An initial concept for an error-based digital twin framework for dynamics applications

This work introduces the beginnings of an error-based mathematical framework for digital twins, with the intention of providing an effective platform from which digital twins of engineering applications can be built. The framework assumes a digital twin to be some optimal combination of a physics- and data-based model and operates by weighting the contribution of each model depending on its relative mean square error compared to data measured from the physical system being twinned (the so-called physical twin). These weightings then provide a quantifiable measure of the ratio of physics- to data-based components in the resulting digital twin, and this offers a means of consistently comparing different digital twin models. The framework aims to improve the initial physics-based model of the system over time by updating it to the optimal model combination. The initial framework is applied to a simulated Duffing oscillator, where the equivalent linear system is assumed as the physics-based model. The data-based model is learnt by identifying the system parameters from the measured system response with polynomial regression. The digital twin framework aims to detect the type of nonlinearity from the measured data (cubic in this case) and is successful in improving the physics-based model. The framework is then extended to acceleration data recorded from the vibration response of a physical 3 degree-of-freedom structure, in order to analyse its performance in a real-world application. In this case, the assumed physics-based model uses estimated system parameters, and the data-based model is trained with a genetic algorithm to improve the accuracy of results. The digital twin framework improves the parameter estimations of the physics-based model. It is anticipated that by developing this error-based framework and incorporating other aspects such as uncertainty analysis and optimisation, a unified method of implementing digital twins will be enabled for future research efforts.