Mathematical Framework for Digital Risk Twins in Safety-Critical Systems

Many core technologies of Industry 4.0 have gained substantial advancement in recent years. Digital Twin (DT) has become the key technology and tool for manufacturing industries to realize intelligent cyber-physical integration and digital transformation by leveraging these technologies. Although there have been many DT-related works, there is no standard definition, unified framework, and implementation approach of DT until now. Widely developing DTs for the manufacturing industry is still challenging. Thus, this paper proposes a novel implementation framework of digital twins for intelligent manufacturing, denoted as IF-DTiM, which possesses several distinct merits to distinguish itself from previous works. First, IF-DTiM fully utilizes new-generation container technology so that DT-related applications and services can be packaged in a self-contained way, rapidly deployed, and robustly operated with the capabilities of failover, autoscaling, and load balancing. Second, it leverages existing intelligent cloud manufacturing services to realize the intelligence for DT externally in a scalable and plug-and-play manner instead of using traditional approaches to embed intelligence in DT. Third, IF-DTiM contains Product DT for products, Equipment DT (i.e., EQ DT) for equipment, and Process DT for production lines, which can generically fulfill the demands and scenarios to achieve intelligent manufacturing for various manufacturing industries. Testing results show that IF-DTiM can achieve remarkable performance in rapid deployment and real-time data exchanges of DT-related applications. Finally, we develop an example DTiM system for CNC machining based on IF-DTiM to demonstrate its efficacy and applicability in facilitating the manufacturing industry to build their DT systems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Developing Digital Twin (DT) systems to realize intelligent manufacturing is challenging. The proposed IF-DTiM (Implementation Framework of Digital Twins for Intelligent Manufacturing) provides a novel container-technology and cloud-manufacturing-service-based systematic methodology for building DTiM. In this paper, we present the system architecture and several operational scenarios (e.g., how to create and use DTs) of IF-DTiM, together with the design of its core functional mechanisms (e.g., rapid deployment scheme for DT, real-time data exchange for DT, DT interface pattern, and general workflow architecture for DT). Also, an example DTiM system for CNC machining based on IF-DTiM is presented to facilitate the practitioners to adopt the designs and niches in IF-DTiM to build their desired DTiM systems.

Digital twin (DT) systems, which involve creating virtual replicas of physical objects or systems, have the potential to transform healthcare by offering personalised and predictive models that grant deeper insight into a patient's condition. This review explores current concepts in DT systems for musculoskeletal (MSK) applications through an overview of the key components, technologies, clinical uses, challenges, and future directions that define this rapidly growing field. DT systems leverage computational models such as multibody dynamics and finite element analysis to simulate the mechanical behaviour of MSK structures, while integration with wearable technologies allows real-time monitoring and feedback, facilitating preventive measures, and adaptive care strategies. Early applications of DT systems to MSK include optimising the monitoring of exercise and rehabilitation, analysing joint mechanics for personalised surgical techniques, and predicting post-operative outcomes. While still under development, these advancements promise to revolutionise MSK care by improving surgical planning, reducing complications, and personalising patient rehabilitation strategies. Integrating advanced machine learning algorithms can enhance the predictive abilities of DTs and provide a better understanding of disease processes through explainable artificial intelligence (AI). Despite their potential, DT systems face significant challenges. These include integrating multi-modal data, modelling ageing and damage, efficiently using computational resources and developing clinically accurate and impactful models. Addressing these challenges will require multidisciplinary collaboration. Furthermore, guaranteeing patient privacy and protection against bias is extremely important, as is navigating regulatory requirements for clinical adoption. DT systems present a significant opportunity to improve patient care, made possible by recent technological advancements in several fields, including wearable sensors, computational modelling of biological structures, and AI. As these technologies continue to mature and their integration is streamlined, DT systems may fast-track medical innovation, ushering in a new era of rapid improvement of treatment outcomes and broadening the scope of preventive medicine. Level of Evidence: Level V.

The ready-mix concrete supply chain is highly disruptive due to its product perishability and Just-in-Time (JIT) production style. A lack of technology makes the ready-mix concrete (RMC) industry suffer from frequent production failures, ultimately causing high customer dissatisfaction and loss of revenues. In this paper, we propose the first-ever digital twin (DT) system in the RMC industry that can serve as a decision support tool to manage production risk efficiently and effectively via predictive maintenance. This study focuses on the feasibility of digital twins for the RMC industry in three main areas holistically: (1) the technical feasibility of the digital twin system for ready-mix concrete plant production risk management; (2) the business value of the proposed product to the construction industry; (3) the challenges of implementation in the real-world RMC industry. The proposed digital twin system consists of three main phases: (1) an IoT system to get the real-time production cycle times; (2) a digital twin operational working model with descriptive analytics; (3) an advanced analytical dashboard with predictive analytics to make predictive maintenance decisions. Our proposed digital twin solution can provide efficient and interpretable predictive maintenance insights in real time based on anomaly detection, production bottleneck identification, process disruption forecast and cycle time analysis. Finally, this study emphasizes that state-of-the-art solutions such as digital twins can effectively manage the production risks of ready-mix concrete plants by automatically detecting and predicting the bottlenecks without waiting until a production failure happens to react.

Aiming at the increasingly complex management and dispatching problems of power system, this paper combines Beidou precise space-time technology with digital twin system theory, and puts forward a method of constructing intelligent management and dispatching platform of power grid. The method combines Beidou and IoT (Internet of Things) sensors to form a digital twin management and scheduling platform which can perform state prediction, fault diagnosis, self-healing and other functions. Firstly, this paper analyzes the overall architecture of Beidou digital power twin system, then discusses the construction method of digital twin in power system from the aspects of digital twin modeling theory, data acquisition intelligent terminal based on Beidou, operation mode of digital twin platform, etc. Finally, the application test analysis is carried out. The research results show that the method proposed in this paper has reference value for improving the management and dispatching capability of smart grid.

This paper is concerned with the first work on the integration of digital twin (DT), 5G, cloud platform, and virtual reality (VR) technologies for unmanned aerial vehicles (UAVs) autonomy development. DT focuses on connecting the virtual and physical world as an emerging strategic technology. Initially, it was implemented through mirror models of physical objects to realize the monitoring of their whole life cycle in the manufacturing area. In recent years, DT technologies have been applied in different fields, and some typical DT solutions have been proposed to solve complex system problems. In this paper, we study the problem of how to combine the DT and other emerging technologies for UAV autonomy development and supervision, aiming to propose a basic DT framework to integrate DT and UAVs as reference rules for building DT systems, which includes four parts, that is, Virtual Space, Real Space, Service Center, and Data and Model Processing Center. Based on the proposed basic DT framework, a cloud-based DT system is then further constructed in which cloud platform, 5G, and VR are integrated seamlessly. The running and implementation processes of each subsystem are introduced in detail. Multiple experiments are conducted to verify the usefulness of proposed DT system, that is, real-time system monitoring and cloud processing, VR connection, human–robot interaction through VR technology, and so on. The experimental results show that the proposed DTUAV system can be used in the interaction of virtual and physical systems, remote supervision, intelligence integration of swarm of unmanned vehicles, and so on. The development in our work introduces the DT into unmanned system applications and can promote relevant research in this direction. All implementation codes of the system will be shared in https://github.com/DTUAV .

Background Digital twins are gaining ever-increasing attention from academies and industries to standardization bodies worldwide owing to their great capabilities and fundamental values in the coming fourth industrial revolution. However, there is no consistent set of definitions or concept system of the digital twin domain yet. Especially, the polysemy problem of the term “digital twin” is leading to ambiguities and an obstacle to standardization. Methods This paper summarizes the principles and guidelines of developing a concept system mentioned in two international standards, enriches them to a methodology of developing a concept system with (1) system thinking viewpoints and systems engineering methods, (2) procedures for analyzing the semantic relationships among candidate superordinate concepts, and (3) a three-dimensional taxonomy framework with procedures of developing a taxonomy, and proposed a maturity level model for terminology work. Results This paper analyzes the polysemy phenomenon of the term "digital twin”, identifies the necessity to differentiate digital twin entity and digital twin system from the general term “digital twin”, and proposes a disciplinary definition of "digital twin". After analyzing twenty-one definitions of digital twin and summarizing ten superordinate concepts from them, this paper proposes that a digital twin entity is a kind of digital asset not just a digital representation. Based on the new superordinate concept and definition of digital twin entity, a systematic digital twin concept system is developed with 210 concepts and fifty definitions. Conclusions This work resolves the polysemy problem of the term “digital twin” and demonstrates the effectiveness of the enhanced methodology of developing a concept system. The proposed digital twin concept system could be a benchmark for future digital twin terminology work and useful input to the development of digital twin system reference architecture standard and lays a solid foundation for future concept systems development of other domains.

This chapter presents a Digital Twin Pipeline Framework of the COGNITWIN project that supports Hybrid and Cognitive Digital Twins, through four Big Data and AI pipeline steps adapted for Digital Twins. The pipeline steps are Data Acquisition, Data Representation, AI/Machine learning, and Visualisation and Control. Big Data and AI Technology selections of the Digital Twin system are related to the different technology areas in the BDV Reference Model. A Hybrid Digital Twin is defined as a combination of a data-driven Digital Twin with First-order Physical models. The chapter illustrates the use of a Hybrid Digital Twin approach by describing an application example of Spiral Welded Steel Industrial Machinery maintenance, with a focus on the Digital Twin support for Predictive Maintenance. A further extension is in progress to support Cognitive Digital Twins includes support for learning, understanding, and planning, including the use of domain and human knowledge. By using digital, hybrid, and cognitive twins, the project’s presented pilot aims to reduce energy consumption and average duration of machine downtimes. Data-driven artificial intelligence methods and predictive analytics models that are deployed in the Digital Twin pipeline have been detailed with a focus on decreasing the machinery’s unplanned downtime. We conclude that the presented pipeline can be used for similar cases in the process industry.

Background: Digital twins are gaining ever-increasing attention from academies and industries to standardization bodies all over the world owing to their great capabilities and fundamental values in the coming fourth industrial revolution. However, there is no consistent set of definitions or concept system for the digital twin domain yet. Methods: This paper summarizes the methodology of developing a concept system with integrating ISO standards guidelines and system thinking methods, analyzes the polysemy phenomenon of the term "digital twin", and identifies the necessity to differentiate digital twin entity and digital twin system from the general term “digital twin”. Results: After analyzing nineteen definitions of digital twin (entity) and summarizing ten superordinate concepts from these definitions, this paper proposes that a digital twin entity is a kind of digital asset rather than digital representation. Based on the new superordinate concept and definition of digital twin entity, a systematic digital twin concept system is developed which consists of four parts: top-level ontology and taxonomy of entity, digital twin entity related concepts, digital twin system related concepts, and taxonomy framework related concepts. Conclusions: This work demonstrates the power and effectiveness of the combination of ISO terminology work standards, system thinking methods, and information modeling tools, lays a solid foundation for future concept systems development of other domains, and will provide useful input to the efforts of digital twin standardization.

Background: Digital twins are gaining ever-increasing attention from academies and industries to standardization bodies worldwide owing to their great capabilities and fundamental values in the coming fourth industrial revolution. However, there is no consistent set of definitions or concept system of the digital twin domain yet. Especially, the polysemy problem of the term “digital twin” is leading to ambiguities and an obstacle to standardization. Methods: This paper summarizes the principles and guidelines of developing a concept system mentioned in two international standards, enriches them to a methodology of developing a concept system with (1) system thinking viewpoints and systems engineering methods, (2) procedures for analyzing the semantic relationships among candidate superordinate concepts, and (3) a three-dimensional taxonomy framework with procedures of developing a taxonomy, and proposed a maturity level model for terminology work which offers a high-level vision of digital twin terminology work. Results: This paper analyzes the polysemy phenomenon of the term "digital twin” and identifies the necessity to differentiate digital twin entity and digital twin system from the general term “digital twin”. After analyzing twenty-one definitions of digital twin and summarizing ten superordinate concepts from them, this paper proposes that a digital twin entity is a kind of digital asset rather than digital representation. Based on the new superordinate concept and definition of digital twin entity, a systematic digital twin concept system is developed with one hundred concepts and fifty definitions. Conclusions: This work resolves the polysemy problem of the term “digital twin” and demonstrates the effectiveness of the enhanced methodology of developing a concept system. The proposed digital twin concept system could be a benchmark for future digital twin terminology work and useful input to the development of digital twin system reference architecture standard and lays a solid foundation for future concept systems development of other domains.

This paper combines the digital twin system modeling method to conduct an in‐depth study and analysis of graph‐theoretic combinatorial optimization. This paper provides new ideas and approaches for optimal numerical analysis work by studying the digital twin modeling method that integrates digital modeling and graph theory combination, provides theoretical support for safe, stable, and economic operation of the system, proposes a solution for digital twin model based on big data platform, focuses on the nearest neighbor propagation (AP) and graph theory combination, solves the digital twin real‐time monitoring data asynchronous, incomplete problem, and applies the algorithm to the digital twin model based on the big data platform for data preprocessing to achieve better results. This paper also presents a web‐based digital twin system based on intelligent practical needs, analysis, and comparison of existing models, combined with digital twin technology, detailing the differences and connections between the various levels of numerical analysis and the implementation of this data in various fields, such as user management, equipment health management, product quality management, and workshop 3D navigation and detailed modeling of the digital twin system based on this numerical analysis to realize remote online monitoring, analysis, and management. In this paper, for the numerical analysis process, firstly, the key technologies of modeling and simulation operation control of production line based on digital twin are studied, and the rapid response manufacturing system based on a digital twin is designed and validated. Secondly, a scheduling technology framework for capacity simulation evaluation and optimization is established, and batching optimization, outsourcing decision, and rolling scheduling techniques are thus proposed to form a batching optimization algorithm based on priority rules, which realizes batching processing, outsourcing decision, and rolling scheduling of production orders to optimize equipment utilization and capacity. Finally, digital twin‐based modeling is designed, and the validation results demonstrate the system’s superior performance in achieving information interaction between physical and virtual production lines, optimization of numerical analysis, and display of results.

With the rise of digital twin technology, the application of digital twin technology to industrial automation provides a new direction for the digital transformation of the global smart manufacturing industry. In order to further improve production efficiency, as well as realize enterprise digital empowerment, this paper takes a welding robot arm as the research object and constructs a welding robot arm digital twin system. Using three-dimensional modeling technology and model rendering, the welding robot arm digital twin simulation environment was built. Parent-child hierarchy and particle effects were used to truly restore the movement characteristics of the robot arm and the welding effect, with the help of TCP communication and Bluetooth communication to realize data transmission between the virtual segment and the physical end. A variety of UI components were used to design the human-machine interaction interface of the digital twin system, ultimately realizing the data-driven digital twin system. Finally, according to the digital twin maturity model constructed by Prof. Tao Fei's team, the system was scored using five dimensions and 19 evaluation factors. After testing the system, we found that the combination of digital twin technology and automation is feasible and achieves the expected results.

Chapter 5 - Intelligent digital twin reference architecture models for medical and healthcare industry

Blockchain empowered access control for digital twin system with attribute-based encryption

The semi-physical marine engine room simulator is one of the necessary equipment for the training of marine engineers worldwide. However, its maintenance has become a problem for a long time due to its complexity and vulnerability. Although the semi-physical marine engine room simulator fails frequently, its failures are usually small-scale communication failures, which are easy to solve for experts. For such kind of micro faults, the cost of field maintenance by experts is very high due to the long journey. Generally, most manufactures will choose to assist the users&#x2019; maintenance by telephone or email firstly. If it does not work, they will have to send experts for field maintenance which is expensive for users. In this paper, we propose a digital twin architecture of the semi-physical marine engine room simulator to assist users in remote maintenance. The digital twin system is a multi-twins architecture consisting of the user digital twin and the manufacturer digital twin. The user digital twin is a technical guidance platform for information reception and display, through which the user can get technical adviser from the experts in the 3D virtual environment. The manufacture digital twin is a platform for monitoring and troubleshooting by experts. The communication faults are the main faults of the semi-physical marine engine room simulator, which are easy to monitor. Consequently, it is possible to realize remote maintenance assistance through the digital twin system without a lot of time cost and economic cost.

The evaluation and optimization of wells with intelligent completion, whether multilayer or multilateral, requires a deep understanding of inflow characteristics at each inflow control valve (ICV). Zonal testing is crucial for gathering fluids and reservoir data; nonetheless, it leads to production deferment, which is undesirable by most operators. In this paper, we present how a wells’ digital twins on an edge Internet of Things (IoT) device will provide real-time virtual measurements as well as ICV optimization opportunities to maximize oil production. We present a digital twin solution for a synthetic well equipped with an electric submersible pump (ESP) and two ICVs. The digital twin system is composed of two primary components together called the estimator. One aspect is a physics-based well model that accurately calculates pressure losses and flow characteristics, and the other is an iterative algorithm that employs real-time field data, encompassing production and ESP operational data to dynamically recalibrate and update the digital twin representation of the well. By capturing the well’s dynamic state, the digital twin enables the optimizer, an optimization workflow that suggests optimal ICV positions and ESP pump frequencies, aiming to maximize oil production while maintaining water-cut constraints within individual layers. To validate the approach, we rigorously tested various well scenarios. Our approach involved flow tests with different ICV positions. In addition, we conducted a comprehensive parametric analysis, considering temporal variations in water cuts and the productivity index (PI) of individual layers. Recognizing that factors such as pressure fluctuations, wellbore conditions, and reservoir dynamics significantly impact overall productivity and inflow characteristics, the estimator within the digital twin avatar of the well is automated to allow fine tuning of PI and/or water cut for each layer to recalibrate itself dynamically. The estimator adeptly captures transient changes in the well, and our results demonstrate that initial calibration efforts substantially enhance its accuracy over time. The optimizer, an extension of the digital twin model, is tested against operational constraints of oil and water production to recommend ICV positions with projected flow rates and water cuts for each layer. Our findings align closely with a physics-based simulator, validating the approach within a 10% error range. This entire digital twin workflow helps provide a consistent and reliable well monitoring mechanism for the well along with reliable recommendations for production optimization decisions. The novelty in this approach is to provide accurate real-time flowrate estimates of complex multilateral/multilayer wells with intelligent completions. The digital twin workflow provides virtual sensing that helps estimate downhole well conditions with great reliability for production management and optimization.