聚合物绝缘材料耐电痕性研究及其非线性分析
|
摘要
聚合物绝缘材料有着特殊的电气破坏现象:其表面在特定条件(潮湿与污秽)下会发生电痕劣化现象,并在周围产生更多的碳化物,形成碳化导电通路,甚至导致整个绝缘击穿。采用比漏电痕指数(CTI)方法评定材料的耐电痕性有很大的分散性,试验条件的略微改变都会对其产生较大影响,因此有必要对电痕劣化现象进行深入研究。耐电痕试验中采集的放电电流对分析聚合物材料的耐电性有重要作用,已有的文献主要通过计算放电量、进行频谱和功率谱分析等方法研究放电电流的内在特性。由于耐电痕劣化试验放电是一个非常复杂的过程,若仅考虑上述指标是不够科学的。研究放电电流的非线性特征量有助于理解放电过程的内在机理,这是由于:1)放电过程是一个非周期、非随机和非确定的复杂过程;2)经过小波变换去除工频信号的放电电流波形,其轮廓具有Mandelbrot所描述的分形体特征。本文运用递归图技术、递归定量分析方法、重构混沌吸引子、庞加莱截面法和计算分形维数、最大李雅谱诺夫指数等非线性指标,提供可视化(如混沌吸引子、递归图、庞加莱截面)或定量(如递归定量指标等)方法,揭示放电电流在m维相空间中的动力学特性。
混沌状态被认为是局部放电和电树枝的最终形态,而电痕与混沌的关系并未有报道,本文对于耐电痕试验放电过程是否可以进入混沌状态,进行了不同层面的讨论,所得结果为:放电电流的最大李雅谱诺夫指数为正;放电电流的分形维数随着嵌入维数的增加逐渐达到饱和值;放电电流的递归图具有典型混沌信号的拓扑和细纹理结构;放电电流吸引子的庞加莱截面有大量成片的、有分形特征的不动点。由此可知耐电痕试验最终将进入混沌状态。
聚合物绝缘材料越来越多的应用在各种辐射环境中,在强辐射线的照射下聚合物绝缘会发生一系列的化学变化,其中最主要的变化是分子链交联和降解反应,有必要对辐射条件下材料的耐电痕性能进行评定。辐射线对聚合物耐电痕性能的影响非常复杂,本文主要基于IEC60112耐电痕试验,运用递归图技术和递归定量分析等方法,对交联型和降解型聚合物进行耐电痕性评定。所得结果表明递归图方法可以将辐射剂量的影响,定性的展现在二维可视化图像中,而递归定量分析方法则量化了这种影响。
尽管阻燃剂可以延迟材料的起始闪络电压和火的传播速度,但同样会影响材料的电气特性。关于阻燃剂对材料耐电痕性能影响的文献较少,本文主要讨论不同溴族阻燃剂剂量对聚合物材料耐电痕性能的影响。主要方法为分析放电电流的非线性特征,并测量材料的比漏电痕指数等。所得结果表明,递归图和分形维数等非线性指标评定阻燃剂剂量的影响同样有效。
递归图等非线性方法对评定聚合电痕劣化不同阶段也是非常有效的,混沌吸引子的演化轨道、递归图的拓扑结构和分形维数的变化规律等,都和耐电痕试验的放电阶段有较好匹配。另外,本文同时对不同电压波形,如交、直流时,材料耐电痕性能进行非线性分析,所得结果表明非线性方法同样有效。
Tracking failure is a dielectric breakdown phenomena occurring on polymer surfaces comprising carbonized conductive path, resulting in a permanent loss of the surface dielectric performance. Because the resulting comparative tracking index (CTI) has wide variation, an attempt has been made to evaluate the resistance to tracking more consistently. Numerous studies have been conducted to characterize the properties of discharge currents by calculating the discharge quantity or analyzing the power spectrum. However, discharge is a complicated process and reproducible results of the indices mentioned above are difficult to obtain. Studying the non-linear characteristics of the discharge current can assist in understanding the underlying mechanism of the process because: 1)the surface discharge process is complex and irregular; 2) after the power frequency is filtered, the platform outlines of the discharge waveform as first discussed by Mandelbrot. In this paper, recurrence plots (RPs), recurrence quantification analysis (RQA), fractal dimensions, largest Lyapunov exponent, chaos attractors and Poincarémaps, which can provide quantitative, qualitative, visualization description of statistics characteristic of the discharge current in m-phase space, are reconstructed or calculated to extract information from the discharge currents.
It is found that the largest Lyapunov exponent of the discharge is positive, the fractal dimensions as a function of embedding dimension will saturate at a value, the recurrence plots shows the chaotic frame-work patterns, and the he Poincarémaps will have the chaotic characteristics. The results show that the discharge currents of the tracking test do exhibit chaotic behavior.
Due to the widespread use of polymeric insulating materials in radiation environments, there is an increasing demand to evaluate the radiation effects on the surface dielectric characteristics of polymeric insulating materials. The resistance to tracking of polymer materials can be changed by gamma-ray radiation through altering the molecular structure. Because the radiation has complex effect on the molecular structure of polymer materials through mechanism like chain scission, cross-linking and oxidation, it is hard to demonstrate the effect on resistance to tracking. This paper presents the recurrence plot (RP) and recurrence quantification analysis (RQA) approaches to analyze the surface discharge of gamma-ray irradiated polymeric insulating materials based on the tracking test described in IEC60112. Recurrence plots of the discharge currents are derived. It is found that the resistance to tracking could be projected on a map as a function of the dosage of irradiation. The recurrence plots and recurrence quantification analysis are sensitive and give visual and quantitative methods for identification of the dosage of irradiation effects on the resistance to tracking.
In order to satisfy the safety of fireproofing, the flame retardants are used in almost all polymer insulating materials. Although the flame retardant can hinder the fire from spreading, it may have negative influence on the electrical insulation. However, the research about the effect of flame retardant on the electrical insulation is very few. Consequently it is important to investigate the influence of the flame retardant on the dielectric strength. In order to assess the performance of the insulation degradation, the non-linear analysis methods are adopted in this research. The recurrence plot topological structures and fractal dimensions are studied. It has been shown that the methods are valid. For varied discharging stages, the attractors of discharge current show different characteristics in evolutionary tracks, the topological structure and grain direction of recurrence plots show significant differences, and the fractal dimensions of discharge current change obviously.
混沌状态被认为是局部放电和电树枝的最终形态,而电痕与混沌的关系并未有报道,本文对于耐电痕试验放电过程是否可以进入混沌状态,进行了不同层面的讨论,所得结果为:放电电流的最大李雅谱诺夫指数为正;放电电流的分形维数随着嵌入维数的增加逐渐达到饱和值;放电电流的递归图具有典型混沌信号的拓扑和细纹理结构;放电电流吸引子的庞加莱截面有大量成片的、有分形特征的不动点。由此可知耐电痕试验最终将进入混沌状态。
聚合物绝缘材料越来越多的应用在各种辐射环境中,在强辐射线的照射下聚合物绝缘会发生一系列的化学变化,其中最主要的变化是分子链交联和降解反应,有必要对辐射条件下材料的耐电痕性能进行评定。辐射线对聚合物耐电痕性能的影响非常复杂,本文主要基于IEC60112耐电痕试验,运用递归图技术和递归定量分析等方法,对交联型和降解型聚合物进行耐电痕性评定。所得结果表明递归图方法可以将辐射剂量的影响,定性的展现在二维可视化图像中,而递归定量分析方法则量化了这种影响。
尽管阻燃剂可以延迟材料的起始闪络电压和火的传播速度,但同样会影响材料的电气特性。关于阻燃剂对材料耐电痕性能影响的文献较少,本文主要讨论不同溴族阻燃剂剂量对聚合物材料耐电痕性能的影响。主要方法为分析放电电流的非线性特征,并测量材料的比漏电痕指数等。所得结果表明,递归图和分形维数等非线性指标评定阻燃剂剂量的影响同样有效。
递归图等非线性方法对评定聚合电痕劣化不同阶段也是非常有效的,混沌吸引子的演化轨道、递归图的拓扑结构和分形维数的变化规律等,都和耐电痕试验的放电阶段有较好匹配。另外,本文同时对不同电压波形,如交、直流时,材料耐电痕性能进行非线性分析,所得结果表明非线性方法同样有效。
Tracking failure is a dielectric breakdown phenomena occurring on polymer surfaces comprising carbonized conductive path, resulting in a permanent loss of the surface dielectric performance. Because the resulting comparative tracking index (CTI) has wide variation, an attempt has been made to evaluate the resistance to tracking more consistently. Numerous studies have been conducted to characterize the properties of discharge currents by calculating the discharge quantity or analyzing the power spectrum. However, discharge is a complicated process and reproducible results of the indices mentioned above are difficult to obtain. Studying the non-linear characteristics of the discharge current can assist in understanding the underlying mechanism of the process because: 1)the surface discharge process is complex and irregular; 2) after the power frequency is filtered, the platform outlines of the discharge waveform as first discussed by Mandelbrot. In this paper, recurrence plots (RPs), recurrence quantification analysis (RQA), fractal dimensions, largest Lyapunov exponent, chaos attractors and Poincarémaps, which can provide quantitative, qualitative, visualization description of statistics characteristic of the discharge current in m-phase space, are reconstructed or calculated to extract information from the discharge currents.
It is found that the largest Lyapunov exponent of the discharge is positive, the fractal dimensions as a function of embedding dimension will saturate at a value, the recurrence plots shows the chaotic frame-work patterns, and the he Poincarémaps will have the chaotic characteristics. The results show that the discharge currents of the tracking test do exhibit chaotic behavior.
Due to the widespread use of polymeric insulating materials in radiation environments, there is an increasing demand to evaluate the radiation effects on the surface dielectric characteristics of polymeric insulating materials. The resistance to tracking of polymer materials can be changed by gamma-ray radiation through altering the molecular structure. Because the radiation has complex effect on the molecular structure of polymer materials through mechanism like chain scission, cross-linking and oxidation, it is hard to demonstrate the effect on resistance to tracking. This paper presents the recurrence plot (RP) and recurrence quantification analysis (RQA) approaches to analyze the surface discharge of gamma-ray irradiated polymeric insulating materials based on the tracking test described in IEC60112. Recurrence plots of the discharge currents are derived. It is found that the resistance to tracking could be projected on a map as a function of the dosage of irradiation. The recurrence plots and recurrence quantification analysis are sensitive and give visual and quantitative methods for identification of the dosage of irradiation effects on the resistance to tracking.
In order to satisfy the safety of fireproofing, the flame retardants are used in almost all polymer insulating materials. Although the flame retardant can hinder the fire from spreading, it may have negative influence on the electrical insulation. However, the research about the effect of flame retardant on the electrical insulation is very few. Consequently it is important to investigate the influence of the flame retardant on the dielectric strength. In order to assess the performance of the insulation degradation, the non-linear analysis methods are adopted in this research. The recurrence plot topological structures and fractal dimensions are studied. It has been shown that the methods are valid. For varied discharging stages, the attractors of discharge current show different characteristics in evolutionary tracks, the topological structure and grain direction of recurrence plots show significant differences, and the fractal dimensions of discharge current change obviously.
引文
[1] Yoshimora N, Kumagai S, Du B. Research in Japan on the tracking phenomenon of electrical insulating materials. Electrical Insulation Magazine, IEEE, 1997, 13(5): 8-19
[2] IEC Publ.112. Recommended Method for Determining the Comparative Tracking Index of Solid Insulating Materials under Moist Conditions, 2nd edition, 1971
[3] IEC Publ.112. Method for Deternining the Comparative and the Proof Tracking Indices of Solid Insulting Material under Moist Conditions , 3rd edition, 1979
[4] IEC Publ. 60112. Method for the Determination of the Proof and the Comparative Tracking Indices of Solid Insulating Materials , 4th edition, 2003
[5] ASTM D2132-62T. Dust and fog tracking and erosion resistance of insulating materials
[6] IEC60587.Test method for evaluating resistance to tracking and erosion of electrical insulating materials used under severe ambient conditions
[7] Tu Deming,Yin Yi and Lei Qingquan. Space Charge on Distribution,TSC and TSL Spectra in Ployethelene Aged by Electrical Stress.Pro.ICPADM,Xi'an,China,2000: 46-50
[8] Y.Tanaka,G.Chen and Y.zhao. Effect of Additives on Morphology and Space Charge Accumulation in Low Density Ploythelene. IEEE Trans. Dielectrics and Electrical Insulation. 2003, 10(1): 148-154
[9] T.Takada,H.Miyake and Y.Tanaka.Pulse Acoustic Technology for Measurement of Charge Distribution in Dielectrics Materials for Spacecraft. IEEE Trans. Plasma Science. 2006, 34(5) :2176-2184
[10] A,Kumada and S.Qkabe. Measurement of Surface Charge on Opposite Sides of a Planar Insulator Using an Electostatic Probe. IEEE Trans. Dielectrics and Electrical Insulation. 2004, 11(6) : 919~928
[11] S.Kobayashi and S.Yasufuku. Degradation(electric discharge).Polymer Materials Encyclopedia. CRC press. 1996:1781-1787
[12] Dissado.L.A.Deterministic Chaos in Breakdown.I EEE Trans. Dielectrics and Electrical Insulation, 2002,9(5) : 752-762
[13] Dissado.L.A. Propagation of electrical tree structures in solid polymeric insulation[J], IEEE Transactions on Dielectrics and Electrical Insulation, 1997,4(3):259
[14] Dissado.L.A.,Suzuok.Y, Kaneiwa.H. Are Partial Discharges in Artificial Tubes Chaotic? Pro.Properties and Applications of Dielectric Materials, Nagoya, 2003:S9-1
[15] Irurzun. I. M. Bergero. P. Mola.V et al. Dielectric breakdown in solids modeled by DBM and DLA[J]. Chaos, Solitons and Fractals, 2002,13:1333~43
[16]贾志东，乐波，蒋雄伟等,分形几何在电介质科学中的应用，高电压技术1999，25（3）1~3
[17]卢侃，孙建，混沌学传奇，上海：上海翻译出版社，1991
[18]吴祥兴，陈忠，混沌学导论，上海：上海科学技术文学出版社，1996
[19]郝柏林，从抛物线谈起－混沌动力学引论，上海：上海科技教育出版社，1995
[20] Lorenz. Deterministic Non-periodic Flow. J.Atmos.Sci, 1963, 20:130-141
[21] Henon, Michel, Heiles, et al. The applicability of the third integral of motion: Some numerical experiments. Astronomical Journal, 1964, 69:73-79
[22] Takens F. Detecting Strange Attractors in Turbulence. Lecture Notes in Mathematics, Springer, 1981, 898, 366-381
[23] T. Y. Li and York. J.A.. Period Three Implies Chaos. Am Math Monthly, 1975,82: 985-992
[24] May.R. Simple mathematical models with very complicated dynamics. Nature, 1976,261:459-467
[25] Wolf.A, Swift. J. B., Swinney.H.L., et al. Determining Lyapunov exponents from a time series. Physical D, 1985, 16(3) :285-317
[26] Baranaand.G, Tsuda.I. A new method for computing Lyapunov exponents, Pys.Lett.A, 1990, 151:27-32
[27] Rosenstein.M.T, Collins.J.J,De luca. C.J. Apractial method for calculating largest Lyapunov exponents from small data sets. PhysicaD,1993,65:117-134
[28] Stoop.R and Parisi.J. Calculation of Lyapunov Exponents avoiding spurious elements.Physica D, 1991, 50:89-94
[29] Chaoming S, Lazaros K. G, Shlomo H.H, Makse.A .How to calculate the fractal dimension of a complex network: the box covering algorithm. J. Stat. Mech. 2007: P03006
[30] Grassberger. P. and Procacia.I. Measuring the strangeness of strange attractors. PhysicaD, 1983,9:189-208
[31] Carwright. J.H.E. Nonlinear stiCarwright.ffness, Lyapunov exponents, and attractor dimension, Phys.Lett.A, 1999, 264:298-302
[32] Brown.R, Bryant.P and Abarbanel. H.D.I.. Computing the Lyapunov spectrum of a dynamical system from an observed time series. Phys.Rev.A, 1991, 38:3017-3026
[33] Main.J and Wunner.G. Periodic orbit quantization of mixed regular chaotic systems, Phys.Rev.Lett., 1999,82:3038-3041
[34] Fraser. A. M., Swinney. H.L.Independent coordinates for strange attractors from mutual information. Phys.Rev.A, 1986,33:1134-1140
[35] Beims.M. W, Manchein.C, and Rost.J.M. Origin of chaos in soft interactions and signatures of nonergodicity. Phys. Rev. E76, 2007:056203
[36] Pelino.V and Maimone.F. Energetics, skeletal dynamics, and long-term predictions on Kolmogorov-Lorenz systems Phys. Rev. E 76, 2007:046214
[37] Aguirre. L. A. and Furtado.E. C. Building dynamical models from data and prior knowledge: The case of the first period-doubling bifurcation. Rev. E 76, 2007:046219
[38] Seghete.V and Menyuk. C. R. Solitons in the midst of chaos. Rev. A76, 2007: 043803
[39] Mokkadrem.A Estimation of the entropy and information of absolutely continuous random variables. IEEE Trans.Inform.Theory, 1989,35(1) : 193-196
[40] Fraser.A.M Information and entropy in strange attractors. IEEE Trans.Inform.Theory,1989,35(2) :245-262
[41] Dutta.R and Shukla.P Complex systems with half-integer spins: Symplectic ensembles. Phys. Rev. E 76, 2007: 051124
[42] Ribeiro.A.S. Dynamics of a two-dimensional model of cell tissues with coupledstochastic gene networks Phys. Rev. E 76, 2007:051915
[43] Mandelbrot. B.B. How long is the British coastline? Science,1967,156,636-638.
[44] Mandelbrot. B.B. Fractal: Form, Chance and Dimension [M]. 1975.
[45] Pentland.A. Fractal-based description of natural scenes. IEEE.Trans. Pami,1984,6(6):661-674
[46] Stallard.G.M.The Hausdoff Dimension of Julia sets of Hyperbolic meromorphic functions. Ergodic Theory Dynam. Systems, 2003, II. 20(3) : 895-910
[47] G.M.Stallard, The Hausdorff dimension of Julia sets of entire functions. Journal of London Mathematics Society, 2000,61(2) :471--488
[48] Kennedy .S.Kand Lin.W. Fract—A FORTRAN subroutine to calculate the variables necessary to determine the fractal dimension of closed forms. Computers and Geosciences 1986, 12:705-712.
[49] Kennedy .S.Kand Lin.W. A fractal technique for the classification of projectile point shapes. Geoarchaeology 1988, 3: 297-301.
[50] Bak, P. How Nature Works: The Science of Self-Organized Criticality. New York: Springer-Verlag. 1996
[51] Brakensiek.D.L, Rawls, W.J., et al. Fractal description of macroporosity. Soil Sci. Soc. Am. J. 1992, 56(6) : 1721-1723.
[52] Besicovitch.A.S,Ursell.H.D, Sets of fractional dimensions (v):on dimensional numbers of some continuous curves, J. Lond.Math. Soc. 1937, 12 (45) : 18-25.
[53] Mandelbrot.B.B, Passoja.D.E and .Paulley.A.J. Fractal character of fracture surfaces of metals. Nature, 308, 1984: 721-722.
[54] He, L.& Zhu, J. The fractal character of processed metal surfaces.Wear,1997, 208: 17-24.
[55]Bogana, M., Donadio,D., Benedek, G. & Colombo, L. Simulation of atomic force microscopy of fractal nanostructured carbon films. Europhys. Lett. 2001, 54:72-76
[56] Sanucier.A and Muller.J. Textural Analysis of Disordered Materials with Multifractals. Phyisca A, 1999, 267:221-238
[57]孙霞等，分形原理及其应用[M].中国科学技术大学出版社，2003
[58] Eckmann .J.P, Kamphorst S.Q,Ruelle.D. Recurrence plots of dynamical systems. Europhys Lett., 1987, 4: 973~977
[59]Zbilut.J.P,Giulian A and Webber. C.L. Recurrence Quantification Analysis and Principal Componets in the Detection of Short Complex Signals. Physics Letters A,1998,237:131-135
[60] J.P.Zbilut and C.L.Webber. Embedding and delays as derived from quantification of recurrence plots . Physics Letters A, 1992,171(3-4): 199-203
[61] Marwan.N,Kurths.J. Nonlinear Analysis of Bivariate Date with Cross Recurrence Plots. Physics Letters A, 2002, 302:299-307
[62] Casdagli.M.C.Recurrence plots Revisited.Physica D. 1997,108:12-44
[63] Kamosawa.T,Yoshimura.N,Nishida.M,et al.Influence of Ultraviolet Rays on Tracking Deterioration of Epoxy Resin[J]. Trans. IEE Japan, 1988,108-A(9):397-404
[64] Chen.G, Davies. A. E, Banford H. M. Influence of Radiation Environments on Space Charge Formation inγ-irradiated LDPE", IEEE Trans. Dielectr. Electr. Insul. 1999, 6: 882- 886
[65] Banford.H.M, Fouracre.R.A, Faucitano.A, et al. The influence of chemical structure on the dielectric behavior of polypropylene. IEEE Trans. Dielectrics and Electrical Insulation, 1996, 3: 594-598
[66] Banford.H.M, Fouracre.R.A, MacGregor.S.J,et al. An Investigation of radiation-induced ageing in cable insulation via loss measurements at high and low frequencies. Conf.IEEE Int. Symp. Elect. Insul., 1998:558-561.
[67] Li.H.M, Fouracre.R.A,Given.M.J,et al. The Effects on polyetheretherketone and polyethersulfone of electron andγirradiation. IEEE Trans. Dielectrics and Electrical Insulation, 1999,6:295-303
[68] Kim.K.Y, Lee.C, Kim.P.J,et al. DielecKim.K.Ytric properties on the radiation and thermal aged PEEK. IEEE Int. Conf. Solid. Dielectr.,2004, 1:332-335
[69]Agarwal.V.K, Banford.H.M, Bernstein.B.S,et al. The mysteries of multifactor ageing.IEEEElect. Insul. Mag., 1995,11(3) :37-43.
[70] Anandakumaran.K, Seidl.W, Castaldo.P.V Condition assessment of cable insulation systems in operating nuclear power plants. IEEE Trans. Dielectrics and Electrical Insulation, 1999, 6: 376-384
[71] Kuriyama.I, Hayakawa.N and Nakase.Y. Radiation resistance of cable insulating materials for nuclear power generating stations. IEEE Trans. Dielectrics and Electrical Insulation, 1978, 13:164-171
[72] Du B.X, Suzuki A, Kobayashi S. Effects of Gamma-rays Irradiation on Tracking Resistance of Organic Instating Matericals. Transactions on IEEJ,1996,116-A(5) : 461-467
[73] Du.B X. Wavelet analysis of scintillation discharge current on dc tracking resistance of gamma-ray irradiation polyethylene and polycarbonate. Radioisotopes. 2001, 50:1-11
[74] Du.B. X. and Yamano.Y. Effects of atmospheric pressure on dc resistance to tracking of polymer insulating materials. IEEE Trans. Dielectrics and Electrical Insulation, 2005,12:1162-1171
[75] Du.B.X. Suzuki.A,Kishi.K,et al. Effects of atmospheric pressure on tracking failure of organic insulating materials, Trans.IEEJ,1995,116-A(12) :1284-1293
[76]欧育湘，实用阻燃技术[M]，北京：化学工业出版社，2002
[77] Du.B.X, Jun.X, Discharge characteristics on modified polycarbonate by adding flame, IEEE Conference on electrical insulation and dielectric phenomena, 2004:559-562
[78] Du.B.X, Shigeo Kobayashi.Effects of the Content of Flame Retardant on the Surface Discharge of Polycarbonate. Trans. IEEJ., 122-A(4), 2002:404-408
[79] Du.B.X, Suzuki A, Kobayashi S. Effects of Sample Temperatures on Tracking Resistance of Polymer insulating materials. Trans. IEEJ., 1996, 116-A (8) :725-730
[80] Du B X. Discharge energy and dc tracking resistance of polymer insulating materials, IEEE Trans. Dielectrics and Electrical Insulation, 2001,8(6):897-901
[81] Wang.X, Chen. L,Yoshimura. N, Erosion by acid rain accelerating the tracking of polystyrene insulating material. Phy.D:Appl, 2000, Phys.33(9) : 1117-1127
[82] Du B X, S.Kobayashi. Effects of magnetic field on surface dielectric breakdown of contaminated printed wiring board. IEE Jappan, 2003,123-A(6) :562-568
[83] Kaplan D.Glass.L.O. Understanding Nonlinear Dynamics [M]. Springer-Verla, 1995
[84] Parker. T.S, Chua.L.O. Chaos: a Tutorial for Engineers. Processing of IEEE, 1987, 75:982-1008
[85] Thomopson.C, Mulpur A, Mehta. V. Transition to Chaos in Acoustically Driven Flow (Acoustic Streaming).JASA, 1991, 90(4) :2097-2103
[86] Gao J.B. Detecting Nonstationarity and State Transitions in a Time Series.Physical Review E, 2001, 63:066202
[87] Paciorek.K. J.L, Kratzer.R.H, Lee. F. FC, et al .Moist tracking investigation oforganic insulating materials. IEEE Trans EI, 1982,17(5) :423—428
[88]吉村升，西田真，能登文敏，有机绝缘材料的耐电痕性[J]。日本静电学会志，1982，6(2) :72—79
[89] Mason. J. H., Gleizer. H., Sens. M. A. and Tan. A. L. DC tracking and erosion on glass and porcelain. 5th Int.Sympos. High Voltage Eng., Braunschweig, Germany, Paper 52.02:1987.
[90] Gleizer.H, Tana.A.L and Mason.J.H. Electrolytic corrosion as an adjunct to DC tracking and erosion on insulators. IEE conf. 289, DMMAConf. 1988. : 135-138
[91] Norman.R.S and Kesel.A.A. Internal Oxide ion Mechanism for Non-tracking Organic Insulation. AIEE Trans. Pt.(Power Apparatus Syst.), 1958,77:632
[92] Cooper and M.Prober. The action of Oxygen Corona and of Ozone on Ploythelene. Journal of Polymer Science. 1960,44:397-409
[93] Masom.J.H. Environmental Factors Affecting dc Resistance to Tracking of Polyethylene. IEEE Trans. Dielectrics and Electrical Insulation, 2004,11(5):911-912
[94] Mason.J.H. DC salt-fog tests on glass and porcelaincap and pin insulators. IEEDMMAconf. 289, 1988: 139-142
[95] Stimper. K, Sachsenweger.C, Middendorf .W. H. The chemistry of insulationtracking with copper electrodes[J].IEEE Trans Electrical Insulation, 1988,23(6) :987-991
[96] Packard N.H, Crutchfield J. P, Farmer J.D et al. Geometry from a time series. Phys Rev Lett, 1980, 45:712-716
[97] Eckman J.P, Ruller D. Ergodic theory of chaos and strange attractors. Review of Modern Physics, 1985,57(3):617-656
[98] Buzug.Th and Pfister.G.. Comparison of algorithms calculating optimal embedding parameters for delay time coordinates. Physica D, 1992, (58): 127-137
[99] Lim.T.P and Sadasivan. P. Postprocessing methods for finding the embedding dimension of chaotic time series [Phys. Rev. E,2005, 72: 027204
[100] Cellucci.C.J, Albano.A.M, and Rapp.P.E. Comparative study of embedding methods Phys. Rev. E 67, 2003:066210
[101] Kennel M, Brown R and Abarbanel H D I 1992 Phys. Rev. A 45 3403
[102] Cao L.Y. Practical method for determining the minimum embedding dimension of a scalar tim series. Physica D, 1997, 110 :43-50
[103] Broomhead.D.S and King.G.P. Extracting qualitative dynamics from experimental data. Physica D, 1986, 20:217-236
[104] Sugihara.G and May. R.M. Nonlinear forecasting as a way of distinguishing chaos form measurement error in time series. Nature. 1990,344:734-741
[105] Meng .Q.F, Peng .Y.H, Xue P.J. A new method of determining the optimal embedding dimension based on nonlinear prediction. Chinese Physics, 2007, 16(5): 1009-1963
[106] Liebert.W, Pawelzik.K and Schuster.H.G.. Proper choice of the time delay for the analysis of chaotic time series. Phys.Lett. A, 1989, 142:107-111
[107] Liebert.W, Pawelzik.K and Schuster.H.G.. Optimal embeddings of chaotic attractors from topological considerations. Europhys.Lett. 1991, 14:521
[108] Kim H S, Eykholt R, Salas J D. Nonlinear Dynamics, Delay Times, and Embedding Windows. Physica D, 1999, 127, 48-60
[109] Abarbanel, H.D.I., Brown, R., Sidorowich, J.J., & Tsimring, L.S. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys,1993, 64( 5): 1331-1393
[110] Marwan N, Wessel.N, Meyerfeld, et al. Recurrence Plot-Based Measure of Complexity and Their Application to Heart-Rate-Variability Data. Physical Review E, 2002,66:026702
[111] Marwan N. Recurrence plots and cross recurrence plots [online]. http://www.recurrence-plot.tk//glance.php
[112] Gao.J.B. Recurrence Time statistics for chaotic systems and their applications. Physical Review letters,1999,83(16):3178-3181
[113]程正兴，小波分析算法与应用[M]，西安：西安交通大学出版社，1998
[114]秦前清，杨宗凯，实用小波分析，西安：西安电子科技大学出版社，1994
[115]成礼智，郭汉伟，小波与离散变换理论及工程实践，北京：清华大学出版社，2005
[116] Gollub.J.P., Romer.E.J. and Socolar. J.E. Trajectory divergence for coupled relaxation oscillators: measurements and models. J. Stat. Phys, 1980, 23, (3): 321-333
[117] Wright.J. Method for Calculating a Lyapunov Exponent. Phys. Rev. 1984, A29 :2923.
[118] J.D. Farmer, E. Ott and J.A. Yorke. The Dimension of Chaotic Attractors. Physica 7D, 1983, 607 C: 153-180.
[119] Oseledec V.I..A Multiplicative Ergodic Theorem Lyapunov Characteristic Numbers for Dynamical Systems. Trans. Moscow Math. Soc. 1968,19:197-231
[120] Benettin.G, Galgani.L,Giorgilli.A and Strelcyn.J.M. Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems; A Method for Computing All of Them. Meccanica.1980, 15:9-20.
[121] Shimada.I and Nagashima.T. A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems. Prog TheorPhys, 1979,61(6) :1605 - 1615
[122] Shaw.R. Strange Attractors, Chaotic Behavior, and Information Flow. Z Naturf, 1981, 36A: 80-112
[123] Rosenstein.M.T, Collins.J.J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D, 1993, 65:117-134
[124] Warwick.T. Computing accurate Poincarémaps. Physica D. 2002, 171: 127-137
[125] Hénon.M. On the numerical computation of Poincarémaps, Physica D 5 (1982) 412-414.
[126] Chen.G, R. Fouracre.A, Banford H.M.and Tedford.D.J. The effects of gamma irradiation on thermally stimulated discharge current spectra in low-density polyethylene"Radiat. Phys. Chem., 1991, 37:523-530
[127] Hegazy.E.A, Sasuga.T, Nishii.M and Seguchi.T. Irradiation effects on aromatic polymers: 2. Gas evolution during electron-beam irradiation. Polymer, 1992,33(14): 29042910
[128] Chen.G.., Banford.H.M, Davies.A. Effect of gamma-irradiation on electrical breakdown stress of LDPE. Conduction and Breakdown in Solid Dielectrics, 1995 :556-560
[129] Fu, M,Chen. G, Dissado. L. A, et al. The Effect of Gamma Irradiation on Space Charge Behaviour and Dielectric Spectroscopy of Low-density Polyethylene. Solid Dielectrics, 2007. ICSD '07. IEEE International Conference on 8-13 July 2007:442 - 445
[130] Fouracre.R.A, Banford.H.M, Tedford. D.J. et al. Gamma irradiation effects in two epoxy resins and a polyimide. Electrical Insulation and Dielectric Phenomena, 1989. Annual Report., Conference on 29 Oct.-2 Nov. 1989:198 -203
[131] Vogel.H. Flammfestmachen von Kunststoffen [M]. Huthig-Verlag, Heidelberg, 1966
[132] Hilado.C.J. Flammability Handbook for Plastics [M]. Technomic, Stamford,Conn.1969
[133] Lyons.J.W. The chemistry and uses of fire retardants. Wiley-Intersicence. London, 1970
[2] IEC Publ.112. Recommended Method for Determining the Comparative Tracking Index of Solid Insulating Materials under Moist Conditions, 2nd edition, 1971
[3] IEC Publ.112. Method for Deternining the Comparative and the Proof Tracking Indices of Solid Insulting Material under Moist Conditions , 3rd edition, 1979
[4] IEC Publ. 60112. Method for the Determination of the Proof and the Comparative Tracking Indices of Solid Insulating Materials , 4th edition, 2003
[5] ASTM D2132-62T. Dust and fog tracking and erosion resistance of insulating materials
[6] IEC60587.Test method for evaluating resistance to tracking and erosion of electrical insulating materials used under severe ambient conditions
[7] Tu Deming,Yin Yi and Lei Qingquan. Space Charge on Distribution,TSC and TSL Spectra in Ployethelene Aged by Electrical Stress.Pro.ICPADM,Xi'an,China,2000: 46-50
[8] Y.Tanaka,G.Chen and Y.zhao. Effect of Additives on Morphology and Space Charge Accumulation in Low Density Ploythelene. IEEE Trans. Dielectrics and Electrical Insulation. 2003, 10(1): 148-154
[9] T.Takada,H.Miyake and Y.Tanaka.Pulse Acoustic Technology for Measurement of Charge Distribution in Dielectrics Materials for Spacecraft. IEEE Trans. Plasma Science. 2006, 34(5) :2176-2184
[10] A,Kumada and S.Qkabe. Measurement of Surface Charge on Opposite Sides of a Planar Insulator Using an Electostatic Probe. IEEE Trans. Dielectrics and Electrical Insulation. 2004, 11(6) : 919~928
[11] S.Kobayashi and S.Yasufuku. Degradation(electric discharge).Polymer Materials Encyclopedia. CRC press. 1996:1781-1787
[12] Dissado.L.A.Deterministic Chaos in Breakdown.I EEE Trans. Dielectrics and Electrical Insulation, 2002,9(5) : 752-762
[13] Dissado.L.A. Propagation of electrical tree structures in solid polymeric insulation[J], IEEE Transactions on Dielectrics and Electrical Insulation, 1997,4(3):259
[14] Dissado.L.A.,Suzuok.Y, Kaneiwa.H. Are Partial Discharges in Artificial Tubes Chaotic? Pro.Properties and Applications of Dielectric Materials, Nagoya, 2003:S9-1
[15] Irurzun. I. M. Bergero. P. Mola.V et al. Dielectric breakdown in solids modeled by DBM and DLA[J]. Chaos, Solitons and Fractals, 2002,13:1333~43
[16]贾志东，乐波，蒋雄伟等,分形几何在电介质科学中的应用，高电压技术1999，25（3）1~3
[17]卢侃，孙建，混沌学传奇，上海：上海翻译出版社，1991
[18]吴祥兴，陈忠，混沌学导论，上海：上海科学技术文学出版社，1996
[19]郝柏林，从抛物线谈起－混沌动力学引论，上海：上海科技教育出版社，1995
[20] Lorenz. Deterministic Non-periodic Flow. J.Atmos.Sci, 1963, 20:130-141
[21] Henon, Michel, Heiles, et al. The applicability of the third integral of motion: Some numerical experiments. Astronomical Journal, 1964, 69:73-79
[22] Takens F. Detecting Strange Attractors in Turbulence. Lecture Notes in Mathematics, Springer, 1981, 898, 366-381
[23] T. Y. Li and York. J.A.. Period Three Implies Chaos. Am Math Monthly, 1975,82: 985-992
[24] May.R. Simple mathematical models with very complicated dynamics. Nature, 1976,261:459-467
[25] Wolf.A, Swift. J. B., Swinney.H.L., et al. Determining Lyapunov exponents from a time series. Physical D, 1985, 16(3) :285-317
[26] Baranaand.G, Tsuda.I. A new method for computing Lyapunov exponents, Pys.Lett.A, 1990, 151:27-32
[27] Rosenstein.M.T, Collins.J.J,De luca. C.J. Apractial method for calculating largest Lyapunov exponents from small data sets. PhysicaD,1993,65:117-134
[28] Stoop.R and Parisi.J. Calculation of Lyapunov Exponents avoiding spurious elements.Physica D, 1991, 50:89-94
[29] Chaoming S, Lazaros K. G, Shlomo H.H, Makse.A .How to calculate the fractal dimension of a complex network: the box covering algorithm. J. Stat. Mech. 2007: P03006
[30] Grassberger. P. and Procacia.I. Measuring the strangeness of strange attractors. PhysicaD, 1983,9:189-208
[31] Carwright. J.H.E. Nonlinear stiCarwright.ffness, Lyapunov exponents, and attractor dimension, Phys.Lett.A, 1999, 264:298-302
[32] Brown.R, Bryant.P and Abarbanel. H.D.I.. Computing the Lyapunov spectrum of a dynamical system from an observed time series. Phys.Rev.A, 1991, 38:3017-3026
[33] Main.J and Wunner.G. Periodic orbit quantization of mixed regular chaotic systems, Phys.Rev.Lett., 1999,82:3038-3041
[34] Fraser. A. M., Swinney. H.L.Independent coordinates for strange attractors from mutual information. Phys.Rev.A, 1986,33:1134-1140
[35] Beims.M. W, Manchein.C, and Rost.J.M. Origin of chaos in soft interactions and signatures of nonergodicity. Phys. Rev. E76, 2007:056203
[36] Pelino.V and Maimone.F. Energetics, skeletal dynamics, and long-term predictions on Kolmogorov-Lorenz systems Phys. Rev. E 76, 2007:046214
[37] Aguirre. L. A. and Furtado.E. C. Building dynamical models from data and prior knowledge: The case of the first period-doubling bifurcation. Rev. E 76, 2007:046219
[38] Seghete.V and Menyuk. C. R. Solitons in the midst of chaos. Rev. A76, 2007: 043803
[39] Mokkadrem.A Estimation of the entropy and information of absolutely continuous random variables. IEEE Trans.Inform.Theory, 1989,35(1) : 193-196
[40] Fraser.A.M Information and entropy in strange attractors. IEEE Trans.Inform.Theory,1989,35(2) :245-262
[41] Dutta.R and Shukla.P Complex systems with half-integer spins: Symplectic ensembles. Phys. Rev. E 76, 2007: 051124
[42] Ribeiro.A.S. Dynamics of a two-dimensional model of cell tissues with coupledstochastic gene networks Phys. Rev. E 76, 2007:051915
[43] Mandelbrot. B.B. How long is the British coastline? Science,1967,156,636-638.
[44] Mandelbrot. B.B. Fractal: Form, Chance and Dimension [M]. 1975.
[45] Pentland.A. Fractal-based description of natural scenes. IEEE.Trans. Pami,1984,6(6):661-674
[46] Stallard.G.M.The Hausdoff Dimension of Julia sets of Hyperbolic meromorphic functions. Ergodic Theory Dynam. Systems, 2003, II. 20(3) : 895-910
[47] G.M.Stallard, The Hausdorff dimension of Julia sets of entire functions. Journal of London Mathematics Society, 2000,61(2) :471--488
[48] Kennedy .S.Kand Lin.W. Fract—A FORTRAN subroutine to calculate the variables necessary to determine the fractal dimension of closed forms. Computers and Geosciences 1986, 12:705-712.
[49] Kennedy .S.Kand Lin.W. A fractal technique for the classification of projectile point shapes. Geoarchaeology 1988, 3: 297-301.
[50] Bak, P. How Nature Works: The Science of Self-Organized Criticality. New York: Springer-Verlag. 1996
[51] Brakensiek.D.L, Rawls, W.J., et al. Fractal description of macroporosity. Soil Sci. Soc. Am. J. 1992, 56(6) : 1721-1723.
[52] Besicovitch.A.S,Ursell.H.D, Sets of fractional dimensions (v):on dimensional numbers of some continuous curves, J. Lond.Math. Soc. 1937, 12 (45) : 18-25.
[53] Mandelbrot.B.B, Passoja.D.E and .Paulley.A.J. Fractal character of fracture surfaces of metals. Nature, 308, 1984: 721-722.
[54] He, L.& Zhu, J. The fractal character of processed metal surfaces.Wear,1997, 208: 17-24.
[55]Bogana, M., Donadio,D., Benedek, G. & Colombo, L. Simulation of atomic force microscopy of fractal nanostructured carbon films. Europhys. Lett. 2001, 54:72-76
[56] Sanucier.A and Muller.J. Textural Analysis of Disordered Materials with Multifractals. Phyisca A, 1999, 267:221-238
[57]孙霞等，分形原理及其应用[M].中国科学技术大学出版社，2003
[58] Eckmann .J.P, Kamphorst S.Q,Ruelle.D. Recurrence plots of dynamical systems. Europhys Lett., 1987, 4: 973~977
[59]Zbilut.J.P,Giulian A and Webber. C.L. Recurrence Quantification Analysis and Principal Componets in the Detection of Short Complex Signals. Physics Letters A,1998,237:131-135
[60] J.P.Zbilut and C.L.Webber. Embedding and delays as derived from quantification of recurrence plots . Physics Letters A, 1992,171(3-4): 199-203
[61] Marwan.N,Kurths.J. Nonlinear Analysis of Bivariate Date with Cross Recurrence Plots. Physics Letters A, 2002, 302:299-307
[62] Casdagli.M.C.Recurrence plots Revisited.Physica D. 1997,108:12-44
[63] Kamosawa.T,Yoshimura.N,Nishida.M,et al.Influence of Ultraviolet Rays on Tracking Deterioration of Epoxy Resin[J]. Trans. IEE Japan, 1988,108-A(9):397-404
[64] Chen.G, Davies. A. E, Banford H. M. Influence of Radiation Environments on Space Charge Formation inγ-irradiated LDPE", IEEE Trans. Dielectr. Electr. Insul. 1999, 6: 882- 886
[65] Banford.H.M, Fouracre.R.A, Faucitano.A, et al. The influence of chemical structure on the dielectric behavior of polypropylene. IEEE Trans. Dielectrics and Electrical Insulation, 1996, 3: 594-598
[66] Banford.H.M, Fouracre.R.A, MacGregor.S.J,et al. An Investigation of radiation-induced ageing in cable insulation via loss measurements at high and low frequencies. Conf.IEEE Int. Symp. Elect. Insul., 1998:558-561.
[67] Li.H.M, Fouracre.R.A,Given.M.J,et al. The Effects on polyetheretherketone and polyethersulfone of electron andγirradiation. IEEE Trans. Dielectrics and Electrical Insulation, 1999,6:295-303
[68] Kim.K.Y, Lee.C, Kim.P.J,et al. DielecKim.K.Ytric properties on the radiation and thermal aged PEEK. IEEE Int. Conf. Solid. Dielectr.,2004, 1:332-335
[69]Agarwal.V.K, Banford.H.M, Bernstein.B.S,et al. The mysteries of multifactor ageing.IEEEElect. Insul. Mag., 1995,11(3) :37-43.
[70] Anandakumaran.K, Seidl.W, Castaldo.P.V Condition assessment of cable insulation systems in operating nuclear power plants. IEEE Trans. Dielectrics and Electrical Insulation, 1999, 6: 376-384
[71] Kuriyama.I, Hayakawa.N and Nakase.Y. Radiation resistance of cable insulating materials for nuclear power generating stations. IEEE Trans. Dielectrics and Electrical Insulation, 1978, 13:164-171
[72] Du B.X, Suzuki A, Kobayashi S. Effects of Gamma-rays Irradiation on Tracking Resistance of Organic Instating Matericals. Transactions on IEEJ,1996,116-A(5) : 461-467
[73] Du.B X. Wavelet analysis of scintillation discharge current on dc tracking resistance of gamma-ray irradiation polyethylene and polycarbonate. Radioisotopes. 2001, 50:1-11
[74] Du.B. X. and Yamano.Y. Effects of atmospheric pressure on dc resistance to tracking of polymer insulating materials. IEEE Trans. Dielectrics and Electrical Insulation, 2005,12:1162-1171
[75] Du.B.X. Suzuki.A,Kishi.K,et al. Effects of atmospheric pressure on tracking failure of organic insulating materials, Trans.IEEJ,1995,116-A(12) :1284-1293
[76]欧育湘，实用阻燃技术[M]，北京：化学工业出版社，2002
[77] Du.B.X, Jun.X, Discharge characteristics on modified polycarbonate by adding flame, IEEE Conference on electrical insulation and dielectric phenomena, 2004:559-562
[78] Du.B.X, Shigeo Kobayashi.Effects of the Content of Flame Retardant on the Surface Discharge of Polycarbonate. Trans. IEEJ., 122-A(4), 2002:404-408
[79] Du.B.X, Suzuki A, Kobayashi S. Effects of Sample Temperatures on Tracking Resistance of Polymer insulating materials. Trans. IEEJ., 1996, 116-A (8) :725-730
[80] Du B X. Discharge energy and dc tracking resistance of polymer insulating materials, IEEE Trans. Dielectrics and Electrical Insulation, 2001,8(6):897-901
[81] Wang.X, Chen. L,Yoshimura. N, Erosion by acid rain accelerating the tracking of polystyrene insulating material. Phy.D:Appl, 2000, Phys.33(9) : 1117-1127
[82] Du B X, S.Kobayashi. Effects of magnetic field on surface dielectric breakdown of contaminated printed wiring board. IEE Jappan, 2003,123-A(6) :562-568
[83] Kaplan D.Glass.L.O. Understanding Nonlinear Dynamics [M]. Springer-Verla, 1995
[84] Parker. T.S, Chua.L.O. Chaos: a Tutorial for Engineers. Processing of IEEE, 1987, 75:982-1008
[85] Thomopson.C, Mulpur A, Mehta. V. Transition to Chaos in Acoustically Driven Flow (Acoustic Streaming).JASA, 1991, 90(4) :2097-2103
[86] Gao J.B. Detecting Nonstationarity and State Transitions in a Time Series.Physical Review E, 2001, 63:066202
[87] Paciorek.K. J.L, Kratzer.R.H, Lee. F. FC, et al .Moist tracking investigation oforganic insulating materials. IEEE Trans EI, 1982,17(5) :423—428
[88]吉村升，西田真，能登文敏，有机绝缘材料的耐电痕性[J]。日本静电学会志，1982，6(2) :72—79
[89] Mason. J. H., Gleizer. H., Sens. M. A. and Tan. A. L. DC tracking and erosion on glass and porcelain. 5th Int.Sympos. High Voltage Eng., Braunschweig, Germany, Paper 52.02:1987.
[90] Gleizer.H, Tana.A.L and Mason.J.H. Electrolytic corrosion as an adjunct to DC tracking and erosion on insulators. IEE conf. 289, DMMAConf. 1988. : 135-138
[91] Norman.R.S and Kesel.A.A. Internal Oxide ion Mechanism for Non-tracking Organic Insulation. AIEE Trans. Pt.(Power Apparatus Syst.), 1958,77:632
[92] Cooper and M.Prober. The action of Oxygen Corona and of Ozone on Ploythelene. Journal of Polymer Science. 1960,44:397-409
[93] Masom.J.H. Environmental Factors Affecting dc Resistance to Tracking of Polyethylene. IEEE Trans. Dielectrics and Electrical Insulation, 2004,11(5):911-912
[94] Mason.J.H. DC salt-fog tests on glass and porcelaincap and pin insulators. IEEDMMAconf. 289, 1988: 139-142
[95] Stimper. K, Sachsenweger.C, Middendorf .W. H. The chemistry of insulationtracking with copper electrodes[J].IEEE Trans Electrical Insulation, 1988,23(6) :987-991
[96] Packard N.H, Crutchfield J. P, Farmer J.D et al. Geometry from a time series. Phys Rev Lett, 1980, 45:712-716
[97] Eckman J.P, Ruller D. Ergodic theory of chaos and strange attractors. Review of Modern Physics, 1985,57(3):617-656
[98] Buzug.Th and Pfister.G.. Comparison of algorithms calculating optimal embedding parameters for delay time coordinates. Physica D, 1992, (58): 127-137
[99] Lim.T.P and Sadasivan. P. Postprocessing methods for finding the embedding dimension of chaotic time series [Phys. Rev. E,2005, 72: 027204
[100] Cellucci.C.J, Albano.A.M, and Rapp.P.E. Comparative study of embedding methods Phys. Rev. E 67, 2003:066210
[101] Kennel M, Brown R and Abarbanel H D I 1992 Phys. Rev. A 45 3403
[102] Cao L.Y. Practical method for determining the minimum embedding dimension of a scalar tim series. Physica D, 1997, 110 :43-50
[103] Broomhead.D.S and King.G.P. Extracting qualitative dynamics from experimental data. Physica D, 1986, 20:217-236
[104] Sugihara.G and May. R.M. Nonlinear forecasting as a way of distinguishing chaos form measurement error in time series. Nature. 1990,344:734-741
[105] Meng .Q.F, Peng .Y.H, Xue P.J. A new method of determining the optimal embedding dimension based on nonlinear prediction. Chinese Physics, 2007, 16(5): 1009-1963
[106] Liebert.W, Pawelzik.K and Schuster.H.G.. Proper choice of the time delay for the analysis of chaotic time series. Phys.Lett. A, 1989, 142:107-111
[107] Liebert.W, Pawelzik.K and Schuster.H.G.. Optimal embeddings of chaotic attractors from topological considerations. Europhys.Lett. 1991, 14:521
[108] Kim H S, Eykholt R, Salas J D. Nonlinear Dynamics, Delay Times, and Embedding Windows. Physica D, 1999, 127, 48-60
[109] Abarbanel, H.D.I., Brown, R., Sidorowich, J.J., & Tsimring, L.S. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys,1993, 64( 5): 1331-1393
[110] Marwan N, Wessel.N, Meyerfeld, et al. Recurrence Plot-Based Measure of Complexity and Their Application to Heart-Rate-Variability Data. Physical Review E, 2002,66:026702
[111] Marwan N. Recurrence plots and cross recurrence plots [online]. http://www.recurrence-plot.tk//glance.php
[112] Gao.J.B. Recurrence Time statistics for chaotic systems and their applications. Physical Review letters,1999,83(16):3178-3181
[113]程正兴，小波分析算法与应用[M]，西安：西安交通大学出版社，1998
[114]秦前清，杨宗凯，实用小波分析，西安：西安电子科技大学出版社，1994
[115]成礼智，郭汉伟，小波与离散变换理论及工程实践，北京：清华大学出版社，2005
[116] Gollub.J.P., Romer.E.J. and Socolar. J.E. Trajectory divergence for coupled relaxation oscillators: measurements and models. J. Stat. Phys, 1980, 23, (3): 321-333
[117] Wright.J. Method for Calculating a Lyapunov Exponent. Phys. Rev. 1984, A29 :2923.
[118] J.D. Farmer, E. Ott and J.A. Yorke. The Dimension of Chaotic Attractors. Physica 7D, 1983, 607 C: 153-180.
[119] Oseledec V.I..A Multiplicative Ergodic Theorem Lyapunov Characteristic Numbers for Dynamical Systems. Trans. Moscow Math. Soc. 1968,19:197-231
[120] Benettin.G, Galgani.L,Giorgilli.A and Strelcyn.J.M. Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems; A Method for Computing All of Them. Meccanica.1980, 15:9-20.
[121] Shimada.I and Nagashima.T. A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems. Prog TheorPhys, 1979,61(6) :1605 - 1615
[122] Shaw.R. Strange Attractors, Chaotic Behavior, and Information Flow. Z Naturf, 1981, 36A: 80-112
[123] Rosenstein.M.T, Collins.J.J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D, 1993, 65:117-134
[124] Warwick.T. Computing accurate Poincarémaps. Physica D. 2002, 171: 127-137
[125] Hénon.M. On the numerical computation of Poincarémaps, Physica D 5 (1982) 412-414.
[126] Chen.G, R. Fouracre.A, Banford H.M.and Tedford.D.J. The effects of gamma irradiation on thermally stimulated discharge current spectra in low-density polyethylene"Radiat. Phys. Chem., 1991, 37:523-530
[127] Hegazy.E.A, Sasuga.T, Nishii.M and Seguchi.T. Irradiation effects on aromatic polymers: 2. Gas evolution during electron-beam irradiation. Polymer, 1992,33(14): 29042910
[128] Chen.G.., Banford.H.M, Davies.A. Effect of gamma-irradiation on electrical breakdown stress of LDPE. Conduction and Breakdown in Solid Dielectrics, 1995 :556-560
[129] Fu, M,Chen. G, Dissado. L. A, et al. The Effect of Gamma Irradiation on Space Charge Behaviour and Dielectric Spectroscopy of Low-density Polyethylene. Solid Dielectrics, 2007. ICSD '07. IEEE International Conference on 8-13 July 2007:442 - 445
[130] Fouracre.R.A, Banford.H.M, Tedford. D.J. et al. Gamma irradiation effects in two epoxy resins and a polyimide. Electrical Insulation and Dielectric Phenomena, 1989. Annual Report., Conference on 29 Oct.-2 Nov. 1989:198 -203
[131] Vogel.H. Flammfestmachen von Kunststoffen [M]. Huthig-Verlag, Heidelberg, 1966
[132] Hilado.C.J. Flammability Handbook for Plastics [M]. Technomic, Stamford,Conn.1969
[133] Lyons.J.W. The chemistry and uses of fire retardants. Wiley-Intersicence. London, 1970
© 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 |