  Digital twin technology has a huge potential for widespread applications in
different industrial sectors such as infrastructure, aerospace, and automotive.
However, practical adoptions of this technology have been slower, mainly due to
a lack of application-specific details. Here we focus on a digital twin
framework for linear single-degree-of-freedom structural dynamic systems
evolving in two different operational time scales in addition to its intrinsic
dynamic time-scale. Our approach strategically separates into two components --
(a) a physics-based nominal model for data processing and response predictions,
and (b) a data-driven machine learning model for the time-evolution of the
system parameters. The physics-based nominal model is system-specific and
selected based on the problem under consideration. On the other hand, the
data-driven machine learning model is generic. For tracking the multi-scale
evolution of the system parameters, we propose to exploit a mixture of experts
as the data-driven model. Within the mixture of experts model, Gaussian Process
(GP) is used as the expert model. The primary idea is to let each expert track
the evolution of the system parameters at a single time-scale. For learning the
hyperparameters of the `mixture of experts using GP', an efficient framework
the exploits expectation-maximization and sequential Monte Carlo sampler is
used. Performance of the digital twin is illustrated on a multi-timescale
dynamical system with stiffness and/or mass variations. The digital twin is
found to be robust and yields reasonably accurate results. One exciting feature
of the proposed digital twin is its capability to provide reasonable
predictions at future time-steps. Aspects related to the data quality and data
quantity are also investigated.
