基于LS-SVM的气液两相流参数测量研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
两相流广泛存在于动力、石油、冶金、核能和化工等领域。两相流参数的测量对生产过程的计量、控制以及环保等具有非常重要的意义,但是两相流流动特性复杂,两相流参数检测的难度相当大。空隙率是众多两相流参数中的一个重要检测参数,现有的多种空隙率测量方法还未能满足实际工业应用要求,空隙率测量技术仍有待进一步研究。本文重点针对气液两相流空隙率的测量进行了研究,主要工作和创新点如下:
     1.提出了一种最小二乘支持向量机(LS-SVM)的改进方法。针对现有LS-SVM的不足,运用训练数据点筛选策略,根据LS-SVM模型训练误差的大小,剔除训练数据中误差过大和过小的数据点,从而获得模型的“稀疏性”,提高了模型的泛化能力和鲁棒性。仿真验证和实际空隙率测量的实验验证,表明LS-SVM的改进是成功的。
     2.将实数编码的遗传算法(RC-GA)引入到LS-SVM参数优化中,解决了LS-SVM使用时存在的参数选取困难的问题。将LS-SVM的参数选取问题看作优化问题,建立优化问题的目标函数,凭借RC-GA强大的全局搜索能力,搜索最优LS-SVM参数。仿真结果和实际空隙率测量实验表明RC-GA方法是有效的。
     3.提出了基于12电极电容层析成像技术(ECT)和LS-SVM的油气两相流空隙率在线测量的新方法。运用该方法测量空隙率时,首先辨识流型,然后选择与流型辨识结果相对应的空隙率模型计算获得空隙率。该方法省去了常用ECT方法测量空隙率时复杂而耗时的图像重建过程,提高了空隙率测量的实时性。实验结果证明了本方法的有效性。
     4.提出了基于16电极电阻层析成像技术(ERT)和LS-SVM的气水两相流空隙率测量的新方法。该方法由ERT传感器获得104个测量值,然后把ERT传感器得到的104个(去除16个与激励电极对相邻的测量值后为88个)测量值作为已经建立好的空隙率测量模型的输入,计算获得空隙率。实验结果表明本方法是有效的。
Two-phase flow exists widely in many industrial fields such as power,petroleum, metallurgy, nuclear energy, chemical engineering and so on.Measurement of two-phase flow parameters is very important for the metrology,control and environment protection in modem production processes. However, the inherent complexity of two-phase flow system leads to many difficulties in measuring the parameters of two-phase flow. Voidage is one of the most important parameters. Although many voidage measurement methods have been proposed, it is still difficult to measure the voidage due to the complexity of the characteristics of two-phase flow. It is necessary to explore new methods for voidage measurement.The author mainly focuses on the research of voidage measurement of gas-liquid two-phase flow. The main works of the dissertation are listed as follows:
     1. An improved Least Squares Support Vector Machine (LS-SVM) was proposed to overcome the drawback existing in the present LS-SVM. According to the training errors of LS-SVM model, data points with too large or too small errors were discarded, and thus the generalization ability and robustness of LS-SVM model was improved. The improved LS-SVM was verified by simulation data.Experimental results of voidage measurements also demonstrate that the improvement of LS-SVM is effective.
     2. Real-Coded Genetic Algorithm (RC-GA) was introduced to solve the difficult problem of parameters selection in LS-SVM. The issue of parameters selection in LS-SVM was regarded as an optimization problem. A RC-GA with global searching capability was employed to search the optimal parameters in LS-SVM. Experimental results show that the RC-GA based parameters optimization method is effective.
     3. Based on Electrical Capacitance Tomography (ECT) and LS-SVM, a new method was proposed for on-line voidage measurement of oil-gas two-phase flow. LS-SVM was used to establish the voidage measurement models under different flow patterns. In the measurement process, the flow pattern of oil-gas two-phase flow was first identified, and then, the voidage was computed using the voidage model corresponding to the identified flow pattern. This new method implemented voidage measurement without complicated and time-consuming image reconstruction. And thus the real-time performance of voidage measurement was improved. Experimental results show that the new method is effective.
     4. Based on Electrical Resistance Tomography (ERT) technique and LS-SVM, a new voidage measurement method of gas-liquid two-phase flow was proposed. In this method, the ERT sensor was employed to obtain the 104 independent resistance values. These 104 measurements values (88 measurements after reducing dimension by eliminating 16 adjacent values) were the input of the voidage measurement model which was established by LS-SVM. The output of the model was the voidage. Experimental results prove the effectiveness of the new method.
引文
[1] 李海青 等.两相流参数检测及应用.杭州:浙江大学出版社,1991.
    [2] 林宗虎 等.气液两相流和沸腾传热.西安:西安交通大学出版社,1987.
    [3] 吴浩江.油气水多相流流型智能识别的研究.西安交通大学博士学位论文,1999.
    [4] 陈学俊.迅速发展中的一门新兴交叉学科—多相流热物理的进展.西安交通大学学报,1996,30(4):7-17.
    [5] 陈甘棠,王樟茂.流态化技术的理论和应用.北京:中国石化出版社,1996.
    [6] 林宗虎,王栋,王树众,林益.多相流的近期工程应用趋向,西安交通大学学报,2001,35(9):886-890.
    [7] 林宗虎.变幻流动的科学—多相流体力学.北京:清华大学出版社,2000.
    [8] 李海青,乔贺堂.多相流测试技术现状及趋势.北京:石油工业出版社,1996.
    [9] 林宗虎.管路内气液两相流特性及其工程应用.西安:西安交通大学出版社,1992.
    [10] 徐苓安.相关流量测量技术.天津:天津大学出版社,1988.
    [11] 黄志尧,王保良,李海青.用于两相流流型显示和空隙率测量的电容层析成像技术.化工学报,2001,52(11):1035-1038.
    [12] 丁浩.新型信息处理技术在气液两相流流型辨识中的应用研究.浙江大学博士学位论文,2005.
    [13] Hewitt G F. Measurement of two phase flow parameters. London: Academic Press, 1978.
    [14] Lynch G F, Segal S L. Direct measurement of the void fraction of a two-phase fluid by nuclear magnetic resonance. International Journal of Mass Transfer, 1977, 20(1): 7-14.
    [15] 徐苓安.相关流量测量技术.天津:天津大学出版社,1988.
    [16] 李海青,黄志尧 等.特种检测技术及应用.杭州:浙江大学出版社,2000.
    [17] 陈鸥,杨献勇,徐光捷.气液两相流中液相局部速度测量实验.清华大学学报(自然科学版),2005,45(2):238-241.
    [18] Beck M S, Bayars M, Dyakowski T, et al. Principles and industrial applications of electrical capacitance tomography. Measurement & Control, 1997, 30: 197-200.
    [19] 李海青,黄志尧 等.软测量技术原理及应用.北京:化学工业出版社,2000.
    [20] 冀海峰,黄志尧,吴贤国,李海青.基于小波变换的气固流化床压力波动信号的分析.高校化学工程学报,2000,14(6):553-557.
    [21] 劳力云.基于动态差压信号分析的两相流参数辨识方法研究.浙江大学博士学位论文,1998.
    [22] 黄雄斌,包雨云,施力田,王英琛.应用电导探针测定固—液两相流的局部速度.高校化学工程学报,1995,9(2):187-190.
    [23] 王微微.气液两相流参数监测新方法研究.杭州,浙江大学博士学位论文,2005.
    [24] 劳力云,郑之初,吴应湘,李东晖.关于气液两相流流型及其判别的若干问题.力学进展,2002,32(2):235-249.
    [25] 张贤达.现代信号处理(第二版).北京:清华大学出版社,2002.
    [26] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. A, 1998,454: 903-995.
    [27] Sun B, Zhang H J, Cheng L, Zhao Y X. Flow Regime Identification of Gas-liquid Two-phase Flow Based on HHT. Chinese Journal of Chemical Engineering, 2006, 14(1):24-30.
    [28] 白博峰,郭烈锦,赵亮.汽(气)液两相流流型在线识别的研究进展.力学进展,2001,31(3):437-446.
    [29] 白博峰,郭烈锦,陈学俊.气液两相流流型在线智能识别.中国电机工程 学报,2001,21(7):46-50
    [30] 白博峰,郭烈锦,陈学俊.基于反传神经网络和压差波动识别气液两相流流型.化工学报,2000,51(6):848-852.
    [31] Bankoff S G. A variable density single-fluid model for two-phase with particular reference to steam-water flow. Transactions ASME Series C, 1960, 82(4): 265-272.
    [32] 唐人虎,陈听宽,罗毓珊,尹飞.高温高压下用光纤探针测量截面含汽率的实验研究.化工学报,2001,52(6):560-563.
    [33] Luke S P, Williams R A. Industrial applications of electrical tomography to solid conveying. Measurement & Control, 1997, 30: 201-205.
    [34] Reinecke N, Mewes D. Recent developments and industrial/research applications of capacitance tomography. Measurement Science and Technology, 1996, 7(3): 325-327.
    [35] 魏颖.电阻层析成像技术(ERT)及其在两相流测量中应用研究.东北大学博士学位论文,2001.
    [36] Wang M. Seeing a new dimension--The past decade's developments on electrical impedance tomography. Progress in natural science, 2005, 15(13): 1-13.
    [37] Beck M S, Williams R A. Process tomography: a European innovation and its applications. Measurement Science and Technology, 1996, 7(3): 215-224.
    [38] Huang S M, Plaskowski A, Xie X G, et al. Capacitance-based tomographic flow imaging system. Electrics Letters, 1988, 24(7):418-419.
    [39] Fasching G E, Loudin W J, Smith N S. Capacitive system for three-dimensional imaging of fluidized-bed density. IEEE Transactions on Instrumentation and Measurement, 1994, 43 (1): 56-62.
    [40] Xie C G, Plaskowski A, Beck M S. 8-electrode capacitance system for two-component flow identification part 2: Flow regime identification, IEE Proceedings-A, 1989, 136(4): 184-190.
    [41] Isaksen tO, Nordtvedt J E. A new reconstruction algorithm for process tomography. Measurement Science and Technology, 1993, 4(12): 1464-1475.
    [42] Isaksen tO. A review of reconstruction techniques for capacitance tomography. Measurement Science and Technology, 1996, 7(3): 325-337.
    [43] Nooralahiyan A Y, Hoyle B S. Three-component tomographic flow imaging using artificial neural network reconstruction. Chemical Engineering Science, 1997, 52(13): 2139-2148.
    [44] Yang W Q, Spink D M, York T A, et al. An image reconstruction algorithm based on Landweber's iteration method for electrical capacitance tomography. 1999, 10(11): 1065-1069.
    [45] Liu S, Fu L, Yang W Q. Optimization of an iterative image reconstruction algorithm for electrical capacitance tomography. Measurement Science and Technology, 1999, 10(7): 37-39.
    [46] 董向元,陈琪,李惊涛等.基于快速投影LANDWEBER法德电容层析成像图像重建算法研究.中国电机工程学报,2005,25(14):89-92.
    [47] 杨钢,王玉涛,邵富群,王师.电容层析成像图像重建中的迭代算法.仪器仪表学报,2006,27(12):1591-1594.
    [48] 杨钢,王玉涛,邵富群,王师.用ECT图像重建的预处理Landweber迭代算法.东北大学学报,2006,27(9):953-956.
    [49] Lu G, Peng L H, Zhang B F, Liao Y B. Preconditioned Landweber iteration algorithm for electrical capacitance tomography. Flow Measurement and Instrumentation, 2005, 16: 163-167.
    [50] 马宁,苏祥芳,王延平.基于电路网络理论的电容层析成像方法.电子学报,2000,28(1):30-34.
    [51] Huang Z Y, Wang B L, Li H Q. Application of electrical capacitance tomography to void fraction measurement of two-phase flow. IEEE Transactions on Instrumentation and Measurement, 2003, 52(1): 7-11.
    [52] 黄善仿,张修刚,王栋,林宗虎.水平管内两相流动网丝电容层析成像.热能动力工程,2006,21(4):414-417,439.
    [53] 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.天津大学学报,2005,38(1):1-4.
    [54] 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.天津大学学报,2006,39(3):306-309.
    [55] 杨钢,邵富群,王师.ECT图像重建中最小坡度正则化参数选择方法.东北大学学报(自然科学版)2006,27(8):855-858.
    [56] 王海刚,刘石,杨五强,姜凡.电容层析成像三维成像算法研究与软件设计.仪器仪表学报,2004,25(6):701-704
    [57] 赵进创,陆建波,傅文利等.电容层析成像系统三维图像重建及其在两相流体积测量中的应用研究.仪器仪表学报,2005,26(2):202-205.
    [58] 王海刚,刘石,姜凡,杨五强.旋风分离固体颗粒浓度三维电容层析成像分布.工程热物理学报,2006,27(1):177-179.
    [59] 彭黎辉,陆耿,杨伍强.电容成像图像重建算法原理及评价.清华大学学报,2004,44(4):478-483.
    [60] 董向元,刘石,阎润生等.电容层析成像中通用迭代法的研究.仪器仪表学报,2006,27(1):23—25,30.
    [61] Isaksen φ, Dico A S, Hammer E A. A capacitance-based tomography system for interface measurement in separation vessels. Measurement Science and Technology, 1994, 5(10): 1262-1271.
    [62] Mosorov V, Sankowski D, Mazurkiewicz L, Dyakowski T. The best-correlated pixels method for solid mass flow measurements using electrical capacitance tomography. Measurement Science and Technology, 2002, 13(12): 1810-1814.
    [63] Zhu K, Madhusudana R S, Wang C H, Sundaresan S. Electrical capacitance tomography measurements on vertical and inclined pneumatic conveying of granular solids. Chemical Engineering Science, 2003, 58(18): 4.225-4245.
    [64] 张淯淳,彭黎辉,姚亚,张宝芬.采用改进的PCA算法测量两相流相浓度.清华大学学报(自然科学版),2003,43(3):400-401,403.
    [65] 吴新杰,王师,王凤翔.基于粗糙集理论两相流流型辨识方法研究.仪器仪表学报,2003,24(3):221-225.
    [66] 刘石,潘忠刚,燕贵章,王海刚.应用电容层析成象和差压对比法对流化床内固体颗粒浓度分布的测量研究.工程热物理学报,2000,21(6):759-763.
    [67] 刘石,王海刚,姜凡,徐查中.循环流化床固体分布的层析成象测量.工程热物理学报,2001,22(5):645-648.
    [68] 黄志尧,冀海峰,王保良,李海青.电容层析成像技术在线测量气固流化床空隙率的研究.高校化学工程学报,2002,16(5):490-495.
    [69] 王雷,冀海峰,黄志尧,李海青.基于ECT传感器和模式识别的气液两相流空隙率测量新方法研究.仪器仪表学报,2005,26(6):57-561.
    [70] Yang W Q and Liu S. Electrical capacitance tomography with square sensor. Electronics Letters, 1999, 35(4): 295-296.
    [71] 王化祥,张立峰,朱学明.电容层析成像系统阵列电极的优化设计.天津大学学报,2003,36(3):307-310.
    [72] Niu G, Jia Z H, Wang J. Void fraction measurement in oil-gas transportation pipeline using an improved electrical capacitance tomography system. Journal of Chemical Engineering of Chinese Universities, 2004, 12(4): 476-481.
    [73] 马敏,王化祥,田莉敏.基于DSP的数字化电容层析成像系统.传感技术学报,2006,19(3):705-708.
    [74] 王海刚,阎润生,刘石,杨五强,姜凡.电容层析技术在旋风分离器及料腿中固体颗粒浓度、速度和流量测试中的应用.动力工程,2004,24(5):675-680.
    [75] 姜凡,刘石,王海刚,杨五强.电容层析成像技术在流化床气固两相流测量 中的应用.动力工程,2004,24(6):831-835.
    [76] Wang B L, Ji H F, Huang Z Y, Li H Q. A high-speed data acquisition system for ECT based on the differential sampling method. IEEE Sensors Journal, 2005, 5(2): 308-312.
    [77] 牟昌华.电容层析成像敏感分布及图像重建算法研究.清华大学博士学位论文,2005.
    [78] 高彦丽,章勇高,邵富群.ECT技术在高炉物料分布监测中的应用研究.仪器仪表学报,2006,27(1):19—22.
    [79] 余金华.电阻层析成像技术图像重建算法的研究.浙江大学博士学位论文,2005
    [80] Wang M. et al. ERT of metal walled vessels and pipelines. Electronics letters, 1994, 30(10): 771-773.
    [81] 邓湘.基于层析成象技术的智能化两相流测量系统研究.天津大学博士学位论文,2001.
    [82] Wilkinson A J, Randall E W, Cilliers J J, et al. A 1000-measurement frames/second ERT data capture system with real-time visualization. IEEE Sensors Journal, 2005, 5(2): 300-307.
    [83] 董峰,乔旭彤,姜之旭,徐苓安.应用电阻层系成像技术测量垂直管道气/液两相流分相含率.天津大学学报,2004,37(6):510-514.
    [84] Dong F, Tan C, Liu J W, Xu Y B, and Wang H X. Development of single drive electrode electrical resistance tomography system. IEEE Transactions on Instrumentation and Measurement, 2006, 55(4): 1208-1214.
    [85] Wang H X, Wang C, and Yin W L. A Pre-iteration method for the inverse problem in electrical impedance tomography. IEEE Transactions on Instrumentation and Measurement, 2004, 53(4): 1093-1096.
    [86] 王化祥,曹章.电阻抗层析成像系统“软场”非线性特性—基于统计的方法.天津大学学报,2006,39(5):543-547.
    [87] Dong F, Xu Y B, Hua L, and Wang H X. Two methods for measurement of gas-liquid flows in vertical upward pipe using dual-plane ERT System. IEEE Transactions on Instrumentation and Measurement, 2006, 55(5): 1576-1586.
    [88] Heikkinen H M, Kourunen J, Savolainen T, et al. Real time three-dimensional electrical impedance tomography applied in multiphase flow imaging. Measurement Science Technology. 2006, 17: 2083-2087.
    [89] 张恒喜,郭基联,朱家元,虞健飞.小样本多元数据分析方法及应用.西安:西北工业大学出版社,2002.
    [90] 加肇祺,张学工等.模式识别.北京:清华大学出版社,2000.
    [91] Burges C J C. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 1998, 2 (2): 1-43.
    [92] 张学工.关于统计学习理论与支持向量机.自动化学报,2000,26(1):32-42.
    [93] Vapnik V N. The nature of statistical learning theory. New York: Springer-Vedag, 1995.
    [94] Vapnik V N. Statistical learning theory. New York: Wiley, 1998.
    [95] 许建华,张学工,李衍达.支持向量机的新发展.控制与决策,2004,19(5):181-184,193.
    [96] 田盛丰.基于核函数的学习算法.北方交通大学学报,2003,27(2):1-8.
    [97] Cortes C, Vapnik V N. Support-vector networks. Machine Learning, 1995, 20(3): 273-297.
    [98] Osuna E, Freund R, Girosi F. Training support vector machine, an application to face detection. In: Proc. Of CVPR'97, Puerto Rico, 1997.
    [99] 王晓丹,王积勤.支持向量机训练和实现算法综述.计算机工程与应用,2004,13:75-78.
    [100] Bradley P S, Mangasarian O L. Massive data discrimination via linear support vector machine. Technical Report 98-05, Madison, WI: University of Wisconsin, 1998.
    
    [101]Platt J C. Sequential minimal optimization: A fast algorithm for training support vector machines. Technical Report MSR-TR-98-14, Microsoft Research, 1998.
    
    [102] Suykens J A K, Vandwalle J. Least squares support vector machine classifiers.Neural Processing Letters, 1999, 9(3): 290-300.
    
    [103] Suykens J A K, Lukas L, Vandewalle J. Sparse least squares support vector machines classifiers. The 8th European Symposium on Artificial Neural Networks. Brugers, 2000,37-42.
    
    [104] Mangasrian O L, Musicant D R. Successive overtaxation for support vector machines. IEEE Transactions on Neural Networks, 1999,10(5):1032-1037.
    
    [105] Zhang X G Using class center vectors to build support vector machines.Neural networks for signal processing. New York: IEEE Press, 1999.
    
    [106]Mangasarian O L. Generalized support vector machines. Advances in Large Margin Classifiers. MIT Press, 2000.
    
    [107]Scholkopf B, Smola A J, Williamson R C, et al. New support vector algorithms. Neural Computation, 2000,12 (5): 1207-1245.
    
    [108] Lin C F and Wang S D. Fuzzy Support Vector Machines. IEEE Transactions on Neural Networks, 2002,13(2): 464-471.
    
    [109] Zhang L, Zhou W D, and Jiao L C. Wavelet support vector machine. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 2004,34(1): 34-39.
    
    [110]Shilton M, Palaniswami M, Ralph D, and Tsoi A C. Incremental training of support vector machines. IEEE Transactions on Neural Networks, 2005, 16(1):114-130.
    
    [111]Waring C A, and Liu X W. Face detection using spectral histograms and SVMs. IEEE Transactions on System, Man, and Cybernetics—part B: Cybernetics, 2005, 35(3):467-476.
    
    [112] Christopher A and Liu X W. Face detection using spectral histograms and SVMs. IEEE Transactions on Systems, Man, and Cybernetics—Part B:Cybernetics, 2005,35(3): 467-476.
    
    [113] Lin C C, Chen S H, Truong T K, and Chang Y. Audio classification and categorization based on wavelets and support vector machine. IEEE Transactions on Speech and Audio Processing, 2005,13(5): 644-651.
    
    [114] Sun B Y, Huang D S, and Fang H T. Lidar signal denoising using least-squares support vector machine. IEEE Signal Processing Letters, 2005,12(2): 101-104.
    [115]Lv H, Wang W Y, Wang C, Zhuo Q. Off-line Chinese signature verification based on support vector machines. Pattern Recognition Letters, 2005, 26:2390-2399.
    [116]Xin D and Wu Z H. Speaker recognition using continuous density support vector machines. Electronics Letters, 2001, 37(17): 1099-1101.
    
    [117] Shi Z W and Han M. Support vector echo-state machine for chaotic time-series prediction [J]. IEEE Transactions on Neural Networks, 2007, 18(2), 359-372.
    [118] Ming G, Du R, Zhang G C, Xu Y S. Fault diagnosis using support vector machine with an application in sheet metal stamping operations. Mechanical Systems and Signal Processing. 2004,18:143-159.
    
    [119] Cho S, Asfour S, Onar A, Kaundiny N. Tool breakage detection using support vector machine learning in a milling process. International Journal of Machine Tools & Manufacture, 2005, 45: 241-249.
    [120] Pai P F, Hong W C. Software reliability forecasting by support vector machines with simulated annealing algorithms. The Journal of Systems and Software, 2006, 79: 747-755.
    [121] Yan W W, Shao H H, Wang X F. Soft sensing modeling based on support vector machine and Bayesian model selection. Computers and Chemical Engineering, 2004, 28: 1489-1498.
    [122] Suykens J A K, Vandewalle J, De Moor B. Optimal control by least squares support vector machines. Neural Networks, 2001, 14: 23-35.
    [123] 李洪兴.模糊数学.北京:国防工业出版社,1994.
    [124] 李金宗.模式识别导论.北京:高等教育出版社,1994.
    [125] 邵晓寅,黄志尧,冀海峰,李海青.基于电容层析成像和模糊模式识别的油气两相流流型辨识新方法的研究.高校化学工程学报,2003,17(6):616-621.
    [126] 刘铁军.工程电导测试技术及应用研究.浙江大学博士学位论文,2006.
    [127] 黄海波.基于双极性脉冲电流激励的电阻层析成像系统的研制及其在两相流测量中的应用研究.浙江大学硕士学位论文,2004.
    [128] 朱建平.微弱电容/电导检测技术在过程工业中的应用.浙江大学硕士学位论文,2006.
    [129] Zhu J P, Wang B L, Huang Z Y, and Li H Q. Design of ERT system. Journal of Zhejiang University SCIENCE, 6A (12): 1446-1448.
    [130] Suykens J A K, De Brabanter J, Lukas L, Van Gestel T, Vandewalle J. Weighted least squares support vector machines: robustness and sparse approximation. Neurocomputing, 2002, 48: 85-105.
    [131] Boser B E, Guyon I M, Vapnik V N. A Training Algorithm for Optimal Margin Classifiers. In: Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory, 1992:144-152.
    [132] Chapelle O, Vapnik V, Bousquet O, Mukherjee S. Choosing multiple parameters for support vector machines. Machine Learning, 2002, 46: 131-159.
    [133] 余志雄,周创兵,李俊平,史超.基于v-SVR算法的边坡稳定性预测.岩土力学与工程学报,2005,24(14):2468-2475.
    [134] Browne M W. Cross-validation methods. Journal of Mathematical Psychology, 2000, 44(1): 108-132.
    [135] Gestel T Van, Suykens J A K, Baesens B, et al. Benchmarking least squares support vector machine classifiers. Machine Learning, 2004, 54(1): 5-32.
    [136] Chuang C C, Su S F. Robust support vector regression networks for function approximation with outliers. IEEE Transaction on Neural Networks, 2002, 13(6): 1322-1330.
    [137] 袁小芳,王耀南.基于混沌优化算法的支持向量机参数选取方法.控制与决策,2006,21(1),111-113,117.
    [138] Michflewicz Z. Genetic Algorithms+Data Structures=Evolution Programs. Vedag: Springer, 992.
    [139] 王小平,曹立明.遗传算法—理论、应用与软件实现.西安:西安交通大学出版社.2002.
    [140] 雷英杰,张善文,李续武,周创明.MATLAB遗产算法工具箱及应用.西安:西安电子科技大学出版社,2005.
    [141] 周明,孙树栋.遗传算法原理及应用.北京:国防工业出版社,2002.
    [142] Friedman J H. Multivariate adaptive regression splines. The Annals of Statistics, 1991, 19(1): 1-67.
    [143] Hwang J N, Martin S H, Martin M R, Schimer J. Regression modeling in back-propagation and projection pursuit learning. IEEE Transactions on Neural Network, 1994, 5(3): 342-352.
    [144] Randall E W, Wiklinson A J, Cilliers J J, Xie W and Neething S J. Current pulse technique for electrical resistance tomography measurement. In: Proceedings of the second World congress on Industrial Process Tomography, 2001: 493-501.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700