Rapid Screening for Retired Batteries Based on Lithium-Ion Battery IC Curve Prediction

Abstract

In order to solve the issue of low efficiency in retired battery clustering, a method for quickly obtaining a charging curve and Incremental Capacity (IC) curve based on Convolutional Neural Networks (CNN) is proposed. By training a CNN model, the method enables accurate prediction of complete IC curves and V-Q curves from local charging curves starting at any beginning. The prediction accuracy was validated using the Oxford battery degradation dataset, and transfer learning was conducted by fine-tuning the model trained on LCO batteries for use with LFP batteries, which reduced the RMSE of the estimation and validated the generalizability of the model. Peak parameters were extracted from both the original and predicted IC curves for clustering, and the t-test was applied to eliminate outliers, which significantly reduced the time required to obtain clustering features and improved clustering efficiency.

1. Introduction

With record sales, the electric vehicle industry holds great promise. The decommissioning standard stipulates that EV power batteries must be decommissioned once their capacity falls below 80% of the rated value to ensure safety [1,2,3]. Although retired batteries no longer meet vehicle standards, they still have high utilization value and can be used in energy storage applications or power communication base stations, small electric devices, etc. [4,5]. By 2025, the global amount of retired batteries is projected to surpass 100 GWh, so the reuse of retired batteries will create significant economic and environmental benefits [6,7,8].

After long-term use, there is a high inconsistency between the capacity, internal resistance, and other parameters of the cells in their battery packs. Before implementing echelon utilization, it is essential to address the consistency of retired batteries. If this issue is not resolved, the module’s capacity will be restricted by the battery with the lowest capacity [9], and may even lead to overcharging or over-discharging of certain batteries within the module, resulting in thermal runaway, which poses a serious safety hazard. Therefore, it is necessary to select suitable indicators that can reflect the consistency of the battery for screening. The selection of clustering features is key to the echelon utilization of retired batteries. There are multiple aging mechanisms in batteries, including loss of lithium inventory (LLI), loss of active material (LAM), and thickening of the solid electrolyte interphase (SEI), all of which ultimately result in the increase in internal resistance and the reduction in battery capacity [10].

Remaining capacity and internal resistance, as significant aging characteristics [11], are the most common clustering features in the echelon utilization of retired batteries [12]. However, the capacity and internal resistance of lithium batteries are typically not directly obtainable online. Additionally, obtaining capacity requires a complete charge–discharge cycle under specified conditions, while obtaining internal resistance necessitates offline impedance testing, which cannot be directly measured online by the battery management system (BMS) [13].

Electrochemical impedance spectroscopy (EIS) is a non-destructive testing method that can reflect the changes in LLI, LAM, and SEI as the battery ages. However, obtaining EIS requires sinusoidal voltage, which imposes high demands on the instruments and testing environment [14]. Incremental capacity analysis (ICA) [15], which is also a non-destructive testing method, achieves online measurement by taking the first derivative of the voltage–capacity curve, eliminating the need for complex equipment. Many researchers have demonstrated that the reduction, shift, and disappearance of the IC peak can estimate the actual capacity of the battery and reveal battery aging [16], making it widely used in battery aging studies. For retired LFP batteries, every peak in the IC curve has a unique form, height, and location, reflecting the electrochemical processes of the battery [17]. Schaltz, E applied ICA to NMC batteries, determining that the IC peak values and their voltage positions are directly related to the actual capacity of the battery, with an improved Gaussian process regression method achieving a maximum capacity prediction error of 3.5% [18].

Locorotondo, E et al. proposed a SOH estimation method for LFP batteries based on an improved Ampere-Count Method combined with ICA. This method focuses on specific features in the Ah-V curve, providing a reliable indicator for SOH estimation. Since this feature appears within the regular charge–discharge cycle range of electric vehicles, it is highly suitable for online SOH estimation without relying on a complete charge–discharge cycle test [19].

The effectiveness of ICA for battery capacity estimation has been widely proven. Based on extracting features from the peaks of the IC curve, Jiang proposed a clustering method for retired batteries that combines capacity and internal resistance [20]. Zhou proposed a cascade utilization method based on ICA and support vector machines and conducted verification experiments [21]. Chen and Zhang, using the capacity incremental analysis method, extracted features from the battery’s capacity incremental curve and performed clustering using the binary K-means algorithm [22] and fuzzy C-means algorithm [23], demonstrating good performance in terms of clustering accuracy and efficiency.

Although ICA has been proven to reflect the battery’s health status without requiring destructive testing and with low demands on testing equipment, the acquisition of the IC curve in the aforementioned methods requires a complete charge or discharge cycle, which is time-consuming. To address the issue of the lengthy acquisition time for the IC curve and to improve the efficiency of retired battery echelon utilization, this paper proposes an IC curve prediction method based on CNN, which realizes the prediction of the complete IC curve and the V-Q curve by using the local charging voltage segments starting from any time point, which significantly reduce the acquisition time.

The effectiveness of this method for different types of batteries was verified using LCO batteries from the Oxford battery degradation dataset and experiments based on LFP batteries.

2. IC Curve-Based Screening Method for Retired Batteries

As the same types of lithium batteries with different aging degrees are charged with the same amount of power, batteries with lower capacity degradation exhibit a smaller increase in voltage, while those with higher capacity degradation show a larger increase in voltage. Therefore, the voltage–capacity (V-Q) curve can reflect the changes in battery aging such as capacity and internal resistance. However, the features of the V-Q curve are not distinct, and the voltage plateau is particularly difficult to utilize directly. Thus, it is necessary to convert it into an IC curve with clear peak features, as shown in Figure 1, where IC_B represents the height of the peak on the left side, IC_A represents the height of the peak on the right side, and V_A is the voltage value corresponding to the position of the right-side peak.

The IC curve is calculated by taking the first derivative (dQ/dV) of the V-Q curve under constant current charging, representing the change in battery capacity corresponding to a unit change in voltage. During the voltage plateau period of the V-Q curve, the voltage remains essentially constant while the capacity increases rapidly, so it transforms into the peak of the IC curve. In practice, due to the influence of sampling intervals, the data may be discontinuous; therefore, ΔQ/ΔV is typically used as a substitute for the derivative, which is available when ΔV is small enough:

$$IC={\displaystyle \frac{dQ}{dV}}\approx {\displaystyle \frac{\Delta Q}{\Delta V}}$$

(1)

The IC curve is significantly affected by battery degradation, as shown in Figure 2.

As the number of battery cycles increases, the peak height of the IC curve gradually decreases and the peak position shifts to the right, indicating a strong correlation between the peak height and position with the degree of battery aging. Current research has demonstrated that the peak height and peak position are linearly correlated with capacity and internal resistance, which could reflect the changes in battery capacity and internal resistance as aging progresses [24]. Therefore, the left-side peak height (IC_B), right-side peak height (IC_A), and corresponding voltage (V_A) of the IC curve are used as clustering features.

3. IC Curve Prediction Based on CNN

The method based on the IC curve addresses the difficulty of extracting aging features from the V-Q curve. However, the acquisition of the IC curve still requires a complete charge cycle, which does not change the problem of time consumption. Therefore, this section proposes a method based on CNN [25], which predicts the complete V-Q curve from local charging curves and derives the IC curve, which significantly reduces the time required to obtain the IC curve.

3.1. Data Preprocessing

During the constant-current charging process of batteries, the capacity Q of the battery can be considered as a function of the voltage:

$$Q(V)={\displaystyle {\int }_{V_{low}}^{V_{up}}\left|I(\tau )\right|}d\tau$$

(2)

where V_low represents the lower voltage limit of the battery, V_up represents the upper voltage limit, and Q(V) denotes the constant current charging curve.

Q(V) is sampled at V, where V is discretized at intervals of Δu (in this paper, Δu is taken to be 0.01 V), as in Equation (3):

$$V=\left[V_{low}, V_{low}+\Delta u, V_{low}+2\Delta u, \dots , V_{low}+N\Delta u\right]$$

(3)

Therefore, the V-Q curve can be changed to a 2 × (N + 1) matrix with V in the first row and Q(V) in the second row, where N is the number of samples for the discretized curve, as in Equation (4):

$$N=\left(V_{up}-V_{low}\right)/\Delta u$$

(4)

In order to solve the problems of the starting and ending voltages for charging not being fixed and the charging process often being incomplete, this study extracts segments of the charging curves to use as the input matrix I for CNN to estimate the entire curve, as in Equation (5):

$$I=\left[\begin{array}{l}V\left(t,t+1, \dots ,t+m\right)\\ Q\left(V\left(t,t+1, \dots ,t+m\right)\right)-Q\left(V\left(t-1\right)\right)\end{array}\right]$$

(5)

where (1 ≤ m ≤ N − 1, 2 ≤ t ≤ N + 1 − m). The input matrix I consists of two rows, V and Q(V), the sequence V of equal steps represents the sampling location of the discretized Q(V), and the sequence V is the same for different curves while Q(V) varies by age.

Equation (5) sets the initial value of capacity to zero by subtracting the Q corresponding to V(t − 1) from the capacity sequence in I, and starts calculating the charging capacity up to the moment V(t + m). This approach does not rely on a complete charging process and can extract the input matrix from any voltage. With the help of a trained CNN, it can estimate the complete V-Q curve and IC curve from a local charging segment of length (N-m).

In order to eliminate the effect of different scales of training data and unify the data to the same scale, therefore, the training data need to be normalized before inputting them into the CNN, as in Equation (6):

$$x_{norm}={\displaystyle \frac{x-\mu }{\sigma }}$$

(6)

where x_norm denotes the normalized training set; x is the original data, i.e., the sequence of V and Q before normalization; µ is the original mean of V and Q; and σ is the original standard deviation of V and Q. The normalized training data have a mean of 0 and a variance of 1, which eliminate the physical significance of the data and ensure the comparability of the data.

3.2. CNN Structure

The CNN structure and parameters used in this paper are shown in

Table 1. The CNN structure used for prediction.

Layer	Form
Input	Partial V and Q data after discretization of the constant-current charging process: [V1, V2, …, Vn; Q1, Q2, …, Qn]
Output	V and Q data for the complete charging cycle
1	One-dimensional partial time series voltage and capacity data
2, 3	2 × (Conv1D-16@ 3 × 3 and Maxpool1D@ 3 × 3)
4, 5	2 × (Conv1D-8@ 3 × 3 and Maxpool1D@ 3 × 3)
6, 7	2 × (Conv1D-8@ 3 × 3 and Maxpool1D@ 3 × 3)
8	Dense-140
9	Dropout: dropout rate:0.2
10	1 × 140 Output layer

.

In this case, the first layer of the CNN is the input layer, which receives the processed data. The second layer is the convolutional layer, containing two filters, each with 16 convolutional kernels of size 3 × 3, and the activation function is ReLU. The third layer is the pooling layer, with a pooling window size of 3 × 3 and using max pooling. The fourth and fifth layers, as well as the sixth and seventh layers, are also convolutional and pooling layers, working on the same principles as the second and third layers. The eighth layer is a fully connected layer (Dense) with 140 neuron nodes, using the ReLU activation function. The ninth layer is a dropout layer with a dropout rate of 0.2, which randomly sets some neurons to zero to prevent overfitting. The tenth layer is the output layer, which has a total of 140 neurons corresponding to the 140 sampling points of the complete curve, used to output the predicted complete charging curve.

3.3. Overall Methodology and Process

The overall prediction and clustering process of this paper is shown in Figure 3.

(1)

Charging data processing: Extract the voltage and capacity data during batteries constant-current charging process and discretize them as training data for CNN;

(2)

Build the CNN according to the previous content, set appropriate parameters for different layers of the CNN such as input, convolution, and pooling layers, and adjust the weights, batch sizes, and number of loops of the CNN;

(3)

Training CNN: Split the training data into a training set and validation set and shuffle the training data to prevent model overfitting. Then, train the CNN until its prediction accuracy meets the actual need;

(4)

IC curve prediction: Use the discretized constant-current charging segments of batteries as inputs to the CNN to predict the entire curve;

(5)

Clustering based on IC curve features: Extract the IC_A, IC_B, and V_A of each battery as clustering features and combine with a t-test to exclude outliers in the clustering results.

4. Prediction Results and Analysis

4.1. Oxford Battery Degradation Dataset

Battery data were obtained from the Oxford battery degradation dataset [26], which consists of eight pouch LCO batteries with a rated capacity of 0.74 Ah. The batteries were discharged at a constant current of 2 C and then recharged at a constant current rate of 1 C under a constant temperature of 40 °C. The battery capacity test was performed after every 100 charging and discharging cycles. The voltage limits of the battery are 2.7 V and 4.2 V. According to the abovementioned method, discretize the charging curve within the range of 2.8 V to 4.2 V with an interval of Δu = 0.01 V, using these as training data and normalizing them. The training set consists of batteries 1–6 and the rest of the batteries form the test set.

For test batteries, a voltage window of 300 mV was used as the input for the CNN. During the 0 to 7000 cycles, a total of 7 curves were extracted every 1000 cycles as validation data to demonstrate that the proposed method is applicable to the complete lifecycle of the battery. The Root Mean Squared Error (RMSE) was used as the evaluation index of the charging curve estimation results, as in Equation (7):

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle {\sum }_{i=1}^N{(Q(V(i))-Q\prime (V(i)))}^2}}$$

(7)

where Q is the actual capacity sequence of the battery and Q′ is the estimation result of the capacity sequence. Figure 4 shows the best and worst prediction results of the V-Q curve and IC curve for LCO batteries throughout their entire life cycle, as well as the impact of different starting points of the input voltage window on the prediction error.

As shown in Figure 4, the proposed method can accurately predict the complete V-Q curve and IC curve of the battery throughout its entire lifecycle, with the worst prediction result having a maximum RMSE of 14.21 mAh, which is 1.92% of the battery’s rated capacity of 740 mAh. The worst results in Figure 4 occurred when the voltage window input to the CNN starts from the lower voltage limit, resulting in the poorest prediction of the IC curve and a larger peak error. This is due to the rapid rise in voltage during the initial phase of constant-current charging, where the 300 mV window duration is too short, leading to insufficient information. In practical applications, if the battery starts charging from the lower voltage limit, extending the charging time appropriately and shifting the starting point of the voltage window to the right can avoid this issue. When the voltage window starts at 3.5 V to 3.9 V, the RMSE shows a significant decrease, which corresponds to the voltage range of the IC peak, reflecting the correlation between the IC peak and battery aging. Additionally, during the 6000 and 7000 cycles, the decreasing trend of RMSE with the rightward shift of the voltage window was not obvious in the first half, which is due to the B peak of the IC curve almost disappearing because of the deep aging of the battery. At this point, the battery capacity was only about 75% of the rated capacity, which is far below the 80% retirement standard. In practice, batteries are usually retired when their capacity is greater than 80%, so this issue would not occur in actual situations.

When the 300 mV voltage window started at 2.8 V, it lasted only 9.8 min. Compared to the complete 56 min 1 C charging process, the CNN reduced the curve acquisition time by approximately 82%. The voltage window that includes the IC peak had a duration of 34 min, reducing the curve acquisition time by 40%. Even if the voltage window does not include the peak interval, the proposed CNN can still maintain a high prediction accuracy.

4.2. Selection of Window Length

In order to select the appropriate length of the voltage window, the CNN model was trained with a length of 100–900 mV and a step size of 50 mV. The RMSE of the prediction results for the voltage window of each length is shown in Figure 5.

The window length of 200 mV already yields good prediction results. Increasing the window length can improve prediction accuracy, but once the window length exceeds 300 mV, the improvement in accuracy becomes limited while significantly increasing the acquisition time of the voltage window. Therefore, considering these factors, this paper chose a voltage window of 300 mV. In practical applications, an appropriate window length can be selected according to the specific needs to balance the accuracy and efficiency.

4.3. Transfer Learning and Experimental Validation

To reduce the training time and data requirements of the neural network model and to improve the model’s generalizability, transfer learning is used to avoid the need to build and train a new model each time for new battery data. Transfer learning reduces the model’s demand for training data and the time required by fine-tuning a pre-trained model from one domain and applying it to a similar domain. For Li-ion battery charging curve prediction, even though the material, rated capacity, and charging rate may vary between batteries, there is always a similarity in their constant-current charging curves.

The experiment used 20 pieces of 18,650 LFP batteries, as shown in Figure 6. The battery’s rated capacity is 1.1 Ah, and its rated voltage is 3.2 V. The cutoff voltages for charging and discharging are 2.5 V and 3.6 V, respectively. The battery tester used is the ZEKTECH EBT-A40P programmable tester, with a voltage range of 0–4.5 V and a current range of 0.1–10 A. The voltage and current measurement accuracies are 0.2% ± 0.003 V and 0.2% ± 0.005 A, respectively. Each battery was cycled using a constant current charge rate of 0.5 C and a constant current discharge rate of 1 C, with a 15 min interval between cycles. Each battery underwent 200 cycles in total.

Before transfer learning, the pre-trained model based on the Oxford dataset needs to be adjusted to be applicable to the experimental battery data. The number of neurons in the fully connected and output layers of the per-trained model needs to be modified to correspond to the experimental battery, and the capacity of the experimental battery of 1.1 Ah is converted to 0.74 Ah of the Oxford battery according to Equation (8) during the normalization process.

$$Q_t={\displaystyle \frac{Q_{exp}}{1.1}}\times 0.74$$

(8)

where Q_t is the adjusted battery capacity, and Q_exp is the rated capacity of the experimental battery.

The training was conducted separately for both direct training and transfer learning for the experimental LFP batteries, each repeated 20 times, resulting in 20 CNN models. To ensure validation across all batteries, the first four batteries were initially used as the training set for training, and then the last four batteries were used as the training set to obtain the prediction results for the first four batteries. Taking battery 5 as an example, its prediction results for direct training and transfer learning are shown in Figure 7.

Figure 8 shows the RMSE distribution of the prediction results for 20 groups of CNN models on the experimental LFP batteries. Transfer learning was applied by fine-tuning the pre-trained models based on LCO batteries, and then training them further using data from LFP batteries. The final average RMSE of the transfer learning model was 3.62, which is lower than the average RMSE of 4.02 from direct training, with less fluctuation as well. Furthermore, as shown in Figure 4, we verified the prediction performance of the CNN on LCO batteries. In this section, the prediction performance on LFP batteries is validated using both transfer learning and direct training, confirming that the proposed CNN model is applicable to the batteries with these two different materials.

5. Clustering Results for Original and Predicted Curves

The clustering was performed using the Bisecting K-means algorithm. The Bisecting K-means algorithm processes only one cluster center per iteration, making it less prone to getting stuck in local optima. First specify the number of clusters, K, and treat all sample points as a single cluster. Then, for each cluster, the error after splitting it in different ways is calculated, and the division method with the smallest error is selected until the preset K value is met.

5.1. Clustering Results Based on IC Features

For the 20 LFP batteries mentioned in Section 3.3, ICA, ICB, and VA were extracted as clustering features from the original IC curve of the battery’s final cycle and the predicted IC curve based on the 300 mV voltage interval. The selected voltage interval was 3.1–3.4 V to avoid the initial voltage being too close to the lower limit, which could cause large errors, and to ensure that the charging time is not excessively long, approximately 30% of the total time. The clustering results based on the original curves and predicted results are shown in Figure 9 and

Table 2. Clustering results based on the original curve and prediction of LFP batteries.

Cluster	Based on the Original Curve	Based on Predicted Results	Difference
1	1, 2, 5, 6, 7, 8, 15, 16, 17, 20	1, 2, 5, 6, 7, 8, 15, 16, 17, 20	/
2	4, 9, 10, 18, 19	4, 9, 10, 18, 19	/
3	3, 11, 12, 13, 14	3, 11, 12, 13, 14	/

.

Since the predicted curves cannot be exactly the same as the original curves, there is a slight difference in the location of the points in Figure 9, but the clustering results of the two are the same, as shown in Table 2.

Additionally, cluster 3 contains some outlier samples with parameters significantly different from the other batteries, which could affect the clustering results if retained. To address this issue, a t-test was introduced to examine and eliminate these samples.

The steps of the t-test are as follows: calculate the length between each sample point and the averaging point of the cluster and consider the point furthest from the mean as suspect x_i. Then, calculate the average value M and variance D excluding x_i. Determine the critical confidence level α; the higher the value of α, the more concentrated the sample points. Reducing the value of α allows more sample points to be retained, and the value of α can be decided based on actual needs. Finally, determine whether the suspect point needs to be eliminated: if x_i-M > αD, the point is removed; otherwise, it is retained. Excluded outlier samples in Figure 10 are shown in gray.

5.2. Clustering Results Analysis

The clustering results were evaluated using the Silhouette Coefficient (SC), the Calinski–Harabasz Index (CHI), and the Davies–Bouldin Index (DBI) as evaluation functions. The calculation methods are as follows:

$$SC(i)={\displaystyle \frac{b(i)-a(i)}{\max \{b(i)-a(i)\}}}$$

(9)

where a(i) is the average distance between sample i and the other samples in the same cluster, and b(i) is the average distance between sample i and the samples in the nearest different cluster.

$$CHI={\displaystyle \frac{BCSS/(k-1)}{WCSS/(n-k)}}$$

(10)

where k is the number of clusters, n is the number of batteries, and BCSS and WCSS are the inter-cluster and intra-cluster discrete matrices, respectively.

$$DBI={\displaystyle \frac{1}{k}}{\displaystyle \sum _{i=1}^k\underset{j\ne i}{\max }}\left({\displaystyle \frac{S_i+S_j}{d\left({\omega }_i,{\omega }_j\right)}}\right)$$

(11)

where k is the number of clusters and S_i is the average distance from samples in cluster i to the cluster center.

Among the three evaluation functions, the closer the SC is to 1, the higher the CHI, and the lower the DBI, the better the clustering results. The clustering metric results based on the original curves, predicted curves, and after the t-test are shown in Figure 11, where the CHI has been scaled for easier plotting.

After a t-test to exclude outliers, the clustering results based on the original curves showed an improvement in SC and CHI from 0.62 and 1.324 to 0.81 and 1.582, respectively, while DBI decreased from 0.694 to 0.495. Similarly, for the clustering results based on the predicted curves, SC and CHI improved from 0.60 and 1.297 to 0.79 and 1.538, respectively, and DBI decreased from 0.71 to 0.523. Overall, after the t-test, SC and CHI increased by approximately 30% and 20%, respectively, while DBI decreased by about 25%. This demonstrates that excluding outliers through the t-test effectively improved the clustering results. Moreover, compared to the clustering results based on the original curves, the clustering results based on the predicted IC curves significantly reduced the time required with minimal impact on clustering effectiveness, proving that the proposed method can shorten the time required to obtain the IC curve while maintaining good clustering consistency with the original curve data.

6. Conclusions

This paper addresses the issues of long testing times and low efficiency in the screening process of retired batteries by constructing a convolutional neural network model. The model uses short charging curve segments of lithium batteries as input to accurately predict the complete IC curve and V-Q curve, significantly reducing the time required to obtain the IC curve. The model’s generalizability was experimentally validated. Finally, the curve features were extracted from both the original IC curve and the predicted IC curve based on the charging segments, using incremental capacity analyses as clustering indicators. The Bisecting K-means algorithm was used for clustering, and the clustering results were compared. A t-test was conducted to eliminate outliers, and the accuracy of the proposed solution was demonstrated using three evaluation metrics: SC, CHI, and DBI.

In summary, this paper provides a neural network-based solution to improve the efficiency of retired battery screening. In the future, more retired lithium batteries will be used to further verify the model’s generalizability and accuracy, as well as to explore and extract more precise clustering features to enhance precision.