  The potential of digital twin technology is immense, specifically in the
infrastructure, aerospace, and automotive sector. However, practical
implementation of this technology is not at an expected speed, specifically
because of lack of application-specific details. In this paper, we propose a
novel digital twin framework for stochastic nonlinear multi-degree of freedom
(MDOF) dynamical systems. The approach proposed in this paper strategically
decouples the problem into two time-scales -- (a) a fast time-scale governing
the system dynamics and (b) a slow time-scale governing the degradation in the
system. The proposed digital twin has four components - (a) a physics-based
nominal model (low-fidelity), (b) a Bayesian filtering algorithm a (c) a
supervised machine learning algorithm and (d) a high-fidelity model for
predicting future responses. The physics-based nominal model combined with
Bayesian filtering is used combined parameter state estimation and the
supervised machine learning algorithm is used for learning the temporal
evolution of the parameters. While the proposed framework can be used with any
choice of Bayesian filtering and machine learning algorithm, we propose to use
unscented Kalman filter and Gaussian process. Performance of the proposed
approach is illustrated using two examples. Results obtained indicate the
applicability and excellent performance of the proposed digital twin framework.
