Multidimensional Variability Analysis of Complex Power Distribution Networks via Scalable Stochastic Collocation Approach

Prasad, Aditi Krishna; Roy, Sourajeet

doi:10.1109/tcpmt.2015.2477717

Cited by 17 publications

(8 citation statements)

References 54 publications

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“…Furthermore, different cubature formulas for dealing with multidimensional integrals may be used for the generation of collocation points. One of the examples is Stroud cubature based SC method whose application for the variability analysis of PDNs within SPICE environments is reported in [12] and, for efficient computation of RCS from scatterers of uncertain shapes, in [19].…”

Section: An Outline Of the Stochastic Collocation Methodsmentioning

confidence: 99%

“…Again, utilizing the expansion of function over Lagrange polynomial basis (1) yields (12) which can be also written as…”

Section: An Outline Of the Stochastic Collocation Methodsmentioning

confidence: 99%

“…The combination of the nonintrusive, sampling based nature of Monte Carlo simulations with the polynomial approximation of output value, which is the characteristic of gPCE methods, made stochastic collocation one of the most researched and applied stochastic approaches [7][8][9]. The 2 Mathematical Problems in Engineering examples of successful coupling of SCM and its variations with different deterministic codes have been reported in stochastic dosimetry [10,11], in the analysis of complex power distribution networks (PDN) [12], in the design of integrated circuits (ICs), microelectromechanical systems, (MEMSs), and photonic circuits [13,14], in the simulation of EMcircuit systems [15,16], and in the area of antenna modeling [17][18][19] and electromagnetic compatibility (EMC) of space applications [20]. This paper reviews the previous work of the authors pertaining to the use of SC techniques in areas of CEM such as ground penetrating radar (GPR), EM-thermal dosimetry of the eye and brain, and buried lines and grounding systems [21].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Collocation Applications in Computational Electromagnetics

Poljak

Šesnić

Cvetković

et al. 2018

Mathematical Problems in Engineering

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The paper reviews the application of deterministic-stochastic models in some areas of computational electromagnetics. Namely, in certain problems there is an uncertainty in the input data set as some properties of a system are partly or entirely unknown. Thus, a simple stochastic collocation (SC) method is used to determine relevant statistics about given responses. The SC approach also provides the assessment of related confidence intervals in the set of calculated numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via SC method, is shown to be robust and efficient approach providing a satisfactory convergence rate. This review paper provides certain computational examples from the previous work by the authors illustrating successful application of SC technique in the areas of ground penetrating radar (GPR), human exposure to electromagnetic fields, and buried lines and grounding systems.

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Section: An Outline Of the Stochastic Collocation Methodsmentioning

confidence: 99%

“…Again, utilizing the expansion of function over Lagrange polynomial basis (1) yields (12) which can be also written as…”

Section: An Outline Of the Stochastic Collocation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic Collocation Applications in Computational Electromagnetics

Poljak

Šesnić

Cvetković

et al. 2018

Mathematical Problems in Engineering

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“…Later, in order to include non-linear loads, it is improved to tackle the time-domain stochastic behaviour of circuits, such as the transfer function trajectory method [18] and multi-dimensional Hermite series method [19]. For the purpose of including these stochastic models in a general circuit simulator, some researchers are focusing on the stochastic modelling of circuits in a SPICE-compatible environment [20][21][22][23][24]. It should be stressed that the main approaches described in [20][21][22][23][24] have been dependent on the SPICE-built-in TL macro-model without including the effect of the external electromagnetic field.…”

Section: Introductionmentioning

confidence: 99%

SPICE‐compatible admittance equivalent circuit for stochastic transmission line under external field illumination

Yang

Sun

Zhao

et al. 2019

IET Science, Measurement & Technology

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“…Several alternative methods have been studied with the objective of speeding up the MC while preserving accuracy [1][2][3][4][5][6][7]. A class of techniques based on the stochastic collocation (SC) method has been proposed [4,5,[8][9][10].…”

Section: General Backgroundmentioning

confidence: 99%

Uncertainty Quantification in Large Scale Systems Design

Ye¹

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One of the main challenges facing designers of high-speed integrated circuits and interconnects is predicting the effect of the variability of geometrical and physical parameters on the circuit performance. Monte Carlo (MC) simulation has been traditionally used in commercial circuit and electromagnetic (EM) simulators for predicting the statistical distribution of circuit and system performance metrics. However, the high computational cost associated with the MC simulation is a significant limiting factor especially for large circuits.In this thesis, an algorithm based on Parametric Model Order Reduction (PMOR) is presented for statistical analysis of large microwave and high-speed circuits with multiple stochastic parameters. Using the proposed algorithm, a set of local reducedorder parameterized circuits are derived based on adaptive frequency sampling and implicit multi-moment matching projection techniques. The local models preserve the stochastic parameters as symbolic quantities. As a result, stochastic response of the circuit can be obtained by simulating the local reduced models instead of the original large system leading to significant reduction in the computational cost compared to traditional Monte-Carlo techniques.In addition, a method is presented for high-dimensional variability analysis. This algorithm is based on two main concepts, namely node tearing for parameter partitioning and sparse grid interpolation. Node-tearing is used to localize the parameters I would also like to thank the staff at department of Electronics in Carleton University, especially Mrs. Blazenka Power. Their constantly and patiently supports made this adventure so much easier and for that, I am thankful.In the end, I would like to express my deep love to my parents for their love and care. Without their encouragement, I could not have reached this far. What they have sacrificed, I could not forget. Their courage, always inspires me. To them, I dedicate this thesis. vi

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Multidimensional Variability Analysis of Complex Power Distribution Networks via Scalable Stochastic Collocation Approach

Cited by 17 publications

References 54 publications

Stochastic Collocation Applications in Computational Electromagnetics

Stochastic Collocation Applications in Computational Electromagnetics

SPICE‐compatible admittance equivalent circuit for stochastic transmission line under external field illumination

Uncertainty Quantification in Large Scale Systems Design

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