摘要
设备在服役期内的安全性、可靠性越来越受到业界的重视。起重机广泛应用于众多基础建设项目，工作环境恶劣复杂，是事故率最高的特种机械设备之一。设备关键部件发生故障，就可能破坏整台设备甚至影响整个生产过程，不仅造成巨大的经济损失，甚至可能导致灾难性的人员伤亡事故。实时监控设备运行状态、及时对其故障进行诊断是避免非计划停机和保障起重机安全生产的重要措施。
基于数据驱动的状态监控与智能诊断是当前研究的一个热点，同时也面临着一系列理论和技术上的挑战：复杂噪声环境下有用信号的提取；设备运行状态有效特征的提取；基于实时在线智能故障诊断模型的建立；以及针对故障样本稀缺和故障模式不完备情况下智能诊断模型的建立等。本文研究复杂工作环境下工程机械状态监控与故障诊断的共性关键理论方法与技术，并应用于大型汽车起重机主泵。主要内容包括：
（1）小波去噪是信号处理领域中的重要方法，如何确定小波分解层数是一个关键问题。本文针对加性高斯白噪声的情况，提出了基于blockbootstrap进行白化检验确定小波分解层数的新方法。主要包含三个步骤：首先对信号进行小波分解，利用延迟自相关量考察小波系数的相关性；其次，根据每层系数相关性的程度，采用block bootstrap过程或者bootstrap过程对原始的小波系数进行采样产生新的bootstrap样本；最后，由于有用信号和噪声在小波空间上不同的传播特性，对获得的小波系数样本进行白化检验，继而确定合适的分解层数。实验表明，该方法对白噪声污染信号能够获得合适的分解层数和良好的去噪效果。
（2）小波阈值的选取是小波去噪的另一个关键因素。本文提出了一个基于Advanced False Discovery Rate （AFDR）的多假设检验方法确定小波阈值的新方法，该方法基于对真的原假设数目的估计，选择合适的step wise过程（step-up，step-down，step-up-down）。AFDR过程与标准的FDR过程相比，有两个主要特点：通过减少比较的次数，提高了多假设检验的效率；提高了检验的势。对应的的自适应小波去噪方法主要包含两个步骤，第一，模型在小波域得到更紧凑的表示，第二，根据小波系数本身的特点，选择最合适的FDR过程。仿真数据和实际实验表明，算法能够灵活调整显著性水平的大小并有效去噪，本方法滤波效果与其它经典的滤波技术相比，具有一定的优势。
（3）基于小波leaders多重分形分析提出了振动信号特征提取新方法。在本文算法中，由尺度指数、多重分形谱和log累积量构成多重分形特征对设备不同故障状态和故障程度进行诊断，并对各分形特征及其组合的分类性能进行评估。8个小波包能量特征也被引入到特征集合，实验在轴承11组故障数据集上表明，能够获得较为理想的分类效果。同时表明，多重分形特征结合小波包能量特征的分类性能优于多重分形特征或小波包能量特征或时域统计特征，也优于时域统计特征与小波包能量特征或多重分形特征的组合特征。利用距离评价准则，对组合特征进行选择，冗余特征的去除，使分类性能进一步得到提高。
（4）提出了基于粒子群相关向量机（Relevance Vector Machines withParticle Swarm Optimization，PSO-RVM）的智能诊断方法，其中粒子群算法用于优化相关向量机核函数的参数，各二值相关向量机按二叉树的组织形式构成系统的诊断模型。实验表明该方法所得模型需要的相关向量个数很少，而且能够得到比较高的诊断精度，适合对实时性要求高的在线诊断系统。另外，针对机械运行最初阶段，往往只有正常状态的样本，到一定阶段后故障样本才逐渐增多，常规故障诊断模型无法进行有效的训练这一问题，本文提出了一个基于蚁群支持向量数据描述(SupportVector Data Description with Ant Colony Optimization，ANT-SVDD)新异类检测和Davies Bouldin指数（Davies Bouldin Index，DBI）K均值聚类方法结合的机械故障诊断框架。首先对正常状态样本建立SVDD模型，并利用蚁群算法对SVDD模型参数进行优化。当拒绝样本数目累积到设定的阈值时，对这些样本利用K均值聚类方法进行处理，获得能够进行标记的类别，其中，K均值聚类的类型数目由Davies Bouldin指数辅助确定。最后，对这些标记出的各类样本，分别建立SVDD模型进行训练，由这些SVDD分类器按照二叉树形式组成对系统状态的完整诊断模型。实验验证了所提算法的有效性。
（5）提出了汽车起重机智能维护总体框架设计和数据库系统设计，并利用本文所提出的状态监控和故障诊断关键技术，进行汽车起重机主泵基于小波预处理技术的状态监控分析和基于PSO-RVM、ANT-SVDD聚类的智能诊断研究。信号消噪前后的包络谱表明，利用所提出的预处理技术，可以明显改善信号质量，提高状态监控的准确性。针对汽车起重机柱塞泵6种状态，包括正常，轴承内圈故障，滚动体故障，柱塞故障，配流盘故障，斜盘故障，建立PSO-RVM诊断模型，并与后向传播神经网络（Back-Propagation Artificial Neural Network，BP-ANN）,蚁群优化神经网络（Ant Colony Optimization Artificial Neural Network，ANT-ANN）,相关向量机方法（Relevance Vector Machines，RVM），粒子群支持向量机（Support Vector Machines with Particle Swarm Optimization，PSO-SVM）进行比较。诊断结果表明，PSO-RVM比BP-ANN、ANT-ANN、RVM具有更高的识别精度，与PSO-SVM识别精度相当，分别达到99.17%和99.58%，但是所需相关向量的数目远小于支持向量的个数，每个二分类RVM的相关向量数目是对应SVM的支持向量数目的1/12－1/3。进一步验证了PSO-RVM更适合在线实时监控。利用主泵相同的数据，首先对主泵正常状态建立ANT-SVDD模型，然后对异常样本根据DB指数进行聚类，将由新发现类型样本建立的ANT-SVDD分类器组合进系统诊断模型，实现了主泵新增故障类的智能诊断。
The safety and reliability of equipments during their service life hasarisen increasing attention in group in the industry and customer. Crane is animportant construction machinery to ensure the successful completion ofmany major infrastructural projects. Since the machinery always works in thesevere working condition, it is one of the special machines with the highestaccident rate. Once the key parts break down, the whole equipment may bedestroyed even whole production, the efficiency will be affected and even thecatastrophic accidents will occur. The real-time condition monitoring andon-time fault diagnosis of crane is an effective measure to avoid it unplanneddowntime and ensure safety in production.
The study of condition monitoring and on line intelligence faultdiagnosis of construction machinery is one of the hot spot. However, it stillhas many challenges, such as the real signal recovery from the contaminatedoriginal signal, the effective features extraction, the establishment of real timefault diagnosis model, and the diagnosis model for the absence of faultcondition samples. This dissertation focuses on the key technology ofcondition monitoring and fault diagnosis of construction machinery, and itsapplication on plunger pump in large truck crane in the complicated workingconditions. The main contents are as follows:
(1) Due to its good localization and multi-resolution features in thetime-frequency domain, the wavelet transform has been widely used, andvarious signals with different signal to noise ratio (SNR) have correspondingsuitable decomposition levels to obtain effective filtering results. This studydescribes a novel scheme of selecting the appropriate decomposition levelbased on block bootstrap and white noise test. The scheme consists of threemain steps. Firstly, decompose the vibration signal into wavelet domain, andthe correlations between the wavelet coefficients are measured by lag autocorrelations. Secondly, according to the intensity of correlation at eachlevel, either the block bootstrap or general bootstrap procedure is adopted toproduce new pseudo-samples from the original wavelet coefficients series.Finally, as actual signal and noise have different translating characters alongthe levels in wavelet domain, the suitable decomposition level is achievedthrough whitening test on the wavelet coefficients, and the accuracy of thetest is also obtained by the pseudo-samples. The simulation and experimentresults show that the proposed procedure can be used to determine the seemlydecomposition level adaptively and obtain the superior filtering capability forthe signal contaminated with white noise.
(2) The threshold is another key factor for wavelet denoising. A novelapproach is proposed by using advanced false discovery rate procedure(AFDR). The main idea is based on controlling false discovery rate (FDR)through combination of all three stepwise procedures (step-up, step-down,step-up-down) and estimation of the number of true null hypotheses. TheAFDR procedure differs from the standard FDR procedure in two respects,i.e., enhancing the efficiency by reducing the number of tested hypotheses andimproving the power. The proposed procedure consists of two main steps:firstly, the signal is represented more parsimoniously in wavelet domain;secondly, a most appropriate stepwise FDR procedure is selected according tothe character of wavelet coefficients. Both the numerical simulation resultsand the experimental results show that the proposed approach is a competitiveshrinkage method compared with other popular techniques.
(3) A novel method based on wavelet leaders multifractal features formachinery fault diagnosis is proposed. The multifractal features, combined byscaling exponents, multifractal spectrum, and log cumulants, are utilized toclassify various fault types and evaluate various fault conditions of rollingelement bearing, and the classification performance of each feature and theircombinations are evaluated. Eight wavelet packet energy features are alsointroduced together with multifractal features. Experiments on11fault datasets of bearing show that a promising classification performance is achieved. At the same time, the experimental results show that the classificationperformance of the classifier trained with eight wavelet packet energy featuresin tandem with multifractal features outperforms that of the classifier trainedonly with wavelet packet energy features, time domain features, ormultifractal features, and it is also superior than that of wavelet packet energyfeatures in tandem with time domain features, or multifractal featurescombined with time domain features. The feature selection method based ondistance evaluation technique is exploited to select the most relevant featuresand discard the redundant features, and therefore the reliability of thediagnosis performance is further improved.
（4）Promptly and accurately dealing with the equipment breakdown isvery important in terms of reliability and downtime decreasing. A novel faultdiagnosis method based on particle swarm optimization (PSO) and relevancevector machine (RVM) is proposed. The particle swarm optimizationalgorithm is utilized to determine the kernel width parameter of the kernelfunction in RVM, and the two-class RVMs with binary tree architecture aretrained to recognize the condition of mechanism. For multi-fault modesamples, the experiments show that a very sparse diagnosis model is realizedand a promising classification performance is achieved, which is veryappropriate for on-line real-time application. In addition, at the initializationrunning period of the rotating mechanism, the collected samples are alwaysones in the normal condition, and the fault signals only appears after a certainrunning time, so the general fault diagnosis model can not be trainedeffectively. In this paper, a hybrid fault diagnosis scheme for rotatingmechanism is proposed based on ant colony SVDD (Ant-SVDD) and DaviesBouldin index (DBI) K-Cluster method. Firstly, the SVDD model isconstructed for the samples in the normal condition, and the ant colonyalgorithm is utilized to optimize the SVDD parameters. Secondly, when thenumber of rejected samples reaches the given threshold, the K-Cluster methodis employed to classify these samples and the labels is obtained. Furthermore,the number of the classification is determined in accordance with the Davies Bouldin index. Finally, the one class samples are trained with SVDDindividually, and the SVDD classifiers are combined to a complete diagnosismodel based on a binary tree structure. For the multi-fault mode samples ofrolling element bearing, experiments show that a promising classificationperformance is achieved.
(5) The system architecture and the database system of the intelligentmaintenance are designed for truck crane, and with the proposed keytechnology of condition monitoring and fault diagnosis, the wavelet transformpreprocessing based condition analysis and PSO-RVM, ANT-SVDD clustermethod based intelligent diagnosis for pump in truck crane are realized. Theenvelope of the signal before and after denoising shows that the signal qualitygets a great improvement, which improves the accuracy of conditionmonitoring. The proposed diagnosis methods are employed in the diagnosis ofplunger pump in truck crane. The six states, including normal state, bearinginner race fault, bearing roller fault, plunger wear fault, thrust plate wear fault,and swash plate wear fault, are used to test the classification performance ofthe proposed PSO-RVM model, which compares with the classical models,such as back-propagation artificial neural network (BP ANN), ant colonyoptimization artificial neural network (ANT ANN), relevance vectormachines (RVM), and support vector machines with particle swarmoptimization (PSO-SVM), respectively. The experimental results show thatthe PSO-RVM is superior to the first three classical models, and has acomparable performance to the PSO-SVM, the diagnostic accuracy achievingas high as99.17%and99.58%, respectively. But the needed number ofrelevance vector is far fewer than that of support vector, and the former isabout1/12to1/3of the latter, which indicates that the proposed PSO-SVMmodel is more suitable for applications that requires low complexity andreal-time monitoring. With the same pump data, the ANT-SVDD model isbuilt for the normal state, and then the DBI K-cluster method is employed forthe novelty samples. The ANT-SVDD classifier for the new labeled samplesis constructed and combined into the total diagnosis model. This technology realizes the intelligent diagnosis for the new fault class.
引文
[1]国家质检总局.关于2010年全国特种设备安全状况的情况通报.http://tzsbaqjcj.aqsiq.gov.cn/tzwj/zjwh/201106/t20110620_187726.htm.2011.
[2]国家质检总局.2007年特种设备事故年报.http://tzsbaqjcj.aqsiq.gov.cn/sgzl/sgnb/200905/t20090512_114698.htm.2007.
[3]温熙森.模式识别与状态监控[M].北京:机械工业出版社.2007.
[4]中华人民共和国国务院.国家中长期科学和技术发展规划纲要（2006-2020）[M].北京:中国法制出版社.2006.
[5]国家自然科学基金委员会工程与材料科学部.机械工程学科发展战略报告（2011～2020）[M].科学出版社.2010.
[6]国家自然科学基金委员会.国家自然科学基金“十二五”发展规划.http://www.nsfc.gov.cn/Portal0/InfoModule_523/34577.htm.2011.
[7]孙朝岐.汽车起重机[M].长沙:三一职业技能培训丛书.2007.
[8]刘延俊.液压与气压传动[M].北京:机械工业出版社.2005.
[9]李彦明,何创新,刘成良,陈斌.工程机械远程监控信息流的数据管理与规划研究[J].高技术通讯.2008,18(11):1195-1199.
[10]龚雪,张克仁.工程机械故障诊断技术的现状和发展趋势[J].建筑机械.2010,(23):93-95,97.
[11]代晴华.工程机械远程监控系统.中国. CN02114341.2[P].2003-04-09.
[12]徐皑冬,李正,刘明哲等.符合全球移动通信标准的工程机械远程监控系统.中国.CN200610047368.9[P].2008-02-06.
[13]何创新,李彦明,刘成良.工程机械远程状态信息采集方法研究与应用[J].仪器仪表学报.2009,30(4):728-732.
[14] Chen H, Chua PSK, Lim G. Adaptive wavelet transform for vibration signal modelling andapplication in fault diagnosis of water hydraulic motor[J]. Mechanical Systems and SignalProcessing.2006,20(8):2022-2045.
[15] Wang Q, Chen H, Chua P, Hian LG. Fault detection of water hydraulic motor by demodulatedvibration signal analysis with the hilbert transform and genetic algorithm[J]. Journal of Testingand Evaluation.2011,39(2):102905-102914.
[16] Zhao Z, Jia M, Wang F, Wang S. Intermittent chaos and sliding window symbol sequencestatistics-based early fault diagnosis for hydraulic pump on hydraulic tube tester[J]. MechanicalSystems and Signal Processing.2009,23(5):1573-1585.
[17]唐宏宾,吴运新,滑广军,马昌训.基于EMD包络谱分析的液压泵故障诊断方法[J].振动与冲击.2012,31(9):44-48.
[18] Chen HX, Chua PSK, Lim GH. Fault degradation assessment of water hydraulic motor byimpulse vibration signal with Wavelet Packet Analysis and Kolmogorov-Smirnov Test[J].Mechanical Systems and Signal Processing.2008,22(7):1670-1684.
[19] Peng Z, Chu F, Tse PW. Singularity analysis of the vibration signals by means of waveletmodulus maximal method[J]. Mechanical Systems and Signal Processing.2007,21(2):780-794.
[20]李晗,萧德云.基于数据驱动的故障诊断方法综述[J].控制与决策.2011,26(01):1-9,16.
[21] De La Rosa J.J.G, Moreno-Mu oz A, Gallego A, Piotrkowski R, Castro E. On-sitenon-destructive measurement of termite activity using the spectral kurtosis and the discretewavelet transform[J]. Measurement: Journal of the International Measurement Confederation.2010,43(10):1472-1488.
[22]胡广书.数字信号处理-理论、算法与实现[M].北京:清华大学出版社.2003.
[23]纪少波,程勇,王锡平,杨滨.基于SRC模式识别方法的柴油机故障诊断研究[J].振动与冲击.2008,27(1):140-142,154.
[24]朱大奇,陈亮,刘乾.一种水下机器人传感器故障诊断与容错控制方法[J].控制与决策.2009,24(9):1335-1339.
[25] Mayer D, Atzrodt H, Herold S, Thomaier M. An approach for the model based monitoring ofpiezoelectric actuators[J]. Computers&Structures.2008,86(3):314-321.
[26]李富才,董丽静,何正嘉.巴特沃斯小波构造及其故障诊断应用研究[J].声学学报.2003,28(6):550-554.
[27]王小卉,杨洁明. EMD与二阶循环平稳分析在电动机轴承故障诊断中的应用[J].轴承.2010,(11):37-40.
[28] Yang XB, Jin XQ, Du ZM, Zhu YH. A novel model-based fault detection method fortemperature sensor using fractal correlation dimension[J]. Building and Environment.2011,46(4):970-979.
[29] Ming Y, Chen J, Dong G. Weak fault feature extraction of rolling bearing based on cyclic Wienerfilter and envelope spectrum[J]. Mechanical Systems and Signal Processing.2011,25(5):1773-1785.
[30]姚华,单贵平,孙健国.基于卡尔曼滤波器及神经网络的发动机故障诊断[J].航空动力学报.2008,23(6):1111-1117.
[31] Izadian A, Famouri P. Fault diagnosis of MEMS lateral comb resonators using multiple-modeladaptive estimators[J]. IEEE Transactions on Control Systems Technology.2010,18(5):1233-1240.
[32] Arulampalam M, Maskell S, Gordon N, Clapp T. A tutorial on particle filters for onlinenonlinear/non-Gaussian Bayesian tracking[J]. IEEE Transactions on Signal Processing.2002,50(2):174-188.
[33]段琢华,蔡自兴,于金霞.移动机器人软故障检测与补偿的自适应粒子滤波算法[J].中国科学(E辑:信息科学).2008,38(4):565-578.
[34] Orchard ME, Vachtsevanos GJ. A particle-filtering approach for on-line fault diagnosis andfailure prognosis[J]. Transactions of the Institute of Measurement and Control.2009,31(3-4):221-246.
[35] Al-Raheem KF, Roy A, Ramachandran KP, Harrison DK, Grainger S. Rolling element bearingfaults diagnosis based on autocorrelation of optimized: Wavelet de-noising technique[J].International Journal of Advanced Manufacturing Technology.2009,40(3-4):393-402.
[36] Wang Y, He Z, Zi Y. Enhancement of signal denoising and multiple fault signatures detecting inrotating machinery using dual-tree complex wavelet transform[J]. Mechanical Systems andSignal Processing.2010,24(1):119-137.
[37]于志伟,苏宝库,曾鸣.小波包分析技术在大型电机转子故障诊断系统中的应用[J].中国电机工程学报.2005,25(22):158-162.
[38] Wang X, Zi Y, He Z. Multiwavelet denoising with improved neighboring coefficients forapplication on rolling bearing fault diagnosis[J]. Mechanical Systems and Signal Processing.2011,25(1):285-304.
[39]王凤利,段树林,于洪亮,高洪涛.基于提升小波和局域波的柴油机故障诊断[J].内燃机学报.2011,29(4):321-326.
[40] Yuan J, He Z, Zi Y. Gear fault detection using customized multiwavelet lifting schemes[J].Mechanical Systems and Signal Processing.2010,24(5):1509-1528.
[41] Verma AK, Sreeiith B. Rolling element bearing fault diagnosis using adaptive Morlet waveletfilter[J]. International Journal of COMADEM.2009,12(4):25-32.
[42] Su W, Wang F, Zhu H, Zhang Z, Guo Z. Rolling element bearing faults diagnosis based onoptimal Morlet wavelet filter and autocorrelation enhancement[J]. Mechanical Systems andSignal Processing.2010,24(5):1458-1472.
[43] Xu K, Wang X, Li Y. Fundamental wave extraction and frequency measurement based on IIRwavelet filter banks[J]. Measurement.2007,40(6):665-671.
[44] Kaewpijit S, Moigne JL, El-Ghazawi T. Automatic reduction of hyperspectral imagery usingwavelet spectral analysis[J]. IEEE Transactions on Geoscience and Remote Sensing.2003,41(4PART I):863-871.
[45] Cocchi M, Durante C, Foca G, Marchetti A, Tassi L, Ulrici A. Durum wheat adulterationdetection by NIR spectroscopy multivariate calibration[J]. Talanta.2006,68(5):1505-1511.
[46] Palacios-Santander JM, Cubillana-Aguilera LM, Cocchi M, Ulrici A, Naranjo-Rodríguez I,Seeber R, Hidalgo-Hidalgo de Cisneros JL. Multicomponent analysis in the wavelet domain ofhighly overlapped electrochemical signals: Resolution of quaternary mixtures of chlorophenolsusing a peg-modified Sonogel-Carbon electrode[J]. Chemometrics and intelligent laboratorysystems.2008,91(2):110-120.
[47]张吉先,钟秋海,戴亚平.小波门限消噪法应用中分解层数及阈值的确定[J].中国电机工程学报.2004,24(02):119-123.
[48] Yuan H, Gao J, Guo HZ, Lu C. An efficient method to process the quantized acoustoelectriccurrent: Wavelet transform[J]. IEEE Transactions on Instrumentation and Measurement.2011,60(3):696-702.
[49] Efron B. Computers and the theory of statistics: thinking the unthinkable[J]. SIAM review.1979,21(4):460-480.
[50] Singh K. On the asymptotic accuracy of Efron's bootstrap[J]. The Annals of Statistics.1981,9(6):1187-1195.
[51] Künsch HR. The jackknife and the bootstrap for general stationary observations[J]. The Annalsof Statistics.1989,17(3):1217-1241.
[52] Politis DN, Romano JP. Acircular block-resampling procedure for stationary data[M]. LePage R.,Billard L.(Eds.), Exploring the Limits of Bootstrap. New York: John Wiley.1992:263–270.
[53] Zoubir AM, Boashash B. The bootstrap and its application in signal processing: An attractivetool for assessing the accuracy of estimators and testing hypothesis for parameters in smalldata-sample situations[J]. IEEE Signal Processing Magazine.1998,15(1):56-76.
[54] Sun R, Tsung F, Qu L. Combining bootstrap and genetic programming for feature discovery indiesel engine diagnosis[J]. International Journal of Industrial Engineering: Theory Applicationsand Practice.2004,11(3):273-281.
[55] Donoho D. De-noising by soft-thresholding[J]. IEEE transactions on information theory.1995,41(3):613-627.
[56] Vidakovic B, Ruggeri F. BAMS method: Theory and simulations[J]. Sankhy: The Indian Journalof Statistics, Series B.2001,63(2):234-249.
[57] Antoniadis A, Bigot J, Sapatinas T. Wavelet estimators in nonparametric regression: Acomparative simulation study[J]. Journal of Statistical Software.2001,6(6):1-83.
[58] Johnstone IM, Silverman BW. Empirical bayes selection of wavelet thresholds[J]. Annals ofStatistics.2005,33(4):1700-1752.
[59] Donoho D, JOHNSTONE J. Ideal spatial adaptation by wavelet shrinkage[J]. Biometrika.1994,81(3):425-455.
[60] Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerfulapproach to multiple testing[J]. Journal of the Royal Statistical Society. Series B(Methodological).1995:289-300.
[61] Benjamini Y, Liu W. A step-down multiple hypotheses testing procedure that controls the falsediscovery rate under independence[J]. Journal of Statistical Planning and Inference.1999,82(1-2):163-170.
[62] Benjamini Y, Hochberg Y. On the adaptive control of the false discovery rate in multiple testingwith independent statistics[J]. Journal of Educational and Behavioral Statistics.2000,25(1):60-83.
[63] Troendle JF. Stepwise normal theory multiple test procedures controlling the false discoveryrate[J]. Journal of Statistical Planning and Inference.2000,84(1-2):139-158.
[64] Tamhane AC, Liu W, Dunnett CW. A generalized step-up-down multiple test procedure[J].Canadian Journal of Statistics.1998,26(2):353-363.
[65] Sarkar SK. Some results on false discovery rate in stepwise multiple testing procedures[J].Annals of Statistics.2002,30(1):239-257.
[66] Tadesse MG, Ibrahim JG, Vannucci M, Gentleman R. Wavelet thresholding with Bayesian falsediscovery rate control[J]. Biometrics.2005,61(1):25-35.
[67] Lavrik I, Young Jung Y, Ruggeri F, Vidakovic B. Bayesian false discovery rate wavelet shrinkage:theory and applications[J]. Communications in Statistics-Simulation and Computation.2008,37(6):1086-1100.
[68] Srikanth R, Casanova R, Laurienti PJ, Peiffer AM, Maldjian JA. Estimation of false discoveryrates for wavelet-denoised statistical parametric maps[J]. NeuroImage.2006,33(1):72-84.
[69] Jayaswal P, Verma SN, Wadhwani AK. Development of EBP-Artificial neural network expertsystem for rolling element bearing fault diagnosis[J]. JVC/Journal of Vibration and Control.2011,17(8):1131-1148.
[70] Widodo A, Kim EY, Son JD, Yang BS, Tan ACC, Gu DS, Choi BK, Mathew J. Fault diagnosis oflow speed bearing based on relevance vector machine and support vector machine[J]. ExpertSystems with Applications.2009,36(3PART2):7252-7261.
[71] Caesarendra W, Widodo A, Yang BS. Application of relevance vector machine and logisticregression for machine degradation assessment[J]. Mechanical Systems and Signal Processing.2010,24(4):1161-1171.
[72] Lei Y, He Z, Zi Y, Hu Q. Fault diagnosis of rotating machinery based on multiple ANFIScombination with GAs[J]. Mechanical Systems and Signal Processing.2007,21(5):2280-2294.
[73] Samuel PD, Pines DJ. A review of vibration-based techniques for helicopter transmissiondiagnostics[J]. Journal of Sound and Vibration.2005,282(1-2):475-508.
[74] Lei Y, Zuo MJ. Gear crack level identification based on weighted K nearest neighborclassification algorithm[J]. Mechanical Systems and Signal Processing.2009,23(5):1535-1547.
[75] Lei Y, Zuo MJ, He Z, Zi Y. A multidimensional hybrid intelligent method for gear faultdiagnosis[J]. Expert Systems with Applications.2010,37(2):1419-1430.
[76] Xu Z, Xuan J, Shi T, Wu B, Hu Y. Application of a modified fuzzy ARTMAP withfeature-weight learning for the fault diagnosis of bearing[J]. Expert Systems with Applications.2009,36(6):9961-9968.
[77] Widodo A, Yang BS. Support vector machine in machine condition monitoring and faultdiagnosis[J]. Mechanical Systems and Signal Processing.2007,21(6):2560-2574.
[78] Cheng J, Yu D, Tang J, Yang Y. Application of frequency family separation method based uponEMD and local Hilbert energy spectrum method to gear fault diagnosis[J]. Mechanism andMachine Theory.2008,43(6):712-723.
[79] Xu H, Chen G, Wang X, Liang J. The application of EMD and ARMA Bi-cepstrum faultdiagnosis method in gearbox of overhead traveling crane. Advanced Materials Research.2011,308-310:88-91.
[80] Yang Y, Yu D, Cheng J. A fault diagnosis approach for roller bearing based on IMF envelopespectrum and SVM[J]. Measurement: Journal of the International Measurement Confederation.2007,40(9-10):943-950.
[81]王少萍,王占林.液压泵轴承故障的诊断方法[J].北京航空航天大学学报.1993,4:26-31.
[82] Kankar PK, Sharma SC, Harsha SP. Fault diagnosis of ball bearings using continuous wavelettransform[J]. Applied Soft Computing Journal.2011,11(2):2300-2312.
[83] Saravanan N, Ramachandran KI. Incipient gear box fault diagnosis using discrete wavelettransform (DWT) for feature extraction and classification using artificial neural network(ANN)[J]. Expert Systems with Applications.2010,37(6):4168-4181.
[84] Bin GF, Gao JJ, Li XJ, Dhillon BS. Early fault diagnosis of rotating machinery based on waveletpackets-Empirical mode decomposition feature extraction and neural network[J]. MechanicalSystems and Signal Processing.2012,27(1):696-711.
[85] Huang Y, Liu C, Zha XF, Li Y. An enhanced feature extraction model using lifting-based waveletpacket transform scheme and sampling-importance-resampling analysis[J]. Mechanical Systemsand Signal Processing.2009,23(8):2470-2487.
[86] Li F, Meng G, Ye L, Chen P. Wavelet transform-based higher-order statistics for fault diagnosisin rolling element bearings[J]. JVC/Journal of Vibration and Control.2008,14(11):1691-1709.
[87] Wang Z, Chen J, Dong G, Zhou Y. Constrained independent component analysis and itsapplication to machine fault diagnosis[J]. Mechanical Systems and Signal Processing.2011,25(7):2501-2512.
[88] Ruiz JRR, Garcia Espinosa A, Romeral L, Cusidó J. Demagnetization diagnosis in permanentmagnet synchronous motors under non-stationary speed conditions[J]. Electric Power SystemsResearch.2010,80(10):1277-1285.
[89] Logan D, Mathew J. Using the correlation dimension for vibration fault diagnosis of rollingelement bearings--I. Basic concepts[J]. Mechanical Systems and Signal Processing.1996,10(3):241-250.
[90] Logan D, Mathew J. Using the correlation dimension for vibration fault diagnosis of rollingelement bearings--II. Selection of experimental parameters[J]. Mechanical Systems and SignalProcessing.1996,10(3):251-264.
[91] Castillo O, Melin P. A hybrid fuzzy‐fractal approach for time series analysis and plantmonitoring[J]. International journal of intelligent systems.2002,17(8):751-765.
[92] Purkait P, Chakravorti S. Impulse fault classification in transformers by fractal analysis[J]. IEEETransactions on Dielectrics and Electrical Insulation.2003,10(1):109-116.
[93] Chen CH, Shyu RJ, Ma CK. A new fault diagnosis method of rotating machinery[J]. Shock andVibration.2008,15(6):585-598.
[94] de Moura EP, Vieira AP, M.A.S. I, Silva AA. Applications of detrended-fluctuation analysis togearbox fault diagnosis[J]. Mechanical Systems and Signal Processing.2009,23(3):682-689.
[95] Yang J, Zhang Y, Zhu Y. Intelligent fault diagnosis of rolling element bearing based on SVMsand fractal dimension[J]. Mechanical Systems and Signal Processing.2007,21(5):2012-2024.
[96] Loutridis S. Self-Similarity in Vibration Time Series: Application to Gear Fault Diagnostics[J].Journal of Vibration and Acoustics.2008,130(3):0310041-0310049.
[97] Bacry E, Muzy J, Arnéodo A. Singularity spectrum of fractal signals from wavelet analysis:Exact results[J]. Journal of Statistical Physics.1993,70(3):635-674.
[98] Lopes R, Betrouni N. Fractal and multifractal analysis: A review[J]. Medical Image Analysis.2009,13(4):634-649.
[99] Arneodo A, Audit B, Decoster N, Muzy JF, Vaillant C.2. Wavelet Based Multifractal Formalism:Applications to DNA Sequences, Satellite Images of the Cloud Structure, and Stock MarketData[J]. The science of disasters: climate disruptions, heart attacks, and market crashes.2002,2:27.
[100] Rodrigues Neto C, Zanandrea A, Ramos FM, Rosa RR, Bolzan MJA, Sa LDA. Multiscaleanalysis from turbulent time series with wavelet transform[J]. Physica A: Statistical Mechanicsand its Applications.2001,295(1-2):215-218.
[101] Enescu B, Ito K, Struzik ZR. Wavelet-based multiscale resolution analysis of real and simulatedtime-series of earthquakes[J]. Geophysical Journal International.2006,164(1):63-74.
[102] Yuhai S, Yuzhe K, Xiangguo C. Fault Pattern Recognition of Turbine-Generator Set Based onWavelet Network and Fractal Theory [C].8th International Conference on ElectronicMeasurement and Instruments (ICEMI).2007:3414-3417.
[103] Serrano E, Figliola A. Wavelet Leaders: A new method to estimate the multifractal singularityspectra[J]. Physica A: Statistical Mechanics and its Applications.2009,388(14):2793-2805.
[104] Lashermes B, Jaffard S, Abry P. Wavelet leader based multifractal analysis [C]. IEEEInternational Conference on Acoustics, Speech and Signal Processing (ICASSP).2005:161-164.
[105] Wendt H, Abry P, Jaffard S, Ji H, Shen Z. Wavelet leader multifractal analysis for textureclassification [C]. International Conference on Image Processing(ICIP).2009:3829-3832.
[106] Xu Y, Yang X, Ling H, Ji H. A new texture descriptor using multifractal analysis inmulti-orientation wavelet pyramid [C]. Proceedings of the IEEE Computer Society Conferenceon Computer Vision and Pattern Recognition.2010:161-168.
[107] Abry P, Wendt H, Jaffard S, Helgason H, Goncalves P, Pereira E, Gharib C, Gaucherand P, DoretM. Methodology for multifractal analysis of heart rate variability: from LF/HF ratio to waveletleaders[C]. IEEE Engineering in Medicine and Biology Society.2010:106-109.
[108] Lashermes B, Roux SG, Abry P, Jaffard S. Comprehensive multifractal analysis of turbulentvelocity using the wavelet leaders[J]. European Physical Journal B.2008,61(2):201-215.
[109] Ciuciu P, Abry P, Rabrait C, Wendt H. Log wavelet leaders cumulant based multifractal analysisof EVI fMRI time series: Evidence of scaling in ongoing and evoked brain activity[J]. IEEEJournal on Selected Topics in Signal Processing.2008,2(6):929-943.
[110] Pearson. K. On lines and planes of closest fit to systems of points in space[J]. Phil Mag.1901,6(2):559-572.
[111] He Q, Yan R, Kong F, Du R. Machine condition monitoring using principal componentrepresentations[J]. Mechanical Systems and Signal Processing.2009,23(2):446-466.
[112] Sch lkopf B, Smola, A., Müller, K.-R. Nonlinear Component Analysis as a Kernel EigenvalueProblem[J]. Neural Computation.1998,10(5):1299-1319.
[113] Ni J, Zhang C, Yang SX. An adaptive approach based on KPCA and SVM for real-time faultdiagnosis of HVCBs[J]. IEEE Transactions on Power Delivery.2011,26(3):1960-1971.
[114] Fisher RA. The use of multiple measurements in taxonomic problems[J]. Annals of HumanGenetics.1936,7(2):179-188.
[115] Yang BS, Han T, An JL. ART-KOHONEN neural network for fault diagnosis of rotatingmachinery[J]. Mechanical Systems and Signal Processing.2004,18(3):645-657.
[116]陈晓梅,孟晓风,乔仁晓.基于BNB-HSSE计算全体碰集的方法[J].仪器仪表学报.2010,31(1):61-67.
[117] Wandekokem ED, de Aquino Franzosi FT, Rauber TW, Varejao FM, Batista RJ. Data-drivenfault diagnosis of oil rig motor pumps applying automatic definition and selection of features[C]. IEEE International Symposium on Diagnostics for Electric Machines, Power Electronicsand Drives (SDEMPED).2009:1-7.
[118] Sabeti M, Boostani R, Katebi S, Price G. Selection of relevant features for EEG signalclassification of schizophrenic patients[J]. Biomedical Signal Processing and Control.2007,2(2):122-134.
[119] Dunn J. Some recent investigations of a new fuzzy partitioning algorithm and its application topattern classification problems[J]. Journal of Cybernetics.1974,(4):1-15.
[120]崔宝珍,王泽兵,潘宏侠.小波分析-模糊聚类法用于滚动轴承故障诊断[J].振动、测试与诊断.2008,28(2):151-154,183.
[121] Ye Z, Guoqiang C, Yang J, Zhang J, Shi Q, Zeng H. Fault diagnosis of railway rolling bearingbased on wavelet analysis and FCM[J]. International Journal of Digital Content Technology andits Applications.2011,5(3):47-58.
[122]蒋玲莉,刘义伦,李学军,陈安华. EMD模糊聚类法及在滚动轴承故障诊断中的应用[J].机械强度.2011,33(05):650-654.
[123] Duda RO, Hart PE, Stork DG. Pattern Classification2nd ed[M]. New York: Wiley.2001.
[124] He QP, Wang J. Fault detection using the k-nearest neighbor rule for semiconductormanufacturing processes[J]. IEEE Transactions on Semiconductor Manufacturing.2007,20(4):345-354.
[125] Haji M, Toliyat HA. Pattern recognition-A technique for induction machines rotor broken bardetection[J]. IEEE Transactions on Energy Conversion.2001,16(4):312-317.
[126] Huang Y, McMurran R, Dhadyalla G, Peter Jones R. Probability based vehicle fault diagnosis:Bayesian network method[J]. Journal of Intelligent Manufacturing.2008,19(3):301-311.
[127] Zeng L, Wang H. Machine-fault classification: A fuzzy-set approach[J]. The InternationalJournal of Advanced Manufacturing Technology.1991,6(1):83-93.
[128] Mechefske CK. Objective machinery fault diagnosis using fuzzy logic[J]. Mechanical Systemsand Signal Processing.1998,12(6):855-862.
[129] Jayaswal P, Verma SN, Wadhwani AK. Application of ANN, Fuzzy Logic and WaveletTransform in machine fault diagnosis using vibration signal analysis[J]. Journal of Quality inMaintenance Engineering.2010,16(2):190-213.
[130] Tang J, Hu Y, Lin T, Chen Y. Analog circuit fault diagnosis based on fuzzy support vectormachine and kernel density estimation [C].3rd International Conference on Advanced ComputerTheory and Engineering (ICACTE).2010:V4544-V4548.
[131] Wu Q. Hybrid fuzzy support vector classifier machine and modified genetic algorithm forautomatic car assembly fault diagnosis[J]. Expert Systems with Applications.2011,38(3):1457-1463.
[132] Bouhouche S, Laksir Yazid L, Hocine S, Bast J. Evaluation using onlinesupport-vector-machines and fuzzy reasoning. Application to condition monitoring of speedsrolling process[J]. Control Engineering Practice.2010,18(9):1060-1068.
[133] Venkatasubramanian V, Chan K. Neural network methodology for process fault diagnosis[J].AIChE Journal.1989,35(12):1993-2002.
[134] Part, Ling L, Huang Y, Qu L. Research on fault diagnosis based on BP neural network optimizedby chaos ant colony algorithm [J]. Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).2010:257-264.
[135] Vapnik VN. Statistical learning theory [M]. New York: Wiley.1998.
[136] Abbasion S, Rafsanjani A, Farshidianfar A, Irani N. Rolling element bearings multi-faultclassification based on the wavelet denoising and support vector machine[J]. MechanicalSystems and Signal Processing.2007,21(7):2933-2945.
[137] Cui J, Wang Y. A novel approach of analog circuit fault diagnosis using support vector machinesclassifier[J]. Measurement: Journal of the International Measurement Confederation.2011,44(1):281-289.
[138] Hu Q, He Z, Zhang Z, Zi Y. Fault diagnosis of rotating machinery based on improved waveletpackage transform and SVMs ensemble[J]. Mechanical Systems and Signal Processing.2007,21(2):688-705.
[139] Tipping ME. Sparse Bayesian Learning and the Relevance Vector Machine[J]. Journal ofMachine Learning Research.2001,1(3):211-244.
[140] He C, Liu C, Li Y, Yuan J. Intelligent fault diagnosis of rotating machinery based on multiplerelevance vector machines with variance radial basis function kernel[J]. Proceedings of theInstitution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.2011,225(7):1718-1729.
[141] De Martino F, de Borst AW, Valente G, Goebel R, Formisano E. Predicting EEG single trialresponses with simultaneous fMRI and Relevance Vector Machine regression[J]. NeuroImage.2011,56(2):826-836.
[142] Manimala K, Selvi K, Ahila R. Optimization techniques for improving power quality datamining using wavelet packet based support vector machine[J]. Neurocomputing.2012,77(1):36-47.
[143] Pedrycz W, Park B, Pizzi N. Identifying core sets of discriminatory features using particleswarm optimization[J]. Expert Systems with Applications.2009,36(3):4610-4616.
[144] Korürek M, Dogan B. ECG beat classification using particle swarm optimization and radialbasis function neural network[J]. Expert Systems with Applications.2010,37(12):7563-7569.
[145] Fei S. Diagnostic study on arrhythmia cordis based on particle swarm optimization-basedsupport vector machine[J]. Expert Systems with Applications.2010,37(10):6748-6752.
[146] Dorigo M, Gambardella LM. Ant colony system: A cooperative learning approach to thetraveling salesman problem[J]. Evolutionary Computation, IEEE Transactions on.1997,1(1):53-66.
[147] Kirkpatrick S. Optimization by simulated annealing: Quantitative studies[J]. Journal ofStatistical Physics.1984,34(5):975-986.
[148] Holland JH. Genetic algorithms[J]. ScientificAmerican.1992,267(1):66-72.
[149] Kalinli A, Acar MC, Gündüz Z. New approaches to determine the ultimate bearing capacity ofshallow foundations based on artificial neural networks and ant colony optimization[J].Engineering Geology.2011,117(1-2):29-38.
[150] Chou PH, Wu MJ, Chen KK. Integrating support vector machine and genetic algorithm toimplement dynamic wafer quality prediction system[J]. Expert Systems with Applications.2010,37(6):4413-4424.
[151]隋文涛,路长厚, Wang W,张丹.基于模拟退火与LSSVM的轴承故障诊断[J].振动.测试与诊断.2010,30(2):119-122,206.
[152] Polikar R, Udpa L, Udpa SS, Honavar V. Learn++: An incremental learning algorithm forsupervised neural networks[J]. IEEE Transactions on Systems, Man and Cybernetics Part C:Applications and Reviews.2001,31(4):497-508.
[153] Hua X, Ding S. Incremental learning algorithm for support vector data description[J]. Journal ofSoftware.2011,6(7):1166-1173.
[154] Duarte Jr EP, Pozo ATR, Nassu BT. Fault diagnosis of multiprocessor systems based on geneticand estimation of distribution algorithms: A performance evaluation[J]. International Journal onArtificial Intelligence Tools.2010,19(1):1-18.
[155]李世其,段学燕,刘燕.一种决策树增量学习算法在故障诊断中的应用[J].华中科技大学学报.2006,34(04):79-81.
[156]吴丹,金敏.基于容错度自适应支持向量机的液压泵故障诊断[J].中国机械工程.2011,22(21):2582-2587.
[157] Part, Vilakazi CB, Marwala T. Incremental learning and its application to bushing conditionmonitoring [J]. Lecture Notes in Computer Science (including subseries Lecture Notes inArtificial Intelligence and Lecture Notes in Bioinformatics).2007:1237-1246.
[158] Li Y, Pont MJ, Barrie Jones N. Improving the performance of radial basis function classifiers incondition monitoring and fault diagnosis applications where 'unknown' faults may occur[J].Pattern Recognition Letters.2002,23(5):569-577.
[159] Markou M, Singh S. Novelty detection: A review-Part1: Statistical approaches[J]. SignalProcessing.2003,83(12):2481-2497.
[160] Markou M, Singh S. Novelty detection: A review-Part2:: Neural network based approaches[J].Signal Processing.2003,83(12):2499-2521.
[161] Zorriassatine F, Al-Habaibeh A, Parkin RM, Jackson MR, Coy J. Novelty detection for practicalpattern recognition in condition monitoring of multivariate processes: A case study[J].International Journal of Advanced Manufacturing Technology.2005,25(9-10):954-963.
[162] Hadizadeh H, Shokouhi SB. Random texture defect detection using1-D hidden markov modelsbased on local binary patterns[C]. IEICE Transactions on Information and Systems.2008,E91-D(7):1937-1945.
[163] Filev DP, Tseng F. Real time novelty detection modeling for machine health prognostics [C].Annual Conference of the North American Fuzzy Information Processing Society (NAFIPS).2006:529-534.
[164] Viswanath P, Murty MN, Kambala S. An efficient Parzen-window based network intrusiondetector using a pattern synthesis technique [J]. Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).2005:799-804.
[165] Albrecht S, Busch J, Kloppenburg M, Metze F, Tavan P. Generalized radial basis functionnetworks for classification and novelty detection: Self-organization of optimal Bayesiandecision[J]. Neural Networks.2000,13(10):1075-1093.
[166] Pereira CMM, De Mello RF. Aradial basis function neural network approach to detect novelties:Applications on health datasets [C]. Joint Conferences on Pervasive Computing (JCPC).2009:143-148.
[167] Tax DMJ, Duin RPW. Support vector domain description[J]. Pattern Recognition Letters.1999,20(11-13):1191-1199.
[168] Pan Y, Chen J, Guo L. Robust bearing performance degradation assessment method based onimproved wavelet packet-support vector data description[J]. Mechanical Systems and SignalProcessing.2009,23(3):669-681.
[169]姜万录,牛慧峰,刘思远.免疫支持向量机复合故障诊断方法及试验研究[J].振动与冲击.2011,30(06):176-180,212.
[170] Chilengue Z, Dente JA, Branco PJC. An artificial immune system approach for fault detection inthe stator and rotor circuits of induction machines[J]. Electric Power Systems Research.2011,81(1):158-169.
[171]何创新.大型履带起重机远程精益监测与免疫智能诊断方法研究[D].上海:上海交通大学,2010.
[172] Donoho DL, Johnstone IM. Adapting to Unknown Smoothness Via Wavelet Shrinkage[J].Journal of the American Statistical Association.1995,90(432):1200-1224.
[173] Mallat S, Hwang WL. Singularity detection and processing with wavelets[J]. InformationTheory, IEEE Transactions on.1992,38(2):617-643.
[174] Politis DN, White H. Automatic block-length selection for the dependent bootstrap[J].Econometric Reviews.2004,23(1):53-70.
[175] Patton A, Politis DN, White H. Correction to “Automatic block-length selection for thedependent bootstrap”by D. Politis and H. White[J]. Econometric Reviews.2009,28(4):372-375.
[176] Gould AL. Sample size re-estimation: recent developments and practical considerations [J].Statistics in Medicine.2001,20(17-18):2625-2643.
[177] Lilliefors HW. On the Kolmogorov-Smirnov test for normality with mean and varianceunknown[J]. Journal of the American Statistical Association.1967:399-402.
[178] Ribeiro MV, Romano JMT, Duque CA. An improved method for signal processing andcompression in power quality evaluation[J]. IEEE Transactions on Power Delivery.2004,19(2):464-471.
[179] Loparo KA. Bearings vibration data set. Case Western ReserveUniversity(http://www.eecs.cwru.edu/laboratory/bearing/download.html).
[180] Rafiee J, Rafiee MA, Tse PW. Application of mother wavelet functions for automatic gear andbearing fault diagnosis[J]. Expert Systems with Applications.2010,37(6):4568-4579.
[181] Abramovich F, Benjamini Y. Adaptive thresholding of wavelet coefficients[J]. ComputationalStatistics and Data Analysis.1996,22(4):351-362.
[182] Dudoit S, van der Laan MJ. Multiple testing procedures with applications to genomics [M]. NewYork: Springer.2008.
[183] Storey JD. A direct approach to false discovery rates[J]. Journal of the Royal Statistical Society.Series B: Statistical Methodology.2002,64(3):479-498.
[184] Storey JD, Taylor JE, Siegmund D. Strong control, conservative point estimation andsimultaneous conservative consistency of false discovery rates: A unified approach[J]. Journal ofthe Royal Statistical Society. Series B: Statistical Methodology.2004,66(1):187-205.
[185] Benjamini Y, Krieger A, Yekutieli D. Adaptive linear step-up procedures that control the falsediscovery rate[J]. Biometrika.2006,93(3):491-507.
[186] Schweder T, Spj tvoll E. Plots of p-values to evaluate many tests simultaneously [J]. Biometrika.1982,69(3):493-502.
[187]张磊,潘泉.一种子波域滤波算法的改进[J].电子学报.1999,27(2):19-21.
[188] Shen X, Huang HC, Cressie N. Nonparametric hypothesis testing for a spatial signal[J]. Journalof the American Statistical Association.2002,97(460):1122-1140.
[189] Langaas M, Lindqvist BH, Ferkingstad E. Estimating the proportion of true null hypotheses,with application to DNA microarray data[J]. Journal of the Royal Statistical Society. Series B:Statistical Methodology.2005,67(4):555-572.
[190] Lei Y, He Z, Zi Y, Chen X. New clustering algorithm-based fault diagnosis using compensationdistance evaluation technique[J]. Mechanical Systems and Signal Processing.2008,22(2):419-435.
[191] Wendt H, Abry P, Jaffard S. Bootstrap for empirical multifractal analysis[J]. IEEE SignalProcessing Magazine.2007,24(4):38-48.
[192] Chhabra AB, Meneveau C, Jensen RV, Sreenivasan K. Direct determination of the f (α)singularity spectrum and its application to fully developed turbulence[J]. Physical Review A.1989,40(9):5284-5294.
[193] Wendt H, Roux SG, Jaffard S, Abry P. Wavelet leaders and bootstrap for multifractal analysis ofimages[J]. Signal Processing.2009,89(6):1100-1114.
[194] Abry P, Helgason H, Goncalvès P, Pereira E, Gaucherand P, Doret M. Multifractal analysis ofECG for intrapartum diagnosis of fetal asphyxia [C]. IEEE International Conference onAcoustics, Speech and Signal Processing (ICASSP).2010:566-569.
[195] Boser BE, Guyon IM, Vapnik VN. A training algorithm for optimal margin classifiers [C].Proceeding of the1992Fifth Annual ACM Workshop.1992:144-152.
[196] Yang J, Zhang Y. Application research of support vector machines in condition trend predictionof mechanical equipment[J]. Lecture Notes in Computer Science.2005,3498(III):857-864.
[197] Figliola A, Serrano E, Paccosi G, Rosenblatt M. About the effectiveness of different methods forthe estimation of the multifractal spectrum of natural series [J]. International Journal ofBifurcation and Chaos.2010,20(2):331-339.
[198] Jaffard S, Abry P, Roux S, Vedel B, Wendt H. The contribution of wavelets in multifractalanalysis[M]. A. Damlamian, S. Jaffard, L.T. Tsien (Eds.). Series in Contemporary AppliedMathematics. Higher Education Press, World Scientific Publishing.2009.
[199] Singh S, Markou M. An approach to novelty detection applied to the classification of imageregions[J]. IEEE Transactions on Knowledge and Data Engineering.2004,16(4):396-407.