In the context of the “dual-carbon” strategy and the rapid expansion of renewable energy integration, electrochemical energy storage has become a cornerstone of modern power systems. Large-scale deployment of energy storage battery packs, however, brings serious safety challenges. Micro short-circuit (MSC) faults in chemical energy storage batteries occur when internal or external conductive paths create low-resistance connections between electrodes, producing weak fault signatures that are easily masked by environmental variations, state-of-charge (SOC) changes, and load fluctuations. Early detection of MSC faults is critical to preventing thermal runaway and catastrophic failure. This thesis focuses on developing a reliable fault diagnosis framework for energy storage battery packs based on electrochemical impedance spectroscopy (EIS), fast wavelet-based impedance measurement, and a deep learning classifier that combines convolutional neural networks (CNNs) with Transformer models optimized by a secretary bird optimization algorithm (SBOA). The proposed methods are experimentally validated on commercial 18650 lithium-ion cells under various operating conditions.
1. Introduction and Motivation
The safe operation of energy storage battery systems is a major concern for grid-scale applications, electric vehicles, and distributed energy resources. In particular, lithium-ion battery packs are prone to micro short-circuit faults caused by overcharging, over-discharging, high-rate cycling, mechanical abuse, and manufacturing defects. An MSC fault often begins with a high equivalent resistance in the early stage, which produces almost negligible voltage or current variation in the battery pack. As the fault evolves, the equivalent resistance decreases, the short-circuit current increases, and the released heat can eventually trigger thermal runaway. Therefore, early detection and accurate classification of MSC faults are indispensable for reliable battery management systems.
Conventional fault diagnosis methods rely on voltage, current, temperature, capacity, gas, or pressure signals. Voltage-based methods can detect severe faults but are insensitive to weak micro-short-circuit signatures. Temperature-based methods suffer from measurement latency and difficulty in directly measuring internal temperature. Capacity-based methods are affected by aging and state of health (SOH). Impedance-based methods, on the other hand, directly reflect internal electrochemical processes and provide rich frequency-domain information that is highly sensitive to early-stage degradation and micro short circuits. Electrochemical impedance spectroscopy (EIS) has therefore become a powerful tool for energy storage battery health monitoring and fault diagnosis.
Traditional EIS measurements use a frequency sweep, which is time-consuming and requires expensive equipment such as a potentiostat or a frequency response analyzer. For online applications, the measurement speed must be significantly improved. To address this limitation, this work uses a fast EIS measurement method based on the continuous wavelet transform (CWT). The proposed method extracts the complex impedance from the transient voltage and current signals that occur when an energy storage battery is switched from rest to constant-current discharge or charge. This approach reduces the measurement time from tens of minutes to less than three minutes while maintaining acceptable accuracy. In addition, the distribution of relaxation times (DRT) technique is applied to separate overlapping impedance processes, enabling physical interpretation of each fault-related impedance component.
This thesis makes two main contributions. First, for external MSC faults, a quantitative diagnosis index is constructed from the ratio of the SEI film resistance to the diffusion resistance extracted from the equivalent circuit model. This index is validated under different temperatures and can indicate the severity of the external short circuit. Second, for internal MSC faults, a deep learning framework combining ResNet18, Transformer, and SBOA is developed. The raw voltage and EIS data are encoded into two-dimensional images using wavelet time-frequency analysis and Gramian angular field (GAF). The CNN extracts local spatial features, the Transformer captures global dependencies, and SBOA optimizes the fusion weights of different fault feature channels. The proposed method achieves more than 99% classification accuracy in internal MSC fault diagnosis across a wide temperature range.
2. Theoretical Foundations of EIS and Fast Measurement
2.1 Equivalent Circuit Models for Energy Storage Battery Impedance
The impedance of an energy storage battery is usually described by an equivalent circuit model that consists of a bulk resistor \(R_1\), several parallel resistor-capacitor (RC) branches, and possibly a constant phase element (CPE) or a finite-length Warburg (FLW) element. In the Nyquist plot, a pure resistor appears as a point on the real axis, a capacitor appears as a vertical line in the negative imaginary direction, and an inductor appears as a vertical line in the positive imaginary direction. The CPE is used to model non-ideal capacitive behavior caused by surface roughness, porous electrodes, and distributed relaxation times. Its impedance is
$$Z_{\text{CPE}}(\omega) = \frac{1}{Y_0 (j\omega)^\alpha},$$
where \(Y_0\) is the CPE admittance constant, \(\omega\) is the angular frequency, and \(0 < \alpha < 1\). The FLW element models semi-infinite or finite-length diffusion, or
$$Z_{\text{FLW}}(\omega) = R_D \frac{\tanh \left[(j\omega \tau_0)^\alpha\right]}{(j\omega \tau_0)^\alpha}, \quad 0.5 \le \alpha \le 1,$$
with \(\tau_0 = l^2 / D_{\text{eff}}\), where \(l\) is the diffusion length and \(D_{\text{eff}}\) is the effective diffusion coefficient. For a multi-level RC network, the total impedance is
$$Z(\omega) = R_1 + \sum_{i=1}^{n} \frac{R_i}{1 + j\omega R_i C_i}.$$
In this thesis, a three-time-constant equivalent circuit model is adopted, where \(R_1\) represents the ohmic resistance, \(R_2\) and \(C_2\) model the solid electrolyte interface (SEI) film, \(R_3\) and \(C_3\) model the charge transfer process, and \(R_4\) and \(C_4\) model the diffusive mass transport. The DRT analysis is used to identify the number of relaxation processes before model fitting.
2.2 Fast EIS Measurement Based on Wavelet Transform
When an energy storage battery is suddenly connected to a constant-current charge or discharge, the resulting voltage and current transients contain a wide range of frequency components. The continuous wavelet transform can localize these components in both time and frequency domains, enabling the calculation of the impedance over a broad frequency range from a single transient. The Morlet wavelet is chosen as the mother wavelet because of its good time-frequency localization and its similarity to the sinusoidal perturbation used in conventional EIS. The Morlet wavelet is defined as
$$\psi(t_m) = \frac{1}{\sqrt{\pi f_b}} \exp\left[-\frac{t_m^2}{f_b}\right] \exp\left[j 2\pi f_c t_m\right],$$
with
$$t_m = \frac{t – b}{a},$$
where \(a\) is the scale parameter, \(b\) is the translation parameter, \(f_c\) is the center frequency, and \(f_b\) is the bandwidth parameter. The scale \(a\) determines the analyzing frequency \(f = f_c/a\). The wavelet coefficients of the voltage and current signals are
$$U(a,b) = \frac{1}{\sqrt{a}} \int_{-\infty}^{\infty} u(t) \operatorname{conj}\left[\psi\left(\frac{t-b}{a}\right)\right] dt,$$
$$I(a,b) = \frac{1}{\sqrt{a}} \int_{-\infty}^{\infty} i(t) \operatorname{conj}\left[\psi\left(\frac{t-b}{a}\right)\right] dt.$$
Because the wavelet transform is linear, the complex impedance at each frequency can be directly obtained as
$$Z(a,b) = \frac{U(a,b)}{I(a,b)}.$$
The parameters \(a\), \(b\), \(f_c\), and \(f_b\) must be carefully selected to balance time and frequency resolution. In this work, the sampling frequency is set to 10 kHz, the discharge duration is 50 seconds, the charge duration is 50 seconds, and the initial rest period is 50 seconds. The center frequency is 10 kHz and the bandwidth parameter is \(7\times 10^{-8} \, \mathrm{s^2}\). The scale range is chosen to cover frequencies from 0.1 Hz to 1 kHz. Validation using a simulated second-order RC circuit shows that the wavelet-computed impedance matches the theoretical values with high accuracy.
2.3 Distribution of Relaxation Times
Because different electrochemical processes inside an energy storage battery occur at different time constants, the measured EIS often contains overlapping arcs that are difficult to separate in the Nyquist plot. The distribution of relaxation times (DRT) method transforms the impedance spectrum into a distribution function of relaxation times, given by
$$Z(\omega) = R_0 + R_{\mathrm{pol}} \int_0^\infty \frac{g(\tau)}{1 + j\omega \tau} d\tau,$$
where \(R_0\) is the ohmic resistance, \(R_{\mathrm{pol}}\) is the total polarization resistance, and \(g(\tau)\) is the distribution function satisfying \(\int_0^\infty g(\tau)d\tau = 1\). In practice, the logarithm scale is used, and the function \(G(\tau) = \tau g(\tau)\) is obtained by solving a regularized inverse problem. DRT converts the measured EIS into peaks, each corresponding to a distinct physical process. In this thesis, DRT is used to identify the number of RC branches and to extract the characteristic time constants of the SEI film, charge transfer, and diffusion processes.
3. Experimental Platform and Data Acquisition
3.1 Test Setup
The experiments are conducted using commercial 18650 lithium-ion cells with a nickel-cobalt-aluminum (NCA) cathode and a graphite anode. The nominal capacity is 2500 mAh, and the voltage range is 2.75 V to 4.2 V. The experimental platform includes a LANBTS battery test system for charging and discharging, a BTC-506 temperature chamber for thermal control, a CH Instruments electrochemical workstation for benchmark EIS measurement, and a DAQ122 data acquisition card for high-speed voltage and current logging. A 10 mΩ precision resistor is used as a current shunt to improve measurement resolution. The test platform enables controlled experiments under different temperatures, SOC levels, and discharge rates.
Three types of experiments are designed. In the normal charge/discharge experiment, the battery is fully discharged at 1C to 2.75 V, rested for one hour, charged at 1C to 4.2 V, then charged at constant voltage until the current drops below 0.05C. This cycle is repeated three times. In the fast-EIS experiment, the battery is set to 95% SOC, rested for 50 s, discharged at 1C for 50 s, and then charged at 1C for 50 s. The voltage and current are sampled at 10 kHz. In the MSC fault experiments, external short circuits are implemented by connecting resistors of 50 Ω, 20 Ω, and 10 Ω in parallel with the battery terminals. Internal short circuits are simulated using an equivalent circuit in which a series of resistors are connected internally through a switching network. A 0.01 Ω high-precision sampling resistor is inserted to monitor the short-circuit current.
3.2 Consistency Screening and Grouping
Because cell-to-cell variations can obscure impedance differences caused by faults, a consistency screening procedure is performed before assembling the battery modules. The screening method is based on the principle that cells connected in series carry the same current; therefore, voltage differences at the end of discharge reflect internal resistance and capacity mismatches. The experimental procedure is summarized below:
| Step | Operation | Criteria |
|---|---|---|
| 1 | Charge the series-connected 15 cells at 1C to 4.2 V | Record end-of-charge voltage |
| 2 | Rest for 30 minutes | Record rest voltage |
| 3 | Discharge at 1C to 2.75 V | Record end-of-discharge voltage |
| 4 | Rest for 30 minutes | Record rest voltage after discharge |
| 5 | Calculate mean and standard deviation of the three voltages | Accept cells within \(V_{\mathrm{av}} \pm \delta\) |
Among the 15 initially screened cells, the end-of-discharge voltage showed the largest standard deviation of 0.328 V. After applying the criterion, four cells were rejected, and the standard deviation of the remaining cells decreased to 0.152 V, a reduction of 53.7%. A total of 90 cells were processed in six batches, and the final selected cells were formed into 30 modules of three series-connected cells. Each module was then paired in parallel to create 15 “3S2P” module configurations. This grouping ensures that the modules have consistent electrical characteristics and provides reliable data for fault diagnosis experiments.
4. Effects of Operating Conditions on the Measured Impedance
4.1 Validation of the Wavelet-Based Fast EIS
Figure 1 shows the comparison between the wavelet-obtained impedance and the conventional EIS measurement for a single cell at 25 °C and 1C rate. The frequency range covered is 0.6 Hz to 747.84 Hz. The mean relative error in the impedance modulus is 3.62%, and the maximum relative error is 7.46%. The measurement time is reduced from about 20 minutes to 3 minutes. These results confirm the effectiveness of the wavelet-based method for fast EIS acquisition of energy storage battery cells.
4.2 Series and Parallel Configuration
To understand how the module configuration affects the impedance signature, the wavelet-based EIS is measured for one, two, and three cells connected in series, and then for one, two, and three cells connected in parallel. The series configuration results are shown in Table 1.
| Configuration | \(R_1\) (mΩ) | \(R_2\) (mΩ) | \(R_3\) (mΩ) | \(R_4\) (mΩ) |
|---|---|---|---|---|
| 1S | 20.1 | 11.3 | 26.5 | 31.2 |
| 2S | 40.3 | 22.9 | 53.4 | 62.1 |
| 3S | 61.0 | 34.2 | 80.1 | 93.6 |
As expected, all resistances increase almost linearly with the number of series cells. The DRT analysis shows that the peak heights of P1 (SEI film), P2 (charge transfer), and P3 (diffusion) all increase with series cell count. In contrast, the parallel configuration reduces the total impedance, as shown in Table 2.
| Configuration | \(R_1\) (mΩ) | \(R_2\) (mΩ) | \(R_3\) (mΩ) | \(R_4\) (mΩ) |
|---|---|---|---|---|
| 1P | 20.1 | 11.3 | 26.5 | 31.2 |
| 2P | 10.2 | 5.7 | 13.4 | 15.8 |
| 3P | 6.9 | 3.8 | 8.8 | 10.5 |
This is consistent with the parallel resistance mixing law. The DRT peaks also decrease with parallel cell count because the current is shared among cells, reducing the per-cell polarization.
4.3 Influence of Charge/Discharge Rate
The rate at which an energy storage battery is charged or discharged affects the accuracy of the wavelet-based impedance measurement. When the current is too high, the excitation signal deviates from linearity, generating harmonics that distort the low-frequency impedance. The results show that at 1C rate, the calculated EIS closely matches the reference EIS from the electrochemical workstation. At 1.5C and 2C rates, the low-frequency part of the impedance curve deviates significantly from the reference. Therefore, the subsequent fault diagnosis experiments are performed at 1C rate to maintain acceptable accuracy.
4.4 Influence of SOC
The state of charge has a strong influence on the impedance of an energy storage battery. The EIS curves for 95%, 75%, 50%, and 25% SOC are measured using the wavelet method. The Nyquist plots show that as SOC decreases, the entire impedance spectrum shifts toward the lower-right direction, and the radius of the semicircle shrinks. The extracted resistances are listed in Table 3.
| SOC (%) | \(R_1\) (mΩ) | \(R_2\) (mΩ) | \(R_3\) (mΩ) | \(R_4\) (mΩ) |
|---|---|---|---|---|
| 95 | 20.3 | 11.5 | 26.9 | 31.5 |
| 75 | 20.1 | 10.8 | 25.8 | 29.7 |
| 50 | 19.9 | 9.9 | 24.2 | 27.4 |
| 25 | 20.0 | 10.6 | 22.6 | 24.8 |
The ohmic resistance \(R_1\) is nearly independent of SOC, while the SEI resistance \(R_2\) first decreases from 95% to 50% SOC and then slightly increases at 25% SOC. The charge transfer resistance \(R_3\) and diffusion resistance \(R_4\) decrease monotonically with SOC. The reduction in \(R_3\) and \(R_4\) is mainly due to the lower open-circuit voltage at low SOC, which reduces the amplitude of the voltage wavelet coefficient relative to the current wavelet coefficient.
4.5 Influence of Temperature
Temperature is another critical factor affecting energy storage battery impedance. The EIS spectra are measured at 10 °C, 25 °C, and 40 °C. The extracted equivalent circuit parameters are shown in Table 4.
| Temperature (°C) | \(R_1\) (mΩ) | \(R_2\) (mΩ) | \(R_3\) (mΩ) | \(R_4\) (mΩ) |
|---|---|---|---|---|
| 10 | 28.5 | 18.9 | 41.2 | 52.6 |
| 25 | 20.1 | 11.3 | 26.5 | 31.2 |
| 40 | 15.8 | 7.6 | 17.3 | 19.4 |
Low temperatures significantly increase all impedance components. This is attributed to reduced ionic conductivity, higher activation energy for charge transfer, and slower diffusion of lithium ions. The DRT analysis shows that the P1 peak increases markedly at low temperature, indicating that the SEI film resistance is highly temperature-sensitive.
5. External Micro Short-Circuit Fault Diagnosis
5.1 Impedance Characteristics under External MSC
To simulate external micro short circuits, resistors of 50 Ω, 20 Ω, and 10 Ω are connected in parallel with a 3S battery module. The wavelet-based EIS is measured under normal and fault conditions. The DRT and equivalent circuit fitting are applied to obtain the resistance values. Table 5 summarizes the extracted resistances for different short-circuit severities at 25 °C.
| Fault condition | \(R_1\) (mΩ) | \(R_2\) (mΩ) | \(R_3\) (mΩ) | \(R_4\) (mΩ) |
|---|---|---|---|---|
| Normal | 61.2 | 34.5 | 80.3 | 93.8 |
| 50 Ω | 68.4 | 42.1 | 76.9 | 91.5 |
| 20 Ω | 74.9 | 53.8 | 72.4 | 90.7 |
| 10 Ω | 85.2 | 66.3 | 68.6 | 89.9 |
As the fault severity increases, the ohmic resistance \(R_1\) and the SEI resistance \(R_2\) increase significantly, while the charge transfer resistance \(R_3\) decreases and the diffusion resistance \(R_4\) remains almost constant. The increase in \(R_2\) is explained by the enhanced electrochemical stress and the partial destruction and reformation of the SEI film. The decrease in \(R_3\) can be attributed to a local increase in active surface area or the partial bypass of the normal charge transfer path by the external short circuit.
5.2 Fault Severity Index \(K\)
Because \(R_2\) changes rapidly with fault severity while \(R_4\) is stable, a normalized fault severity index is defined as
$$K = \frac{Z}{Z_0}, \quad Z = \frac{R_2}{R_4}, \quad Z_0 = \left(\frac{R_2}{R_4}\right)_{\mathrm{normal}}.$$
Under normal conditions, \(K \approx 1\). As the short circuit worsens, \(K\) increases monotonically. To verify the robustness of this index, 18 module groups (each containing three series cells) are tested at 10 °C, 25 °C, and 40 °C. The recorded \(K\) ranges are summarized in Table 6.
| Temperature | Normal | 50 Ω | 20 Ω | 10 Ω |
|---|---|---|---|---|
| 10 °C | 0.915–1.075 | 1.101–1.186 | 1.236–1.328 | 1.529–1.727 |
| 25 °C | 0.974–1.030 | 1.092–1.296 | 1.458–1.536 | 1.984–2.135 |
| 40 °C | 0.874–1.031 | 1.118–1.221 | 1.589–1.640 | 2.238–2.507 |
The index \(K\) provides effective fault-level discrimination at all tested temperatures. At higher temperatures, the index increases more markedly for the same short-circuit resistance, indicating a higher sensitivity to fault development under elevated thermal conditions. The non-overlapping intervals of \(K\) for different fault levels confirm that the index can be used as a reliable diagnostic criterion.
6. Internal Micro Short-Circuit Fault Diagnosis Using SBOA-CNN-Transformer
6.1 Impedance Features of Internal MSC
Internal MSC faults produce different impedance responses compared to external faults. For internal faults, the short-circuit path exists inside the cell, and the measured voltage or current external characteristics may be only weakly affected in the early stage. The wavelet-based EIS for internal short circuits of varying severity is measured on a 3S module. The extracted resistances are shown in Table 7.
| Fault condition | \(R_1\) (mΩ) | \(R_2\) (mΩ) | \(R_3\) (mΩ) | \(R_4\) (mΩ) |
|---|---|---|---|---|
| Normal | 61.2 | 34.5 | 80.3 | 93.8 |
| 50 Ω | 65.3 | 31.8 | 84.2 | 91.9 |
| 20 Ω | 71.5 | 29.4 | 87.1 | 90.4 |
| 10 Ω | 79.8 | 27.2 | 82.6 | 89.7 |
Unlike external MSC, internal MSC leads to an increase in \(R_1\) and a decrease in \(R_2\). The charge transfer resistance first increases and then decreases. These subtle differences are difficult to capture through simple resistance comparisons, especially in the presence of noise and temperature variations. Therefore, deep learning is used to automatically extract and classify the fault features.
6.2 Data Augmentation and Image Encoding
To train the deep learning network, the dataset is expanded by adding Gaussian noise to the original voltage and current signals. The augmented signal is obtained by
$$u'(t) = u(t) + \alpha_x \sigma_x \varepsilon(t),$$
where \(\sigma_x\) is the standard deviation of the original signal, \(\varepsilon(t)\) is a standard normal random sequence, and \(\alpha_x = 0.01\) is the noise strength coefficient. The original data consist of 15 modules, four fault states, and three temperatures, generating 180 raw samples. Each sample is enlarged 40 times, yielding 7200 samples, with 1800 samples per fault class. This augmentation enhances the model’s robustness to sensor noise and prevents overfitting.
Two types of two-dimensional images are generated from the augmented signals. The voltage signals are transformed into wavelet time-frequency images using the Morlet wavelet, which provides rich time-frequency features. The EIS data are transformed using the Gramian angular field (GAF) method, which maps the normalized impedance points into polar coordinates and computes the cosine of the sum of the angles:
$$\phi_i = \arccos(\tilde{x}_i), \quad r_i = \frac{t_i}{N}, \quad G_{ij} = \cos(\phi_i + \phi_j).$$
Here, \(\tilde{x}_i\) is the normalized impedance value at time index \(t_i\), and \(N\) is the total number of impedance points. The composite images, formed by combining the wavelet time-frequency image and the GAF image, are resized to \(60 \times 60\) pixels and used as the input of the deep learning model.
6.3 Architecture of the SBOA-CNN-Transformer Model
The proposed fault diagnosis model combines three major components: a ResNet18 CNN, a Transformer encoder, and the SBOA weight optimization layer. The overall workflow is shown below.
- Step 1: The 60×60 composite images are fed into ResNet18. The network processes the images through five stages, including 7×7 convolution, batch normalization, max-pooling, and four residual modules. The output is a set of feature maps with dimension \(9 \times 4 \times 4\) for each fault state.
- Step 2: Four sets of feature maps (corresponding to normal, 50 Ω, 20 Ω, and 10 Ω faults) are obtained. Each set is assigned a learnable weight \(W_1, W_2, W_3, W_4\), respectively, satisfying \(0 \le W_i \le 1\) and \(\sum W_i = 1\).
- Step 3: The SBOA is employed to search for the optimal weight vector \(W = [W_1, W_2, W_3, W_4]\). The algorithm simulates Secretary Bird hunting and escape behaviors in three phases: global exploration, local exploitation, and escape. The position update equations are as follows.
In the exploration phase when \(t < T/3\), the position is updated based on the differential evolution strategy:
$$x_{i,j}^{\mathrm{newP1}} = x_{i,j} + \left(x_{\mathrm{random_1}} – x_{\mathrm{random_2}}\right) \times R_s,$$
$$X_i^{\mathrm{newP1}} = \begin{cases} x_{i,j}^{\mathrm{newP1}}, & F_i^{\mathrm{newP1}} < F_i, \\ X_i, & \text{otherwise.} \end{cases}$$
In the exploitation phase when \(T/3 < t < 2T/3\), the position is updated using the best solution and Brownian motion:
$$x_{i,j}^{\mathrm{newP1}} = x_{\mathrm{best}} + \left(t/T\right)^{2} \times R_B \times \left(x_{\mathrm{best}} \times 0.5 – x_{i,j}\right),$$
with \(R_B = \mathrm{randn}(1,\mathrm{Dim})\). In the final attack phase when \(2T/3 < t < T\), the Levy flight is combined with a non-linear perturbation:
$$x_{i,j}^{\mathrm{newP1}} = x_{\mathrm{best}} + \left(1 – t/T\right)^{2 \times t/T} \times R_L \times x_{i,j}.$$
After the hunting phase, the escape phase is implemented with a 50% probability. Two candidate strategies are considered:
$$C_1: x_{i,j}^{\mathrm{newP2}} = x_{\mathrm{best}} + (2r – 1) \left(1 – t/T\right)^2 x_{i,j},$$
$$C_2: x_{i,j}^{\mathrm{newP2}} = x_{i,j} + R_s \times (x_{\mathrm{random}} – K_s x_{i,j}),$$
where \(K_s\) is randomly chosen as 1 or 2. Greedy selection is always applied to keep the better solution.
- Step 4: The fused feature maps are flattened into a sequence of feature vectors. A learnable class token and position embeddings are added. The sequence is processed by a Transformer encoder with multi-head self-attention layers, which captures global dependencies between different fault features.
- Step 5: The final representation of the class token is passed through a multilayer perceptron (MLP) with softmax activation to output the fault class probability distribution. The training loss is the cross-entropy loss, and the weights are optimized by SBOA and gradient descent.
6.4 Training Setup
The model is implemented in Python 3.9 using PyCharm. The hardware includes an Intel Xeon Gold 6234 CPU and an NVIDIA GeForce RTX 3090 GPU with 24 GB memory. The batch size is 32, the epoch number is 100, and the learning rate is \(3\times 10^{-4}\). The training dataset is randomly split into 80% training and 20% testing. The performance is evaluated using accuracy, confusion matrix, ROC curve, and t-SNE visualization.
6.5 Results at 25 °C
The training and testing accuracy curves at 25 °C are shown in Figure 2. The accuracy increases rapidly during the first 20 epochs and reaches 99.8% on the training set and 99.63% on the testing set after 100 epochs. The ROC curve has an AUC value of 0.97913, indicating excellent discrimination capability. The confusion matrix shows that all fault classes are correctly classified with only a few misclassifications. The detailed classification results are listed in Table 8.
| Fault class | Predicted normal | Predicted 50 Ω | Predicted 20 Ω | Predicted 10 Ω | Recall |
|---|---|---|---|---|---|
| Actual normal | 123 | 2 | 0 | 0 | 98.4% |
| Actual 50 Ω | 2 | 115 | 0 | 0 | 98.3% |
| Actual 20 Ω | 0 | 0 | 122 | 0 | 100% |
| Actual 10 Ω | 0 | 0 | 0 | 116 | 100% |
6.6 Generalization to Different Temperatures
To evaluate the model’s generalization, the same training procedure is applied to experimental data collected at 10 °C and 40 °C. The testing accuracies are shown in Table 9.
| Temperature | Test accuracy |
|---|---|
| 10 °C | 99.35% |
| 25 °C | 99.63% |
| 40 °C | 99.24% |
These results confirm that the SBOA-CNN-Transformer model is robust across the entire tested temperature range. The t-SNE visualizations show clear separation of the four fault classes at each temperature, indicating that the learned feature space is discriminative.
6.7 Comparison with Other Methods
The proposed model is compared with three baseline methods: VGG-16, ResNet34, and a CNN-Transformer without SBOA. The model complexity and accuracy are summarized in Tables 10 and 11.
| Method | Parameters (×10⁶) | Memory (MB) | Testing time (s) |
|---|---|---|---|
| VGG-16 | 34.015 | 2.09 | 0.069 |
| ResNet34 | 21.328 | 41.18 | 0.059 |
| CNN-Transformer | 134.461 | 266.47 | 0.061 |
| SBOA-CNN-Transformer | 147.016 | 282.32 | 0.082 |
| Method | 10 °C accuracy | 25 °C accuracy | 40 °C accuracy |
|---|---|---|---|
| VGG-16 | 89.44% | 89.56% | 89.72% |
| ResNet34 | 92.51% | 91.91% | 92.02% |
| CNN-Transformer | 94.15% | 94.56% | 94.11% |
| SBOA-CNN-Transformer | 99.35% | 99.63% | 99.24% |
The SBOA-CNN-Transformer outperforms all baselines by a distinct margin. The SBOA weight optimization contributes to more than a 5% improvement over the standard CNN-Transformer, demonstrating the effectiveness of the bio-inspired optimization in fusing information from different fault feature channels. Although the model has a higher parameter count, the testing time remains acceptable for offline analysis and near-real-time monitoring.
7. Conclusions and Future Perspectives
In this thesis, a comprehensive impedance-based micro short-circuit fault diagnosis framework for energy storage battery systems is developed. The main conclusions are summarized as follows.
First, the wavelet-based fast EIS measurement is validated on commercial 18650 cells. The method accurately reconstructs the impedance spectrum in the frequency range of 0.6 Hz to 747.84 Hz with a mean modulus error of 3.62%. It is found that the measurement accuracy is significantly influenced by operating conditions. A low charge/discharge rate (1C), a high SOC level, and a moderate ambient temperature (25 °C) provide the most reliable results. The impedance of a series-connected energy storage battery module increases almost linearly with the number of cells, while a parallel configuration reduces the total impedance. SOC mainly affects the SEI and diffusion resistances, while temperature strongly influences all impedance components.
Second, for external MSC faults, a simple yet robust diagnosis index \(K = (R_2/R_4)/(R_2/R_4)_{\mathrm{normal}}\) is proposed. This index shows a monotonic increase with fault severity and produces non-overlapping intervals for normal, light, moderate, and severe fault conditions at 10 °C, 25 °C, and 40 °C. The index is therefore suitable for quantitative evaluation of external micro short-circuit levels.
Third, for internal MSC faults, an advanced deep learning model combining ResNet18, Transformer, and the secretary bird optimization algorithm is developed. The model uses wavelet time-frequency images and Gramian angular field images as inputs, which enrich the feature representation of the subtle fault signatures. The SBOA dynamically optimizes the fusion weights of the fault channels, while the Transformer captures long-range dependencies. The proposed SBOA-CNN-Transformer achieves accuracies of 99.35%, 99.63%, and 99.24% at 10 °C, 25 °C, and 40 °C, respectively, significantly outperforming VGG-16, ResNet34, and a standard CNN-Transformer. The confusion matrix and ROC analyses confirm its strong classification performance.
Future research could extend the method to more complex module configurations, higher C-rates, and aged cells with different state-of-health levels. Online implementation with lightweight neural networks and edge computing would further accelerate the deployment of the proposed diagnosis technique in real-world energy storage battery management systems.