Vibration-based inverse graphical technique for thickness estimation of bulk acoustic wave (BAW) resonators: application for corrosion monitoring of sacrificial anodes

Abstract

Resonant acoustic sensors have been used in a variety of applications that leverage the large sensitivity of mechanical resonance frequency to shift in geometric or mechanical properties of the sensor induced by the measurand. In applications such as structural health monitoring, accurate damage quantification requires development of precise models for resonator-measurand interactions or advanced system identification or optimization algorithms. In this paper, we utilize a graphical technique originally proposed for damage assessment in beams, to determine the extent of corrosion of sacrificial zinc anode discs instrumented with piezoelectric transducers. We develop analytical models for expressing natural resonance frequencies of the radial and transverse vibration modes of a disc in terms of material and geometric properties of its constituent elements. The underlying parameters (in this case, the thicknesses of the zinc and zinc oxide films) are extracted from measured resonance frequencies by finding roots of the characteristic determinant of these modes through graphical technique. Even though accelerated corrosion induced by impressed current results in non-uniform corrosion of the anode, the graphical technique with uniform-corrosion model shows excellent agreement with experimental results and is suitable for in-situ monitoring of sacrificial anodes used in cathodic protection systems. This technique requires no calibration or model of corrosion dynamics, and is computationally inexpensive unlike optimization techniques.