基于支持向量机的旋转机械故障诊断与预测方法研究
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摘要
随着现代科学技术的迅猛发展,旋转机械不断朝着大型化、复杂化、高速化、连续化和自动化的方向发展。这些发展在带来较高生产效率的同时,对设备的安全运转也提出了更高的要求,一旦发生故障,将造成巨大的经济损失,甚至会导致灾难性的人员伤亡事故和严重的社会影响。对设备的故障进行诊断,以及根据历史数据对设备运行状态进行预测,是保证设备安全可靠运行的重要措施,只有如此才能及时有效的处理存在的问题,将故障消除在萌芽状态。本文研究基于支持向量机理论对设备运行状态进行故障诊断并根据历史运行数据对设备未来状态进行预测的方法,建立了设备运行状态预报和故障诊断模型,并对一些关键问题的解决进行了深入研究。本文主要创新工作如下：
1、提出了基于遗传算法的支持向量机样本平衡方法
对于故障诊断来说,故障样本一般少于正常样本,所以普遍存在不平衡样本问题。支持向量机在遇到样本不平衡问题时,往往造成“少样本类”的误诊。针对该问题,本文提出了基于遗传算法的样本平衡方法,利用遗传算法中的交叉、变异方式生成子代样本,对“少样本类”进行繁殖扩充,得到更多的该类样本进而达到两类样本的平衡。为使扩充的样本更具有针对性,更有利于形成正确的“分类超平面”,给出了父代样本的选择方法以及子代样本的评价方法。
2、分析了EMD方法产生虚假分量的原因,并提出了一种识别虚假分量的方法
作为特征提取的方法,EMD能够较好的处理非平稳、非线性问题,但利用EMD方法对信号进行处理时常常会引入虚假分量,影响分析的准确性,是严重制约EMD方法发展的瓶颈问题。为了消除虚假分量的影响,更好地发挥EMD方法在特征提取中的作用,本文提出基于K-L散度的虚假分量识别方法,该方法利用K-L散度来评价EMD分解得到的各个分量与原信号的关系程度,分量与原信号之间的K-L散度越小,关系程度越大,分量的真实性就越高,反之虚假性就越高,虚假分量通过设定阈值进行判别。同时,文中研究并给出了阂值设定方法。
3、提出了基于EMD特征提取的支持向量机算法
在根据历史数据对运行状态进行预测时,特征参数与预测点的关联程度在很大程度上决定了预测值的准确性。目前,特征参数的选取方法主要有两种：一种是基于实测数据的特征,即采集与预测值相关联的影响因素作为特征,如对风电功率预测时选取风速、气压等因素作为特征,但对于振动等一些预测量来说,其影响因素往往十分复杂,不易明确,利用这种方式也就无法建立高精度预测模型；另一种是通过对时间序列的计算得到其特征参数,这类方法中最具代表性且最常用的方法是基于相空间重构的方法,方法利用混沌理论计算嵌入维数和时间延迟重构相空间,得到时间序列的特征,然而嵌入维数以及时间延迟的确定只是从时间序列的动力学特性角度来考虑的,用其构造的特征对于预测模型来说并不一定合适,所以往往会由于二者选取的不恰当而无法得到合适的特征,进而造成预测的精度大大降低。故本文针对预测模型特征选取的问题,提出了基于EMD特征提取的支持向量机算法(EMD-SVM),利用EMD分解后各时间点的分量值作为特征,并与该时间点对应的时间序列值(目标值)共同构成样本,建立预测模型,并通过实验证明其较高的准确性和稳定性。
4、针对支持向量机存在大规模样本问题提出了基于信息熵的样本长度选择方法
大规模训练样本问题一直是困扰SVM计算速度提升的瓶颈,过多的训练样本会大大的增加计算成本,而且不一定会带来更准确的预测结果,甚至会导致更严重的偏差。所以,训练样本的长度必须控制在合适的范围内。针对该问题,本文提出了基于信息熵的样本长度选择方法。该方法的基本思想是选取与预测点最相关的历史数据作为训练样本,保证数据信息的完备性和不冗余。靠近预测点的历史数据通常与预测点之间关系越强,这些数据作为训练样本对于预测点来说意义较大；随着距离的增加(时间不断向前推移)关联性越弱,对于预测点意义较小,将这些数据加入到训练样本中会表现出数据波动性增大,平稳性降低,需要对这些点进行删减。本文方法基于这一思想,在历史数据中从前向后依次选取不同的位置作为起始点截取时间序列,计算不同起始点截得时间序列的信息熵值。将对应信息熵最小的起始点作为新时间坐标轴的“0点坐标”,坐标轴负半轴的数据时间久远且与当前状态相关程度低,需剔除,正半轴数据与当前相关程度高,故用来作为训练样本,如此可以保证信息的完备性,同时避免了建立模型时的寻优过程对相关程度较低的训练样本的“照料”。文中通过理论分析和实验的方式从计算时间和预测精度的角度考察了方法的有效性。
With the rapid development of modern science and technology, rotating machinery continues melting towards maximization, complex, high speed, continuous process and automation directions. Not only do these developments lead to higher productivity but also higher requirements are put forward for the safe operation of the rotating machinery, which once goes wrong, enormous economic losses, even catastrophic casualties and serious social impact will be caused. Diagnosing the fault of the equipment and predicting its running state according to historical data are two important measures to ensure its safe and reliable operation. Only in this way, the existing abnormal problems will be detected timely and effectively, so that the fault can be eliminated in the bud. Hence, in this thesis, the two above measures based on support vector machine theory were investigated, a model of fault diagnosis and state prediction was set up, and a further study went on the solution to some key problems. The main achievements consist of as following aspects:
1. Put forward a sample balance method of SVM based on genetic algorithm.
For fault diagnosis, fault samples are generally less than the normal samples, so the problem of imbalanced samples universal exists. Using SVM to analyse the imbalanced samples often results in the misdiagnosis of less sample class. Thus, a sample balance method based on SVM of genetic algorithm were put forward to solve the problem, which can be explained by using the crossover and mutation of genetic algorithm to generate progeny sample, breeding and extending the less sample class to obtain more samples, and finally reaching the balance of the two kinds of samples. In order to make the extended samples more pertinence and more conducive to form the correct classification hyperplane, selection method of the parent sample and evaluation method of the progeny sample were given.
2. Analysed the causes of illusive component resulted from EMD, and proposed a method to identify the illusive component.
As a feature extraction method, EMD can not only deal with the non-stationary and non-linear problem preferably but to often introduce illusive component by using it for signal processing, which affects the accuracy of the analysis and seriously restrains the development of EMD. For the sake of eliminating the effection of the illusive component and preferably playing EMD in the role of feature extraction, an effective method to identify illusive component was proposed, which used K-L divergence to evaluate the degree of relationship between the decomposition components of EMD and original signal. The smaller K-L divergence the greater degree of relationship as there was higher authenticity of the component, conversely higher falsity. The illusive component can be distinguished through the threshold setting, and the method of which was given.
3. Raised SVM algorithm based on EMD feature extraction.
Correlation degree of the characteristic parameter and the predicted point, to a great extent, determines the accuracy of the predicted value while using historical data to predict the running state. At present, there are mainly two selection methods of characteristic parameters:one is to take the measured data, which are the influencing factors associated with predicted value, as the characteristic parameter, such as the wind speed and the air pressure are regarded as the characteristic parameters on predicting the power of wind power, but some pre-measure for vibration, due to the influencing factors are often very complex and difficult to clear, a high-precision prediction model will not be able to be created by using this method; the other is that the characteristic parameters are obtained by calculating the time series, and the most representative and most commonly used one is the method based on phase space reconstruction, which makes use of chaos theory to calculate embedded dimension and time delay for reconstructing phase space and consequently obtaining the characteristics of the time series. However, the determination of embedded dimension and time delay were only considered from the view of dynamics, the characteristic parameters obtained by what is not necessarily appropriate for the prediction model. It is for the inappropriate selection, the appropriate characteristic parameters can not be obtained, resulting in the prediction accuracy greatly reduced. For the problem of feature extraction of prediction model, SVM algorithm based on EMD feature extraction (EMD-SVM) was raised, which took the component value of each time point decomposed from EMD as characteristic parameters and together with the time series value (target value) constituted the sample to establish the prediction model, and its high stability and accuracy were proved by experiments.
4. Aim at the problem of large-scale training sample of SVM, a new length selection method of the sample based on information entropy was put forward.
The problem of large-scale training samples has always been a bottleneck plagued the computing speed promotion of SVM. Excessive training samples will greatly increase the calculation cost, not necessarily lead to more accurate prediction results, and even result in more serious deviation. Therefore, the length of the training samples must be controlled within a proper range. Aiming at the above problems, a new length selection method of the sample based on information entropy was put forward. The main idea of the method is to choose the historical data, which most relevant to the prediction point, as the training samples to guarantee the completeness and non-redundancy of the data information. The stronger the relevance of historical data and prediction point is, the larger significance the data as the training samples for forecasting point will be; it goes the other way around with the increasing distance (time goes forward), under the premise of adding the above date to the training sample, the volatility increases and the stationarity reduces, thus prediction point need to be abridged. In this thesis, the time series were cut out through selecting different position from front to back in turn as a starting point in the historical data, of which information entropy were calculated. The starting point corresponding to the minimum information entropy was regarded as the0point coordinate of the new time axis. The negative half shaft data were abridged because of the remoteness and the low degree of correlation with the current state, and due to the high degree of correlation, the positive half shaft data were taken as the training samples, thus completeness of the information can be guaranteed, at the same time the consideration was avoided for the lower related degree training sample in the optimization process of modeling. From the view of computation time and prediction accuracy, the validity of the method was investigated by means of theoretical analysis and experiment.
1、提出了基于遗传算法的支持向量机样本平衡方法
对于故障诊断来说,故障样本一般少于正常样本,所以普遍存在不平衡样本问题。支持向量机在遇到样本不平衡问题时,往往造成“少样本类”的误诊。针对该问题,本文提出了基于遗传算法的样本平衡方法,利用遗传算法中的交叉、变异方式生成子代样本,对“少样本类”进行繁殖扩充,得到更多的该类样本进而达到两类样本的平衡。为使扩充的样本更具有针对性,更有利于形成正确的“分类超平面”,给出了父代样本的选择方法以及子代样本的评价方法。
2、分析了EMD方法产生虚假分量的原因,并提出了一种识别虚假分量的方法
作为特征提取的方法,EMD能够较好的处理非平稳、非线性问题,但利用EMD方法对信号进行处理时常常会引入虚假分量,影响分析的准确性,是严重制约EMD方法发展的瓶颈问题。为了消除虚假分量的影响,更好地发挥EMD方法在特征提取中的作用,本文提出基于K-L散度的虚假分量识别方法,该方法利用K-L散度来评价EMD分解得到的各个分量与原信号的关系程度,分量与原信号之间的K-L散度越小,关系程度越大,分量的真实性就越高,反之虚假性就越高,虚假分量通过设定阈值进行判别。同时,文中研究并给出了阂值设定方法。
3、提出了基于EMD特征提取的支持向量机算法
在根据历史数据对运行状态进行预测时,特征参数与预测点的关联程度在很大程度上决定了预测值的准确性。目前,特征参数的选取方法主要有两种：一种是基于实测数据的特征,即采集与预测值相关联的影响因素作为特征,如对风电功率预测时选取风速、气压等因素作为特征,但对于振动等一些预测量来说,其影响因素往往十分复杂,不易明确,利用这种方式也就无法建立高精度预测模型；另一种是通过对时间序列的计算得到其特征参数,这类方法中最具代表性且最常用的方法是基于相空间重构的方法,方法利用混沌理论计算嵌入维数和时间延迟重构相空间,得到时间序列的特征,然而嵌入维数以及时间延迟的确定只是从时间序列的动力学特性角度来考虑的,用其构造的特征对于预测模型来说并不一定合适,所以往往会由于二者选取的不恰当而无法得到合适的特征,进而造成预测的精度大大降低。故本文针对预测模型特征选取的问题,提出了基于EMD特征提取的支持向量机算法(EMD-SVM),利用EMD分解后各时间点的分量值作为特征,并与该时间点对应的时间序列值(目标值)共同构成样本,建立预测模型,并通过实验证明其较高的准确性和稳定性。
4、针对支持向量机存在大规模样本问题提出了基于信息熵的样本长度选择方法
大规模训练样本问题一直是困扰SVM计算速度提升的瓶颈,过多的训练样本会大大的增加计算成本,而且不一定会带来更准确的预测结果,甚至会导致更严重的偏差。所以,训练样本的长度必须控制在合适的范围内。针对该问题,本文提出了基于信息熵的样本长度选择方法。该方法的基本思想是选取与预测点最相关的历史数据作为训练样本,保证数据信息的完备性和不冗余。靠近预测点的历史数据通常与预测点之间关系越强,这些数据作为训练样本对于预测点来说意义较大；随着距离的增加(时间不断向前推移)关联性越弱,对于预测点意义较小,将这些数据加入到训练样本中会表现出数据波动性增大,平稳性降低,需要对这些点进行删减。本文方法基于这一思想,在历史数据中从前向后依次选取不同的位置作为起始点截取时间序列,计算不同起始点截得时间序列的信息熵值。将对应信息熵最小的起始点作为新时间坐标轴的“0点坐标”,坐标轴负半轴的数据时间久远且与当前状态相关程度低,需剔除,正半轴数据与当前相关程度高,故用来作为训练样本,如此可以保证信息的完备性,同时避免了建立模型时的寻优过程对相关程度较低的训练样本的“照料”。文中通过理论分析和实验的方式从计算时间和预测精度的角度考察了方法的有效性。
With the rapid development of modern science and technology, rotating machinery continues melting towards maximization, complex, high speed, continuous process and automation directions. Not only do these developments lead to higher productivity but also higher requirements are put forward for the safe operation of the rotating machinery, which once goes wrong, enormous economic losses, even catastrophic casualties and serious social impact will be caused. Diagnosing the fault of the equipment and predicting its running state according to historical data are two important measures to ensure its safe and reliable operation. Only in this way, the existing abnormal problems will be detected timely and effectively, so that the fault can be eliminated in the bud. Hence, in this thesis, the two above measures based on support vector machine theory were investigated, a model of fault diagnosis and state prediction was set up, and a further study went on the solution to some key problems. The main achievements consist of as following aspects:
1. Put forward a sample balance method of SVM based on genetic algorithm.
For fault diagnosis, fault samples are generally less than the normal samples, so the problem of imbalanced samples universal exists. Using SVM to analyse the imbalanced samples often results in the misdiagnosis of less sample class. Thus, a sample balance method based on SVM of genetic algorithm were put forward to solve the problem, which can be explained by using the crossover and mutation of genetic algorithm to generate progeny sample, breeding and extending the less sample class to obtain more samples, and finally reaching the balance of the two kinds of samples. In order to make the extended samples more pertinence and more conducive to form the correct classification hyperplane, selection method of the parent sample and evaluation method of the progeny sample were given.
2. Analysed the causes of illusive component resulted from EMD, and proposed a method to identify the illusive component.
As a feature extraction method, EMD can not only deal with the non-stationary and non-linear problem preferably but to often introduce illusive component by using it for signal processing, which affects the accuracy of the analysis and seriously restrains the development of EMD. For the sake of eliminating the effection of the illusive component and preferably playing EMD in the role of feature extraction, an effective method to identify illusive component was proposed, which used K-L divergence to evaluate the degree of relationship between the decomposition components of EMD and original signal. The smaller K-L divergence the greater degree of relationship as there was higher authenticity of the component, conversely higher falsity. The illusive component can be distinguished through the threshold setting, and the method of which was given.
3. Raised SVM algorithm based on EMD feature extraction.
Correlation degree of the characteristic parameter and the predicted point, to a great extent, determines the accuracy of the predicted value while using historical data to predict the running state. At present, there are mainly two selection methods of characteristic parameters:one is to take the measured data, which are the influencing factors associated with predicted value, as the characteristic parameter, such as the wind speed and the air pressure are regarded as the characteristic parameters on predicting the power of wind power, but some pre-measure for vibration, due to the influencing factors are often very complex and difficult to clear, a high-precision prediction model will not be able to be created by using this method; the other is that the characteristic parameters are obtained by calculating the time series, and the most representative and most commonly used one is the method based on phase space reconstruction, which makes use of chaos theory to calculate embedded dimension and time delay for reconstructing phase space and consequently obtaining the characteristics of the time series. However, the determination of embedded dimension and time delay were only considered from the view of dynamics, the characteristic parameters obtained by what is not necessarily appropriate for the prediction model. It is for the inappropriate selection, the appropriate characteristic parameters can not be obtained, resulting in the prediction accuracy greatly reduced. For the problem of feature extraction of prediction model, SVM algorithm based on EMD feature extraction (EMD-SVM) was raised, which took the component value of each time point decomposed from EMD as characteristic parameters and together with the time series value (target value) constituted the sample to establish the prediction model, and its high stability and accuracy were proved by experiments.
4. Aim at the problem of large-scale training sample of SVM, a new length selection method of the sample based on information entropy was put forward.
The problem of large-scale training samples has always been a bottleneck plagued the computing speed promotion of SVM. Excessive training samples will greatly increase the calculation cost, not necessarily lead to more accurate prediction results, and even result in more serious deviation. Therefore, the length of the training samples must be controlled within a proper range. Aiming at the above problems, a new length selection method of the sample based on information entropy was put forward. The main idea of the method is to choose the historical data, which most relevant to the prediction point, as the training samples to guarantee the completeness and non-redundancy of the data information. The stronger the relevance of historical data and prediction point is, the larger significance the data as the training samples for forecasting point will be; it goes the other way around with the increasing distance (time goes forward), under the premise of adding the above date to the training sample, the volatility increases and the stationarity reduces, thus prediction point need to be abridged. In this thesis, the time series were cut out through selecting different position from front to back in turn as a starting point in the historical data, of which information entropy were calculated. The starting point corresponding to the minimum information entropy was regarded as the0point coordinate of the new time axis. The negative half shaft data were abridged because of the remoteness and the low degree of correlation with the current state, and due to the high degree of correlation, the positive half shaft data were taken as the training samples, thus completeness of the information can be guaranteed, at the same time the consideration was avoided for the lower related degree training sample in the optimization process of modeling. From the view of computation time and prediction accuracy, the validity of the method was investigated by means of theoretical analysis and experiment.
引文
[1]黄文虎,夏松波,刘瑞岩.设备故障诊断原理、技术及应用[M].科学技术出版社,1996
[2]John Sohre. Trouble-shooting to stop vibration of centrifugal [J]. Petrop/Chem. Engineer.1968,11:22-23
[3]白木万博(日).机械振动讲演论文集[M].郑州机械研究所,1984
[4]DE Bently. Forced subrotative speed dynamic action of rotating machinery. ASME paper.1974(74-PET):16
[5]高金吉.高速涡轮机械振动故障机理及诊断方法的研究[M].北京：清华大学.1993
[6]徐敏.设备故障诊断手册[M].1998
[7]陈安华,钟掘.转子系统非线性振动的辨识建模[J].中国有色金属学报.1997
[8]J.W. Cooley, J.W. Tukey. An algorithm for the machine calculation of complex Fourier series [J]. Mathematics of computation.1965:297-301
[9]胡丽莹,肖蓬.快速傅里叶变换在频谱分析中的应用[J].福建师范大学学报：自然科学版.2011,27(4)：27-30
[10]肖玮,涂亚庆,何丽.DTFT频谱细化特性分析及其快速算法设计[J].电子与信息学报.2011,33(6)：1395-1401
[11]张宪超,蒋增荣.离散傅里叶变换的算术傅里叶变换算法[J].电子学报.2000,28(005)：105-107
[12]E. Al-Ammar, G.G. Karady. Transfer function analysis using STFT for improvement of the fault detection sensitivity in transformer impulse test [C]. Power Engineering Society General Meeting,2005. IEEE,2005, IEEE: 1855-1862
[13]J.Y.H. Yigang. New Digital Algorithm for Measuring Electric Frequency Based on Adaptive Short-Time Fourier Transform [J]. Journal of Electronic Measurement and Instrument.2006,2:002
[14]胡晓依,何庆复,王华胜,et al.基于STFT的振动信号解调方法及其在轴承故障检测中的应用[J].振动与冲击.2008,27(002)：82-86
[15]S.G. Mallat. A theory for multiresolution signal decomposition:the wavelet representation [J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on.1989,11(7):674-693
[16]S. Mallat, W.L. Hwang. Singularity detection and processing with wavelets [J]. Information Theory, IEEE Transactions on.1992,38(2):617-643
[17]I. Daubechies. The wavelet transform, time-frequency localization and signal analysis [J]. Information Theory, IEEE Transactions on.1990,36(5):961-1005
[18]陈果.一种改进的谐波小波及其在转子故障诊断中的应用[J].机械工程学报.2011,47(001)：8-16
[19]L. Cohen. Time-frequency distributions-a review [J]. Proceedings of the IEEE.1989,77(7):941-981
[20]来五星,轩建平,史铁林,et al. Wigner-Vill时频分布研究及其在齿轮故障诊断中的应用[J].振动工程学报.2003,16(2)：247-250
[21]N.E. Huang, Z. Shen, S.R. Long, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis [J]. Proceedings of the Royal Society of London. Series A:Mathematical, Physical and Engineering Sciences.1998,454(1971):903-995
[22]N.E. Huang, Z. Shen, S.R. Long. A new view of nonlinear water waves:The Hilbert Spectrum 1 [J]. Annual Review of Fluid Mechanics.1999,31(1): 417-457
[23]周志峰,胡秀娟.基于改进EMD的汽车动态称重信号处理[J].数据采集与处理.2009,23(6)：751-755
[24]韩中合,朱霄珣,李文华,et al.基于EMD消除Wigner-Vill分布交叉项的研究[J].汽轮机技术.2010(003)：211-214
[25]周志锋,蔡萍,许嘉,et al.基于经验模态分解的汽车动态称重数据处理[J].中国机械工程.2006,16(20)：1813-1816
[26]N.E.Huang, H.H. Shih, Z. Shen, et al. The ages of large amplitude coastal seiches on the Caribbean Coast of Puerto Rico [J]. Journal of physical oceanography.2000,30(8):2001-2012
[27]N.E.Huang, C.C. Chern, K.Huang, et al. A new spectral representation of earthquake data:Hilbert spectral analysis of station TCU129, Chi-Chi, Taiwan, 21 September 1999. Bulletin of the Seismological Society of America.2001, 91 (5):1310-1338
[28]C.H. Loh, T.C. Wu, N.E. Huang. Application of the empirical mode decomposition-Hilbert spectrum method to identify near-fault ground-motion characteristics and structural responses [J]. Bulletin of the Seismological Society of America.2001,91(5):1339-1357
[29]沈路,周晓军,张志刚,et a1.Hilbert-Huang变换中的一种端点延拓方法[J].振动与冲击.2009,28(008)：168-171
[30]M. Datig, T. Schlurmann. Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves [J]. Ocean Engineering.2004,31(14):1783-1834
[31]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用.2004,40(16)：84-86
[32]Y.Deng, W.Wang, C. Qian, et al. Boundary-processing-technique in EMD method and Hilbert transform [J]. Chinese Science Bulletin.2001,46(11): 954-960
[33]张郁山,梁建文,胡聿贤.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展.2003,13(10)：1054-1059
[34]杨建文,贾民平.希尔伯特-黄谱的端点效应分析及处理方法研究[J].振动工程学报.2006,19(2)：283-288
[35]盖强.局域波时频分析方法的理论研究与应用[D].大连：大连理工大学.2001
[36]赵进平.Improvement of the mirror extending in empirical mode decomposition method and the technology for eliminating frequency mixing[J].高技术通讯：英文版.2002,8(3)：40-47
[37]胡爱军.Hilbert-Huang变换在旋转机械振动信号分析中的应用研究[D].华北电力大学(河北).2008
[38]Q. Chen, N. Huang, S. Riemenschneider, et al. A B-spline approach for empirical mode decompositions [J]. Advances in Computational Mathematics.2006,24(1):171-195
[39]钟佑明,金涛,秦树人.希尔伯特-黄变换中的一种新包络线算法[J].数据采集与处理.2005,20(1)：13-17
[40]张之猛,刘晨晨,刘伯胜,et al.经验模态分解中的包络线拟合算法仿真分析[J].系统仿真学报.2009(023)：7690-7693
[41]N.E. Huang. A new view of nonlinear waves:The Hilbert spectrum [J].Annual Review of Fluid Mechanics.1999,31:417-457
[42]H. Li, L. Yang, D. Huang. The study of the intermittency test filtering character of Hilbert-Huang transform [J]. Mathematics and Computers in Simulation.2005,70(1):22-32
[43]赵进平.异常事件对EMD方法的影响及其解决方法研究[J].青岛海洋大学学报.2001,31(6)：805-814
[44]曹冲锋,杨世锡,杨将新.基于白噪声统计特性的振动模式提取方法[J].机械工程学报.2010(003)：65-70
[45]李雪耀,邹晓杰,张汝波,et al.谱熵和主成分分析用于EMD分解研究[J].哈尔滨工程大学学报.2009(7)：797-803
[46]林丽,余轮.基于相关系数的EMD改进算法[J].计算机与数字工程.2009,36(12)：28-29
[47]张金,张耀辉,黄漫国.倒频谱分析法及其在齿轮箱故障诊断中的应用[J].机械工程师.2005(8)：34-36
[48]刘进明,应怀樵.FFT谱连续细化分析的富里叶变换法[J].振动工程学报.1995,8(2)：162-166
[49]李辉,郑海起,唐力伟.基于倒阶次谱分析的齿轮故障诊断研究[J].振动与冲击.2006,25(005)：65-68
[50]崔江,王友仁,刘权.基于高阶谱与支持向量机的电力电子电路故障诊断技术[J].中国电机工程学报.2007,27(10)：62-66
[51]宁绍斌.二维全息谱分析在电厂通风机转子故障诊断中的应用[J].南华大学学报：自然科学版.2008(4)
[52]吕志民,徐金梧.分形维数及其在滚动轴承故障的诊断中的应用[J].机械工程学报.1999,35(002)：88-91
[53]邹恩,混沌学,李祥飞,et al.混沌控制及其优化应用[J].国防科技大学出版社,2002
[54]I. Karanta. Expert systems in forecast model building [C]. Publications of the Finnish Artificial Intelligence Society,9th Finnish Artificial Intelligence Conference,2000:77-85
[55]PK Dash, AC Liew, S. Rahman. Fuzzy neural network and fuzzy expert system for load forecasting [J]. Generation, Transmission and Distribution, IEE Proceedings-,1996, IET:106-114
[56]GA Adepoju, SOA Ogunjuyigbe, KO Alawode. Application of Neural Network to Load Forecasting in Nigerian Electrical Power System [J]. The Pacific Journal of Science and Technology.2007,8(1):68-72
[57]U.B. Filik, M. Kurban. A new approach for the short-term load forecasting with auto regressive and artificial neural network models [J]. International Journal of Computational Intelligence Research.2007,3(1):66-71
[58]M. Daneshdoost, M. Lotfalian, G. Bumroonggit, et al. Neural network with fuzzy set-based classification for short-term load forecasting [J]. Power Systems, IEEE Transactions on.1998,13(4)-.1386-1391
[59]沈路,贺小明.组合预测在风机振动预测中的应用[J].中国设备工程.2006,9：43-45
[60]陈铁华,陈启卷.模糊聚类分析在水电机组振动故障诊断中的应用[J].中国电机工程学报.2002,22(3)：43-47
[61]张彼德,孙才新.诊断汽轮发电机组振动故障的一种模糊聚类分析方法[J].汽轮机技术.2002,44(5)：289-291
[62]王清.基于模糊聚类和灰色理论的齿轮箱故障诊断研究[J].太原：中北大学.2006
[63]A. Kowalski, D. Szynal. An optimal prediction in general ARMA models [J]. Journal of multivariate analysis.1990,34(1):14-36
[64]李艳芳.电力负荷预测[J].南昌高专学报.2008,22(6)：143-145
[65]吴捷,严华.基于自适应成模糊逻辑系统的短期负荷预测方法[J].电力系统自动化.1999,23(17)：35-37
[66]A. Majidian, MH Saidi. Comparison of fuzzy logic and neural network in life prediction of boiler tubes [J]. International journal of fatigue.2007,29(3): 489-498
[67]B.E. Boser, I.M. Guyon, V.N. Vapnik. A training algorithm for optimal margin classifiers [J]. Proceedings of the fifth annual workshop on Computational learning theory,1992, ACM:144-152
[68]V. Vapnik. The nature of statistical learning theory [J]. springer,1999
[69]E. Osuna, R. Freund, F. Girosi. An improved training algorithm for support vector machines [J]. Neural Networks for Signal Processing [1997] VII. Proceedings of the 1997 IEEE Workshop,1997, IEEE:276-285
[70]T.Joachims. Making large scale SVM learning practical [J].1999
[71]J.C. Platt.12 Fast Training of Support Vector Machines using Sequential Minimal Optimization [J].1999
[72]S.S. Keerthi, S.K. Shevade, C. Bhattacharyya, et al. Improvements to Platt's SMO algorithm for SVM classifier design [J]. Neural Computation.2001,13 (3):637-649
[73]D. Pavlov, D. Chudova, P.Smyth. Towards scalable support vector machines using squashing [C]. Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining,2000, ACM:295-299
[74]V. Tresp. Scaling kernel-based systems to large data sets [J]. Data Mining and Knowledge Discovery.2001,5(3):197-211
[75]苑津莎,张英慧,牛丽仙,et a1.基于SOFM和支持向量机回归的短期负荷预测方法[J].电力科学与工程.2009,25(008)：27-29
[76]李林峰,孙长银.基于FCM聚类与SVM的电力系统短期负荷预测[J].江苏电机工程.2007,26(3)：47-50
[77]P.W. Chen, J.Y. Wang, H.M. Lee. Model selection of SVMs using GA approach [C]. Neural Networks,2004. Proceedings.2004 IEEE International Joint Conference on,2004, IEEE:2035-2040
[78]Z. Chunhong, J. Licheng. Automatic parameters selection for SVM based on GA [J]. Intelligent Control and Automation,2004. WCICA 2004. Fifth World Congress on,2004, IEEE:1869-1872
[79]齐志泉,田英杰,徐志洁.支持向量机中的核参数选择问题[J].控制工程.2005,12(4)：379-381
[80]邵信光,杨慧中,陈刚.基于粒子群优化算法的支持向量机参数选择及其应用[J].控制理论与应用.2006,23(5)：740-743
[81]巩知乐,张德贤,胡明明.一种改进的支持向量机的文本分类算法[J].计算机仿真.2009(7)：164-167
[82]刘国海,周大为,徐海霞,et al.基于SVM的微生物发酵过程软测量建模研究[J].仪器仪表学报.2009,30(6)：1228-1232
[83]胡小兵,黄席樾.蚁群优化算法及其应用[J].计算机仿真.2004,21(5)：81-85
[84]王欣,杜康,秦斌,et al.基于果蝇优化算法的LSSVR干燥速率建模[J].控制工程.2012,19(004)：630-633
[85]G. Baudat, F. Anouar. Generalized discriminant analysis using a kernel approach [J]. Neural computation.2000,12(10):2385-2404
[86]M. Szummer, T.S. Jaakkola. Kernel expansions with unlabeled examples [J]. Advances in Neural Information Processing Systems.2001:626-632
[87]P. Rujan, M. Marchand. Computing the Bayes kernel classifier [J].1999
[88]陈念贻.模式识别方法在化学化工中的应用[M].科学出版社,2000
[89]范劲松,方廷健.特征选择和提取要素的分析及其评价[J].计算机工程与应用.2001,37(13)：95-99
[90]宋晖,薛云,张良均.基于SVM分类问题的核函数选择仿真研究[J].计 算机与现代化.2011(8)：133-136
[91]刘向东,骆斌,陈兆乾.支持向量机最优模型选择的研究[J].计算机研究与发展.2005,42(4)：576-581
[92]姚程宽.不平衡样本集中SVM的应用综述[J].计算机应用与软件.2008,25(9)：1-2
[93]何渊淘,邓伟.改进的不均衡样本集支持向量机预处理方法[J].计算机工程与应用.2010,46(010)：：36-37
[94]黄秀丽,王蔚.SVM在非平衡数据集中的应用[J].计算机技术与发展.2009,19(6)：190-193
[95]H.G. Chew, D.J. Crisp, R.E. Bogner, et al. Target detection in radar imagery using support vector machines with training size biasing [J]. Proc. Int. Conf. on Control, Automation, Robotics, and Vision (ICARCV),2000
[96]王娟娟,任秋实.基于SMO的不同惩罚系数的SVM算法[J].信息技术.2006,30(010)：45-46
[97]刘万里,刘三阳,薛贞霞.不平衡支持向量机的平衡方法[J].模式识别与人工智能.2008,21(002)：136-141
[98]R. Akbani, S. Kwek, N. Japkowicz. Applying support vector machines to imbalanced datasets [J]. Machine Learning:ECML 2004.2004:39-50
[99]T. Maciejewski, J. Stefanowski. Local neighbourhood extension of smote for mining imbalanced data [J]. Computational Intelligence and Data Mining (CIDM),2011 IEEE Symposium on,2011, IEEE:104-111
[100]杨智明,彭宇,彭喜元.基于支持向量机的不平衡数据集分类方法研究[J].仪器仪表学报.2009,5(30)：1094-1099
[101]王计生,喻俊馨,黄惟公.小波包分析和支持向量机在刀具故障诊断中的应用[J].振动.测试与诊断.2008,28(3)：273-276
[102]于德介,杨宇,程军圣.一种基于SVM和EMD的齿轮故障诊断方法[J].机械工程学报.2005,41(1)：140-144
[103]程军圣,于德介,杨宇.基于EMD和SVM的滚动轴承故障诊断方法[J].航空动力学报.2006,21(3)：575-580
[104]吕建新,吴虎胜,王茂生,et al.基于EMD和SVM的农用柴油机故障诊断研究[J].安徽农业科学.2010(017)：9225-9228
[105]饶俊,王太勇.基于多类SVM与改进EMD的故障诊断[J].组合机床与自动化加工技术.2010(006)：29-31
[106]翟永杰,刘林,王朋.基于ADE-SVM和模糊理论的电力系统中期负荷 预测[J].电力系统保护与控制.2012,40(8)：110-115
[107]王义民,方卫民,席秋义,et al.基于LS-SVM和PSO相结合的电力负荷预测研究[J].水力发电学报.2010(4)：245-250
[108]冯广斌,吴震宇,袁惠群.基于混沌理论与SVM的内燃机振动信号趋势预测[J].振动.测试与诊断.2011,31(001)：64-69
[109]张华,曾杰.基于支持向量机的风速预测模型研究[J].太阳能学报.2010,31(007)：928-932
[110]张学工.关于统计学习理论与支持向量机[J].自动化学报.2000,26(1)：32-42
[111]张艳秋,王蔚.利用遗传算法优化的支持向量机垃圾邮件分类[J].计算机应用.2009,29(10)：62-63
[112]罗瑜,李涛,何大可,et al.基于部件和支持向量机的人脸分类[J].计算机工程.2008,34(4)：198-200
[113]申宇皓,孟晨,傅振华,et al.基于改进支持向量机的仿真电路故障诊断研究[J].计算机仿真.2010(001)：346-350
[114]崔江,王友仁.基于支持向量机与最近邻分类器的模拟电路故障诊断新策略[J].仪器仪表学报.2010,31(1)：45-50
[115]沈志熙,黄席樾,马笑潇.基于EMD和支持向量机的柴油机故障诊断[J].振动.测试与诊断.2010,30(001)：19-22
[116]贾嵘,洪刚,薛建辉,et al.粒子群优化-最小二乘支持向量机算法在高压断路器机械故障诊断中的应用[J].电网技术.2010,34(3)：197-200
[117]非线性,动态逆,谢春利,et al.基于最小二乘支持向量机的非线性系统鲁棒自适应跟踪控制
[118]穆朝絮,张瑞民,孙长银.基于粒子群优化的非线性系统最小二乘支持向量机预测控制方法[J].控制理论与应用.2010,27(2)：164-168
[119]顾燕萍,赵文杰,吴占松.基于最小二乘支持向量机的电站锅炉燃烧优化[J].中国电机工程学报.2010,30(17)：91-97
[120]霍明.短期负荷预测的支持向量机模型参数优化方法研究[D].湖南大学.2009
[121]王晓兰,王明伟.基于小波分解和最小二乘支持向量机的短期风速预测[J].电网技术.2010,34(1)：179-184
[122]崔万照,朱长纯,保文星,et al.混沌时间序列的支持向量机预测[J].物理学报.2005,53(10)：3303-3310
[123]郑恩辉.基于支持向量机的代价敏感数据挖掘研究与应用[D].杭州：浙 江大学.2006
[124]贾淑矿.基于支持向量机算法的多模型建模方法研究及应用[D].江南大学.2009
[125]江田汉,束炯.基于LSSVM的混沌时间序列的多步预测[J].控制与决策.2006,21(1)：77-80
[126]V.N. Vapnik. An overview of statistical learning theory[J]. Neural Networks, IEEE Transactions on.1999,10(5):988-999
[127]邓乃扬,田英杰.数据挖掘中的新方法：支持向量机[M].科学出版社,2004
[128]方瑞明.支持向量机理论及其应用分析[M].中国电力出版社,2007
[129]刘大同,彭喜元,于江,et al.采用加速减量策略的快速在线支持向量回归算法[J].电子测量与仪器学报.2009,23(12)：27-32
[130]杨淑莹.模式识别与智能计算[M].北京：电子工业出版社,2008：298-318.
[131]向玲,朱永利,唐贵基.HHT方法在转子振动故障诊断中的应用[J].中国电机工程学报.2007,27(35)：84-89
[132]胡维平,杜明辉.信号采样率对经验模态分解的影响研究[J].信号处理.2007,23(4)：637-640
[133]黄迪山.经验模态分解中虚假模态分量消除法[J].振动.测试与诊断.2011,31(3)：381-384
[134]S. Amari, A. Cichocki, H.H. Yang. A new learning algorithm for blind signal separation[J]. Advances in Neural Information Processing Systems.1996:757-763
[135]P.J. Moreno, P. Ho, N. Vasconcelos. A Kullback-Leibler divergence based kernel for SVM classification in multimedia applications[J]. Advances in Neural Information Processing Systems.2003,16:1385-1393
[136]J.R. Hershey, P.A. Olsen. Approximating the Kullback Leibler divergence between Gaussian mixture models[J],2007, Ieee:IV-317-IV-320
[137]林丽,余轮.基于相关系数的EMD改进算法[J].计算机与数字工程,2008,36(12)：28-36.
[138]石峰,莫忠息.信息论基础[M].武汉大学出版社,2002
[139]傅祖芸.信息论：基础理论与应用[M].电子工业出版社,2001
[140]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用[M].武汉大学出版社,2002
[141]L. Cao. Practical method for determining the minimum embedding dimension of a scalar time series[J]. Physica D:Nonlinear Phenomena.1997, 110(1):43-50
[142]祝志慧,孙云莲,季宇.基于EMD和SVM的短期负荷预测[J].高电压技术,2007,33(5)：118-122
[143]刘兴杰,米增强,杨奇逊,樊小.一种基于EMD的短期风速多步预测方法[J].电工技术学报,2010,25(4)：165-170
[144]王晓兰,李辉.基于EMD分解的风电场风速和输出功率年度预测[J].太阳能学报,2011,32(3)：301-306
[145]曹慧.支持向量机方法在风电场风速预测中的应用研究[D].北京：华北电力大学.2010
[146]王文波,费浦生,羿旭明.基于EMD与神经网络的中国股票市场预测[J].系统工程理论与实践.2010,6：1027-1033
[147]玄兆燕,杨公训.经验模态分解法在大气时间序列预测中的应用[J].自动化学报.2008,1：97-101
[148]王军栋,齐维贵.基于EMD-SVM的江水浊度预测方法研究[J].电子学报.2009,10：2130-2133
[149]高波,张钦宇,梁永生,刘宁宁,黄程波,张乃通.基于EMD及ARMA的自相似网络流量预测[J].通信学报.2011,4：47-56
[150]朱志勇,林睦纲,张深基.基于小波变换与支持向量机的短期电力负荷预测[J].微计算机应用,2005,26(4)：440-442
[2]John Sohre. Trouble-shooting to stop vibration of centrifugal [J]. Petrop/Chem. Engineer.1968,11:22-23
[3]白木万博(日).机械振动讲演论文集[M].郑州机械研究所,1984
[4]DE Bently. Forced subrotative speed dynamic action of rotating machinery. ASME paper.1974(74-PET):16
[5]高金吉.高速涡轮机械振动故障机理及诊断方法的研究[M].北京：清华大学.1993
[6]徐敏.设备故障诊断手册[M].1998
[7]陈安华,钟掘.转子系统非线性振动的辨识建模[J].中国有色金属学报.1997
[8]J.W. Cooley, J.W. Tukey. An algorithm for the machine calculation of complex Fourier series [J]. Mathematics of computation.1965:297-301
[9]胡丽莹,肖蓬.快速傅里叶变换在频谱分析中的应用[J].福建师范大学学报：自然科学版.2011,27(4)：27-30
[10]肖玮,涂亚庆,何丽.DTFT频谱细化特性分析及其快速算法设计[J].电子与信息学报.2011,33(6)：1395-1401
[11]张宪超,蒋增荣.离散傅里叶变换的算术傅里叶变换算法[J].电子学报.2000,28(005)：105-107
[12]E. Al-Ammar, G.G. Karady. Transfer function analysis using STFT for improvement of the fault detection sensitivity in transformer impulse test [C]. Power Engineering Society General Meeting,2005. IEEE,2005, IEEE: 1855-1862
[13]J.Y.H. Yigang. New Digital Algorithm for Measuring Electric Frequency Based on Adaptive Short-Time Fourier Transform [J]. Journal of Electronic Measurement and Instrument.2006,2:002
[14]胡晓依,何庆复,王华胜,et al.基于STFT的振动信号解调方法及其在轴承故障检测中的应用[J].振动与冲击.2008,27(002)：82-86
[15]S.G. Mallat. A theory for multiresolution signal decomposition:the wavelet representation [J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on.1989,11(7):674-693
[16]S. Mallat, W.L. Hwang. Singularity detection and processing with wavelets [J]. Information Theory, IEEE Transactions on.1992,38(2):617-643
[17]I. Daubechies. The wavelet transform, time-frequency localization and signal analysis [J]. Information Theory, IEEE Transactions on.1990,36(5):961-1005
[18]陈果.一种改进的谐波小波及其在转子故障诊断中的应用[J].机械工程学报.2011,47(001)：8-16
[19]L. Cohen. Time-frequency distributions-a review [J]. Proceedings of the IEEE.1989,77(7):941-981
[20]来五星,轩建平,史铁林,et al. Wigner-Vill时频分布研究及其在齿轮故障诊断中的应用[J].振动工程学报.2003,16(2)：247-250
[21]N.E. Huang, Z. Shen, S.R. Long, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis [J]. Proceedings of the Royal Society of London. Series A:Mathematical, Physical and Engineering Sciences.1998,454(1971):903-995
[22]N.E. Huang, Z. Shen, S.R. Long. A new view of nonlinear water waves:The Hilbert Spectrum 1 [J]. Annual Review of Fluid Mechanics.1999,31(1): 417-457
[23]周志峰,胡秀娟.基于改进EMD的汽车动态称重信号处理[J].数据采集与处理.2009,23(6)：751-755
[24]韩中合,朱霄珣,李文华,et al.基于EMD消除Wigner-Vill分布交叉项的研究[J].汽轮机技术.2010(003)：211-214
[25]周志锋,蔡萍,许嘉,et al.基于经验模态分解的汽车动态称重数据处理[J].中国机械工程.2006,16(20)：1813-1816
[26]N.E.Huang, H.H. Shih, Z. Shen, et al. The ages of large amplitude coastal seiches on the Caribbean Coast of Puerto Rico [J]. Journal of physical oceanography.2000,30(8):2001-2012
[27]N.E.Huang, C.C. Chern, K.Huang, et al. A new spectral representation of earthquake data:Hilbert spectral analysis of station TCU129, Chi-Chi, Taiwan, 21 September 1999. Bulletin of the Seismological Society of America.2001, 91 (5):1310-1338
[28]C.H. Loh, T.C. Wu, N.E. Huang. Application of the empirical mode decomposition-Hilbert spectrum method to identify near-fault ground-motion characteristics and structural responses [J]. Bulletin of the Seismological Society of America.2001,91(5):1339-1357
[29]沈路,周晓军,张志刚,et a1.Hilbert-Huang变换中的一种端点延拓方法[J].振动与冲击.2009,28(008)：168-171
[30]M. Datig, T. Schlurmann. Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves [J]. Ocean Engineering.2004,31(14):1783-1834
[31]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用.2004,40(16)：84-86
[32]Y.Deng, W.Wang, C. Qian, et al. Boundary-processing-technique in EMD method and Hilbert transform [J]. Chinese Science Bulletin.2001,46(11): 954-960
[33]张郁山,梁建文,胡聿贤.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展.2003,13(10)：1054-1059
[34]杨建文,贾民平.希尔伯特-黄谱的端点效应分析及处理方法研究[J].振动工程学报.2006,19(2)：283-288
[35]盖强.局域波时频分析方法的理论研究与应用[D].大连：大连理工大学.2001
[36]赵进平.Improvement of the mirror extending in empirical mode decomposition method and the technology for eliminating frequency mixing[J].高技术通讯：英文版.2002,8(3)：40-47
[37]胡爱军.Hilbert-Huang变换在旋转机械振动信号分析中的应用研究[D].华北电力大学(河北).2008
[38]Q. Chen, N. Huang, S. Riemenschneider, et al. A B-spline approach for empirical mode decompositions [J]. Advances in Computational Mathematics.2006,24(1):171-195
[39]钟佑明,金涛,秦树人.希尔伯特-黄变换中的一种新包络线算法[J].数据采集与处理.2005,20(1)：13-17
[40]张之猛,刘晨晨,刘伯胜,et al.经验模态分解中的包络线拟合算法仿真分析[J].系统仿真学报.2009(023)：7690-7693
[41]N.E. Huang. A new view of nonlinear waves:The Hilbert spectrum [J].Annual Review of Fluid Mechanics.1999,31:417-457
[42]H. Li, L. Yang, D. Huang. The study of the intermittency test filtering character of Hilbert-Huang transform [J]. Mathematics and Computers in Simulation.2005,70(1):22-32
[43]赵进平.异常事件对EMD方法的影响及其解决方法研究[J].青岛海洋大学学报.2001,31(6)：805-814
[44]曹冲锋,杨世锡,杨将新.基于白噪声统计特性的振动模式提取方法[J].机械工程学报.2010(003)：65-70
[45]李雪耀,邹晓杰,张汝波,et al.谱熵和主成分分析用于EMD分解研究[J].哈尔滨工程大学学报.2009(7)：797-803
[46]林丽,余轮.基于相关系数的EMD改进算法[J].计算机与数字工程.2009,36(12)：28-29
[47]张金,张耀辉,黄漫国.倒频谱分析法及其在齿轮箱故障诊断中的应用[J].机械工程师.2005(8)：34-36
[48]刘进明,应怀樵.FFT谱连续细化分析的富里叶变换法[J].振动工程学报.1995,8(2)：162-166
[49]李辉,郑海起,唐力伟.基于倒阶次谱分析的齿轮故障诊断研究[J].振动与冲击.2006,25(005)：65-68
[50]崔江,王友仁,刘权.基于高阶谱与支持向量机的电力电子电路故障诊断技术[J].中国电机工程学报.2007,27(10)：62-66
[51]宁绍斌.二维全息谱分析在电厂通风机转子故障诊断中的应用[J].南华大学学报：自然科学版.2008(4)
[52]吕志民,徐金梧.分形维数及其在滚动轴承故障的诊断中的应用[J].机械工程学报.1999,35(002)：88-91
[53]邹恩,混沌学,李祥飞,et al.混沌控制及其优化应用[J].国防科技大学出版社,2002
[54]I. Karanta. Expert systems in forecast model building [C]. Publications of the Finnish Artificial Intelligence Society,9th Finnish Artificial Intelligence Conference,2000:77-85
[55]PK Dash, AC Liew, S. Rahman. Fuzzy neural network and fuzzy expert system for load forecasting [J]. Generation, Transmission and Distribution, IEE Proceedings-,1996, IET:106-114
[56]GA Adepoju, SOA Ogunjuyigbe, KO Alawode. Application of Neural Network to Load Forecasting in Nigerian Electrical Power System [J]. The Pacific Journal of Science and Technology.2007,8(1):68-72
[57]U.B. Filik, M. Kurban. A new approach for the short-term load forecasting with auto regressive and artificial neural network models [J]. International Journal of Computational Intelligence Research.2007,3(1):66-71
[58]M. Daneshdoost, M. Lotfalian, G. Bumroonggit, et al. Neural network with fuzzy set-based classification for short-term load forecasting [J]. Power Systems, IEEE Transactions on.1998,13(4)-.1386-1391
[59]沈路,贺小明.组合预测在风机振动预测中的应用[J].中国设备工程.2006,9：43-45
[60]陈铁华,陈启卷.模糊聚类分析在水电机组振动故障诊断中的应用[J].中国电机工程学报.2002,22(3)：43-47
[61]张彼德,孙才新.诊断汽轮发电机组振动故障的一种模糊聚类分析方法[J].汽轮机技术.2002,44(5)：289-291
[62]王清.基于模糊聚类和灰色理论的齿轮箱故障诊断研究[J].太原：中北大学.2006
[63]A. Kowalski, D. Szynal. An optimal prediction in general ARMA models [J]. Journal of multivariate analysis.1990,34(1):14-36
[64]李艳芳.电力负荷预测[J].南昌高专学报.2008,22(6)：143-145
[65]吴捷,严华.基于自适应成模糊逻辑系统的短期负荷预测方法[J].电力系统自动化.1999,23(17)：35-37
[66]A. Majidian, MH Saidi. Comparison of fuzzy logic and neural network in life prediction of boiler tubes [J]. International journal of fatigue.2007,29(3): 489-498
[67]B.E. Boser, I.M. Guyon, V.N. Vapnik. A training algorithm for optimal margin classifiers [J]. Proceedings of the fifth annual workshop on Computational learning theory,1992, ACM:144-152
[68]V. Vapnik. The nature of statistical learning theory [J]. springer,1999
[69]E. Osuna, R. Freund, F. Girosi. An improved training algorithm for support vector machines [J]. Neural Networks for Signal Processing [1997] VII. Proceedings of the 1997 IEEE Workshop,1997, IEEE:276-285
[70]T.Joachims. Making large scale SVM learning practical [J].1999
[71]J.C. Platt.12 Fast Training of Support Vector Machines using Sequential Minimal Optimization [J].1999
[72]S.S. Keerthi, S.K. Shevade, C. Bhattacharyya, et al. Improvements to Platt's SMO algorithm for SVM classifier design [J]. Neural Computation.2001,13 (3):637-649
[73]D. Pavlov, D. Chudova, P.Smyth. Towards scalable support vector machines using squashing [C]. Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining,2000, ACM:295-299
[74]V. Tresp. Scaling kernel-based systems to large data sets [J]. Data Mining and Knowledge Discovery.2001,5(3):197-211
[75]苑津莎,张英慧,牛丽仙,et a1.基于SOFM和支持向量机回归的短期负荷预测方法[J].电力科学与工程.2009,25(008)：27-29
[76]李林峰,孙长银.基于FCM聚类与SVM的电力系统短期负荷预测[J].江苏电机工程.2007,26(3)：47-50
[77]P.W. Chen, J.Y. Wang, H.M. Lee. Model selection of SVMs using GA approach [C]. Neural Networks,2004. Proceedings.2004 IEEE International Joint Conference on,2004, IEEE:2035-2040
[78]Z. Chunhong, J. Licheng. Automatic parameters selection for SVM based on GA [J]. Intelligent Control and Automation,2004. WCICA 2004. Fifth World Congress on,2004, IEEE:1869-1872
[79]齐志泉,田英杰,徐志洁.支持向量机中的核参数选择问题[J].控制工程.2005,12(4)：379-381
[80]邵信光,杨慧中,陈刚.基于粒子群优化算法的支持向量机参数选择及其应用[J].控制理论与应用.2006,23(5)：740-743
[81]巩知乐,张德贤,胡明明.一种改进的支持向量机的文本分类算法[J].计算机仿真.2009(7)：164-167
[82]刘国海,周大为,徐海霞,et al.基于SVM的微生物发酵过程软测量建模研究[J].仪器仪表学报.2009,30(6)：1228-1232
[83]胡小兵,黄席樾.蚁群优化算法及其应用[J].计算机仿真.2004,21(5)：81-85
[84]王欣,杜康,秦斌,et al.基于果蝇优化算法的LSSVR干燥速率建模[J].控制工程.2012,19(004)：630-633
[85]G. Baudat, F. Anouar. Generalized discriminant analysis using a kernel approach [J]. Neural computation.2000,12(10):2385-2404
[86]M. Szummer, T.S. Jaakkola. Kernel expansions with unlabeled examples [J]. Advances in Neural Information Processing Systems.2001:626-632
[87]P. Rujan, M. Marchand. Computing the Bayes kernel classifier [J].1999
[88]陈念贻.模式识别方法在化学化工中的应用[M].科学出版社,2000
[89]范劲松,方廷健.特征选择和提取要素的分析及其评价[J].计算机工程与应用.2001,37(13)：95-99
[90]宋晖,薛云,张良均.基于SVM分类问题的核函数选择仿真研究[J].计 算机与现代化.2011(8)：133-136
[91]刘向东,骆斌,陈兆乾.支持向量机最优模型选择的研究[J].计算机研究与发展.2005,42(4)：576-581
[92]姚程宽.不平衡样本集中SVM的应用综述[J].计算机应用与软件.2008,25(9)：1-2
[93]何渊淘,邓伟.改进的不均衡样本集支持向量机预处理方法[J].计算机工程与应用.2010,46(010)：：36-37
[94]黄秀丽,王蔚.SVM在非平衡数据集中的应用[J].计算机技术与发展.2009,19(6)：190-193
[95]H.G. Chew, D.J. Crisp, R.E. Bogner, et al. Target detection in radar imagery using support vector machines with training size biasing [J]. Proc. Int. Conf. on Control, Automation, Robotics, and Vision (ICARCV),2000
[96]王娟娟,任秋实.基于SMO的不同惩罚系数的SVM算法[J].信息技术.2006,30(010)：45-46
[97]刘万里,刘三阳,薛贞霞.不平衡支持向量机的平衡方法[J].模式识别与人工智能.2008,21(002)：136-141
[98]R. Akbani, S. Kwek, N. Japkowicz. Applying support vector machines to imbalanced datasets [J]. Machine Learning:ECML 2004.2004:39-50
[99]T. Maciejewski, J. Stefanowski. Local neighbourhood extension of smote for mining imbalanced data [J]. Computational Intelligence and Data Mining (CIDM),2011 IEEE Symposium on,2011, IEEE:104-111
[100]杨智明,彭宇,彭喜元.基于支持向量机的不平衡数据集分类方法研究[J].仪器仪表学报.2009,5(30)：1094-1099
[101]王计生,喻俊馨,黄惟公.小波包分析和支持向量机在刀具故障诊断中的应用[J].振动.测试与诊断.2008,28(3)：273-276
[102]于德介,杨宇,程军圣.一种基于SVM和EMD的齿轮故障诊断方法[J].机械工程学报.2005,41(1)：140-144
[103]程军圣,于德介,杨宇.基于EMD和SVM的滚动轴承故障诊断方法[J].航空动力学报.2006,21(3)：575-580
[104]吕建新,吴虎胜,王茂生,et al.基于EMD和SVM的农用柴油机故障诊断研究[J].安徽农业科学.2010(017)：9225-9228
[105]饶俊,王太勇.基于多类SVM与改进EMD的故障诊断[J].组合机床与自动化加工技术.2010(006)：29-31
[106]翟永杰,刘林,王朋.基于ADE-SVM和模糊理论的电力系统中期负荷 预测[J].电力系统保护与控制.2012,40(8)：110-115
[107]王义民,方卫民,席秋义,et al.基于LS-SVM和PSO相结合的电力负荷预测研究[J].水力发电学报.2010(4)：245-250
[108]冯广斌,吴震宇,袁惠群.基于混沌理论与SVM的内燃机振动信号趋势预测[J].振动.测试与诊断.2011,31(001)：64-69
[109]张华,曾杰.基于支持向量机的风速预测模型研究[J].太阳能学报.2010,31(007)：928-932
[110]张学工.关于统计学习理论与支持向量机[J].自动化学报.2000,26(1)：32-42
[111]张艳秋,王蔚.利用遗传算法优化的支持向量机垃圾邮件分类[J].计算机应用.2009,29(10)：62-63
[112]罗瑜,李涛,何大可,et al.基于部件和支持向量机的人脸分类[J].计算机工程.2008,34(4)：198-200
[113]申宇皓,孟晨,傅振华,et al.基于改进支持向量机的仿真电路故障诊断研究[J].计算机仿真.2010(001)：346-350
[114]崔江,王友仁.基于支持向量机与最近邻分类器的模拟电路故障诊断新策略[J].仪器仪表学报.2010,31(1)：45-50
[115]沈志熙,黄席樾,马笑潇.基于EMD和支持向量机的柴油机故障诊断[J].振动.测试与诊断.2010,30(001)：19-22
[116]贾嵘,洪刚,薛建辉,et al.粒子群优化-最小二乘支持向量机算法在高压断路器机械故障诊断中的应用[J].电网技术.2010,34(3)：197-200
[117]非线性,动态逆,谢春利,et al.基于最小二乘支持向量机的非线性系统鲁棒自适应跟踪控制
[118]穆朝絮,张瑞民,孙长银.基于粒子群优化的非线性系统最小二乘支持向量机预测控制方法[J].控制理论与应用.2010,27(2)：164-168
[119]顾燕萍,赵文杰,吴占松.基于最小二乘支持向量机的电站锅炉燃烧优化[J].中国电机工程学报.2010,30(17)：91-97
[120]霍明.短期负荷预测的支持向量机模型参数优化方法研究[D].湖南大学.2009
[121]王晓兰,王明伟.基于小波分解和最小二乘支持向量机的短期风速预测[J].电网技术.2010,34(1)：179-184
[122]崔万照,朱长纯,保文星,et al.混沌时间序列的支持向量机预测[J].物理学报.2005,53(10)：3303-3310
[123]郑恩辉.基于支持向量机的代价敏感数据挖掘研究与应用[D].杭州：浙 江大学.2006
[124]贾淑矿.基于支持向量机算法的多模型建模方法研究及应用[D].江南大学.2009
[125]江田汉,束炯.基于LSSVM的混沌时间序列的多步预测[J].控制与决策.2006,21(1)：77-80
[126]V.N. Vapnik. An overview of statistical learning theory[J]. Neural Networks, IEEE Transactions on.1999,10(5):988-999
[127]邓乃扬,田英杰.数据挖掘中的新方法：支持向量机[M].科学出版社,2004
[128]方瑞明.支持向量机理论及其应用分析[M].中国电力出版社,2007
[129]刘大同,彭喜元,于江,et al.采用加速减量策略的快速在线支持向量回归算法[J].电子测量与仪器学报.2009,23(12)：27-32
[130]杨淑莹.模式识别与智能计算[M].北京：电子工业出版社,2008：298-318.
[131]向玲,朱永利,唐贵基.HHT方法在转子振动故障诊断中的应用[J].中国电机工程学报.2007,27(35)：84-89
[132]胡维平,杜明辉.信号采样率对经验模态分解的影响研究[J].信号处理.2007,23(4)：637-640
[133]黄迪山.经验模态分解中虚假模态分量消除法[J].振动.测试与诊断.2011,31(3)：381-384
[134]S. Amari, A. Cichocki, H.H. Yang. A new learning algorithm for blind signal separation[J]. Advances in Neural Information Processing Systems.1996:757-763
[135]P.J. Moreno, P. Ho, N. Vasconcelos. A Kullback-Leibler divergence based kernel for SVM classification in multimedia applications[J]. Advances in Neural Information Processing Systems.2003,16:1385-1393
[136]J.R. Hershey, P.A. Olsen. Approximating the Kullback Leibler divergence between Gaussian mixture models[J],2007, Ieee:IV-317-IV-320
[137]林丽,余轮.基于相关系数的EMD改进算法[J].计算机与数字工程,2008,36(12)：28-36.
[138]石峰,莫忠息.信息论基础[M].武汉大学出版社,2002
[139]傅祖芸.信息论：基础理论与应用[M].电子工业出版社,2001
[140]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用[M].武汉大学出版社,2002
[141]L. Cao. Practical method for determining the minimum embedding dimension of a scalar time series[J]. Physica D:Nonlinear Phenomena.1997, 110(1):43-50
[142]祝志慧,孙云莲,季宇.基于EMD和SVM的短期负荷预测[J].高电压技术,2007,33(5)：118-122
[143]刘兴杰,米增强,杨奇逊,樊小.一种基于EMD的短期风速多步预测方法[J].电工技术学报,2010,25(4)：165-170
[144]王晓兰,李辉.基于EMD分解的风电场风速和输出功率年度预测[J].太阳能学报,2011,32(3)：301-306
[145]曹慧.支持向量机方法在风电场风速预测中的应用研究[D].北京：华北电力大学.2010
[146]王文波,费浦生,羿旭明.基于EMD与神经网络的中国股票市场预测[J].系统工程理论与实践.2010,6：1027-1033
[147]玄兆燕,杨公训.经验模态分解法在大气时间序列预测中的应用[J].自动化学报.2008,1：97-101
[148]王军栋,齐维贵.基于EMD-SVM的江水浊度预测方法研究[J].电子学报.2009,10：2130-2133
[149]高波,张钦宇,梁永生,刘宁宁,黄程波,张乃通.基于EMD及ARMA的自相似网络流量预测[J].通信学报.2011,4：47-56
[150]朱志勇,林睦纲,张深基.基于小波变换与支持向量机的短期电力负荷预测[J].微计算机应用,2005,26(4)：440-442