Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

doi:10.1088/1674-1056/23/5/050503

中国物理B ›› 2014, Vol. 23 ›› Issue (5): 50503-050503.doi: 10.1088/1674-1056/23/5/050503

Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

Bilal Shoaib^a, Ijaz Mansoor Qureshi^b, Shafqatullah^c, Ihsanulhaq^a

a Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad, Pakistan;
b Department of Electrical Engineering, AIR University, Islamabad, Pakistan;
c School of Engineering and Applied Sciences, ISRA University, Islamabad, Pakistan

收稿日期:2013-10-08 修回日期:2013-11-21 出版日期:2014-05-15 发布日期:2014-05-15
基金资助:
Project supported by the Higher Education Commission of Pakistan.

Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

Bilal Shoaib^a, Ijaz Mansoor Qureshi^b, Shafqatullah^c, Ihsanulhaq^a

a Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad, Pakistan;
b Department of Electrical Engineering, AIR University, Islamabad, Pakistan;
c School of Engineering and Applied Sciences, ISRA University, Islamabad, Pakistan

Received:2013-10-08 Revised:2013-11-21 Online:2014-05-15 Published:2014-05-15
Contact: Bilal Shoaib E-mail:bilal.phdee42@iiu.edu.pk
About author:05.45.Df; 05.30.Pr; 05.45.Tp; 92.60.Wc
Supported by:
Project supported by the Higher Education Commission of Pakistan.

摘要/Abstract

摘要： This paper presents an adaptive step-size modified fractional least mean square (AMFLMS) algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.

关键词: fractional LMS, kernel LMS, Reimann-Lioville derivative, Mackey glass and Lorenz time series

Abstract: This paper presents an adaptive step-size modified fractional least mean square (AMFLMS) algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.

Key words: fractional LMS, kernel LMS, Reimann-Lioville derivative, Mackey glass and Lorenz time series

中图分类号: (Fractals)

05.45.Df

05.30.Pr (Fractional statistics systems) 05.45.Tp (Time series analysis) 92.60.Wc (Weather analysis and prediction)

Bilal Shoaib, Ijaz Mansoor Qureshi, Shafqatullah, Ihsanulhaq. Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction[J]. 中国物理B, 2014, 23(5): 50503-050503.

Bilal Shoaib, Ijaz Mansoor Qureshi, Shafqatullah, Ihsanulhaq. Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction[J]. Chin. Phys. B, 2014, 23(5): 50503-050503.

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Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

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