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Perturbative reformulation of the stochastic Galerkin Method for statistical analysis of wiring structures with several random parameters

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Abstract
In this paper, a novel approach for statistical analysis of cable harnesses characterized by several random parameters is proposed, which is based on a perturbative reformulation of the well-known stochastic Galerkin method (SGM). With respect to the traditional SGM, the proposed method avoids the solution of an augmented multiconductor transmission line (MTL), whose dimensions may become prohibitive in case of structures characterized by several wires and random parameters. Namely, it resorts to the iterative and repeated solution of a MTL having the same number of wires as the original structure, where the effects of random variations of geometrical parameters are included by means of equivalent sources. The proposed approach is here applied to collect statistical information of voltages and currents at the terminations of a shielded cable. Through such an example, involving a large number of wires (7) and random variables (12), it is proven that the proposed method yields a significant reduction of computational time with respect to the traditional SGM, at the same time providing similar accuracy in the prediction of statistical moments.
Keywords
INTERCONNECTS, CABLES, Multiconductor transmission lines, perturbation technique, shielded, cable, statistical analysis, stochastic Galerkin method

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Citation

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MLA
Wu, Xinglong, Flavia Grassi, Sergio A. Pignari, et al. “Perturbative Reformulation of the Stochastic Galerkin Method for Statistical Analysis of Wiring Structures with Several Random Parameters.” 2018 IEEE SYMPOSIUM ON ELECTROMAGNETIC COMPATIBILITY, SIGNAL INTEGRITY AND POWER INTEGRITY (EMC, SI & PI). New york: Ieee, 2018. 170–174. Print.
APA
Wu, Xinglong, Grassi, F., Pignari, S. A., Manfredi, P., & Vande Ginste, D. (2018). Perturbative reformulation of the stochastic Galerkin Method for statistical analysis of wiring structures with several random parameters. 2018 IEEE SYMPOSIUM ON ELECTROMAGNETIC COMPATIBILITY, SIGNAL INTEGRITY AND POWER INTEGRITY (EMC, SI & PI) (pp. 170–174). Presented at the IEEE Symposium on Electromagnetic Compatibility, Signal Integrity and Power Integrity (EMC, SI & PI), New york: Ieee.
Chicago author-date
Wu, Xinglong, Flavia Grassi, Sergio A. Pignari, Paolo Manfredi, and Dries Vande Ginste. 2018. “Perturbative Reformulation of the Stochastic Galerkin Method for Statistical Analysis of Wiring Structures with Several Random Parameters.” In 2018 IEEE SYMPOSIUM ON ELECTROMAGNETIC COMPATIBILITY, SIGNAL INTEGRITY AND POWER INTEGRITY (EMC, SI & PI), 170–174. New york: Ieee.
Chicago author-date (all authors)
Wu, Xinglong, Flavia Grassi, Sergio A. Pignari, Paolo Manfredi, and Dries Vande Ginste. 2018. “Perturbative Reformulation of the Stochastic Galerkin Method for Statistical Analysis of Wiring Structures with Several Random Parameters.” In 2018 IEEE SYMPOSIUM ON ELECTROMAGNETIC COMPATIBILITY, SIGNAL INTEGRITY AND POWER INTEGRITY (EMC, SI & PI), 170–174. New york: Ieee.
Vancouver
1.
Wu X, Grassi F, Pignari SA, Manfredi P, Vande Ginste D. Perturbative reformulation of the stochastic Galerkin Method for statistical analysis of wiring structures with several random parameters. 2018 IEEE SYMPOSIUM ON ELECTROMAGNETIC COMPATIBILITY, SIGNAL INTEGRITY AND POWER INTEGRITY (EMC, SI & PI). New york: Ieee; 2018. p. 170–4.
IEEE
[1]
X. Wu, F. Grassi, S. A. Pignari, P. Manfredi, and D. Vande Ginste, “Perturbative reformulation of the stochastic Galerkin Method for statistical analysis of wiring structures with several random parameters,” in 2018 IEEE SYMPOSIUM ON ELECTROMAGNETIC COMPATIBILITY, SIGNAL INTEGRITY AND POWER INTEGRITY (EMC, SI & PI), Long Beach, CA, 2018, pp. 170–174.
@inproceedings{8583129,
  abstract     = {{In this paper, a novel approach for statistical analysis of cable harnesses characterized by several random parameters is proposed, which is based on a perturbative reformulation of the well-known stochastic Galerkin method (SGM). With respect to the traditional SGM, the proposed method avoids the solution of an augmented multiconductor transmission line (MTL), whose dimensions may become prohibitive in case of structures characterized by several wires and random parameters. Namely, it resorts to the iterative and repeated solution of a MTL having the same number of wires as the original structure, where the effects of random variations of geometrical parameters are included by means of equivalent sources. The proposed approach is here applied to collect statistical information of voltages and currents at the terminations of a shielded cable. Through such an example, involving a large number of wires (7) and random variables (12), it is proven that the proposed method yields a significant reduction of computational time with respect to the traditional SGM, at the same time providing similar accuracy in the prediction of statistical moments.}},
  author       = {{Wu, Xinglong and Grassi, Flavia and Pignari, Sergio A. and Manfredi, Paolo and Vande Ginste, Dries}},
  booktitle    = {{2018 IEEE SYMPOSIUM ON ELECTROMAGNETIC COMPATIBILITY, SIGNAL INTEGRITY AND POWER INTEGRITY (EMC, SI & PI)}},
  isbn         = {{978-1-5386-6621-0}},
  keywords     = {{INTERCONNECTS,CABLES,Multiconductor transmission lines,perturbation technique,shielded,cable,statistical analysis,stochastic Galerkin method}},
  language     = {{eng}},
  location     = {{Long Beach, CA}},
  pages        = {{170--174}},
  publisher    = {{Ieee}},
  title        = {{Perturbative reformulation of the stochastic Galerkin Method for statistical analysis of wiring structures with several random parameters}},
  year         = {{2018}},
}

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