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Equivalent ultrasonic impedance in multilayer media. A parameter estimation problem

This article deals with ultrasonic transmission through multilayer systems. The equivalent ultrasonic impedance of such systems is based on the transmission line built as a convenient model to reduce the computational time for numerical evaluation. Also, the one dimensional wave equation is considered as the full model for the propagation of a plane wave inside the material. From numerical simulations, we obtained signals useful to assess the equivalent model. Results clearly depict coherence between the models since there are full agreements in the computed velocity and stress at each interface.The identification of the parameters involved in the model, characteristic acoustic impedance and time of flight, related to the layer densities and propagation velocities, is posed as a non-linear parameter estimation problem. An ultrasonic transmission is set up and the complete waveform is recorded after travelling through the layers. The minimization of a least squares objective function defined to measure the misfit between the real and predicted waveforms, in frequency, was successfully performed and the estimated parameters give useful information for the mechanical characterization of the sample.