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Forecasting battery capacity and power degradation with multi-task learning

Weihan Li, Haotian Zhang, Bruis van Vlijmen, Philipp Dechent, Dirk Uwe Sauer

arXiv:2111.14937v2eess.SYcs.SY

TL;DR

Predicting capacity and power fade early is difficult because battery ageing is nonlinear and varies across cells. This paper uses multi-task sequence-to-sequence learning to forecast both degradation trajectories, knee-points, and end-of-life points. It reports low prediction errors, robustness to estimation noise, and improved accuracy with lower computation time than single-task models.

  • Problem

    Early-life prediction of capacity and power fade is challenging because coupled nonlinear ageing mechanisms and intrinsic manufacturing variability create cell-specific degradation, while power prediction evidence is limited.

    Source: INTRODUCTION · pp. 2, 4

  • Method

    A multi-task sequence-to-sequence model uses past capacity and resistance data to forecast both degradation trajectories, including knee-points and end-of-life points.

    Source: INTRODUCTION · p. 4, CONCLUSIONS · pp. 22–23

  • Results

    The model reports average mean absolute errors of 2.37% for capacity and 1.24% for power degradation, and improves prediction accuracy while reducing computation time by 50% versus single-task models.

    Source: INTRODUCTION · p. 5, CONCLUSIONS · p. 23

  • Takeaways & Limitations

    The results highlight multi-task learning's effectiveness for battery degradation prediction and its potential application to other cell chemistries and energy-storage systems.

    Source: INTRODUCTION · p. 5

    The work is a proof of concept; performance still needs validation on experimental datasets with greater stress-factor variation and field data under mixed operating conditions.

    Source: Applications and Outlook · p. 21

Abstract

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Lithium-ion batteries degrade due to usage and exposure to environmental conditions, which affects their capability to store energy and supply power. Accurately predicting the capacity and power fade of lithium-ion battery cells is challenging due to intrinsic manufacturing variances and coupled nonlinear ageing mechanisms. In this paper, we propose a data-driven prognostics framework to predict both capacity and power fade simultaneously with multi-task learning. The model is able to predict the degradation trajectory of both capacity and internal resistance together with knee-points and end-of-life points accurately at early-life stage. The validation shows an average percentage error of 2.37% and 1.24% for the prediction of capacity fade and resistance rise, respectively. The model's ability to accurately predict the degradation, facing capacity and resistance estimation errors, further demonstrates the model's robustness and generalizability. Compared with single-task learning models for forecasting capacity and power degradation, the model shows a significant prediction accuracy improvement and computational cost reduction. This work presents the highlights of multi-task learning in the degradation prognostics for lithium-ion batteries.

INTRODUCTION

Early prediction of both capacity and power degradation is difficult because ageing is nonlinear and varies across cells. The paper proposes a multi-task sequence-to-sequence framework to predict both trajectories, including knee and end-of-life points.

INTRODUCTION

  • Early-life forecasting is challenging because coupled nonlinear ageing mechanisms and stress factors interact with intrinsic manufacturing variability to produce divergent late-life degradation.Relevant mechanisms include SEI growth, lithium plating, and particle cracking; stress factors include temperature, current rate, and depth of discharge.Source: INTRODUCTION · p. 2
  • Accurate early prediction of both capacity and power fade matters because pack lifetime depends on the weakest cell, and cell safety issues can trigger thermal runaway.The introduction also connects prediction to first- and second-life applications and laboratory testing costs.Source: INTRODUCTION · pp. 2, 4
  • Data-driven methods learn ageing patterns from data, whereas model-based approaches struggle to represent intrinsic cell variation while balancing model complexity and prediction accuracy.The text notes that machine-learning models can capture slight early-life differences when high-quality ageing data are available.Source: INTRODUCTION · pp. 2–3
  • Point-prediction models omit full trajectories and knee-points, while iterative curve-prediction models can require expert features, inaccessible measurements, and high computation.Prior one-shot trajectory prediction reduced computation 15 times versus an iterative approach, but power-degradation prediction remains limited and prior joint models relied on standardized constant-current profiles.Source: INTRODUCTION · pp. 3–4
  • The multi-task model predicts capacity and power degradation trajectories, knee-points, and end-of-life points from as few as 100 cycles, improving accuracy and reducing computation time by 50% versus single-task models.The framework uses multi-task learning with sequence-to-sequence models.Source: INTRODUCTION · pp. 4–5

AGEING DATA ANALYSIS

The ageing analysis uses 48 cells tested under a shared scenario and compares capacity and resistance degradation metrics. Knee-point timing tracks end-of-life more closely than the degradation value at the knee, underscoring nonlinear relationships between degradation state and lifetime.

AGEING DATA ANALYSIS

  • The dataset comprises 48 Sanyo/Panasonic 18650 NMC/Graphite cells aged at 25°C, with capacity and resistance measured as SOH-C and SOH-R indices.Capacity EOL is defined at 80% and 65% of nominal capacity for first and second life; power EOL is defined at 120% and 130% of average initial resistance.Source: AGEING DATA ANALYSIS · p. 5
  • Cycle life at the capacity knee-point is strongly correlated with EOL80, but remaining capacity at that knee-point is poorly correlated with EOL80.The authors suggest that the capacity at which rapid degradation begins may not indicate cycle life.Source: AGEING DATA ANALYSIS · p. 6, Figure 1 · p. 7
  • Cycle life at the resistance knee-point is strongly correlated with EOL120, while resistance at the knee-point is poorly correlated with EOL120.The authors interpret this pattern as further evidence of a nonlinear relationship between degradation state and the degradation knee.Source: AGEING DATA ANALYSIS · p. 6, Figure 1 · p. 7
  • The cells share an ageing scenario, but degradation-trend variance grows from mid-life; capacity and power fade show similar features despite nonlinear relationships that may vary with materials and operation mode.The authors note that power EOL thresholds can be adapted to use cases, including 200% of initial resistance in some cases.Source: AGEING DATA ANALYSIS · pp. 6–7

PROGNOSTICS FRAMEWORK

The prognostics framework uses past capacity and resistance data to forecast both future trajectories. Its multi-task sequence-to-sequence model shares a representation across tasks and can operate without iterative prediction or retraining.

PROGNOSTICS FRAMEWORK

  • The proposed framework separates model training from deployment and updating, with cloud-based parameter updates and forecasts for cells or packs.It is designed to forecast first- and second-life end-of-life points and degradation knee-points.Source: PROGNOSTICS FRAMEWORK · p. 8
  • The multi-task model uses hard parameter sharing, allowing capacity and resistance prediction tasks to influence shared parameters, unlike single-task models with separate parameters.The shared representation is intended to capture both tasks and help avoid overfitting.Source: PROGNOSTICS FRAMEWORK · pp. 8–9
  • The model takes remaining-capacity and internal-resistance histories from beginning of life to the present and outputs both future trajectories.Input and output sequence lengths vary as the cell ages and more historical data becomes available.Source: PROGNOSTICS FRAMEWORK · p. 9
  • An RNN-based sequence-to-sequence model predicts trajectories at any time point without iterative calculation or retraining.Its encoder represents the input sequence with a hidden vector, and decoders regenerate the future capacity and resistance sequences.Source: PROGNOSTICS FRAMEWORK · pp. 9–10
  • Evaluation uses ideal and noisy-input scenarios, with 10 cells—20% of the dataset—held out for testing.The noisy-input scenario represents degradation-diagnosis errors.Source: PROGNOSTICS FRAMEWORK · p. 10

Degradation Prediction from Normal Input

Under normal input, the MTL model predicts capacity and resistance degradation trajectories accurately, including with 100 cycles of data. More input generally improves accuracy, although errors can increase at some time points and the input-length effect across degradation regions remains uncertain.

Degradation Prediction from Normal Input

Degradation Prediction under Diagnosis Errors

Compared with single-task models, the MTL model generally improves degradation prediction while reducing computational cost. Under noisy inputs, its median prediction errors remain stable across capacity and power degradation, and it also performs well on cells aged under varying charging conditions.

Degradation Prediction under Diagnosis Errors

Comparison with Single-Task Learning Models

Model Performance under Other Datasets

  • On 124 LFP/graphite cells aged under varying charging scenarios, mean capacity and resistance curve MAPEs are 1.54% and 1.62%.The authors report good accuracy despite the dataset's varying charging conditions and large degradation variances.Source: Model Performance under Other Datasets · p. 21

Applications and Outlook

The authors identify validation on more variable experimental data and field data with mixed operating conditions as future work. They also describe possible uses of predicted end-of-life and knee-points for maintenance planning, especially in second-life applications.

Applications and Outlook

  • Further validation is needed on experimental datasets with more varied stress factors and field data with mixed operating conditions.The work is presented as a proof of concept for multi-feature co-prediction.Source: Applications and Outlook · p. 21
  • Fine-tuning the model across datasets or battery cells is proposed as a way to increase data efficiency and generalization.Source: Applications and Outlook · p. 21
  • Predicted end-of-life and knee-points for capacity and power fade can support predictive-maintenance planning, especially for second-life applications.The authors also suggest that a few hundred laboratory cycles may suffice for many tests before predicting expected service life.Source: Applications and Outlook · p. 22

CONCLUSIONS

The paper presents a multi-task prognostics framework for simultaneous capacity and power degradation prediction. It predicts full future trajectories, end-of-life points, and knee-points from as few as 100 cycles.

CONCLUSIONS

  • The framework uses past capacity and resistance sequences as inputs to a multi-task sequence-to-sequence model trained on ageing data from 48 NMC/graphite cylindrical cells.The approach uses multi-stage training and regularization without further feature engineering.Source: CONCLUSIONS · p. 22
  • From as few as 100 cycles, the model predicts full capacity and power trajectories together with first- and second-life endpoints and degradation knee-points.Reported mean absolute errors are 2.37% for capacity and 1.24% for power degradation prediction.Source: CONCLUSIONS · p. 23

EXPERIMENTAL PROCEDURES

The procedures describe a shared-encoder, task-specific-decoder approach to forecasting battery degradation, alongside single-task baselines and evaluation of trajectory, knee-point, and end-of-life predictions. They also document knee-point identification and the study’s data and code availability.

Resource Availability

Data and Code Availability

  • The study provides the raw and pre-processed datasets for 48 cells, data-analysis code, and deep-learning model code online.The raw dataset is available through a DOI, and the pre-processed data and code are hosted in a repository.Source: Data and Code Availability · p. 24

Knee-Point Identification

  • Knee points are identified offline at maximum curvature after smoothing and normalization, then tracked online on predicted curves using the knee-point gradient.The offline method transforms the normalized curve to a concave, increasing form; the online method identifies the corresponding point on the predicted curve’s gradient.Source: Knee-Point Identification · p. 24

Multi-Task Learning with Sequence-to-Sequence Models

  • The MTL model uses a shared encoder and separate capacity and resistance decoders, with L1 and L2 regularization to build a sparse model.The encoder and decoders use stacked bidirectional LSTMs; L1 sets some minimal weights to zero, while L2 constrains maximum weight values.Source: Multi-Task Learning with… · pp. 24–25

Single-Task Learning with Sequence-to-Sequence Models

  • The single-task baselines use separate sequence-to-sequence models with four-layer bidirectional LSTM encoders and decoders to predict future degradation arrays in one shot.A repeat-vector layer converts the encoder’s two-dimensional hidden vector to a three-dimensional decoder input.Source: Single-Task Learning with… · p. 26

Model Training

  • Training uses a 6:2:2 random split, four bidirectional LSTM layers of 64 nodes per encoder and decoder, and five-cycle input and 20-cycle output time steps.A multi-stage optimization updates capacity and resistance components in sequence before updating both decoders and the shared encoder using a weighted sum of losses.Source: Model Training · pp. 26–27

Evaluation Criteria

  • Evaluation uses trajectory MAPE summaries and absolute cycle errors for first- and second-life EOLs and knee points.Mean, median, and maximum MAPE across cell lifetime curves are reported; the modified MAE skips zero-padding positions during training.Source: Evaluation Criteria · pp. 27–28, Model Training · p. 27

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