Physics Instead of AI Black Box AI Determines the Health Status of Lithium-ion Batteries

How can the health status of a lithium-ion battery be determined precisely without blindly trusting AI? A new approach combines artificial intelligence with physical aging conditions and significantly reduces the prediction error compared to purely data-driven models.

The state of health of a lithium-ion battery cannot be directly measured with a sensor. At the same time, the state of health determines how much energy a battery can still store, what performance it delivers, and when it should be replaced. Researchers have therefore developed an AI method that recognizes aging patterns from charging data but does not rely exclusively on training data. Physically motivated boundary conditions are intended to prevent the model from delivering mathematically plausible but unrealistic results for an aging battery.

Why the State of Health is so Difficult to determine

In a new lithium-ion cell, the available and original capacity largely correspond to each other. However, with increasing use, the cell undergoes irreversible changes. The solid electrolyte interphase grows, active lithium is lost, electrode materials degrade, electrolyte is consumed, and internal resistance increases. As a result, the available capacity and performance of the battery decrease.

The state of health, or SOH for short, typically describes this aging state as the ratio between the currently available and the original or nominal capacity. This value is of great importance for a battery management system. It plays a role, for example, in lifetime prediction, fault detection, and assessment of potential second use.

The problem is that the SOH cannot be measured directly. A battery management system has parameters such as current, voltage, and temperature. However, the health status must first be derived from these signals.

Conventional methods for SOH determination each have specific disadvantages. Capacity tests can provide a reliable reference value but require a complete charge and discharge cycle. Electrochemical impedance spectroscopy provides information about ohmic resistance, charge transfer, and diffusion processes but requires additional measurement technology. Therefore, such methods are only limitedly suitable for continuous state determination in vehicles or other battery systems.

When AI Learns Aging from the dData

An alternative is data-driven methods. Instead of mathematically modeling all electrochemical processes within the cell, machine learning models search for correlations between measurable signals and the actual SOH.

Deep learning methods, in particular, offer interesting possibilities for this. Recurrent networks like LSTM or GRU can capture temporal dependencies within an aging sequence. Transformers, on the other hand, are suitable for modeling complex relationships between different features.

However, this creates a new problem: a purely data-driven model initially knows nothing about the physics of a battery. It optimizes its parameters to best reproduce the training data. Measurement noise, changed operating conditions, or local capacity regeneration can thus be interpreted as relevant aging effects. Particularly with limited training data, there is a risk of overfitting and predictions that fit the dataset but are physically implausible. This is exactly where the work of Yanyu Huang, Jianwei Huang, Wensheng Yu, and Xiaoxian Yang comes into play.

Five Features Reveal the Battery's Condition

The researchers do not limit their approach to the sheer number of charge cycles. Instead, they analyze changes during the charging process. For this, five health indicators are derived from the constant current/constant voltage charging and the incremental capacity curve.

These include the duration of the constant current charging phase, the average voltage during this phase, the peak value of the IC curve, the voltage at this IC peak, and the average IC value. These parameters capture different aspects of battery aging.

With increasing aging, a cell tends to reach its final charging voltage during the constant current phase earlier. Consequently, the constant current charging time decreases. At the same time, the voltage level shifts upward due to increasing polarization.

The IC curve also changes. Its characteristic peak decreases and broadens, while its position shifts to higher voltages. The attenuation of the peak is associated, among other things, with the loss of active material and a decreasing reversible reaction capacity. In this way, the charge and IC curves provide information about changes that correlate with the aging state of the cell.

The limitation to five parameters is deliberately chosen. Too many similar features would create additional redundancy and multicollinearity.

Transformer and GRU Take on Different Tasks

For the analysis, the researchers combine two different deep learning architectures. The Transformer primarily examines the global relationships between the five health indicators. For instance, it is meant to detect how shortened charging times, changes in voltage, and the shape of the IC curve develop together.

The GRU, on the other hand, takes on the temporal perspective. It processes the aging sequence and is tasked with remembering how the relevant features change over successive cycles.

The authors themselves describe this division of labor as two different questions: the Transformer determines which health features vary together, while the GRU captures how these changes develop over the course of the cycles.

The model uses a sliding window of three consecutive cycles for this task. The health indicators are standardized and then processed by the two network branches.

Cross-Attention Connects Both Perspectives

The results of the Transformer and GRU are not simply concatenated. Instead, the researchers use a cross-attention mechanism. In this, the representation generated by the Transformer serves as the query, while the GRU representation provides the key and value.

Simply put, the Transformer can use the current combination of health indicators to selectively retrieve the information from the temporal aging history that is particularly relevant to the current state. A downstream regression stage then calculates the SOH from this.

Physics intervenes in the training

PI stands for "Physics-Informed." The researchers aim to incorporate physical knowledge about battery aging into the training of the neural network. For this purpose, the SOH is not merely considered an unknown function of the cycle number. Instead, it depends on both the cycle or time and the determined health indicators. Additionally, the authors introduce a second relationship for the temporal change rate of the SOH.

Since the actual aging dynamics of a battery are very complex and change, for example, with cell type and aging phase, this function is also not analytically predefined. Instead, an additional neural network approximates the degradation dynamics.

During training, the SOH change predicted by the main network and the rate of change determined by the additional dynamics model are compared. The difference generates an additional error term. This prompts the main model not only to correctly predict individual SOH values but also to produce a plausible local progression of aging.

This approach significantly differs from a purely data-driven method: the quality of a solution during training is not determined solely by the gap between prediction and measurement.

A Battery Does Not Age Backward

A second constraint concerns the fundamental direction of aging. Over a longer period, the available capacity of a lithium-ion battery generally decreases. A model whose predicted SOH constantly jumps between higher and lower values would therefore produce a dubious result.

A strictly monotonically decreasing curve would also be problematic. In real measurement series, local capacity recoveries can occur, for example, due to temperature changes, rest periods, or measurement effects.

The authors, therefore, apply a weak monotonicity condition. If the predicted SOH rises between two consecutive cycles, this is penalized with an additional error term during training. However, such increases are not completely prohibited.

The entire optimization thus consists of three components: the classic data error, an error for the consistency of the degradation dynamics, and the weak monotonicity condition. The physical conditions are required exclusively during training. During the subsequent SOH determination, the model only needs the health indicators and the cycle index.

Three Datasets Put the Model to the Test

For validation, the researchers use six batteries from three public datasets from Oxford, CALCE, and NASA. The selection is particularly interesting because their aging processes differ significantly. The two Oxford cells each cover more than 8,000 cycles and show a comparatively steady decline in SOH. The CALCE cells each include 620 cycles and exhibit more pronounced nonlinear changes. The NASA cells, on the other hand, cover 166 cycles, show faster degradation, and display local capacity regeneration.

For regular experiments, the researchers use the first 40% of the cycles as training data and the remaining 60% for testing. Ten percent of the training portion is further reserved for validation. Comparisons include a pure GRU, a Transformer, the combined CTG model without physical constraints, and the complete PI-CTG.

Physics-Informed AI Significantly Reduces the Error

The combination of different approaches is reflected in the results. The pure GRU achieves an average RMSE of 0.0228 across the six batteries studied. For the Transformer, this decreases to 0.0199. When Transformer and GRU are combined into the CTG model via cross-attention, the value is reduced to 0.0132.

With the additional physical constraints, PI-CTG achieves an average RMSE of 0.0072. The average MAPE is 0.7768%, and R² is 0.9730. This means PI-CTG reduces the average RMSE by around 68% compared to GRU, around 64% compared to the Transformer, and nearly 45% compared to the already combined CTG model.

Even the individual values of the six studied batteries remain below 0.01 RMSE. The model is capable of replicating relatively consistent aging curves as well as nonlinear trends and local capacity regeneration.

An ablation analysis also supports the assumption that not only the more complex network is responsible for the improvement. In the examined NASA dataset B0006, CTG without physical conditions achieves an RMSE of 0.0156. When only the condition for degradation dynamics is added, it drops to 0.0101. The monotonicity condition alone reduces it to 0.0115. With both conditions and a weighting of 0.5 each, the model achieves 0.0091. A weighting of 0.7 for degradation dynamics and 0.3 for monotonicity further improves the value in this experiment to 0.0081.

Does the Model also Work with Unknown Cells?

For practical application, it is not sufficient to predict the aging curve of a cell whose previous cycles were already part of the training. Therefore, the authors additionally conduct leave-one-battery-out experiments within the respective datasets.

For example, one Oxford cell is used for training and the second for testing. The researchers apply the same principle to CALCE and NASA.

For Oxford, the model achieves an RMSE of 0.0038 and an R² of 0.9951. For CALCE, the RMSE is 0.0075 and R² is 0.9907. For the NASA cells, the RMSE rises to 0.0110, while R² is 0.9905. The authors attribute the higher error, among other factors, to the stronger capacity regeneration effects and differences between the NASA cells.

The results thus show, at least within the same dataset, that the learned relationships can be transferred to a cell not previously used for training.

Which Metrics Are Actually Crucial?

However, even with a good prediction, a typical problem of neural networks remains: Why does the model arrive at a particular result? To at least partially open this black box, the researchers use SHAP. This allows for an estimation of the contribution of individual input features to the model's prediction.

Across all the batteries studied, the constant current charging time, the IC peak, and the average IC value play a particularly important role. However, their ranking differs between cells. For example, in an Oxford cell, the constant current charging time contributes the most, while in a NASA cell, the average IC value dominates.

The difference between correlation and actual contribution to the model is particularly interesting. A feature can have a strong correlation with SOH yet provide only a relatively small additional informational contribution. The reason lies partly in the strongly correlated health indicators. For instance, the correlation between constant current charging time and average IC value is around 0.94. If both contain similar information about aging, the model can obtain a large portion of it from just one of the features.

The SHAP values should therefore not be understood as a ranking of electrochemical aging mechanisms. They describe which information the specific model uses for its prediction.

From Research Model to Battery Management System

The results demonstrate the potential of the approach but also its current limitations. Six batteries from established research datasets were examined. A real battery system faces significantly greater variations in cell chemistry, temperature, charging power, usage, and cell deviation.

This is exactly where the authors Yanyu Huang, Jianwei Huang, Wensheng Yu, and Xiaoxian Yang see further research needs. In the future, factors such as temperature, internal resistance, and C-rate should be considered as additional operating variables. Additionally, transfer learning methods aim to improve the transfer between different material systems as well as charging and discharging protocols. Model compression and online updates will ultimately enable practical implementation in battery management systems. A third option arises between detailed electrochemical models on one hand and purely data-driven neural networks on the other. The neural network is allowed to learn complex relationships from measurement data on its own but is constrained during training by boundaries derived from the known aging behavior of the battery.

This means that physics is not replaced by artificial intelligence. It takes on a corrective role, preventing a data-driven model from losing sight of physical reality in the search for the mathematically best solution.