The digital twin of discrete dynamic systems: Initial approaches and future challenges

•The digital twin concept is investigated using a discrete damped dynamic system model.•The concept of “slow time” is proposed to differentiate the evolution of the digital twin from its dynamics.•Stiffness and mass variation in the discrete system is considered.•Sensor errors are modeled in the update process of the digital twin.•The digital twin is expressed as a benchmark closed form solution. This paper employs a discrete damped dynamic system to investigate the emerging concept of a digital twin. Dynamic systems are well understood across engineering and science domains, and represent a familiar and convenient platform for exploring the various aspects of a digital twin design. The aim is to create a framework accessible to engineering sciences related to the aerospace, electrical, mechanical and computational area. The virtual model of the physical system is expressed as a differential equation in two-time scales, with the concept of a slow time being used to separate the evolution of the system properties from the instantaneous time. Cases involving stiffness variation and mass variation are considered, individually and together. It is assumed that the damped natural frequency and the time response are measured through sensors placed on the physical system. Issues of errors and reduced sampling rate in sensor measurements on the digital twin are investigated. The digital twin is expressed as an analytical solution through closed-form expressions and the effect of sensor errors is brought out through the simulations. Several key concepts introduced in this paper are summarized and ideas for urgent future research needs are proposed. The current work breaks free from the qualitative description of digital twins pervading the literature and can be used as benchmark solutions to validate digital twin of experimental dynamic systems and their implementation using sensors, the internet of things and deployment on the cloud computing systems.