Developing a Digital Twin of part cooling in an injection moulding process through a Dynamic Mode Decomposition-Kalman Filter approach

A framework for creating a Digital Twin for spatiotemporal process monitoring is proposed based on Dynamic Mode Decomposition and the Kalman filter (DMD-KF). Many material processes require optimisation of complex spatiotemporal dynamics which are difficult to monitor with limited sensor measurements at accessible locations in the process. The DMD-KF approach facilitates the extraction of a spatiotemporal dynamic model with minimal computation time from numerical simulations, integrated with real-time sensor measurements of the accessible states to correct model errors. The method is demonstrated for real-time spatiotemporal monitoring of component cooling in the injection moulding process. Injection Moulding is a high-volume manufacturing process, which faces challenges in dimensional precision due to shrinkage and warpage defects which manifest post-production due to the gradual relaxation of internal residual stresses. To prevent internal stresses, the component should be sufficiently free of significant temperature differentials prior to ejection from the mould. However, the inaccessible nature of the mould tool limits sensor access for monitoring of the cooling phase. Dynamic Mode Decomposition (DMD) allows a best fit, linear state–space model of the temperature dynamics of 3D spatial nodes of the component to be extracted from a computationally-intensive finite element model of the process. Using only two thermocouple measurements, integrated with the DMD model via a Kalman Filter (KF), allows for construction of the 3D temperature map of the component inside the mould in real time. Simulation of different processing scenarios highlights that even with a DMD model developed under significantly different process conditions than used in implementation, the KF corrections still effectively estimate the temperature of critical states with with a root mean square error of 1.4 °C. The DMD-KF approach shows high potential for real-time spatio-temporal monitoring and quality prediction across diverse manufacturing processes. • A spatiotemporal digital twin is developed for injection moulding cooling. • A data-driven model is built from simulation using Dynamic Mode Decomposition (DMD). • Real-time sensor data is integrated with the DMD model using a Kalman Filter (KF). • The KF ensures robust prediction despite unmodelled process changes. • Real time 3D temperature profile matched simulation within 1 °C at ejection time.