基于厚尾双学生氏t分布的非线性状态空间系统鲁棒辨识方法

刘鑫; 海洋; 代伟

doi:10.12263/DZXB.20230957

您当前的位置：

首页 >

文章列表页 >

基于厚尾双学生氏t分布的非线性状态空间系统鲁棒辨识方法

学术论文 | 更新时间：2025-12-08

- 基于厚尾双学生氏t分布的非线性状态空间系统鲁棒辨识方法
- Robust Identification of Nonlinear State-Space System Based on Dual Heavy-Tailed Noise Distributions
- 电子学报 2024年52卷第9期页码：3052-3064
- 作者机构：
  
  1.中国矿业大学人工智能研究院，江苏徐州 221116
  2.中国矿业大学信息与控制工程学院，江苏徐州 221116
- 作者简介：
  
  [ "刘鑫男，1990年7月出生于江苏省盐城市.现为中国矿业大学人工智能研究院副教授、硕士生导师.从事系统辨识、数据驱动的工业建模和软测量方面的研究. E-mail: 15B904027@hit.edu.cn" ]
  [ "海洋男，1999年5月出生于辽宁省阜新市.现为中国矿业大学信息与控制工程学院硕士研究生.主要研究方向为系统辨识，数据驱动的工程建模. E-mail: ts22060067a31@cumt.edu.cn" ]
  [ "代伟男，1984年3月出生于河南省安阳市.现为现为中国矿业大学信息与控制工程学院教授、博士生导师.从事复杂工业过程建模、运行优化与控制方面的研究.E-mail: weidai@cumt.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(62103134;62373361);国家重点研发计划(2022YFB3304700);中国博士后基金(2023M743776)
- DOI：10.12263/DZXB.20230957
  中图分类号： TP27
- 收稿：2023-10-16，
  
  修回：2024-02-24，
  
  纸质出版：2024-09-25
- 稿件说明：
移动端阅览
刘鑫, 海洋, 代伟. 基于厚尾双学生氏t分布的非线性状态空间系统鲁棒辨识方法[J]. 电子学报, 2024, 52(09): 3052-3064.

LIU Xin, HAI Yang, DAI Wei. Robust Identification of Nonlinear State-Space System Based on Dual Heavy-Tailed Noise Distributions[J]. Acta Electronica Sinica, 2024, 52(09): 3052-3064.
刘鑫, 海洋, 代伟. 基于厚尾双学生氏t分布的非线性状态空间系统鲁棒辨识方法[J]. 电子学报, 2024, 52(09): 3052-3064. DOI：10.12263/DZXB.20230957

LIU Xin, HAI Yang, DAI Wei. Robust Identification of Nonlinear State-Space System Based on Dual Heavy-Tailed Noise Distributions[J]. Acta Electronica Sinica, 2024, 52(09): 3052-3064. DOI：10.12263/DZXB.20230957

摘要

状态空间模型作为一种常见且重要的模型结构在自动化领域有着广泛的应用，本文针对异常值干扰下的非线性状态空间系统辨识问题开展研究.与现有的辨识方法不同，本文充分考虑了状态转移过程和输出量测过程均受到异常值干扰的情况，提出了一种更加全面的鲁棒辨识算法.首先利用两个相互独立的学生氏t分布分别对状态噪声和输出噪声进行建模以保障算法的鲁棒性；其次利用粒子平滑算法估计状态变量的后验概率分布以解决状态未知问题；最后利用期望最大化算法实现未知参数估计.在算法实现过程中使用了学生氏t分布表达式的数学分解，这样做的好处是：（1）更加有利于算法的推导和实现；（2）更清晰地解释了算法的鲁棒性能.并且本文通过数值算例和应用算例验证了该方法的有效性.

Abstract

The state space model is a common and important model structure for automation and control. In this paper

the robust identification of nonlinear state-space model corrupted by outliers is investigated. The outliers imposed on both the state transition process and the output measurement process are considered and a more comprehensive and robust identification algorithm is proposed. To ensure the robustness of the proposed algorithm

two independent heavy-tailed Student's t-distributions are used to describe the state noise and the output noise

respectively. Then the particle smoothing method is applied to estimate the posterior distribution of the unknown states. Finally

the expectation maximization algorithm is used to realize the parameter estimation problem. The mathematical decomposition of the Student's t-distribution is employed in the identification process which brings two main advantages: (1) facilitating the derivation and implementation of the proposed algorithm; (2) providing a more clearer explanation of the robustness of the algorithm. The usefulness of the proposed algorithm is demonstrated via the numerical and mechanical examples.

关键词

Keywords

references

刘鑫 . 时滞取值概率未知下的线性时滞系统辨识方法 [J ] . 自动化学报 , 2023 , 49 ( 10 ): 2136 - 2144 .

LIU X . Identification of linear time-delay systems with unknown delay distributions in its value range [J ] . Acta Automatica Sinica , 2023 , 49 ( 10 ): 2136 - 2144 . (in Chinese)

DING F , LIU X M , HAYAT T . Hierarchical least squares identification for feedback nonlinear equation-error systems [J ] . Journal of the Franklin Institute , 2020 , 357 ( 5 ): 2958 - 2977 .

HAN R J , SALEHI Y , HUANG B , et al . Parameter estimation for nonlinear systems with multirate measurements and random delays [J ] . AIChE Journal , 2021 , 67 ( 9 ): 17327-1- 17327 - 15 .

LIU X , YANG X Q , LIU X F . Nonlinear state-space system identification with robust Laplace model [J ] . International Journal of Control , 2021 , 94 ( 6 ): 1492 - 1501 .

LIU Q , LIN W Y , JIANG S L , et al . Robust estimation of Wiener models in the presence of outliers using the VB approach [J ] . IEEE Transactions on Industrial Electronics , 2021 , 68 ( 11 ): 11390 - 11399 .

HOU J , SU H , YU C P , et al . Bias-correction errors-in-variables Hammerstein model identification [J ] . IEEE Transactions on Industrial Electronics , 2023 , 70 ( 7 ): 7268 - 7279 .

PODUSENKO A , AKBAYRAK S , SENOZ I , et al . Message passing-based system identification for NARMAX models [C ] // 2022 IEEE 61st Conference on Decision and Control (CDC) . Piscataway : IEEE , 2022 : 7309 - 7314 .

GU Y , ZHU Q M , NOURI H . Identification and U-control of a state-space system with time-delay [J ] . International Journal of Adaptive Control and Signal Processing , 2022 , 36 ( 1 ): 138 - 154 .

ZOU Y D , HU W Q , XIAO Z H , et al . Design of intelligent nonlinear robust controller for hydro-turbine governing system based on state-dynamic-measurement hybrid feedback linearization method [J ] . Renewable Energy , 2023 , 204 : 635 - 651 .

张宏伟 . 时空学习驱动的混合重要性高斯滤波 [EB/OL ] . ( 2023-09-26 )[ 2023-11-16 ] . https://doi.org/10.12263/DZXB.20230056 https://doi.org/10.12263/DZXB.20230056 .

奚畅 , 蔡志明 , 袁骏 . 被动声纳粒子滤波检测前跟踪的检测门限设置方法 [J ] . 电子学报 , 2022 , 50 ( 7 ): 1722 - 1734 .

XI C , CAI Z M , YUAN J . A method of determining detection threshold for particle filter track-before-detect in pas⁃ sive sonar [J ] . Acta Electronica Sinica , 2022 , 50 ( 7 ): 1722 - 1734 . (in Chinese)

BRUNOT M , JANOT A , CARRILLO F , et al . State space estimation method for robot identification [J ] . Ifac Papersonline , 2016 , 49 ( 21 ): 228 - 233 .

LIU K . Identification of linear time-varying systems [J ] . Journal of Sound Vibration , 1997 , 206 ( 4 ): 487 - 505 .

GHIAUS C , GHAZAL R , JOUBERT P , et al . Gray-box state-space model and parameter identification of desiccant wheels [J ] . Applied Thermal Engineering , 2013 , 51 ( 1/2 ): 742 - 752 .

LIU X P , YANG X Q . Identification of nonlinear state-space systems with skewed measurement noises [J ] . IEEE Transactions on Circuits and Systems I: Regular Papers , 2022 , 69 ( 11 ): 4654 - 4662 .

GOPALUNI R B . A particle filter approach to identification of nonlinear processes under missing observations [J ] . The Canadian Journal of Chemical Engineering , 2008 , 86 ( 6 ): 1081 - 1092 .

LIU X T , LI Q L , WANG L , et al . Data-driven state of charge estimation for power battery with improved extended Kalman filter [J ] . IEEE Transactions on Instrumentation and Measurement , 2023 , 72 : 1 - 10 .

陈云翔 , 王泽洲 , 蔡忠义 , 等 . 基于EM-EKF与隐含比例退化模型的机载电子设备剩余寿命自适应预测 [J ] . 电子学报 , 2021 , 49 ( 3 ): 500 - 509 .

CHEN Y X , WANG Z Z , CAI Z Y , et al . Adaptive prediction of remaining useful lifetime for the airborne electronic equipment based on the EM-EKF algorithm and hidden degradation model with the proportion relationship [J ] . Acta Electronica Sinica , 2021 , 49 ( 3 ): 500 - 509 . (in Chinese)

ZHU F , FU J Q . A novel state-of-health estimation for lithium-ion battery via unscented Kalman filter and improved unscented particle filter [J ] . IEEE Sensors ournal , 2021 , 21 ( 22 ): 25449 - 25456 .

LI G H , NIU D B , SONG E B . A multiple-model state estimator based on the unscented Kalman filter [C ] // 2020 39th Chinese Control Conference (CCC) . Piscataway : IEEE , 2020 : 3011 - 3016 .

卢春光 , 张永顺 , 李志汇 , 等 . 量测随机延迟下带厚尾噪声的鲁棒Student's t随机容积卡尔曼滤波器 [J ] . 电子学报 , 2019 , 47 ( 9 ): 1830 - 1840 .

LU C G , ZHANG Y S , LI Z H , et al . Robust Student's t-based stochastic cubature Kalman filter with heavy-tailed noises and randomly delayed measurements [J ] . Acta Electronica Sinica , 2019 , 47 ( 9 ): 1830 - 1840 . (in Chinese)

SWATI . Continuous discrete cubature quadrature Kalman filter [J ] . Asian Journal of Control , 2022 , 24 ( 1 ): 483 - 493 .

GUO F , HARIPRASAD K , HUANG B , et al . Robust identification for nonlinear errors-in-variables systems using the EM algorithm [J ] . Journal of Process Control , 2017 , 54 : 129 - 137 .

CHEN B D , DANG L J , GU Y T , et al . Minimum error entropy Kalman filter [J ] . IEEE Transactions on Systems, Man, and Cybernetics: Systems , 2021 , 51 ( 9 ): 5819 - 5829 .

BAI M M , HUANG Y L , ZHANG Y G , et al . Statistical similarity measure-based adaptive outlier-robust state estimator with applications [J ] . IEEE Transactions on Automatic Control , 2022 , 67 ( 8 ): 4354 - 4361 .

王国庆 , 杨春雨 , 马磊 . 基于多变量Laplace分布的非线性系统分布式鲁棒状态估计 [J ] . 电子学报 , 2022 , 50 ( 11 ): 2610 - 2618 .

WANG G Q , YANG C Y , MA L . Distributed robust state estimation for nonlinear systems based on multivariate Laplace distribution [J ] . Acta Electronica Sinica , 2022 , 50 ( 11 ): 2610 - 2618 . (in Chinese)

黄玉龙 , 张勇刚 , 李宁 , 等 . 一种带有色量测噪声的非线性系统辨识方法 [J ] . 自动化学报 , 2015 , 41 ( 11 ): 1877 - 1892 .

HUANG Y L , ZHANG Y G , LI N , et al . An identification method for nonlinear systems with colored measurement noise [J ] . Acta Automatica Sinica , 2015 , 41 ( 11 ): 1877 - 1892 . (in Chinese)

LIU X , YANG X Q . Robust identification approach for nonlinear state-space models [J ] . Neurocomputing , 2019 , 333 : 329 - 338 .

CHEN B D , LIU X , ZHAO H Q , et al . Maximum correntropy Kalman filter [J ] . Automatica , 2017 , 76 : 70 - 77 .

SAMMAKNEJAD N , ZHAO Y J , HUANG B . A review of the expectation maximization algorithm in data-driven process identification [J ] . Journal of Process Control , 2019 , 73 : 123 - 136 .

WANG D P , ZHANG H , HUANG H L . An adaptive robust student's t-based Kalman filter based on multi-sensor fusion [C ] // 15th International Conference on Intelligent Robotics and Applications (ICIRA) . Cham : Springer International Publishing , 2022 : 603 - 613 .

YANG X Q , YIN S . Robust global identification and output estimation for LPV dual-rate systems subjected to random output time-delays [J ] . IEEE Transactions on Industrial Informatics , 2017 , 13 ( 6 ): 2876 - 2885 .

YANG X Q , LIU X , HAN B X . LPV model identification with an unknown scheduling variable in the presence of missing observations-a robust global approach [J ] . IET Control Theory & Applications , 2018 , 12 ( 10 ): 1465 - 1473 .

王国庆 , 杨春雨 , 马磊 , 等 . 基于高斯-广义双曲混合分布的非线性卡尔曼滤波 [J ] . 自动化学报 , 2023 , 49 ( 2 ): 448 - 460 .

WANG G Q , YANG C Y , MA L , et al . Nonlinear Kalman filter based on gaussian-generalized-hyperbolic mixing distribution [J ] . Acta Automatica Sinica , 2023 , 49 ( 2 ): 448 - 460 . (in Chinese)

SCHÖN T B , WILLS A , NINNESS B . System identification of nonlinear state-space models [J ] . Automatica , 2011 , 47 ( 1 ): 39 - 49 .

JABALI M B A , KAZEMI M H . Uncertain polytopic LPV modelling of robot manipulators and trajectory tracking [J ] . International Journal of Control, Automation and Systems , 2017 , 15 ( 2 ): 883 - 891 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

一种模型选择优化准则及其在高光谱图像非监督分类中的应用