Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method  

作　　者：Yi-fei PU Jian WANG 

机构地区：[1]College of Computer Science,Sichuan University,Chengdu 610065,China [2]College of Science,China University of Petroleum,Qingdao 266580,China

出　　处：《Frontiers of Information Technology & Electronic Engineering》2020年第6期809-833,共25页信息与电子工程前沿（英文版）

基　　金：Project supported by the National Key Research and Development Program of China(No.2018YFC0830300);the National Natural Science Foundation of China(No.61571312)。

摘　　要：We introduce the fractional-order global optimal backpropagation machine,which is trained by an improved fractionalorder steepest descent method(FSDM).This is a fractional-order backpropagation neural network(FBPNN),a state-of-the-art fractional-order branch of the family of backpropagation neural networks(BPNNs),different from the majority of the previous classic first-order BPNNs which are trained by the traditional first-order steepest descent method.The reverse incremental search of the proposed FBPNN is in the negative directions of the approximate fractional-order partial derivatives of the square error.First,the theoretical concept of an FBPNN trained by an improved FSDM is described mathematically.Then,the mathematical proof of fractional-order global optimal convergence,an assumption of the structure,and fractional-order multi-scale global optimization of the FBPNN are analyzed in detail.Finally,we perform three(types of)experiments to compare the performances of an FBPNN and a classic first-order BPNN,i.e.,example function approximation,fractional-order multi-scale global optimization,and comparison of global search and error fitting abilities with real data.The higher optimal search ability of an FBPNN to determine the global optimal solution is the major advantage that makes the FBPNN superior to a classic first-order BPNN.

关 键 词：Fractional calculus Fractional-order backpropagation algorithm Fractional-order steepest descent method Mean square error Fractional-order multi-scale global optimization 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] O224[自动化与计算机技术—控制科学与工程]