Process monitoring as a crucial component for ensuring production safety and efficiency, plays a significant role in modern industrial production. However, due to the dynamic complexity and uncertainty of production processes, traditional monitoring solutions have significant limitations in terms of adaptivity and interpretability, which affect the real-time response capabilities and decision transparency of monitoring systems. To address these challenges, an incremental graph attention autoencoder with probabilistic inference (I-GATEPi) is proposed to facilitate the adaptability and interpretability of monitoring. This framework consists of incremental learning based on self-organizing map (SOM) and spatial structure representation learning based on GATEPi. Incremental learning endows the framework with adaptability, while spatial structure representation learning provides interpretability, with both elements embedding and reinforcing each other. The effectiveness and feasibility of the proposed method are verified through two practical industrial cases.