Causally Consistent Residual Learning for Lithium-Ion Batteries: Aging Compensation Without Parameter Re-Identification, Validated on Unseen NASA Randomized-Usage Cells

Battery management systems rely on equivalent-circuit models (ECMs) that become progressively wrong as the cell ages. Classical adaptive remedies — periodic parameter re-identification, extended Kalman filtering, or model-predictive control — all assume the controller can refit its model to the true plant. We propose a residual-learning alternative: the controller retains a fixed, possibly mismatched ECM (the K step) and learns a bounded nonlinear correction from a causally valid one-step-ahead prediction error (the R step). The correction is trained online by closed-form ridge regression on an 8-feature representation that includes RC polarization, SOC, SOH, and thermal transients, requires no back-propagation, and trains in under 1 ms per update. We evaluate the framework on a digital twin calibrated from real NASA degradation trajectories (OCV–SOC tables, SOH evolution, and resistance growth) for four cells drawn from four distinct NASA Ames Randomized Battery Usage profiles. Across 960 Monte-Carlo simulations (4 cells × 3 scenarios × 4 methods × 20 trials), K-R reduces peak voltage overshoot by 23.8–30.0 % at 25 °C SOH = 0.80 aged cells, 15.3–16.8 % at 5 °C cold-start, and scales consistently with mismatch severity, all with p < 10⁻³. The residual is shown to be strongly structured (lag-1 autocorrelation 0.90–0.99), confirming that mismatch is learnable rather than stochastic. A two-fold cross-cell validation (reservoir weights trained on two cells, frozen, tested on two unseen cells) degrades performance by only 0.1–2.7 mV in every one of 12 test configurations, confirming that the residual structure is transferable across NASA usage profiles. An ablation shows the benefit comes from causally correct residual definition and feature engineering — not from network nonlinearity — motivating a simpler linear-ridge deployment. We also report an honest negative result: K-R over-corrects in fresh cells at moderate temperature, and we propose a gating rule keyed to |eK| or estimated SOH to suppress the correction in low-mismatch regimes. The evaluation is a digital-twin controller-in-the-loop simulation; hardware-in-the-loop validation is identified as the natural next step.