Empirical models for the error induced in piezoelectric ceramic transducer-based acoustic ranging instrumentation and measurement

Abstract

This article presents experimental methods and analytics for developing statistical models for ultrasonic sensors to improve reliability, repeatability, and signal-to-noise ratio (SNR) in static environments. The experiments use commercial piezoelectric ceramic transducers and over 4100 calibrated readings for three specimens of different materials. Using commercial piezoelectric ceramic transducers, the spatial-temporal approach considers range, environmental factors, material characteristics, and their interactions. A true value approach is used to formulate the error as a function of the distance measured in the time-of-flight (ToF) method at zero azimuth angular directivity. The three statistical models, linear temperature, averaged linear regression, and averaged cubic regression models, are formulated and validated. The most influential parameters in the calibrating distance with an acoustic sensor are the range, coupled effect of temperature, and material characteristics, followed by temperature. The linear model increases the SNR within 0–40 cm from ±20 dB to ≈80 dB, and the cubic model increases the repeatability of the measurement by reducing the absolute error for the entire range of sensors from ±3 cm to less than −1 cm.