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Estimating unmeasured process variables using a combination of process physics and physical sensors

Process variables not measured can be inferred from available measurements by solving the conservation equations represented by the digital twin.  The digital twin embodies the performance of the component as a set of analytic relations representing the physical mechanisms of degradation and performance. These so-called virtual sensors provide information for assessing component performance status. In the figure, a digital twin for the system essentially doubles the number of process variables for which values are known.

The calculation of performance indexes may be straight forward, for example centrifugal pump efficiency calculated from measurements of hydraulic variables. But in cases where there is no direct measurement of the degradation process, such as stress corrosion cracking and mechanical fatigue, the digital twin needs to be a multi-physics calculation.  Measurements of stressor variables such as temperature and chemistry are input variables to the calculation while the degree of degradation is output as a virtual sensor.