November 20, 2019

Optimization and prediction of microstructure properties for Lithium-Ion secondary batteries

Industry: Electronics | Software: pSeven | Company: SCSK


Over recent years, electrical vehicles (EV) become more and more popular. Lithium-ion secondary batteries, which are the core technology of EV, are characterized by the high energy density. These batteries are also commonly used for portable electronics and are growing in popularity for military and aerospace applications. 

Lithium-ion secondary battery is a battery that charges and discharges when lithium ions (represented by blue circles in Fig. 1) move between the positive and negative electrodes. The term “secondary” means that the battery can be used again after recharging.


Fig. 1. Battery operation principle

During discharge, the (positive) lithium ions move from the negative electrode (anode) to the positive electrode (cathode) through the electrolyte while the electrons flow through the external circuit in the same direction. When the cell is charging, the reverse occurs with the lithium ions, and electrons move back into the negative electrode in a net higher energy state. Battery voltage, energy density, life, and safety can drastically change depending on materials choice.

In order to efficiently use lithium-ion batteries for EV, their performance and capacity should be increased while saving weight.  Conductivity and diffusivity are the most important parameters that depend on battery material and microstructure. The objective is to maximize both of those parameters to increase the battery capacity and reduce losses.


In general, batteries are filled with particles and conductive aid (binder). Increasing the filling ratio of particles to conductive aid improves the electrical conductivity, but decreases the porosity and therefore decreases the diffusivity (Fig. 2), so there is a trade-off relationship. Thus, we have two contradictory targets to optimize in order to improve battery performance.


Fig. 2. Electrode composite material structure

Particle shape, orientation and binder contact angle are the other important parameters of the battery material, and may impact the battery properties. So, they should also be varied in the study, along with filing rates of particle and binder.

Investigation of material properties impact is possible by direct simulation of the microstructure using GeoDict. It is a material simulation software providing a qualitative and quantitative analysis of geometric and physical properties of materials.

This study consists of two stages: optimization and predictive modeling. Optimization goal is to maximize the electrical conductivity and diffusivity of the battery, thus improving overall performance. Predictive modeling goal is to build a high-accuracy approximation model to predict battery properties for any combination of parameters without using heavy simulation.

Optimization study

Simulation automation

In order to solve the optimization problem, we need to automate the simulation in GeoDict software. One of the benefits of using pSeven is the automation of optimization and predictive modeling processes by integrating external software and data into workflows using a convenient graphical interface. The automated simulation workflow consists of several blocks, each of them solving its own task (Fig. 3).


Fig. 3. pSeven workflow for optimization problem solution

The study of material microstructure in CAE software demands accurate meshing. So, the simulation takes about 2 hours per single point, which makes the optimization process very expensive.

Problem statement and method

We have 6 variables of microstructure varying to achieve the maximum of electrical conductivity and diffusion rate of the battery (Table 1, Fig. 4). 

Table 1. Optimizer configuration

  lower limit  upper limit 
Binder filling rate, % 1.0 20.0 
Particle packing rate, % 40.0  60.0
Particle size(X), μm 3.0e-6  20e-6 
Particle size (Y), μm 3.0e-6  20e-6 
Particle orientation 0.0 1.0 
Binder contact angle, deg 0.0  60.0 
Electrical conductivity, S/m Maximization   
Diffusion rate, %  Maximization   


Fig. 4. Material microstructure

Since the simulation problem requires a lot of computational resources, Surrogate-based optimization (SBO) method is used to drive the optimization process. SBO allows to set a budget of calculations and obtain the best solution possible within this limit. The budget was set to 120 points, and 14 optimal solutions were obtained as a result.

Optimization result

The optimization with two competing targets results in a set of different optimal configuration. Pareto frontier with details for three particular points is shown in Fig. 5.


Fig. 5.Optimization result

For these key points, the optimal value of Particle size_Y has its lower bound. Thus,  particles tend to be flat and align along the ions flow in all the optimal configurations (Fig. 6).


Variables Trade-off Structure with high electrical conductivity Structure with high diffusion rate
Binder filling rate 1.0  13.0 20.0
Particle size_X 15.0e-6 20.0e-6 20.0e-6
Particle size_Y 3.0e-6 3.0e-6 3.0e-6
Particle orientation_X
Binder contact angle 45  22  20 

Fig. 6. Optimal variables values for key points of Pareto frontier

Results analysis allows for the conclusion that the higher the binder filling rate is, the higher is the electrical conductivity, and the higher the binder contact angle is, the higher is the diffusivity. Trade-off analysis of Pareto frontier allows exploring all the optimal designs with maximum electrical conductivity and diffusivity to choose the one that is best suited for a particular application and conditions.

Predictive modeling study

Problem statement and method

As mentioned above, the simulation of a single point in GeoDict requires a lot of computational resources and time. In order to predict the battery properties faster, a CAE model can be replaced by an approximation model which is accurate enough and also much faster in evaluation. Such replacement enables massive studies of various parameters combinations and hides the complexity of the simulation model to allow the non-experts evaluating new designs.

We need data covering the evaluation range to build an approximation model, and this data should be accurate enough. If a training sample is extremely small, the predictive accuracy of the surrogate model will be reduced. Also, the low data accuracy makes it is difficult to accurately predict the actual response value even if the number of sample points is huge. However, it is expensive to obtain enough of high-accuracy points. On the other hand, simulations with a coarse mesh result in a big data sample but of low fidelity.

The solution is to combine the data of various fidelity in order to train a single approximation model with good accuracy. We will apply the Data Fusion method available in pSeven. Data Fusion is a highly powerful tool that contributes to predictive modeling techniques and handles datasets of variable fidelity (see more in pSeven documentation: Data Fusion).

In order to use DF, we will generate 30 points of high-fidelity with a fine mesh (about 2.0 h/time), and 120 points of low-fidelity with a coarse mesh (about 5.0 min/ time).

Design of experiments includes 6 variables of material structure and 2 objectives – electrical conductivity and diffusion rate – same as in the previous step (Table 2).

Table 2. Problem configuration

  lower limit  upper limit 
Binder filling rate, % 1.0 20.0 
Particle packing rate, % 40.0  60.0
Particle size(X), μm 3.0e-6  20e-6 
Particle size (Y), μm 3.0e-6  20e-6 
Particle orientation_X 0.0 1.0 
Binder contact angle, deg 0.0  60.0 
Electrical conductivity, S/m    
Diffusion rate, %     

The aim is to build a high-accuracy surrogate model by Data Fusion to predict battery properties.

Predictive modeling result

In order to show the increase in final accuracy, achieved with Data Fusion technique, we also trained approximation model for each dataset (low- and high-accuracy) separately (Fig. 7).


  Electrical conductvity (R2) Electrical conductvity (RMSE) Diffusion rate (R2) Diffusion rate (RMSE)
Only 30 high reliability data 0.08  1.74 0.63 0.07
Only 120 low reliability data 0.33 1.82 0.65 0.06
Data fusion model 0.88 0.50 0.96 0.02

Fig. 7. Data fusion model prediction results

Data Fusion technique allows obtaining a highly accurate approximation model based on data of various fidelity. Note that if only high fidelity data was used, the total simulation time to collect the sample would be at least twice as long.


We considered two scenarios:

a) optimization of the material microstructure to maximize the electrical conductivity and diffusivity of the battery

b) building a surrogate model for the fast prediction of those properties without using heavy simulation.

A time-consuming simulation was the main challenge of optimization part of the problem, so the Surrogate-Based Optimization technique was applied. The Pareto frontier of 14 optimal solutions was obtained with only 120 simulation runs.

In order to build an accurate approximation model and avoid excessive calculations, two data samples were used together: 30 high-fidelity points and 120 low-fidelity points. Thanks to Data Fusion technique in pSeven, an accurate approximation model can be trained using both samples. Data fusion model contains much less predictive errors compared to the models based on each data sample. Moreover, it takes much less simulation time to generate data than time needed for the high-fidelity data only.

Original article by Kenta Aoshima, Engineer, SCSK Corporation

October 8 | Toulouse, France

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