Developing a reliable battery fault diagnosis system is crucial for electric vehicles (EVs) to ensure seamless operation and maximize battery lifespan. Nevertheless, the diversity in battery specifications across various EV models, coupled with the distinct parameter alterations caused by different fault types, presents formidable challenges for real-time diagnostic systems. To address these challenges, this paper presents an innovative approach using the Generalized Dimensionless Indicator (GDI) and an adaptive threshold mechanism. We apply Successive Variational Mode Decomposition (SVMD) to isolate and reduce noise in voltage data, extracting distance and trend deviations to form the GDI. This standardized indicator quantifies battery health deviations. A kernel ridge regression model dynamically adjusts thresholds for accurate fault classification across various conditions, minimizing false positives. Experimental results demonstrate the method's effectiveness in detecting faulty battery cells early, preventing thermal runaway and vehicle malfunction, and outperforming alternative methods in diagnosis speed and accuracy.