Statistical Calibration via Gaussianization in Hot-Wire Anemometry

A statistical method is introduced, that is based on Gaussianization to estimate the nonlinear calibration curve of a hot-wire probe, relating the input flow velocity to the output (measured) voltage. The method uses as input a measured sequence of voltage samples, corresponding to different unknown flow velocities in the desired operational range, and only two measured voltages along with their known (calibrated) flow velocities. The method relies on the conditions that (1) the velocity signal is Gaussian distributed (or has another known distribution), and (2) the measured signal covers the desired velocity range over which the sensor is to be calibrated. The novel calibration method is validated against standard calibration methods using data acquired by hot-wire probes in wind-tunnel experiments. In these experiments, a hot-wire probe is placed at a certain region downstream of a cube-shaped body in a freestream of air flow, properly selected, so that the central limit theorem, when applied to the random velocity increments composing the instantaneous velocity in the wake, roughly holds, and renders the measured signal nearly Gaussian distributed. The statistical distribution of the velocity field in the wake is validated by mapping the first four statistical moments of the measured signals in different regions of the wake and comparing them with corresponding moments of the Gaussian distribution. The experimental data are used to evaluate the sensitivity of the method to the distribution of the measured signal, and the method is demonstrated to possess some robustness with respect to deviations from the Gaussian distribution.