Wavelet denoising treatment of dual electroresistivity probe signals measured from liquid-gas two phase bubble column

The simple wavelet transform (WT) denoising algorithm developed by Manojit Roy is found to be inadequate and result in distortion of the cleaned signal measured by dual electroresistivity probes which are used in the present work for the determination of bubble parameters in a gas-liquid bubble column, such as local gas hold up and bubble velocities. The reason is that during denoising part of the bubble energy, mainly arising from the contribution of small bubbles, could not be identified and therefore is removed. An improved method of choosing the appropriate thresholding scale levels for denoising such signals was developed by adopting a multiresolution analysis of the noisy time series data, i.e., after differentiation of the series by WT, the resulting curve of wavelet scale-wise power distribution and the slopes of the line between each two adjacent scales in the curve are calculated, then the scale at which the maximum absolute value of the slop locates will be chosen as the new thresholding scale level. The algorithm was verified by comparing the gas hold up calculated by using the proposed method to treat the data measured by the dual electroresistivity probe with the same gas hold up measured by the pressure drop method, and a good agreement is found.