A Particle-Swarm-Confinement-based Zonotopic Space Filtering Algorithm and Its Application to State of Charge Estimation for Lithium-Ion Batteries

HUO Leiting; WANG Ziyun; WANG Yan

doi:10.11999/JEIT250437

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2025 >

HUO Leiting, WANG Ziyun, WANG Yan. A Particle-Swarm-Confinement-based Zonotopic Space Filtering Algorithm and Its Application to State of Charge Estimation for Lithium-Ion Batteries[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250437

Citation:

HUO Leiting, WANG Ziyun, WANG Yan. A Particle-Swarm-Confinement-based Zonotopic Space Filtering Algorithm and Its Application to State of Charge Estimation for Lithium-Ion Batteries[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250437

Citation:

HUO Leiting, WANG Ziyun, WANG Yan. A Particle-Swarm-Confinement-based Zonotopic Space Filtering Algorithm and Its Application to State of Charge Estimation for Lithium-Ion Batteries[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250437

PDF( 2534 KB)

A Particle-Swarm-Confinement-based Zonotopic Space Filtering Algorithm and Its Application to State of Charge Estimation for Lithium-Ion Batteries

doi: 10.11999/JEIT250437 cstr: 32379.14.JEIT250437

HUO Leiting^{1, 2},
WANG Ziyun^{1, 2
,
,},
WANG Yan^{1, 2}

1.
Engineering Research Center of Internet of Things Technology Applications (Ministry of Education), Jiangnan University, Wuxi 214122, China
2.
School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China

Funds: The Natural Science Foundation of China (62473174), The Natural Science Foundation of Jiangsu Province (BK20221533)

Received Date: 2025-05-20
Rev Recd Date: 2025-08-20

Available Online: 2025-08-27

Abstract

Abstract

Objective The State of Charge (SOC) is a critical indicator for evaluating the remaining capacity and health status of lithium-ion batteries, which are widely deployed in electric vehicles, portable electronics, and energy storage systems. Accurate SOC estimation is essential for maintaining safe operation, extending battery life, and optimizing energy utilization. However, practical SOC estimation is complicated by measurement uncertainties and disturbances, particularly Unknown But Bounded (UBB) noise arising from sensor errors, environmental fluctuations, and battery aging. Conventional filtering algorithms, such as Kalman filters, often depend on probabilistic noise assumptions and tend to perform poorly when actual noise characteristics deviate from Gaussian distributions. This study addresses these limitations by proposing a Particle-Swarm-Confinement-based Zonotopic Space Filtering (PSC-ZSF) algorithm to enhance estimation robustness and reduce conservatism, with specific emphasis on high-dimensional dynamic systems such as lithium-ion battery SOC estimation. Methods The PSC-ZSF algorithm combines the robustness of set-membership filtering with the global optimization capabilities of Particle Swarm Optimization (PSO), integrating geometric uncertainty representation with heuristic search strategies. A zonotopic feasible state set is first constructed by propagating system model predictions and refining them with measurement updates, thereby representing the bounded uncertainty in system states. A swarm of particles is then randomly initialized within this zonotopic space to explore potential state estimates. Particle movement follows PSO-based velocity and position updates, leveraging both individual experience and swarm intelligence to identify optimal state estimates. Fitness functions quantify the consistency between candidate states and observed measurements, guiding particle convergence toward more plausible regions. To maintain algorithm stability, a boundary detection mechanism identifies particles that exceed the zonotopic feasible region. Out-of-bound particles are projected back into the feasible set by solving a quadratic programming problem that minimizes positional distortion while preserving spatial characteristics. Additionally, a dynamic contraction strategy adaptively tightens the zonotopic boundaries by scaling the normal vectors of the defining hyperplanes, effectively shrinking the search space as the particle swarm converges. This contraction improves estimation precision and reduces conservatism without incurring excessive computational overhead. The approach utilizes Minkowski sum properties intrinsic to zonotopes and utilizes efficient geometric computations to balance accuracy and efficiency. For experimental validation, the PSC-ZSF algorithm is applied to SOC estimation of lithium-ion batteries modeled by a discrete-time equivalent circuit that incorporates polarization resistance and capacitance effects. Real-world data are collected from a 18650 lithium-ion battery undergoing constant current discharge at room temperature. The system model considers UBB process and measurement noise, with parameters calibrated through empirical measurements. The performance of the proposed method is benchmarked against Ellipsoidal Set-Membership Filtering (ESMF) and Zonotopic Set-Membership Filtering (ZSMF) methods by comparing feasible state set volumes and the tightness of estimated boundaries. Results and Discussions The proposed PSC-ZSF algorithm demonstrates reliable confinement of particle swarms within the zonotopic feasible region throughout iterative optimization, effectively preventing particle divergence and improving estimation stability and reliability (Fig. 1). Comparative analysis indicates that PSC-ZSF consistently achieves significantly smaller feasible state set volumes at each time step compared to ESMF and ZSMF methods, reflecting reduced estimation redundancy and improved compactness (Fig. 3). The ESMF method guarantees that the true state remains enclosed; however, it produces overly conservative ellipsoidal bounds, especially under conditions of rapid system dynamics, which compromises estimation informativeness and responsiveness. The ZSMF method improves upon this by employing zonotopic bounds but still yields relatively broad estimation regions due to fixed zonotope geometries and cautious boundary updates. In contrast, PSC-ZSF adaptively refines the zonotopic boundaries based on real-time particle swarm distributions, leading to consistently tighter, more accurate boundaries that closely track the true SOC and polarization voltage trajectories (Figs. 4 and 5). This adaptive boundary contraction strategy enhances estimation precision while preserving robustness. Moreover, computational complexity analysis shows that although particle projection and boundary scaling introduce additional per-iteration operations, the accelerated convergence of PSC-ZSF reduces overall iteration requirements. This trade-off ensures computational feasibility for real-time SOC estimation in battery management systems. Conclusions This study proposes a Particle-Swarm-Confinement-Based Zonotopic Space Filtering (PSC-ZSF) algorithm that integrates set-membership filtering with PSO to address state estimation under unknown but bounded noise. The PSC-ZSF algorithm ensures that particle swarms remain confined within a zonotopic feasible region through optimal projection and dynamically contracts the zonotope boundaries via hyperplane scaling. This approach improves estimation accuracy and reduces conservatism. Application to lithium-ion battery SOC estimation confirms the approach’s superiority over conventional approaches, providing more precise and stable state boundaries while maintaining computational efficiency suitable for real-time applications. Future work will focus on extending the PSC-ZSF algorithm to complex dynamic systems such as autonomous vehicle navigation and smart grid state estimation to further assess scalability and practical applicability.
- State estimation,
- Zonotopic space,
- Particle Swarm Optimization (PSO),
- Filtering,
- State of Charge (SOC)

FullText(HTML)

References(24)

References

[1]	张照娓, 郭天滋, 高明裕, 等. 电动汽车锂离子电池荷电状态估算方法研究综述[J]. 电子与信息学报, 2021, 43(7): 1803–1815. doi: 10.11999/JEIT200487. ZHANG Zhaowei, GUO Tianzi, GAO Mingyu, et al. Review of SoC estimation methods for electric vehicle Li-ion batteries[J]. Journal of Electronics & Information Technology, 2021, 43(7): 1803–1815. doi: 10.11999/JEIT200487.
[2]	王翔, 张巍, 田会臻, 等. 新能源汽车锂离子电池动静态荷电状态估计方法[J/OL]. 电力电子技术. https://doi.org/10.20222/j.cnki.cn61-1124/tm.20250509.022, 2025. (查阅网上资料,请确认本条文献格式). WANG Xiang, ZHANG Wei, TIAN Huizhen, et al. Methods for dynamic and static state-of-charge estimation of lithium-ion batteries in new energy vehicles[J/OL]. Power Electronics Technology. https://doi.org/10.20222/j.cnki.cn61-1124/tm.20250509.022, 2025. (查阅网上资料,未找到对应的英文翻译,请确认).
[3]	LI Haibin, ZHAO Hongwei, LIU Dinghong, et al. Electro-thermal coupling modeling and heat generation decoupling analysis of semi-solid-state lithium-ion battery[J]. Electrochimica Acta, 2025, 512: 145455. doi: 10.1016/j.electacta.2024.145455.
[4]	王振华, 张文瀚, 崔骞, 等. 集员卡尔曼滤波器在电机故障诊断中的应用[J]. 控制理论与应用, 2023, 40(10): 1721–1729. doi: 10.7641/CTA.2023.20649. WANG Zhenhua, ZHANG Wenhan, CUI Qian, et al. Application of set-membership Kalman filter in motor fault diagnosis[J]. Control Theory & Applications, 2023, 40(10): 1721–1729. doi: 10.7641/CTA.2023.20649.
[5]	SHI Huiyuan, LI Ping, CAO Jiangtao, et al. Robust fuzzy predictive control for discrete-time systems with interval time-varying delays and unknown disturbances[J]. IEEE Transactions on Fuzzy Systems, 2020, 28(7): 1504–1516. doi: 10.1109/TFUZZ.2019.2959539.
[6]	ROSTAMI M and LOTFIFARD S. Distributed dynamic state estimation of power systems[J]. IEEE Transactions on Industrial Informatics, 2018, 14(8): 3395–3404. doi: 10.1109/TII.2017.2777495.
[7]	GUO Kai, ZHANG Zekun, ZHENG Dongdong, et al. Set-membership adaptive robot control with deterministically bounded learning gains[J]. IEEE Transactions on Industrial Informatics, 2023, 19(8): 8564–8574. doi: 10.1109/TII.2022.3220892.
[8]	SONG Wenchao, HE Jingbo, LIN Junjie, et al. Bias analysis of PMU-based state estimation and its linear Bayesian improvement[J]. IEEE Transactions on Industrial Informatics, 2024, 20(2): 1607–1617. doi: 10.1109/TII.2023.3280328.
[9]	WANG Ziyun, LI Siyu, WANG Yan, et al. Fault isolability evaluation based on orthographic projection for linear system with bounded noise[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2024, 71(7): 3448–3452. doi: 10.1109/TCSII.2024.3362712.
[10]	王子赟, 占雅聪, 陈宇乾, 等. 基于多胞空间可行集滤波的噪声不确定切换系统故障诊断[J]. 控制与决策, 2023, 38(7): 1909–1917. doi: 10.13195/j.kzyjc.2021.1938. WANG Ziyun, ZHAN Yacong, CHEN Yuqian, et al. Polyhedron spatial feasible set filtering based fault diagnosis for switched system with unknown noise term[J]. Control and Decision, 2023, 38(7): 1909–1917. doi: 10.13195/j.kzyjc.2021.1938.
[11]	XING Yashan, NA Jing, and COSTA-CASTELLÓ R. Real-time adaptive parameter estimation for a polymer electrolyte membrane fuel cell[J]. IEEE Transactions on Industrial Informatics, 2019, 15(11): 6048–6057. doi: 10.1109/TII.2019.2915569.
[12]	ZHAN Yacong, WANG Ziyun, WANG Yan, et al. Zonotope and Gaussian Kalman filters based state estimation algorithm for linear system with dual noise term[J]. IET Control Theory & Applications, 2023, 17(5): 516–526. doi: 10.1049/cth2.12388.
[13]	XIONG Rui, CAO Jiayi, YU Quanqing, et al. Critical review on the battery state of charge estimation methods for electric vehicles[J]. IEEE Access, 2018, 6: 1832–1843. doi: 10.1109/ACCESS.2017.2780258.
[14]	QU Danyang, ZHAO Yiwen, ZHAO Xingang, et al. Recursive parallelotope set-membership estimation algorithm in nonlinear system[C]. 2022 28th International Conference on Mechatronics and Machine Vision in Practice (M2VIP), Nanjing, China, 2022: 1–6. doi: 10.1109/M2VIP55626.2022.10041063.
[15]	ZHOU M, HU Q, GU Z, et al. Observer-based robust control for uncertain time-delay systems with input saturation via zonotopic approach[J]. IEEE Access, 2020, 8: 65212–65223. doi: 10.1109/ACCESS.2020.2982519. (查阅网上资料,未找到本条文献信息,请确认).
[16]	CASINI M, GARULLI A, and VICINO A. Set membership state estimation for discrete-time linear systems with binary sensor measurements[J]. Automatica, 2024, 159: 111396. doi: 10.1016/j.automatica.2023.111396.
[17]	TANG Wentao, WANG Zhenhua, and SHEN Yi. Fault detection and isolation for discrete-time descriptor systems based on H_/L∞ observer and zonotopic residual evaluation[J]. International Journal of Control, 2020, 93(8): 1867–1878. doi: 10.1080/00207179.2018.1535716.
[18]	ZHANG Yuchen, CHEN Bo, and YU Li. Distributed zonotopic estimation for interconnected systems: A fusing overlapping states strategy[J]. Automatica, 2023, 155: 111144. doi: 10.1016/j.automatica.2023.111144.
[19]	SHAMI T M, EL-SALEH A A, ALSWAITTI M, et al. Particle swarm optimization: A comprehensive survey[J]. IEEE Access, 2022, 10: 10031–10061. doi: 10.1109/ACCESS.2022.3142859.
[20]	李冀, 周战洪, 贺红林, 等. 基于围猎改进哈里斯鹰优化的粒子滤波方法[J]. 电子与信息学报, 2023, 45(6): 2284–2292. doi: 10.11999/JEIT220532. LI Ji, ZHOU Zhanhong, HE Honglin, et al. A particle filter method based on Harris hawks optimization improved by encircling strategy[J]. Journal of Electronics & Information Technology, 2023, 45(6): 2284–2292. doi: 10.11999/JEIT220532.
[21]	王子赟, 季钢, 沈谦逸, 等. 基于粒子群的正交超平行空间滤波及其在SOC估计中的应用[J]. 控制与决策, 2025, 40(2): 599–607. doi: 10.13195/j.kzyjc.2024.0191. WANG Ziyun, JI Gang, SHEN Qianyi, et al. Particle swarm optimization based orthometric hyperparallel space filtering and its application in SOC estimation[J]. Control and Decision, 2025, 40(2): 599–607. doi: 10.13195/j.kzyjc.2024.0191.
[22]	WANG Zhenhua, ZHANG Yilian, SHEN Mouquan, et al. Ellipsoidal set-membership filtering for discrete-time linear time-varying systems[J]. IEEE Transactions on Automatic Control, 2023, 68(9): 5767–5774. doi: 10.1109/TAC.2022.3228205.
[23]	IFQIR S, VICENÇ P, DALIL I, et al. Zonotopic set-membership state estimation for switched systems[J]. Journal of the Franklin Institute, 2022, 359(16): 9241–9270. doi: 10.1016/j.jfranklin.2022.08.044.
[24]	SOLDI G, MEYER F, BRACA P, et al. Self-tuning algorithms for multisensor-multitarget tracking using belief propagation[J]. IEEE Transactions on Signal Processing, 2019, 67(15): 3922–3937. doi: 10.1109/TSP.2019.2916764.