Nonlinear model selection - Application to an indirect inductive measurement of conductivity

Abstract : An efficient method and algorithm for experimental data processing based on parametric inversion is proposed. This method is applied to a metallic rod conductivity measurement based on induced secondary voltage technique. Firstly, the case of an ideal excitation circuit is studied. For this case, when the excitation signal is a current step, a model of the data can be obtained in a closed-form as an infinite sum of exponential functions whose relaxation times are related to the physical properties of the inspected material. Therefore, for time points greater than the largest relaxation constant, only one term is sufficient; but, for these times, the signal-to-noise ratio is smaller, so the variance of the estimated conductivity is larger. When taking into account some data at earlier time points, N terms are necessary to minimize the residual modelling error. The conductivity variance is then smaller but the identification process is more complex. A trade-off has been achieved between these two aspects. Finally, the choice of an L1 norm criterion upon the identification error is used to reject outliers from experimental data. Secondly, a more realistic circuit is considered (the primary time constant is taken into account). In that case, two steps are necessary to calculate the direct model. A nonlinear equation is solved and the results are put into a closed-form expression (an infinite sum of exponential functions).
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Submitted on : Friday, February 22, 2008 - 4:07:21 PM
Last modification on : Thursday, March 29, 2018 - 11:06:03 AM

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Marie-Eve Davoust, Gilles Fleury. Nonlinear model selection - Application to an indirect inductive measurement of conductivity. IEEE Transactions on Instrumentation and Measurement, Institute of Electrical and Electronics Engineers, 2006, Vol. 55 (N°6), pp. 2055-2061. ⟨10.1109/TIM.2006.887121⟩. ⟨hal-00258592⟩

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