}=F\left(t_{A_i}^1, t_{A_i}^2\right)$ represents a dwell function for agent $A_i$ [48]. An example of the movements of one agent after initialization is shown in Figure 6.

When loading nodes and probabilities, a matrix of probabilities is created, containing transition values for each pair of states. The initially populated matrix is shown in

Table 2. State probabilities matrix example.

	N1	N2	N3	N4	N5
N1	0	0.7	0.15	0.05	0.1
N2	0.1	0	0.2	0	0.7
N3	0.2	0.4	0	0.2	0.2
N4	0.3	0.3	0.4	0	0.4
N5	0.2	0.2	0.5	0.1	0

. The next state probability is calculated using a uniform distribution by choosing a random number between 0 and 1.

When deciding where to transfer next, the previously calculated state probability is compared with probability ranges extracted from the matrix. The algorithm is designed to find the range of random numbers, so the next state can be chosen. The function $T\left({\mathrm{N}}_i\right)$ decides the next node based on the current node $i$ and state probabilities (e.g., ${next}_i=l | p_l=\max p_{ij}, j=1,K$).

The second service creates actuation plans containing temporal distributions of on-off signals derived from gathered time series. Such an actuation plan can be part of a DT that replicates the physical entity of the room, thus making it a cognitive DT with some, albeit very modest, cognitive ability.

To achieve syntactic and semantic interoperability, all data is stored in JSON format with the structure and semantics described by the corresponding JSON schema.

The simulation of movement enables knowledge-related activation of IoT devices, particularly motion detection sensors, in a physical system. A DT platform for real-time monitoring can be fed with data generated from the simulator, which could enable the prediction of agent behavior and, consequently, optimization of energy consumption inside smart buildings. Moreover, the proposed model can be generalized to represent any task from a class of tasks where some simulation produces time series describing system behavior from which actuation plans can be derived.

4.2.2. Managing Learning Process and Learner’s Knowledge

In the second validation case, the implementation of a cognitive DT with a distinctive ability to learn and improve its knowledge is shown. This case aims to demonstrate how the platform copes with complex DTs that require the ability to learn and adapt. The knowledge in this context refers to the learner’s ability to solve problems in a specific domain, and this ability is represented by the corresponding KS. In short, a KS is a knowledge structure (a set of all possible knowledge states for a given domain) that is union-closed. These KSs can be represented by a surmise relation that assigns to each problem a set of preconditions, which are problems that a learner must be able to solve. In a special family of KSs that is additionally intersection-closed, the surmise relation is quasi-ordering, meaning it is reflexive and transitive. In this context, the improvement of the learner’s knowledge can be seen as the construction of the intersection-closed KS of a given domain. In our validation case, the ontology of learning CDT (Figure 4) is constructed as a domain model, and two different approaches are applied for KS construction. The first approach is a minimized and corrected IITA [69], which is the de facto standard data-driven KS construction algorithm. The second approach is a neuroevolutionary method proposed in [49].

The proposed approaches can be observed as an instance of the generalized CDT architecture. The concrete architecture of that validation case is shown in Figure 7.

IITA is a data-analytic method used to derive a surmise relation on an item set. It generates competing binary relations and computes a fit measure for each relation to identify the one that best fits the data. The main concept in IITA is to estimate the number of counterexamples for each quasi-order and then find the minimum discrepancy between the observed and expected number of counterexamples among all competing quasi-orders. The resulting KS is represented by an adjacency matrix.

In [56], the KS is conceptualized as a directed acyclic graph, where knowledge states are represented as vertices, and surmise the relations define the edges. Drawing an analogy to feed-forward neural networks, which are also directed acyclic graphs with neurons (input, hidden, and output) as vertices and synapses as edges, a comparison can be made. In this analogy, an empty knowledge state corresponds to an input neuron, while a knowledge state consisting of all the items from the domain corresponds to an output neuron. All the other knowledge states correspond to hidden neurons, and not every neuron needs to be connected to all the neurons in the adjacent layer. To construct a KS represented by ANNs, the genetic algorithm for the generation of evolving ANNs is applied.

The NeuroEvolution of Augmenting Topologies (NEAT) algorithm was compared against the IITA algorithm, which utilizes the KST library for Python, developed by the authors of this paper https://github.com/milansegedinac/kst (accessed on 15 June 2023). The results published in [56] demonstrate that the NEAT approach outperformed the minimized and corrected IITA algorithm, especially for large LSs.

Another instance of platform utilization in this domain involves the improvement of the quality of the KS constructed by domain experts. This improvement is achieved by employing the QUERY algorithm and identifying the domain experts’ misconceptions about the way students learn the domain, as proposed in [70]. By following this procedure, it becomes possible to enhance the quality of the KS constructed by domain experts and to identify any misconceptions that the domain experts may have. The expected KS, constructed by the experts, is depicted in Figure 8.

From the students’ responses, the real KS was constructed by using the IITA algorithm (Figure 9).

In the platform that we propose, the KSs are just two separate instances of the common model in the inference layer. As such, they can be easily compared in the inference layer. Such a comparison yields the differences between them (Figure 10) and provides insights into the experts’ misconceptions about the way students learn the domain. A full interpretation of the experts’ misconception about stoichiometry is provided in paper [70].

In this validation case, the observation is achieved by assessing students’ knowledge, so the only component in the observation/actuation layer is the knowledge test. The current solution in this phase does not support any personalized instruction, so there are currently no components in charge of actuation in that layer.

The data collected by assessing students’ knowledge are stored as item lists in a relational database, corresponding to the data layer in the generalized architecture.

The inference layer represents the structure of KSs. In the observed case, two comparative representations of KSs were used. The first one, which is appropriate for the NEAT algorithm, relies on the set of analogies between ANNs and KSs, allowing us to represent the KSs as neural networks using TensorFlow. The second one, which is suitable for the IITA and QUERY algorithms, relies on the KST library and represents KSs using an adjacency matrix.

Since three approaches to KS construction are being applied, the simulation layer also consists of three separate components: the implementation of the adopted NEAT algorithm, the implementation of the IITA algorithm, and the implementation of the QUERY algorithm.

To achieve syntactic and semantic interoperability in this case, JSON was used to represent the IITA adjacency matrix, and the ONNX standard [71], an open format for representing machine learning models, was used to represent the corresponding ANN. JSON format played a significant role in achieving interoperability because ONNX ends up with JSON files serving serialization/deserialization.

4.3. Discussion

In this section, the implications of the research results on the interoperability, domain specificity and sustainability of digital twins are discussed. Also, the research results are positioned in the context of reference models and abstract architectures.

The implications of the research results for achieving interoperability in the development of DTs refer to the use of Semantic Web technologies, especially the OWL language as a unifying language that enables formally describing and verifying interoperability conditions. The implication for reaching an abstract representation is reflected in the domain neutrality and the possibility of formally representing the DT model through ontology and ontological languages that can be reasoned over. The sustainability implication is in the support of the development of DTs in a way that enables a holistic view of the system and reusage of the resources.

We analyzed the CP2S reference model of the DT architecture for cloud-based cyber-physical systems and the three-dimensional reference architecture of the CDT proposed in the work [14] from the viewpoint of their possible representation through our approach. The results of the analysis are shown in

Table 3. Mapping reference architectures to Abstract architecture.

C2PS Digital Twin Architecture Reference Model	Properties
	Computation	Control	Communication
Mapping to Abstract architecture	Ontology of C2PS Things in Inference layer + Simulation layer for analytical modelling of operational modes + Data layer	Decision system modelling in simulation layer + Cloud interactions modelling in inference layer + Data acquisition and devices actuation in observation/actuation layer + data layer	Modelling subsystems modes of interactions in Inference layer + Modelling composition of C2PS Things in simulation layer + Data layer
Three-dimensional CDT reference architecture	Dimensions
	Full Lifecycle phases	System hierarchy levels	Functional layers
Mapping to Abstract architecture	ABPM (adapted business process model) ontology in inference layer annotated by metadata from simulation layer.	Hierarchical model of the system (HMS) represented by an ontology at inference layer.	Multilayer model of functions (MLFM) represented by an upper DT ontology defining layers and domain ontologies defining DTs at inference layer and simulation layer.
Three-dimensional CDT reference architecture	Perspectives
	Lifecycle phases and System hierarchy levels	Functional layers and System hierarchy levels	Lifecycle phases and Functional layers
Mapping to Abstract architecture	ABPM-driven access to HMS.	HMS-driven access to MLFM.	ABPM-driven access to MFLM.

.

In both observed cases, the key properties and capabilities of the platform are reflected in the possibility of creating a domain model that further manages the development and use of DTs. Since the platform is open, it is planned to build a repository of domain models for reuse.

5. Conclusions and Future Work

The DT concept first appeared 20 years ago. An important feature of the concept is its evolution which led to a CDT that includes mental processes of perception and reasoning. The DT concept, even in its primary form, naturally fits into the digital transformation we are witnessing, while the CDT concept enables the expansion and deepening of digital transformation towards symbiotic autonomous systems. This makes the growing interest in the digital twins in industry and academia quite understandable.

Concerning sustainability, DTs address two main issues: (1) the ability of the DT paradigm to achieve sustainability in various application domains, and (2) the sustainability of the development of DTs in terms of reuse of development resources. Research in this paper touches on both issues. Regarding the first issue, the abstract model enables holistic view of limiting resources, while the second issue refers to the ability of the proposed abstract DT model to adapt to different domains of application while reusing existing resources.

In this paper, we proposed an abstract architecture consisting of two models: an abstract platform model and an abstract DT model. We also presented a pilot implementation of a software platform for sustainable DT development, which is available upon request. The abstract platform model is an ontology-based four-layer architecture that includes an observation/actuation layer, a data management layer, a reasoning layer, and a simulation layer. The DT architecture abstract model is the DT domain ontology mapped to the platform abstract model, ensuring domain neutrality. The proposed abstract architecture enables ontology-based reasoning using OWL and a service-oriented software architecture of loosely coupled distributed components. In the pilot implementation, we used a microservice architecture to enable loosely coupled services for modeling, representing, storing, and reasoning about DTs. Asynchronous communication was achieved through message queues, and cloud solutions provided scalability. We validated the proposed approach through two diverse scenarios. The first scenario demonstrated the application of the platform to energy efficiency management in IoT systems within smart buildings. The second scenario focused on knowledge quality management based on KST. The proposed architecture offers several advantages, including:

• A separate domain model of the DT, enabling domain neutrality.
• Separate layers of modeling and simulation, enabling the use of various models and the study of the behavior of physical artifacts in different conditions.
• The main functionalities are organized in layers, allowing for easy extension and maintenance.

The potential benefits and impact of a domain-neutral platform on sustainability in the domain of DT development are in the possibility of automating the design and development of DTs and DT-systems with the support of machine reasoning. The platform has the potential to facilitate cross-domain collaboration, knowledge transfer, and interoperability among DTs using semantic technologies.

The main limitations of the proposed architecture are:

• Using the platform requires specific knowledge in the domain of semantic modeling and semantic technologies.
• The life cycle is not explicitly modeled.
• The composition of layered DTs is not explicitly modeled.
• The storage and retrieval of “layered” DTs is not modeled with sufficient detail.

Further research is aimed at eliminating or at least mitigating these limitations. To alleviate the requirement for specific knowledge in the domain of semantic modeling and semantic technologies, there are plans to enrich the model with design and programming patterns corresponding to architecture layer, as well as cross-layer, patterns. Ongoing research is exploring the possibilities of explicitly modeling the life cycle through a “wrapping” DT. Research is also planned to address composition distribution by layers and the use of reasoning in composition. Additionally, there is a need to model the storage and semantic search of “layered” DTs in more detail and explore the possibilities of using semantic search in the DT composition process.