Rational Polynomial Chaos Expansions for the Stochastic Macromodeling of Network Responses

This paper introduces rational polynomial chaos expansions for the stochastic modeling of the frequency-domain responses of linear electrical networks. The proposed method models stochastic network responses as a ratio of polynomial chaos expansions, rather than the standard single polynomial expans...

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Veröffentlicht in:IEEE transactions on circuits and systems. I, Regular papers Jg. 67; H. 1; S. 225 - 234
Hauptverfasser: Manfredi, Paolo, Grivet-Talocia, Stefano
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.01.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Chaos
Computational modeling
Computer networks
Electrical networks
Frequency-domain analysis
Impedance
Integrated circuit modeling
Iterative methods
Linear systems
Multiport systems
polynomial chaos
Polynomials
Rational functions
rational modeling
Stochastic models
Stochastic processes
uncertainty quantification
variability analysis
ISSN:1549-8328, 1558-0806
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Abstract This paper introduces rational polynomial chaos expansions for the stochastic modeling of the frequency-domain responses of linear electrical networks. The proposed method models stochastic network responses as a ratio of polynomial chaos expansions, rather than the standard single polynomial expansion. This approach is motivated by the fact that network responses are best represented by rational functions of both frequency and parameters. In particular, it is proven that the rational stochastic model is exact for lumped networks. The model coefficients are computed via an iterative re-weighted linear least-square regression. Several application examples, concerning both lumped and a distributed systems, illustrate and validate the advocated methodology.
AbstractList This paper introduces rational polynomial chaos expansions for the stochastic modeling of the frequency-domain responses of linear electrical networks. The proposed method models stochastic network responses as a ratio of polynomial chaos expansions, rather than the standard single polynomial expansion. This approach is motivated by the fact that network responses are best represented by rational functions of both frequency and parameters. In particular, it is proven that the rational stochastic model is exact for lumped networks. The model coefficients are computed via an iterative re-weighted linear least-square regression. Several application examples, concerning both lumped and a distributed systems, illustrate and validate the advocated methodology.
Author Grivet-Talocia, Stefano
Manfredi, Paolo
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SubjectTerms Chaos
Computational modeling
Computer networks
Electrical networks
Frequency-domain analysis
Impedance
Integrated circuit modeling
Iterative methods
Linear systems
Multiport systems
polynomial chaos
Polynomials
Rational functions
rational modeling
Stochastic models
Stochastic processes
uncertainty quantification
variability analysis
Title Rational Polynomial Chaos Expansions for the Stochastic Macromodeling of Network Responses
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