The detection and isolation of early and minor faults in vehicle battery systems is vital to safe driving and improving power utilization. This paper proposes a data-driven model to achieve accurate, early, and economical fault detection and isolation. The model is based on kernel principal component analysis (KPCA), which maps complex nonlinear data from the input space into a high-dimensional feature space to gain a detection model with good performance. To overcome the difficulty of hyperparameter selection, KPCA is trained using Bayesian Optimization (BO) iterations with a small amount of labeled data and a large amount of unlabeled data. This step can obtain the optimal hyperparameter to greatly improve the model fault detection capability, which is beneficial for detecting both early faults and minor faults. In addition, a unified contribution graph based on the partial differentiation of KPCA was adopted to build a reasonable isolation scheme. The semi-supervised model of KPCA based on Bayesian Optimization and contribution graph is developed to reveal the relationship between fault and variable. Finally, the proposed method is fully tested on four fault datasets and the results prove the excellent detection capability in the early stage of faults compared with other methods and the accurate fault isolation capability from the occurrence to the end of the fault.