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

作　　者：BilalShoaib Ijaz Mansoor Qureshi Shafqatullah Ihsanulhaq 

机构地区：[1]Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University Islamabad, Pakistan [2]Department of Electrical Engineering, AIR University, Islamabad, Pakistan [3]School of Engineering and Applied Sciences, ISRA University, Islamabad, Pakistan

出　　处：《Chinese Physics B》2014年第5期129-137,共9页中国物理B（英文版）

基　　金：Project supported by the Higher Education Commission of Pakistan

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.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 

分 类 号：O415.5[理学—理论物理]