基于新型神经网络的ECT图像重建算法的研究
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摘要
电容层析成像技术(Electrical Capacitance Tomography,ECT)在不破坏以及不干扰被测物场的基础上,通过电容测量值重建出管道或容器内部相异介电常数的空间分布状况。它具有低成本、非侵入等优点,在多相流检测领域应用前景广阔。作为ECT系统研究的关键技术,图像重建算法的好坏直接关系着重建图像的质量和速度。本文是在基于传感器结构参数优化的基础上对图像重建算法进行了较深入的研究,主要完成了以下工作:
1.深入研究了电容层析成像系统的技术特点和系统组成,从理论上分析ECT技术的工作原理,对其未来的发展做了宏观上的展望。通过分析电容层析成像系统的特点,给出了代数神经网络算法在电阻层析成像系统图像重建中的优势;
2.以12电极电容层析成像系统为研究对象,分别采用Matlab和ANSYS软件编程获得各种结构参数的计算机仿真实验数据,通过对比实验数据分析各种结构参数对电容传感器性能的影响。
3.对目前存在的几种典型图像重建算法进行了深入研究,针对图像重建算法的欠定性问题,提出将一种新型的神经网络图像重建算法运用到电容层析成像系统的图像重建过程中,并对该方法进行改进,将整个敏感场分布划分为六个子系统,划分后的网络降低了原始网络的规模,在算法的训练速度和成像质量特别是在流型辨识等方面有了显著的提高。
4.设计了ECT图像重建仿真系统软件,利用该软件可以方便地设置圆形管道、传感器以及流型分布的各项参数,对不同参数情况下的系统环境进行快速图像重建算法的仿真研究。
As a kind of non-destructive and non-intrusive measurement, electrical capacitance tomography (ECT) technique can infer the distribution of the conductivity by measuring the electric potential parameter in the sensitivity field and then get the distribution of object field in the pipe. It has a wide application prospect in two-phase flow measurement with the advantages of low cost and non-invasion etc. As the key technology of ECT system research, image reconstruction algorithm has a significant impact on quality and speed of reconstructed image. More profound study is focused on the key problems such as optimized design of transducers’structure parameter, image reconstruction algorithm. The study we have done is as follows.
1. Profound study is on the technical characteristics and the system composition of ECT system. The mathematical model of capacitance sensitivity field is presented according to the principle analysis of ECT system.By macro perspective, given the future prospects of its development. By analyzing the characteristics of electrical capacitance tomography, giving the advantage of algebra neural network algorithm in the electrical resistance tomography on image reconstruction.
2. Taking 12-electrodes electrical capacitance tomography systems as research objects, computer simulation data of different structure parameters is received by using Matlab and ANSYS. The affection of structure parameter on sensor performance is studied by comparing the received data, too.
3. More profound study is focused on the several kinds of typical reconstruction algorithms. Proposed a new type of neural network image reconstruction algorithm applied to the process of image reconstruction in electrical capacitance tomography system, then, improve it. In view of the problem of ill-posed characteristic, we divided the whole NSSN network into six sub-systems to reduce the scale of network, improve the training speed and the image quality particularly based on the flow pattern, etc. have been significantly improved.
4. We design the simulation software of ECT. On that you can easily set the parameters of circular pipe, resistance sensors and distribution of flow. It also can solve the forward problem and the image reconstruction problem.
1.深入研究了电容层析成像系统的技术特点和系统组成,从理论上分析ECT技术的工作原理,对其未来的发展做了宏观上的展望。通过分析电容层析成像系统的特点,给出了代数神经网络算法在电阻层析成像系统图像重建中的优势;
2.以12电极电容层析成像系统为研究对象,分别采用Matlab和ANSYS软件编程获得各种结构参数的计算机仿真实验数据,通过对比实验数据分析各种结构参数对电容传感器性能的影响。
3.对目前存在的几种典型图像重建算法进行了深入研究,针对图像重建算法的欠定性问题,提出将一种新型的神经网络图像重建算法运用到电容层析成像系统的图像重建过程中,并对该方法进行改进,将整个敏感场分布划分为六个子系统,划分后的网络降低了原始网络的规模,在算法的训练速度和成像质量特别是在流型辨识等方面有了显著的提高。
4.设计了ECT图像重建仿真系统软件,利用该软件可以方便地设置圆形管道、传感器以及流型分布的各项参数,对不同参数情况下的系统环境进行快速图像重建算法的仿真研究。
As a kind of non-destructive and non-intrusive measurement, electrical capacitance tomography (ECT) technique can infer the distribution of the conductivity by measuring the electric potential parameter in the sensitivity field and then get the distribution of object field in the pipe. It has a wide application prospect in two-phase flow measurement with the advantages of low cost and non-invasion etc. As the key technology of ECT system research, image reconstruction algorithm has a significant impact on quality and speed of reconstructed image. More profound study is focused on the key problems such as optimized design of transducers’structure parameter, image reconstruction algorithm. The study we have done is as follows.
1. Profound study is on the technical characteristics and the system composition of ECT system. The mathematical model of capacitance sensitivity field is presented according to the principle analysis of ECT system.By macro perspective, given the future prospects of its development. By analyzing the characteristics of electrical capacitance tomography, giving the advantage of algebra neural network algorithm in the electrical resistance tomography on image reconstruction.
2. Taking 12-electrodes electrical capacitance tomography systems as research objects, computer simulation data of different structure parameters is received by using Matlab and ANSYS. The affection of structure parameter on sensor performance is studied by comparing the received data, too.
3. More profound study is focused on the several kinds of typical reconstruction algorithms. Proposed a new type of neural network image reconstruction algorithm applied to the process of image reconstruction in electrical capacitance tomography system, then, improve it. In view of the problem of ill-posed characteristic, we divided the whole NSSN network into six sub-systems to reduce the scale of network, improve the training speed and the image quality particularly based on the flow pattern, etc. have been significantly improved.
4. We design the simulation software of ECT. On that you can easily set the parameters of circular pipe, resistance sensors and distribution of flow. It also can solve the forward problem and the image reconstruction problem.
引文
[1]马平,周晓宁,田沛.过程层析成像技术的发展及应用[J].化工自动化及仪表,2009,36(1):1-5.
[2]李海青,黄志尧.特种检测技术及应用[M].杭州:浙江大学出版社, 2000:72-82.
[3]吴瑞芬.电阻层析成系统敏感场特性分析与仿真研究[D].哈尔滨:哈尔滨理工大学硕士学位论文,2007:1-4.
[4]彭珍瑞,祁文哲,吴刊选.电容层析成像技术的近期研究进展[J].自动化仪表,2008,29(9):1-5.
[5] LAURENT F.C.JEANMEURE,TOMASZ DYAKOWSKI.Direct Flow Pattern Identification using Electrical Capacitance Tomography [J]. Experimental Thermal and Fluid Science,2002,(26):763-773.
[6] SITH PHONGKITKARUN , CHOLADA PHAISANPHRUKKUN ,JANJIRA JATCHAVALA,et al.Assessment of Gastrointestinal Stromal Tumors with Computed Tomography following Treatment with Imatinib Mesylate [J].WORLD JOURNAL OF GASTROENTEROLOGY,2008,14(6):892-898.
[7] XIUGANG ZHANG,DONG WANG.Recent Development in Process Tomography for Multiphase Flows [J].Journal of Engineering for Thermal Energy and Power,2004,19(3):221-226.
[8] GUO GANG,TONG JINNAN,ZHANG SHIHONG.Cyclostratigraphy of the Induan (Early Triassic) in West Pingdingshan Section,Chaohu,Anhui Province [J]. SCIENCE IN CHINA(EARTH SCIENCES),2008,51(1):21-29.
[9]高彦丽,杨蓓,邵富群.用于ECT系统的低成本、宽带微小电容测量电路[J].电测与仪表,2004,41(465):29-32.
[10]董向元,刘石,阎润生等.电容层析成像中通用迭代法的研究[J].仪器仪表学报,2006,27(1):23-25,30.
[11] HUANG Z Y,WANG B L,Li H Q.Application of Electrical Capacitance Tomography to Void Fraction Measurement of Two Phase Flow [J].IEEE Transactions on Instrumentation and Measurement,2003,52(1):7-11.
[12]王化祥,朱学明,张立峰.用于电容层析成像技术的共轭梯度算法[J].天津大学学报,2005,38(1):1-4.
[13]王化祥,何永勃,朱学明.基于L曲线法的电容层析成像正则化参数优化方法[J].天津大学学报,2006,39(3):306-309.
[14]黄松明,徐苓安.两相流测量的现状和发展趋势[C].第二届全国多相流检测技术学术讨论会论文集,东南大学,1988:9-26.
[15] CECCIO S L,et al.A Review of Electrical Impedance Techniques for the Measurement of Multiphase Flows [J].Fluids Engineering,1996,118(1):391-399.
[16]张兆田,熊小芸.过程层析成像概述[J].中国体视学与图像分析,2005,10(3):145-148.
[17]陈德运,张华,朱波.油水两相流电阻层析成像系统流型的辨识[J].电机与控制学报,2007,11(6):639-643.
[18]魏颖,王师.电阻层析成像技术的研究现状与应用发展趋势[J].信息与控制,2000,29(4):340-345.
[19]赵丰.电容电阻复合成像系统硬件研究[D].南宁:广西大学硕士学位论文,2005:4-6.
[20] YAN H,LIU,LIU C T.Identification of Flow Regimes using Back Propagation Networks Trained on Simulated Data based on a Capacitance Tomography Sensor [J].Measurement Science and Technology,2004,15:432-436.
[21] LIU S,CHEN Q,WANG H G,et al.Electrical Capacitance Tomography for Gas2solids Flow Measurement for Circulating Fluidized Beds [J].Flow Measurement and Instrumentation,2005,16:135-144.
[22] HUANG Z Y,XIE D L,ZHANG H J,et al.Gas2 Oil Two Phase Flow Measurement using an Electrical Capacitance Tomography System and a Venture Meter [J].Flow Measurement and Instrumentation,2005,16:177-182.
[23]彭珍瑞,王保良,黄志尧等.基于电容层析成像和LS2 SVM的空隙率测量[J].浙江大学学报:工学版,2007,41(6):877-880.
[24]陈德运,于晓洋等.油水两相流电容层析成像系统电容测量电路的设计[J].电路与系统学报,2004,9(4):1-3.
[25]陈德运,于晓洋等.油水两相流浓度电容层析成像的测量方法[J].测试技术学报,2006,20(1):1-5.
[26]于晓洋,陈德运等.电容层析成像系统中电容传感器参数优化设计[J].测试技术学报,2004,18(3):1-4.
[27]于晓洋,陈德运,王莉莉等.基于改进信赖域的电容层析成像图像重建算法[J].仪器仪表学报,2010,31(5):1-6.
[28] NIU G,J IA Z H,WANG J.Void Fraction Measurement in Oil2 Gastrans Portation Pipeline using an Improved Electrical Capacitance Tomography System [J].Chinese Journal of Chemical Engineering,2004,12(4):476-481.
[29] WANG B L,J I H F,HUANG Z Y,et al.A High2Speed Data Acquisition System for ECT based on the Differential Sampling Method [J].IEEE Sensors Journal,2005,5(2):308-312.
[30]马敏,王化祥,田莉敏.基于DSP的数字化电容层析成像系统[J].传感技术学报,2006,19(3):705-708.
[31] B BRANDSTER,G STEINER,B KORTSCHAK ,et al .Fusion of Electrical Capacitance with Ultrasound Tomography Implementation Details and Hardware Setup [C].Aizu,4th World Congress on Industrial Process Tomography,Japan,2005:631-636.
[32]颜华,邵富群,王师.电容层析成像传感器的优化设计[J].仪器仪表学报,2000,21(2):139-145.
[33]黄志尧,晏颖,王保良等.电阻层析成像传感器软场特性分析[J].仪器仪表学报,2001,22(6):573-576.
[34] YANG W Q.Hardware Design of Electrical Capacitance Tomography Systems [J].Meas sci & techol.1996,7:225-232.
[35]潘时林,李元科.用于两相流检测电容层析系统成像的迭代算法[J].传感器技术,2004,23(10):72-74.
[36]马西奎.电磁场理论及应用[M].西安:西安交通大学出版社,2000:31-122.
[37] WILLIAM D , et al . Electrical Resistance Tomography [J] . Leading Edge,2004,23(5):438-442.
[38]董锋,崔晓会.电阻层析成像技术的发展[J].仪器仪表学报,2003,24(4):703-705.
[39]邓湘,董峰.基于电阻层析成像技术的两相流流速测量系统[J].自动化仪表,2002,23(11):8-10.
[40]邹璐.电阻层析成像系统仿真建模研究[D].清华大学硕士学位论文,2002:5-7.
[41]孟红记,郑鹏,梅国晖等.基于混沌序列的粒子群优化算法[J].控制与决策,2006,21(3).263-266.
[42]李颖,黄晓霖,王书宁.运用改进的线性规划算法求解分片线性方程组[J].清华大学学报(自然科学版),2009,49(10):17-20.
[43]张建明,房芳,陈立等.基于优选LBP与加权SVM的年龄估计[J].计算机应用研究,2010,27(1):389-392.
[44] JIANRAO HU,MING FU Cao,JIONG CHEN.Characterization of the DNA Encoding a BPI/LBP Homologue in Venom Gland [J] . Current Zoology,2009,55(5):376-382.
[45]徐扬,文振,刘斌.基于迭代共享的SMS交换结构调度算法[J].清华大学学报(自然科学版),2008,48(4):597-600.
[46]张顺利,张定华等.基于SIMD技术的锥束ART算法快速并行图像重建[J].仪器仪表学报,2010,31(3):630-634.
[47]杨启文,陈昊,薛云灿.单参数PID的Hebb学习控制[J].仪器仪表学报,2008,29(2):392-395.
[48]叶晓明,林小竹.慢速权值更新的ART2神经网络研究[J].计算机工程与应用,2010,46(24):146-150.
[49]邹云峰,吴为麟,李智勇.基于自组织映射神经网络的低压故障电弧聚类分析[J].仪器仪表学报,2010,31(3):571-576.
[50]崔立堃，王伟，李卓．Hopfield神经网络在有限元求解中的应用[J].计算机工程与应用,2010,46(16):46-48.
[51]侯天子,杨燕,谭维.I-Miner环境下聚类及可视化研究[J].计算机工程与应用,2010,46(2):113-117.
[52]毛永毅,李明远,张保军.基于BP神经网络的蜂窝无线定位算法[J].计算机工程与应用,2008,44(3):60-63.
[53]王曦,欧阳城添,张小红等.CNN的全局渐近稳定性分析与改进[J].计算机应用与软件,2009,26(4):96-99.
[54]梅冬芳.采用调整函数优化梯度的BP算法改进[J].计算机应用,2006,16(4):102-105.
[55]王兵,李盼池,许少华.一种基于过程神经元网络辨识的PID控制模型及方法[J].计算机应用,2010,30(1):233-239.
[56]田大新,刘衍珩,李宾等.基于Hebb规则的分布神经网络学习算法[J].计算机学报,2007,30(8):1379-1388.
[57]孙斌,王强,周云龙.基于多尺度信息熵特征和RBF神经网络的气液两相流流型识别方法[J].仪器仪表学报,2006,27(7):725-729.
[58]吴成茂,范九伦.确定RBF神经网络隐层节点数的最大矩阵元法[J].计算机工程与应用,2004,20(3):77-79.
[59]王化祥,唐磊,闫勇.电容层析成像图像重建的总变差正则化算法[J].仪器仪表学报,2007,28(11):2014-2018.
[60]张登峰,王执铨,张卫.一种改进的基于VC维的非平稳信号小波消噪方法[J].南京理工大学学报,2009,23(5):648-652.
[61]侯兰宝,杜锋.统计学习在假设稳定下推广误差的界[J].科技资讯,2010,7:236-238.
[62]周水生,周利华.确定最优分类超平面的新算法[J].西安电子科技大学学报,2002,29(6):791-795.
[63]金哲进,张乃尧.未知非线性离散系统的支持向量机内模控制[J].清华大学学报,2009,49(11):1880-1885.
[64] OSUNA E,FREUND R,GIROSI F.An Improved Training Algorithm for Support Vector Machine [M] . Amelea Island : Proceedings of IEEE Workshop on Neural Networks for Signal Processing,1997:276-285.
[65] ANGUITA D,BONI A,RIDELLA S.A Digital Architecture for Support Vector Machines Theory,Algorithm and FPGA Implementation [J].IEEE Transactions on Networks,2003,14(5):993-1009.
[2]李海青,黄志尧.特种检测技术及应用[M].杭州:浙江大学出版社, 2000:72-82.
[3]吴瑞芬.电阻层析成系统敏感场特性分析与仿真研究[D].哈尔滨:哈尔滨理工大学硕士学位论文,2007:1-4.
[4]彭珍瑞,祁文哲,吴刊选.电容层析成像技术的近期研究进展[J].自动化仪表,2008,29(9):1-5.
[5] LAURENT F.C.JEANMEURE,TOMASZ DYAKOWSKI.Direct Flow Pattern Identification using Electrical Capacitance Tomography [J]. Experimental Thermal and Fluid Science,2002,(26):763-773.
[6] SITH PHONGKITKARUN , CHOLADA PHAISANPHRUKKUN ,JANJIRA JATCHAVALA,et al.Assessment of Gastrointestinal Stromal Tumors with Computed Tomography following Treatment with Imatinib Mesylate [J].WORLD JOURNAL OF GASTROENTEROLOGY,2008,14(6):892-898.
[7] XIUGANG ZHANG,DONG WANG.Recent Development in Process Tomography for Multiphase Flows [J].Journal of Engineering for Thermal Energy and Power,2004,19(3):221-226.
[8] GUO GANG,TONG JINNAN,ZHANG SHIHONG.Cyclostratigraphy of the Induan (Early Triassic) in West Pingdingshan Section,Chaohu,Anhui Province [J]. SCIENCE IN CHINA(EARTH SCIENCES),2008,51(1):21-29.
[9]高彦丽,杨蓓,邵富群.用于ECT系统的低成本、宽带微小电容测量电路[J].电测与仪表,2004,41(465):29-32.
[10]董向元,刘石,阎润生等.电容层析成像中通用迭代法的研究[J].仪器仪表学报,2006,27(1):23-25,30.
[11] HUANG Z Y,WANG B L,Li H Q.Application of Electrical Capacitance Tomography to Void Fraction Measurement of Two Phase Flow [J].IEEE Transactions on Instrumentation and Measurement,2003,52(1):7-11.
[12]王化祥,朱学明,张立峰.用于电容层析成像技术的共轭梯度算法[J].天津大学学报,2005,38(1):1-4.
[13]王化祥,何永勃,朱学明.基于L曲线法的电容层析成像正则化参数优化方法[J].天津大学学报,2006,39(3):306-309.
[14]黄松明,徐苓安.两相流测量的现状和发展趋势[C].第二届全国多相流检测技术学术讨论会论文集,东南大学,1988:9-26.
[15] CECCIO S L,et al.A Review of Electrical Impedance Techniques for the Measurement of Multiphase Flows [J].Fluids Engineering,1996,118(1):391-399.
[16]张兆田,熊小芸.过程层析成像概述[J].中国体视学与图像分析,2005,10(3):145-148.
[17]陈德运,张华,朱波.油水两相流电阻层析成像系统流型的辨识[J].电机与控制学报,2007,11(6):639-643.
[18]魏颖,王师.电阻层析成像技术的研究现状与应用发展趋势[J].信息与控制,2000,29(4):340-345.
[19]赵丰.电容电阻复合成像系统硬件研究[D].南宁:广西大学硕士学位论文,2005:4-6.
[20] YAN H,LIU,LIU C T.Identification of Flow Regimes using Back Propagation Networks Trained on Simulated Data based on a Capacitance Tomography Sensor [J].Measurement Science and Technology,2004,15:432-436.
[21] LIU S,CHEN Q,WANG H G,et al.Electrical Capacitance Tomography for Gas2solids Flow Measurement for Circulating Fluidized Beds [J].Flow Measurement and Instrumentation,2005,16:135-144.
[22] HUANG Z Y,XIE D L,ZHANG H J,et al.Gas2 Oil Two Phase Flow Measurement using an Electrical Capacitance Tomography System and a Venture Meter [J].Flow Measurement and Instrumentation,2005,16:177-182.
[23]彭珍瑞,王保良,黄志尧等.基于电容层析成像和LS2 SVM的空隙率测量[J].浙江大学学报:工学版,2007,41(6):877-880.
[24]陈德运,于晓洋等.油水两相流电容层析成像系统电容测量电路的设计[J].电路与系统学报,2004,9(4):1-3.
[25]陈德运,于晓洋等.油水两相流浓度电容层析成像的测量方法[J].测试技术学报,2006,20(1):1-5.
[26]于晓洋,陈德运等.电容层析成像系统中电容传感器参数优化设计[J].测试技术学报,2004,18(3):1-4.
[27]于晓洋,陈德运,王莉莉等.基于改进信赖域的电容层析成像图像重建算法[J].仪器仪表学报,2010,31(5):1-6.
[28] NIU G,J IA Z H,WANG J.Void Fraction Measurement in Oil2 Gastrans Portation Pipeline using an Improved Electrical Capacitance Tomography System [J].Chinese Journal of Chemical Engineering,2004,12(4):476-481.
[29] WANG B L,J I H F,HUANG Z Y,et al.A High2Speed Data Acquisition System for ECT based on the Differential Sampling Method [J].IEEE Sensors Journal,2005,5(2):308-312.
[30]马敏,王化祥,田莉敏.基于DSP的数字化电容层析成像系统[J].传感技术学报,2006,19(3):705-708.
[31] B BRANDSTER,G STEINER,B KORTSCHAK ,et al .Fusion of Electrical Capacitance with Ultrasound Tomography Implementation Details and Hardware Setup [C].Aizu,4th World Congress on Industrial Process Tomography,Japan,2005:631-636.
[32]颜华,邵富群,王师.电容层析成像传感器的优化设计[J].仪器仪表学报,2000,21(2):139-145.
[33]黄志尧,晏颖,王保良等.电阻层析成像传感器软场特性分析[J].仪器仪表学报,2001,22(6):573-576.
[34] YANG W Q.Hardware Design of Electrical Capacitance Tomography Systems [J].Meas sci & techol.1996,7:225-232.
[35]潘时林,李元科.用于两相流检测电容层析系统成像的迭代算法[J].传感器技术,2004,23(10):72-74.
[36]马西奎.电磁场理论及应用[M].西安:西安交通大学出版社,2000:31-122.
[37] WILLIAM D , et al . Electrical Resistance Tomography [J] . Leading Edge,2004,23(5):438-442.
[38]董锋,崔晓会.电阻层析成像技术的发展[J].仪器仪表学报,2003,24(4):703-705.
[39]邓湘,董峰.基于电阻层析成像技术的两相流流速测量系统[J].自动化仪表,2002,23(11):8-10.
[40]邹璐.电阻层析成像系统仿真建模研究[D].清华大学硕士学位论文,2002:5-7.
[41]孟红记,郑鹏,梅国晖等.基于混沌序列的粒子群优化算法[J].控制与决策,2006,21(3).263-266.
[42]李颖,黄晓霖,王书宁.运用改进的线性规划算法求解分片线性方程组[J].清华大学学报(自然科学版),2009,49(10):17-20.
[43]张建明,房芳,陈立等.基于优选LBP与加权SVM的年龄估计[J].计算机应用研究,2010,27(1):389-392.
[44] JIANRAO HU,MING FU Cao,JIONG CHEN.Characterization of the DNA Encoding a BPI/LBP Homologue in Venom Gland [J] . Current Zoology,2009,55(5):376-382.
[45]徐扬,文振,刘斌.基于迭代共享的SMS交换结构调度算法[J].清华大学学报(自然科学版),2008,48(4):597-600.
[46]张顺利,张定华等.基于SIMD技术的锥束ART算法快速并行图像重建[J].仪器仪表学报,2010,31(3):630-634.
[47]杨启文,陈昊,薛云灿.单参数PID的Hebb学习控制[J].仪器仪表学报,2008,29(2):392-395.
[48]叶晓明,林小竹.慢速权值更新的ART2神经网络研究[J].计算机工程与应用,2010,46(24):146-150.
[49]邹云峰,吴为麟,李智勇.基于自组织映射神经网络的低压故障电弧聚类分析[J].仪器仪表学报,2010,31(3):571-576.
[50]崔立堃，王伟，李卓．Hopfield神经网络在有限元求解中的应用[J].计算机工程与应用,2010,46(16):46-48.
[51]侯天子,杨燕,谭维.I-Miner环境下聚类及可视化研究[J].计算机工程与应用,2010,46(2):113-117.
[52]毛永毅,李明远,张保军.基于BP神经网络的蜂窝无线定位算法[J].计算机工程与应用,2008,44(3):60-63.
[53]王曦,欧阳城添,张小红等.CNN的全局渐近稳定性分析与改进[J].计算机应用与软件,2009,26(4):96-99.
[54]梅冬芳.采用调整函数优化梯度的BP算法改进[J].计算机应用,2006,16(4):102-105.
[55]王兵,李盼池,许少华.一种基于过程神经元网络辨识的PID控制模型及方法[J].计算机应用,2010,30(1):233-239.
[56]田大新,刘衍珩,李宾等.基于Hebb规则的分布神经网络学习算法[J].计算机学报,2007,30(8):1379-1388.
[57]孙斌,王强,周云龙.基于多尺度信息熵特征和RBF神经网络的气液两相流流型识别方法[J].仪器仪表学报,2006,27(7):725-729.
[58]吴成茂,范九伦.确定RBF神经网络隐层节点数的最大矩阵元法[J].计算机工程与应用,2004,20(3):77-79.
[59]王化祥,唐磊,闫勇.电容层析成像图像重建的总变差正则化算法[J].仪器仪表学报,2007,28(11):2014-2018.
[60]张登峰,王执铨,张卫.一种改进的基于VC维的非平稳信号小波消噪方法[J].南京理工大学学报,2009,23(5):648-652.
[61]侯兰宝,杜锋.统计学习在假设稳定下推广误差的界[J].科技资讯,2010,7:236-238.
[62]周水生,周利华.确定最优分类超平面的新算法[J].西安电子科技大学学报,2002,29(6):791-795.
[63]金哲进,张乃尧.未知非线性离散系统的支持向量机内模控制[J].清华大学学报,2009,49(11):1880-1885.
[64] OSUNA E,FREUND R,GIROSI F.An Improved Training Algorithm for Support Vector Machine [M] . Amelea Island : Proceedings of IEEE Workshop on Neural Networks for Signal Processing,1997:276-285.
[65] ANGUITA D,BONI A,RIDELLA S.A Digital Architecture for Support Vector Machines Theory,Algorithm and FPGA Implementation [J].IEEE Transactions on Networks,2003,14(5):993-1009.