AUKF-PINN: An adaptive framework for low-energy gamma multiphase flow measurement under noisy industrial conditions

Measuring multiphase flow at drilling sites presents numerous challenges, including detector window adhesion, electromagnetic interference, and temperature drift. These factors significantly increase measurement errors when traditional low-energy gamma flowmeters are directly applied in field conditions. To address this problem, this paper proposes an adaptive unscented Kalman filter and physics-informed neural network fusion algorithm (AUKF-PINN) for real-time and accurate measurement of gas-liquid-solid three-phase flow. This algorithm constructs a four-dimensional extended state space model, which includes the linear mass of the gas phase, liquid phase, solid phase, and the thickness of the adhered layer, achieving joint estimation of physical states and interference states; this model precisely handles the exponential nonlinearity of the Beer-Lambert law using unscented Kalman filtering, avoiding linearization errors; and introduces a lightweight physics-informed neural network to learn the dynamic and noise evolution laws of the adhered layer, ensuring that the network output conforms to basic physical laws; furthermore, an adaptive noise fusion strategy based on innovation matching is designed, combining the physical prior of PINN and the Sage-Husa statistical estimation, to ensure that the filter is always in the optimal gain state. Experimental results based on on-site data from the drilling platform show that AUKF-PINN performs extremely well in predicting the fraction ratio of phases and provides an effective physical information-enhanced filtering example for multiphase flow measurement in complex environments.