Simulation of Correlation Estimation of Porous Structure Properties of Secondary Battery Using Machine Learning
Authors: Ishikawa Shota , Inoue Gen , Kimura Naoki , Tsuge Yoshifumi 
Published: December 2020

In recent years, high capacity and high output of secondary batteries such as lithium ion batteries have been desired. The battery uses a porous electrode layer, and its structural design, such as filling factor and geometrical shape, is performed by trial and error. Therefore, design support technology is required to improve development speed. It is difficult to measure the tortuosity, which is one of the structural characteristics, and various estimation formulas have been proposed, but the theory has not been established yet [1]. In this study, we introduced machine learning, and constructed a model for predicting the tortuosity from cross-sectional images and other structural property values (such as porosity), and used the obtained knowledge to consider the correlation between parameters.
We used Convolutional Neural Network (CNN) [2] and Support Vector Regression (SVR) [3] for the machine learning model. Figure 1 shows the numerical structures simulated actual porous electrodes. The structural parameters were identified by applying a random walk calculation [4] to the numerical structure and used as training data for a machine learning model. Scikit-learn was used to implement SVR, and Keras was used to implement CNN. The computer used was a CERVO Deep Type-DPCMS (CPU: Intel Core i7-7800X, GPU: GeForce RTX 2080 Ti).
Experiments were performed to confirm the validity of the structural parameters obtained by simulation and to verify the prediction performance by machine learning. For the CNN target, a ready-made glass filter (P-16) manufactured by Shibata Kagakusha was used, and for the SVR, an electrode layer consisting of a graphite negative electrode was used. The porosity was calculated from the weight measurement. We assembled the sample in an H-type cell filled with a standard electrolyte (HORIBA, 100-22), and the tortuosity was calculated from the resistance value obtained from the electrochemical impedance measurement.

Figure 2 shows the activation heat map of the CNN after fine tuning using the cross-sectional image of the actual glass filter after learning with the simulated numerical structure [5]. The black part in the left figure is the void. It can be seen from the figure that the fine pores are extracted as features. Therefore, we considered the particle aspect ratio AR [-] as a complication factor of the structure and used it as the input value of SVR. Figure 3 shows the results of the SVR tortuosity prediction and the conventional Bruggeman equation [1], which is a function of only the porosity. It can be seen that the conventional formula has a large deviation and the SVR has a small prediction error. Furthermore, the prediction error was smaller when the aspect ratio was added (MI-SVR) than when only the porosity was set as the input value of the SVR (SI-SVR). Therefore, it is suggested that the tortuosity depends not only on the porosity but also on the aspect ratio. In the negative electrode layer composed of graphite flat particles, good agreement was observed between the measured tortuosity and the predicted value of MI-SVR. Furthermore, a new formula for estimating the tortuosity (Proposal Eq.) that takes into account the effect of the aspect ratio was devised.
We proposed a machine learning model and a formula for estimating the tortuosity of the porous structure. This study suggests that the tortuosity, which was assumed to be a function of only porosity, also has a correlation with the aspect ratio, and was able to predict the tortuosity in the negative electrode layer composed of flat graphite particles. In the future, it is necessary to confirm under more conditions and verify the validity.
Acknowledgment
This research was supported by Kyushu University Education and Research Center for Mathematical and Data Science, and Grants-in-Aid for Scientific Research on Innovative Areas, “Science on Interfacial Ion Dynamics for Solid State Ionics Devices” MEXT, Japan FY2019-2023.

References
[1] L. Shen et al., Chem. Eng. Sci., 62 3748–3755(2007)
[2] Y. LeCun et al., Lect. Notes Comput. Sci., 1681 319–345(1999)
[3] C. Cortes et al., Mach. Learn., 20 3 273–297(1995)
[4] G. Inoue et al., J. Power Sources, 342 476–488 (2017)
[5] R. R. Selvaraju et al., IEEE, 618–626(2017)

Figure 1