建模技术在虚拟仪表中的应用
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摘要
随着测控领域对测试要求的不断提高，传统仪表在精度上、性能上，功能上都取得了长足的进步，但是由于技术落后、成本高以及工业环境差等原因，传统仪表仍然无法满足工艺复杂、被测参数多的场合，尤其是在诸如冶金、化工、煤炭、石油等工业中，传统仪表仍然停留在手动操作阶段，却无法在线实时对参数进行测量。正是基于上述等原因，虚拟仪表以其独有的优势而出现，并且在测控领域逐渐地取代了传统仪表的地位，成为自动控制领域重点研究的方向。
构建一个虚拟仪表的核心是对实际生产过程相应工艺参数进行数学建模，本文拟采用人工神经网络方法来解决这一问题，因而对基于统计建模思想的人工神经网络方法进行了深入研究。其中重点论述了BP神经网络和RBF神经网络，提出了基于BIC准则的BP神经网络隐层节点个数的优选方法，并利用遗传算法对BP网络初始连接权值和阈值进行优化；针对单个RBF网络分类精度不高的缺点，设计了基于Adaboost算法的RBF强分类器。仿真结果表明，本文提出的这些改进方法可以有效的进行网络结构优选并进一步提高网络的训练速度和分类精度。
最后，根据本文所述的建模方法，利用LabVIEW软件编写了一个聚合物黏度软测量系统。该系统可以对从工业现场实时采集的数据进行处理分析，并根据这些数据最终给出聚合物的黏度值。
With the test requirements increased of the monitoring and control areas, thetraditional instruments have made considerable progress with the accuracy, performanceand functions, but due to backward technology, high cost and poor industrialenvironment, they are still unable to meet the occasion of process complex, moremeasured parameters, especially in industries such as metallurgy, chemicals, coal, oiland so on, traditional instruments still remain at the stage of manual operation, can notmeasure parameters online in real time. In case of these reasons above, the virtualinstruments appeared with their unique advantages, and gradually replaced the status ofthe traditional instruments in the measurement and control field, which become thedirection of the key research in the field of automatic control.
The core of builds a virtual instrument is the mathematical modeling of thecorresponding process parameters of actual generation process. This paper proposedartificial neural network approach to solve this problem, so conducted in-depth researchon artificial neural network method based on statistical modeling ideas. This paperfocuses on the BP neural network and RBF neural network, BP neural network hiddenlayer nodes select method based on BIC rule is proposed, and use of genetic algorithmsto optimize the BP network initial connection weights and thresholds; for a single RBFnetwork has the shortcoming of classification accuracy is not high, designs of a RBFstrong classifier based on Adaboost algorithm. The simulations result show that theseimprovements proposed in this paper can effectively optimizes network structure andfurther improve the training speed and classification accuracy of the network.
Finally, based on the modeling approach described in this paper, a polymerviscosity soft measurement system is compiled using the LabVIEW software. Thesystem can deal with and analysis the data which real-time collected from an industrial site, and ultimately gives the value of the polymer viscosity according to these data.
构建一个虚拟仪表的核心是对实际生产过程相应工艺参数进行数学建模，本文拟采用人工神经网络方法来解决这一问题，因而对基于统计建模思想的人工神经网络方法进行了深入研究。其中重点论述了BP神经网络和RBF神经网络，提出了基于BIC准则的BP神经网络隐层节点个数的优选方法，并利用遗传算法对BP网络初始连接权值和阈值进行优化；针对单个RBF网络分类精度不高的缺点，设计了基于Adaboost算法的RBF强分类器。仿真结果表明，本文提出的这些改进方法可以有效的进行网络结构优选并进一步提高网络的训练速度和分类精度。
最后，根据本文所述的建模方法，利用LabVIEW软件编写了一个聚合物黏度软测量系统。该系统可以对从工业现场实时采集的数据进行处理分析，并根据这些数据最终给出聚合物的黏度值。
With the test requirements increased of the monitoring and control areas, thetraditional instruments have made considerable progress with the accuracy, performanceand functions, but due to backward technology, high cost and poor industrialenvironment, they are still unable to meet the occasion of process complex, moremeasured parameters, especially in industries such as metallurgy, chemicals, coal, oiland so on, traditional instruments still remain at the stage of manual operation, can notmeasure parameters online in real time. In case of these reasons above, the virtualinstruments appeared with their unique advantages, and gradually replaced the status ofthe traditional instruments in the measurement and control field, which become thedirection of the key research in the field of automatic control.
The core of builds a virtual instrument is the mathematical modeling of thecorresponding process parameters of actual generation process. This paper proposedartificial neural network approach to solve this problem, so conducted in-depth researchon artificial neural network method based on statistical modeling ideas. This paperfocuses on the BP neural network and RBF neural network, BP neural network hiddenlayer nodes select method based on BIC rule is proposed, and use of genetic algorithmsto optimize the BP network initial connection weights and thresholds; for a single RBFnetwork has the shortcoming of classification accuracy is not high, designs of a RBFstrong classifier based on Adaboost algorithm. The simulations result show that theseimprovements proposed in this paper can effectively optimizes network structure andfurther improve the training speed and classification accuracy of the network.
Finally, based on the modeling approach described in this paper, a polymerviscosity soft measurement system is compiled using the LabVIEW software. Thesystem can deal with and analysis the data which real-time collected from an industrial site, and ultimately gives the value of the polymer viscosity according to these data.
引文
[1]俞金寿.软测量技术及其应用[J].自动化仪表，2008，29(1)：1-7.
[2]丁宝苍，罗小锁，罗霄.先进控制理论[M].北京:电子工业出版社,2010:1-2.
[3]王景芳，廖亦凡.基于支持向量机催化裂化轻柴油凝点软测量[J].石油化工自动化，2008，2：44-47.
[4]程秀玲，单水维.软测量技术在预测钢坯内部温度场的应用研究[J].机电产品开发与创新，2010，23(4)：157-159.
[5]周玲.基于神经网络的涵闸流量软测量建模研究[D].硕士论文，河南大学，2002.
[6]陈明忠.基于支持向量机的微生物发酵过程软测量方法研究[D].硕士论文，江苏大学，2002.
[7]田华阁.聚丙烯装置产品质量软测量技术研究[D].博士论文，中国石油大学，2010.
[8]张毅，周绍磊，杨秀霞.虚拟仪器技术分析与应用[M].北京:机械工业出版社，2004:45-52.
[9]曾孟雄，李力，肖露.智能检测控制技术及应用[M].北京:电子工业出版社，2008:33-37.
[10]Wang Y, Seki H, Ohyama. S, et al. Optimal grade transition control forpolymerization reactors[J]. Computers and Chemical Engineering,2000,24:1555-1561.
[11]孙优贤，褚健.工业过程控制技术[M].北京:化学工业出版社,2005:7-10.
[12]刘君华，郭会军.基于LabVIEW的虚拟仪器设计[M].北京:电子工业出版社,2003:78-84.
[13]Kano M, Nakagawa Y. Recent developments and industrial applications ofdata-based process monitoring and process control[C].16th.European symposiumon Computer aided process engineering and international symposium on processsystems engineering,57-62.
[14]Wang Y，Seki H，Ohyama. S，et al. Optimal grade transition control for MacAvoyT J. Contemplative Stance for chemical process control[J]. Automatica,1992,28(2):441-442.
[15]杨乐平，李海涛，肖凯杨磊.虚拟仪器技术概论[M].北京:电子工业出版社，2002:55-62.
[16]杨梅，卿晓霞，王波.基于改进遗传算法的神经网络优化方法[J].计算机仿真，2009，26(5)：198-201.
[17]张山，和渐浓. BP神经网络的优化算法研究[J].计算机与现代化，2009，5（1）：73-75.
[18]裴锋，汪翠英，李资荣.基于LabVIEW的虚拟仪器算法解决方案[J]，自动化仪表，2005，26(8)：63-65.
[19]吴虹.虚拟仪表设计中建模方法的研究[D].硕士论文，黑龙江大学，2007.
[20]俞金寿，刘爱伦，张克进.软测量技术及其在石油化工中的应用[M].北京:化学工业出版社,2008:6-12.
[21]Fortuna L, Graziani S, Rizzo A, et al. Soft sensors for monitoring and control ofindustrial processes[M]. London：Springer,2006.
[22]Wang J, Yang Y. Study on optimal strategy of grade transition in industrial fluidizedbed gas-phase polyethylene production process[J]. Chinese J. Chem. Eng,2003,11(1):1-8.
[23]俞金寿.软测量技术及其应用[J].自动化仪表，2008，29(6)：2-7．
[24]潘立登，李大字，马俊英.软测量技术原理与应用[M].北京:中国电力出版社,2009:342-357.
[25]P. Sarkar, S. K. Gupta. Steady state simulation of continuous-flow stirred-tankpropylene polymerization reactors[J]. Polymer Engineering and Science,1992,32(11):732-742.
[26]汪小勇，梁军，刘育明，王文庆.基于递推PLS的自适应软测量模型及其应用[J].浙江大学学报，2005，39(5)：676-650.
[27]P. Sarkar, S. K. Gupta. Dynamic simulation of propylene polymerization incontinuous flow stirred tank reactors[J]. Polymer Engineering and Science,1993,33(6):368～374.
[28]崔永超，张湜，王永华.基于支持向量机的软测量建模方法的应用[J].南京工业大学学报(自然科学版)，2007，29(3)：99-102.
[29]Falehini M, Steeco A, Carmienani L. Neural Network Based Detection ofPulmonary Nodules on Chest Radiographs[J]. Radio Med,1999,98(4):259-263.
[30]Nakamura K, Yoshida H, Engelmann R, et al. Computerized Analysis of theLikelihood of Malignancy in Solitary Pulmonary Nodules with Used of ArtificialNeural Networks[J]. Radiology,2002,14(3):823-830.
[31]Haralambos Sarimveis, Philip Doganis, Alex Alexandridis. A classificationtechnique based on radial basis function neural networks[J]. Advances inEngineering Software,2006,37(4):218-221.
[32]J. Zhang, E. B. Martin, A. J. Morris, C. Kiparissides, et al. Inferential estimation ofpolymerquality using stacked neural networks[J]. Computers Chem. Engng,1997,21:1025-1030.
[33]J. J. Buckley, Y. Hayashi. Numerical relationships between neural networks,continuous functions, and fuzzy systems[J]. Fuzzy Sets and Systems,1993,60(1):1-8.
[34]Han M, Sun Y N, Fan Y N. An improved fuzzy neural network based on T-Smodel[J]. Expert Systems with Applications,2008,34:2905-2920.
[35]B. Babuska, H. B. Verbruggen. An overview of fuzzy modeling for control[J].Control Engineering Practice,1996,11(4):1593-1606.
[36]刘严，张秋香.基于PCA-BP神经网络的精馏塔产品组成软测量模型[J].化工进展，2007，26：98-101．
[37]吴建生.基于遗传算法的BP神经网络气象预测建模[D].硕士论文，广西师范大学，2004.
[38]Yufang Lin. Freight Prediction Based on BP Neural Network Improved by ChaosArtificial Fish-swarm Algorithm[J]. Proceedings-International Conference onComputer Science and Software Engineering,2008,5:1287-1290.
[39]王晓娟.基于模糊控制与RBF神经网络的桃病虫害发生预测研究[D].硕士论文，河北农业大学，2011.
[40]吕文涛，陈映鹰，张绍明.基于小波支撑向量机的图像降噪滤波算法[J].遥感信息，2008，3：22-25.
[41]Junna Qiu, Xiaohang Xu. An Algorithm of Data Fusion Based on Improved BPNatural Network[J]. Proceedings-International Conference on Computer Scienceand Software Engineering,2008,1:581-583.
[42]Hong Li, Tao Peng. Prediction of Concrete Compression Strength Based on BP andRBF Neural Network Theories[J]. Journal of Wuhan University of Technology,2009,31(8):33-36.
[43]王小平，曹立明.遗传算法一理论、应用与软件实现[M].西安:西安交通大学出版社,2002:76-82.
[44]高隽.人工神经网络原理及仿真实例[M].北京:机械工业出版社,2008:11-17.
[45]周开利，康耀红.神经网络模型及其MATLAB仿真程序设计[M].北京:清华大学出版社,2005:56-79.
[46]C. Harpham, C. W. Dawson. The effete of different basis functions on a radial basisfunction network for time series prediction: A comparative study[J].Neurocomputing,2006,69(18):2161-2170.
[47]Jianxi Yang, Jianting Zhou, Fan Wang. A Study on the Application of GA-BPNeural Network in the Bridge Reliability Assessment[J]. Proceedings-2008International Conference on Computational Intelligence and Security,2008,1:540-545.
[48]闻新，周露，王丹力. MATLAB神经网络应用设计[M].北京:科学出版社,2002:201-207.
[49]袁曾任.人工神经元网络及其应用[M].北京:清华大学出版社,2007:102-111.
[50]S. McLoone, G. Imin. Nonlinear optimization of RBF networks[J]. InternationalJournal of Systems Science,1998,29(2):179-189.
[51]H. Sarimveis, A. Alexandridis, G. Tsekouras, G. Bafas, et al. A fast and efficientalgorithm fortraining radial basis function neural networks based on a fuzzypartition of the input space[J]. Ind. Eng. Chem. Res,2002,41:751-759.
[52]Mao KZ, Guang Bin H. Neuron selection for RBF neural net work classifier basedon data structure preserving criterion[J]. IEEE Transaction on Neural Network,2005,16(6):1531-1540.
[53]Freund Y, Robert E. S. A Short introduction to boosting [J]. Journal of JapaneseSociety for Artificial Intelligence,1999,14(5):771-778.
[54]Binchinl M, Frasconi P, Gori. Learning Without Local Minama in Radial BasisFunction Networks[J]. IEEE Trans. on Neural Networks,1995,6(3):749-755.
[55]常玉清，王小刚，王福利.基于多神经网络模型的软测量方法及应用[J].东北大学学报，2005，26(6)：519-522．
[56]Daolun Li, Detang Lu, Xiangyan Kong. Implicit Curve Based on Radial BasisFunction Network[J]. Journal of Computer Research and Development,2005,42(4):599-603.
[57]阎平凡，张长水.人工神经网络与模拟进化计算[M].北京:清华大学出版社,2006:23-34.
[58]Meng Joo Er, Weilong Chen, Shiqian Wu. High-Speed Face Recognition Based onDiscrete Cosine Transform and RBF Neural Networks[J]. IEEE Transaction onNeural networks.2005,16(3):679-691.
[59]王跃宣，苏宏业，牟盛静.组件化软测量软件包的开发与应用[J].工业自动化及仪表，2003，30(3)：43-46.
[60]何瑛，宋利，张伟.基于LabVIEW的数据采集卡（DAQ）驱动程序设计[J].电测与仪表，2000，3(4)：35-37.
[61]胡仁喜，王东海，齐东明. LABVIEW8.2虚拟仪器实例指导教程[M].北京:机械工业出版社,2008:45-54.
[62]唐建锋，罗湘南.基于LabVIEW与MATLAB混合编程的虚拟仪器设计及实现[J]，湖南文理学院学报，2004，6(1)：66-67.
[63]张志平，刘正平.在LabVIEW中调用MATLAB的一种方法[J].计算机与现代化，2004，4(5)：94-95.
[2]丁宝苍，罗小锁，罗霄.先进控制理论[M].北京:电子工业出版社,2010:1-2.
[3]王景芳，廖亦凡.基于支持向量机催化裂化轻柴油凝点软测量[J].石油化工自动化，2008，2：44-47.
[4]程秀玲，单水维.软测量技术在预测钢坯内部温度场的应用研究[J].机电产品开发与创新，2010，23(4)：157-159.
[5]周玲.基于神经网络的涵闸流量软测量建模研究[D].硕士论文，河南大学，2002.
[6]陈明忠.基于支持向量机的微生物发酵过程软测量方法研究[D].硕士论文，江苏大学，2002.
[7]田华阁.聚丙烯装置产品质量软测量技术研究[D].博士论文，中国石油大学，2010.
[8]张毅，周绍磊，杨秀霞.虚拟仪器技术分析与应用[M].北京:机械工业出版社，2004:45-52.
[9]曾孟雄，李力，肖露.智能检测控制技术及应用[M].北京:电子工业出版社，2008:33-37.
[10]Wang Y, Seki H, Ohyama. S, et al. Optimal grade transition control forpolymerization reactors[J]. Computers and Chemical Engineering,2000,24:1555-1561.
[11]孙优贤，褚健.工业过程控制技术[M].北京:化学工业出版社,2005:7-10.
[12]刘君华，郭会军.基于LabVIEW的虚拟仪器设计[M].北京:电子工业出版社,2003:78-84.
[13]Kano M, Nakagawa Y. Recent developments and industrial applications ofdata-based process monitoring and process control[C].16th.European symposiumon Computer aided process engineering and international symposium on processsystems engineering,57-62.
[14]Wang Y，Seki H，Ohyama. S，et al. Optimal grade transition control for MacAvoyT J. Contemplative Stance for chemical process control[J]. Automatica,1992,28(2):441-442.
[15]杨乐平，李海涛，肖凯杨磊.虚拟仪器技术概论[M].北京:电子工业出版社，2002:55-62.
[16]杨梅，卿晓霞，王波.基于改进遗传算法的神经网络优化方法[J].计算机仿真，2009，26(5)：198-201.
[17]张山，和渐浓. BP神经网络的优化算法研究[J].计算机与现代化，2009，5（1）：73-75.
[18]裴锋，汪翠英，李资荣.基于LabVIEW的虚拟仪器算法解决方案[J]，自动化仪表，2005，26(8)：63-65.
[19]吴虹.虚拟仪表设计中建模方法的研究[D].硕士论文，黑龙江大学，2007.
[20]俞金寿，刘爱伦，张克进.软测量技术及其在石油化工中的应用[M].北京:化学工业出版社,2008:6-12.
[21]Fortuna L, Graziani S, Rizzo A, et al. Soft sensors for monitoring and control ofindustrial processes[M]. London：Springer,2006.
[22]Wang J, Yang Y. Study on optimal strategy of grade transition in industrial fluidizedbed gas-phase polyethylene production process[J]. Chinese J. Chem. Eng,2003,11(1):1-8.
[23]俞金寿.软测量技术及其应用[J].自动化仪表，2008，29(6)：2-7．
[24]潘立登，李大字，马俊英.软测量技术原理与应用[M].北京:中国电力出版社,2009:342-357.
[25]P. Sarkar, S. K. Gupta. Steady state simulation of continuous-flow stirred-tankpropylene polymerization reactors[J]. Polymer Engineering and Science,1992,32(11):732-742.
[26]汪小勇，梁军，刘育明，王文庆.基于递推PLS的自适应软测量模型及其应用[J].浙江大学学报，2005，39(5)：676-650.
[27]P. Sarkar, S. K. Gupta. Dynamic simulation of propylene polymerization incontinuous flow stirred tank reactors[J]. Polymer Engineering and Science,1993,33(6):368～374.
[28]崔永超，张湜，王永华.基于支持向量机的软测量建模方法的应用[J].南京工业大学学报(自然科学版)，2007，29(3)：99-102.
[29]Falehini M, Steeco A, Carmienani L. Neural Network Based Detection ofPulmonary Nodules on Chest Radiographs[J]. Radio Med,1999,98(4):259-263.
[30]Nakamura K, Yoshida H, Engelmann R, et al. Computerized Analysis of theLikelihood of Malignancy in Solitary Pulmonary Nodules with Used of ArtificialNeural Networks[J]. Radiology,2002,14(3):823-830.
[31]Haralambos Sarimveis, Philip Doganis, Alex Alexandridis. A classificationtechnique based on radial basis function neural networks[J]. Advances inEngineering Software,2006,37(4):218-221.
[32]J. Zhang, E. B. Martin, A. J. Morris, C. Kiparissides, et al. Inferential estimation ofpolymerquality using stacked neural networks[J]. Computers Chem. Engng,1997,21:1025-1030.
[33]J. J. Buckley, Y. Hayashi. Numerical relationships between neural networks,continuous functions, and fuzzy systems[J]. Fuzzy Sets and Systems,1993,60(1):1-8.
[34]Han M, Sun Y N, Fan Y N. An improved fuzzy neural network based on T-Smodel[J]. Expert Systems with Applications,2008,34:2905-2920.
[35]B. Babuska, H. B. Verbruggen. An overview of fuzzy modeling for control[J].Control Engineering Practice,1996,11(4):1593-1606.
[36]刘严，张秋香.基于PCA-BP神经网络的精馏塔产品组成软测量模型[J].化工进展，2007，26：98-101．
[37]吴建生.基于遗传算法的BP神经网络气象预测建模[D].硕士论文，广西师范大学，2004.
[38]Yufang Lin. Freight Prediction Based on BP Neural Network Improved by ChaosArtificial Fish-swarm Algorithm[J]. Proceedings-International Conference onComputer Science and Software Engineering,2008,5:1287-1290.
[39]王晓娟.基于模糊控制与RBF神经网络的桃病虫害发生预测研究[D].硕士论文，河北农业大学，2011.
[40]吕文涛，陈映鹰，张绍明.基于小波支撑向量机的图像降噪滤波算法[J].遥感信息，2008，3：22-25.
[41]Junna Qiu, Xiaohang Xu. An Algorithm of Data Fusion Based on Improved BPNatural Network[J]. Proceedings-International Conference on Computer Scienceand Software Engineering,2008,1:581-583.
[42]Hong Li, Tao Peng. Prediction of Concrete Compression Strength Based on BP andRBF Neural Network Theories[J]. Journal of Wuhan University of Technology,2009,31(8):33-36.
[43]王小平，曹立明.遗传算法一理论、应用与软件实现[M].西安:西安交通大学出版社,2002:76-82.
[44]高隽.人工神经网络原理及仿真实例[M].北京:机械工业出版社,2008:11-17.
[45]周开利，康耀红.神经网络模型及其MATLAB仿真程序设计[M].北京:清华大学出版社,2005:56-79.
[46]C. Harpham, C. W. Dawson. The effete of different basis functions on a radial basisfunction network for time series prediction: A comparative study[J].Neurocomputing,2006,69(18):2161-2170.
[47]Jianxi Yang, Jianting Zhou, Fan Wang. A Study on the Application of GA-BPNeural Network in the Bridge Reliability Assessment[J]. Proceedings-2008International Conference on Computational Intelligence and Security,2008,1:540-545.
[48]闻新，周露，王丹力. MATLAB神经网络应用设计[M].北京:科学出版社,2002:201-207.
[49]袁曾任.人工神经元网络及其应用[M].北京:清华大学出版社,2007:102-111.
[50]S. McLoone, G. Imin. Nonlinear optimization of RBF networks[J]. InternationalJournal of Systems Science,1998,29(2):179-189.
[51]H. Sarimveis, A. Alexandridis, G. Tsekouras, G. Bafas, et al. A fast and efficientalgorithm fortraining radial basis function neural networks based on a fuzzypartition of the input space[J]. Ind. Eng. Chem. Res,2002,41:751-759.
[52]Mao KZ, Guang Bin H. Neuron selection for RBF neural net work classifier basedon data structure preserving criterion[J]. IEEE Transaction on Neural Network,2005,16(6):1531-1540.
[53]Freund Y, Robert E. S. A Short introduction to boosting [J]. Journal of JapaneseSociety for Artificial Intelligence,1999,14(5):771-778.
[54]Binchinl M, Frasconi P, Gori. Learning Without Local Minama in Radial BasisFunction Networks[J]. IEEE Trans. on Neural Networks,1995,6(3):749-755.
[55]常玉清，王小刚，王福利.基于多神经网络模型的软测量方法及应用[J].东北大学学报，2005，26(6)：519-522．
[56]Daolun Li, Detang Lu, Xiangyan Kong. Implicit Curve Based on Radial BasisFunction Network[J]. Journal of Computer Research and Development,2005,42(4):599-603.
[57]阎平凡，张长水.人工神经网络与模拟进化计算[M].北京:清华大学出版社,2006:23-34.
[58]Meng Joo Er, Weilong Chen, Shiqian Wu. High-Speed Face Recognition Based onDiscrete Cosine Transform and RBF Neural Networks[J]. IEEE Transaction onNeural networks.2005,16(3):679-691.
[59]王跃宣，苏宏业，牟盛静.组件化软测量软件包的开发与应用[J].工业自动化及仪表，2003，30(3)：43-46.
[60]何瑛，宋利，张伟.基于LabVIEW的数据采集卡（DAQ）驱动程序设计[J].电测与仪表，2000，3(4)：35-37.
[61]胡仁喜，王东海，齐东明. LABVIEW8.2虚拟仪器实例指导教程[M].北京:机械工业出版社,2008:45-54.
[62]唐建锋，罗湘南.基于LabVIEW与MATLAB混合编程的虚拟仪器设计及实现[J]，湖南文理学院学报，2004，6(1)：66-67.
[63]张志平，刘正平.在LabVIEW中调用MATLAB的一种方法[J].计算机与现代化，2004，4(5)：94-95.