Efficient Statistical Extraction of the Per-Unit-Length Capacitance and Inductance Matrices of Cables with Random Parameters
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Abstract
Cable bundles often exhibit random parameter variations due to uncertain or uncontrollable physical properties and wire positioning. Efficient tools, based on the so-called polynomial chaos, exist to rapidly assess the impact of such variations on the per-unit-length capacitance and inductance matrices, and on the pertinent cable response. Nevertheless, the state-of-the-art method for the statistical extraction of the per-unit-length capacitance and inductance matrices of cables suffers from several inefficiencies that hinder its applicability to large problems, in terms of number of random parameters and/or conductors. This paper presents an improved methodology that overcomes the aforementioned limitations by exploiting a recently-published, alternative approach to generate the pertinent polynomial chaos system of equations. A sparse and decoupled system is obtained that provides remarkable benefits in terms of speed, memory consumption and problem size that can be dealt with. The technique is thoroughly validated through the statistical analysis of two canonical structures, i.e. a ribbon cable and a shielded cable with random geometry and position.
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References
G. Capraro and C. R. Paul, A probabilistic approach to wire coupling interference prediction, in Proc. EEE Int. Zurich Symp. Electromagn. Compat, Zurich, Switzerland, 1981, pp. 267-272.
C. R. Paul, Sensitivity of crosstalk to variations in cable bundles, in Proc. EEE Int. Zurich Symp. Electromagn. Compat., Zurich, Switzerland, 1987, pp. 617-622.
S. Shiran, B. Reiser, and H. Cory, A probabilistic model for the evaluation of coupling between transmission lines, EEE Trans. Electromagn. Compat., vol. 35, no. 3, pp. 387-393, Aug. 1993.
A. Ciccolella and F. G. Canavero, Stochastic prediction of wire coupling interference, in Proc. EEE Int. Symp. Electromagn. Compat., Atlanta, GA, Aug. 1995, pp. 51-56.
D. Bellan and S. A. Pignari, A prediction model for crosstalk in large and densely-packed random wire bundles, in Proc. nt. Wroclaw Symp. Electromagn. Compat., Wroclaw, Poland, 2000, pp. 267-269.
D. Bellan, S. A. Pignari, and G. Spadacini, Characterisation of crosstalk in terms of mean value and standard deviation, in EE Proc.-Sci. Meas. Technol., vol. 150, no. 6, pp. 289-295, Nov. 2003.
F. Diouf and F. G. Canavero, Crosstalk statistics via collocation method, in Proc. EEE Int. Symp. Electromagn. Compat., Austin, TX, Aug. 2009, pp. 92-97.
M. Wu, D. G. Beetner, T. H. Hubing, H. Ke, and S. Sun, Statistical prediction of reasonable worst-case crosstalk in cable bundles, EEE Trans. Electromagn. Compat., vol. 51, no. 3, pp. 842-851, Aug. 2009.
D. Bellan and S. A. Pignari, Efficient estimation of crosstalk statistics in random wire bundles with lacing cords, EEE Trans. Electromagn. Compat., vol. 53, no. 1, pp. 209-218, Feb. 2011.
D. Bellan and S. A. Pignari, Statistical superposition of crosstalk effects in cable bundles, China Commun., vol. 10, no. 11, pp. 119-128, Nov. 2013.
S. Lallechere, B. Jannet, P. Bonnet, and F. Paladian, Sensitivity analysis to compute advanced stochastic problems in uncertain and complex electromagnetic environments, Advanced Electromagnetics, vol. 1, no. 3, pp. 13-23, Oct. 2012.
C. Kasmi, M. Helier, M. Darces, and E. Prouff, Design of experiments for factor hierachization in complex structure modelling, Advanced Electromagnetics, vol. 2, no. 1, pp. 59-64, Feb. 2013.
I. S. Stievano, P. Manfredi, and F. G. Canavero, Stochastic analysis of multiconductor cables and interconnects, EEE Trans. Electromagn. Compat., vol. 53, no. 2, pp. 501-507, May 2011.
D. Xiu and G. E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Scientific Computing, vol. 24, no. 2, pp. 619-644, 2002.
P. Manfredi, I .S. Stievano, and F. G. Canavero, Time- and frequency-domain evaluation of stochastic parameters on signal lines, Advanced Electromagnetics, vol. 1, no. 3, pp. 85-93, Oct. 2012.
P. Manfredi and F. G. Canavero, Numerical calculation of polynomial chaos coefficients for stochastic per-unit-length parameters of circular conductors, EEE Trans. Magnetics, vol. 50, no. 3, part 2, article #7026309, Mar. 2014.
D. Xiu, Fast numerical methods for stochastic computations: a review, Commun. Computational Physics, vol. 5, no. 2-4, pp. 242-272, Feb. 2009.
J .C. Clements, C. R. Paul, and A. T. Adams, Computation of the capacitance matrix for systems of dielectric-coated cylindrical conductors, EEE Trans. Electromagn. Compat., vol. EMC-17, no. 4, pp. 238-248, Nov. 1975.
C. R. Paul and A. E. Feather, Computation of the transmission line inductance and capacitance matrices from the generalized capacitance matrix, EEE Trans. Electromagn. Compat., vol. EMC-18, no. 4, pp. 175-183, Nov. 1976.
S.-K. Chang, T. K. Liu, and F. M. Tesche, Calculation of the per-unit-length capacitance matrix for shielded insulated wires, Technical Report, Science Applications Inc. Berkeley Calif, AD-A048 174/7, Sep. 1977.
P. Manfredi and F. G. Canavero, Crosstalk in stochastic cables via numerical multiseries expansion, in Proc. EEE Int. Conference on Electromagnetics in Advanced Applicat., Turin, Italy, Sep. 2013, pp. 1527-1530.
Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos, EEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 32, no. 10, pp. 1533-1545, Oct. 2013.
R. Pulch, Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations, J. Computational Appl. Math., vol. 262, pp. 281-291, May 2014.
C. R. Paul, Analysis of Multiconductor Transmission Lines. New York: Wiley, 1994.
M. Loeve, Probability Theory. 4th edn., New York: Springer-Verlag, 1977.
M. Berveiller, Elements finis stochastiques: approaches intrusive et non intrusive pour des analyses de fiabilite, Ph.D. dissertation, Universit'e Blaise Pascal, Clermont-Ferrand, France, Oct. 2005.
O. Aiouaz, D. Lautru, M.-F. Wong, E. Conil, A. Gati, J. Wiart, and V. F. Hanna, Uncertainty analysis of the specific absorption rate induced in a phantom using a stochastic spectral collocation method, Ann. Telecommun., vol. 66, no. 7-8, pp. 409-418, Aug. 2011.
A. C. M. Austin, N. Sood, J. Siu, and C. D. Sarris, Application of polynomial chaos to quantify uncertainty in deterministic channel models, EEE Trans. Antennas Propag., vol. 61, no. 11, pp. 5754-5761, Nov. 2013.
P. Kersaudy, S. Mostarshedi, B. Sudret, O. Picon, and J. Wiart, Stochastic analysis of scattered field by building facades using polynomial chaos, EEE Trans. Antennas Propag., vol. 62, no. 12, pp. 6382-6393, Dec. 2014.
G. H. Golub, J. H. Welsch, Calculation of Gauss quadrature rules, Math. Comput., pp. 221-230, 1969.
J.-S. Roger Jang, Matrix Inverse in Block Form. Online resource: http://www.cs.nthu.edu.tw/~jang/book/addenda/matinv/matinv/, Mar. 2001. E. V. Haynsworth, On the Schur complement, Basel Math. Notes, no. 20, Jun. 1968.