⚡ electrical engineering

Thermo-Relational State Inference for Lithium-Ion Battery SOC Estimation under Dynamic Thermal Excitation

This paper proposes the Thermo-Relational State Inference Network (TRSI-Net), a novel deep learning framework that significantly improves lithium-ion battery state-of-charge estimation under dynamic thermal excitation by explicitly modeling how thermal evolution alters the historical relevance of terminal measurements through thermally conditioned recalibration and relational memory attention.

Original authors: Yicheng Li, Hui Zeng, Jiayan Xia, Yaqing Shi, Pin Liu

Published 2026-09-07

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CC BY 4.0

Original authors: Yicheng Li, Hui Zeng, Jiayan Xia, Yaqing Shi, Pin Liu

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Modern life runs on stored energy. From the electric cars that glide silently through city streets to the massive battery banks that stabilize the power grid, lithium-ion batteries are the silent engines of our electrified future. However, these batteries are not simple containers of power; they are complex chemical systems that change their behavior depending on how hot or cold they are. To use them safely and efficiently, a computer system inside the device must constantly know exactly how much energy remains. This is called the "state of charge." If the system guesses wrong, a car might stop unexpectedly, or a battery could be damaged by being drained too far. The challenge is that the relationship between what we can measure—like the voltage at the battery's terminals—and the actual energy inside is not fixed. It shifts and warps as the battery heats up during use or cools down in the winter.

For years, engineers have tried to build better ways to track this energy level. Many approaches rely on looking at the battery's history: what happened a second ago, a minute ago, or an hour ago. But these methods often treat the battery's temperature as a simple background number, like a static label on a box. They fail to realize that the temperature itself is a moving target that changes how the battery's past behavior relates to its present state. A specific voltage reading today might mean something completely different than that same voltage reading yesterday if the battery was at a different temperature. This disconnect becomes critical when a battery is subjected to dynamic thermal excitation, a fancy way of saying it is being heated and cooled rapidly while under heavy load, such as during a fast drive or a sudden burst of power.

A team of researchers has developed a new method to solve this specific problem, creating a system that treats the battery's thermal history as a living, breathing part of the calculation. Instead of just adding the current temperature to a list of inputs, their new system, which they call a Thermo-Relational State Inference Network, actively rewrites the meaning of electrical measurements based on how the temperature is changing. It asks two questions for every piece of data: what is the temperature doing right now, and how different is this moment from the moments that came before? By answering these questions, the system can understand that two identical electrical signals might represent different amounts of energy if they occurred under different thermal conditions.

The researchers tested this new approach using a real-world driving profile known as LA92, which mimics the stop-and-go nature of city driving. They used a specific type of battery cell, the Panasonic NCR18650PF, and subjected it to a changing thermal environment where the surrounding air temperature shifted from about 10 degrees Celsius to 25 degrees Celsius. In this test, the battery's surface temperature and the air temperature were measured separately, allowing the system to see exactly how the battery reacted to the changing heat. The goal was to see if the new system could track the battery's energy level more accurately than existing methods when the thermal conditions were constantly in flux.

The results were striking. The new system tracked the battery's energy level with an average error of just 0.47 percent. To put this in perspective, if you were trying to guess the weight of a 100-kilogram object, this system would be off by less than half a kilogram. In comparison, the strongest existing method used for this test made errors more than twice as large, missing the mark by an average of 1.24 percent. The new system also reduced the size of its biggest mistakes by 65 percent compared to the previous best approach. This means that not only was the average guess better, but the system also avoided the large, sudden jumps in error that can happen when a battery's temperature changes rapidly.

What makes this achievement possible is a shift in how the computer thinks about time and heat. The researchers built a system that does not just look at the battery's past in a straight line. Instead, it creates a "thermal relation field," a mental map that connects every moment in the battery's history to every other moment based on two factors: how much time has passed and how different the temperature was at those two times. If the battery was hot ten minutes ago and is cold now, the system understands that the data from ten minutes ago is less relevant to the current moment than if the temperature had stayed the same. This allows the system to weigh the importance of past events dynamically, rather than treating all past data as equally useful.

The system also includes a mechanism to adjust the electrical signals themselves before they are analyzed. As the temperature changes, the battery's internal chemistry shifts, making the voltage and current readings behave differently. The new system uses the current temperature, how fast the temperature is changing, and the difference between the battery's surface and the surrounding air to automatically recalibrate these electrical signals. It essentially translates the raw numbers into a language that makes sense for the current thermal environment. This happens in real-time, ensuring that the system is always interpreting the data correctly for the conditions it is facing.

To prove that these specific features were the reason for the success, the researchers ran a series of tests where they removed one part of the system at a time. When they removed the ability to compare thermal differences between past and present, the error rate jumped significantly. When they replaced the complex temperature adjustment with a simpler, one-way scaling method, the system became less stable and made larger mistakes. These tests confirmed that the improvement did not come from just having more data or a bigger computer model, but from the specific way the system linked thermal changes to historical relevance. The system works because it explicitly models the fact that the meaning of a battery's electrical signal depends on the thermal story that led up to it.

The study was conducted using data from a publicly available dataset collected at the University of Wisconsin–Madison, ensuring that the results are based on real-world measurements rather than computer simulations. The researchers were careful to test their system on a driving profile that was completely separate from the data used to train it, proving that the system could generalize to new situations. While the test was limited to a specific type of battery and a moderate range of temperatures, the findings offer a clear path forward for battery management systems. By acknowledging that the past is not just a sequence of events but a sequence of changing thermal states, this new approach provides a more robust and accurate way to monitor the energy stored in our most critical devices. It suggests that the future of battery management lies not in ignoring the heat, but in understanding how that heat reshapes the story of the battery's life.

Technical Summary: Thermo-Relational State Inference for Lithium-Ion Battery SOC Estimation under Dynamic Thermal Excitation

Problem Statement
Accurate State-of-Charge (SOC) estimation for lithium-ion batteries under dynamic thermal excitation is complicated by the time-varying relationship between terminal measurements (voltage, current) and the latent charge state. Existing data-driven approaches typically treat ambient temperature as a static input vector or a simple feature reweighting mechanism. However, these methods fail to explicitly model how thermal evolution alters the pairwise historical relevance of observations. Under moving thermal boundaries, two measurements with similar electrical characteristics may correspond to different battery states if their thermal conditions differ, and historical observations separated by the same temporal distance may provide different information if recorded under different thermal states. Current attention-based models often rely on generic temporal or feature similarity, leaving the effect of thermal evolution on historical dependence largely implicit.

Methodology: TRSI-Net
The authors propose the Thermo-Relational State Inference Network (TRSI-Net), which formulates SOC estimation as thermally conditioned relational inference. The architecture operates on a causal historical window of electrothermal measurements and consists of four sequential stages:

Thermally Conditioned Affine Recalibration (TCAR): This module adapts the latent electrical representation of each time step to its local thermal condition. It utilizes a compact thermal-state descriptor comprising ambient temperature ( $T_a$ ), its temporal variation ( $\Delta T_a$ ), and the surface-to-ambient temperature difference ( $T_s - T_a$ ). TCAR applies a bounded scaling factor and an additive translation term to the latent electrical features while preserving the original measurements via a residual projection. This allows the model to adjust feature sensitivity and operating levels without requiring an explicit electrothermal model.
Thermal Relation Field (TRF): To model historical dependence, TRF defines a pairwise relation between any two time steps $i$ and $j$ in the history. This relation is a composite of two components: relative temporal separation and the pairwise thermal-state discrepancy (the difference between their thermal-state descriptors). This ensures that observations at the same temporal distance receive different relational weights if their thermal conditions differ.
Thermo-Relational Memory Attention (TRMA): This stage integrates the TRF into a single-head scaled dot-product attention mechanism. The attention score combines content-based feature compatibility with the pairwise relation term from TRF. A causal mask ensures that future observations are excluded. The result is a sequence of memory states where each position aggregates information from the history based on both feature similarity and thermal comparability.
Global Relational Readout (GRR): Instead of relying on a single final state (as in standard RNNs) or a second query-based attention stage, GRR performs a temporal mean aggregation over the entire relation-enhanced memory sequence. This pooled representation undergoes a residual feed-forward transformation to refine the global memory before projecting it to the final SOC estimate via a sigmoid activation.

Key Contributions
The paper identifies three principal contributions:

Thermally Conditioned Representation: A mechanism (TCAR) that continuously adjusts latent electrical representations based on a compact thermal descriptor, accounting for the changing meaning of electrical measurements under dynamic thermal boundaries without explicit electrothermal modeling.
Thermo-Relational Formulation: A novel approach (TRF + TRMA) that explicitly models historical dependence as a function of both temporal separation and thermal-state discrepancy, allowing thermal evolution to directly influence temporal information propagation.
Lightweight Global Readout: A strategy (GRR) that aggregates distributed information across the entire historical window after relation modeling, avoiding the need for additional selective retrieval stages while retaining information that may not be concentrated at the terminal state.

Experimental Results
The framework was evaluated on the Panasonic NCR18650PF dataset using the LA92 driving profile as a held-out test trajectory with a dynamic ambient temperature transition from approximately 10°C to 25°C.

Performance: TRSI-Net achieved a Mean Absolute Error (MAE) of 0.47%, a Root Mean Square Error (RMSE) of 0.56%, and an $R^2$ of 99.94%.
Comparison: Relative to the strongest baseline (DA-GRU), TRSI-Net reduced MAE by 62.1% and RMSE by 65.0%. It also outperformed Transformer and A-CNN-LSTM architectures significantly.
Ablation Study: Removing the thermal-discrepancy term from the relation field caused the largest performance degradation (MAE increased to 0.734%), confirming that explicit pairwise thermal-state modeling provides information beyond chronological separation alone. Replacing TCAR with simple multiplicative gating or bypassing the relational memory also resulted in significant error increases, validating the necessity of both affine recalibration and thermo-relational memory formation.

Significance and Claims
The authors claim that the study demonstrates that explicitly modeling thermal-state-dependent historical relationships improves SOC tracking under dynamic thermal excitation. The results support the premise that under moving thermal boundaries, historical relevance is not determined by temporal separation alone. The proposed formulation remains fully causal, making it suitable for online Battery Management System (BMS) applications. The authors note limitations, including validation restricted to a single cell platform and a specific temperature range, and acknowledge the quadratic complexity of the pairwise relation field. However, within these bounds, the work presents a coherent route to robust SOC estimation by integrating thermal conditioning into both feature representation and historical relation modeling.

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