## 1 Introduction  
Owing to their high energy density, long cycle life, and non-polluting advantages, lithium-ion batteries are widely used in energy storage stations [1]. Through series and parallel connections, a lithium battery can be formed into a battery pack and achieve the required capacity and voltage, meeting the requirements of actual application scenarios [2, 3]. The processes and materials used in the production of battery cells make it impossible for them to be completely consistent from the start. As lithium-ion batteries are used over time, this inconsistency will cause increasingly significant differences in capacity and voltage among battery cells, leading some battery cells to reach the end of their lives prematurely. This triggers an overall capacity loss, shortens the overall lifespan of the battery pack, and even leads to overheating, thermal runaway, and other accidents [4], affecting the performance and safety of the battery pack. Furthermore, the voltage data of battery cells in a battery pack generally consist of valid measurement data and measurement errors. The presence of measurement errors is a normal phenomenon in experiments, mainly due to the sensor drift and random noise in the sensor output data, obscuring the actual measurement data. However, when measurement errors are large and deviate from normal measurement data, they are considered abnormal voltage data. Such abnormal voltage data occur because the battery has experienced over-charging, over-discharging, imbalance, thermal runaway, and other faults [5; 6], causing voltage changes abnormally. Consistency anomaly detection of the battery voltage can help to achieve early warning of battery faults and avoid safety accidents in energy storage stations. A large number of scholars have conducted research on the detection of abnormal voltage in battery cells, mainly including data-driven approaches and statistical analysis approaches [7]. Data-driven approaches can select machine learning models based on the characteristics of the dataset and then use the model to obtain the historical regression of the voltage time series, identifying batteries that exhibit abnormal external signal characteristics under the same operating conditions [8]. Data-driven approaches usually include Local Outlier Factor (LOF) algorithms [9], K-means algorithms [10], neural network algorithms [11], Gaussian Process Regression (GPR) [12], etc. Since the K-means clustering algorithm is less efficient when dealing with large amounts of data, reference [13] proposes a fault identification method for inconsistent voltage in battery cells based on K-means++ clustering with dynamic \(k\)-values, which can identify abnormal cells up to 6 days earlier. Reference [14] uses the BP neural network and 3\(\sigma\)-MSS strategy to detect and calculate the abnormal changes in battery voltages within the battery pack and then verifies the calculation results using the LOF algorithm and clustering algorithms. Based on the EV data collected by NMMP-NEV, reference [15] proposes an improved GPR-based method for recognizing abnormal charging capacities and uses a Box-Cox transform with the value of 3\(\sigma\) to determine the threshold. However, some data-driven approaches compare detected parameters with preset thresholds, which may lead to errors or misjudgments. Others require a large amount of training data, and the calculation cost of manually preprocessing and training data is high. Moreover, the data quality, which is affected by various factors, can also affect the calculation accuracy and robustness of data-driven models. Statistical analysis approaches estimate the probability distribution of data, identifying values with low probability density as outliers [16; 17]. Common approaches include the 3\(\sigma\) criterion, boxplots, information entropy, and measures describing data variability such as the mean squared error, standard deviation, coefficient of variation, and interquartile range.