•A BIW weld quality inspection method using vibration response signals has been proposed.•The LGHGNN model is designed for intelligent detection of BIW weld quality.•The cluster upgrade graph pooling is proposed to elevate node features.•Hierarchical information interaction and collaborative output.•Parallel anomaly detection for multi-label corresponding to multiple regions. To enhance the assembly quality in Body-in-White (BIW) assembly, this paper proposes an intelligent detection method for the nugget quality of Resistance Spot Weld (RSW) based on weld joint vibration excitation response signals. The method proposes a novel deep learning model, the Local-Global Hierarchical Graph Neural Network (LGHGNN). LGHGNN can automatically construct graph structures and, by introducing a newly designed upgrade pooling operation, extends the traditional flat structure of graph networks into a hierarchical structure within three-dimensional space. Therefore, LGHGNN achieves layered interaction of local-global information, enabling the model to focus on local details while gaining a broader learning perspective. Additionally, this paper proposes a strategy for multi-label unsupervised anomaly detection that involves layered interaction and collaborative decision-making for local and global graphs. The effectiveness of LGHGNN is demonstrated through its application in the BIW right front door assembly, achieving a remarkable 97.5% average accuracy in multi-region parallel anomaly detection.