基于数字图像处理技术的气液两相流型识别与演化规律研究
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摘要
两相流动现象广泛存在于自然界和现代工业生产过程中,与人类的生活及生产密切相关,两相流流动参数检测对生产过程及工艺优化具有重要意义。但由于两相流存在复杂相间界面效应及相对运动,尤其是流型转变动力学机理至今尚未十分清楚,加之理论与技术上的欠缺,两相流参数检测问题,特别是复杂流体流量测量和流型识别问题长期未能得到很好解决。图像处理技术是一门新兴的检测技术,近年来图像处理在工业检测中的应用越来越受到人们的重视。在两相流系统的参数检测中,图像处理技术也得到了广泛的应用。采用图像处理技术与现代信息处理技术融合的检测理论与方法,是解决复杂两相流流动参数检测的有效途径。
本文采用图像处理与多尺度非线性分析等相结合的方法研究了气液两相流的流动特性,应用特征挖掘及信息融合的软测量方法实现了两相流流型参数测量。取得了创新性研究成果。
在气液两相流型图像边缘分割的诸多算法中,对等高线方法进行了改进,首先对图像进行二维高斯核梯度模的求取,在梯度模对图像边缘增强的基础上进行经验模态分解,取得高频信息层子图像并进行叠加,后应用开闭运算进行细节噪声去除与边缘修补,最后应用等高线理论进行特征提取和表达。通过对比发现,这种图像特征表达方法不仅能够对图像的边缘特征有一个很好的检测,而且能够保留一些经典算法所保留不了的细节信息,考虑到气液两相流复杂的动力学机理,此方法应用于此,能够为气液两相流图像特征提取提供一个新思路。
应用了一种新的时间序列的提取方法,将气液两相流视频信号的每一帧图像分块成小的区域,每相邻两帧图像的相邻两区域进行灰度相似值与最大差值计算,分别组成时间序列。对时间序列分别求取最大李亚普诺夫指数,组成最大李亚普诺夫指数矩阵。利用李亚普诺夫指数的特征将气液两相流视频划分为混沌特性不同的区域,分别对其从整体以及细节两部分进行分析,分别采用0,1分布图谱、二维和三维等高线图谱以及概率密度谱结合最大李亚普诺夫指数矩阵的分形盒维数、香农熵以及均值等特征,对气液两相流型流动机理进行辅助分析。实验结果表明对图像小区域分块结合最大李亚普诺夫指数提取的方法能够区别出不同流型的流动特性,气液两相流视频图像的背景与变化相界面具有强度不同的混沌特性,是一种有效的分析气液两相流图像信号的新方法。
将EMD分解与HURST指数、递归图特征相结合对气液两相流型从整体到细节进行了剖析,并提取递归特征中的典型的对角线平均长度值与香农熵值两个特征值,观察其随气相表观速度增加的变化情况,对气液两相流型的动力学特征进行定量分析。研究发现随着气相表观速度的增加,双分析特征的变化规律更为明显。在高频与低频段,三种流型存在单分形特征,而在中频段则呈现出双分形摸样,从整体与局部两方面对三种流型的流动机理进行了分析。在递归分析中,对角线平均长度与递归香农熵两个特征值的变化体现出了气泡与气塞乃至整个泡群的运动规律。在EMD分解后的高频信息层中段塞流较泡状流与雾状流存在明显峰值。总之,基于图像灰度波动信号的多尺度非线性分析方法是理解与表征气液两相流动力学特性的有效途径。
将应用于桥梁建筑性能分析的随机子空间方法应用到气液两相流型图像灰度波动信号的分析中,而用于确定系统阶次的一种比较新颖的方法稳定图也被应用到气液两相流灰度波动信号的分析中,并结合直线度特征值对复杂气液两相流时间序列进行定量表征。建立了基于随机子空间方法进行流型辨识的新标准,雾状流相角在1.35-2.07之间,泡状流相角在4.01-4.36之间,段塞流相角在-0.52-0之间,其不受实验工况的变化所影响,完全由流型内部模态结构所决定,能够准确的对流型信号进行区分。
The phenomenon of the two-phase flow is widly found in nature and modern industrial production process, and it is closely related to the human life and production. The measurement of the flow parameters is of great significance for industrialproducing process and the optimization of process. Because of complex interfacial effect and relative motion between the phases, it is difficult to identify accurately the two-phase flow patterns. In particular the mechanism of the transition from flow patterns to dynamics has not yet been very clear. And the lack of theory and technology, the measurement of two phase flow parameters failed to get very good solved, especially the complex fluid flow measurement and flow patterns' identification problem.Image processing technology is a new measurement technology, in recent years the image processing was applicated to the industrial measurement more and more by people. Image processing technology was also be taked a wide range of applications in the two phase flow system.Therefore it's an effective approach to solve the measurement of complex two phase flow parameters by the fusion of image processing and modern information processing method and theory.the nonlinear dynamic characteristics of two phase flow patterns were studied by using multiscale nonlinear analyzing method and image processing.The flowrate of two phase flow was measured by soft measurement method based on characteristics extracting and information fusion.And the innovative research fruits are shown as below:
In so many image edge division algorithms, the paper improved the contour method and applicated in the images of gas-liquid two-phase flow patterns. To get effective extraction from the main objective of the gas-liquid two-phase flow images, in this paper, the2-Dimensional Gaussian kernel gradient, the multi-scale image decomposition techniques, the opening and closing operations, and the contour theory are combined together to put forward a way of the expression of the image characteristics. The new method can be described as follows:first, the decomposition of the empirical mode is based on the gradient mode enhancing image edge to get the high-frequency information sub-images and superpose them; then, the application of the opening and closing operation is to reduce the details'noise and repair the edge; finally extracting and expressing the features are by using the contour theory. By comparison, this way of expression can not only get the edge features of the image very well, but also retain some details, which can not be reserved by some classical algorithm. This method applied here can provide a new idea for extracting features from gas-liquid two-phase flow images.
Each frame of the video signal is divided into smaller areas by a new method for extracting time series.The gray similar values and the maximum gray scale difference of each two adjacent frame are calculated,then formed the time series.The largest Lyapunov exponents of time series are respectively extracted,and the largest Lyapunov exponent matrix is composed.The videos of gas-liquid two-flow patterns are divided into different chaotic characteristic areas by the characteristics of Lyapunov exponent.Then they are respectively analyzed from overall and details by zero and one distribution map and3D map. The flowing mechanism of gas-liquid two-phase flow is analyzed,combined the fractal box dimension and Shannon entropy of the largest Lyapunov exponent matrix.The results show that the method of the gray similar values series of small areas combined extracting the largest Lyapunov exponent can distinguish the flowing characteristics of different flow patterns;the background and changed phase interface of gas-liquid two-phased flow video have chaotic charateristics of different intensity,which is an effective method for analyzing the gas-liquid two-phase flow signals.
Empirical Mode Decomposition (EMD) method, HURST exponents and Recurrence Plot (RP) were combined together to analyze the gas-liquid two-phase flow from the whole to the details. At the same time the various signals are checked in the chaotic recursion chart by which the two typical characteristics (diagonal average length's and Shannon entropy) are obtained. The results show that the change regularity of the characteristic of dual-fractal is more obvious with the increase of gas surface measured velocity. In the high frequency section and low frequency section, all of the three flow patterns have simple fractal characteristic. But in the middle frequency section, the flow patterns appear to be dual fractal characteristic. The flow mechanism of the three flow patterns is analyzed partly and wholly.The Movement Law of bubble, gas slug and the whole bubble group present the change of two characteristics that are diagonal average length's and recursive Shannon entropy's. After the decomposition by the EMD method the slug flow and the mist flow in the high frequency section have obvious peaks.Anyway, it is an effective way to understand and characterize the dynamic characteristics of two-phase flow patterns that the multi-scale non-linear analysis method is based on image gray-scale fluctuation signals.
The Stochastic subspsace parameter identification(SSI) which was used in the analysis of the construction of the bridge will be applized in the analysis of the grey fluctuation signals of gas-liquid two-phase flow patterns'images. And the stability graph which can determine the order of the system also be used in the analysis of the fluctuation signals of gas-liquid two-phase flow patterns'images.Complex time series can be quantitative characterized combining straightness eigenvalue.The feature vector of the pressure fluctuation sequence of three typical gas-liquid two-phase flow were extracted by application of random sub-space. It can be distinguished by amplitude and phase angle, of which the phase angle feature is the most reliable. The phase angle of mist flow is between1.35to2.07. The phase angle of bubbly flow is between4.01to4.36. The phase angle of slug flow is between-0.52to0. Changes of experimental conditions will not bring any effects. Determined entirely by flow pattern internal modal structure, the flow pattern signal can be accurately distinguished.
本文采用图像处理与多尺度非线性分析等相结合的方法研究了气液两相流的流动特性,应用特征挖掘及信息融合的软测量方法实现了两相流流型参数测量。取得了创新性研究成果。
在气液两相流型图像边缘分割的诸多算法中,对等高线方法进行了改进,首先对图像进行二维高斯核梯度模的求取,在梯度模对图像边缘增强的基础上进行经验模态分解,取得高频信息层子图像并进行叠加,后应用开闭运算进行细节噪声去除与边缘修补,最后应用等高线理论进行特征提取和表达。通过对比发现,这种图像特征表达方法不仅能够对图像的边缘特征有一个很好的检测,而且能够保留一些经典算法所保留不了的细节信息,考虑到气液两相流复杂的动力学机理,此方法应用于此,能够为气液两相流图像特征提取提供一个新思路。
应用了一种新的时间序列的提取方法,将气液两相流视频信号的每一帧图像分块成小的区域,每相邻两帧图像的相邻两区域进行灰度相似值与最大差值计算,分别组成时间序列。对时间序列分别求取最大李亚普诺夫指数,组成最大李亚普诺夫指数矩阵。利用李亚普诺夫指数的特征将气液两相流视频划分为混沌特性不同的区域,分别对其从整体以及细节两部分进行分析,分别采用0,1分布图谱、二维和三维等高线图谱以及概率密度谱结合最大李亚普诺夫指数矩阵的分形盒维数、香农熵以及均值等特征,对气液两相流型流动机理进行辅助分析。实验结果表明对图像小区域分块结合最大李亚普诺夫指数提取的方法能够区别出不同流型的流动特性,气液两相流视频图像的背景与变化相界面具有强度不同的混沌特性,是一种有效的分析气液两相流图像信号的新方法。
将EMD分解与HURST指数、递归图特征相结合对气液两相流型从整体到细节进行了剖析,并提取递归特征中的典型的对角线平均长度值与香农熵值两个特征值,观察其随气相表观速度增加的变化情况,对气液两相流型的动力学特征进行定量分析。研究发现随着气相表观速度的增加,双分析特征的变化规律更为明显。在高频与低频段,三种流型存在单分形特征,而在中频段则呈现出双分形摸样,从整体与局部两方面对三种流型的流动机理进行了分析。在递归分析中,对角线平均长度与递归香农熵两个特征值的变化体现出了气泡与气塞乃至整个泡群的运动规律。在EMD分解后的高频信息层中段塞流较泡状流与雾状流存在明显峰值。总之,基于图像灰度波动信号的多尺度非线性分析方法是理解与表征气液两相流动力学特性的有效途径。
将应用于桥梁建筑性能分析的随机子空间方法应用到气液两相流型图像灰度波动信号的分析中,而用于确定系统阶次的一种比较新颖的方法稳定图也被应用到气液两相流灰度波动信号的分析中,并结合直线度特征值对复杂气液两相流时间序列进行定量表征。建立了基于随机子空间方法进行流型辨识的新标准,雾状流相角在1.35-2.07之间,泡状流相角在4.01-4.36之间,段塞流相角在-0.52-0之间,其不受实验工况的变化所影响,完全由流型内部模态结构所决定,能够准确的对流型信号进行区分。
The phenomenon of the two-phase flow is widly found in nature and modern industrial production process, and it is closely related to the human life and production. The measurement of the flow parameters is of great significance for industrialproducing process and the optimization of process. Because of complex interfacial effect and relative motion between the phases, it is difficult to identify accurately the two-phase flow patterns. In particular the mechanism of the transition from flow patterns to dynamics has not yet been very clear. And the lack of theory and technology, the measurement of two phase flow parameters failed to get very good solved, especially the complex fluid flow measurement and flow patterns' identification problem.Image processing technology is a new measurement technology, in recent years the image processing was applicated to the industrial measurement more and more by people. Image processing technology was also be taked a wide range of applications in the two phase flow system.Therefore it's an effective approach to solve the measurement of complex two phase flow parameters by the fusion of image processing and modern information processing method and theory.the nonlinear dynamic characteristics of two phase flow patterns were studied by using multiscale nonlinear analyzing method and image processing.The flowrate of two phase flow was measured by soft measurement method based on characteristics extracting and information fusion.And the innovative research fruits are shown as below:
In so many image edge division algorithms, the paper improved the contour method and applicated in the images of gas-liquid two-phase flow patterns. To get effective extraction from the main objective of the gas-liquid two-phase flow images, in this paper, the2-Dimensional Gaussian kernel gradient, the multi-scale image decomposition techniques, the opening and closing operations, and the contour theory are combined together to put forward a way of the expression of the image characteristics. The new method can be described as follows:first, the decomposition of the empirical mode is based on the gradient mode enhancing image edge to get the high-frequency information sub-images and superpose them; then, the application of the opening and closing operation is to reduce the details'noise and repair the edge; finally extracting and expressing the features are by using the contour theory. By comparison, this way of expression can not only get the edge features of the image very well, but also retain some details, which can not be reserved by some classical algorithm. This method applied here can provide a new idea for extracting features from gas-liquid two-phase flow images.
Each frame of the video signal is divided into smaller areas by a new method for extracting time series.The gray similar values and the maximum gray scale difference of each two adjacent frame are calculated,then formed the time series.The largest Lyapunov exponents of time series are respectively extracted,and the largest Lyapunov exponent matrix is composed.The videos of gas-liquid two-flow patterns are divided into different chaotic characteristic areas by the characteristics of Lyapunov exponent.Then they are respectively analyzed from overall and details by zero and one distribution map and3D map. The flowing mechanism of gas-liquid two-phase flow is analyzed,combined the fractal box dimension and Shannon entropy of the largest Lyapunov exponent matrix.The results show that the method of the gray similar values series of small areas combined extracting the largest Lyapunov exponent can distinguish the flowing characteristics of different flow patterns;the background and changed phase interface of gas-liquid two-phased flow video have chaotic charateristics of different intensity,which is an effective method for analyzing the gas-liquid two-phase flow signals.
Empirical Mode Decomposition (EMD) method, HURST exponents and Recurrence Plot (RP) were combined together to analyze the gas-liquid two-phase flow from the whole to the details. At the same time the various signals are checked in the chaotic recursion chart by which the two typical characteristics (diagonal average length's and Shannon entropy) are obtained. The results show that the change regularity of the characteristic of dual-fractal is more obvious with the increase of gas surface measured velocity. In the high frequency section and low frequency section, all of the three flow patterns have simple fractal characteristic. But in the middle frequency section, the flow patterns appear to be dual fractal characteristic. The flow mechanism of the three flow patterns is analyzed partly and wholly.The Movement Law of bubble, gas slug and the whole bubble group present the change of two characteristics that are diagonal average length's and recursive Shannon entropy's. After the decomposition by the EMD method the slug flow and the mist flow in the high frequency section have obvious peaks.Anyway, it is an effective way to understand and characterize the dynamic characteristics of two-phase flow patterns that the multi-scale non-linear analysis method is based on image gray-scale fluctuation signals.
The Stochastic subspsace parameter identification(SSI) which was used in the analysis of the construction of the bridge will be applized in the analysis of the grey fluctuation signals of gas-liquid two-phase flow patterns'images. And the stability graph which can determine the order of the system also be used in the analysis of the fluctuation signals of gas-liquid two-phase flow patterns'images.Complex time series can be quantitative characterized combining straightness eigenvalue.The feature vector of the pressure fluctuation sequence of three typical gas-liquid two-phase flow were extracted by application of random sub-space. It can be distinguished by amplitude and phase angle, of which the phase angle feature is the most reliable. The phase angle of mist flow is between1.35to2.07. The phase angle of bubbly flow is between4.01to4.36. The phase angle of slug flow is between-0.52to0. Changes of experimental conditions will not bring any effects. Determined entirely by flow pattern internal modal structure, the flow pattern signal can be accurately distinguished.
引文
[1]李海青.两相流参数检测及应用[M].杭州：浙江大学出版社,1991：1-8
[2]陈学俊.多相流热物理学[M].西安：西安交通大学出版社,2005：1-7
[3]林宗虎.气液固多相流测量[M].北京：中国计量出版社,1988：3-5
[4]吴应湘.李清平,郑之初,等.海洋油气开发中的多相流技术[J].中国造船,2005,46(B11)：314-321
[5]张琦.应用于多相流参数检测的电容层析成像系统研究[D].南京理工大学硕士学位论文,2004：3-7
[6]Lockhart R W, Martineli R C. Proposed correlation of data for isothermal two-phase flow in pipes[J]. Chemical Engineering Progress,1949,45:39-48
[7]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,2000：24-29
[8]冀海峰,黄志尧,等.小波分析技术在多相流系统中的应用[J].石油化工,2001,30(2)：126-130
[9]周云龙,王强,杨志行,等.基于子波能量特征的气液两相流流型辨识方法研究[J].化工学报,2007,58(8)：1948-1954
[10]周云龙,王强,孙斌,等.基于希尔伯特—黄变换与Elman神经网络的气液两相流流型识别方法[J].中国电机工程学报,2007,27(11)：50-56
[11]周云龙,孙斌.基于神经网络和D-S证据理论的气液两相流流型识别方法[J].化工学报,2006,57(3)：607-613
[12]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
[13]周云龙,孙斌,陆军.改进BP神经网络在气液两相流流型识别中的应用[J].化工学报,2005,56(1)：110-115
[14]孙斌,周云龙.基于支持向量机和小波包能量特征的气液两相流流型识别方法[J].中国电机工程学报,2005,25(17)：93-99
[15]孙斌,周云龙.基于小波包能量特征的气液两相流流型识别方法[J].化学工程,2006,34(2)：33-36
[16]周云龙,孙斌.基于神经网络和D-S证据理论的气液两相流流型识别方法[J].化工学报,2006,57(3)：607-613
[17]金宁德,郑桂波,胡凌云.垂直上升管中气液两相流电导波动信号的混沌特性分析[J].地球物理学报,2006,49(5)：1552-1560
[18]王微微,耿艳峰,黄志尧.应用数据融合方法辨识油气两相流流型[J].传感技术学报,2007,20(9)：2128-2132
[19]彭珍瑞,王保良,黄志尧,等.基于改进的LS-SVM测量油气两相流空隙率[J].高校化学工程学报,2008,22(1)：18-22
[20]王海琴,何利民,李志彪.下倾管段塞流液塞频率波动的非线性分析[J].化工学报,57(9)：2086-2090
[21]盖德.希特斯洛尼.多相流动和传热手册[M].北京：机械工业出版社,1993： 121-134
[22]林宗虎,王树众,王栋.气液两相流和沸腾传热[M].西安：西安交通大学出版社,2003：56-61
[23]徐济望.沸腾传热和气液两相流[M].北京：原子能出版社,1993：67-73
[24]林宗虎.气-液-固多相流体测量[M].北京：中国计量出版社,1988：2-9
[25]Xie C G. Review of image reconstruction methods for proeess tomography[C]. Proeeedings of EC ATT, Karlsruhe, Germany,1993,21-25
[26]Yan He, Liu L J, Xu H. Image reconstruction in electrical capacitance tomography using multiple linear regression and regularization[J]. Measure Science and Technology,2001,12:575-581
[27]Huang Z Y, Wang B L, Li H Q. Application of electrical capacitance tomography to the void Fraction measurement[J]. IEEE Transaction on Instrumentation and Measurement,2003,52(1):7-12
[28]黄志尧,冀海峰,王保良,等.电容层析成像技术在线测量气固流化床空隙率的研究[J].高校化学工程学报,2002,16(5)：49-495
[29]王雷.电容层析成像系统的研制及其在两相流参数检测中的应用研究[D].浙江大学博士学位论文,2003：4-6
[30]刘石,雷兢,李志宏.基于改进正则法的ECT图像重建算法[J].仪器仪表学报,2007,28(11)：1977-1981
[31]刘石,陈琪,李志宏.多孔介质中燃烧火焰的ECT成像研究[J].工程热物理学报,2008,29(12)：2164-2166
[32]王化祥,唐磊.基于TV正则化算法的电容层析成像自适应剖分方法[J].电子测量技术,2006,29(5)：8-11
[33]王化祥,王琦,郝魁红.最小交叉熵图像重建算法[J].仪器仪表学报,2009,30(12)：2574-2579
[34]王化祥,范文茹,胡理.基于GMRES和Tikhonov正则化的生物电阻抗图像重建算法[J].生物医学工程学杂志,2009,26(4)：701-705
[35]王化祥,唐磊,崔自强.油/气两相流高速电容层析成像可视化系统[J].中国电机工程学报,2009,29(5)：61-65
[36]陆耀军,董守平.二维粒子图像测速系统的研制[J].实验力学,2002,16(3)：338-346
[37]Cenedese A, Paglialunga A. Digital direet analysis of a multiexposed photograph in PIV[M]. Experiments in Fluids,1990,18(5):273-280
[38]Teo C L, Lim K B, Hong G S. A Neural Net Approach in Analyzing Photograph in PIV Systems[M]. Decision Aiding for Complex Systems, Conference Proeeedings, 1991,3:1535-1538
[39]许联锋,陈刚,李建中,等.气液两相流中气泡运动速度场的PIV分析与研究[J].实验力学,2002,17(4)：458-463
[40]武旗,张义云,姜华,等.两相流稀相微粒速度场测量技术研究[J].西安交通大学学报,2003,37(7)：734-737
[41]Kadambi J R, Martin W T, Amirthaganesh S, Wernet M P. Partivle sizing using particle imaging Velocimetry for two-phase flows[J]. Powder Technology, 100(1998):251-259
[42]Kawaji M. Two-phase flow measurements using a photochromic dye activation technique[J]. Nuclear Engineering and Design,1998,184:379-392
[43]Popovich A T, Hummel R L. A new method for non-disturbing turbulent flow measurements very close to a wall[J]. Chemical Engineering Science,1967,22, 21-29
[44]Kawaji M. Two-phase flow measurements using a photochromic dye activation technique[J]. Nuclear Engineering and Design,1998,184:379-392
[45]Fourar M, Bories S. Experimental study of air-water two-phase flow through a fracture (narrow channel) [J]. International Journal of Multiphase Flow,1995,21 (4):621-637
[46]Gopal M, Jepson W P. Development of digital Image analysis techniques for the study of velocity and void profiles in slug flow[J]. International Journal of Multiphase Flow,1997,23 (5):945-965
[47]Hay J, Liu Z C, Hanratty T J. A backlighed imageing technique for particle size measurements in two-phase flows[J]. Experiments in Fluids,1998,25:226-232
[48]Dinh T B, Choi T S. Application of image processing techniques in air/water two phase flow[J]. Mechanics Research Communications,1999,26 (4):463-468
[49]Fore L B, Ibrahim B B, Beus S G. Visual measurements of droplet size in gas-liquid annular flow[J]. International Journal of Multiphase Flow,2002,28:1895-1910
[50]Grau R A, Heiskanen K. Visual technique for measuring bubble size in flotation machines[J]. Minerals Eingineering,2002,15:507-513
[51]Luo R, Song Q, Yang X Y, et al. A three-dimensional photographic measurement of phase distribution in dilute bubble flow[J]. Experiments in Fluids,2002,32: 116-120
[52]施丽莲,蔡晋辉,周泽魁.基于图像处理的气液两相流流型识别[J].浙江大学学报(工学版),2005,39(8)：1128-1131
[53]施丽莲.基于数字图像识别技术的气液两相流参数检测的研究[D].浙江大学博士学位论文,2004：3-5
[54]王振亚,金宁德,王淳,等.基于图像纹理分析的两相流流型时空演化特性[J].化工学报,2008,59(5)：1122-1130
[55]王红一,董峰.气液两相流中上升气泡体积的计算方法[J].仪器仪表学报,2009,30(11)：2444-2449
[56]周云龙,孙斌,李洪伟.多相流参数检测理论及其应用[M].北京：科学出版社,2010：64-67
[57]周云龙,孙斌,陈飞.气液两相流型智能识别理论及方法[M].北京：科学出版社,2007：4-8
[58]周云龙,陈飞,孙斌.基于灰度共生矩阵和支持向量机的气液两相流流型识别[J].化工学报,2007,58(9)：2232-2236
[59]Chen F, Zhou Y L, Li H W. Identification method of Gas-Liquid Two-Phase Flow Regime based on Image Moment Invariants and SVM[C].7th International Symposium on Test and Measurement, Beijing,2007,1318-1321
[60]周云龙,陈飞,刘川.基于图像处理和Elman神经网络的气液两相流流型识别[J].中国电机工程学报,2007,27(29)：108-112
[61]周云龙,陈飞,孙斌.基于图像不变矩和概率神经网络的气液两相流流型识别[J].化学工程,2008,36(8)：28-31
[62]周云龙,陈飞,孙斌.基于图像小波包信息熵和遗传神经网络的气液两相流流型识别[J].核动力工程,2008,29(1)：115-120
[63]Hay K J, Liu Z C, Hanratty T J. A backlighted imaging technique for particle size measurements in two phase flows[J]. Experiments in Fluids,1998,25 (3):226-232
[64]吴剑华,孟辉波,禹言芳,等.SK型静态混合器壁压脉动信号的多尺度多分形特性[J].化工学报,2009,60(8)：1965-1973
[65]阮秋琦.数字图像处理学[M].北京：电子工业出版社,2001.325-328
[66]Dai F, Zhen N N, Xue J R. Feature Representation of Natural Images Based on Contours[J]. JOURNAL OF XI'AN JIAOTONG UNIVERSITY,2008,42 (4): 385-388
[67]单树民,胡佳宁,李峰.基于二维EMD的纹理分类方法[J].计算机工程与设计,2007,28(23)：5800-5801
[68]Catt F, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion[J]. SIAM J Number Anal,1992,29(2):182-193
[69]Damerval C,Meignen S, Perrier V. A fast algorithm for bidimensional EMD[J]. IEEE Signal Processing Letters,2005,12(10):701-704.
[70]李光伟,陈志杰,李建勋.Delaunay三角剖分插值用于超分辨成像[J].电子科技大学学报,2009,38(4)：617-619
[71]王晓峰,黄德双,等.叶片图像特征提取与识别技术的研究[J].计算机工程与应用,2006,3(03)：190-193
[72]李鹏阳,郝重阳,祝双武.基于图像连通区域数的刀具磨损状态特征提取实验研究[J].中国图象图形学报,2008,13(8)：1476-1480
[73]马鲜艳.多特征融合的图形图象分类算法[J].微电子学与计算机,2009,26(6)：250-252
[74]吕兴虎,胡金华.基于列相关分析的工作表面纹理描述[J].研究探讨,2006,12：43-44
[75]Riglis E. Modeling complexity in visual images[D]. Edinburgh:Heriot-Watt University,1998:66-68
[76]Budziak D, Martendal E, Carasek E. Preparation and characterization of new solid-phase microextraction fibers obtained by sol-gel technology and zirconium oxide electrode posited on NiTialloy[J]. Chromatogra. A,2008,1187:34-39
[77]杨小冬,宁新宝,何爱军,等. 基于多尺度的人体ECG信号质量指数谱分析[J].物理学报,2008,57(3)：1514-1520
[78]汪秉宏.地震的多重分形统计特征研究[J].地球科学进展.1997,12(6)：535-540
[79]宗艳波,金宁德,王振亚,等. 倾斜油水两相流流型混沌吸引子形态周界测度分析[J].物理学报,2009,58(11)：7544-7550
[80]Kurths J, Voss A, Saparin P. Quantitative analysis of heart rate variability[J]. Chaos, 1995,5:88-94
[81]Parlitz U, Berg S, Luther S, Schirdewan A, Kurths J. Classifying cardiac biosignals using ordinal pattern statistics and symbolic dynamics[J]. Computers in Biology and Medicine,2012,42:319-327
[82]Song A L,Huang X L. Optimum parameters setting in symbolic dynamics of heart rate variability analysis[J]. Acta Physica Sinica,2011,60 (2):020901-020509
[83]孙斌,周云龙.水平管内空气-水两相流压差波动信号的混沌特征分析[J].哈尔滨工业大学学报,2006,38(11)：1963-1967
[84]孙斌,周云龙.气液两相流压差波动信号的Hurst指数计算与分析[J].华北电力大学学报,2004,31(5)：48-51
[85]李天云,赵妍,李楠. 基于EMD和Hilbert变换应用于暂态信号分析[J].电力系统自动化,2005,29(4)：49-52
[86]李后强,汪富泉.分形理论及其在分子科学中的应用[M].北京：科学出版社,1997：191-193
[87]Mandelbrot B B, Wallis J R. Some long-run properties of geophysical records[J]. Water Resources Research,1969,5(2):321-340
[88]Mandelbrot B B, Wallis J R. Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence[J]. Water Resources Research,1969,5(5):967-988
[89]钟秉林,黄仁.机械故障诊断学[M].机械工业出版社,2003,67-68
[90]Eckmann J P, Karmphorst S O, Karmphorst, Rulle D. Recurrence plot of dynamical systems [J]. Europhysics Letter,1987,49,4(9):973-977.
[91]金宁德,陈万鹏.混沌递归分析在油水两相流流型识别中的应用[J].化工学报,2006,57(2)：274-280
[92]Zbilut J P, Webber C L Jr. Embeddings and delays as derived from quantification of recurrence plots [J]. Physica Letter A,1992,171(3/4):199-203
[93]Li S C, Liu F Y, Dai E F, Wu S H. Recurrence quantification analysis for geographical differences of the coupling relationship between NDVI and climatic factors[J]. Acta Scientiarum Naturalium Universitais Pekinensis,2008,44(3): 483-489
[94]董芳,金宁德,宗艳波.两相流流型动力学特征多尺度递归定量分析[J].物理学报,2008,57(10)：6145-6154
[95]Cohen L. T ime-Frequency Analysis[J]. IEEE Signal Processing,1999,16(1): 22-28
[96]何四华,杨绍清,石爱国,等.基于图像序列区域混沌特征的海面舰船目标检测算法[J].交通运输工程学报,2009,9(1)：73-76
[97]Wolf A, Swift J B, Swinney H L. Determining lyapunov exponents from a time series[J]. Physica D,1985,16(3):285-317
[98]Grassberger P, Procaccia I. Characterization of strange attractors[J]. Physica Review Letter,1983,50(5):346-349.
[99]Abraham N B, Albano A M, Das B. Calculating the dimension of att ractors f rom small data sets[J]. Physics Letters A,1986,114:217-221
[100]Cao H J,Jing Z J. Chaotic dynamics of Josephson equation driven by constant DC and AC forcings[J]. Chaos, Solitons&Fractals,2001,12:1887-1895
[101]Drahos J, Tihon J, Serio C. Deterministic chaos analysis of pressure fluctuations in a horizontal pipe at intermittent flow regime[J]. The Chemical Engineering Journal,1996,64:149-156
[102]Rosenstein M T, Collins J J, Deluca C J. A practical method for calculating largest Lyapunov exponents from small data sets[J]. Physica D,1993,65:117-134
[103]王宏禹.非平稳随机信号分析与处理[M].第1版,北京：国防工业出版社,1999：4-7
[104]Lardies J. State-space identification of vibrating systems from multi-output measurements[J]. Mechanical Systems and Signal Processing,1998,12(4):432-447
[105]杨利芳,于开平,庞世伟,等.用于线性时变结构系统辨识的子空间方法比较研究[J].振动与冲击,2007,26(3)：8-12
[106]Gontier C. Energetic classify ing of vibration modes in subspace stochastic modal analysis[J]. Mechanical Systems and Signal Processing.2005, (19):1-19
[107]Chang J, Zhang Q W, Sun L M. Application of improved stabilization diagram in modal parameter identification by stochastic subspace identification[C]. Proceedings of The 2nd International Conference on Structural Health Monitoring of Intelligent In frastructure, Shenzhen,2005,1:863-868
[108]Huang N E, Shen Z, Long S R. The empirical mode decomposition and the Hilbert spectrum for nonlinear non-stationary time series analysis[J]. Proceedings of the Royal Society of London.1998,1971(454):903-995
[109]罗文波,夏松波,王莉,等.对用稳定图识别真假模态的一点改进[J].应用力学学报,1999,16,112-116
[110]郑桂波,金宁德.两相流流型多尺度熵及动力学特性分析[J].物理学报,2009,58(7)：4485-4492
[2]陈学俊.多相流热物理学[M].西安：西安交通大学出版社,2005：1-7
[3]林宗虎.气液固多相流测量[M].北京：中国计量出版社,1988：3-5
[4]吴应湘.李清平,郑之初,等.海洋油气开发中的多相流技术[J].中国造船,2005,46(B11)：314-321
[5]张琦.应用于多相流参数检测的电容层析成像系统研究[D].南京理工大学硕士学位论文,2004：3-7
[6]Lockhart R W, Martineli R C. Proposed correlation of data for isothermal two-phase flow in pipes[J]. Chemical Engineering Progress,1949,45:39-48
[7]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,2000：24-29
[8]冀海峰,黄志尧,等.小波分析技术在多相流系统中的应用[J].石油化工,2001,30(2)：126-130
[9]周云龙,王强,杨志行,等.基于子波能量特征的气液两相流流型辨识方法研究[J].化工学报,2007,58(8)：1948-1954
[10]周云龙,王强,孙斌,等.基于希尔伯特—黄变换与Elman神经网络的气液两相流流型识别方法[J].中国电机工程学报,2007,27(11)：50-56
[11]周云龙,孙斌.基于神经网络和D-S证据理论的气液两相流流型识别方法[J].化工学报,2006,57(3)：607-613
[12]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
[13]周云龙,孙斌,陆军.改进BP神经网络在气液两相流流型识别中的应用[J].化工学报,2005,56(1)：110-115
[14]孙斌,周云龙.基于支持向量机和小波包能量特征的气液两相流流型识别方法[J].中国电机工程学报,2005,25(17)：93-99
[15]孙斌,周云龙.基于小波包能量特征的气液两相流流型识别方法[J].化学工程,2006,34(2)：33-36
[16]周云龙,孙斌.基于神经网络和D-S证据理论的气液两相流流型识别方法[J].化工学报,2006,57(3)：607-613
[17]金宁德,郑桂波,胡凌云.垂直上升管中气液两相流电导波动信号的混沌特性分析[J].地球物理学报,2006,49(5)：1552-1560
[18]王微微,耿艳峰,黄志尧.应用数据融合方法辨识油气两相流流型[J].传感技术学报,2007,20(9)：2128-2132
[19]彭珍瑞,王保良,黄志尧,等.基于改进的LS-SVM测量油气两相流空隙率[J].高校化学工程学报,2008,22(1)：18-22
[20]王海琴,何利民,李志彪.下倾管段塞流液塞频率波动的非线性分析[J].化工学报,57(9)：2086-2090
[21]盖德.希特斯洛尼.多相流动和传热手册[M].北京：机械工业出版社,1993： 121-134
[22]林宗虎,王树众,王栋.气液两相流和沸腾传热[M].西安：西安交通大学出版社,2003：56-61
[23]徐济望.沸腾传热和气液两相流[M].北京：原子能出版社,1993：67-73
[24]林宗虎.气-液-固多相流体测量[M].北京：中国计量出版社,1988：2-9
[25]Xie C G. Review of image reconstruction methods for proeess tomography[C]. Proeeedings of EC ATT, Karlsruhe, Germany,1993,21-25
[26]Yan He, Liu L J, Xu H. Image reconstruction in electrical capacitance tomography using multiple linear regression and regularization[J]. Measure Science and Technology,2001,12:575-581
[27]Huang Z Y, Wang B L, Li H Q. Application of electrical capacitance tomography to the void Fraction measurement[J]. IEEE Transaction on Instrumentation and Measurement,2003,52(1):7-12
[28]黄志尧,冀海峰,王保良,等.电容层析成像技术在线测量气固流化床空隙率的研究[J].高校化学工程学报,2002,16(5)：49-495
[29]王雷.电容层析成像系统的研制及其在两相流参数检测中的应用研究[D].浙江大学博士学位论文,2003：4-6
[30]刘石,雷兢,李志宏.基于改进正则法的ECT图像重建算法[J].仪器仪表学报,2007,28(11)：1977-1981
[31]刘石,陈琪,李志宏.多孔介质中燃烧火焰的ECT成像研究[J].工程热物理学报,2008,29(12)：2164-2166
[32]王化祥,唐磊.基于TV正则化算法的电容层析成像自适应剖分方法[J].电子测量技术,2006,29(5)：8-11
[33]王化祥,王琦,郝魁红.最小交叉熵图像重建算法[J].仪器仪表学报,2009,30(12)：2574-2579
[34]王化祥,范文茹,胡理.基于GMRES和Tikhonov正则化的生物电阻抗图像重建算法[J].生物医学工程学杂志,2009,26(4)：701-705
[35]王化祥,唐磊,崔自强.油/气两相流高速电容层析成像可视化系统[J].中国电机工程学报,2009,29(5)：61-65
[36]陆耀军,董守平.二维粒子图像测速系统的研制[J].实验力学,2002,16(3)：338-346
[37]Cenedese A, Paglialunga A. Digital direet analysis of a multiexposed photograph in PIV[M]. Experiments in Fluids,1990,18(5):273-280
[38]Teo C L, Lim K B, Hong G S. A Neural Net Approach in Analyzing Photograph in PIV Systems[M]. Decision Aiding for Complex Systems, Conference Proeeedings, 1991,3:1535-1538
[39]许联锋,陈刚,李建中,等.气液两相流中气泡运动速度场的PIV分析与研究[J].实验力学,2002,17(4)：458-463
[40]武旗,张义云,姜华,等.两相流稀相微粒速度场测量技术研究[J].西安交通大学学报,2003,37(7)：734-737
[41]Kadambi J R, Martin W T, Amirthaganesh S, Wernet M P. Partivle sizing using particle imaging Velocimetry for two-phase flows[J]. Powder Technology, 100(1998):251-259
[42]Kawaji M. Two-phase flow measurements using a photochromic dye activation technique[J]. Nuclear Engineering and Design,1998,184:379-392
[43]Popovich A T, Hummel R L. A new method for non-disturbing turbulent flow measurements very close to a wall[J]. Chemical Engineering Science,1967,22, 21-29
[44]Kawaji M. Two-phase flow measurements using a photochromic dye activation technique[J]. Nuclear Engineering and Design,1998,184:379-392
[45]Fourar M, Bories S. Experimental study of air-water two-phase flow through a fracture (narrow channel) [J]. International Journal of Multiphase Flow,1995,21 (4):621-637
[46]Gopal M, Jepson W P. Development of digital Image analysis techniques for the study of velocity and void profiles in slug flow[J]. International Journal of Multiphase Flow,1997,23 (5):945-965
[47]Hay J, Liu Z C, Hanratty T J. A backlighed imageing technique for particle size measurements in two-phase flows[J]. Experiments in Fluids,1998,25:226-232
[48]Dinh T B, Choi T S. Application of image processing techniques in air/water two phase flow[J]. Mechanics Research Communications,1999,26 (4):463-468
[49]Fore L B, Ibrahim B B, Beus S G. Visual measurements of droplet size in gas-liquid annular flow[J]. International Journal of Multiphase Flow,2002,28:1895-1910
[50]Grau R A, Heiskanen K. Visual technique for measuring bubble size in flotation machines[J]. Minerals Eingineering,2002,15:507-513
[51]Luo R, Song Q, Yang X Y, et al. A three-dimensional photographic measurement of phase distribution in dilute bubble flow[J]. Experiments in Fluids,2002,32: 116-120
[52]施丽莲,蔡晋辉,周泽魁.基于图像处理的气液两相流流型识别[J].浙江大学学报(工学版),2005,39(8)：1128-1131
[53]施丽莲.基于数字图像识别技术的气液两相流参数检测的研究[D].浙江大学博士学位论文,2004：3-5
[54]王振亚,金宁德,王淳,等.基于图像纹理分析的两相流流型时空演化特性[J].化工学报,2008,59(5)：1122-1130
[55]王红一,董峰.气液两相流中上升气泡体积的计算方法[J].仪器仪表学报,2009,30(11)：2444-2449
[56]周云龙,孙斌,李洪伟.多相流参数检测理论及其应用[M].北京：科学出版社,2010：64-67
[57]周云龙,孙斌,陈飞.气液两相流型智能识别理论及方法[M].北京：科学出版社,2007：4-8
[58]周云龙,陈飞,孙斌.基于灰度共生矩阵和支持向量机的气液两相流流型识别[J].化工学报,2007,58(9)：2232-2236
[59]Chen F, Zhou Y L, Li H W. Identification method of Gas-Liquid Two-Phase Flow Regime based on Image Moment Invariants and SVM[C].7th International Symposium on Test and Measurement, Beijing,2007,1318-1321
[60]周云龙,陈飞,刘川.基于图像处理和Elman神经网络的气液两相流流型识别[J].中国电机工程学报,2007,27(29)：108-112
[61]周云龙,陈飞,孙斌.基于图像不变矩和概率神经网络的气液两相流流型识别[J].化学工程,2008,36(8)：28-31
[62]周云龙,陈飞,孙斌.基于图像小波包信息熵和遗传神经网络的气液两相流流型识别[J].核动力工程,2008,29(1)：115-120
[63]Hay K J, Liu Z C, Hanratty T J. A backlighted imaging technique for particle size measurements in two phase flows[J]. Experiments in Fluids,1998,25 (3):226-232
[64]吴剑华,孟辉波,禹言芳,等.SK型静态混合器壁压脉动信号的多尺度多分形特性[J].化工学报,2009,60(8)：1965-1973
[65]阮秋琦.数字图像处理学[M].北京：电子工业出版社,2001.325-328
[66]Dai F, Zhen N N, Xue J R. Feature Representation of Natural Images Based on Contours[J]. JOURNAL OF XI'AN JIAOTONG UNIVERSITY,2008,42 (4): 385-388
[67]单树民,胡佳宁,李峰.基于二维EMD的纹理分类方法[J].计算机工程与设计,2007,28(23)：5800-5801
[68]Catt F, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion[J]. SIAM J Number Anal,1992,29(2):182-193
[69]Damerval C,Meignen S, Perrier V. A fast algorithm for bidimensional EMD[J]. IEEE Signal Processing Letters,2005,12(10):701-704.
[70]李光伟,陈志杰,李建勋.Delaunay三角剖分插值用于超分辨成像[J].电子科技大学学报,2009,38(4)：617-619
[71]王晓峰,黄德双,等.叶片图像特征提取与识别技术的研究[J].计算机工程与应用,2006,3(03)：190-193
[72]李鹏阳,郝重阳,祝双武.基于图像连通区域数的刀具磨损状态特征提取实验研究[J].中国图象图形学报,2008,13(8)：1476-1480
[73]马鲜艳.多特征融合的图形图象分类算法[J].微电子学与计算机,2009,26(6)：250-252
[74]吕兴虎,胡金华.基于列相关分析的工作表面纹理描述[J].研究探讨,2006,12：43-44
[75]Riglis E. Modeling complexity in visual images[D]. Edinburgh:Heriot-Watt University,1998:66-68
[76]Budziak D, Martendal E, Carasek E. Preparation and characterization of new solid-phase microextraction fibers obtained by sol-gel technology and zirconium oxide electrode posited on NiTialloy[J]. Chromatogra. A,2008,1187:34-39
[77]杨小冬,宁新宝,何爱军,等. 基于多尺度的人体ECG信号质量指数谱分析[J].物理学报,2008,57(3)：1514-1520
[78]汪秉宏.地震的多重分形统计特征研究[J].地球科学进展.1997,12(6)：535-540
[79]宗艳波,金宁德,王振亚,等. 倾斜油水两相流流型混沌吸引子形态周界测度分析[J].物理学报,2009,58(11)：7544-7550
[80]Kurths J, Voss A, Saparin P. Quantitative analysis of heart rate variability[J]. Chaos, 1995,5:88-94
[81]Parlitz U, Berg S, Luther S, Schirdewan A, Kurths J. Classifying cardiac biosignals using ordinal pattern statistics and symbolic dynamics[J]. Computers in Biology and Medicine,2012,42:319-327
[82]Song A L,Huang X L. Optimum parameters setting in symbolic dynamics of heart rate variability analysis[J]. Acta Physica Sinica,2011,60 (2):020901-020509
[83]孙斌,周云龙.水平管内空气-水两相流压差波动信号的混沌特征分析[J].哈尔滨工业大学学报,2006,38(11)：1963-1967
[84]孙斌,周云龙.气液两相流压差波动信号的Hurst指数计算与分析[J].华北电力大学学报,2004,31(5)：48-51
[85]李天云,赵妍,李楠. 基于EMD和Hilbert变换应用于暂态信号分析[J].电力系统自动化,2005,29(4)：49-52
[86]李后强,汪富泉.分形理论及其在分子科学中的应用[M].北京：科学出版社,1997：191-193
[87]Mandelbrot B B, Wallis J R. Some long-run properties of geophysical records[J]. Water Resources Research,1969,5(2):321-340
[88]Mandelbrot B B, Wallis J R. Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence[J]. Water Resources Research,1969,5(5):967-988
[89]钟秉林,黄仁.机械故障诊断学[M].机械工业出版社,2003,67-68
[90]Eckmann J P, Karmphorst S O, Karmphorst, Rulle D. Recurrence plot of dynamical systems [J]. Europhysics Letter,1987,49,4(9):973-977.
[91]金宁德,陈万鹏.混沌递归分析在油水两相流流型识别中的应用[J].化工学报,2006,57(2)：274-280
[92]Zbilut J P, Webber C L Jr. Embeddings and delays as derived from quantification of recurrence plots [J]. Physica Letter A,1992,171(3/4):199-203
[93]Li S C, Liu F Y, Dai E F, Wu S H. Recurrence quantification analysis for geographical differences of the coupling relationship between NDVI and climatic factors[J]. Acta Scientiarum Naturalium Universitais Pekinensis,2008,44(3): 483-489
[94]董芳,金宁德,宗艳波.两相流流型动力学特征多尺度递归定量分析[J].物理学报,2008,57(10)：6145-6154
[95]Cohen L. T ime-Frequency Analysis[J]. IEEE Signal Processing,1999,16(1): 22-28
[96]何四华,杨绍清,石爱国,等.基于图像序列区域混沌特征的海面舰船目标检测算法[J].交通运输工程学报,2009,9(1)：73-76
[97]Wolf A, Swift J B, Swinney H L. Determining lyapunov exponents from a time series[J]. Physica D,1985,16(3):285-317
[98]Grassberger P, Procaccia I. Characterization of strange attractors[J]. Physica Review Letter,1983,50(5):346-349.
[99]Abraham N B, Albano A M, Das B. Calculating the dimension of att ractors f rom small data sets[J]. Physics Letters A,1986,114:217-221
[100]Cao H J,Jing Z J. Chaotic dynamics of Josephson equation driven by constant DC and AC forcings[J]. Chaos, Solitons&Fractals,2001,12:1887-1895
[101]Drahos J, Tihon J, Serio C. Deterministic chaos analysis of pressure fluctuations in a horizontal pipe at intermittent flow regime[J]. The Chemical Engineering Journal,1996,64:149-156
[102]Rosenstein M T, Collins J J, Deluca C J. A practical method for calculating largest Lyapunov exponents from small data sets[J]. Physica D,1993,65:117-134
[103]王宏禹.非平稳随机信号分析与处理[M].第1版,北京：国防工业出版社,1999：4-7
[104]Lardies J. State-space identification of vibrating systems from multi-output measurements[J]. Mechanical Systems and Signal Processing,1998,12(4):432-447
[105]杨利芳,于开平,庞世伟,等.用于线性时变结构系统辨识的子空间方法比较研究[J].振动与冲击,2007,26(3)：8-12
[106]Gontier C. Energetic classify ing of vibration modes in subspace stochastic modal analysis[J]. Mechanical Systems and Signal Processing.2005, (19):1-19
[107]Chang J, Zhang Q W, Sun L M. Application of improved stabilization diagram in modal parameter identification by stochastic subspace identification[C]. Proceedings of The 2nd International Conference on Structural Health Monitoring of Intelligent In frastructure, Shenzhen,2005,1:863-868
[108]Huang N E, Shen Z, Long S R. The empirical mode decomposition and the Hilbert spectrum for nonlinear non-stationary time series analysis[J]. Proceedings of the Royal Society of London.1998,1971(454):903-995
[109]罗文波,夏松波,王莉,等.对用稳定图识别真假模态的一点改进[J].应用力学学报,1999,16,112-116
[110]郑桂波,金宁德.两相流流型多尺度熵及动力学特性分析[J].物理学报,2009,58(7)：4485-4492