Abstract:To address the issues of low detection accuracy in existing flotation foam-layer thickness measurement, large errors in interface determination, and poor adaptability to complex operating conditions, this paper proposes a thickness-detection method for flotation foam layers based on a Mann-Kendall adaptive threshold and proportional-fitting compensation. Firstly, an electrical conductivity model for industrial flotation processes is established, and the differences in conductivity characteristics between the pulp layer and the foam layer are analyzed. Secondly, a trend-testing method based on the Mann-Kendall statistic is introduced. By assessing the monotonic trend of the overall voltage sequence, the presence of a foam layer is identified. Combined with the voltage difference at the pulp-foam interface, an adaptive threshold suitable for various operating conditions is constructed based on the Pauta criterion to accurately determine the interface position. Finally, an equivalent-resistance model of the interface is established according to the relationship between gas holdup and foam-layer conductivity. A foam-thickness compensation algorithm based on the proportional coefficient between the pulp layer and the foam layer is proposed to correct measurement deviations caused by operating-condition disturbances and foam nonuniformity, thereby enabling accurate measurement of flotation foam-layer thickness. Simulation and field-measurement results show that the Mann-Kendall adaptive-threshold method can accurately identify the pulp-foam interface under different flotation conditions. Compared with existing methods, the proposed proportional-coefficient fitting approach provides better overall foam-layer thickness estimation with higher measurement accuracy. The absolute error of thickness compensation is within 5 mm, and the actual measurement error of the final flotation foam layer thickness is within ±1 cm, which meets the requirements for measuring the foam layer thickness in the industrial field of the flotation process and provides accurate and reliable technical support for the real -time monitoring and automatic control of the flotation process.