A physics-informed dynamic deep autoencoder for accurate state-of-health prediction of lithium-ion battery

Abstract

Lithium-ion batteries (LIBs) are currently the standard for energy storage in portable consumer electronic devices. They are also used in electric vehicles and in some large industrial settings and for grid power storage. The adverse consequences of a dramatic battery failure can be significant compared with the cost of timely replacement or maintenance. Consequently, accurate state-of-health (SOH) prediction is important to inform maintenance or replacement decisions. In this work, we address current challenges related to accuracy and interpretability in data-driven SOH prediction for LIBs by devising a novel physics-informed machine learning prognostic model, termed PIDDA. PIDDA includes three elements: an autoencoder, a physics-informed model training, and a physics-based prediction adjustment. We examine and benchmark our model against alternative data-driven SOH prediction models using the NASA battery prognostic dataset. The computational experiments demonstrate that PIDDA (1) provides significantly higher prediction accuracy; (2) requires less prior data for its predictions; (3) produces more informative and interpretable predictions than alternative models. We conclude with an ablation study of PIDDA to analyze the relative effectiveness of two of its elements, the physics equations in the model training and the physics-based prediction adjustment. The results show that the former (training) provides the heavy lifting in accuracy improvement, roughly two-thirds, and the latter (adjustment) the remaining incremental improvement.

Appendices

Appendix 1: Regression analysis of state equation coefficients

In this appendix, we build a regression model regarding state coefficients $\theta_{1}$ and $\theta_{2}$ to the state temperature to the LIB dataset. We take 100 samples of the $\theta_{1}$ and $\theta_{2}$ values across the entire temperature range of the battery prognostic dataset and conducted polynomial regression with different orders. We randomly split the dataset into 80% training and 20% testing. In order to prevent the overfitting of the regression, we use the $l_{2}$ regularization. The coefficient of determination $R^{2}$ results for different orders of polynomial regression is shown in Fig. 

Fig. 13

$R^{2}$ value for different order polynomial regression on $\theta_{1} \left( T \right)$ and $\theta_{2} \left( T \right)$

13.

From Fig. 13, first, the $\theta_{1}$ and $\theta_{2}$ model $R^{2}$ values are high that the polynomial regression model can accurately model the relationship between state coefficients to temperature. Second, $R^{2}$ value of testing is significantly smaller compared with that of training without $l_{2}$ regularization. This problem is mitigated and solved by applying $l_{2}$ regularization to the regression. Finally, we identify the most accurate model with the highest $R^{2}$ value as the fourth polynomial model with $l_{2}$ regularization. The regression results of the fourth-order polynomial for $\theta_{1}$ and $\theta_{2}$ are shown in Fig. 

Fig. 14

Fourth-order polynomial regression with $l_{2}$ regularization results of state equation coefficients (a: $\theta_{1} \left( T \right)$; b: $\theta_{2} \left( T \right)$)

14.

Appendix 2: Structure and weight parameters of the En-ResNet

Here, we introduce the details of the output size, memory requirement per image, and the number of weights of En-ResNet as shown in Table 6. We use 32-bit floating numbers for variables in the data processing that one variable takes $\frac{32}{8}=4$ bytes. According to Table 6, the number of weights is 0.100 M. The memory usage is the hard requirement of the hardware and weight size indicates the training requirement of the model.

Table 6 Output size, hardware memory, and weight size of Pro-ResNet

Appendix 3: Structure and weight parameters of the De-ResNet

Here, we introduce the details of the output size, memory requirement per image, and the number of weights of De-ResNet as shown in Table 7. We use 32-bit floating numbers for variables in the data processing that one variable takes $\frac{32}{8}=4$ bytes. According to Table 7, the number of weights is 15.04 M. The memory usage is the hard requirement of the hardware, and weight size indicates the training requirement of the model.

Table 7 Output size, hardware memory, and weight size of De-ResNet

Appendix 4: PIDDA and pure data-driven predictions for battery No. 6

In this appendix, we discuss the PIDDA and pure data-driven approach prediction on battery No. 6. The comparison of the capacity and SOH predictions of PIDDA, no adjustment, and pure data-driven model is shown in Fig. 

Fig. 15

Capacity and SOH predictions of PIDDA, no adjustment, and pure data-driven model for battery No. 6

15. The RMSE of the capacity and SOH of the PIDDA, no adjustment, and pure data-driven approach is provided in Table

Table 8 RMSE and improve rate in the ablation study

8.

The results of battery No. 6 are similar to those of battery No. 7, and the PIDDA can significantly improve the prediction accuracy compared with the pure data-driven model.