Remaining useful life and state of health prediction for lithium batteries based on differential thermal voltammetry and a deep le

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Software and algorithms

TensorFlow 2.3	TensorFlow	https://tensorflow.google.cn/
Python 3.8	Python	https://www.python.org/

Resource availability

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Xinhua Liu ( liuxinhua19@buaa.edu.cn ).

Materials availability

This study did not generate new materials.

Method details

Differential thermal voltammetry signal analysis

The DTV method is an important tool for tracking battery health conditions, which could be utilized to evaluate the patterns of battery degradation process. It can help to extract feature variables that reflect microscopic battery degradation characteristics. The battery degradation is a complex physicochemical process. Therefore, the analysis of internal mechanism and measurement of parameters could be challenging. The change of entropy is a function of temperature, and the DTV method could provide obvious information related to entropy. Some feature variables, such as positions and heights of peak and valleys of the curve, are directly concerned with the impedance increment and nonuniform of electrode performance during battery degradation process, reflecting the phase transition characteristic. The phase transition characteristic is closely related to the battery degradation, thus providing close links between DTV features and battery degradation. The parameters of DTV methods could be calculated by differentiate the temperature of the battery surface to the terminal voltage during charging, described as follows.

D T V = \frac{d T}{d t} / \frac{d V}{d t} = \frac{d T}{d V}

(Equation 16)

Where T represents the battery surface temperature, V the battery terminal voltage. That is, we could obtain DTV only by obtaining temperature and voltage data from the battery during charging or discharging.

Bayesian optimization

The Bayesian optimization method is utilized for hyperparameters search of model. As for deep-learning neural network, the hyperparameters are pre-set parameters rather than the parameter obtained through training. The hyperparameters have a great effect on the performance of neural networks. With the improvement of health prediction accuracy, the value of hyperparameters cannot be applied to different types of batteries. Reasonable selection of hyperparameters can optimize the results of network calculation. The hyperparameter value is automatically adjusted by Bayesian optimization algorithm. The optimal hyperparameter value could be computed as follows:

d^{*} = a r g m i n J (d), D \in (a, b), (d \in D)

(Equation 17)

Where d represents the hyperparameter value, d∗ the optimal value and (a, b) the interval of optimization.

Dropout technique

To solve the overfitting problem, the dropout method is utilized to randomly drops neurons in the network, improving the generalization ability and training speed of model.[45] With the dropout technique, the neurons from in the neural network are randomly dropped, addressing the overfitting problem more efficiently during training. Neurons with all incoming and outgoing connections are temporarily removed from the network. The neuron is temporarily removed from the network along with all its incoming and outgoing connections. Each neuron is retained according to a specific fixed probability p. The dropout layer is placed between the two fully connected layers. Consequently, a “thinned” network from origin neural network is obtained with dropout technique applied. The new network consists of all the neurons that survive in dropout process, being less sensitive to the specific weights of neurons.

RMSprop algorithm

The RMSprop technique is utilized to train the deep-learning neural network. Compared to other optimization methods, the RMSprop technique further improves convergence speed and convergence character. The update of the network parameters weight W and bias b can be described as:

J (W, b) = \frac{1}{m} \sum_{j = 1}^{m} {({\hat{y}}_{j} - y_{i})}^{2}

(Equation 18)

S_{1}^{t} = β_{1} S_{1}^{t - 1} + (1 - β_{1}) \frac{\partial^{2} J^{t - 1}}{\partial W^{2}}

(Equation 19)

S_{2}^{t} = β_{2} S_{2}^{t - 1} + (1 - β_{2}) \frac{\partial^{2} J^{t - 1}}{\partial b^{2}}

(Equation 20)

W^{t} = W^{t - 1} - α \frac{\partial J^{t - 1}}{\partial W \sqrt{S_{1}^{t}}}

(Equation 21)

b^{t} = b^{t - 1} - α \frac{\partial J^{t - 1}}{\partial b \sqrt{S_{2}^{t}}}

(Equation 22)

where $J (\cdot)$ represents the cost function of the LSTM NN, $t$ the number of training iteration, $y$ the real value, $\hat{y}$ the predicted value respectively, $β$ the update coefficient of $S$ , and $α$ the learning rate.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (No. 52102470).

Author contributions

Conceived and designed the experiments and analyzed data: L.Z., Z.Z, and X.L.; Performed most of experiments: L.Z., W.W., and H.Y.; Writing – Original Draft: L.Z.; Writing – Review & Editing: X.Y., F.L., and S.L.; Conceptualization, Methodology: S.Y., Z.Z., and X.L.; All authors contributed to and approved the paper.

Declaration of interests

The authors declare no competing interests.

Notes

Published: December 22, 2022

Data and code availability

No additional data was used. This paper does not report original code. Any additional information for reanalyzing this work is available from the lead contact upon request.

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