Approach for simultaneous determination of thickness and sound velocity in layered structures based on sound field simulations

摘要

For imaging in NDT or in medical diagnostics, the value of sound velocity is assumed a priori. Interfaces of hidden objects are imaged by the measured time of flight (ToF). The supposed locations and extensions of these objects are incorrect if the actual sound velocity differs from the assumed. For material characterization the thickness of a specimen is determined by mechanical measurements and the sound velocity is determined by ToF-measurements. For multi-layered structures the mechanical determination of the thickness of the different layers is impossible non-destructively. It is necessary to determine both quantities simultaneously to get information about the thickness and the material of the different layers.A variation method is introduced in [1] allowing the simultaneous determination of sound velocity and thickness of up to two layers by focusing with an annular array at a fixed position. It works by varying the focus positions and the assumed sound velocity, which is used to calculate the delay times for each control mode by means of FERMAT’s principle. The amplitude of the echo signals is determined as a function of the control mode. Because the sound field depends on the sound velocity of the medium and the control mode evaluating the amplitude of the echo signals yields additional information besides the time of flight. Alternatively, in [2], a fast and efficient method for a simultaneous determination of sound velocity and thickness of a two- layered structure has been presented. It analyses the different signal parts of an echo reflected from the examined interface. These signal parts correspond to different propagation paths. The difference in time of flight between the signal parts contains the information about thickness and sound velocity of the layer. These time differences are used as an input for an inverse geometric model. Although an accuracy of over 95% had been reached, increasing this accuracy fails, because in both cases the analysis of the signals only uses a geometric model neglecting the wave properties.A half-analytical method based on GREEN’s functions and point sources synthesis is used to calculate the sound field in the multi-layered structures. The echoes of several interfaces are calculated for each element of the used array. Using the same parameter of specimen and the array as in the experiments the evaluation of the simulated signal yields correct time differences based on the wave propagation. They allow assuming effective, corrected source points for the geometric model. With such an optimization of the geometric model an accuracy of 99% can be reached for simulated signals. Measurements are executed on two-layered structures consisting of a first layer of water and a second layer of steel, cupper or aluminum with a thickness of d = 6 mm, 8 mm, 10 mm and 12 mm. For the second layer a deviation for the combined determination of sound velocity and thickness between 3% and 5% is reached with the geometric model for both evaluation methods. With the corrected source point the accuracy can be improved.