State of Health Estimation of Batteries Using a Time-Informed Dynamic Sequence-Inverted Transformer

TL;DR

The paper tackles battery State of Health (SoH) estimation from irregular, variable-length discharge cycles by defining $SoH(t) = \frac{C_{current}(t)}{C_{rated}}$ and proposing Time-Informed Dynamic Sequence Inverted Transformer (TIDSIT). TIDSIT processes raw multivariate time-series data with continuous-time embeddings, data variate embeddings, temporal attention on padded sequences, and a SoH history embedding within a transformer encoder to produce end-to-end SoH estimates. On the NASA Ames battery degradation dataset, it achieves over a 50% reduction in prediction error (RMSE $=0.0047$, RMSE% $=0.58\%$) over strong baselines and transformer variants, demonstrating robust performance under irregular sampling and varying cycle lengths. The approach offers a scalable, feature-free solution for batteries and has potential applicability to other irregular time-series health-monitoring tasks.

Abstract

The rapid adoption of battery-powered vehicles and energy storage systems over the past decade has made battery health monitoring increasingly critical. Batteries play a central role in the efficiency and safety of these systems, yet they inevitably degrade over time due to repeated charge-discharge cycles. This degradation leads to reduced energy efficiency and potential overheating, posing significant safety concerns. Accurate estimation of a State of Health (SoH) of battery is therefore essential for ensuring operational reliability and safety. Several machine learning architectures, such as LSTMs, transformers, and encoder-based models, have been proposed to estimate SoH from discharge cycle data. However, these models struggle with the irregularities inherent in real-world measurements: discharge readings are often recorded at non-uniform intervals, and the lengths of discharge cycles vary significantly. To address this, most existing approaches extract features from the sequences rather than processing them in full, which introduces information loss and compromises accuracy. To overcome these challenges, we propose a novel architecture: Time-Informed Dynamic Sequence Inverted Transformer (TIDSIT). TIDSIT incorporates continuous time embeddings to effectively represent irregularly sampled data and utilizes padded sequences with temporal attention mechanisms to manage variable-length inputs without discarding sequence information. Experimental results on the NASA battery degradation dataset show that TIDSIT significantly outperforms existing models, achieving over 50% reduction in prediction error and maintaining an SoH prediction error below 0.58%. Furthermore, the architecture is generalizable and holds promise for broader applications in health monitoring tasks involving irregular time-series data.

Figures (3)

• Figure 1: Visualization of five randomly selected discharge cycles showing raw input features—voltage (V), temperature (°C), and current (A)—plotted against time. The figure highlights two key characteristics of real-world battery data: (1) irregular sampling intervals within each cycle, and (2) variable sequence lengths across cycles. Notably, later cycles become progressively shorter, illustrating the effect of battery degradation on discharge duration over time.
• Figure 2: Schematic of the proposed Time-Informed Dynamic Sequence Inverted Transformer (TIDSIT) architecture for battery SoH estimation. Each input consists of a multivariate, irregularly sampled discharge cycle, represented as a sequence of sensor readings—voltage, current, and temperature—along with corresponding timestamps. To accommodate varying sequence lengths, raw features are first passed through a temporal attention block with padding masks, allowing the model to handle variable-length inputs without information loss. The output is processed by a data variate embedding layer that learns a distinct representation for each sensor channel. In parallel, continuous-time embeddings are computed based on the non-uniform timestamps and added to the variable-specific representations, preserving fine-grained temporal structure. A learned SoH history embedding—derived from the SoH values of the past few discharge cycles—is then concatenated with the fused output. The resulting enriched sequence is passed through a transformer encoder where multi-head self-attention captures both intra-step interactions and long-range dependencies. Finally, the output is aggregated and passed through a feed-forward network and a projection head to yield the predicted scalar SoH for the current cycle.
• Figure 3: Predicted versus ground truth SoH values for the B0007 battery (unseen during training). (a)–(d) compare the SoH prediction performance of different transformer variants: (a) TIDSIT, (b) Reformer, (c) Flowformer, and (d) Informer. The figure demonstrates the model’s generalization capability by accurately tracking the degradation trend on unseen test data.TIDSIT demonstrates the best alignment with the true degradation trajectory, indicating superior generalization to real-world battery behavior with irregular sampling and variable cycle lengths.