A Connectivity-Based Outlier Factor Method for Rapid Battery Internal Short-Circuit Diagnosis

Abstract

Internal short-circuit (ISC) is a critical failure mode in lithium-ion (Li-ion) batteries that can trigger thermal runaway and pose serious risks to both environmental and human safety. Early-stage ISC faults are particularly challenging to detect due to their subtle characteristics and the masking effects of voltage fluctuations. To address these challenges, this study proposes a rapid and accurate ISC diagnosis method based on the connectivity-based outlier factor (COF) algorithm. The key innovation lies in the preprocessing of terminal voltage to amplify fault signatures and suppress natural fluctuations, thereby enhancing sensitivity to early anomalies. The COF algorithm is then applied to identify ISC faults in real time. Validation under urban-dynamometer driving schedule (UDDS) conditions demonstrates the method’s effectiveness: it successfully detects early ISC faults with an equivalent resistance as high as 100 Ω within 207 s of onset. This unsupervised, data-driven approach improves fault detection speed and accuracy, contributing to the advancement of safe, reliable, and sustainable LIB deployment in clean energy and transportation systems.

1. Introduction

Lithium-ion (Li-ion) batteries have been widely used in energy storage systems, smart grids, and other clean energy applications due to their advantages in terms of long lifespan, high-energy density, and low self-discharge rate [1,2,3]. However, recent fire accidents caused by battery thermal runaway have drawn public attention to battery safety problems [4,5,6]. Internal short-circuit (ISC) fault is a direct cause of the thermal runaway of the Li-ion battery, which seriously affects the safe use of Li-ion battery systems [7,8,9].

ISC refers to the accidental connection between anode and cathode inside the battery through a resistor [10,11,12]. In the early stage of ISC fault, the fault characteristics are not obvious due to the battery’s significant short-circuit resistance. In the later stages, parameters such as voltage and temperature change dramatically, displaying clear fault characteristics [13,14,15]. However, ISC fault generates a significant amount of heat in a short period of time, and even if the fault is diagnosed, thermal runaway accidents may still be unavoidable [16,17,18]. Therefore, rapid diagnosis of early ISC faults with unclear fault characteristics is crucial for the safe management of battery systems.

As shown in

Table 1. Comparison of various methods.

Method Type
Model-Based Approach	Data-Driven Approach	Proposed Method
Relies on accurate battery modeling, which is complex and susceptible to noise and actual operating conditions.	Poses difficulties in accurately identifying early ISC features and is easily affected by noise	Does not require building complex models, strong early ISC identification capabilities.

, many available ISC diagnostic methods have been proposed, primarily including model-based and data-driven approaches [19,20]. Model-based methods typically construct a battery model by analyzing the battery’s electrochemical principles. Fault detection is then performed by comparing the model’s parameters or estimated states with actual measurement data [21,22]. Meng et al. [23] constructed an equivalent circuit model based on the 2RC-network. Then, a fault estimator based on the self-adjusting state of the weighted function was designed for short-circuit fault diagnosis. Hu et al. [24] designed a battery-equivalent circuit model that can adjust the model parameters online. Then, an ISC diagnosis method was designed based on an extended Kalman filter and a recursive least-squares algorithm with a mutated forgetting factor, which can quantify the degree of fault by estimating the equivalent resistance. Cao et al. [25] employed the mean difference model (MDM) to characterize the behavior of large-scale battery packs and subsequently developed an ISC fault diagnosis approach based on this model. They introduced an adaptive hybrid prediction algorithm that integrates MDM with a bidirectional long short-term memory (Bi-LSTM) neural network to forecast the voltage of individual cells. The presence of ISC was then identified by analyzing the residuals between the predicted and measured voltage states. However, achieving accurate battery modeling in model-based approaches requires significant effort, and the accuracy of fault diagnosis heavily depends on the precision of the model [26]. Additionally, this approach is susceptible to interference and noise in practical applications [27,28].

Data-driven approaches have been investigated due to their ability to directly extract useful features from battery measurements to detect faults, eliminating the need for accurate battery modeling [29,30]. For example, Li et al. [31] proposed a multivariate multiscale sample entropy method to extract fault features from voltage, current, and temperature signals. Short-circuit fault detection was achieved by evaluating the residual differences between the entropy values of the monitored cell and those of a healthy reference cell. Mao et al. [32] developed a method for diagnosing slight short-circuit faults in Li-ion batteries based on extreme value-sample entropy. First, the maximum and minimum voltage sequences are extracted from the original voltage data. Then, the sample entropy of the sum and difference sequences is calculated to diagnose ISC faults. Wu et al. [33] developed an ISC fault diagnosis method using voltage cosine similarity. Specifically, they first constructed a two-dimensional feature vector from voltage and current measurements. Then, they applied the cosine similarity algorithm to perform secondary processing on the feature vector, effectively separating the fault signal features. These approaches are characterized by high computational efficiency and minimal resource consumption [34]. However, due to the pronounced nonlinear characteristics of Li-ion batteries and the subtle nature of early-stage ISC faults, conventional methods often struggle to identify such failures accurately and in a timely manner [35].

To overcome the aforementioned limitations, this study introduces a rapid and precise approach for the diagnosis of early-stage ISC faults. The method involves applying an outlier detection technique based on the connectivity-based outlier factor (COF) to the processed voltage signal, using the resulting anomaly score as a key fault indicator. Notably, the voltage signal undergoes tailored preprocessing to enhance the visibility of fault features, thereby enabling the early identification of abnormalities and helping to mitigate fault escalation. In summary, this work makes three primary contributions:

(1)

A COF-based ISC fault diagnosis method is proposed, effectively amplifying the abnormal data in the voltage signal and improving the ability to diagnose early ISC faults.

(2)

The voltage sequence is processed to enhance fault characteristics, minimize the effects of voltage fluctuations during battery discharge, and accelerate the fault diagnosis process.

(3)

An ISC fault experiment is conducted under urban-dynamometer driving schedule (UDDS) working conditions to verify the effectiveness of the proposed method under different fault severities and varying conditions.

The rest of this paper is organized as follows: In Section 2, the ISC fault diagnosis scheme proposed in this study is introduced in detail. Section 3 describes the experimental platform and the acquisition of fault data. Section 4 gives the results of the ISC diagnostic experiments and analysis. Section 5 concludes the paper.

2. Methodology

This section presents an ISC fault diagnosis scheme based on the COF, aiming to enable rapid and precise identification of ISC faults. Specifically, the principle of the COF anomaly detection algorithm is first introduced, followed by the ISC fault diagnosis framework based on COF.

2.1. Connectivity-Based Outlier Factor Algorithm

The COF algorithm is a method for anomaly detection that relies on the connectivity between data points. The core idea of the algorithm is to evaluate the degree of abnormality of each point relative to its neighbors by calculating the connectivity among data points [36]. Compared to other outlier detection algorithms, such as random forest and k-nearest neighbor, this algorithm not only effectively processes high-dimensional data but also resists the interference of noisy data to a certain extent [37]. In addition, the COF algorithm is an unsupervised anomaly detection method that does not require model training. This is particularly useful in practical situations where high-quality battery failure data are scarce.

The anomaly detection principle of the COF algorithm is shown in Figure 1. The details are as follows:

(1) Calculate the k-nearest neighbors of each data point. The k-nearest neighbors refer to the k data points that are closest to a given data point in terms of Euclidean distance or other distance metrics.

(2) For each data point 𝑝, the COF algorithm calculates the average of the connectivity distances (shortest path lengths) from the data point 𝑝 to its k-nearest neighbors to estimate its local density.

(3) Compare the local density of the data point 𝑝 with the local density of its k-nearest neighbors to calculate the COF value. The specific formula is as follows:

$$COF\left(𝑝\right)={\displaystyle \frac{\frac{1}{k}{\sum }_{q\in N_k\left(𝑝\right)}{L}_k\left(𝑝,q\right)}{\frac{1}{k}{\sum }_{q\in N_k\left(𝑝\right)}\frac{1}{k}{\sum }_{r\in N_k\left(q\right)}{L}_k\left(q,r\right)}},$$

(1)

where $N_k\left(𝑝\right)$ and $N_k\left(q\right)$ represent the k-nearest neighbors of data points 𝑝 and q, respectively; $L_k\left(𝑝,q\right)$ represents the connectivity distance from data point 𝑝 to q; and $L_k\left(q,r\right)$ represents the connectivity distance from data point q to $r$.

(4) If point p is not an outlier, its COF value should be close to 1. Specifically, the detection of anomalies is performed by comparing the calculated COF value against a set threshold. If the COF value exceeds the threshold, the point is determined to be abnormal; otherwise, it is considered normal.

2.2. Fault Diagnosis Scheme

In a series-connected battery pack, individual cells typically follow consistent voltage trends. However, when an ISC fault occurs in a cell, its voltage behavior diverges from the group pattern, rendering it an outlier. This paper diagnoses faults based on outlier detection. Specifically, utilizing the COF outlier detection algorithm, a fault diagnosis framework is developed, which includes feature extraction and fault diagnosis strategy, as outlined below.

2.2.1. Feature Extraction

ISC faults cause abnormal voltage trends, but this abnormality is very small in the early stages of the fault and can be affected by natural fluctuations during battery discharge. Therefore, it is necessary to preprocess the battery voltage to enhance fault features and reduce the influence of such fluctuations. This paper uses the average value of different battery voltages at the same time to process each individual battery voltage. The specific formula is as follows:

$$z_i\left(t\right)={\displaystyle \frac{V_i\left(t\right)-\overline{V}\left(t\right)}{\overline{V}\left(t\right)}},$$

(2)

where $z_i\left(t\right)$ is the standard score of cell i at time t, $V_i\left(t\right)$ is the terminal voltage of cell i at time t, and $\overline{V}\left(t\right)$ is the average voltage of all battery cells at time t. When there is no fault, the voltage trends of each cell are similar, so the processed voltages remain consistent. However, when an ISC fault occurs, the voltage trend of the faulty cell becomes abnormal. This processing method amplifies the differences between the voltages, making it easier to capture the fault characteristics.

The data are then processed using a moving window to obtain the input for the COF algorithm. It can be expressed as follows:

$${\mathit{x}}_{\mathit{i}}=\left\{{\mathit{z}}_{\mathit{i}}\left(\mathit{t}-\mathit{W}+\mathbf{1}\right), {\mathit{z}}_{\mathit{i}}\left(\mathit{t}-\mathit{W}+\mathbf{2}\right),\dots ,{\mathit{z}}_{\mathit{i}}\left(\mathit{t}\right)\right\};\mathit{i}=\mathbf{1},\mathbf{2},\dots ,\mathit{N},$$

(3)

where W is the width of the sliding window, N is the total number of batteries in the module, and $x_i$ is an input point. All $x_i$ together constitute a set of inputs to the COF algorithm. It is worth noting that the size of W affects both the anti-interference capability of the diagnostic method and the required computing power. Specifically, a larger W enhances the anti-interference ability of the diagnostic method but also demands more computing power.

2.2.2. Fault Diagnosis

After the processed data are input into the COF anomaly diagnosis algorithm, each data point is assigned an anomaly score. Under normal operating conditions, the anomaly scores of these points are expected to be close to 1. However, scores exceeding 1 do not automatically indicate the presence of outliers, as they may result from normal data variations. Thus, to more effectively identify true outliers, it is necessary to establish a threshold. In this paper, the threshold $J$ is determined by evaluating the anomaly scores of normal battery data. The diagnostic logic is defined as follows:

$$\left\{\begin{array}{l}{F}_i\left(t\right)\ge JFault\\ F_i\left(t\right)<JNormal\end{array},\right.$$

(4)

where $F_i\left(t\right)$ is the abnormality score of cell i at time t. Once the anomaly score surpasses the defined threshold, the corresponding faulty battery is identified, and its data are excluded from further analysis to maintain the reliability of the fault indicators.

Using the COF anomaly detection method described above, ISC faults can be accurately diagnosed. The specific process of the proposed method is illustrated in Figure 2. First, the voltage of the series-connected battery module is measured by a voltage sensor. Next, the battery voltage is processed to amplify fault characteristics and mitigate the interference of natural voltage fluctuations. The fault indicator is derived from the anomaly score of the COF anomaly detection method. When the anomaly score exceeds the threshold, the fault indicator identifies and locates the occurrence of the fault.

3. Design of Experiment

To evaluate the performance and accuracy of the proposed fault diagnosis method, an experimental setup was established. As illustrated in Figure 3, the platform comprises a battery module, a thermal chamber(Giant Force Instrument Enterprise Co., Ltd., Jinan, China), an Arbin battery tester(Arbin Instrument; Jinan, China), and a host computer. The battery module consists of six series-connected 18650-type nickel–cobalt–manganese (NCM) Li-ion battery, with detailed parameters listed in

Table 2. Battery parameters.

Battery Type	Nominal Voltage (V)	Nominal Capacity (Ah)	Charge Cutoff Voltage (V)	Discharge Cutoff Voltage (V)
INR18650-2P	3.7	2000	4.2	2.5

. The cells are labeled from 1 to 6. The thermal chamber maintains a constant temperature of 25 °C. The Arbin battery tester controls the operating conditions of the batteries, including current, voltage, and charge/discharge profiles. Simultaneously, it collaborates with the host computer to monitor and log the voltage and current data of the cells. The sampling rate is set at 1 Hz. The cells are charged at a constant current of 2 C to 4.2 V, then charged at a constant voltage of 4.2 V until the current drops to 0.05 C. After charging, cells are left to rest for 1 h before commencing the failure experiment.

Because the proposed method only considers the voltage characteristics, using parallel resistance to simulate ISC faults is a good choice [38]. The resistance values of the selected resistors are 1, 5, 10, 50, and 100 Ω, which helps to evaluate the performance of the proposed method under different degrees of ISC faults. The resistor is represented by R_isc and is controlled by a switch. Six hundred seconds after the start of the experiment, a specific resistor is connected in parallel to cell 4. Specifically, the fault conditions are shown in

Table 3. Details of the fault experiments.

Experiment Number	Fault Type	Fault Parameters	Start Time
01	No fault status	None	0 s
02	ISC fault	1 Ω	600 s
03	ISC fault	5 Ω	600 s
04	ISC fault	10 Ω	600 s
05	ISC fault	50 Ω	600 s
06	ISC fault	100 Ω	600 s

. In addition, the specific test condition of the battery is the UDDS cycle at 25 °C.

4. Results and Discussion

4.1. Fault Experiment Data Results and Processing

After the fault experiment, the ISC fault experiment data are shown in Figure 4. Specifically, it includes normal module voltage data and ISC fault data when the equivalent resistors R_isc = 1 Ω, 5 Ω, 10 Ω, 50 Ω, and 100 Ω. Figure 4a shows that the cell voltage curves are nearly identical, indicating a high level of consistency among the cells in the series-connected battery module. However, it is important to note that strong consistency does not imply complete uniformity, as slight inconsistencies between the cells are still evident in the enlarged view. Analysis of the fault data in Figure 4b–f reveals that when an ISC fault occurs, the voltage of the faulty battery deviates from the normal battery voltage and progressively becomes abnormal. The smaller the equivalent resistor R_isc, the more pronounced this divergence becomes. However, when the R_isc is large (indicating an early-stage ISC fault), the fault characteristics are minimal and often only become apparent after a long period. For example, in an ISC fault with R_isc = 100 Ω, the fault characteristics may only be noticeable after one or two charge and discharge cycles. Detecting such minor faults can serve as an early warning, preventing further damage and playing a crucial role in avoiding serious safety incidents.

Therefore, the obtained raw data needs to be processed to amplify the fault characteristics, and the results are shown in Figure 5. It is evident that for normal module data, the magnitude remains similar after processing. In contrast, for fault data, the fault characteristics are significantly amplified, and the influence of voltage fluctuations during battery discharge is reduced. For instance, in the case of an ISC fault with R_isc = 100 Ω, the curve of the faulty battery becomes clearly distinguishable from the normal battery curve after processing, with the fault characteristics significantly amplified.

4.2. Fault Diagnosis Results

After processing the data, a sliding window is needed to extract the input for the COF algorithm. The selection of the width W of the sliding window should be noted. Careful attention should be given to selecting the sliding window width W, as its size impacts both the anti-interference capability of the diagnostic method and the computational power required. In this paper, W = 60 is selected based on a balance between threshold selection and computational complexity.

After inputting the extracted features into the COF algorithm, the fault diagnosis results are shown in Figure 6 and

Table 4. Fault detection results.

Fault Trigger Time	Diagnosis Time (s)
	1 Ω	5 Ω	10 Ω	50 Ω	100 Ω
600 s	604 s	619 s	629 s	723 s	807 s

. Figure 6a presents the results under fault-free conditions, in which the anomaly scores of all cells remain between 1 and 2. Although cell 4 consistently exhibits the highest anomaly score among all cells—reaching a maximum of 1.49—none of the scores exceed the predefined threshold of 1.8. This demonstrates that the method does not generate false positives under normal operating conditions, thus ensuring diagnostic reliability and redundancy. Figure 6b–f illustrate the diagnosis results for ISC faults of varying severity. The analysis results indicate that for more severe ISC faults (R_isc < 10 Ω), the proposed method can rapidly detect the fault (within 30 s) and accurately locate the faulty cell. For early-stage ISC faults, although the anomaly score changes gradually, the proposed method can still detect the fault at a relatively fast speed. For example, with an ISC fault of R_isc = 100 Ω, the method completed the fault detection in 107 s. These results confirm that the proposed method maintains both high sensitivity to faults and robustness against false alarms, enabling the reliable and timely detection of ISC faults across a wide range of fault conditions.

4.3. Comparison with Autoencoder-Based Methods

Autoencoder is a machine learning technique commonly used for anomaly detection. Similar to the COF algorithm in this article, the autoencoder-based anomaly detection method is an unsupervised learning approach. It does not require fault data for model training; instead, it only relies on normal operational data to train the model and achieve effective anomaly detection [39]. The principle of using autoencoders for anomaly detection is as follows. In anomaly detection using autoencoders, only normal samples are used for training, and no fault data are provided. As a result, the autoencoder reconstructs data that closely resemble normal samples. When abnormal samples are introduced, the reconstruction error increases significantly. Fault detection is then achieved by assessing the magnitude of this reconstruction error [40].

In addition, the proposed method is verified on experimental data with an equivalent resistance of 10 Ω obtained from experiments at different temperatures, as shown in Figure 7. Obviously, at 15 °C, the proposed method can still quickly and accurately detect ISC faults, and the detection time is 27 s, which is close to 29 s at 25 °C, which proves the robustness of the proposed ISC fault diagnosis method at different temperatures.

To compare the performances of the two fault diagnosis methods, the battery voltage data for ISC faults with equivalent resistances of 1 Ω and 50 Ω, as shown in Figure 4b,e, are evaluated using the autoencoder-based fault diagnosis method. Figure 8 shows the fault diagnosis results of the autoencoder-based method, where MSEi is the reconstruction error corresponding to cell i, and i = 1, 2, 3, 4, 5, and 6.

Table 5. Comparison of the effects of different models.

Method	Fault Trigger Time	Diagnosis Time (s)
		1 Ω	50 Ω
Proposed method	600 s	604 s	723 s
Autoencoder	600 s	612 s	8340 s

shows the comparison results between the proposed method and the autoencoder-based method. When the ISC fault with an equivalent resistance of 1 Ω occurs, the autoencoder-based fault detection method completes the diagnosis in 612 s, which is slightly slower than the 604 s required by the method proposed in this paper. Nevertheless, it still achieves fault detection relatively quickly. When the ISC fault with an equivalent resistor of 50 Ω occurs due to the relatively weak nature of the fault, the autoencoder-based method completes fault detection in 8340 s, which is significantly slower than the 723 s required by the method proposed in this paper. Through comparison, it can be concluded that the proposed method outperforms the autoencoder-based fault diagnosis method, regardless of the severity of the ISC fault. In addition, in terms of computing speed, both completed the processing of a set of data within 1 s. However, it is worth noting that the autoencoder needs to be fully trained before fault detection, and its training time is as long as thousands of seconds.

5. Conclusions

ISC faults in Li-ion batteries present a serious safety risk and can potentially lead to thermal runaway. Therefore, detecting ISC faults is crucial for ensuring safe battery operation. To achieve this goal, this paper proposes a fault diagnosis method for series-connected Li-ion batteries. The fault diagnosis scheme is implemented based on COF outlier detection. Specifically, the battery voltage is processed to amplify the fault signature while reducing the impact of natural voltage fluctuations during discharge. The processed voltage is then evaluated using the COF anomaly detection algorithm, with the anomaly score serving as the fault indicator for ISC. A threshold is established for this fault indicator to detect abnormal voltage drops. When the threshold is exceeded, an ISC fault is diagnosed. It is worth noting that by processing the voltage sequence, the voltage anomaly caused by the fault can be amplified, thus ensuring the feasibility of the proposed method for diagnosing early ISC. Furthermore, ISC faults are simulated by connecting external resistors in parallel, generating multiple sets of fault data with different severity levels. Fault tests are performed on a six-cell-series battery module under the UDDS driving cycle, showing that the proposed diagnosis method can detect ISC faults both accurately and quickly. Moreover, the results indicate that the proposed method maintains strong performance even for early ISC faults. For instance, when an ISC fault with an equivalent resistance of R_isc = 100 Ω occurs, the method is capable of detecting the fault 207 s after its onset.

The challenge faced by the proposed method is that the threshold used is a fixed threshold set according to the anomaly score of historical normal data, which may cause misdiagnosis when the inconsistency of each battery increases as the battery pack continues to operate. Future work will focus on the following aspects: exploring more advanced threshold setting methods such as adaptive thresholding to better balance detection speed and false alarm rate, validating the proposed method in practical application scenarios, and extending the applicability of the method to a broader range of faults, such as connection faults and over-discharge faults.