Automated distribution-free interval estimation for lithium-Ion battery state of health using multiple health indicators

GUO Ziyao; ZHANG Xiaotong; PANG Xiaoqiong; WANG Zhuqing

doi:10.19799/j.cnki.2095-4239.2025.1031

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Automated distribution-free interval estimation for lithium-Ion battery state of health using multiple health indicators

Energy Storage Test\: Methods and Evaluation | 更新时间：2026-07-01

- Automated distribution-free interval estimation for lithium-Ion battery state of health using multiple health indicators
- Energy Storage Science and Technology Vol. 15, Issue 4, Pages: 1375-1386(2026)
- 作者机构：
  
  1.中北大学计算机科学与技术学院，山西太原 030051
  2.太原理工大学计算机科学与技术学院，山西太原 030024
- 作者简介：
- 基金信息：
- DOI：10.19799/j.cnki.2095-4239.2025.1031
  CLC： TM 912
- Received：18 November 2025，
  
  Revised：2025-12-22，
  
  Published：28 April 2026
- 稿件说明：
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郭子瑶, 张晓桐, 庞晓琼, 等. 多健康指标的锂离子电池健康状态无分布区间估计[J]. 储能科学与技术, 2026, 15(4): 1375-1386.

GUO Ziyao, ZHANG Xiaotong, PANG Xiaoqiong, et al. Automated distribution-free interval estimation for lithium-Ion battery state of health using multiple health indicators[J]. Energy Storage Science and Technology, 2026, 15(4): 1375-1386.
郭子瑶, 张晓桐, 庞晓琼, 等. 多健康指标的锂离子电池健康状态无分布区间估计[J]. 储能科学与技术, 2026, 15(4): 1375-1386. DOI： 10.19799/j.cnki.2095-4239.2025.1031.

GUO Ziyao, ZHANG Xiaotong, PANG Xiaoqiong, et al. Automated distribution-free interval estimation for lithium-Ion battery state of health using multiple health indicators[J]. Energy Storage Science and Technology, 2026, 15(4): 1375-1386. DOI： 10.19799/j.cnki.2095-4239.2025.1031.

摘要

针对现有锂离子电池健康状态(state of health，SOH)点估计方法难以量化估计不确定性的问题，本工作聚焦于更具实际应用价值的SOH区间估计方法。现有大多数区间估计方法是基于分布假设的，当现实数据偏离这些假设时，会引入估计偏差，进而影响估计的可靠性。为此，无分布的上下界估计(lower upper bound estimate，LUBE)方法逐渐受到关注，但其仍面临若干挑战：其一，损失函数不可微，导致模型优化困难；其二，部分研究采用Sigmoid函数将不可微的损失函数转变为可微损失函数，但Sigmoid函数的引入往往需人工调整斜率参数；其三，现有的研究多建立在容量这一理想健康指标上，然而容量的精确测量成本高昂，限制了该方法在实际场景中的适用性。为此，本工作提出一种面向多健康指标的锂离子电池SOH无分布区间估计方法。首先，采用核主成分分析(kernel principal component analysis， KPCA)方法对提取的多健康指标进行非线性降维。在此基础上，构建一个双输出神经网络模型，通过引入一种无需手动调整斜率参数的损失函数，使模型能够基于降维后的数据，稳定地输出高质量的预测区间。在公开可用的CALCE数据集上的实验结果表明，本工作所提方法不仅满足预定义置信水平的要求，还进一步提升了预测区间的质量。

Abstract

To address the limitations of conventional state of health (SOH) point estimation methods for lithium-ion batteries

this study develops a more practical SOH interval estimation method. Most previous interval estimation methods rely on distribution assumptions. However

when real-world battery data deviate from these assumptions

estimation biases may be introduced

consequently reducing estimation reliability. Consequently

the distribution-free lower upper bound estimation (LUBE) method has gradually attracted attention

although it still faces critical challenges. First

the loss function is non-differentiable

complicating model optimization. Second

several studies employed Sigmoid functions to transform non-differentiable loss functions into differentiable loss functions; however

this approach often requires manual slope-parameter tuning. Third

previous studies mostly rely on capacity as an ideal health indicator; however

accurately measuring capacity is costly

and this limits the real-world applicability of this method. To address these shortcomings

this study proposes a distribution-free SOH interval estimation method for quantifying LIB SOH using multiple health indicators. First

the kernel principal component analysis (KPCA) method is applied to reduce the dimensionality of the extracted health indicators. Based on this

a dual-output neural network model is constructed; this model introduces a loss function that eliminates the need for manual slope-parameter tuning

enabling it to stably output high-quality prediction intervals based on the reduced-dimensional data. Experimental results using the publicly available CALCE dataset demonstrate that the proposed method consistently meets nominal-confidence-level requirements while significantly improving prediction-interval quality.

关键词

Keywords

references

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