A non-invasive method for estimating fish length distributions in industrial aquaculture using ultrasonic multiple scattering

This is the authors' abstract. We don't add key points for this paper.

Real-time monitoring of fish growth remains technically challenging in intensive, turbid aquaculture environments. Conventional methods are often costly or rely on prior information. This study presents a low-cost, non-invasive technique for estimating the average body length of fish schools using ultrasonic multiple scattering. Based on the theory of ultrasonic multiple scattering, a method for estimating the average body length of fish schools is proposed. The elastic mean free path l s , defined as the average distance an ultrasonic wave travels between two successive scattering events, is extracted from the decay of reverberation intensity and satisfies the relationship l s = 1 n σ T with the scatterer number (n) and the total scattering cross-section ( σ T ). Furthermore, an empirical quadratic model σ T = α L 2 is established to link the scattering cross-section with fish body length ( L ), enabling the inversion of biological parameters without relying on pre-existing target strength databases, requiring only a one-time species-specific calibration. To minimize the impact of water temperature variation, a segmented calibration strategy was implemented using a pre-defined parameter lookup table for sound velocity and scattering cross-section compensation. Experimental results showed a mean absolute error (MAE) of 0.685 cm for grass goldfish (4–20 cm) under static water conditions. When water temperature fluctuated between 15 and 25 °C , the proposed calibration reduced MAE from 2.3 cm to 1.2 cm. This system provides a cost-effective and compatible solution for continuous growth monitoring, supporting improved feeding management and disease prevention in industrial aquaculture.