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 crosssectional 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 nonrestrictive electrostatic sensors in spatial sensitivity, it is difficult to accurately measure the velocity of particles in large-diameter pipes. In this article, 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 12 pairs of strip-shaped electrodes. Experimental tests were conducted on a laboratory test rig to measure the crosssectional 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.