Digital twin of a pipe conveying fluid: Flow rate anomaly detection and quantification via multi-fidelity Kalman filters and event based cameras signals

This work is motivated by the need for scalable Digital Twins (DT) for hydro turbines. We propose a DT framework using Bayesian algorithms embedded with machine learning techniques to study a simplified pipe conveying fluid (PCF) system. The Unscented Kalman Filter (UKF) is employed for parameter identification by estimating the unknown flow rate that excites the pipe by leveraging the known nonlinear dynamical equations. Experimental validation using event-based camera data and a 3D reconstruction algorithm demonstrates the effectiveness of the UKF, estimating the flow rate with an average estimation error of 6%. To enhance scalability and enable real-time anomaly detection, a Linear Kalman Filter (LKF) is coupled with Dynamic Mode Decomposition (DMD). DMD is trained on the states estimated by the UKF, providing physical insight to the data-driven model order reduction method. This embedded LKF-DMD approach reduces the complexity of the model and accelerates the computation by three orders of magnitude, from 12 s to 1 0 − 3 s per iteration. When the flow velocity changes, anomaly detection is performed by applying a steepest-ascent hill climbing method which quantifies the change in entropy of the distribution of the Euclidean distance between the trained DMD modal phase diagram and the LKF estimates. The integration of the UKF for system identification, and the accelerated LKF-DMD for state estimation and anomaly detection within a unified DT framework, which have been validated using the lab-scale PCF setup, highlights the potential of these techniques to develop scalable and predictive maintenance tools for engineering systems. • A Digital twin framework of a pipe conveying fluid is proposed. • An efficient approach reconstructs the 3D pipe motion with event-based cameras. • The integration of Bayesian methods enhanced with a data-driven technique is provided. • Anomaly detection and quantification through parameter identification is performed. • Validation is realized with a true experimental setup in real-time.