The significant differences in the instability mechanism and process of static and transient voltage makes united analysis a challenging problem. An approach is proposed to identify weak grid links considering the voltage instability patterns at multiple time scales. The input features for static and transient voltage stability assessment are established. Principal component analysis is used for dimensionality reduction, and the improved k-means++ method is used to partition the power grid and select representative buses for transient voltage analysis. The risk levels of power system static and transient voltage instability are quantified, and a united multi-time-scale voltage stability assessment model is constructed based on deep belief networks (DBN) to extract voltage instability patterns. The coupling between voltage instability patterns and power grid links is analyzed. Quantitative indices are built to identify the power grid weak links. Finally, the effectiveness of the proposed method is validated through case studies.