Prediction of the rate of penetration (ROP) is integral to drilling optimization. Many scholars have established intelligent prediction models of the ROP. However, these models face challenges in adapting to different formation properties across well sections or regions, limiting their applicability. In this paper, we explore a novel prediction framework combining feature construction and incremental updating. The framework fine-tunes the model using a pre-trained ROP representation. Our method adopts genetic programming to construct interpretable features, which fuse bit properties with engineering and hydraulic parameters. The model is incrementally updated with constant data streams, enabling it to learn the static and dynamic data. We conduct ablation experiments to analyze the impact of interpretable features’ construction and incremental updating. The results on field drilling datasets demonstrate that the proposed model achieves robustness against forgetting while maintaining high accuracy in ROP prediction. The model effectively extracts information from data streams and constructs interpretable representational features, which influence the current ROP, with a mean absolute percentage error of 7.5% on the new dataset, 40% lower than the static-trained model. This work provides a theoretical reference for the interpretability and transferability of ROP intelligent prediction models.