Measurement of Cross-Sectional Velocity Distribution of Pneumatically Conveyed Particles in a Square-Shaped Pipe Through Gaussian Process Regression-Assisted Nonrestrictive Electrostatic Sensing

Online continuous measurement of the cross-sectional velocity distribution of pneumatically conveyed solids in a square-shaped pipe is desirable in monitoring and optimizing circulating fluidized beds, coal-fired power plants and exhaust pipes. Due to the limitation of non-restrictive electrostatic sensors in spatial sensitivity, it is difficult to accurately measure the velocity of particles in large-diameter pipes. In this paper, a novel approach is presented for the measurement of cross-sectional particle velocity distribution in a square-shaped pipe using sensors and Gaussian process regression (GPR). The electrostatic sensor includes twelve pairs of strip-shaped electrodes. Experimental tests were conducted on a laboratory test rig to measure the cross-sectional particle velocities in a vertical square-shaped pipe under various experimental conditions. The GPR model is developed to infer the relationship between the input variables of velocities and the cross-sectional velocity distribution of particles in nine areas of the pipe cross-section and the performance of the built models was compared with other machine learning models. The relative error of velocities predicted under all the experimental conditions is within ±3%. When the training dataset is not comprehensive enough, the performance of the model is negatively affected, and the relative error range is ‒9% to +15%. With fewer measurement electrodes (input variables), the relative error of the predicted velocities in each area increases slightly, but remains within ±5%. Results obtained suggest that the electrostatic sensor in conjunction with the GPR model is a feasible approach to obtain the cross-sectional velocity distribution of pneumatically conveyed particles in a square-shaped pipe.