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| Variable fractional-order gradient descent method |
| LI Jiawei1, 2, SHEN Yongjun1, 2, YANG Shaopu1, 2 |
1. State Key Lab of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University,
Shijiazhuang 050043, China;
2.Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China |
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Abstract The gradient descent method is a classical convex optimization algorithm.Here, combined with the theory of fractional-order advanced calculus, the fractional-order gradient descent method was investigated.It was shown that compared with the conventional gradient descent method, the fractional-order gradient descent method with the order larger than 1 has faster convergence speed and lower convergence accuracy, while it with the order less than 1 has higher convergence accuracy and slower convergence speed.In order to combine advantages of different fractional-order gradient descent methods and solve the contradiction between convergence speed and convergence accuracy, 3 improved variable fractional-order gradient descent methods were proposed based on the published study results to obtain better optimization algorithm performances.Typical examples were taken to verify relevant conclusions.
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Received: 09 December 2019
Published: 15 May 2021
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［1］XUE Dingyu, ZHAO Chunna, CHEN Yangquan .Fractional order PID control of a DC-motor with elastic shaft: a case study ［C］∥Proceedings of the 2006 American Control Conference.Minneapolis, 2006.
［2］张小龙, 魏井福, 东亚斌, 等.滚珠自动控制转子系统强迫振动研究(1/2次分数谐波振动)［J］.振动与冲击, 2017, 36(21): 23-27.
ZHANG Xiaolong, WEI Jingfu, DONG Yabin, et al.Forced vibration of the rotor controlled by an automatic ball balancer(1/2 order subharmonic vibration)［J］.Journal of Vibration and Shock, 2017, 36(21): 23-27.
［3］HARTLEY T T, LORENZO C F .Fractional-order system identification based on continuous order-distributions ［J］.Signal Processing,2003,83(11):2287-2300.
［4］林晓然.分数阶非线性系统动力学特性及其图像处理应用研究 ［D］.重庆：重庆大学,2018.
［5］STEPHEN B, LIEVEN V .Convex optimization ［M］.Cambridge: Cambridge University Press, 2004.
［6］WONG Chingchang,CHEN Chiachang .A hybrid clustering and gradient descent approach for fuzzy modeling ［J］.IEEE Transactions on Systems,Man,and Cybernetics,Part B: Cybernetics,1999,29(6):686-693.
［7］LIN Q, LOXTON R, XU C, et al.Parameter estimation for nonlinear time-delay system with noisy output measurements ［J］.Automatica, 2015, 60: 48-56.
［8］KRETSCHMER F，LEWIS B.An improved algorithm for adaptive filters processing ［J］.IEEE Transactions on Aerospace and Electronic Systems,1979, 1(14): 172-177.
［9］BALLA-ARABE S, GAO X B, WANG B.A fast and robust level set method for image segmentation using fuzzy clustering and lattice Boltzmann method［J］.IEEE Transactions on Cybernetics, 2013, 43(3): 910-920.
［10］VAUDREY M A, BAUMANN W T, SAUNDERS W R.Stability and operating constrains of adaptive LMS-based feedback control ［J］.Automatica,2003, 39(4): 595-605.
［11］LIN J Y, LIAO C W.New IIR filter-based adaptive algorithm in active noise control applications:commutation error-introduced LMS algorithm and associated convergence assessment by a deterministic approach ［J］.Automatica, 2008, 44(11): 2916-2922.
［12］PU Y F, ZHOU J L, ZHANG Y, et al.Fractional extreme value adaptive training method:fractional steepest descent approach ［J］.IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(4): 653-662.
［13］CHEN Y Q, GAO Q, WEI Y H, et al.Study on fractional order gradient methods ［J］.Applied Mathematics and Computation, 2017, 314: 310-321.
［14］程松松.分数阶LMS自适应滤波算法研究［D］.合肥：中国科学技术大学，2018.
［15］李大字, 卢婷, 靳其兵.基于分数阶梯度下降法的分数阶非线性系统预测控制［J］.系统仿真技术, 2017, 13(2): 127-131.
LI Dazi, LU Ting, JIN Qiping.Predictive control with fractional gradient descent for fractional-order nonlinear system ［J］.System Simulation Technology, 2017, 13(2): 127-131.
［16］CHENG S S, WEI Y H, CHEN Y Q, et al.An innovative fractional order LMS based on variable initial value and gradient order［J］.Signal Processing, 2017, 133: 260-269.
［17］CUI R, WEI Y H, CHEN Y Q, et al.An innovative parameter estimation for fractional-order systems in the presence of outliers ［J］.Nonlinear Dynamics, 2017, 89(1): 453-463.
［18］CHENG S S, WEI Y H, SHENG D, et al.Identification for Hammerstein nonlinear ARMAX systems based on multi-innovation fractional order stochastic gradient ［J］.Signal Processing, 2018, 142: 1-10.
［19］
CORLISS G, LOWERY D.Choosing a stepsize for Taylor series methods for solving ODE'S［J］.Journal of Computational and Applied Mathematics ,1977,3(4): 251-256.
［20］WEI Y H,GAO Q,CHEN Y Q,et al.Infinite series representation of fractional calculus［C］∥2019 Chinese Automation Congress.Hangzhou: CAC, 2019. |
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