基于核递归最大总广义相关熵的时间序列预测  

Kernel recursive maximum total generalized correntropy for time series prediction

作　　者：韩敏[1] 夏慧娟 HAN Miny;XIA Hui-juan(Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education,Dalian University of Technology,Dalian Liaoning 116024,China;Faculty of Electronic Information and Electrical Engineering,Dalian University of Technology,Dalian Liaoning 116024,China)

机构地区：[1]大连理工大学工业装备智能控制与优化教育部重点实验室,辽宁大连116024 [2]大连理工大学电子信息与电气工程学部,辽宁大连116024

出　　处：《控制理论与应用》2024年第10期1944-1950,共7页Control Theory & Applications

基　　金：国家自然科学基金项目(62173063)资助.

摘　　要：针对核自适应滤波器(KAF)在非高斯和脉冲噪声环境下预测性能下降问题,本文提出了一种新颖的鲁棒算法,称为核递归最大总广义相关熵(KRMTGC)算法.首先,简要介绍系统模型和最大总相关熵(MTC)准则;其次,在核空间采用灵活的总广义相关熵准则取代MTC准则,详细推导出KRMTGC算法,该算法对异常值或非高斯噪声具有更强的鲁棒性;此外,为进一步控制KRMTGC算法中核矩阵无限扩张模式,采用矢量量化思想降低计算复杂度,提出量化KRMTGC算法;然后,研究分析KRMTGC算法的局部收敛特性;最后,通过在基准Rossler系统和真实厄尔尼诺–南方涛动时间序列预测中的仿真结果表明:相比其他KAF算法,所提算法具有更优的预测速度和预测精度.In order to address the problem that the predictive performance of kernel adaptivefilter(KAF)is degraded in non-Gaussian and impulsive noise environments,a novel robust algorithm called kernel recursive maximum total gen-eralized correntropy(KRMTGC)algorithm is proposed.Firstly,the system model and maximum total correntropy(MTC)are briefly introduced.Secondly,theflexible total generalized correntropy criterion is utilized to replace the MTC criterion in the kernel space,and the KRMTGC algorithm is derived in detail,which exhibits enhanced robustness against outliers and non-Gaussian noise.Moreover,to further control the infinite expansion mode of the kernel matrix of the KRMTGC algorithm,the quantized KRMTGC algorithm is proposed by using vector quantization to reduce the computational com-plexity.Then,the local convergence performance of the KRMTGC algorithm is analyzed.Finally,simulation results of the benchmark Rossler system and the real-world El Ni˜no-Southern Oscillation time series prediction demonstrate that the proposed algorithm outperforms other KAF algorithms in terms of prediction speed and accuracy.

关 键 词：核自适应滤波器 总广义相关熵 矢量量化 时间序列 预测 

分 类 号：TN713[电子电信—电路与系统] O211.61[理学—概率论与数理统计]