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We provide some basic and sensible definitions of different types of digitaltwins and recommendations on when and how to use them. Following up on ourrecent publication of the Learning Causal Digital Twin, this article reports ona stochastic formulation and solution of the problem. Structural VectorAutoregressive Model (SVAR) for Causal estimation is recast as a state-spacemodel. Kalman filter (and smoother) is then employed to estimate causal factorsin a system of connected machine bearings. The previous neural networkalgorithm and Kalman Smoother produced very similar results; however, KalmanFilter/Smoother may show better performance for noisy data from industrial IoTsources.

Stochastic Formulation of Causal Digital Twin: Kalman Filter Algorithm