Accurate liquid-level monitoring is vital for the safe operation of Liquefied Petroleum Gas (LPG) carriers. Conventional radar gauges are expensive and vulnerable to performance degradation under dynamic conditions. This paper proposes a Robust Graph Transformer Networks (RGTNs)–based Soft Sensor to enhance reliability and accuracy in radar level estimation. The RGTNs integrates a graph attention network for spatial dependency modeling and a Transformer for temporal feature extraction, enabling effective spatiotemporal fusion. Real-world experiments on an LPG carrier demonstrate that RGTNs achieves superior performance, with an R2 of 0.9704, MAE of 151.12 mm, and RMSE of 198.33 mm, outperforming existing models. By fusing radar measurements with thermodynamically coupled auxiliary sensors through learned spatial and temporal attention, the proposed framework provides a scalable and physically interpretable solution for liquid-level monitoring in LPG storage applications under dynamic marine operating conditions.
Bai et al. (Sun,) studied this question.