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

This article focuses on the development and validation of a multi-frequency ultrasonic backscattering measurement system for simultaneously determining particle size and concentration distributions of suspended particles in liquid–solid two-phase suspensions within pipelines. Utilizing a self-receiving single transducer operating at multiple frequencies, the system employs advanced signal processing techniques—variational mode decomposition (VMD), the sparrow search algorithm (SSA), and Pearson correlation coefficient (PCC)—to denoise and reconstruct echo signals, enabling accurate inversion of particle parameters via a novel minimum concentration gradient continuity (MCGC) method. Experimental results with polystyrene particles demonstrate a mean absolute percentage error (MAPE) of 18.74% in concentration measurements, with 77.55% of predictions within 20% relative error, validating the system's effectiveness for real-time monitoring in pipeline environments. The study highlights the advantages of multi-frequency single-transducer design for ease of installation and improved measurement accuracy, while noting limitations related to transducer bandwidth and concentration range that warrant further research.