A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale (2012.05841v3)

Abstract: A unifying mathematical formulation is needed to move from one-off digital twins built through custom implementations to robust digital twin implementations at scale. This work proposes a probabilistic graphical model as a formal mathematical representation of a digital twin and its associated physical asset. We create an abstraction of the asset-twin system as a set of coupled dynamical systems, evolving over time through their respective state-spaces and interacting via observed data and control inputs. The formal definition of this coupled system as a probabilistic graphical model enables us to draw upon well-established theory and methods from Bayesian statistics, dynamical systems, and control theory. The declarative and general nature of the proposed digital twin model make it rigorous yet flexible, enabling its application at scale in a diverse range of application areas. We demonstrate how the model is instantiated to enable a structural digital twin of an unmanned aerial vehicle (UAV). The digital twin is calibrated using experimental data from a physical UAV asset. Its use in dynamic decision making is then illustrated in a synthetic example where the UAV undergoes an in-flight damage event and the digital twin is dynamically updated using sensor data. The graphical model foundation ensures that the digital twin calibration and updating process is principled, unified, and able to scale to an entire fleet of digital twins.

• The paper presents a Bayesian-based probabilistic graphical model framework that addresses scalability and uncertainty in digital twin implementations.
• It demonstrates the model’s application in a UAV case study, showcasing continuous calibration and predictive simulation for in-flight health monitoring.
• Results indicate reduced parameter uncertainty and enhanced insights into structural dynamics, highlighting practical cross-industry applications.

A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale

This paper presents a robust mathematical foundation for the development and deployment of digital twins at scale, leveraging a probabilistic graphical model. The authors, Kapteyn, Pretorius, and Willcox, introduce a formalism incorporating Bayesian statistics and dynamical systems theory to address the current challenges in digital twin implementations, where bespoke, resource-intensive solutions are prevalent.

The proposed model holistically captures the asset-twin interaction as a coupled dynamical system, allowing for continuous update and calibration through data assimilation. This is achieved by structuring the digital twin as a probabilistic graphical model (PGM), facilitating not only the representation of the system dynamics but also enabling powerful Bayesian inference frameworks to be effectively utilized for updating the digital state. The PGM components include digital states, quantities of interest, and rewards that are all strongly supported by interactions and dependencies, represented as conditional probability densities within the model.

A significant portion of the paper is dedicated to the demonstration of the model's application to a structural digital twin of an unmanned aerial vehicle (UAV). This example showcases the comprehensive and versatile nature of the framework, detailing the calibration phase where real-world experimental data inform parameter updates within the finite element structural models of the UAV. During the operational phase, the digital twin's dynamic state estimation is exemplified through the UAV's in-flight health monitoring, wherein the graphical model supports predictive simulation to guide real-time decision-making. Notably, the UAV case paper underscores the model’s capability for end-to-end uncertainty quantification, which enables sophisticated planning and execution guided by the digital twin.

The numerical results presented indicate that the model can efficiently transition from capturing manufacturing variations during the UAV's calibration to applicable in-flight monitoring. For instance, the calibration phase reveals a decrease in uncertainty regarding the UAV's material property parameters, demonstrating the model's efficacy in parameter estimation and system adaptability. The model facilitates extraction of complex quantities like damping coefficients which are critical for understanding structural dynamics under operational conditions.

The practical implications of this research are significant, especially for industries where system reliability and maintenance planning are crucial, such as aerospace, healthcare, and infrastructure management. The proposed framework allows for scalable implementations that leverage the full potential of digital twins, ensuring systems can adapt in real-time to dynamic environmental conditions and operational requirements.

However, the authors acknowledge potential limitations, such as the computational demands associated with high-fidelity simulations necessary for PGMs, suggesting solutions like reduced-order modeling for practicality. Additionally, the challenge of comprehensive model inadequacy remains, necessitating refined approximations and continuous validation against physical counterparts.

Future developments will likely explore the integration of advanced learning algorithms to enhance the planning capabilities within the graphical model framework, potentially leading to even more effective automated decision-making in digital twins. Overall, while not termed revolutionary, this work offers a vital step towards scalable digital twin ecosystems that can meaningfully interact with and improve the reliability and functionality of physical assets across various sectors.