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A Framework for Discharge Time Prediction of Energy Storage Units Based on Coupled Dynamics and Multi-Factor Aging Models

Jiaye Yang, Hansheng Su, Wangzi Zhu

arXiv:2609.11086v1cs.CE

TL;DR

Existing approaches have limited joint representation of load, electrical, thermal, and aging behavior in remaining-runtime prediction. This paper couples these factors in a physically interpretable TTE framework; chronological hold-out testing reports smartphone and battery-aging errors, while broader validation remains necessary.

  • Problem

    Existing methods have limitations in jointly representing load-driven power, electrical behavior, thermal dynamics, aging-adjusted capacity, and remaining discharge time.

    Source: §I · p. 1

  • Method

    The framework combines usage-driven load-power decomposition, electrical closure, semi-empirical aging, and coupled SOC–temperature dynamics for TTE prediction.

    Source: §I · p. 1

  • Results

    Smartphone TTE MAPE was 4.81 ± 0.61%; the average-power baseline had 12.40% MAPE, and NASA B0005 capacity-loss RMSE was 0.031 Ah.

    Source: WINDOWS REPEATED UNTIL DEPLETION) · p. 5, §V · p. 6

  • Takeaways & Limitations

    The results demonstrate feasibility and interpretability of the framework for the investigated smartphone session and battery-aging case study.

    Source: §I · p. 1, §V · p. 6

    Broader validation is needed; the aging model was evaluated using one public cell, and the electrical and thermal models use linear OCV–SOC, constant efficiency, and a lumped thermal node.

    Source: §V · p. 6

Abstract

from arXiv · show

This paper presents a physically interpretable framework for predicting time to empty (TTE) in portable embedded systems. The framework couples usage-driven load-power decomposition, electrical power-voltage-current closure, a semi-empirical aging model, and SOC-temperature dynamics. Smartphone telemetry is mapped to battery current through an interpretable load model and conversion-efficiency correction. Battery capacity loss is modeled by combining Arrhenius temperature dependence, SEI diffusion behavior, and cycle-related power-law degradation. The coupled dynamic model then predicts TTE under different initial SOC values, ambient temperatures, and usage profiles. Chronological hold-out evaluation on a 6.9-h smartphone discharge session yielded a current RMSE of 0.0095 $\pm$ 0.0006 A, a temperature RMSE of 2.93 $\pm$ 0.24$^\circ$C, and a TTE MAPE of 4.81 $\pm$ 0.61%. Evaluation on NASA cell B0005 produced a capacity-loss RMSE of 0.031 Ah. Baseline, ablation, and counterfactual analyses further illustrate the contributions of thermal and aging corrections and the relative influence of load features. The results demonstrate the feasibility and interpretability of the proposed framework, while broader validation across devices and batteries remains necessary.

I. INTRODUCTION

The paper addresses the challenge of jointly modeling usage-driven power, electrical behavior, thermal dynamics, aging-adjusted capacity, and remaining discharge time. It proposes a continuous-time framework that links these factors to predict time to empty.

I. INTRODUCTION

  • The framework integrates load-power decomposition, electrical power–voltage–current closure, semi-empirical aging, and coupled SOC–temperature dynamics to predict time to empty.It is evaluated using smartphone discharge telemetry and NASA B0005 aging data, with broader cross-device and cross-battery validation still needed.Source: §I · p. 1

II. RESEARCH ON MOBILE PHONE BATTERY DEGRADATION

  • Prior work describes smartphone power by component and studies battery state and degradation, but often treats load, electrical, thermal, and aging behavior separately.The paper identifies limited joint representation of these factors and remaining discharge time as the research gap.Source: §I · p. 1, §II · p. 1

III. BATTERY 𝑆𝑆𝑆𝑆𝑆𝑆(𝑡𝑡) CONTINUOUS TIME MECHANISM

  • The proposed continuous-time modeling process links observable behavior to load power, battery power, current and terminal voltage, SOC change, and TTE.This closed-loop sequence is presented as the basis for a mechanism-driven, falsifiable battery model.Source: §III · p. 2

A. Power-Voltage-Current Closure

  • Telemetry-derived device-side load power is converted to battery power using a constant efficiency, then mapped to discharge current through an electrical power–voltage–current closure.The model uses a first-order Thevenin relation and linear OCV–SOC approximation for the smartphone data’s covered SOC range.Source: A. Power-Voltage-Current Closure · p. 2

B. Usage-Driven Load Power Decomposition

The load model decomposes device-side power into a fixed baseline and contributions from binary and continuous usage features, providing an interpretable telemetry-to-power mapping.

B. Usage-Driven Load Power Decomposition

  • The load-power model combines a fixed baseline with binary on/off component costs and continuous-intensity feature costs, then clips predicted power to be nonnegative.Examples include screen or GPS state as binary features, and brightness, CPU use, network throughput, or background-process count as continuous signals.Source: B. Usage-Driven Load Power Decomposition · p. 2
  • The linear decomposition is intended for fitting short sessions and supports ablation and counterfactual analysis.The paper motivates this interpretable, non-overparameterized form by sparse and heterogeneous public Android telemetry.Source: B. Usage-Driven Load Power Decomposition · p. 2
  • When direct battery telemetry is available, constrained least squares estimates nonnegative baseline and component costs; partial proxies are fitted on aligned segments.The resulting load-power series is propagated into the model.Source: B. Usage-Driven Load Power Decomposition · p. 3

C. Impact of Aging on Battery Capacity

The section defines battery state of health through usable capacity relative to initial rated capacity and identifies cumulative capacity loss as the quantity to determine.

C. Impact of Aging on Battery Capacity

1) Effect of Temperature on Aging

The aging model accounts for temperature-dependent reaction rates and time-dependent SEI growth, combining these effects in a capacity-loss-rate model.

1) Effect of Temperature on Aging

  • The temperature-aging subsection uses an Arrhenius relationship for the reaction rate constant, with activation energy and the universal gas constant identified explicitly.The text relates temperature dependence to the capacity-loss rate.Source: 1) Effect of Temperature on Aging · p. 3

2) Time-Dependent Aging: SEI Diffusion-Controlled Model

3) Effect of Charge-Discharge Cycling

The paper models cycling-related capacity loss through SEI growth, then adopts a generalized power law to represent multiple degradation mechanisms.

3) Effect of Charge-Discharge Cycling

  • Cycling-induced aging primarily affects capacity loss through SEI thickening.The paper considers both uniform growth with cycle number and self-inhibiting growth, in which thickening suppresses further side reactions.Source: 3) Effect of Charge-Discharge Cycling · p. 3
  • A generalized power-law expression is adopted to represent multiple degradation mechanisms.The exponent b compactly represents mixed degradation behavior; interacting mechanisms such as SEI growth and lithium plating may shift aging from approximately linear to nonlinear.Source: 3) Effect of Charge-Discharge Cycling · p. 3

4) Final Aging Model and Parameter Identification

The final capacity-loss model integrates time, temperature, and cycling effects, with parameters identified on chronologically partitioned NASA B0005 cycles and evaluated on an independent test set.

4) Final Aging Model and Parameter Identification

  • The final capacity-loss model integrates time, temperature, and cycling effects.Its parameters were estimated by nonlinear least squares using measured discharge capacity and battery temperature.Source: 4) Final Aging Model and Parameter… · p. 4
  • Cycles 1–118 identified parameters, cycles 119–143 supported model selection, and cycles 144–168 formed an independent test set.No test-cycle data were used during parameter fitting; the B0005 cell has a rated capacity of 2 Ah and 168 available discharge cycles.Source: 4) Final Aging Model and Parameter… · p. 4
  • 0.031 Ah capacity-loss RMSE and 0.026 Ah MAE were obtained on independent test cycles 144–168.Fig. 2 plots predicted and measured capacity loss, with distinct markers for training, validation, and independent test cycles.Source: Figure 2 · p. 4, 4) Final Aging Model and Parameter… · p. 4

IV. TIME-TO-EMPTY PREDICTION AND MODEL EVALUATION ACROSS MULTIPLE SCENARIOS

The section predicts time to empty by simulating coupled SOC–temperature dynamics under a scenario power trace, and reports hold-out errors for smartphone telemetry alongside limits on the model’s operating scope.

IV. TIME-TO-EMPTY PREDICTION AND MODEL EVALUATION ACROSS MULTIPLE SCENARIOS

A. Coupled SOC–Temperature Dynamics and Event-Based

  • For a single discharge event, SOH is held constant and charging is excluded; absent ambient-temperature data, the model assumes 24°C.The definition avoids reliance on a device-specific shutdown-voltage heuristic and is robust to OS-level SOC smoothing.Source: A. Coupled SOC–Temperature Dynamics… · p. 4
  • The lumped-temperature approximation suits relatively low-rate smartphone data but does not resolve internal gradients under rapid pulses or extreme thermal conditions.The paper notes that rapid pulse loads, strong internal gradients, extreme temperatures, or highly nonlinear OCV regions may require higher-order electrical and thermal models.Source: A. Coupled SOC–Temperature Dynamics… · pp. 4–5
  • The implementation ignores transient polarization and uses a one-dimensional linear OCV–SOC relation to improve identifiability under noisy telemetry.The paper reports that modeling transient polarization did not provide a stable accuracy gain for discharge-current reconstruction.Source: A. Coupled SOC–Temperature Dynamics… · p. 4
  • SOC evolves by charge conservation, while temperature affects internal resistance and effective capacity through compact Arrhenius-like approximations.The model uses a lumped thermal balance for load, ohmic heating, and cooling, and approximates conversion loss with constant efficiency.Source: A. Coupled SOC–Temperature Dynamics… · p. 4
  • 0.0095 ± 0.0006 A current RMSE, 2.93 ± 0.24°C temperature RMSE, and 4.81 ± 0.61% TTE MAPE were achieved on chronological hold-out evaluation.The TTE MAE was 0.10 ± 0.05 h; repeated Light, Typical, and Heavy load windows were controlled simulations, not independent experimental validation.Source: A. Coupled SOC–Temperature Dynamics… · p. 5

B. TTE Grid Output, Evaluation Metrics, And Uncertainty

The proposed model achieved the lowest TTE error among the compared baselines and ablations. The grid analysis reports a pronounced cold penalty, and the ablation comparison finds a larger TTE-error increase when temperature correction is removed than when aging correction is removed.

B. TTE Grid Output, Evaluation Metrics, And Uncertainty

WINDOWS REPEATED UNTIL DEPLETION)

  • The uncertainty analysis samples parameter and residual variability across simulations and reports median TTE with a 95% interval.The interval uses the 2.5% and 97.5% quantiles.Source: WINDOWS REPEATED UNTIL DEPLETION) · p. 5
  • 4.81% MAPE, down from 12.40% for the average-power baseline, was the lowest TTE error among the proposed model, two baselines, and two ablated variants.The comparison used the same independent test interval.Source: WINDOWS REPEATED UNTIL DEPLETION) · p. 5, Table III · p. 5

INDEPENDENT TEST INTERVAL

  • Removing temperature correction caused a larger increase in TTE error than removing aging correction in the evaluated smartphone session.The aging correction also improved prediction by adjusting available capacity at the beginning of discharge.Source: INDEPENDENT TEST INTERVAL · p. 5

C. Drivers of Rapid Drain Based on Counterfactual TTE

The section relates usage proxies to battery power with a ridge-regression model and uses feature-group scaling to estimate counterfactual TTE impacts. The reported coefficients describe within-session associations, not causal effects; simulated temperature trajectories are used to examine thermal-model plausibility.

C. Drivers of Rapid Drain Based on Counterfactual TTE

  • Standardized ridge-regression coefficients indicate each feature’s relative association with battery power within the present discharge session, not causal effects.Continuous features were standardized using training-set means and standard deviations.Source: Figure 3 · p. 5, C. Drivers of Rapid Drain Based on… · p. 6
  • Counterfactual TTE impact is estimated by scaling a feature group by κ and re-simulating; large Δg indicates high impact, while Δg≈0 indicates weak influence in the current dataset and scenario.Feature groups can include CPU, radios, or display.Source: C. Drivers of Rapid Drain Based on… · p. 6
  • Fig. 4 shows simulated, not directly measured, battery-temperature trajectories under the Typical load profile to examine whether fitted thermal parameters produce plausible heating and cooling.The trajectories span different ambient temperatures.Source: C. Drivers of Rapid Drain Based on… · p. 6, Figure 4 · p. 6

V. CONCLUSION

The framework integrates usage-driven load decomposition, electrical closure, semi-empirical aging, and coupled SOC–temperature dynamics; evaluations reported smartphone discharge metrics and NASA-cell capacity-loss error.

V. CONCLUSION

  • Current RMSE was 0.0095 ± 0.0006 A, temperature RMSE 2.93 ± 0.24°C, TTE MAPE 4.81 ± 0.61%, and NASA B0005 capacity-loss test RMSE 0.031 Ah.Source: §V · p. 6
  • Coupling thermal and aging corrections improved TTE prediction under the investigated conditions.Source: §V · p. 6
  • The smartphone evaluation used one device and one continuous session, with Typical and Heavy profiles built from repeated windows; aging evaluation used one public cell.Source: §V · p. 6
  • The electrical and thermal models assume linear OCV–SOC, constant conversion efficiency, and a lumped thermal node; future work targets richer models and broader validation.Source: §V · p. 6
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