基于混沌多项式展开法的线束串扰统计模型
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摘要
针对线束导线在实际情况中为非确定性几何布置的这一问题,提出了一种基于混沌多项式展开法的线束串扰统计分析方法。该方法根据线束导线位置变量的分布类型选取相应的正交多项式对线束导线分布参数进行展开,结合边界条件,采用模式理论对基于混沌多项式展开的多导体传输线方程扩展形式进行求解,进而得到电压和电流向量的混沌多项式展开表达式,并利用混沌多项式展开法的相关性质得到表征线束串扰统计特征的相关参数。通过与传统的蒙特卡法进行对比可知,该方法在保证计算结果准确可靠的同时,计算效率也得到了大幅度的提高,从而实现复杂系统线束电磁兼容性能的高效预测。
For the phenomenon that the position of cable bundle in reality is non-deterministic geometric,this paper proposes the statistical analysis method of cable bundle crosstalk model based on Polynomial Chaos Expansion.The orthogonal polynomial basis functions are chosen based on the distribution pattern of the variables related to the positions of wires in the cable bundle,and the distributed parameters of the wires can be expressed by the Polynomial Chaos Expansion.With the boundary conditions,the extended MTL can be solved by the modeling methodology,and then the voltage vector and current vector can be expressed by the Polynomial Chaos Expansion.According to the properties of the Polynomial Chaos Expansion,the mean,standard deviation and variation range of the cable bundle crosstalk can be obtained,and the probability density function of the cable bundle crosstalk can also becalculatedthrough numerical method. Thus,the efficient prediction of electromagnetic compatibility of cable bundle in complex system has realized.
For the phenomenon that the position of cable bundle in reality is non-deterministic geometric,this paper proposes the statistical analysis method of cable bundle crosstalk model based on Polynomial Chaos Expansion.The orthogonal polynomial basis functions are chosen based on the distribution pattern of the variables related to the positions of wires in the cable bundle,and the distributed parameters of the wires can be expressed by the Polynomial Chaos Expansion.With the boundary conditions,the extended MTL can be solved by the modeling methodology,and then the voltage vector and current vector can be expressed by the Polynomial Chaos Expansion.According to the properties of the Polynomial Chaos Expansion,the mean,standard deviation and variation range of the cable bundle crosstalk can be obtained,and the probability density function of the cable bundle crosstalk can also becalculatedthrough numerical method. Thus,the efficient prediction of electromagnetic compatibility of cable bundle in complex system has realized.
引文
[1]Paul Clayton R.电磁兼容导论[M].闻映红,译.北京:人民邮电出版社,2007:324.
[2]Frei S,Jobava R G,Topchishvili D.Complex approaches for the calculation of EMC problems of large systems[C]∥International Symposium on Electromagnetic Compatibility,Santa Clara,USA,2004:826-831.
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[4]孙亚秀,卓庆坤,姜庆辉,等.基于多导体传输线理论的差模激励新型线束串扰模型研究[J].物理学报,2015,64(4):1-13.Sun Ya-xiu,Zhuo Qing-kun,Jiang Qing-hui,et al.New differential-mode-source cable bundle crosstalk model based on multiconductor transmission lines theory[J].Acta Phys Sin,2015,64(4):1-13.
[5]Ni G Y,Yan L,Yuan N C.Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field[J].Chinese Physics B,2008,17(10):3629-3634.
[6]Paul Clayton R.多导体传输线分析[M].杨晓宪,郑涛,译.北京:中国电力出版社,2013:312-313.
[7]吴振军,王丽芳,廖承林.分析端接频变负载的多导体传输线FDTD新方法[J].物理学报,2009,58(9):6146-6151.Wu Zhen-jun,Wang Li-fang,Liao Cheng-lin.A novel FDTD method for multi-conductor transmission lines terminating in frequency-dependent loads[J].Acta Phys Sin,2009,58(9):6146-6151.
[8]Ferrieres X,Parmantier J P,Bertuol S,et al.Application of a hybrid finite difference/finite volume method to solve an automotive EMC problem[J].IEEE Transactions on Electromagnetic Compatibility,2004,46(4):624-634.
[9]Zhang Q,Liou J J,Mcmacken J,et al.Development of robust interconnect model based on design of experiments and multiobjective optimization[J].IEEE Transactions on Electron Devices,2001,48(9):1885-1891.
[10]Bellan D,Pignari S.A.probabilistic model for the response of an electrically short two-conductor transmission line driven by a random plane wave field[J].IEEE Transactions on Electromagnetic Compatibility,2001,43(2):130-139.
[11]Shiran S,Reiser B,Cory H.A probabilistic method for the evaluation of coupling between transmission lines[J].IEEE Transactions on Electromagnetic Compatibility,1993,35(3):387-393.
[12]Salio S,Canavero F,Lefebvre J,et al.Statistical description of signal propagation on random bundles of wires[C]∥The 13th International Zurich Symposium Electromagnetic Compatibility,Zurich Switizerland,1999:499-504.
[13]高印寒,王天皓,杨开宇,等.汽车线束的动态串扰特性预测[J].吉林大学学报:工学版,2014,44(5):1258-1263.Gao Yin-han,Wang Tian-hao,Yang Kai-yu,et al.Prediction of the dynamic crosstalk of automotive wiring hardness[J].Journal of Jilin University(Engineering and Technology Edition)2014,44(5):1258-1263.
[14]Sun S,Liu G,Drewniak J L,et al.Hand-assembled cable bundle modeling for crosstalk and commonmode radiation prediction[J].IEEE Transactions on Electromagnetic Compatibility,2007,49(3):708-718.
[15]Wu M,Beetner D,Hubing T,et al.Estimation of the statistical variation of crosstalk in wiring harnesses[C]∥IEEE International Symposium on Electromagnetic Compatibility,Detroit,USA,2008:614-619.
[16]Wu M,Beetner D G,Hubing T H,et al.Statistical prediction of"reasonable worst-case"crosstalk in cable bundles[J].IEEE Transactions on Electromagnetic Compatibility,2009,51(3):842-851.
[17]Diouf F,Canavero F.Crosstalk statistics via collocation method[C]∥IEEE International Symposium on Electromagnetic Compotibility,Austin,TX,USA,2009:92-97.
[18]Salio S,Canavero F,Lecointe D,et al.Crosstalk prediction on wire bundles by Kriging approach[C]∥IEEE International Symposium on Electromagnetic Compatibility,Washington DC,USA,2000:197-202.
[19]Bellan D,Pignari S A,Spadacini G.Characterisation of crosstalk in terms of mean value and standard deviation multiconductor transmission lines[J].IEE Proceedings on Science,Measurement and Technology,2003,150(6):289-295.
[20]Bellan D,Pignari S A,Spadacini G.Characterisation of crosstalk in terms of mean value and standard deviation multiconductor transmission lines[J].IEE Proceedings on Science,Measurement and Technology,2003,150(6):289-295.
[21]Halligan M S,Beetner D G.Maximum crosstalk estimation in weakly coupled transmission lines[J].IEEE Transactions on Electromagnetic Compatibility,2014,56(3):736-744.
[22]Wiener N.The homogeneous chaos[J].American Journal of Mathematics,1938,60(1):897-936.
[23]Ghanem R G,Spanos P D.Stochastic Finite Elements:a Spectral Approach[M].Berlin:Springer,1991:224.
[24]Ghanem R.Ingredients for a general purpose stochastic finite elements implementation[J].Computer Methods in Applied Mechanics&Engineering,1999,168(1-4):19-34.
[25]Finette S.A stochastic representation of environmental uncertainty and its coupling to acoustic wave propagation in ocean waveguides[J].Acoustical Society of America Journal,2006,120(5):2567.
[26]Xiu D,Karniadakis G E.The wiener-askey polynomial chaos for stochastic differential equations[J].SIAM Journal on Scientific Computing,2002,24(2):619-644.
[27]Xiu D,Karniadakis G E.A new stochastic approach to transient heat conduction modeling with uncertainty[J].International Journal of Heat&Mass Transfer,2003,46(24):4681-4693.
[28]Stievano I S,Manfredi P,Canavero F G.Carbon nanotube interconnects:process variation via polynomial chaos[J].IEEE Transactions on Electromagnetic Compatibility,2012,54(1):140-148.
[29]Cameron R H,Martin W T.The orthogonal development of non-linear functionals in series of fourierhermite functionals[J].Annals of Mathematics,1947,48(48):385-392.
[30]王晓东,康顺.多项式混沌方法在随机方腔流动模拟中的应用[J].中国科学:技术科学,2011,33(6):790-798.Wang Xiao-dong,Kang Shun.Application of polynomial chaos on numerical simulation of stochastic cavity flow[J].Science China:Technological Sciences,2011,33(6):790-798.
[31]高印寒,王瑞宝,马玉刚,等.汽车线束导线间寄生电容及串扰的解析预测模型[J].吉林大学学报:工学版,2011,41(增刊1):144-149.Gao Yin-han,Wang Rui-bao,Ma Yu-gang,et al.Analytical prediction of parasitic capacitance and crosstalk in automotive cable bundles[J].Journal of Jilin University(Engineering and Technology Edition),2011,41(Sup.1)144-149.
[32]Paul C R.Decoupling the multiconductor transmission line equations[J].IEEE Transactions on Microwave Theory&Techniques,1996,44(8):1429-1440.
[33]Papoulis A.Probability,Random Variables and Stochastic Processes[M].3rd ed.New York:McGrawHill,1991:207-209.
[2]Frei S,Jobava R G,Topchishvili D.Complex approaches for the calculation of EMC problems of large systems[C]∥International Symposium on Electromagnetic Compatibility,Santa Clara,USA,2004:826-831.
[3]Capraro G T,Paul C R.Design of the routing for EMC[C]∥The 21st International Symposium on Electromagnetic Compatibility,1979.
[4]孙亚秀,卓庆坤,姜庆辉,等.基于多导体传输线理论的差模激励新型线束串扰模型研究[J].物理学报,2015,64(4):1-13.Sun Ya-xiu,Zhuo Qing-kun,Jiang Qing-hui,et al.New differential-mode-source cable bundle crosstalk model based on multiconductor transmission lines theory[J].Acta Phys Sin,2015,64(4):1-13.
[5]Ni G Y,Yan L,Yuan N C.Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field[J].Chinese Physics B,2008,17(10):3629-3634.
[6]Paul Clayton R.多导体传输线分析[M].杨晓宪,郑涛,译.北京:中国电力出版社,2013:312-313.
[7]吴振军,王丽芳,廖承林.分析端接频变负载的多导体传输线FDTD新方法[J].物理学报,2009,58(9):6146-6151.Wu Zhen-jun,Wang Li-fang,Liao Cheng-lin.A novel FDTD method for multi-conductor transmission lines terminating in frequency-dependent loads[J].Acta Phys Sin,2009,58(9):6146-6151.
[8]Ferrieres X,Parmantier J P,Bertuol S,et al.Application of a hybrid finite difference/finite volume method to solve an automotive EMC problem[J].IEEE Transactions on Electromagnetic Compatibility,2004,46(4):624-634.
[9]Zhang Q,Liou J J,Mcmacken J,et al.Development of robust interconnect model based on design of experiments and multiobjective optimization[J].IEEE Transactions on Electron Devices,2001,48(9):1885-1891.
[10]Bellan D,Pignari S.A.probabilistic model for the response of an electrically short two-conductor transmission line driven by a random plane wave field[J].IEEE Transactions on Electromagnetic Compatibility,2001,43(2):130-139.
[11]Shiran S,Reiser B,Cory H.A probabilistic method for the evaluation of coupling between transmission lines[J].IEEE Transactions on Electromagnetic Compatibility,1993,35(3):387-393.
[12]Salio S,Canavero F,Lefebvre J,et al.Statistical description of signal propagation on random bundles of wires[C]∥The 13th International Zurich Symposium Electromagnetic Compatibility,Zurich Switizerland,1999:499-504.
[13]高印寒,王天皓,杨开宇,等.汽车线束的动态串扰特性预测[J].吉林大学学报:工学版,2014,44(5):1258-1263.Gao Yin-han,Wang Tian-hao,Yang Kai-yu,et al.Prediction of the dynamic crosstalk of automotive wiring hardness[J].Journal of Jilin University(Engineering and Technology Edition)2014,44(5):1258-1263.
[14]Sun S,Liu G,Drewniak J L,et al.Hand-assembled cable bundle modeling for crosstalk and commonmode radiation prediction[J].IEEE Transactions on Electromagnetic Compatibility,2007,49(3):708-718.
[15]Wu M,Beetner D,Hubing T,et al.Estimation of the statistical variation of crosstalk in wiring harnesses[C]∥IEEE International Symposium on Electromagnetic Compatibility,Detroit,USA,2008:614-619.
[16]Wu M,Beetner D G,Hubing T H,et al.Statistical prediction of"reasonable worst-case"crosstalk in cable bundles[J].IEEE Transactions on Electromagnetic Compatibility,2009,51(3):842-851.
[17]Diouf F,Canavero F.Crosstalk statistics via collocation method[C]∥IEEE International Symposium on Electromagnetic Compotibility,Austin,TX,USA,2009:92-97.
[18]Salio S,Canavero F,Lecointe D,et al.Crosstalk prediction on wire bundles by Kriging approach[C]∥IEEE International Symposium on Electromagnetic Compatibility,Washington DC,USA,2000:197-202.
[19]Bellan D,Pignari S A,Spadacini G.Characterisation of crosstalk in terms of mean value and standard deviation multiconductor transmission lines[J].IEE Proceedings on Science,Measurement and Technology,2003,150(6):289-295.
[20]Bellan D,Pignari S A,Spadacini G.Characterisation of crosstalk in terms of mean value and standard deviation multiconductor transmission lines[J].IEE Proceedings on Science,Measurement and Technology,2003,150(6):289-295.
[21]Halligan M S,Beetner D G.Maximum crosstalk estimation in weakly coupled transmission lines[J].IEEE Transactions on Electromagnetic Compatibility,2014,56(3):736-744.
[22]Wiener N.The homogeneous chaos[J].American Journal of Mathematics,1938,60(1):897-936.
[23]Ghanem R G,Spanos P D.Stochastic Finite Elements:a Spectral Approach[M].Berlin:Springer,1991:224.
[24]Ghanem R.Ingredients for a general purpose stochastic finite elements implementation[J].Computer Methods in Applied Mechanics&Engineering,1999,168(1-4):19-34.
[25]Finette S.A stochastic representation of environmental uncertainty and its coupling to acoustic wave propagation in ocean waveguides[J].Acoustical Society of America Journal,2006,120(5):2567.
[26]Xiu D,Karniadakis G E.The wiener-askey polynomial chaos for stochastic differential equations[J].SIAM Journal on Scientific Computing,2002,24(2):619-644.
[27]Xiu D,Karniadakis G E.A new stochastic approach to transient heat conduction modeling with uncertainty[J].International Journal of Heat&Mass Transfer,2003,46(24):4681-4693.
[28]Stievano I S,Manfredi P,Canavero F G.Carbon nanotube interconnects:process variation via polynomial chaos[J].IEEE Transactions on Electromagnetic Compatibility,2012,54(1):140-148.
[29]Cameron R H,Martin W T.The orthogonal development of non-linear functionals in series of fourierhermite functionals[J].Annals of Mathematics,1947,48(48):385-392.
[30]王晓东,康顺.多项式混沌方法在随机方腔流动模拟中的应用[J].中国科学:技术科学,2011,33(6):790-798.Wang Xiao-dong,Kang Shun.Application of polynomial chaos on numerical simulation of stochastic cavity flow[J].Science China:Technological Sciences,2011,33(6):790-798.
[31]高印寒,王瑞宝,马玉刚,等.汽车线束导线间寄生电容及串扰的解析预测模型[J].吉林大学学报:工学版,2011,41(增刊1):144-149.Gao Yin-han,Wang Rui-bao,Ma Yu-gang,et al.Analytical prediction of parasitic capacitance and crosstalk in automotive cable bundles[J].Journal of Jilin University(Engineering and Technology Edition),2011,41(Sup.1)144-149.
[32]Paul C R.Decoupling the multiconductor transmission line equations[J].IEEE Transactions on Microwave Theory&Techniques,1996,44(8):1429-1440.
[33]Papoulis A.Probability,Random Variables and Stochastic Processes[M].3rd ed.New York:McGrawHill,1991:207-209.