Particle size distribution measurement in suspension based on a random forest algorithm

The conversion of ultrasonic particle size distribution (PSD) is traditionally modelled as a first-kind Fredholm integral equation problem, requiring integration with theoretical models to calculate the PSD. In this paper, we propose a novel machine learning-based approach for PSD measurement using an ultrasonic–physical property parameter fusion model coupled with a random forest algorithm. This method employs feature and label parameter training to construct a random forest model that predicts the PSD from input feature parameters, eliminating the need for complex theoretical model selection and inversion algorithms. Forty sets of experimental samples were used to obtain feature parameters for PSD prediction. The results, comparing the predicted PSD of three differently distributed suspended sediment samples with those obtained through a screening method, demonstrate coefficients of determination all above 0.8 and median diameter errors of 6.25%, 2.47% and 1.64%, respectively. In addition, we compared the proposed model with traditional inversion algorithms and the artificial bee colony algorithm, demonstrating that the random forest-based method delivers more accurate and reliable PSD measurements. These findings highlight the potential of this approach as a promising alternative for future studies.