Model-based Stochastic Inversion of Coil Impedance for Determination of Tube Inner Radius and Electromagnetic Properties

We present a stochastic formulation of the inverse problem of determination of the inner radius and electromagnetic properties of metal tubes from the measured coil impedance. The inversion procedure is based on the Monte Carlo Markov chain method and the analytical impedance model developed and validated in our previous work. The impedance measurement uncertainty is included as the prior probability distribution. We use the MetropolisHasting algorithm to sample the posterior probability distributions of the tube properties. We illustrate the method using simulated measurement data sets. We corroborated from the simulation results that the requirements on electronic instrumentation and impedance measurement correspond to the targeted accuracy and precision of the tube inner radius.