Physics-Informed Fractional-Order Recurrent Neural Network for Fast Battery Degradation with Vehicle Charging Snippets
Abstract
1. Introduction
- A physics-informed recurrent neural network (PIRNN) with ICA and FOGD methods is proposed for capacity estimation in LIBs with fast degradation. The peak magnitudes of the IC curves are extracted as input characteristics for the neural network, and a fractional-order gradient is applied to the backpropagation process.
- The proposed PIRNN can learn the battery information of running EVs during training convergence and achieve stable capacity estimation accuracy (relative error < 3%) using a LiFeP battery dataset over three-quarters of a lifetime. This demonstrates that the proposed PIRNN can be applied to realistic batteries from running EVs and hold its accuracy.
- A battery dataset with fast degradation is constructed based on ten running EVs covering the years 2018–2022 and with over a 40,000 km mileage. The dataset contains 5697 charging snippets and covers almost the whole battery lifetime, which can be the validation dataset for kinds of machine learning algorithms.
2. Preliminary
2.1. Fractional-Order Calculus and Derivative
2.2. Fractional-Order Gradient
3. Battery Dataset and Its Fractional-Order Information
3.1. EV Dataset and Battery Degradation
3.1.1. Battery Capacity
3.1.2. Battery Dataset with Vehicle Charging Snippets
3.2. Fractional-Order Information of Battery
3.2.1. Fractional-Order Equivalent Circuit Model
3.2.2. Incremental Capacity Analysis
4. Physics-Informed Fractional-Order Recurrent Neural Network for Battery Degradation
4.1. Physics-Informed Input with ICA Characteristics
4.2. Physics-Informed Structure of RNN
4.3. Fractional-Order Gradient Descent Method
- Step 1: perform initialization, with , , the learning rate , the fractional order , and so on.
- Step 2: obtain the battery dataset, and then preprocess the data (including extraction of inputs such as ICA magnitude) and divide the battery data into training, validating, and testing data.
- Step 3: perform the feedforward process, in a discrete form, with data flows in the PIRNN from the input layer to output layer, and then calculate the MSE ().
- Step 4: perform the backpropagation process, starting from the output layer, to calculate the gradients between layers, and then update the weight and bias with (16).
- Step 5: Perform validation. Check if satisfies the target value or if the maximum epoch is arrived at. If so, go to step 6; if not, go to step 3 and .
- Step 6: If satisfies the target value of the loss function , the training process is completed, and capacity estimation and analysis should be conducted. Otherwise, if the maximum epoch is arrived at, adjust the parameters and redo the procedure.
5. Algorithm Verification and Experimental Results
5.1. Experimental Setup
5.2. Estimation Results for Battery Degradation
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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EV No. | Snippets Amount | Time Range | Mileage Range (km) | SOH Range (Ah) |
---|---|---|---|---|
EV1 | 698 | 18 September 2018–28 Febraury 2022 | 8730–52,992 | 124.9076–97.9608 |
EV2 | 290 | 11 October 2018–29 March 2022 | 87–21,987 | 131.0177–115.6695 |
EV3 | 660 | 22 September 2018–28 Febraury 2022 | 4400–47,461 | 128.4828–102.3552 |
EV7 | 571 | 10 December 2018–31 January 2022 | 7605–43,792 | 123.3471–105.1326 |
EV5 | 633 | 19 September 2018–16 September 2021 | 8355–46,569 | 120.4993–105.9154 |
EV6 | 562 | 18 September 2018-2 March 2022 | 8395–45,933 | 122.0545–107.6695 |
EV7 | 650 | 18 September 2018–1 March 2022 | 7725–46,737 | 115.7236–108.9408 |
EV8 | 487 | 18 September 2018–31 January 2022 | 8165–40,186 | 123.4687–88.0738 |
EV9 | 590 | 18 September 2018–20 July 2021 | 7660–45,148 | 121.3203–107.3435 |
EV10 | 556 | 18 September 2018–20 December 2021 | 8538–44,569 | 119.3115–110.6705 |
No. | 1 | 2 | 3 | 4 | 5 | 6 |
Type | average current | start SOC | end SOC | DOC | start voltage | end voltage |
No. | 7 | 8 | 9 | 10 | 11 | 12 |
Type | mileage | Ah quantity | start temperature | end temperature | peak1 magnitude | peak2 magnitude |
Name | Value | Name | Value |
---|---|---|---|
state delays in PIRNN | 1:2 | hidden layer size | 8 |
performance function | MSE | maximum epoch | 3000 |
train function | FOGD | train–validation–test | 0.8:0.05:0.15 |
learning rate | 0.0001 | training goal | 1 |
fractional order | 0.8 | validation times | 50 |
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Wang, Y.; Wei, M.; Dai, F.; Zou, D.; Lu, C.; Han, X.; Chen, Y.; Ji, C. Physics-Informed Fractional-Order Recurrent Neural Network for Fast Battery Degradation with Vehicle Charging Snippets. Fractal Fract. 2025, 9, 91. https://doi.org/10.3390/fractalfract9020091
Wang Y, Wei M, Dai F, Zou D, Lu C, Han X, Chen Y, Ji C. Physics-Informed Fractional-Order Recurrent Neural Network for Fast Battery Degradation with Vehicle Charging Snippets. Fractal and Fractional. 2025; 9(2):91. https://doi.org/10.3390/fractalfract9020091
Chicago/Turabian StyleWang, Yanan, Min Wei, Feng Dai, Daijiang Zou, Chen Lu, Xuebing Han, Yangquan Chen, and Changwei Ji. 2025. "Physics-Informed Fractional-Order Recurrent Neural Network for Fast Battery Degradation with Vehicle Charging Snippets" Fractal and Fractional 9, no. 2: 91. https://doi.org/10.3390/fractalfract9020091
APA StyleWang, Y., Wei, M., Dai, F., Zou, D., Lu, C., Han, X., Chen, Y., & Ji, C. (2025). Physics-Informed Fractional-Order Recurrent Neural Network for Fast Battery Degradation with Vehicle Charging Snippets. Fractal and Fractional, 9(2), 91. https://doi.org/10.3390/fractalfract9020091