Building a Simple Digital Twin for Lithium‑Ion Batteries Using Python and Neural Networks

This article explains how to create a simple yet practical digital twin of a lithium‑ion battery using Python, Keras neural networks, and Plotly for visualization.

1. Virtual Systems and Digital Twins

Digital twins are a key component of Industry 4.0, replicating physical assets in a virtual world to simulate their dynamics. By modeling subsystems such as pumps, valves, and sensors, a virtual system can mimic the real system, allowing changes, performance evaluation, or scenario prediction.

2. Lithium‑Ion Battery Digital Model

Lithium‑ion batteries are critical for portable devices, electric vehicles, and grid storage, but they degrade over charge‑discharge cycles. An empirical degradation model can describe capacity loss, where the remaining capacity L is a function of cycle count, discharge time, depth of discharge, average state of charge, and temperature.

The model parameters include a linear degradation rate fd that depends on discharge time t, depth of discharge δ, average state of charge σ, and cell temperature Tc.

3. Experimental Data

The model is validated against NASA Ames Prognostics Center battery aging data (cell 5). Capacity versus cycle number is plotted and compared with the physical model.

4. Building a Hybrid Digital Twin

A hybrid approach combines the physics‑based model with a neural network trained on the experimental data to correct model errors.

Define inputs and outputs:

#Define inputs and outputs

# input: the simulation capacity

X_in = (dfb['C. Capacity'])

# output: difference between experimental values and simulation

X_out = (dfb['Capacity']) - (dfb['C. Capacity'])

X_in_train, X_in_test, X_out_train, X_out_test = train_test_split(X_in, X_out, test_size=0.33)

Simple neural network architecture:

model = Sequential()

model.add(Dense(64, activation='relu', input_shape=(1,)))

model.add(Dense(32, activation='relu'))

model.add(Dense(1))

Training configuration:

epochs = 100

loss = 'mse'

model.compile(optimizer=SGD(learning_rate=0.001), loss=loss, metrics=['mae'])

history = model.fit(X_in_train, X_out_train, shuffle=True, epochs=epochs, batch_size=20, validation_data=(X_in_test, X_out_test), verbose=1)

After training, the neural network predicts the residual between the physics model and the measured data, and the corrected twin is obtained:

# Our digital twin by improving our model with experimental data

X_twin = X_in + model.predict(X_in).reshape(-1)

The resulting hybrid digital twin more accurately follows the observed capacity degradation, as shown in the comparison plot.

5. Prediction

The hybrid twin can be used to predict future battery performance and guide operational decisions.

6. Conclusion

Digital twins are an emerging topic in Industry 4.0. This tutorial shows how a minimal Python implementation can create a digital twin, and how incorporating experimental data yields a hybrid model that requires less data than a pure machine‑learning approach while achieving higher accuracy.