The growing concerns over environmental pollution and energy crises have significantly accelerated the adoption of battery EV cars as a sustainable transportation solution. At the heart of every battery EV car lies its energy storage system, where Lithium-ion (Li-ion) batteries have emerged as the dominant technology due to their high energy density, superior power performance, and extended cycle life. To meet the stringent voltage and range requirements of modern battery EV cars, hundreds or thousands of individual Li-ion cells are connected in series and parallel to form a battery pack. However, the inherent complexity of the electrochemical reactions within Li-ion cells, coupled with inevitable inconsistencies among individual cells within a pack, makes these systems susceptible to various failures. Such faults in a battery EV car can lead to reduced performance, accelerated degradation, and in severe cases, catastrophic safety incidents like thermal runaway, posing a significant risk to vehicle safety.
Common faults in battery EV car battery packs include over-voltage, under-voltage, connection looseness, sensor faults, internal short circuits (ISC), and external short circuits (ESC). The diagnosis of these faults is challenging because the internal states of Li-ion batteries are not directly measurable. Furthermore, Li-ion batteries exhibit strong nonlinearity, time-varying characteristics, hysteresis, and inconsistency, making it difficult to discern abnormalities hidden within the measured terminal voltages. Existing diagnostic approaches can be broadly categorized into model-based, signal-processing-based, and knowledge-based methods.
Model-based methods rely on accurate mathematical models of the battery. By comparing measured data with model predictions, residuals are generated and analyzed to detect and isolate faults. For instance, an Extended Kalman Filter (EKF) observer can be designed using a cross-voltage measurement topology to generate residuals. Statistical tools like the Cumulative Sum (CUSUM) and sample entropy of residuals can then be used for fault detection and distinguishing between short circuits and connection faults. While precise, these methods are heavily dependent on model accuracy, are difficult to adapt to varying conditions and aging, and involve high computational costs for complex models.
Signal-processing-based methods analyze operational data directly without requiring a precise physical model, making them suitable for nonlinear systems like those in a battery EV car. Techniques such as zero-mean processing combined with correlation coefficients, sample entropy, and modified threshold methods are used to identify anomalies in voltage signals by measuring similarity or irregularity. These methods are generally robust but can struggle when multiple faults occur simultaneously, as their overlapping signal features become difficult to disentangle, limiting their effectiveness in multi-fault scenarios for a battery EV car.
Knowledge-based methods utilize expert knowledge, historical data, and reasoning systems (e.g., knowledge graphs, neural networks) for diagnosis. They can handle complex, multi-fault situations by learning patterns from data. However, acquiring comprehensive, high-quality fault data and expert knowledge specific to every battery EV car configuration is often impractical, limiting the widespread application of these methods.
To address the limitations of existing methods, particularly the challenge of diagnosing multiple concurrent faults in a battery EV car battery pack, this paper proposes a novel online multi-fault diagnosis strategy. This strategy synergistically combines the principles of knowledge-based and signal-processing-based methods. The core innovation involves using Variational Mode Decomposition (VMD) to extract the low-frequency components of cell voltage signals, which effectively amplifies and isolates fault signatures obscured by operational noise and dynamic responses. A feature extraction algorithm based on Manhattan distance is then employed to quantify the dissimilarity between voltage profiles. Crucially, by integrating a cross-voltage measurement circuit, unique fault fingerprints are constructed for four common fault types. Finally, a streamlined online diagnostic procedure is designed and validated through experiments, demonstrating the method’s accuracy, speed, and robustness to noise, making it a practical solution for enhancing the safety and reliability of battery EV cars.
Fault Feature Extraction Methodology
Design of Cross-Voltage Measurement Circuit
Accurate diagnosis, particularly the need to distinguish connection faults from other cell-level faults, requires insightful measurement. A non-hardware-redundant cross-voltage measurement circuit is adopted for this purpose. In this topology, a voltage sensor labeled $$v_q$$ is connected to the positive terminal of cell $$C_{q-1}$$ and the negative terminal of cell $$C_{q+1}$$. Consequently, the measured voltage $$v_q$$ is influenced not only by the terminal voltage of cell $$C_q$$ but also by the connection resistances of the busbars $$l_{q-1,q}$$ and $$l_{q,q+1}$$.
This design creates a unique signature for connection faults. For example, if a high-resistance connection fault occurs at busbar $$l_{q-1,q}$$, the abnormal voltage drop will be captured by both sensor $$v_{q-1}$$ and sensor $$v_q$$. In contrast, a fault intrinsic to a cell (e.g., under-voltage) or its sensor will primarily affect only one sensor in the pair. This cross-coupling effect, achieved without adding extra sensors or increasing their measurement range, provides the crucial information needed to isolate connection faults from other types in a battery EV car battery pack.
Extraction of Low-Frequency Components via VMD
The terminal voltage signal from a battery EV car battery pack is non-stationary, containing dynamic responses to current transients and slower variations representing the cell’s state. To isolate the fault-relevant information, the low-frequency components corresponding to the cell’s state must be extracted. Variational Mode Decomposition (VMD) is a powerful, noise-robust signal processing technique that decomposes a signal into a discrete number of band-limited intrinsic mode functions (IMFs).
VMD solves a constrained variational problem: to find a set of IMFs $$\{u_k(t)\}$$ and their corresponding center frequencies $$\{\omega_k\}$$ such that the sum of the bandwidths of all modes is minimized, while the sum of all modes reconstructs the original signal $$f(t)$$. The formulation is as follows:
$$
\min_{\{u_k\},\{\omega_k\}} \left\{ \sum_{k=1}^{K} \left\| \partial_t \left[ \left( \delta(t) + \frac{j}{\pi t} \right) * u_k(t) \right] e^{-j\omega_k t} \right\|_2^2 \right\}
$$
$$
\text{s.t.} \sum_{k=1}^{K} u_k(t) = f(t)
$$
where $$K$$ is the preset number of modes, $$\partial_t$$ denotes the partial derivative with respect to time, $$\delta(t)$$ is the Dirac delta function, $$*$$ represents convolution, and $$j$$ is the imaginary unit.
To solve this, the constrained problem is transformed into an unconstrained one using a quadratic penalty term $$\alpha$$ and Lagrangian multipliers $$\lambda(t)$$. The augmented Lagrangian $$\mathcal{L}$$ is:
$$
\begin{aligned}
\mathcal{L}(\{u_k\},\{\omega_k\},\lambda) &= \alpha \sum_{k} \left\| \partial_t \left[ \left( \delta(t) + \frac{j}{\pi t} \right) * u_k(t) \right] e^{-j\omega_k t} \right\|_2^2 \\
&+ \left\| f(t) – \sum_{k} u_k(t) \right\|_2^2 + \left\langle \lambda(t), f(t) – \sum_{k} u_k(t) \right\rangle
\end{aligned}
$$
The solution is found iteratively using the Alternating Direction Method of Multipliers (ADMM). In the frequency domain, the updates for mode $$u_k$$ and its center frequency $$\omega_k$$ at iteration $$n+1$$ are:
$$
\hat{u}_k^{n+1}(\omega) = \frac{\hat{f}(\omega) – \sum_{i \neq k} \hat{u}_i(\omega) + \frac{\hat{\lambda}(\omega)}{2}}{1 + 2\alpha (\omega – \omega_k)^2}
$$
$$
\omega_k^{n+1} = \frac{\int_0^\infty \omega |\hat{u}_k^{n+1}(\omega)|^2 d\omega}{\int_0^\infty |\hat{u}_k^{n+1}(\omega)|^2 d\omega}
$$
where $$\hat{\cdot}$$ denotes the Fourier transform. The iteration stops when the convergence condition is met:
$$\frac{\sum_k \|\hat{u}_k^{n+1} – \hat{u}_k^{n}\|_2^2}{\|\hat{u}_k^{n}\|_2^2} < \epsilon$$, with $$\epsilon$$ being a tolerance (e.g., $$1 \times 10^{-6}$$).
For battery voltage signals, the high-frequency IMFs correspond to the dynamic response to current excitation. The low-frequency IMFs, however, reflect the underlying state of the cell. Differences in the low-frequency components among cells amplify the inconsistencies caused by faults, providing a cleaner signal for subsequent feature extraction in the battery EV car diagnostic process.
Feature Extraction Based on Manhattan Distance
In a healthy series-connected battery pack within a battery EV car, the terminal voltages of all cells should be highly consistent under the same current load. A fault disrupts this consistency. Therefore, the dissimilarity between cell voltage curves serves as a primary fault indicator. A Manhattan distance-based similarity measure is employed for its computational efficiency and effectiveness.
For two voltage time series (after extracting the low-frequency component) from cell $$x$$ and cell $$y$$, denoted as vectors $$X = [x_1, x_2, …, x_z]$$ and $$Y = [y_1, y_2, …, y_z]$$ of length $$z$$, the dissimilarity $$M(x,y)$$ is calculated as follows:
First, the instantaneous absolute deviation is computed:
$$m’_i = |x_i – y_i|$$
To account for the inherent, normal inconsistency between cells in a battery EV car pack, a threshold $$\mu$$ is applied. Only deviations exceeding this threshold are accumulated.
$$
m_i = \begin{cases}
m’_i – \mu, & \text{if } m’_i > \mu \\
0, & \text{if } m’_i \leq \mu
\end{cases}
$$
The total dissimilarity (Manhattan distance) $$M(x,y)$$ is the sum of these accumulated deviations over the time window:
$$M(x,y) = \sum_{i=1}^{z} m_i$$
A larger $$M(x,y)$$ indicates lower similarity between the two voltage curves. However, $$M(x,y)$$ alone does not convey the positional relationship (which cell’s voltage is higher). Therefore, a polarity indicator $$P(x,y)$$ is introduced. Treating $$X$$ as the curve under test and $$Y$$ as a reference (e.g., a neighboring cell), the polarity for the window is defined based on the dominant trend:
$$
P(x,y) = \text{sign}\left( \sum_{i=1}^{z} (x_i – y_i) \right)
$$
where $$\text{sign}(\cdot)$$ returns 1 if the sum is positive, -1 if negative, and 0 if the sum is zero (indicating curves frequently crossing).
For an $$N$$-cell battery pack, the feature vectors for a given time window are constructed from the measurements of $$N$$ sensors (in the cross-topology, this yields $$N$$ measurements for $$N-1$$ cells and two end measurements). The dissimilarity set $$\text{Set}_M$$ and polarity set $$\text{Set}_P$$ between adjacent sensors are defined as:
$$
\text{Set}_M = [M(v_1, v_2), M(v_2, v_3), …, M(v_{N-1}, v_N)]
$$
$$
\text{Set}_P = [P(v_1, v_2), P(v_2, v_3), …, P(v_{N-1}, v_N)]
$$
These sets form the basis for fault detection and identification in the battery EV car battery pack.
Diagnostic Principle and Online Strategy
Correspondence Between Fault Features and Fault Types
The key to multi-fault diagnosis is constructing unique fault signatures that can unequivocally distinguish between different failure modes. By analyzing the impact of each fault type on the measured voltage signals in the cross-topology, distinct patterns in the $$\text{Set}_M$$ and $$\text{Set}_P$$ features can be established. The following table summarizes the diagnostic logic, where a fault is assumed to occur at cell $$C_q$$ or its adjacent connection $$l_{q-1,q}$$.
| Fault Type | Fault Location | Affected Sensor(s) | Polarity (P) | Similarity (M) |
|---|---|---|---|---|
| Under-Voltage (e.g., ISC) | Cell $$C_q$$ | $$v_{q-1}, v_q$$ | $$P(v_{q-1}, v_q) > 0$$, $$P(v_q, v_{q+1}) < 0$$ | High for both pairs |
| Over-Voltage (e.g., charging fault) | Cell $$C_q$$ | $$v_{q-1}, v_q$$ | $$P(v_{q-1}, v_q) < 0$$, $$P(v_q, v_{q+1}) > 0$$ | High for both pairs |
| Connection Fault | Busbar $$l_{q-1,q}$$ | $$v_{q-2}, v_{q-1}, v_q$$ | $$P(v_{q-2}, v_{q-1})$$ and $$P(v_{q-1}, v_q)$$ are unstable (~0) | High for pairs involving $$v_{q-1}$$ & $$v_q$$ |
| Sensor Fault (Stuck or Drift) | Sensor $$v_q$$ | $$v_q$$ primarily | $$P(v_{q-1}, v_q)$$ and $$P(v_q, v_{q+1})$$ are unstable (~0) | High for pairs involving $$v_q$$ |
Under-Voltage Fault: Modeled as a shunt resistance across the cell, it causes the cell’s terminal voltage to be persistently lower than neighbors during both charge and discharge. In the cross-topology, sensor $$v_{q-1}$$ (measuring across $$C_{q-2}^+$$ to $$C_q^-$$) will read higher than normal relative to $$v_{q-2}$$, giving a positive polarity. Sensor $$v_q$$ (measuring across $$C_{q-1}^+$$ to $$C_{q+1}^-$$) will read lower than normal relative to $$v_{q+1}$$, giving a negative polarity. Both pairs show high dissimilarity (M).
Over-Voltage Fault: Causes a persistent voltage elevation. The opposite polarity pattern to under-voltage is observed: $$P(v_{q-1}, v_q)$$ becomes negative and $$P(v_q, v_{q+1})$$ becomes positive, with high M.
Connection Fault: A high-resistance connection acts as a voltage divider. The voltage disturbance depends on current direction (charge/discharge), causing the measured voltages to fluctuate above and below expected values. This leads to an unstable, near-zero average polarity for the sensor pairs spanning the faulty connection. The fault affects two adjacent sensors distinctly.
Sensor Fault: A stuck or drifting sensor reading creates an artificial voltage offset. Like a connection fault, it causes unstable polarity in adjacent comparisons. However, the fault is isolated to a single sensor’s measurement. The cross-topology helps confirm this: if $$v_q$$ is faulty, both $$M(v_{q-1}, v_q)$$ and $$M(v_q, v_{q+1})$$ are high with unstable polarity, but $$M(v_{q-2}, v_{q-1})$$ remains normal, isolating the fault to the $$v_q$$ node.
Online Diagnostic Scheme
Based on the above principles, a practical online diagnostic scheme for a battery EV car Battery Management System (BMS) is designed. The procedure operates on a sliding time window of raw voltage data.
Step 1: Data Windowing. For each cell/sensor, a voltage sequence of the most recent $$h$$ seconds is collected at sampling frequency $$f_s$$: $$V_q = [v_q(i-h+1), v_q(i-h+2), …, v_q(i)]$$, where $$i$$ is the current time step.
Step 2: Signal Processing and Feature Calculation.
1. Apply VMD to each voltage sequence $$V_q$$ to extract its low-frequency component $$V_q^{LF}$$.
2. For the pack, compute the dissimilarity set $$\text{Set}_M$$ and polarity set $$\text{Set}_P$$ using the $$V_q^{LF}$$ sequences according to the Manhattan distance formulas.
Step 3: Fault Detection.
Check if any value in $$\text{Set}_M$$ exceeds a predefined fault threshold $$\alpha$$. If $$\max(\text{Set}_M) > \alpha$$, a fault is detected. Proceed to identification. Otherwise, slide the time window forward and return to Step 1.
Step 4: Fault Identification and Localization.
1. Identify the sensor index $$q$$ corresponding to the largest $$M$$ value in $$\text{Set}_M$$ (e.g., $$M(v_{q-1}, v_q)$$).
2. Analyze the polarity $$P$$ values associated with sensor $$v_{q-1}$$ and $$v_q$$ (i.e., $$P(v_{q-2}, v_{q-1})$$, $$P(v_{q-1}, v_q)$$, $$P(v_q, v_{q+1})$$).
3. Match the pattern of high M and specific P values to the fault signature table above to determine the fault type (Under-Voltage, Over-Voltage, Connection, Sensor).
4. The index $$q$$ pinpoints the faulty cell ($$C_q$$), connection ($$l_{q-1,q}$$), or sensor ($$v_q$$).
Parameters: Time window length $$h = 30$$ s, fault threshold $$\alpha = 5$$, inconsistency threshold $$\mu = 0.015$$ V, VMD mode number $$K=5$$.
Experimental Validation and Analysis
Experimental Setup and Test Profile
The proposed strategy was validated using a lab-scale battery pack for a battery EV car. The test platform consisted of a high-precision battery cycler (NBT), a host computer, and a thermal chamber. The device under test was a series-connected pack of five Panasonic NCR18650B Li-ion cells (nominal capacity 3400 mAh). Before testing, each cell was charged to 4.2 V using a constant-current-constant-voltage (CC-CV) protocol at 1C rate and rested for 2 hours. To simulate real-world driving conditions of a battery EV car, the pack was subjected to repeated Urban Dynamometer Driving Schedule (UDDS) profiles, with a maximum current of 1C (3.4 A). Voltage and current data were recorded at 10 Hz. All tests were conducted at a controlled temperature of 25°C.
Fault Simulation
Four distinct faults were sequentially injected into the pack during operation, as detailed in the table below.
| Operational State | Simulation Method | Duration (s) |
|---|---|---|
| Normal | Baseline UDDS operation | 0-335, 404-603, etc. |
| Under-Voltage Fault | Parallel a 6.5 Ω resistor across Cell #2 | 336-403 |
| Over-Voltage Fault | Inject a constant 1.6 A charging current into Cell #4 | 604-647 |
| Connection Fault | Replace connection between Cell #3 & #4 with a 0.06 Ω resistor (vs. 0.01 Ω normal) | 914-974 |
| Sensor Fault (Stick & Mutation) | Add a fixed offset (stick) and random noise (σ=0.05 V) to the reading of Sensor #3 | 1054-1084 / 1167-1197 |
Results and Discussion
Under-Voltage and Over-Voltage Fault Diagnosis: When the under-voltage fault was injected on Cell #2 at 336 s, the dissimilarity metrics $$M(v_1, v_2)$$ and $$M(v_2, v_3)$$ exceeded the threshold $$\alpha$$ within 13 s. The corresponding polarities were $$P(v_1, v_2) > 0$$ and $$P(v_2, v_3) < 0$$, perfectly matching the under-voltage signature. The algorithm correctly diagnosed an under-voltage fault at Cell #2. Similarly, at 604 s, the over-voltage fault on Cell #4 caused $$M(v_3, v_4)$$ and $$M(v_4, v_5)$$ to exceed $$\alpha$$ in 14 s, with polarities $$P(v_3, v_4) < 0$$ and $$P(v_4, v_5) > 0$$, leading to a correct diagnosis of an over-voltage fault at Cell #4.
Connection Fault Diagnosis: At 914 s, the high-resistance connection fault between Cells #3 and #4 was introduced. The key observation was that the fault manifested in non-adjacent sensor pairs due to the cross-topology. Specifically, $$M(v_2, v_3)$$ and $$M(v_4, v_5)$$ showed significant increases and exceeded $$\alpha$$ after 41 s, while the polarities for these pairs were unstable. According to the diagnostic logic, this pattern—where sensors spaced one cell apart show high dissimilarity—is unique to a connection fault, allowing for accurate identification.
Sensor Fault Diagnosis: For the sensor stick (1054-1084 s) and mutation (1167-1197 s) faults on Sensor #3, the algorithm detected high values for $$M(v_2, v_3)$$ and $$M(v_3, v_4)$$ within 10 s and 30 s, respectively. The critical feature was that the polarities $$P(v_2, v_3)$$ and $$P(v_3, v_4)$$ were approximately zero throughout the window, indicating no consistent voltage offset in the actual cells. This, combined with the fault being isolated to a single sensor node, confirmed a sensor fault.
Noise Robustness of the Algorithm
To evaluate robustness, significant random noise (standard deviation of 15 mV) was added to the voltage data during the Cell #2 under-voltage fault test. The raw voltage curves became intertwined, masking the clear fault signature. However, after processing with VMD, the low-frequency components were successfully extracted. These denoised components clearly showed the separation between the faulty and healthy cell voltages. The Manhattan distance feature $$M(v_1, v_2)$$ still rose above the threshold $$\alpha$$ 16 seconds after fault inception, and the polarities $$P(v_1, v_2) > 0$$ and $$P(v_2, v_3) < 0$$ were correctly identified, allowing for accurate diagnosis despite the noisy conditions. This demonstrates the VMD algorithm’s crucial role in enhancing the noise immunity of the diagnostic strategy for real-world battery EV car applications.
Comparative Analysis of Diagnostic Methods
The performance of diagnostic algorithms is influenced by numerous factors like threshold settings, window size, and noise levels, making direct quantitative comparison challenging. The following table provides a qualitative comparison across key dimensions relevant to battery EV car applications.
| Diagnostic Method | Diagnostic Precision | Multi-Fault Capable | Computational Cost | Robustness |
|---|---|---|---|---|
| Model-Based Methods | High | Often No | High | Low (Model-dependent) |
| Signal-Processing-Based Methods | Medium-Low | Generally No | Medium | High |
| Knowledge-Based Methods | High | Yes | High (Training/Inference) | High |
| Proposed Method | Medium-High | Yes | Low | High |
The proposed strategy effectively merges the strengths of signal-processing and knowledge-based approaches. It circumvents the need for precise models (overcoming a key limitation of model-based methods) and the requirement for extensive fault datasets (a hurdle for pure knowledge-based methods). By constructing specific fault signatures (knowledge) from processed signal features, it achieves reliable multi-fault diagnosis with relatively low computational overhead and high robustness, making it a pragmatic and valuable solution for enhancing the safety and reliability of battery EV car battery packs.
Conclusion
Ensuring the safe and reliable operation of battery packs is paramount for the widespread adoption of battery EV cars. This paper presented a novel online multi-fault diagnosis strategy based on Variational Mode Decomposition (VMD). The method begins by extracting the low-frequency components of cell voltage signals using VMD, which effectively amplifies fault signatures and suppresses noise. A Manhattan distance-based algorithm is then used to quantify voltage inconsistencies. The integration of a cross-voltage measurement circuit is instrumental in creating unique fault fingerprints for four critical fault types: under-voltage, over-voltage, connection, and sensor faults. A complete online diagnostic workflow was designed based on this principle.
Experimental results on a lab-scale battery EV car battery pack demonstrated that the proposed strategy can rapidly and accurately diagnose all four fault types. The method successfully isolated connection faults from cell faults and identified sensor failures. Furthermore, the test under noisy conditions confirmed the algorithm’s robustness, a crucial feature for real-world automotive environments. The strategy offers a balanced solution with good diagnostic accuracy, multi-fault capability, low computational cost, and high robustness, presenting significant practical value for implementation in Battery Management Systems to improve the safety and longevity of battery EV cars.