Measurement and inversion of concentration distribution in suspensions using a multi-frequency ultrasonic backscatter approach

Accurate measurement of suspended particle concentration in pipelines is essential for analyzing the fluid mixing density and particle settlement. However, measuring concentration distributions along the flow path poses significant challenges due to the inherent complexity and variability of liquid–solid two-phase suspensions. In this study, we developed a sensor measurement system based on multi-frequency acoustic emission technology and a self-receiving single probe. The effects of suspended particle size, concentration, and ultrasonic transducer dimensions on acoustic wave propagation were analyzed using the COMSOL Multiphysics system. For multi-frequency echo signals, variational mode decomposition and the sparrow search algorithm were employed to decompose and optimize the signal, followed by reconstruction using the Pearson correlation coefficient. By combining the energy ratio method with the minimum concentration difference method, we propose a new approach for simultaneous measurement of particle size and concentration along the pipeline transmission path. Experimental results indicate that along the transmission path, the mean absolute percentage error is 18.74%, and 77.55% of the predicted results exhibit relative errors below 20%.