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Early Cycle Charge Trajectory Generative Prediction and Full Life Cycle Health Management of Iron-Chromium Flow Batteries Based on FlowBD-E1

Suyang Zhuang, Zekun Jiang, Tianhang Zhou

arXiv:2608.14637v1cs.LGstat.ME

TL;DR

Fe-Cr flow-battery prognostics need to capture evolving full charge trajectories rather than only scalar ageing labels. FlowBD-E1 forecasts these trajectories from early cycles, achieving 0.731% joint V/I MAPE and below 1% SOH MAPE over the remaining lifecycle.

  • Problem

    Fe-Cr redox flow batteries are attractive for stationary storage but face long-term operational challenges linked to their chemistry.

  • Method

    FlowBD-E1 combines a lifecycle Transformer with an age-aware FiLM decoder and compares SLE, RLF and TFU deployment strategies.

  • Results

    0.731% joint V/I MAPE was achieved over the remaining lifecycle, with SOH estimates below 1% MAPE and sub-percent errors against LSTM and TCN baselines.

  • Takeaways & Limitations

    The study demonstrates complete future charge-trajectory prediction for an industrial Fe-Cr redox flow battery.

  • Takeaways & Limitations

    Additional evidence is required before the model can be treated as a universal RFB lifetime predictor.

Abstract

from arXiv · show

Long-duration stationary energy storage requires batteries whose degradation can be detected before substantial capacity loss has accumulated. Iron-chromium redox flow batteries are attractive for this role because they use abundant and low-cost active species, yet their operation is shaped by slow chromium kinetics, hydrogen evolution, membrane crossover and electrolyte imbalance. These coupled processes gradually reshape the full charge voltage/current (V/I) trajectory, but most battery prognostic studies either focus on lithium-ion cells or compress ageing into scalar capacity and state-of-health (SOH) labels. Here we study an industrial 33 kW Fe-Cr redox flow battery and introduce FlowBD-E1, an early-cycle generative forecasting framework that predicts complete future charge V/I trajectories from only the first few cycles. The model combines a multi-scale convolutional encoder, a lifecycle Transformer and an age-aware FiLM decoder, and we compare three deployment strategies: single-step latent extrapolation (SLE), recursive latent forecasting (RLF) and teacher-forced updating (TFU). Using the first 9 of 289 cycles, RLF achieved a joint V/I mean absolute percentage error (MAPE) of 0.731% over the remaining lifecycle and produced SOH estimates below 1% MAPE. Ablation and independent-sequence tests showed that the age-aware generative architecture outperformed LSTM and TCN baselines and retained sub-percent errors under industrial validation. These results suggest that early-cycle trajectory generation can turn a short commissioning record into a long-horizon diagnostic signal for flow-battery management.

Summary

The study compares three deployment strategies for an age-aware generative architecture and shows that early-cycle trajectory generation can support long-horizon flow-battery diagnostics. RLF achieved sub-percent trajectory and SOH errors from only the first 9 of 289 cycles.

  • Method: The framework combines a Transformer with an age-aware FiLM decoder and compares SLE, RLF, and TFU deployment strategies.The strategies are single-step latent extrapolation (SLE), recursive latent forecasting (RLF), and teacher-forced updating (TFU).
  • Results: 0.731% joint V/I MAPE was achieved by RLF over the remaining lifecycle using only the first 9 of 289 cycles.The result covers the remaining lifecycle after the initial 9 cycles.
  • Results: Below 1% MAPE, SOH estimates were produced by RLF from the early-cycle record.The passage reports SOH estimates below 1% MAPE alongside the joint V/I trajectory result.
  • Validation: The age-aware generative architecture outperformed LSTM and TCN baselines and retained sub-percent errors under industrial validation.Ablation and independent-sequence tests supported this result.
  • Contribution: Early-cycle trajectory generation turns a short commissioning record into a long-horizon diagnostic signal for flow-battery management.This is the study’s stated contribution for flow-battery management.

Introduction

Fe-Cr flow batteries offer an abundant, low-cost option for long-duration storage, but coupled electrochemical and transport processes make their degradation difficult to predict. FlowBD-E1 addresses this gap by forecasting complete future charge V/I trajectories from a few commissioning cycles and deriving health indicators from the generated waveforms.

  • Motivation: Fe-Cr flow batteries are attractive for large stationary installations because iron and chromium are abundant, inexpensive active species.Their operation is nevertheless complicated by slow chromium kinetics, competing hydrogen evolution and cross-membrane transport that changes electrolyte composition and charge balance.
  • Research gap: Existing studies largely estimate present within-cycle states or scalar ageing metrics, leaving open whether early industrial Fe-Cr cycles forecast complete lifetime charge trajectories.The literature is dominated by lithium-ion cells, while reducing ageing to capacity, SOH or remaining useful life discards voltage- and current-curve shape.
  • Trajectory health signature: Full charge V/I trajectories encode phase-dependent information about polarization, electrolyte transport, concentration state, capacity limitation and side reactions.Generating the waveform first enables subsequent calculation of SOH, charge duration and efficiency-related quantities rather than restricting prediction to scalar SOH.
  • Study contribution: FlowBD-E1 encodes a small number of commissioning cycles into a lifecycle representation that generates future V/I waveforms and health indicators with sub-percent error.The framework treats future charge curves as prediction targets and compares single-step latent extrapolation, recursive latent forecasting and teacher-forced updating.
  • Experimental scope: The method is evaluated on data from a 33 kW industrial single-stack Fe-Cr system, linking sequence modelling with a deployable flow-battery prognostic problem.The study separates autonomous forecasting error from diagnostic upper-bound behaviour through its comparison of SLE, RLF and TFU strategies.

Data and method

The study uses cleaned, normalized and cycle-segmented V/I data from a 33 kW iron-chromium flow battery, organized into independent 289-cycle groups for training, validation and testing. FlowBD-E1 encodes aligned early-cycle trajectories, models lifecycle dependencies, generates future V/I curves with age conditioning, and derives SOH, with SLE, RLF and TFU evaluated as prediction strategies.

  • Data and preprocessing: The dataset comprises 24 independent groups, each containing 289 consecutive charge cycles, split into 20 training, three validation and one independent industrial test group.Raw records include cycle index, operation mode, timestamp, stack voltage and stack current sampled at 1 Hz; preprocessing included cleaning, normalization and cycle segmentation.
  • FlowBD-E1 architecture: FlowBD-E1 uses a multi-scale CNN encoder to map aligned V/I trajectories into latent cycle tokens while retaining local waveform and broader phase features.The encoder applies short-, medium- and long-range convolutional pooling.
  • FlowBD-E1 architecture: A lifecycle Transformer models dependencies across cycle tokens, and an age-aware FiLM decoder reconstructs full future V/I trajectories using target cycle age.The Transformer receives cycle-position information and normalized lifecycle age, while the decoder modulates latent features with target-cycle age.
  • FlowBD-E1 architecture: The health branch estimates SOH from reconstructed voltage features or indirectly through curve integration.FlowBD-E1 therefore combines future trajectory reconstruction with downstream health estimation.
  • Prediction strategies: SLE reuses one latent state with updated age embeddings, RLF autoregressively appends predicted states, and TFU uses true future states as a diagnostic upper bound.TFU is not deployable because it supplies the true encoded latent state for each future cycle.

Results and discussion · Early-cycle information is sufficient for long-horizon trajectory fore- · casting

Early-cycle charge trajectories contain sufficient information for long-horizon forecasting: RLF achieved sub-percent joint V/I errors from as few as one observed cycle and maintained this performance across tested windows. The waveform also supported SOH estimation and commissioning-stage maintenance and scheduling decisions.

  • Early-cycle information is sufficient for long-horizon trajectory forecasting: 0.634% joint V/I MAPE was achieved by RLF with one known cycle, while SLE remained near 3.021%.The result shows that useful lifetime forecasting is learnable from surprisingly little commissioning data.
  • Early-cycle information is sufficient for long-horizon trajectory forecasting: 0.731% joint V/I MAPE was achieved by RLF with a 9-cycle known window, including 0.735% voltage MAPE and 0.726% current MAPE.The n = 9 operating point provided the lowest deployable error among the compared strategies.
  • Early-cycle information is sufficient for long-horizon trajectory forecasting: The early charge curve contains a strong stack fingerprint, including impedance, flow distribution and initial conditions.These features help explain why early waveform information can support long-horizon prediction.
  • Early-cycle information is sufficient for long-horizon trajectory forecasting: RLF stayed below 1% joint V/I MAPE across the tested early-window range.The error landscape further illustrated RLF stability relative to the other deployment strategies.
  • Early-cycle information is sufficient for long-horizon trajectory forecasting: Trajectory generation also supported health estimation, with SOH MAPE reported across the tested early-cycle windows.Figure 2b linked trajectory-prediction performance to SOH estimation.
  • Early-cycle information is sufficient for long-horizon trajectory forecasting: FlowBD-E1 uses the early waveform to infer a latent degradation path, allowing maintenance and scheduling decisions during commissioning.This reframes early operation as a diagnostic opportunity rather than a waiting period.
  • Early-cycle information is sufficient for long-horizon trajectory forecasting: The predictive signal is distributed over the entire curve rather than confined to a single voltage, current or capacity value.This indicates why scalar early-cycle descriptors alone may be insufficient.

Recursive latent forecasting gives the best autonomous strategy

At n = 9, recursive latent forecasting (RLF) was the strongest deployable strategy, achieving the lowest joint V/I MAPE and maintaining its advantage across prediction horizons. Its evolving latent context tracks gradual ageing, while TFU remains useful mainly as a diagnostic reference.

  • Lifecycle rollout: RLF preserved most of its error-reduction advantage throughout the lifecycle, whereas SLE error accumulated with prediction horizon.RLF showed a comparatively stable rollout, while SLE deteriorated farther from the known window.
  • Deployment choice: TFU does not always outperform RLF, supporting RLF as the deployable strategy while retaining TFU as a useful diagnostic reference.Measured future encodings do not remove decoder error and may expose locally accurate but poorly aligned latent states.
  • Mechanism: RLF tracks gradual ageing in latent space because each generated latent token becomes part of the evolving context.This avoids relying on a frozen latent representation as the battery moves farther from the known window.

Generated trajectories preserve voltage-current physics and SOH · evolution

FlowBD-E1’s RLF preserves the evolving coupled voltage-current charge trajectories across early, middle, and late life, while generated-curve SOH tracks measured degradation. At n = 9, it achieves sub-percent direct and integral-based SOH MAPE, with tighter residuals than SLE.

  • evolution: RLF closely follows voltage rise and current decline under constant-power operation across representative charge trajectories.The model was evaluated at cycles 50, 150, and 270 to examine waveform evolution from early to late life.
  • evolution: In the early window, RLF reproduces full charge duration and terminal voltage increase.
  • evolution: In the middle window, RLF tracks the shortened curve and shifted voltage profile.
  • evolution: In the late window, RLF captures elevated plateau voltage and earlier terminal rise associated with advanced ageing.
  • evolution: The SOH trajectory derived from generated curves follows measured decline from approximately 0.96 to 0.61.This links trajectory generation to a health indicator over the observed lifecycle.
  • evolution: At n = 9, RLF achieved a direct SOH MAPE of 0.867%.
  • evolution: At n = 9, RLF achieved an integral-based SOH MAPE of 0.662% from generated V/I curves, while residuals clustered nearer zero than SLE.The integral estimate is derived from the generated voltage/current trajectories rather than a separately trained scalar target, enabling multiple health indicators without retraining.

Architecture ablation confirms the role of age-aware generative de- · coding

The ablation shows that FlowBD-E1’s age-aware generative architecture outperforms LSTM and TCN alternatives, especially during long-horizon rollout. Its explicit separation of lifecycle age, degradation state, and waveform reconstruction supports stable late-cycle prediction.

  • coding: 0.158% voltage MAPE and 0.175% current MAPE were achieved by the full FlowBD-E1 model in the n = 9 ablation.The comparison tested FlowBD-E1 against LSTM and TCN alternatives.
  • coding: Voltage and current R2 values of 0.9983 were obtained under RLF on the 289-cycle sequence.This result accompanies the ablation evaluation of the full model.
  • coding: LSTM and TCN variants were less stable than FlowBD-E1, particularly during long-horizon rollouts.Their errors grew across the prediction horizon, whereas FlowBD-E1 remained nearly flat.
  • coding: FlowBD-E1 had lower average and worst-case errors than the baselines across maximum, mean, and RMSE summaries of MAPE.Its error distribution also concentrated near zero.
  • coding: The full model dominated the aggregate radar-style score in the ablation comparison.Figure 5 combines the architecture and baseline comparison in this aggregate view.
  • coding: The task requires reconstructing future curves whose local features have different meanings at different lifecycle ages, not merely extrapolating a time series.This distinction motivates the age-aware generative design.
  • coding: The FiLM decoder provides age-dependent modulation, while the Transformer represents long-range cycle-to-cycle dependency.Together, these components address age-conditioned waveform reconstruction and temporal dependence.
  • coding: Separating lifecycle age, latent degradation state, and waveform reconstruction appears essential for maintaining low error during late cycles.Late-cycle curve shape is strongly affected by small capacity shifts and terminal polarization changes, which generic LSTM and TCN models do not separate explicitly.

Industrial validation supports deployment beyond the training se- · quence

Independent industrial validation showed that FlowBD-E1 generalized beyond the training sequence, achieving sub-percent voltage and current errors and outperforming the tested baselines across deployment strategies. The evidence supports real-deployment studies, while remaining limited to one Fe-Cr system class and operating protocol.

  • quence: 0.208% voltage MAPE and 0.204% current MAPE were achieved by the full RLF model on an independent 200-cycle sequence using n = 9.The corresponding R2 values were 0.9976 for voltage and 0.9978 for current.
  • quence: FlowBD-E1 was the best model across SLE, RLF and TFU in the independent generalization summary.The comparison covered NoFiLM, LSTM and TCN variants.
  • quence: Lower mean, RMSE and maximum errors than NoFiLM, LSTM and TCN variants indicated that FlowBD-E1 did not merely memorize one sequence.This result directly addresses robustness outside the sequence used for model selection.
  • quence: FlowBD-E1 remained closest to the measured voltage curve under independent validation, while its variants occupied the lowest-error region across model-strategy combinations.The evaluation used measured-versus-predicted trajectory overlays and error-distribution comparisons.
  • quence: The full FlowBD-E1 variants ranked above the baselines in normalized aggregate scoring, including mean, RMSE and maximum-error summaries.These comparisons were presented through polar error plots and a normalized aggregate score.
  • quence: Independent validation suggested that early-cycle trajectory generation was robust enough to support real deployment studies under stack-level flow, thermal, electrolyte and control-system variability.These industrial conditions differ from laboratory cell data and determine practical battery-management value.
  • quence: The evidence remains bounded to one Fe-Cr system class and one operating protocol, requiring cross-power, cross-temperature, cross-electrolyte and multi-site testing before claiming chemistry-wide generality.The stated future tests target transfer beyond the present validation scope.

Conclusions

FlowBD-E1 forecasts complete future charge V/I trajectories for an industrial Fe-Cr redox flow battery from only a small early-cycle record. RLF achieved sub-percent errors, while broader validation is still needed before universal lifetime prediction.

  • Conclusions: FlowBD-E1 forecasts complete future charge V/I trajectories from only a small early-cycle record.The framework targets trajectory generation rather than scalar SOH values alone.
  • Conclusions: FlowBD-E1 combines multi-scale waveform encoding, lifecycle Transformer modelling and age-aware FiLM decoding.These components form the age-aware generative architecture used for future trajectory prediction.
  • Conclusions: Sub-percent errors were retained in industrial validation, and the full age-aware generative architecture was more stable than LSTM and TCN baselines.Ablation and independent-sequence validation supported this comparison.
  • Conclusions: Broader validation across chemistries, operating protocols and field sites is required before the model can be treated as a universal RFB lifetime predictor.The present evidence supports early-cycle generative forecasting as a practical route toward proactive flow-battery management, but defines this validation boundary.
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