State of Health Algorithms

In simple terms the SOH of the cell in terms of capacity can be estimated by calculating the maximum capacity of the cell when fully charged and dividing this by the rated charged capacity held by the system. This maximum fully charged capacity would be best established on a slow charge when the cell is charged from an initially low SOC point to it’s maximum voltage.

The difficulty is that this needs to account for temperature, charge rate and accurate SOC estimation.

EV manufacturers like to calculate SOH using an equation of this form:

SOH = A x DOD + B x Rate + C x Environment Temperature + D x Calendar Life

This is quite complicated in terms of establishing the constants for each term.

We like to find the 50% SOC OCV, slow charge to 100% SOC, using charged capacity / 50% Initial Capacity to get the SOH.

Jerry Wan, Battery Expert at Shenzhen Mushang Electronics Co., Ltd

Direct Measurement and Experimental Methods

These methods involve directly assessing the physical and electrical properties of the battery to determine its degradation, usually under controlled laboratory conditions.

Capacity Measurement: Evaluates the ratio of the battery’s maximum available charge to its nominal capacity by fully charging and discharging the battery under specific conditions.
Internal Resistance and Impedance: As a battery ages, its internal resistance increases. Methods like pulse testing or Electrochemical Impedance Spectroscopy (EIS) measure resistance and impedance across different frequencies to capture degradation mechanisms like solid electrolyte interphase (SEI) growth.
Coulomb Counting: Measures the total charge transferred in and out of the battery, though it requires periodic recalibration to prevent error accumulation over time.
Indirect Experimental Indicators: Techniques like Incremental Capacity Analysis (ICA) and Differential Voltage Analysis (DVA) analyze charge-discharge curves to pinpoint chemical changes, such as the loss of active materials or lithium ions. Emerging methods also analyze mechanical expansion force and differential thermal voltammetry.

We have to note that there is no direct measurement of State of Health, all methods are estimations based on what we can measure. Noise in these measurements just increase the errors in the estimations. Hence controlled laboratory conditions are required to get the best out of these techniques.

Model-Based Methods

These methods rely on mathematical and physical representations to simulate the internal behavior of the battery.

Electrochemical Models (EMs): Models like the Pseudo-Two-Dimensional (P2D) or Single Particle Model (SPM) use differential equations to explicitly simulate lithium-ion transport, electrochemical reactions, and internal degradation. They are highly accurate but computationally heavy.
Equivalent Circuit Models (ECMs): These simplify the battery’s dynamics into an electrical circuit using resistors, capacitors, and voltage sources. They are much less computationally intensive and are widely used for real-time monitoring.
Statistical Filters: Algorithms like the Kalman Filter (KF), Extended Kalman Filter (EKF), and Particle Filter (PF) are often paired with battery models to recursively update state estimations in real-time, correcting prediction errors by adapting to new measurements.

Data-Driven Methods

Instead of relying on physical models, these approaches use historical and real-time operational data (like voltage, current, and temperature) to learn the complex, non-linear relationships that dictate battery aging.

Traditional Machine Learning: Algorithms such as Support Vector Machines (SVM), Random Forests (RF), and Gaussian Process Regression (GPR) are highly effective at providing accurate estimations when dealing with small or noisy datasets.
Deep Learning: Advanced neural networks, including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and Gated Recurrent Units (GRU), excel at capturing long-term dependencies in sequential time-series data, making them ideal for full-lifecycle capacity predictions.
Unsupervised Learning: Methods like Principal Component Analysis (PCA) and K-means clustering are used to compress high-dimensional data, reduce noise, and identify hidden degradation patterns without requiring labeled training data.

Hybrid and Fusion Methods

Because every standalone method has distinct weaknesses—such as the high computational cost of EMs or the “black-box” nature of data-driven methods—hybrid methods combine multiple techniques for superior results.

Multi-Model Fusion: Integrates multiple physical models (e.g., thermal, aging, and electrical models) or combines multiple machine learning models together (e.g., a CNN for feature extraction paired with an LSTM for sequence prediction) to improve robustness.
Physics-Informed Machine Learning: Approaches like Physics-Informed Neural Networks (PINNs) embed fundamental physical constraints (like Fick’s laws of diffusion) directly into the neural network’s learning process. This guarantees that the machine learning outputs obey physical laws, achieving high accuracy with significantly less training data than purely data-driven models.