CAD-Based Digital Twins

• CAD-based digital twins are dynamic digital replicas that integrate precise CAD geometry with real-time sensor data and behavioral models.
• They enable comprehensive lifecycle management by uniting design, simulation, control, and predictive maintenance through formal mathematical and graph-based models.
• Advanced integration methods like multimodel synchronization and tool-driven data fusion ensure seamless digital-physical alignment and adaptive control.

A CAD-based digital twin is a dynamic, information-rich digital representation of a physical system, characterized by the integration of computer-aided design (CAD) models with behavioral, structural, and operational models. This construct extends beyond static 3D models to include synchronized real-time data, formalized system attributes, software deployment specifications, and multi-domain behavioral abstractions. CAD-based digital twins support system lifecycle tasks including design, simulation, control, verification, optimization, maintenance, and adaptation by bridging the physical and digital domains with high fidelity, computational rigor, and actionable analytics.

1. Historical Context and Conceptual Evolution

The concept of the digital twin originates from virtual manufacturing practices developed in the 1990s, notably at Osaka University, and was formalized in the early 2000s as the mirrored space model (MSM). The digital twin paradigm evolved through contributions from virtual manufacturing, model predictive control, and building information modeling (BIM). Early digital twins emphasized geometric and process-centric representations; contemporary approaches incorporate real-time data, simulation, and control, fundamentally transforming the management of engineered systems across their life cycle (Zhou et al., 2022). The integration of CAD systems—providing precise geometric and physical data—represents a foundational layer upon which digital twins synthesize operational, behavioral, and control models (Zhou et al., 2022).

2. Formal Models and Mathematical Foundations

CAD-based digital twins leverage formal mathematical models for both hardware and software. In automotive and cyber-physical domains, hardware is typically represented as a graph whose nodes denote computational devices (e.g., ECUs, controllers, embedded computers, cloud systems), and edges correspond to physical communication paths (e.g., buses, Ethernet, wireless), each annotated with quantitative attributes including computational power, available memory, communication bandwidth, and device interfaces. The property mapping is formalized as

$\mathcal{P}_{HW}: ECU \to 2^{A_{ECU}}$

where $A_{ECU}$ is the set of hardware attributes (Blech, 2020).

Software components are similarly modeled as directed graphs, with nodes representing atomic software units and edges modeling inter-component communication, annotated with attributes such as memory consumption, computational load, criticality, and latency constraints: $\mathcal{P}_{SW}: SWC \to 2^{A_{SWC}}$ The mapping between software and hardware is realized by a function $M: SWC \to ECU$ and the quality of deployment is evaluated via a cost function

$$\mathcal{E}: (\text{ECU}, NL, \mathcal{P}_{HW}) \times (\text{SWC}, E, \mathcal{P}_{SW}) \times (SWC \to ECU) \to \mathbb{Z}$$

that enforces constraints on memory, criticality, resource allocation, and network capacity (Blech, 2020).

Advanced mathematical modeling in digital twins also includes hybrid and physics-informed neural network approaches, embedding physics-based PDEs and data-driven methods to ensure adherence to system laws while leveraging observed sensor streams (Mohammad-Djafari, 27 Feb 2025).

3. Core Integration Methodologies

The seamless fusion of CAD and dynamic behavioral models in a digital twin is achieved by several orthogonal strategies:

• Multimodel Synchronization: TiLA, for example, employs a Globally Asynchronous Locally Synchronous (GALS) model where high-fidelity CAD models (e.g., Modelica-based plant representations) are tightly coupled with control abstractions (e.g., Petri nets, state charts), all synchronized via defined clock domains and connected through industrial protocols such as OPC-UA (Park et al., 2020).
• Graph-based Abstraction: Physical layout data from 3D CAD models and 2D engineering schematics (P&IDs) are converted to directed graphs. These underlying graph models enable cross-referencing, alignment, and eventual graph matching for integrative process simulations and system verification (Sierla et al., 2021, Azangoo et al., 2023).
• Tool-Driven Generation and Data Fusion: Modular toolchains extract geometric and topological information directly from CAD models, augmenting this with functional information from other sources (e.g., P&IDs, historical data) and employing recognition algorithms (image, pattern, OCR) to unify system representations in an intermediate graph model (Azangoo et al., 2023).
• Case and Rule-Based Reasoning: In self-adaptive manufacturing, domain-specific models—analogous to CAD—are combined with case-based reasoning structures, supporting automated retrieval, reuse, revision, and retention of expert knowledge for adaptive operation (Bolender et al., 2021).

4. Life Cycle Management and Real-Time Synchronization

A CAD-based digital twin provides a geometric and behavioral digital replica that is continuously synchronized with its physical counterpart using real-time sensor data, communication protocols, and data collection frameworks:

• Real-Time Sensing and Feedback: Embedded IoT sensors and communication networks enable the twin to mirror current operating conditions, supporting state estimation, model calibration, and anomaly detection (Zhou et al., 2022).
• Bidirectional Data Flow: Digital threads facilitate synchronized updates from the physical system (physical twin) to the digital model (digital shadow/twin), with advanced configurations enabling actuation or control commands to be sent back to the physical layer (Barbie et al., 15 Jan 2024).
• Executable Digital Twins (xDT): These are stand-alone, reduced-order models, calibrated via state estimation, that can be deployed for tasks such as virtual sensing, hardware-in-the-loop, and predictive diagnostics (Auweraer et al., 2022). Model order reduction (e.g., Krylov subspace, Proper Orthogonal Decomposition) is applied to accelerate simulation while maintaining physical fidelity.

5. Advanced Applications and Case Studies

CAD-based digital twins have demonstrated efficacy in a variety of industrial and engineering domains:

• Automotive Software Deployment: Integrated digital twins facilitate the mapping and dynamic deployment of software components to hardware, taking into account criticality, latency, memory, computational requirements, and real-time reconfiguration scenarios (Blech, 2020).
• Manufacturing Control and Fault Diagnosis: TiLA showcases the orchestration of CAD-based dynamics, Petri net controllers, and real-time sensor analytics for early fault identification and production optimization (Park et al., 2020).
• Process Industry Retrofitting: Automated extraction of CAD and process documentation and their unification into a digitized, simulation-ready graph model provides a path for rapidly creating digital twins in legacy (brownfield) industrial environments (Azangoo et al., 2023).
• Structural Health Monitoring: High-fidelity CAD-integrated digital twins support adjoint-based inverse identification of material properties or structural weaknesses by minimizing the discrepancy between measured and computed displacements/strains under various load cases (Löhner et al., 2023).
• Additive Manufacturing (AM): In AM, CAD models form the “as-designed” reference for digital twins, which are then registered and overlaid with multimodal in-process and inspection data (toolpaths, CT scans) in immersive, collaborative virtual reality environments for effective inspection and defect localization (Chheang et al., 21 May 2024).
• Education and Open Science: The public gantry crane digital twin exemplar integrates the CAD/kinematic model for trajectory generation, optimal control, data logging, visualization, and online validation, providing an accessible testbed for research and pedagogy (Mertens et al., 17 Jul 2025).

6. Verification, Formalization, and Challenges

Formal verification of CAD-based digital twins is increasingly addressed via contract-based and model checking approaches. System-level requirements are formalized as assume-guarantee contracts, verified through model checking tools (e.g., UPPAAL) that encode operational specifications as timed automata; this enables black-box validation of digital twin behavior, regardless of the internal implementation (e.g., simulation, CAD-based model, or neural network) (Naeem et al., 7 Apr 2025).

Formal methods, including Object-Z specification, UML class diagrams, and graph-based representations, are leveraged to define the relationships among physical twins, digital models, templates, threads, and prototypes, supporting rigorous development, deployment, and validation workflows (Barbie et al., 15 Jan 2024).

Key challenges highlighted include:

• Maintaining digital-physical alignment as the system evolves (hardware substitutions, upgrades)
• Data integration from heterogeneous sources (CAD, P&IDs, sensor networks)
• Computational resource requirements for real-time simulation, synchronization, and dense model checking
• Complexity and scalability of the unified models as system granularity increases
• The need for standardized interfaces and protocols to support interoperability across CAD, simulation, and operational layers (Zhou et al., 2022, Blech, 2020)

7. Future Directions

Emerging areas include tighter integration of artificial intelligence (physics-informed neural networks, reinforcement learning) for adaptive modeling, robust bidirectional synchronization, and further formalization for automated verification and safety assurance. Research into hybrid modeling (combining PDE-based, data-driven, and stochastic models), advanced model order reduction techniques, and scalable toolchains is ongoing (Mohammad-Djafari, 27 Feb 2025).

The role of CAD models is expected to extend, serving as the geometric substrate for more autonomous, resilient, and federated digital twin ecosystems powering sustainable operation, predictive maintenance, control optimization, and lifecycle management across domains including automotive, process industry, manufacturing, smart infrastructure, and robotics.

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Domain/Application	Role of CAD-based Digital Twin	Key Capabilities
Automotive Systems	Integration of geometry, hardware/software models	Resource mapping, deployment optimization, real-time reconfiguration, compliance validation
Industrial Processes	Fusion of 3D design and control logic	Unified modeling, simulation, and retrofitting for process optimization and fault detection
Smart Manufacturing	Synchronized geometry and control representations	Adaptive control, predictive maintenance, case-based reasoning for sustainable operation
Additive Manufacturing	Overlay of design, process, and inspection data	Collaborative defect detection, VR-based multimodal analysis, root cause analysis
Structural Monitoring	High-fidelity FE/CAD fusion	Weakness localization, load/sensor optimization, adjoint-based inverse identification