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Robust State of Health Estimation of Lithium-ion Batteries Using Convolutional Neural Network and Random Forest

Niankai Yang, Ziyou Song, Heath Hofmann, Jing Sun

arXiv:2010.10452v1eess.SP

TL;DR

Partial discharge truncates battery data and can remove or distort common SOH indicators, complicating capacity-fading estimation. The paper extracts SOH and ΔSOH indicators with two CNNs and fuses them using random forest; comparisons report improved accuracy and robustness across partial-discharge conditions.

  • Problem

    Partial discharge limits available battery data and can cause common SOH indicators to be lost or distorted, making robust real-world SOH estimation challenging.

  • Method

    Two CNNs extract indicators related to SOH and inter-cycle ΔSOH from partial-discharge curves, while random forest combines their outputs into the final estimate.

  • Results

    RF-CNN improves estimation accuracy and robustness over RF-ICA, SOH-CNN, and ΔSOH-CNN across partial-discharge conditions.

  • Takeaways & Limitations

    Combining SOH- and ΔSOH-related indicators provides a framework that leverages CNN learning and supports more interpretable partial-discharge SOH estimation.

Abstract

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The State of Health (SOH) of lithium-ion batteries is directly related to their safety and efficiency, yet effective assessment of SOH remains challenging for real-world applications (e.g., electric vehicle). In this paper, the estimation of SOH (i.e., capacity fading) under partial discharge with different starting and final State of Charge (SOC) levels is investigated. The challenge lies in the fact that partial discharge truncates the data available for SOH estimation, thereby leading to the loss or distortion of common SOH indicators. To address this challenge associated with partial discharge, we explore the convolutional neural network (CNN) to extract indicators for both SOH and changes in SOH ($Δ$SOH) between two successive charge/discharge cycles. The random forest algorithm is then adopted to produce the final SOH estimate by exploiting the indicators from the CNNs. Performance evaluation is conducted using the partial discharge data with different SOC ranges created from a fast-discharging dataset. The proposed approach is compared with i) a differential analysis-based approach and ii) two CNN-based approaches using only SOH and $Δ$SOH indicators, respectively. Through comparison, the proposed approach demonstrates improved estimation accuracy and robustness. Sensitivity analysis of the CNN and random forest models further validates that the proposed approach makes better use of the available partial discharge data for SOH estimation.

I. INTRODUCTION

Accurate SOH estimation is important for safe, reliable battery operation, but partial operation data and imperfect indicator-extraction methods complicate real-world monitoring. The paper proposes an interpretable CNN–random-forest framework that extracts SOH and ΔSOH indicators under partial discharge.

  • Battery SOH is commonly characterized by capacity or internal resistance, with capacity more directly representing energy-storage capability.
  • Full charging or discharging can be infeasible in applications such as electric vehicles and may accelerate battery degradation.
  • ECM-, electrochemical-model-, and differential-analysis-based methods trade accuracy, computational cost, smoothing distortion, or SOC-range applicability under partial operation.
  • End-to-end deep-learning methods can map operating data directly to SOH, but their indicator-extraction process is less interpretable and difficult to combine with expert knowledge.
  • The proposed two-step method uses CNNs to extract SOH and ΔSOH indicators, then random forest to fuse them into a final SOH estimate.
  • The framework combines neural-network learning with physics-based knowledge, interprets model sensitivity, and introduces ΔSOH-related indicators for partial charge or discharge conditions.

II. BACKGROUND

The study constructs and formulates partial-discharge SOH estimation using aging data from lithium-iron-phosphate/graphite cells. Partial curves are created by truncating full discharge curves between initial and final depth-of-discharge values.

  • The dataset contains aging data for 124 commercial A123 lithium-iron-phosphate/graphite batteries with nominal capacity of 1.1 Ah.
  • SOH for each discharge cycle is defined as cell capacity divided by nominal capacity, with cell capacity taken as the maximum discharge capacity over the cycle.
  • Partial-discharge datasets are generated by truncating full discharge curves using different initial and final depth-of-discharge values.
  • The initial DoD is sampled from a Gaussian distribution, while the final DoD equals the initial DoD plus the maximum incremental discharge capacity.
  • The resulting voltage and incremental-discharge-capacity sequences form each partial-discharge curve, and SOH is estimated from present and past partial curves.

III. DA-BASED APPROACHES FOR SOH ESTIMATION UNDER PARTIAL DISCHARGE

The DA-based approach uses incremental capacity analysis to extract SOH indicators from partial-discharge curves, but truncation, smoothing, and cell variation can corrupt these indicators. In particular, the lowest IC minimum may disappear or lose a consistent SOH relationship, degrading robustness.

  • ICA-based indicator extraction: Incremental capacity analysis extracts SOH indicators from smoothed partial-discharge curves, but differential processing can distort or discard information.The approach preprocesses discharge curves before differentiation, creating a potential information-loss source under partial discharge.
  • Indicator loss under truncation: Multiple IC minima correlate with SOH, but their voltage locations shift irregularly across SOH levels, so only the lowest minimum remains consistently identifiable in the examined data.These observations make DA-based estimation heavily dependent on the existence and quality of the lowest IC minimum.
  • Indicator loss under truncation: Partial discharge can eliminate the lowest IC minimum and other IC minima, leaving only limited identifiable features across SOH levels.The lowest IC minimum between 3.15 V and 3.2 V disappears through data truncation, while minima between 3.05 V and 3.15 V disappear after smoothing.
  • Cell-to-cell variation: The lowest IC minimum may not correlate consistently with SOH, and its relationship with SOH varies across cells.The resulting correlation is corrupted under partial discharge and sensitive to cell-to-cell variation, which can degrade DA-based SOH estimation.
  • Operating-condition dataset: A second partial-discharge dataset samples initial DoD around 0.2 and final capacity-related discharge limits uniformly between 0.45 and 0.55 to represent typical electric-vehicle operation.The initial DoD follows N(0.2, 1/900), while Qmax follows U(0.45, 0.55).

IV. CNNS FOR SOH ESTIMATION UNDER PARTIAL DISCHARGE

CNNs are developed to estimate SOH from partial-discharge data, first through direct SOH estimation and then through incremental SOH estimation. The latter is motivated by low consistency between successive direct CNN estimates.

  • CNN-based estimation: A direct SOH-CNN estimates SOH from partial-discharge data, followed by an incremental-SOH CNN motivated by inconsistent successive direct estimates.The section evaluates direct estimation without the low DoD region before introducing incremental SOH estimation.

A. Direct SOH estimation using CNN

CNN is selected to extract locally connected SOH features that can shift within partial-discharge curves, enabling direct SOH estimation without relying on fixed expert indicators.

  • A. Direct SOH estimation using CNN: CNN extracts locally connected features whose locations may shift when partial-discharge SOC ranges differ.Convolution extracts local patterns, while max pooling identifies shifted features within local regions.
  • A. Direct SOH estimation using CNN: The ten-layer CNN maps each partial discharge curve to the SOH for its discharge cycle.The model includes convolutional and fully connected layers and uses five-fold cross-validation.
  • A. Direct SOH estimation using CNN: 1.28% average MAE is obtained by SOH-CNN on partial discharges with initial and final DoD values around 0.2 and 0.7.The evaluation uses the same dataset as the differential-analysis approach.
  • A. Direct SOH estimation using CNN: SOH-CNN achieves satisfactory estimation without explicitly incorporating the lowest IC minimum used by the differential-analysis approach.The CNN can extract numerically correlated indicators without data smoothing, avoiding potential information loss from preprocessing.
  • A. Direct SOH estimation using CNN: SOH-CNN does not produce consistent SOH estimates across successive cycles.The passage attributes this to limited information in a partial-discharge curve and use of only the present cycle's data.

B. Incremental SOH estimation using CNN

∆SOH-CNN uses present and past partial-discharge curves to estimate SOH changes, improving consistency across successive estimates but accumulating estimation error over time.

  • B. Incremental SOH estimation using CNN: ∆SOH-CNN estimates the change in SOH between present and past cycles, then combines it with the past SOH estimate.This formulation targets the accumulative and evolutionary nature of SOH.
  • B. Incremental SOH estimation using CNN: 1.57% average MAE is obtained by ∆SOH-CNN on the same dataset used for direct SOH-CNN.A representative estimation result is presented in Fig. 9.
  • B. Incremental SOH estimation using CNN: ∆SOH-CNN improves consistency among successive SOH estimates compared with SOH-CNN.It uses both present and past discharge curves and learns features related to ∆SOH.
  • B. Incremental SOH estimation using CNN: ∆SOH-CNN has worse MAE than SOH-CNN because estimation errors accumulate over time like an integrator-based estimator.The smaller magnitude of ∆SOH also makes its training targets more susceptible to experimental noise.

V. CNN AND RANDOM FOREST FOR ROBUST SOH ESTIMATION UNDER PARTIAL DISCHARGE

The proposed robust estimator combines sensitivity analysis of two CNNs with a random forest model to integrate their complementary SOH information.

  • V. CNN AND RANDOM FOREST FOR ROBUST SOH ESTIMATION UNDER PARTIAL DISCHARGE: Sensitivity analysis first examines the contribution of different discharge-curve portions to the two CNNs' SOH estimates.The analysis guides the subsequent random forest design.
  • V. CNN AND RANDOM FOREST FOR ROBUST SOH ESTIMATION UNDER PARTIAL DISCHARGE: A random forest model then integrates outputs from both CNNs for enhanced SOH estimation performance.The pipeline combines CNN-based indicator extraction with random-forest fusion.

A. CNN model sensitivity analysis

The two CNNs provide complementary SOH information: direct SOH estimation favors lower MAE, while incremental estimation favors consistency, motivating random-forest fusion.

  • A. CNN model sensitivity analysis: SOH-CNN has smaller MAE, whereas ∆SOH-CNN provides better consistency across successive SOH estimates.Their complementary characteristics motivate combining the two models.
  • A. CNN model sensitivity analysis: The random forest treats the two CNN SOH estimates as indicators and mitigates potential multicollinearity between them.Both estimates are produced from discharge curves, creating possible correlation between the inputs.
  • A. CNN model sensitivity analysis: RF-CNN achieves 0.85% average MAE in the same case study.Its representative estimation performance is shown in Fig. 12.
  • A. CNN model sensitivity analysis: RF-CNN provides better consistency than SOH-CNN and reduces MAE by up to 35% compared with SOH-CNN and ∆SOH-CNN.Both CNN outputs contribute substantially to the final random-forest estimate across five cross-validation folds.

VI. PERFORMANCE EVALUATION

The performance evaluation compares RF-CNN with a differential-analysis approach and with CNN estimators using SOH or ΔSOH indicators under partial discharge. These comparisons assess estimation accuracy and robustness across partial-discharge conditions.

  • The evaluation compares RF-CNN with a DA-based approach and with SOH-CNN and ΔSOH-CNN under partial discharge.The comparison includes approaches using differential analysis, SOH indicators, and changes in SOH indicators.
  • The RF-CNN structure combines SOH1 and SOH2, estimated by SOH-CNN and ΔSOH-CNN, respectively.
  • The evaluation uses partial-discharge datasets with different DoD ranges to examine estimator performance.

A. Comparison with DA based approaches

RF-CNN is compared with RF-ICA and with single-indicator CNN estimators under partial discharge. It achieves lower error than RF-ICA and remains more robust as the available data range decreases.

  • Comparison with DA based approaches: 0.72% MAE for RF-CNN versus 2.31% for RF-ICA under partial discharge with the low DoD region.RF-ICA maps the lowest IC minimum to SOH, while RF-CNN uses CNN-extracted indicators.
  • Comparison with DA based approaches: RF-ICA has worse consistency in successive SOH estimates because it uses only the present discharge curve.The passage states that RF-ICA therefore fails to capture the relationship between past and present SOHs.
  • Comparison with SOH-CNN and ΔSOH-CNN: RF-CNN outperforms SOH-CNN and ΔSOH-CNN on all four partial-discharge conditions.The conditions have final DoD distributions with means located near 0.8, 0.7, 0.6, and 0.5.
  • Comparison with SOH-CNN and ΔSOH-CNN: MAE increases as the data range decreases for all three CNN-based estimators, but RF-CNN shows the smaller increase.The paper attributes RF-CNN’s robustness to richer SOH indicators.

VII. CONCLUSIONS AND FUTURE WORK

The paper proposes RF-CNN for SOH estimation of a single battery cell under partial discharge by combining SOH and ΔSOH indicators from two CNNs with random forest. Evaluation verifies enhanced accuracy and robustness, while future work targets broader operating conditions and battery strings.

  • Conclusions: RF-CNN estimates single-cell SOH under partial discharge by combining SOH and ΔSOH indicators from two CNNs with random forest.The ΔSOH indicator represents change between two consecutive discharge cycles.
  • Conclusions: Evaluation on partial-discharge data with different DoD ranges verifies enhanced accuracy and robustness compared with RF-ICA, SOH-CNN, and ΔSOH-CNN.
  • Conclusions: Sensitivity analysis validates that RF-CNN extracts richer indicators for SOH estimation.
  • Future work: The evaluation uses a fast-discharging dataset with an identical 4 C discharge rate and 30 °C ambient temperature.Future work will evaluate various charge/discharge rates and ambient temperatures.
  • Future work: Future work will extend the approach to overall battery-string SOH estimation.
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