State of health estimation for lithium battery based on multi-source transfer learning

Aiming at the problem that the state of health estimation accuracy decreases when the lithium battery in training and testing sets has different charging conditions, we proposed a solution based on the transfer learning with the multi-source method. This scheme uses the complete aging test data of 16 batteries under different charging conditions as the source domain and extracts aging characteristics respectively to train the basic model. The similarity coefficient was obtained by the similarity evaluation of the first 200 cycles of each source and target battery, and the learning weight of each source battery model was weighted by the similarity coefficient. The experimental results show that the MAE and RMSE of the transfer learning with a multi-source model decreased by 53.63% and 54.97% compared with the single-source estimation model under new charging conditions.


Introduction
Lithium battery (LiB) has the advantages of high energy density, long cycle life, and wide operating temperature range.However, with the widespread application of LiB in various devices, the problem of battery state of health (SOH) estimation has become increasingly prominent [1].The SOH of a LiB is usually expressed by its capacity or internal resistance, and problems such as capacity degradation and internal resistance increase will occur during the cycle use [2].Therefore, accurate estimation of LiB's SOH is helpful to ensure the safe use of batteries, extend battery life, and optimize battery management systems [3].
Machine learning methods have been widely used to estimate SOH during battery degradation [4].Guo et al. [5], Su et al. [6], Lin et al. [7], Chen et al. [8], and Liu et al. [9] respectively studied the performance of SVM, GPR, BPNN, ELM, and CNN-GRU models in battery SOH estimation.The model can fit the relationship between different aging characteristics and SOH and can obtain highprecision results on SOH estimation.However, the above premise for high-precision battery SOH estimation using machine learning models is that the training and testing data have the same distribution.However, due to differences in application conditions (such as differences in charge and discharge rate, charge and discharge depth, temperature, and humidity), there are obvious differences in the degradation modes of batteries in the same batch, resulting in a decline in the accuracy of SOH estimation [10].The obvious solution is to run different complete aging tests for different conditions while collecting large amounts of data to train the estimation model, which is expensive.To solve this problem, transfer learning with a multisource SOH estimation method was proposed.Complete test data under other charging conditions were used as the source domain and aging characteristics were extracted respectively to train the basic model.The similarity coefficient was obtained by the similarity evaluation of the first 200 cycles of each source-target battery.The transfer learning contribution of each source battery model of SOH estimation to the target battery model of SOH estimation was weighted by the similarity coefficient, to improve the SOH estimation accuracy of the target battery under new charging conditions.

Feature extraction and correlation analysis
In this section, the Health Index (HI) reflecting the aging characteristics of the battery was extracted, and correlation analysis was performed to verify the validity of the extracted features, providing feature input for the SOH estimation model in the next section.

Battery aging dataset
Stanford University, MIT, and the Toyota Research Institute [11] provided experimental data on the aging of batteries under an optimized fast charge protocol, consisting of 124 commercially available lithium batteries.Each battery in the dataset is named according to the test batch and the battery serial number in each batch.For example, the battery serial number 17 in the first batch of tests is named b1c17 (Target battery).We extracted data from a total of 17 batteries with cycle lives between 800 and 900, and the information on all batteries used in the experiment is shown in Table 1.

Aging feature extraction
The characteristic that reflects the SOH of the battery is called the HI, and the HI can be extracted from curves such as the constant current charge voltage curve and the Incremental Capacity Analysis (ICA) curve.The constant current charging voltage curve is the curve of the battery voltage changing with time during the constant current charging process, and the constant current charging voltage curve of different cycles will be different.The ICA curve is a battery cycle charge to voltage differential (dQ/dV) with the voltage change curve, and different cycles of the ICA curve will also be different.
Taking the b1c17 battery as an example, the change of the battery charging voltage curve with the number of cycles is shown in Figure 1.The change of the ICA curve with the number of cycles is shown in Figure 2.  It can be observed from Figure 1 that in the voltage rise stage (C1: constant current charging stage), with the increase in the number of cycles, the time to reach the same voltage level will gradually shorten, and the voltage at the same time point will gradually increase.According to the variation characteristics of the voltage curve, two kinds of HI are extracted: charging time of fixed voltage segment (3.0-3.3V) and average charging voltage of fixed period (1-2 minutes).
It can be observed from Figure 2 that the ICA curve has only one valley value.With the increase of cycles, the ICA curve valley value gradually increases, while the ICA curve valley value corresponding to the horizontal coordinate (voltage) gradually decreases.According to ICA curve valley value characteristics, two kinds of HI are extracted: ICA curve valley value and ICA curve valley value position.

Correlation analysis
To quantitatively analyze the rationality of HI selection, the correlation coefficient between HI and SOH was calculated.Commonly used correlation coefficients include Pearson coefficient and Spearman coefficient [12].Since the Pearson coefficient requires variables to obey normal distribution, the Spearman coefficient was selected for correlation analysis.The calculation equation of Spearman correlation coefficient rs is shown in Equation (1).
where di is the rank difference between HIi and SOHi, and N1 is the total number of samples of HI and SOH.

Construction of the SOH estimation model
In this section, we proposed an SOH estimation method that combines Deep Neural Networks (DNN) with multi-source transfer learning methods.The similarity evaluation rules were established to evaluate the similarity between each source unit SOH estimation model and the target unit SOH estimation model.At the same time, the evaluation criteria were given to evaluate the model's accuracy.

Similarity evaluation
Batteries of the same batch will experience different degradation modes under different charging conditions.However, some training data with large differences may hurt the SOH estimation performance of the regression model in the target battery [13].To measure the difference of such degradation modes, a similarity evaluation method was proposed to analyze the degradation modes of the source battery and target battery by using Euclidean distance.Firstly, the mean Euclidean distance δi of source battery i and target battery SOH samples was calculated, and the calculation equation is shown in Equation (2).
where SOHsource, ij is the SOH value of source domain battery i at sample j, SOHtarget, j is the SOH value of target battery at sample j, and N is the number of the first 200-cycle SOH samples of source and target battery.The smaller Euclidean distance means that the source battery is more similar to the target battery.Then, the similarity coefficient of the source battery and the target battery was obtained by using the reciprocal of δi and normalization.The calculation equation of the similarity coefficient wi of the source battery i is shown in Equation (3).
where i is the serial number of batteries in the source domain, Ns is the number of batteries in the source domain, and δi is the mean Euclidean distance of battery i in the source domain.

Model construction
In this subsection, a DNN estimation model was constructed for SOH estimation, and a transfer learning with a multi-source estimation model was constructed based on the DNN estimation model.

Single-source estimation model.
For the construction of the basic battery model in a single source domain, DNN was used as the basic learner to fit the nonlinear relationship between the extracted features and SOH.The SOH estimation model based on DNN is shown in Figure 3.
The DNN model has an input layer, 2 hidden layers, and an output layer.The input layer takes the extracted four kinds of HI as the feature input, and the output layer gets the SOH estimate.In the training process, Adam optimizer is used to perform gradient descent to minimize the loss function.Adam's algorithm calculates the square value of the gradient and the deviation correction in each iteration to adjust the learning rate adaptively so that the network can converge to the optimal solution faster.

Model evaluation
To evaluate the estimation accuracy of the transfer learning with a multi-source model for the SOH of the target battery, error indexes such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) were introduced.The calculation equations are shown in Equation ( 4) and Equation ( 5) respectively.

MCAI-2023
Journal of Physics: Conference Series 2724 (2024) 012039 where N1 is the total number of samples of the actual and estimated SOH values, SOHactual, i is the actual SOH value sample i, and SOHpredictad, i is the estimated SOH value sample i.

Analysis of experimental results
To compare the performance of the transfer learning with the multi-source estimation model proposed in this paper, three sets of comparison experiments were added.In the experiment of DNN (under the same working condition), the training set was the cyclic data of the b1c17 battery (5.4C-3.6C)and the test set was the cyclic data of the b1c17 battery (5.4C-3.6C).In the experiment of DNN (under different working conditions), the training set is the cycle data of the b3c11 battery (5.6C-4.6C)and the test set is the cycle data of the b1c17 battery.In the Long Short-term Memory Fully Connected Transfer Learning (LSTM-FC-TL) experiment [14], the basic model training set is the cycle data of the b3c11 battery.The LSTM layer was fixed during the model parameter fine-tuning phase and the fully connected layer parameters were fine-tuned by using the first 25% cycle data of the b1c17 battery.The SOH estimation error results of each algorithm model are shown in Table 2.All the above models adopt the same hyperparameters.As can be seen from Table 2, the DNN (Same condition) has the best fitting effect on the actual SOH curve of the target battery and obtains the highest accuracy among all models, with an MAE value of 0.42% and an RMSE value of 0.51%.However, complete test data under the same working conditions as the target battery are required.However, the DNN (Different condition) does not require the test data of the same working conditions as the target battery but obtains the worst fitting effect.Compared with the DNN (Same condition), the MAE value increases by 8.19 times, and the RMSE value increases by 7.88 times.When the training set and the test set have different charging conditions, the estimation accuracy of the SOH estimation will decrease significantly.Compared with the DNN (Different condition), the LSTM-FC-TL estimation model fits the SOH curve of the first 25% of the target battery better, and the MAE value decreases by 45.34% and RMSE value decreases by 38.63% in general.The Multi-source SOH estimation model proposed in this paper obtained an estimation accuracy second only to the DNN (Same condition) and had a good fitting effect for the actual SOH degradation curve.Compared with the DNN (Different condition), the MAE value decreased by 53.63% and the RMSE value decreased by 54.97%.

Conclusions
An SOH estimation method based on transfer learning with multi-source was proposed.Under different charging conditions of the training set battery and the test set battery, the SOH estimation accuracy of MAE=1.79% and RMSE=2.04% were obtained, and the aging test of the target battery under the new condition was reduced to 200 cycles.

Figure 2 .
Figure 1.Charging voltage curve.Figure 2. The ICA curve. 1 -source transfer learning estimation model.After feature extraction and model training, the DNN-based SOH estimation model of each source battery was obtained, and then the similarity coefficient between each source region battery degradation curve and the target battery degradation curve was obtained by similarity evaluation.To apply the source domain cell estimation model to the target cell SOH estimation, a multi-source SOH estimation model weighted by similarity coefficient was proposed.The transfer learning with a multi-source estimation model is shown in Figure 4.By extracting four kinds of HI of the target battery and inputting these four kinds of HI into the SOH estimation models of 16 source batteries respectively, the SOH output values of 16 single source estimation models (different working conditions) are obtained.Each SOH value was weighted and summed respectively, and the corresponding weight is the normalized similarity coefficient obtained after similarity evaluation.

Table 1 .
Battery information in the experiment

Table 2 .
SOH estimation error of each algorithm model.