振动故障远程诊断中的分形压缩及分形诊断技术研究
|
摘要
振动故障诊断是目前机械设备维护管理的基本措施之一,而振动故障远程诊断可以充分利用异地专家的知识与经验来解决现场无法解决的复杂故障问题,从而大大提高诊断的专业化水平。研究先进的信息压缩技术以及故障诊断方法,对于提高远程故障诊断的信息传输效率和故障诊断准确性有着非常重要的现实意义。分形理论作为数学思想的新发展,可以用于刻画对象的自相似性和不规则性,在处理非线性系统时具有独特的优点,因而已经成为研究非线性现象的重要工具。本文在分析了信息压缩与故障诊断方法研究现状的基础上,阐述了分形理论基本原理,并将分型理论应用于数据压缩与故障诊断中。针对振动故障信号的特点,提出了相应的分形压缩及分形故障诊断算法,通过转子试验台模拟试验以及实际故障振动数据进行了算法的验证,分析了几种典型故障的维数谱特征,为振动故障远程诊断的实现奠定了基础。
论文的主要工作包括:
1.在对分形压缩的理论基础进行分析研究的基础上,提出了适用于振动信号压缩的分段自仿射模型及算法,分析了模型中相关参数的取值规律,仿真算例及实测信号分析结果表明:该算法具有较高的数据压缩比和很好的信号重构精度,验证了模型的有效性;
2.在分析形态滤波器基本原理的基础上,针对振动信号中可能会夹杂的各类干扰,通过数值仿真和实例分析,详细分析研究了结构元素的形状、高度和宽度以及信号的采样频率对形态学滤波器滤波性能的影响,并根据实验数据得出了应用于振动信号处理的形态滤波器结构元素的设计策略;
3.在分析关联维数算法的基础上,对重构相空间的参数选择以及无标度区的确定两个问题进行了探讨。在对振动信号相关积分双对数点列的分布规律进行分析的基础上,提出了分形无标度区的曲线-直线-曲线拟合自动识别方法以及一种能客观计算振动信号时间序列关联维数的改进算法,并就噪声对信号关联维数计算结果的影响进行了分析,将该算法应用于转子试验台振动信号中,计算及分析结果验证了算法的有效性,表明关联维数可以作为设备状态的量化指标和故障特征量以完成故障诊断;
4.在分析多重分形的常见定义和一般算法的基础上,提出基于广义相关积分来计算多重分形谱的相关算法,该算法是单分形G-P关联维数算法在广义维数谱计算中的一种推广,并将该算法应用于实测振动信号中。计算及分析结果表明:与单一的关联维数相比,振动信号的多重分形谱对振动信号的特征表述更加全面和准确,可以敏感地反映设备运行状态的变化,从而为振动故障诊断提供了一种更有效的方法。
The vibration fault diagnosis is one of basic measures for mechanical device maintenance management, while vibration fault remote diagnosis can fully use the remote experts' knowledge and experience to solve some scene inextricability complex faults, thus greatly enhances the specialized level of diagnosis. The studies on advanced data compression technologies and fault diagnosis methods, have the very vital practical significance for improving the efficiency of information transmission and the accuracy of fault diagnosis in process of remote fault diagnosis. As a new development of mathematical, fractal theory can be used to characterize self-similarity and irregularity of object, and has unique advantages in the handling of nonlinear system, thus already became one of important tools to research nonlinear phenomenons. In this paper, the present situations of the data compression and fault diagnosis methods have been analyzed, while fractal theory was elaborated in the basic principle, and introduced into process of data compression and fault diagnosis respectively. In view of the vibration fault signal's characteristic, the corresponding fractal compression algorithm and the fractal fault diagnosis algorithm were proposed, and these algorithms were confirmed by vibration data sampled in simulation experiments of rotor test platform as well as the actual faults. In tests, multifractal dimension spectrum characteristics of several typical faults have been analyzed, to bottom for the realization of vibration fault remote diagnosis.
The main contribution can be summarized as follows:
1.A piecewise self-affine fractal model was explored for data compression of vibration signal based on the analysis of the theoretical basis on fractal compression. Applications of the model to actual vibration signals as well as simulation signals have been given with good results obtained in respect of data compression ratio and signal reconstruction precision, where estimation of the model parameters has been analyzed.
2.Based on the analysis of the basic principles of morphological filter, with respect to different types of interference possibly included in the vibration signals, the influences of the shape, width and amplitude of the structure element on the performance of morphological filters, and the influences of the vibration signals sampling rate on the size of structure element have been analyzed by numerical simulation and measured examples. By the analysis results, the general rule for shape, size of structure element on the design of morphological filter is elicited, which can be applied for de-noising and filtering of rotating machinery vibration signals.
3.Based on the analysis of the correlation dimension algorithm, the selection of the parameter of reconstructed phase space, as well as identification of scaleless bands were discussed. Then, an algorithm by curve-line-curve fitting piecewise is proposed for fractal scaleless band automatic identification, which is based on the study of the correlation integral algorithm and the distribution rule of the correlation integral series for vibration signal. While an improved algorithm, which can objectively calculate the correlation dimension of vibration signal time series was also proposed with analysis of the noise infulence on the vibration signal correlation dimension calculation results. Final, the correlation dimension calculation and analysis were acted on the rotor measured vibration signals, the results verified the effectiveness of the algorithm and indicated that the correlation dimension can be used as the quantitative index and fault eigenvalue to indicated the equipment status in fault diagnosis.
4.After analysis of the common definitions and general algorithms of multifractal, a new multifractal spectrum algorithm based on generalized correlation integral was proposed. The new algorithm is promotion of single-fractal correlation dimension G-P algorithm on the calculation of multifractal spectrum. By application on measured vibration signals, the result of calculation and analysis showed that compared to single correlation dimension, the multifractal spectrum of vibration signals can state the characteristic of vibration signals more comprehensive and accurate, be sensitive to reflect changes in the operational status of equipment, to provide a more effective method on vibration fault diagnosis.
论文的主要工作包括:
1.在对分形压缩的理论基础进行分析研究的基础上,提出了适用于振动信号压缩的分段自仿射模型及算法,分析了模型中相关参数的取值规律,仿真算例及实测信号分析结果表明:该算法具有较高的数据压缩比和很好的信号重构精度,验证了模型的有效性;
2.在分析形态滤波器基本原理的基础上,针对振动信号中可能会夹杂的各类干扰,通过数值仿真和实例分析,详细分析研究了结构元素的形状、高度和宽度以及信号的采样频率对形态学滤波器滤波性能的影响,并根据实验数据得出了应用于振动信号处理的形态滤波器结构元素的设计策略;
3.在分析关联维数算法的基础上,对重构相空间的参数选择以及无标度区的确定两个问题进行了探讨。在对振动信号相关积分双对数点列的分布规律进行分析的基础上,提出了分形无标度区的曲线-直线-曲线拟合自动识别方法以及一种能客观计算振动信号时间序列关联维数的改进算法,并就噪声对信号关联维数计算结果的影响进行了分析,将该算法应用于转子试验台振动信号中,计算及分析结果验证了算法的有效性,表明关联维数可以作为设备状态的量化指标和故障特征量以完成故障诊断;
4.在分析多重分形的常见定义和一般算法的基础上,提出基于广义相关积分来计算多重分形谱的相关算法,该算法是单分形G-P关联维数算法在广义维数谱计算中的一种推广,并将该算法应用于实测振动信号中。计算及分析结果表明:与单一的关联维数相比,振动信号的多重分形谱对振动信号的特征表述更加全面和准确,可以敏感地反映设备运行状态的变化,从而为振动故障诊断提供了一种更有效的方法。
The vibration fault diagnosis is one of basic measures for mechanical device maintenance management, while vibration fault remote diagnosis can fully use the remote experts' knowledge and experience to solve some scene inextricability complex faults, thus greatly enhances the specialized level of diagnosis. The studies on advanced data compression technologies and fault diagnosis methods, have the very vital practical significance for improving the efficiency of information transmission and the accuracy of fault diagnosis in process of remote fault diagnosis. As a new development of mathematical, fractal theory can be used to characterize self-similarity and irregularity of object, and has unique advantages in the handling of nonlinear system, thus already became one of important tools to research nonlinear phenomenons. In this paper, the present situations of the data compression and fault diagnosis methods have been analyzed, while fractal theory was elaborated in the basic principle, and introduced into process of data compression and fault diagnosis respectively. In view of the vibration fault signal's characteristic, the corresponding fractal compression algorithm and the fractal fault diagnosis algorithm were proposed, and these algorithms were confirmed by vibration data sampled in simulation experiments of rotor test platform as well as the actual faults. In tests, multifractal dimension spectrum characteristics of several typical faults have been analyzed, to bottom for the realization of vibration fault remote diagnosis.
The main contribution can be summarized as follows:
1.A piecewise self-affine fractal model was explored for data compression of vibration signal based on the analysis of the theoretical basis on fractal compression. Applications of the model to actual vibration signals as well as simulation signals have been given with good results obtained in respect of data compression ratio and signal reconstruction precision, where estimation of the model parameters has been analyzed.
2.Based on the analysis of the basic principles of morphological filter, with respect to different types of interference possibly included in the vibration signals, the influences of the shape, width and amplitude of the structure element on the performance of morphological filters, and the influences of the vibration signals sampling rate on the size of structure element have been analyzed by numerical simulation and measured examples. By the analysis results, the general rule for shape, size of structure element on the design of morphological filter is elicited, which can be applied for de-noising and filtering of rotating machinery vibration signals.
3.Based on the analysis of the correlation dimension algorithm, the selection of the parameter of reconstructed phase space, as well as identification of scaleless bands were discussed. Then, an algorithm by curve-line-curve fitting piecewise is proposed for fractal scaleless band automatic identification, which is based on the study of the correlation integral algorithm and the distribution rule of the correlation integral series for vibration signal. While an improved algorithm, which can objectively calculate the correlation dimension of vibration signal time series was also proposed with analysis of the noise infulence on the vibration signal correlation dimension calculation results. Final, the correlation dimension calculation and analysis were acted on the rotor measured vibration signals, the results verified the effectiveness of the algorithm and indicated that the correlation dimension can be used as the quantitative index and fault eigenvalue to indicated the equipment status in fault diagnosis.
4.After analysis of the common definitions and general algorithms of multifractal, a new multifractal spectrum algorithm based on generalized correlation integral was proposed. The new algorithm is promotion of single-fractal correlation dimension G-P algorithm on the calculation of multifractal spectrum. By application on measured vibration signals, the result of calculation and analysis showed that compared to single correlation dimension, the multifractal spectrum of vibration signals can state the characteristic of vibration signals more comprehensive and accurate, be sensitive to reflect changes in the operational status of equipment, to provide a more effective method on vibration fault diagnosis.
引文
[1]Jarventausta P., Verho P., Partanen J. Using fuzzy sets to model the uncertainty in the fault location process of distribution networks. Power Delivery, IEEE Transactions on, 1994, 9 (2) : 954-960.
[2]Caldwell N. H. M., Breton B. C., Halburn D. M. Remote instrument diagnosis on the Internet. Intelligent Systems and their Applications, IEEE, 1998, 13 (3) : 70-76.
[3]Arpaia P., Lucariello G., Zanesco A. Automatic Fault Isolation by Cultural Algorithms With Differential Influence. Instrumentation and Measurement, IEEE Transactions on, 2007, 56 (5) : 1573-1582.
[4]Hajji H. Statistical analysis of network traffic for adaptive faults detection. Neural Networks, IEEE Transactions on, 2005, 16 (5) : 1053-1063.
[5]Hossack J. A., Menal J., Mcarthur S. D. J., et al. A multiagent architecture for protection engineering diagnostic assistance. Power Systems, IEEE Transactions on, 2003, 18 (2) : 639- 647.
[6]Visinsky M. L., Cavallaro J. R., Walker I. D. A dynamic fault tolerance framework for remote robots. Robotics and Automation, IEEE Transactions on, 1995, 11 (4) : 477-490.
[7]Cabanas M. F., Melero M. G., Pedrayes F., et al. A New Online Method Based on Leakage Flux Analysis for the Early Detection and Location of Insulating Failures in Power Transformers: Application to Remote Condition Monitoring. Power Delivery, IEEE Transactions on, 2007, 22 (3) : 1591-1602.
[8]何岭松,王峻峰,杨叔子.基于因特网的设备故障远程协作诊断技术.中国机械工程,1999,10(3):336-338
[9]Li Hongsheng, Shi Tielin, Yang Shuzi, et al. Internet-based remote diagnosis: Concept, system architecture and prototype. Proceedings of the 3th World Congress on Intelligent Control and Automation, Jun 28-Jul 2 2000, : Institute of Electrical and Electronics Engineers Inc., 2000, 719-723.
[10]黎洪生,何岭松.基于因特网远程故障诊断系统架构.华中理工大学学报,2000,28(3):13-15
[11]袁楚明,陈幼平.机械制造设备远程监控与故障诊断技术.机械与电子,2001,(2):54-57
[12]袁楚明,陈幼平,周祖德.基于Internet的远程诊断系统体系结构研究.计算机工程与应用,2001,37(18):45-46
[13]袁楚明,张莉,陈幼平,等.制造企业基于Internet的设备远程诊断与维护系统研究.高技术通讯,2001,11(12):55-59
[14]田兴银,李斌.基于Internet的数控设备远程监测和故障诊断系统研究.计算机与现代化,2002,80(4):8-10
[15]蔡洌,陈幼平,李作清,等.现代制造系统远程故障诊断标准化研究.中国机械工程,2001,12(2):189-192
[16]来五星,李巍华.远程监测诊断系统中延时问题处理.计算机应用,2000,20(5):43-45
[17]张金玉.基于网络的远程诊断与处理支持中心的研究:[博士学位论文].西安:西安交通大学,2000
[18]袁小宏,李辛毅,屈梁生.基于因特网的设备远程诊断中心的设计.中国机械工程,2002,13(10):874-876
[19]张西宁,李艾华,屈梁生.大型回转机械实时在线监测和故障诊断网络系统的研制.机械科学与技术(西安),1998,17(5):817-819
[20]陆颂元,张跃进,童小忠,等.机组群振动状态实时监测故障诊断网络和远程传输系统技术研究.中国电力,2001,34(6):51-54
[21]舒赜,徐晓丽.大型旋转机械远程故障诊断系统RMRDS的研制.制造业自动化,1999,21(6):39-41
[22]蒋东翔,倪维斗,张春,等.电站热力系统远程在线监测与诊断网络系统.清华大学学报:自然科学版,2000,40(2):77-80
[23]孙海军,蒋东翔.基于INTRANET的发电机组远程监测与诊断系统.汽轮机技术,2001,43(4):203-204
[24]赵国华,王雪,谢歆.基于CORBA和智能代理的远程虚拟测试状态监测诊断系统.振动.测试与诊断,2001,21(2):95-99
[25]阳超平,张浩,吴启迪.PLC接入远程服务系统的方案及其实现.电子与自动化,2000,(1):17-20
[26]Ren Wei, Wang Jian, Zhang Hao, et al. The research of remote fault diagnosis system in manufacturing. Proceedings of the 3th World Congress on Intelligent Control and Automation, Jun 28-Jul 2 2000, : Institute of Electrical and Electronics Engineers Inc., 2000, 712-714.
[27]张荣涛.复杂装备远程智能监测,诊断与维护系统研究:[博士学位论文].南京:南京理工大学,2002
[28]刘桂雄,冯云庆,周德光,等.基于因特网的远程测试技术(I)—总体分析与规划.华南理工大学学报:自然科学版,2001,29(9):49-52
[29]冯云庆,刘桂雄,周德光,等.基于因特网的远程测试技术(Ⅱ)—服务器部分的关键技术.华南理工大学学报:自然科学版,2001,29(9):53-56
[30]刘桂雄,冯云庆,周德光,等.基于因特网的远程测试技术(Ⅲ)—客户端部分的关键技术.华南理工大学学报:自然科学版,2001,29(11):15-18
[31]李菊欢,林颖.基于B/S的远程故障诊断系统.现代制造工程,2001,(11):59-60
[32]陈希,楼佩煌.基于Internet的远程FMS故障诊断系统研究.南京航空航天大学学报,2000,32(1):57-62
[33]楼佩煌,陈希.基于Internet的FMS远程故障诊断技术.测控技术,1999,18(11):21-23
[34]楼佩煌,戴勇.基于Internet的远程故障诊断与维修向导系统研究.中国机械工程,2002,13(2):143-146
[35]袁洪芳.FMS设备远程故障诊断技术研究.兵工自动化,2002,21(2):1-4
[36]吴振锋,左洪福,张天宏.基于WEB的航空发动机故障远程诊断技术研究.应用基础与工程科学学报,2001,9(2):245-250
[37]黄向华,张天宏.基于虚拟仪器技术的设备远程故障诊断.测控技术,2002,21(4):34-36
[38]蒋瑜.基于军网的武器装备远程监测诊断系统的构建.兵工自动化,2000,19(4):4-7
[39]杨光,杨拥民,袁杰红,等.基于B/S模型的设备远程诊断系统的研究.测控技术,2001,20(06):16-18
[40]杨拥民,陈仲生.基于B/S模式的远程故障诊断系统.机电一体化,2000,6(6):64-66
[41]黄英,肖旭,魏急波.基于嵌入式Linux的远程监控系统的设计.电子工程师,2002,28(4):11-13
[42]刘坚,于德介,李德刚,等.面向设备e-维护的联盟框架研究.计算机集成制造系统,2005,11(1):145-150
[43]刘坚,于德介,李德刚,等.设备e-维护的系统框架与关键使能技术.中国机械工程,2004,15(13):1171-1176
[44]刘坚,于德介,李蓉,等.基于多Agent联盟框架的设备e-维护研究.湖南大学学报:自然科学版,2005,32(1):10-14
[45]石博强,申焱华.机械故障诊断的分形方法.北京:冶金工业出版社,2001
[46]Mallat S. G. A theory for multiresolution signal decomposition: the wavelet representation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 1989, 11 (7) : 674-693.
[47]Woods J., O'Neil S. Subband coding of images. Acoustics, Speech and Signal Processing, IEEE Transactions on, 1986, 34 (5) : 1278- 1288.
[48]Vetterli M., Herley C. Wavelets and filter banks: theory and design. Signal Processing, IEEE Transactions on, 1992, 40 (9) : 2207-2232.
[49]Aizawa K., Huang T. S. Model-based image coding advanced video coding techniques for very low bit-rate applications. Proceedings of the IEEE, 1995, 83 (2) : 259-271.
[50]Barnsley M. F., Rising H. Fractals Everywhere.: Morgan Kaufmann, 2000.
[51]Jacquin A. E. Image coding based on a fractal theory of iterated contractive image transformations. Image Processing, IEEE Transactions on, 1992, 1 (1) : 18-30.
[52]Williams R. F. Composition of contractions. Bulletin of the Brazilian Mathematical Society, 1971, 2 (2) : 55-59.
[53]Hutchinson J. E. Fractals and Self Similarity.: University of Melbourne, 1979.
[54]Barnsley M. F., Sloan A. D. A better way to compress images. Byte, 1988, 13 (1) : 215-223.
[55]Barnsley M. F., Hurd L. P., Anson L. F. Fractal image compression. Wellesley: AK Peters, 1993.
[56]Jacquin A. E. A Fractal Theory of Iterated Markov Operators with Applications to Digital Image Coding:[D]. Atlanta: Georgia Institute of Technology, 1989.
[57]Jacquin A. E. A novel fractal block-coding technique for digital images. 1990 International Conference on Acoustics, Speech, and Signal Processing, New Mexico, 1990, 2225-2228.
[58]Jacquin A. E. Fractal image coding based on a theory of iterated contractive image transformations. Proceedings of SPIE: Visual Communication and Image Processing, , 1990, 227-239.
[59]Mazel D. S., Hayes M. H. Using iterated function systems to model discrete sequences. Signal Processing, IEEE Transactions on, 1992, 40 (7) : 1724-1734.
[60]张正炳,朱光喜,朱耀庭.一维数字信号的自适应分形编码方法.信号处理,1996,12(1):23-27
[61]徐静波,于洪涛,冉崇森.基于二维空间的语音分形处理算法.声学学报,2006,31(2):109-113
[62]刘云鹏,律方成,李燕青.基于IFS的局部放电超声信号的数据压缩和模式识别.电工技术学报,2003,18(6):93-97
[63]刘云鹏,律方成,陈志业.局部放电超声信号的自仿射IFS模型.高电压技术,2002,28(10):23-25
[64]惠阿丽,林辉,贺博.用分形理论压缩和恢复高压绝缘子泄漏电流.高电压技术,2008,34(7):1395-1400
[65]李信富,李小凡.分形插值地震数据重建方法研究.地球物理学报,2008,51(4):1196-1201
[66]张朝晖,黄惟一.振动波形的分形判别及特征提取.东南大学学报:自然科学版,1999,29(4):26-29
[67]陈予恕.非线性振动系统的分叉和混沌理论.北京:高等教育出版杜,1993
[68]Candela R., Mirelli G., Schifani R. PD recognition by means of statistical and fractal parameters and aneural network. Dielectrics and Electrical Insulation, IEEE Transactions on, 2000, 7 (1) : 87-94.
[69]鲁宏伟,汤燕斌.分维数估计及其在机床颤振混沌研究中的应用.力学与实践,1995,17(4):46-48
[70]吕志民,徐金梧,翟绪圣.分形维数及其在滚动轴承故障的诊断中的应用.机械工程学报,1999,35(2):88-91
[71]姜建东,王晓升.分形几何在回转机械振动信号分析中的应用.中国机械工程,1998,9(10):39-41
[72]姜建东,王晓升,屈梁生.浑沌与分形动力学在机械故障诊断中的应用初探.中国机械工程,1998,9(7):31-34
[73]鄂春盛,蒋东翔.分形几何及其在汽轮机组振动故障征兆提取中的应用.汽轮机技术,1999,41(6):321-324
[74]汪慰军,陈进,吴昭同.关联维数在大型旋转机械故障诊断中的应用.振动工程学报,2000,13(2):229-234
[75]Grassberger P., Procaccia I. Characterization of Strange Attractors. Physical Review Letters, 1983, 50 (5) : 346-349.
[76]Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D: Nonlinear Phenomena, 1983, 9 (2) : 189-208.
[77]李舜酩,李香莲,许庆余.非线性裂纹转子的分形分析.机械科学与技术(西安),1999,18(6):874-877
[78]张清宇,严建华,倪明江,等.分形理论在火焰稳定性诊断中的应用.中国电机工程学报,2004,24(12):248-252
[79]成永红,谢小军,陈玉,等.气体绝缘系统中典型缺陷的超宽频带放电信号的分形分析.中国电机工程学报,2004,24(8):99-102
[80]刘占生,刘成敏,刘树春,等.小波分析和分形几何在转子动静碰摩故障诊断中的应用.哈尔滨工业大学学报,1999,31(1):55-56
[81]梁平,龙新峰,樊福梅.基于分形关联维的汽轮机转子的振动故障诊断.华南理工大学学报:自然科学版,2006,34(4):85-90
[82]汪慰军,陈进,吴昭同,等.关联维数的计算及其在大机组故障诊断中的应用.上海交通大学学报,2000,34(9):1265-1268
[83]张文明,李莉.滚动轴承故障诊断中的分形.北京科技大学学报,1996,18(3):215-219
[84]姜万录,陈东宁,姚成玉.关联维数分析方法及其在液压泵故障诊断中的应用.传感技术学报,2004,17(1):62-65
[85]蒋东翔,黄文虎,徐世昌.分形几何及其在旋转机械故障论断中的应用.哈尔滨工业大学学报,1996,28(2):27-31
[86]刘利娜,韩凤琴,张双全,等.水轮发电机组故障诊断系统中几种征兆的获取.华中科技大学学报:自然科学版,2003,31(3):86-88
[87]陈新,黄洪钟,黄文培,等.分形理论及其在机械工程中的应用.机械科学与技术(西安),2000,19(5):692-695
[88]马骥.分形几何在机械设备故障信号分析中的应用.机械设计与制造,2000,(6):54-55
[89]滕丽娜,陈兆能,佟德纯,等.关联维数在旋转机械支承系统状态监测中的应用.上海交通大学学报,2002,36(9):1377-1380
[90]姜建东,屈梁生.相关维数在大机组故障诊断中的应用.西安交通大学学报,1998,32(4):27-31
[91]肖云魁,李世义,曹亚娟,等.汽车传动轴振动信号分形维数计算.振动,测试与诊断,2005,25(1):43-47
[92]滕丽娜,刘天雄,佟德纯,等.关联维数在设备状态监测中的应用研究.振动工程学报,2002,15(4):399-403
[93]李娜,方彦军.利用关联维数分析机械系统故障信号.振动与冲击,2007,26(4):136-139
[94]夏勇,张振仁.内燃机振动信号的混沌分形特性研究.振动与冲击,2001,20(2):64-66
[95]蔡静之.特征提取在工况监测与故障诊断中的应用.重庆大学学报:自然科学版,2003,26(4):93-95
[96]Theiler J. Spurious dimension from correlation algorithms applied to limited time-series data. Physical Review A, 1986, 34 (3) : 2427-2432.
[97]Ding M., Grebogi C., Ott E., et al. Estimating correlation dimension from a chaotic time series: when does plateau onset occur?. Physica D: Nonlinear Phenomena, 1993, 69 (3-4) : 404-424.
[98]Galka A., Maa T., Pfister G. Estimating the dimension of high-dimensional attractors: A comparison between two algorithms. Physica D: Nonlinear Phenomena, 1998, 121 (3-4) : 237-251.
[99]Kitoh S., Kimura M., Mori T., et al. A fundamental bias in calculating dimensions from finite data sets. Physica D: Nonlinear Phenomena, 2000, 141 (3-4) : 171-182.
[100]Lai Y. C., Lerner D. Effective scaling regime for computing the correlation dimension from chaotic time series. Physica D: Nonlinear Phenomena, 1998, 115 (1-2) : 1-18.
[101]Pisarenko D. V., Pisarenko V. F. Statistical estimation of the correlation dimension. Physics Letters A, 1995, 197 (1) : 31-39.
[102]Theiler J. Statistical precision of dimension estimators. Physical Review A, 1990, 41 (6) : 3038-3051.
[103]Widman G., Lehnertz K., Jansen P., et al. A fast general purpose algorithm for the computation of auto-and cross-correlation integrals from single channel data. Physica D: Nonlinear Phenomena, 1998, 121 (1-2) : 65-74.
[104]Rosenstein M. T., Collins J. J., De Luca C. J. Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica D: Nonlinear Phenomena, 1994, 73 (1) : 82-98.
[105]林嘉宇,王跃科,黄芝平.语音信号相空间重构中的时间延迟的选择--复自相关法.信号处理,1999,15(3):220-225
[106]Fraser A. M., Swinney H. L. Independent coordinates for strange attractors from mutual information. Physical Review A, 1986, 33 (2) : 1134-1140.
[107]杨志安,王光瑞,陈式刚.用等间距格子法计算互信息函数确定延迟时间.计算物理,1995,12(4):443
[108]张雨,任成龙.确定重构相空间维数的方法.国防科技大学学报,2005,27(6):101-105
[109]Kennel M. B., Brown R., Abarbanel Hdi. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 1992, 45 (6) : 3403-3411.
[110]Cao L. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena, 1997, 110 (1-2) : 43-50.
[111]Kugiumtzis D. State space reconstruction parameters in the analysis of chaotic time series—the role of the time window length. Physica D: Nonlinear Phenomena, 1996, 95 (1) : 13-28.
[112]Kim H. S., Eykholt R., Salas J. D. Nonlinear dynamics, delay times, and embedding windows. Physica D: Nonlinear Phenomena, 1999, 127 (1-2) : 48-60.
[113]徐自励,王一扬,周激流.估计非线性时间序列嵌入延迟时间和延迟时间窗的CC平均方法.四川大学学报:工程科学版,2007,39(1):151-155
[114]陆振波,蔡志明,姜可宇.基于改进的C-C方法的相空间重构参数选择.系统仿真学报,2007,19(11):2527-2529
[115]Cellucci C. J., Albano A. M., Rapp P. E. Comparative study of embedding methods. Physical Review E, 2003, 67 (6-2) : 066210/1-066210/13.
[116]党建武,施怡,黄建国.分形研究中无标度区的计算机识别.计算机工程与应用,2003,25(3):25-27
[117]秦海勤,徐可君,江龙平.分形理论应用中无标度区自动识别方法.机械工程学报,2006,42(12):106-109
[118]汪富泉,罗朝盛.G-P算法的改进及其应用.计算物理,1993,10(3):345-351
[119]李后强,汪富泉.分形理论及其在分子科学中的应用.北京:科学出版社,1993
[120]程军圣,于德介,杨宇.基于EMD和分形维数的转子系统故障诊断.中国机械工程,2005,16(12):1088-1091
[121]陈平,李庆民.基于数学形态学的数字滤波器设计与分析.中国电机工程学报,2005,25(11):60-65
[122]林湘宁,刘沛,刘世明.电力系统超高速保护的形态学-小波综合滤波算法.中国电机工程学报,2002,22(9):19-24
[123]Nishida S., Nakamura M., Ikeda A., et al. Signal separation of background EEG and spike by using morphological filter. Medical Engineering and Physics, 1999, 21 (9) : 601-608.
[124]Sun Y., Chan K. L., Krishnan S. M. ECG signal conditioning by morphological filtering. Computers in Biology and Medicine, 2002, 32 (6) : 465-479.
[125]李刚,何宏献,刘巍,等.数学形态滤波器及其在心电图机中的应用.仪器仪表学报,1999,20(4):335-339
[126]胡爱军,唐贵基,安连锁.基于数学形态学的旋转机械振动信号降噪方法.机械工程学报,2006,42(4):127-130
[127]章立军,杨德斌,徐金梧,等.基于数学形态滤波的齿轮故障特征提取方法.机械工程学报,2007,43(2):71-75
[128]杜秋华,杨曙年.形态滤波在滚动轴承缺陷诊断中的应用.轴承,2005,(6):27-31
[129]Shouda J., Zheming L., Shenghe S. Morphological filter based noise removal from vibration signals of fighter plane. Proceedings of 2001 International Symposium on Intelligent Multimedia, Video and Speech, Hong Kong, 2001, 251-254.
[130]杨晓冬,朱铁光.分形理论在流体机械运行稳定性监测中的应用.流体机械,2004,32(4):4
[131]Arduini F., Fioravanti S., Giusto D. D. A multifractal-based approach to natural scene analysis. Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing, Piscataway, NJ, USA: Publ by IEEE, 1991, 2681-2684.
[132]Grassberger P. Generalized dimensions of strange attractors. Physics letters. A, 1983, 97 (6) : 227-230.
[133]周炜星,王延杰.多重分形奇异谱的几何特性:Ⅰ.经典Renyi定义法.华东理工大学学报:自然科学版,2000,26(4):385-389
[134]周炜星,吴韬.多重分形奇异谱的几何特性:Ⅱ.配分函数法.华东理工大学学报:自然科学版,2000,26(4):390-395
[135]王祖林,周荫清.多重分形谱及其计算.北京航空航天大学学报,2000,26(3):256-258
[136]Chhabra A., Jensen R. V. Direct determination of the f (α) singularity spectrum. Physical Review Letters, 1989, 62 (12) : 1327-1330.
[137]Grassberger P., Badii R., Politi A. Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors. Journal of Statistical Physics, 1988, 51 (1) : 135-178.
[138]朱令人,龙海英.地震多重分形计算的最小生成树法.地震学报,2000,22(4):410-417
[139]Du G., Yeo T. S. A novel multifractal estimation method and its application to remote image segmentation. Geoscience and Remote Sensing, IEEE Transactions on, 2002, 40 (4) : 980-982.
[140]Perrier Edith, Tarquis Ana M., Dathe Annette. A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory. Geoderma, 2006, 134 (3-4) : 284-294.
[141]Saucier Antoine, Richer Jacques, Muller Jiri. Assessing the scope of the multifractal approach to textural characterization with statistical reconstructions of images. Physica A: Statistical Mechanics and its Applications, 2002, 311 (1-2) : 231-259.
[142]Pesquet-Popescu B., Vehel J. L. Stochastic fractal models for image processing. Signal Processing Magazine, IEEE, 2002, 19 (5) : 48- 62.
[143]熊刚,孙霞.TiN/TaN多莫大的子力显微镜图像的多重分形谱.电子显微学报,2000,19(4):437-438
[144]Saucier Antoine, Muller Jiri. Using principal component analysis to enhance the generalized multifractal analysis approach to textural segmentation: Theory and application to microresistivity well logs. Physica A: Statistical Mechanics and its Applications, 2002, 309 (3-4) : 419-444.
[145]孙霞,熊刚.ZnO薄膜原子力显微镜图像的多重分形谱.物理学报,2000,49(5):854-862
[146]蒋爱平,杨悦华,杨兴全.基于多重加权法的多重分形图像分割研究.中国图象图形学报,2007,12(10):1889-1892
[147]李厚强,刘政凯,等.基于分形理论的航空图像分类方法.遥感学报,2001,5(5):353-357
[148]李厚强,刘政凯,等.一种彩色纹理图像的分割方法.计算机学报,2001,24(9):965-971
[149]Butoma B. G., Stolyarov I. D., Petrov A. M., et al. Immunological and multifractal ECG analysis and analysis of status in patients with progressive forms of schizophrenia and schizotypic disorders. International Journal of Psychophysiology, 2008, 69 (3) : 145-146.
[150]Nakamura T., Horio H., Chiba Y. Local Holder exponent analysis of heart rate variability in preterm infants. Biomedical Engineering, IEEE Transactions on, 2006, 53 (1) : 83-88.
[151]Yang Xiaodong, Ning Xinbao, Wang Jun. Multifractal analysis of human synchronous 12-lead ECG signals using multiple scale factors. Physica A: Statistical Mechanics and its Applications, 2007, 384 (2) : 413-422.
[152]Ying Chen, Nash M. P., Xinbao Ning, et al. Multifractal ECG Mapping of Ventricular Epicardium During Regional Ischemia in the Pig. Biomedical Engineering, IEEE Transactions on, 2006, 53 (10) : 1920-1925.
[153]Kiyono K., Struzik Z. R., Aoyagi N., et al. Multiscale probability density function analysis: non-Gaussian and scale-Invariant fluctuations of healthy human heart rate. Biomedical Engineering, IEEE Transactions on, 2006, 53 (1) : 95-102.
[154]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.物理学报,2008,57(3):1514-1521
[155]Riedi R. H., Crouse M. S., Ribeiro V. J., et al. A multifractal wavelet model with application to network traffic. Information Theory, IEEE Transactions on, 1999, 45 (3) : 992-1018.
[156]Takada H. H., Anzaloni A. A multifractual traffic policing mechanism. Communications Letters, IEEE, 2006, 10 (2) : 120- 122.
[157]Liangxiu Han, Zhiwei Cen, Chunbo Chu, et al. A new multifractal network traffic model. Chaos, Solitons & Fractals, 2002, 13 (7) : 1507-1513.
[158]Jianbao Gao, Rubin I. Multifractal analysis and modelling of VBR video traffic. Electronics Letters, 2000, 36 (3) : 278-279.
[159]Gao J., Rubin I. Statistical properties of multiplicative multifractal processes in modelling telecommunications traffic streams. Electronics Letters, 2000, 36 (1) : 101-102.
[160]Gao J., Rubin I. Superposition of multiplicative multifractal traffic processes. Electronics Letters, 2000, 36 (8) : 761-763.
[161]魏进武,汪斌强,邬江兴.多重分形网络流量的单队列输入排队性能研究.电子学报,2006,34(4):658-663
[162]黄晓东,周源华,张荣福,等.改进的基于乘法多重分形的视频流量模型.上海交通大学学报,2004,38(z1):178-181
[163]洪飞,吴志美.基于小波的多尺度网络流量预测模型.计算机学报,2006,29(1):166-170
[164]王升辉,裘正定.结合多重分形的网络流量非线性预测.通信学报,2007,28(2):45-50
[165]魏进武,邬江兴,陈庶樵.网络流量的联合多重分形模型及特性分析.电子学报,2004,32(9):1459-1463
[166]刘东林,帅典勋.网络流量模型的非线性特征量的提取及分析.电子学报,2003,31(12):1866-1869
[167]Kavasseri R. G., Nagarajan R. Evidence of crossover phenomena in wind-speed data. Circuits and Systems I: Regular Papers, IEEE Transactions on, 2004, 51 (11) : 2255- 2262.
[168]Kerman B. R. Information states in radar imagery of sea ice. Geoscience and Remote Sensing, IEEE Transactions on, 1999, 37 (3) : 1435-1446.
[169]Deidda R. Multifractal analysis and simulation of rainfall fields in space. Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere, 1999, 24 (1-2) : 73-78.
[170]Charalampidis D., Kasparis T., Jones W. L. Removal of nonprecipitation echoes in weather radar using multifractals and intensity. Geoscience and Remote Sensing, IEEE Transactions on, 2002, 40 (5) : 1121-1131.
[171]陈时军,孙龙梅,马丽.板内与板间地震活动时空分布的多重分形特征研究.地震学报,2007,29(1):38-47
[172]汪秉宏.地震的多重分形统计特征研究.地球科学进展,1997,12(6):535-540
[173]朱令人,周仕勇.地震多重分形标度指数谱f(α)的研究.西北地震学报,1992,14(2):30-35
[174]汪秉宏,李东升.地震分布多重分形特征的中期预报意义探讨.地震学刊,1998,(1):9-18
[175]朱令人,周仕勇.地震复杂性前兆与强震多重分形谱异常.地震,1997,17(4):331-339
[176]朱令人,杨马陵.地震时间序列多重分形计算精度估计.中国地震,2000,16(2):166-175
[177]安镇文,杨翠华,王琳瑛,等.地震时空丛集的多重分形研究.地球物理学报,2000,43(1):74-80
[178]王琳瑛,朱传镇,黄容良.地震时空分布结构的多重分形特征的研究.地震,1994,(5):11-19
[179]陈时军,Davidharte,王丽凤,等.广义地震应变能释放的多重分形特征.地震学报,2003,25(2):182-190
[180]蔡强,周成虎,等.华北地震时空多重分形的时间演化特征研究.地震,2002,22(2):74-80
[181]朱令人,龙海英.离散点集(地震)空间分布多重分形计算的精度估算.地震,2000,20(3):1-8
[182]王安东,顾浩鼎.辽宁地区地震活动空间分布的多重分形.地震学报,1996,18(1):34-43
[183]陈时军,马丽,王丽凤,等.强震前后广义地震应变释放过程的丛集特征.地震,2003,23(2):29-38
[184]陈时军,Davidharte,马丽,等.新西兰地区地震活动时空分布的多重分形特征研究.地震学报,2003,25(3):298-307
[185]陈怡然,周轶尘.发动机振动诊断中的多重分形法.内燃机学报,1997,15(1):114-119
[186]黄海英,黄建波,原培新.基于多重分形广义维数的机械故障诊断方法.军械工程学院学报,2001,13(3):30-34
[187]刘彬,王霄,谢平.基于小波多重分形的复杂机械故障诊断方法研究.传感技术学报,2006,19(1):232-234
[188]王金东,李新伟,张忠臣,等.往复压缩机多重分形故障特征提取.压缩机技术,2008,:12-14
[189]徐玉秀,钟建军,闻邦椿.旋转机械动态特性的分形特征及故障诊断.机械工程学报,2005,41(12):186-189
[190]苑宇,马孝江.局域波时频域多重分形在故障诊断中的应用.振动与冲击,2007,26(5):60-63
[191]金萍,陈怡然.内燃机表面振动信号的性质.天津大学学报:自然科学与工程技术版,2000,33(1):63-68
[192]李国宾,段树林,于洪亮,等.发动机振动信号特征参数的多重分形研究.内燃机学报,2008,26(1):87-91
[193]李国宾,关德林.振动信号多重分形分析改进算法.测试技术学报,2006,20(6):543-548
[194]李舜酩,高德平.裂纹转子非线性振动特征的谐波小波与分形识别.航空动力学报,2004,19(5):581-586
[195]彭志科,何永勇,等.小波多重分析及其在振动信号分析中应用的研究.机械工程学报,2002,38(8):59-63
[196]张小明,刘建敏,乔新勇,等.柴油机缸盖振动信号关联维数的影响因素分析.装甲兵工程学院学报,2008,(1):42-45, 95
[197]Mandelbrot B. B. Fractals: Form Chance and Dimension. San Francisco: Freeman, 1977.
[198]Mandelbrot B. B. Les Objects Fractals: Forme Hasard et Dimension. Paris: Flammarion, 1975.
[199]Mandeibrot B. B. The Fractal Geometry of Nature. San Francisco: Feeman, 1982.
[200]谢和平,薛秀谦.分形应用中的数学基础与方法.北京:科学出版社,1997
[201]Falconer K J,曾文曲等译.分形几何数学基础及其应用.沈阳:东北工学院出版社,1991
[202]谢和平等编译.分形几何数学基础与应用.重庆:重庆大学出版社,1991
[203]文志英.分形几何的数学基础.上海:上海科技教育出版社,2000
[204]董连科.分形理论及其应用.沈阳:辽宁科学技术出版社,1991
[205]王东升,曹磊.混沌,分形及其应用.合肥:中国科学技术大学出版社,1995
[206]Lorenz E N.混沌的本质.北京:气象出版社,1997
[207]刘秉正.非线性动力学与混沌基础.长春:东北师范大学出版杜,1995
[208]龙运佳.混沌振动研究.北京:清华大学出版社,1997
[209]崔屹.图像处理和分析--数学形态学方法及应用.北京:科学出版社,2000
[210]Pitas I., Venetsanopoulos A. N. Nonlinear Digital Filters: Principles and Applications. Boston: Kluwer Academic Pub, 1990.
[211]Serra J. Image analysis and mathematical morphology. Newyork: Academic Press, 1982.
[212]Haralick R. M., Sternberg S. R., Zhuang X. Image analysis using mathematical morphology. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, 9 (4) : 532-550.
[213]Serre J. Image analysis and mathematical morphology. Vol. 2, Theoretical advances. London: Academic Press, 1988.
[214]Giardina C. R., Dougherty E. R. Morphological Methods in Image and Signal Processing. Englewood Cliffs, New Jersey: Prentice-Hall, 1988.
[215]Maragos P., Schafer R. Morphological filters--Part I: Their set-theoretic analysis and relations to linear shift-invariant filters. Acoustics, Speech, and Signal Processing, IEEE Transactions on, 1987, 35 (8) : 1153-1169.
[216]Maragos P., Schafer R. Morphological filters--Part II: Their relations to median, order-statistic, and stack filters. Acoustics, Speech, and Signal Processing, IEEE Transactions on, 1987, 35 (8) : 1170-1184.
[217]赵春晖.数学形态滤波器理论及其算法研究:[博士学位论文].哈尔滨:哈尔滨工业大学,1998
[218]陈铿,韩伯棠.混沌时间序列分析中的相空间重构技术综述.计算机科学,2005,32(4):67-70
[219]Packard N. H., Crutchfield J. P., Farmer J. D., et al. Geometry from a Time Series. Physical Review Letters, 1980, 45 (9) : 712-716.
[220]Takens F. Detecting strange attractors in turbulence. Lecture Notes in Mathematics, 1981, 898 (1) : 366-381.
[221]Albano A. M., Passamante A., Farrell Mary Eileen. Using higher-order correlations to define an embedding window. Physica D: Nonlinear Phenomena, 1991, 54 (1-2) : 85-97.
[222]Buzug T., Pfister G. Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors. Physical Review A, 1992, 45 (10) : 7073-7084.
[223]Buzug T., Pfister G. Comparison of algorithms calculating optimal embedding parameters for delay time coordinates. Physica D: Nonlinear Phenomena, 1992, 58 (1-4) : 127-137.
[224]Kember G., Fowler A. C. A correlation function for choosing time delays in phase portrait reconstructions. Physics letters. A, 1993, 179 (2) : 72-80.
[225]Falconer K J,曾文曲等译.分形几何中的技巧.沈阳:东北大学出版社,1999,323
[226]辛厚文.分形理论及其应用.合肥:中国科学技术大学出版社,1993
[227]陈顒.非线性科学在地震预报中的应用.北京:地震出版社,1992
[228]Hua L., Zejun D., Ziqin W. Multifractal behavior of the distribution of secondary-electron-emission sites on solid surfaces. Physical Review B, 1995, 51 (19) : 13554-13559.
[229]Hua L., Ze-Jun D., Ziqin W. Multifractal analysis of the spatial distribution of secondary-electron emission sites. Physical Review B, 1996, 53 (24) : 16631-16636.
[230]Lee C. K., Lee S. L. Multifractal scaling analysis of reactions over fractal surfaces. Surface science, 1995, 325 (3) : 294-310.
[231]Bing W., Yan W., Ziqin W. Multifractal behavior of solid-on-solid growth. Solid State Communications, 1995, 96 (2) : 69-72.
[2]Caldwell N. H. M., Breton B. C., Halburn D. M. Remote instrument diagnosis on the Internet. Intelligent Systems and their Applications, IEEE, 1998, 13 (3) : 70-76.
[3]Arpaia P., Lucariello G., Zanesco A. Automatic Fault Isolation by Cultural Algorithms With Differential Influence. Instrumentation and Measurement, IEEE Transactions on, 2007, 56 (5) : 1573-1582.
[4]Hajji H. Statistical analysis of network traffic for adaptive faults detection. Neural Networks, IEEE Transactions on, 2005, 16 (5) : 1053-1063.
[5]Hossack J. A., Menal J., Mcarthur S. D. J., et al. A multiagent architecture for protection engineering diagnostic assistance. Power Systems, IEEE Transactions on, 2003, 18 (2) : 639- 647.
[6]Visinsky M. L., Cavallaro J. R., Walker I. D. A dynamic fault tolerance framework for remote robots. Robotics and Automation, IEEE Transactions on, 1995, 11 (4) : 477-490.
[7]Cabanas M. F., Melero M. G., Pedrayes F., et al. A New Online Method Based on Leakage Flux Analysis for the Early Detection and Location of Insulating Failures in Power Transformers: Application to Remote Condition Monitoring. Power Delivery, IEEE Transactions on, 2007, 22 (3) : 1591-1602.
[8]何岭松,王峻峰,杨叔子.基于因特网的设备故障远程协作诊断技术.中国机械工程,1999,10(3):336-338
[9]Li Hongsheng, Shi Tielin, Yang Shuzi, et al. Internet-based remote diagnosis: Concept, system architecture and prototype. Proceedings of the 3th World Congress on Intelligent Control and Automation, Jun 28-Jul 2 2000, : Institute of Electrical and Electronics Engineers Inc., 2000, 719-723.
[10]黎洪生,何岭松.基于因特网远程故障诊断系统架构.华中理工大学学报,2000,28(3):13-15
[11]袁楚明,陈幼平.机械制造设备远程监控与故障诊断技术.机械与电子,2001,(2):54-57
[12]袁楚明,陈幼平,周祖德.基于Internet的远程诊断系统体系结构研究.计算机工程与应用,2001,37(18):45-46
[13]袁楚明,张莉,陈幼平,等.制造企业基于Internet的设备远程诊断与维护系统研究.高技术通讯,2001,11(12):55-59
[14]田兴银,李斌.基于Internet的数控设备远程监测和故障诊断系统研究.计算机与现代化,2002,80(4):8-10
[15]蔡洌,陈幼平,李作清,等.现代制造系统远程故障诊断标准化研究.中国机械工程,2001,12(2):189-192
[16]来五星,李巍华.远程监测诊断系统中延时问题处理.计算机应用,2000,20(5):43-45
[17]张金玉.基于网络的远程诊断与处理支持中心的研究:[博士学位论文].西安:西安交通大学,2000
[18]袁小宏,李辛毅,屈梁生.基于因特网的设备远程诊断中心的设计.中国机械工程,2002,13(10):874-876
[19]张西宁,李艾华,屈梁生.大型回转机械实时在线监测和故障诊断网络系统的研制.机械科学与技术(西安),1998,17(5):817-819
[20]陆颂元,张跃进,童小忠,等.机组群振动状态实时监测故障诊断网络和远程传输系统技术研究.中国电力,2001,34(6):51-54
[21]舒赜,徐晓丽.大型旋转机械远程故障诊断系统RMRDS的研制.制造业自动化,1999,21(6):39-41
[22]蒋东翔,倪维斗,张春,等.电站热力系统远程在线监测与诊断网络系统.清华大学学报:自然科学版,2000,40(2):77-80
[23]孙海军,蒋东翔.基于INTRANET的发电机组远程监测与诊断系统.汽轮机技术,2001,43(4):203-204
[24]赵国华,王雪,谢歆.基于CORBA和智能代理的远程虚拟测试状态监测诊断系统.振动.测试与诊断,2001,21(2):95-99
[25]阳超平,张浩,吴启迪.PLC接入远程服务系统的方案及其实现.电子与自动化,2000,(1):17-20
[26]Ren Wei, Wang Jian, Zhang Hao, et al. The research of remote fault diagnosis system in manufacturing. Proceedings of the 3th World Congress on Intelligent Control and Automation, Jun 28-Jul 2 2000, : Institute of Electrical and Electronics Engineers Inc., 2000, 712-714.
[27]张荣涛.复杂装备远程智能监测,诊断与维护系统研究:[博士学位论文].南京:南京理工大学,2002
[28]刘桂雄,冯云庆,周德光,等.基于因特网的远程测试技术(I)—总体分析与规划.华南理工大学学报:自然科学版,2001,29(9):49-52
[29]冯云庆,刘桂雄,周德光,等.基于因特网的远程测试技术(Ⅱ)—服务器部分的关键技术.华南理工大学学报:自然科学版,2001,29(9):53-56
[30]刘桂雄,冯云庆,周德光,等.基于因特网的远程测试技术(Ⅲ)—客户端部分的关键技术.华南理工大学学报:自然科学版,2001,29(11):15-18
[31]李菊欢,林颖.基于B/S的远程故障诊断系统.现代制造工程,2001,(11):59-60
[32]陈希,楼佩煌.基于Internet的远程FMS故障诊断系统研究.南京航空航天大学学报,2000,32(1):57-62
[33]楼佩煌,陈希.基于Internet的FMS远程故障诊断技术.测控技术,1999,18(11):21-23
[34]楼佩煌,戴勇.基于Internet的远程故障诊断与维修向导系统研究.中国机械工程,2002,13(2):143-146
[35]袁洪芳.FMS设备远程故障诊断技术研究.兵工自动化,2002,21(2):1-4
[36]吴振锋,左洪福,张天宏.基于WEB的航空发动机故障远程诊断技术研究.应用基础与工程科学学报,2001,9(2):245-250
[37]黄向华,张天宏.基于虚拟仪器技术的设备远程故障诊断.测控技术,2002,21(4):34-36
[38]蒋瑜.基于军网的武器装备远程监测诊断系统的构建.兵工自动化,2000,19(4):4-7
[39]杨光,杨拥民,袁杰红,等.基于B/S模型的设备远程诊断系统的研究.测控技术,2001,20(06):16-18
[40]杨拥民,陈仲生.基于B/S模式的远程故障诊断系统.机电一体化,2000,6(6):64-66
[41]黄英,肖旭,魏急波.基于嵌入式Linux的远程监控系统的设计.电子工程师,2002,28(4):11-13
[42]刘坚,于德介,李德刚,等.面向设备e-维护的联盟框架研究.计算机集成制造系统,2005,11(1):145-150
[43]刘坚,于德介,李德刚,等.设备e-维护的系统框架与关键使能技术.中国机械工程,2004,15(13):1171-1176
[44]刘坚,于德介,李蓉,等.基于多Agent联盟框架的设备e-维护研究.湖南大学学报:自然科学版,2005,32(1):10-14
[45]石博强,申焱华.机械故障诊断的分形方法.北京:冶金工业出版社,2001
[46]Mallat S. G. A theory for multiresolution signal decomposition: the wavelet representation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 1989, 11 (7) : 674-693.
[47]Woods J., O'Neil S. Subband coding of images. Acoustics, Speech and Signal Processing, IEEE Transactions on, 1986, 34 (5) : 1278- 1288.
[48]Vetterli M., Herley C. Wavelets and filter banks: theory and design. Signal Processing, IEEE Transactions on, 1992, 40 (9) : 2207-2232.
[49]Aizawa K., Huang T. S. Model-based image coding advanced video coding techniques for very low bit-rate applications. Proceedings of the IEEE, 1995, 83 (2) : 259-271.
[50]Barnsley M. F., Rising H. Fractals Everywhere.: Morgan Kaufmann, 2000.
[51]Jacquin A. E. Image coding based on a fractal theory of iterated contractive image transformations. Image Processing, IEEE Transactions on, 1992, 1 (1) : 18-30.
[52]Williams R. F. Composition of contractions. Bulletin of the Brazilian Mathematical Society, 1971, 2 (2) : 55-59.
[53]Hutchinson J. E. Fractals and Self Similarity.: University of Melbourne, 1979.
[54]Barnsley M. F., Sloan A. D. A better way to compress images. Byte, 1988, 13 (1) : 215-223.
[55]Barnsley M. F., Hurd L. P., Anson L. F. Fractal image compression. Wellesley: AK Peters, 1993.
[56]Jacquin A. E. A Fractal Theory of Iterated Markov Operators with Applications to Digital Image Coding:[D]. Atlanta: Georgia Institute of Technology, 1989.
[57]Jacquin A. E. A novel fractal block-coding technique for digital images. 1990 International Conference on Acoustics, Speech, and Signal Processing, New Mexico, 1990, 2225-2228.
[58]Jacquin A. E. Fractal image coding based on a theory of iterated contractive image transformations. Proceedings of SPIE: Visual Communication and Image Processing, , 1990, 227-239.
[59]Mazel D. S., Hayes M. H. Using iterated function systems to model discrete sequences. Signal Processing, IEEE Transactions on, 1992, 40 (7) : 1724-1734.
[60]张正炳,朱光喜,朱耀庭.一维数字信号的自适应分形编码方法.信号处理,1996,12(1):23-27
[61]徐静波,于洪涛,冉崇森.基于二维空间的语音分形处理算法.声学学报,2006,31(2):109-113
[62]刘云鹏,律方成,李燕青.基于IFS的局部放电超声信号的数据压缩和模式识别.电工技术学报,2003,18(6):93-97
[63]刘云鹏,律方成,陈志业.局部放电超声信号的自仿射IFS模型.高电压技术,2002,28(10):23-25
[64]惠阿丽,林辉,贺博.用分形理论压缩和恢复高压绝缘子泄漏电流.高电压技术,2008,34(7):1395-1400
[65]李信富,李小凡.分形插值地震数据重建方法研究.地球物理学报,2008,51(4):1196-1201
[66]张朝晖,黄惟一.振动波形的分形判别及特征提取.东南大学学报:自然科学版,1999,29(4):26-29
[67]陈予恕.非线性振动系统的分叉和混沌理论.北京:高等教育出版杜,1993
[68]Candela R., Mirelli G., Schifani R. PD recognition by means of statistical and fractal parameters and aneural network. Dielectrics and Electrical Insulation, IEEE Transactions on, 2000, 7 (1) : 87-94.
[69]鲁宏伟,汤燕斌.分维数估计及其在机床颤振混沌研究中的应用.力学与实践,1995,17(4):46-48
[70]吕志民,徐金梧,翟绪圣.分形维数及其在滚动轴承故障的诊断中的应用.机械工程学报,1999,35(2):88-91
[71]姜建东,王晓升.分形几何在回转机械振动信号分析中的应用.中国机械工程,1998,9(10):39-41
[72]姜建东,王晓升,屈梁生.浑沌与分形动力学在机械故障诊断中的应用初探.中国机械工程,1998,9(7):31-34
[73]鄂春盛,蒋东翔.分形几何及其在汽轮机组振动故障征兆提取中的应用.汽轮机技术,1999,41(6):321-324
[74]汪慰军,陈进,吴昭同.关联维数在大型旋转机械故障诊断中的应用.振动工程学报,2000,13(2):229-234
[75]Grassberger P., Procaccia I. Characterization of Strange Attractors. Physical Review Letters, 1983, 50 (5) : 346-349.
[76]Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D: Nonlinear Phenomena, 1983, 9 (2) : 189-208.
[77]李舜酩,李香莲,许庆余.非线性裂纹转子的分形分析.机械科学与技术(西安),1999,18(6):874-877
[78]张清宇,严建华,倪明江,等.分形理论在火焰稳定性诊断中的应用.中国电机工程学报,2004,24(12):248-252
[79]成永红,谢小军,陈玉,等.气体绝缘系统中典型缺陷的超宽频带放电信号的分形分析.中国电机工程学报,2004,24(8):99-102
[80]刘占生,刘成敏,刘树春,等.小波分析和分形几何在转子动静碰摩故障诊断中的应用.哈尔滨工业大学学报,1999,31(1):55-56
[81]梁平,龙新峰,樊福梅.基于分形关联维的汽轮机转子的振动故障诊断.华南理工大学学报:自然科学版,2006,34(4):85-90
[82]汪慰军,陈进,吴昭同,等.关联维数的计算及其在大机组故障诊断中的应用.上海交通大学学报,2000,34(9):1265-1268
[83]张文明,李莉.滚动轴承故障诊断中的分形.北京科技大学学报,1996,18(3):215-219
[84]姜万录,陈东宁,姚成玉.关联维数分析方法及其在液压泵故障诊断中的应用.传感技术学报,2004,17(1):62-65
[85]蒋东翔,黄文虎,徐世昌.分形几何及其在旋转机械故障论断中的应用.哈尔滨工业大学学报,1996,28(2):27-31
[86]刘利娜,韩凤琴,张双全,等.水轮发电机组故障诊断系统中几种征兆的获取.华中科技大学学报:自然科学版,2003,31(3):86-88
[87]陈新,黄洪钟,黄文培,等.分形理论及其在机械工程中的应用.机械科学与技术(西安),2000,19(5):692-695
[88]马骥.分形几何在机械设备故障信号分析中的应用.机械设计与制造,2000,(6):54-55
[89]滕丽娜,陈兆能,佟德纯,等.关联维数在旋转机械支承系统状态监测中的应用.上海交通大学学报,2002,36(9):1377-1380
[90]姜建东,屈梁生.相关维数在大机组故障诊断中的应用.西安交通大学学报,1998,32(4):27-31
[91]肖云魁,李世义,曹亚娟,等.汽车传动轴振动信号分形维数计算.振动,测试与诊断,2005,25(1):43-47
[92]滕丽娜,刘天雄,佟德纯,等.关联维数在设备状态监测中的应用研究.振动工程学报,2002,15(4):399-403
[93]李娜,方彦军.利用关联维数分析机械系统故障信号.振动与冲击,2007,26(4):136-139
[94]夏勇,张振仁.内燃机振动信号的混沌分形特性研究.振动与冲击,2001,20(2):64-66
[95]蔡静之.特征提取在工况监测与故障诊断中的应用.重庆大学学报:自然科学版,2003,26(4):93-95
[96]Theiler J. Spurious dimension from correlation algorithms applied to limited time-series data. Physical Review A, 1986, 34 (3) : 2427-2432.
[97]Ding M., Grebogi C., Ott E., et al. Estimating correlation dimension from a chaotic time series: when does plateau onset occur?. Physica D: Nonlinear Phenomena, 1993, 69 (3-4) : 404-424.
[98]Galka A., Maa T., Pfister G. Estimating the dimension of high-dimensional attractors: A comparison between two algorithms. Physica D: Nonlinear Phenomena, 1998, 121 (3-4) : 237-251.
[99]Kitoh S., Kimura M., Mori T., et al. A fundamental bias in calculating dimensions from finite data sets. Physica D: Nonlinear Phenomena, 2000, 141 (3-4) : 171-182.
[100]Lai Y. C., Lerner D. Effective scaling regime for computing the correlation dimension from chaotic time series. Physica D: Nonlinear Phenomena, 1998, 115 (1-2) : 1-18.
[101]Pisarenko D. V., Pisarenko V. F. Statistical estimation of the correlation dimension. Physics Letters A, 1995, 197 (1) : 31-39.
[102]Theiler J. Statistical precision of dimension estimators. Physical Review A, 1990, 41 (6) : 3038-3051.
[103]Widman G., Lehnertz K., Jansen P., et al. A fast general purpose algorithm for the computation of auto-and cross-correlation integrals from single channel data. Physica D: Nonlinear Phenomena, 1998, 121 (1-2) : 65-74.
[104]Rosenstein M. T., Collins J. J., De Luca C. J. Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica D: Nonlinear Phenomena, 1994, 73 (1) : 82-98.
[105]林嘉宇,王跃科,黄芝平.语音信号相空间重构中的时间延迟的选择--复自相关法.信号处理,1999,15(3):220-225
[106]Fraser A. M., Swinney H. L. Independent coordinates for strange attractors from mutual information. Physical Review A, 1986, 33 (2) : 1134-1140.
[107]杨志安,王光瑞,陈式刚.用等间距格子法计算互信息函数确定延迟时间.计算物理,1995,12(4):443
[108]张雨,任成龙.确定重构相空间维数的方法.国防科技大学学报,2005,27(6):101-105
[109]Kennel M. B., Brown R., Abarbanel Hdi. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 1992, 45 (6) : 3403-3411.
[110]Cao L. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena, 1997, 110 (1-2) : 43-50.
[111]Kugiumtzis D. State space reconstruction parameters in the analysis of chaotic time series—the role of the time window length. Physica D: Nonlinear Phenomena, 1996, 95 (1) : 13-28.
[112]Kim H. S., Eykholt R., Salas J. D. Nonlinear dynamics, delay times, and embedding windows. Physica D: Nonlinear Phenomena, 1999, 127 (1-2) : 48-60.
[113]徐自励,王一扬,周激流.估计非线性时间序列嵌入延迟时间和延迟时间窗的CC平均方法.四川大学学报:工程科学版,2007,39(1):151-155
[114]陆振波,蔡志明,姜可宇.基于改进的C-C方法的相空间重构参数选择.系统仿真学报,2007,19(11):2527-2529
[115]Cellucci C. J., Albano A. M., Rapp P. E. Comparative study of embedding methods. Physical Review E, 2003, 67 (6-2) : 066210/1-066210/13.
[116]党建武,施怡,黄建国.分形研究中无标度区的计算机识别.计算机工程与应用,2003,25(3):25-27
[117]秦海勤,徐可君,江龙平.分形理论应用中无标度区自动识别方法.机械工程学报,2006,42(12):106-109
[118]汪富泉,罗朝盛.G-P算法的改进及其应用.计算物理,1993,10(3):345-351
[119]李后强,汪富泉.分形理论及其在分子科学中的应用.北京:科学出版社,1993
[120]程军圣,于德介,杨宇.基于EMD和分形维数的转子系统故障诊断.中国机械工程,2005,16(12):1088-1091
[121]陈平,李庆民.基于数学形态学的数字滤波器设计与分析.中国电机工程学报,2005,25(11):60-65
[122]林湘宁,刘沛,刘世明.电力系统超高速保护的形态学-小波综合滤波算法.中国电机工程学报,2002,22(9):19-24
[123]Nishida S., Nakamura M., Ikeda A., et al. Signal separation of background EEG and spike by using morphological filter. Medical Engineering and Physics, 1999, 21 (9) : 601-608.
[124]Sun Y., Chan K. L., Krishnan S. M. ECG signal conditioning by morphological filtering. Computers in Biology and Medicine, 2002, 32 (6) : 465-479.
[125]李刚,何宏献,刘巍,等.数学形态滤波器及其在心电图机中的应用.仪器仪表学报,1999,20(4):335-339
[126]胡爱军,唐贵基,安连锁.基于数学形态学的旋转机械振动信号降噪方法.机械工程学报,2006,42(4):127-130
[127]章立军,杨德斌,徐金梧,等.基于数学形态滤波的齿轮故障特征提取方法.机械工程学报,2007,43(2):71-75
[128]杜秋华,杨曙年.形态滤波在滚动轴承缺陷诊断中的应用.轴承,2005,(6):27-31
[129]Shouda J., Zheming L., Shenghe S. Morphological filter based noise removal from vibration signals of fighter plane. Proceedings of 2001 International Symposium on Intelligent Multimedia, Video and Speech, Hong Kong, 2001, 251-254.
[130]杨晓冬,朱铁光.分形理论在流体机械运行稳定性监测中的应用.流体机械,2004,32(4):4
[131]Arduini F., Fioravanti S., Giusto D. D. A multifractal-based approach to natural scene analysis. Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing, Piscataway, NJ, USA: Publ by IEEE, 1991, 2681-2684.
[132]Grassberger P. Generalized dimensions of strange attractors. Physics letters. A, 1983, 97 (6) : 227-230.
[133]周炜星,王延杰.多重分形奇异谱的几何特性:Ⅰ.经典Renyi定义法.华东理工大学学报:自然科学版,2000,26(4):385-389
[134]周炜星,吴韬.多重分形奇异谱的几何特性:Ⅱ.配分函数法.华东理工大学学报:自然科学版,2000,26(4):390-395
[135]王祖林,周荫清.多重分形谱及其计算.北京航空航天大学学报,2000,26(3):256-258
[136]Chhabra A., Jensen R. V. Direct determination of the f (α) singularity spectrum. Physical Review Letters, 1989, 62 (12) : 1327-1330.
[137]Grassberger P., Badii R., Politi A. Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors. Journal of Statistical Physics, 1988, 51 (1) : 135-178.
[138]朱令人,龙海英.地震多重分形计算的最小生成树法.地震学报,2000,22(4):410-417
[139]Du G., Yeo T. S. A novel multifractal estimation method and its application to remote image segmentation. Geoscience and Remote Sensing, IEEE Transactions on, 2002, 40 (4) : 980-982.
[140]Perrier Edith, Tarquis Ana M., Dathe Annette. A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory. Geoderma, 2006, 134 (3-4) : 284-294.
[141]Saucier Antoine, Richer Jacques, Muller Jiri. Assessing the scope of the multifractal approach to textural characterization with statistical reconstructions of images. Physica A: Statistical Mechanics and its Applications, 2002, 311 (1-2) : 231-259.
[142]Pesquet-Popescu B., Vehel J. L. Stochastic fractal models for image processing. Signal Processing Magazine, IEEE, 2002, 19 (5) : 48- 62.
[143]熊刚,孙霞.TiN/TaN多莫大的子力显微镜图像的多重分形谱.电子显微学报,2000,19(4):437-438
[144]Saucier Antoine, Muller Jiri. Using principal component analysis to enhance the generalized multifractal analysis approach to textural segmentation: Theory and application to microresistivity well logs. Physica A: Statistical Mechanics and its Applications, 2002, 309 (3-4) : 419-444.
[145]孙霞,熊刚.ZnO薄膜原子力显微镜图像的多重分形谱.物理学报,2000,49(5):854-862
[146]蒋爱平,杨悦华,杨兴全.基于多重加权法的多重分形图像分割研究.中国图象图形学报,2007,12(10):1889-1892
[147]李厚强,刘政凯,等.基于分形理论的航空图像分类方法.遥感学报,2001,5(5):353-357
[148]李厚强,刘政凯,等.一种彩色纹理图像的分割方法.计算机学报,2001,24(9):965-971
[149]Butoma B. G., Stolyarov I. D., Petrov A. M., et al. Immunological and multifractal ECG analysis and analysis of status in patients with progressive forms of schizophrenia and schizotypic disorders. International Journal of Psychophysiology, 2008, 69 (3) : 145-146.
[150]Nakamura T., Horio H., Chiba Y. Local Holder exponent analysis of heart rate variability in preterm infants. Biomedical Engineering, IEEE Transactions on, 2006, 53 (1) : 83-88.
[151]Yang Xiaodong, Ning Xinbao, Wang Jun. Multifractal analysis of human synchronous 12-lead ECG signals using multiple scale factors. Physica A: Statistical Mechanics and its Applications, 2007, 384 (2) : 413-422.
[152]Ying Chen, Nash M. P., Xinbao Ning, et al. Multifractal ECG Mapping of Ventricular Epicardium During Regional Ischemia in the Pig. Biomedical Engineering, IEEE Transactions on, 2006, 53 (10) : 1920-1925.
[153]Kiyono K., Struzik Z. R., Aoyagi N., et al. Multiscale probability density function analysis: non-Gaussian and scale-Invariant fluctuations of healthy human heart rate. Biomedical Engineering, IEEE Transactions on, 2006, 53 (1) : 95-102.
[154]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.物理学报,2008,57(3):1514-1521
[155]Riedi R. H., Crouse M. S., Ribeiro V. J., et al. A multifractal wavelet model with application to network traffic. Information Theory, IEEE Transactions on, 1999, 45 (3) : 992-1018.
[156]Takada H. H., Anzaloni A. A multifractual traffic policing mechanism. Communications Letters, IEEE, 2006, 10 (2) : 120- 122.
[157]Liangxiu Han, Zhiwei Cen, Chunbo Chu, et al. A new multifractal network traffic model. Chaos, Solitons & Fractals, 2002, 13 (7) : 1507-1513.
[158]Jianbao Gao, Rubin I. Multifractal analysis and modelling of VBR video traffic. Electronics Letters, 2000, 36 (3) : 278-279.
[159]Gao J., Rubin I. Statistical properties of multiplicative multifractal processes in modelling telecommunications traffic streams. Electronics Letters, 2000, 36 (1) : 101-102.
[160]Gao J., Rubin I. Superposition of multiplicative multifractal traffic processes. Electronics Letters, 2000, 36 (8) : 761-763.
[161]魏进武,汪斌强,邬江兴.多重分形网络流量的单队列输入排队性能研究.电子学报,2006,34(4):658-663
[162]黄晓东,周源华,张荣福,等.改进的基于乘法多重分形的视频流量模型.上海交通大学学报,2004,38(z1):178-181
[163]洪飞,吴志美.基于小波的多尺度网络流量预测模型.计算机学报,2006,29(1):166-170
[164]王升辉,裘正定.结合多重分形的网络流量非线性预测.通信学报,2007,28(2):45-50
[165]魏进武,邬江兴,陈庶樵.网络流量的联合多重分形模型及特性分析.电子学报,2004,32(9):1459-1463
[166]刘东林,帅典勋.网络流量模型的非线性特征量的提取及分析.电子学报,2003,31(12):1866-1869
[167]Kavasseri R. G., Nagarajan R. Evidence of crossover phenomena in wind-speed data. Circuits and Systems I: Regular Papers, IEEE Transactions on, 2004, 51 (11) : 2255- 2262.
[168]Kerman B. R. Information states in radar imagery of sea ice. Geoscience and Remote Sensing, IEEE Transactions on, 1999, 37 (3) : 1435-1446.
[169]Deidda R. Multifractal analysis and simulation of rainfall fields in space. Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere, 1999, 24 (1-2) : 73-78.
[170]Charalampidis D., Kasparis T., Jones W. L. Removal of nonprecipitation echoes in weather radar using multifractals and intensity. Geoscience and Remote Sensing, IEEE Transactions on, 2002, 40 (5) : 1121-1131.
[171]陈时军,孙龙梅,马丽.板内与板间地震活动时空分布的多重分形特征研究.地震学报,2007,29(1):38-47
[172]汪秉宏.地震的多重分形统计特征研究.地球科学进展,1997,12(6):535-540
[173]朱令人,周仕勇.地震多重分形标度指数谱f(α)的研究.西北地震学报,1992,14(2):30-35
[174]汪秉宏,李东升.地震分布多重分形特征的中期预报意义探讨.地震学刊,1998,(1):9-18
[175]朱令人,周仕勇.地震复杂性前兆与强震多重分形谱异常.地震,1997,17(4):331-339
[176]朱令人,杨马陵.地震时间序列多重分形计算精度估计.中国地震,2000,16(2):166-175
[177]安镇文,杨翠华,王琳瑛,等.地震时空丛集的多重分形研究.地球物理学报,2000,43(1):74-80
[178]王琳瑛,朱传镇,黄容良.地震时空分布结构的多重分形特征的研究.地震,1994,(5):11-19
[179]陈时军,Davidharte,王丽凤,等.广义地震应变能释放的多重分形特征.地震学报,2003,25(2):182-190
[180]蔡强,周成虎,等.华北地震时空多重分形的时间演化特征研究.地震,2002,22(2):74-80
[181]朱令人,龙海英.离散点集(地震)空间分布多重分形计算的精度估算.地震,2000,20(3):1-8
[182]王安东,顾浩鼎.辽宁地区地震活动空间分布的多重分形.地震学报,1996,18(1):34-43
[183]陈时军,马丽,王丽凤,等.强震前后广义地震应变释放过程的丛集特征.地震,2003,23(2):29-38
[184]陈时军,Davidharte,马丽,等.新西兰地区地震活动时空分布的多重分形特征研究.地震学报,2003,25(3):298-307
[185]陈怡然,周轶尘.发动机振动诊断中的多重分形法.内燃机学报,1997,15(1):114-119
[186]黄海英,黄建波,原培新.基于多重分形广义维数的机械故障诊断方法.军械工程学院学报,2001,13(3):30-34
[187]刘彬,王霄,谢平.基于小波多重分形的复杂机械故障诊断方法研究.传感技术学报,2006,19(1):232-234
[188]王金东,李新伟,张忠臣,等.往复压缩机多重分形故障特征提取.压缩机技术,2008,:12-14
[189]徐玉秀,钟建军,闻邦椿.旋转机械动态特性的分形特征及故障诊断.机械工程学报,2005,41(12):186-189
[190]苑宇,马孝江.局域波时频域多重分形在故障诊断中的应用.振动与冲击,2007,26(5):60-63
[191]金萍,陈怡然.内燃机表面振动信号的性质.天津大学学报:自然科学与工程技术版,2000,33(1):63-68
[192]李国宾,段树林,于洪亮,等.发动机振动信号特征参数的多重分形研究.内燃机学报,2008,26(1):87-91
[193]李国宾,关德林.振动信号多重分形分析改进算法.测试技术学报,2006,20(6):543-548
[194]李舜酩,高德平.裂纹转子非线性振动特征的谐波小波与分形识别.航空动力学报,2004,19(5):581-586
[195]彭志科,何永勇,等.小波多重分析及其在振动信号分析中应用的研究.机械工程学报,2002,38(8):59-63
[196]张小明,刘建敏,乔新勇,等.柴油机缸盖振动信号关联维数的影响因素分析.装甲兵工程学院学报,2008,(1):42-45, 95
[197]Mandelbrot B. B. Fractals: Form Chance and Dimension. San Francisco: Freeman, 1977.
[198]Mandelbrot B. B. Les Objects Fractals: Forme Hasard et Dimension. Paris: Flammarion, 1975.
[199]Mandeibrot B. B. The Fractal Geometry of Nature. San Francisco: Feeman, 1982.
[200]谢和平,薛秀谦.分形应用中的数学基础与方法.北京:科学出版社,1997
[201]Falconer K J,曾文曲等译.分形几何数学基础及其应用.沈阳:东北工学院出版社,1991
[202]谢和平等编译.分形几何数学基础与应用.重庆:重庆大学出版社,1991
[203]文志英.分形几何的数学基础.上海:上海科技教育出版社,2000
[204]董连科.分形理论及其应用.沈阳:辽宁科学技术出版社,1991
[205]王东升,曹磊.混沌,分形及其应用.合肥:中国科学技术大学出版社,1995
[206]Lorenz E N.混沌的本质.北京:气象出版社,1997
[207]刘秉正.非线性动力学与混沌基础.长春:东北师范大学出版杜,1995
[208]龙运佳.混沌振动研究.北京:清华大学出版社,1997
[209]崔屹.图像处理和分析--数学形态学方法及应用.北京:科学出版社,2000
[210]Pitas I., Venetsanopoulos A. N. Nonlinear Digital Filters: Principles and Applications. Boston: Kluwer Academic Pub, 1990.
[211]Serra J. Image analysis and mathematical morphology. Newyork: Academic Press, 1982.
[212]Haralick R. M., Sternberg S. R., Zhuang X. Image analysis using mathematical morphology. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, 9 (4) : 532-550.
[213]Serre J. Image analysis and mathematical morphology. Vol. 2, Theoretical advances. London: Academic Press, 1988.
[214]Giardina C. R., Dougherty E. R. Morphological Methods in Image and Signal Processing. Englewood Cliffs, New Jersey: Prentice-Hall, 1988.
[215]Maragos P., Schafer R. Morphological filters--Part I: Their set-theoretic analysis and relations to linear shift-invariant filters. Acoustics, Speech, and Signal Processing, IEEE Transactions on, 1987, 35 (8) : 1153-1169.
[216]Maragos P., Schafer R. Morphological filters--Part II: Their relations to median, order-statistic, and stack filters. Acoustics, Speech, and Signal Processing, IEEE Transactions on, 1987, 35 (8) : 1170-1184.
[217]赵春晖.数学形态滤波器理论及其算法研究:[博士学位论文].哈尔滨:哈尔滨工业大学,1998
[218]陈铿,韩伯棠.混沌时间序列分析中的相空间重构技术综述.计算机科学,2005,32(4):67-70
[219]Packard N. H., Crutchfield J. P., Farmer J. D., et al. Geometry from a Time Series. Physical Review Letters, 1980, 45 (9) : 712-716.
[220]Takens F. Detecting strange attractors in turbulence. Lecture Notes in Mathematics, 1981, 898 (1) : 366-381.
[221]Albano A. M., Passamante A., Farrell Mary Eileen. Using higher-order correlations to define an embedding window. Physica D: Nonlinear Phenomena, 1991, 54 (1-2) : 85-97.
[222]Buzug T., Pfister G. Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors. Physical Review A, 1992, 45 (10) : 7073-7084.
[223]Buzug T., Pfister G. Comparison of algorithms calculating optimal embedding parameters for delay time coordinates. Physica D: Nonlinear Phenomena, 1992, 58 (1-4) : 127-137.
[224]Kember G., Fowler A. C. A correlation function for choosing time delays in phase portrait reconstructions. Physics letters. A, 1993, 179 (2) : 72-80.
[225]Falconer K J,曾文曲等译.分形几何中的技巧.沈阳:东北大学出版社,1999,323
[226]辛厚文.分形理论及其应用.合肥:中国科学技术大学出版社,1993
[227]陈顒.非线性科学在地震预报中的应用.北京:地震出版社,1992
[228]Hua L., Zejun D., Ziqin W. Multifractal behavior of the distribution of secondary-electron-emission sites on solid surfaces. Physical Review B, 1995, 51 (19) : 13554-13559.
[229]Hua L., Ze-Jun D., Ziqin W. Multifractal analysis of the spatial distribution of secondary-electron emission sites. Physical Review B, 1996, 53 (24) : 16631-16636.
[230]Lee C. K., Lee S. L. Multifractal scaling analysis of reactions over fractal surfaces. Surface science, 1995, 325 (3) : 294-310.
[231]Bing W., Yan W., Ziqin W. Multifractal behavior of solid-on-solid growth. Solid State Communications, 1995, 96 (2) : 69-72.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |