Characterization of Off Vertical Return Error in Free-Surface Measurements by Ultrasonic Displacement Sensors

摘要

Ultrasonic displacement sensors are used to measure the free surface elevation of water waves (wave height). These sensors emit a sound burst that echos off the water surface; the time between transmitting the burst and receiving an echo is converted into a measurement of distance. Since echos are received from surface regions that are offset from vertical, these displacement measurements contain off vertical return error. These characteristics of this error source are determined by the development of an analytical model of this effect. This model is verified using computer simulations with sinusoidal and random wave profiles. A limited set of experimentally obtained results are compared to this analytical model. The results obtained from this model include the linear transfer function between actual and measured wave height, the mean value shift in the measured wave height, the echo return angle, and for sinusoidal wave profiles, the second harmonic amplitude in the measured wave height. These results describe the effect this error has on wave height measurements. Except for the echo return angle, the magnitude of these effects are dependent on the height of the sensor above the undisturbed free surface, so the degree of error is controllable. The mean value shift provides a method of measuring wave slope that is independent of a wave dispersion relationship. Since the ultrasonic transducers that are used by this measurement system operated over a limited beamwidth, the echo return angle results aid in selecting these transducers.