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Graduate Exam Abstract


Aditi Krishna Prasad

Ph.D. Final
March 23, 2018, 11:00 am - 1:00 pm
Civil and Environmental Engineering Conference Roo
Accurate Dimension Reduction Based Polynomial Chaos Approach for Uncertainty Quantification of High Speed Networks

Abstract: With the continued miniaturization of VLSI technology to sub-45 nm levels, uncertainty in nanoscale manufacturing processes and operating conditions have been found to translate into unpredictable system-level behavior of integrated circuits. As a result, there is a need for contemporary circuit simulation tools/solvers to model the forward propagation of device level uncertainty to the network response. Recently, techniques based on the robust generalized polynomial chaos (PC) theory have been reported for the uncertainty quantification of high-speed circuit, electromagnetic, and electronic packaging problems. The major bottleneck in all PC approaches is that the computational effort required to generate the metamodel scales in a polynomial fashion with the number of random input dimensions. In order to mitigate this poor scalability of conventional PC approaches, a reduced dimensional PC approach is proposed. This PC approach is based on using a high dimensional model representation (HDMR) to quantify the relative impact of each dimension on the variance of the network response. The reduced dimensional PC approach is further extended to problems with mixed aleatory and epistemic uncertainties. In this mixed PC approach, a parameterized formulation of analysis of variance (ANOVA) is used to identify the statistically significant dimensions and subsequently perform dimension reduction. Mixed problems are however characterized by far greater number of dimensions than purely epistemic or aleatory problems, thus exacerbating the poor scalability of PC expansions. To address this issue, a novel dimension fusion approach is proposed. This approach fuses the epistemic and aleatory dimensions within the same model parameter into a mixed dimension. The accuracy and efficiency of the proposed approaches are validated through multiple numerical examples.

Adviser: Sourajeet Roy
Co-Adviser: N/A
Non-ECE Member: Charles Anderson
Member 3: Ali Pezeshki
Addional Members: Branislav Notaros

Publications:
Journal Papers
[1] A. K. Prasad and S. Roy, “Multidimensional variability analysis of complex power distribution networks via scalable stochastic collocation approach,” IEEE Trans. Comp., Packag. and Manuf. Technol., vol. 5, no. 11, pp. 1656-1668, Nov. 2015
[2] A. K. Prasad, M. Ahadi, and S. Roy, “Multidimensional uncertainty quantification of microwave/RF networks using linear regression and optimal design of experiments,” IEEE Trans. Microwave Theory Techn., vol. 64, no.8, pp. 2433-2446, Aug. 2016
[3] A. K. Prasad and S. Roy, “Accurate reduced dimensional polynomial chaos for efficient uncertainty quantification of microwave/RF networks,” IEEE Trans. Microwave Theory Tech., vol. 65, no.10, pp. 3697-3708, Oct. 2017

Conference Papers
[1] A. K. Prasad, M. Ahadi, and S. Roy, “Polynomial chaos based variability analysis of power distribution networks using a 3D topology of multiconductor transmission lines”, in Proc. 23rd IEEE Conference on Electrical Performance of Electronic Packaging, Oct. 2014, pp. 21-24
[2] A. K. Prasad, M. Ahadi, B. S. Thakur, and S. Roy, “Accurate polynomial chaos expansion for variability analysis using optimal design of experiments,” in Proc. IEEE Int. Conf. Numer. Electromagn., Multiphys. Modeling. Optim, Aug. 2015, pp. 1-4
[3] A. K. Prasad and S. Roy, “Global sensitivity based dimension reduction for fast variability analysis of nonlinear circuits,” in Proc. 24th IEEE Conference on Electrical Performance of Electronic Packaging, Oct. 2015, pp. 97-99
[4] A. K. Prasad, D. Zhou, and S. Roy, “Reduced dimension polynomial chaos approach for efficient uncertainty analysis of multi-walled carbon nanotube interconnects,” in Proc. IEEE MTT-S 64th International Microwave Symposium, May 2016, pp. 1-3
[5] I. Kapse, A. K. Prasad, and S. Roy, “Generalized anisotropic polynomial chaos approach for expedited statistical analysis of non-linear radio- frequency (RF) circuits”, in Proc. IEEE 20th Workshop on Signal and Power Integrity, May 2016, pp. 1-3
[6] M. Ahadi, A. K. Prasad, and S. Roy, “Hyperbolic polynomial chaos expansion (HPCE) and its application to statistical analysis of nonlinear circuits,” in Proc. IEEE 20th Workshop on Signal and Power Integrity, May 2016, pp. 1-4
[7] X. Gao, Y. Wang, N. Spotts, N. Xie, S. Roy, and A. K. Prasad, “Fast uncertainty quantification in engine nacelle inlet design using a reduced dimensional polynomial chaos approach”, AIAA Propulsion and Energy, July 25-27, 2016, Salt Lake City, Utah
[8] X. Gao, J. Weinmeister, N. Xie, S. Roy, and A. K. Prasad, “Combining a reduced polynomial chaos expansion approach with universal kriging”, in 8th AIAA Theoretical Fluid Mechanics Conference , June 5-9, 2017, Denver, Colorado
[9] I. Kapse, A. K. Prasad and S. Roy, “Analyzing Impact of Epistemic Uncertainty in High-Speed Circuit Simulation Using Fuzzy Variables and Global Polynomial Chaos Surrogates”, in Proc. IEEE Int. Conf. Numer. Electromagn., Multiphys. Modeling. Optim, May. 2017, pp. 320-322
[10] A. K. Prasad and S. Roy, “A novel dimension fusion based polynomial chaos approach for mixed aleatory-epistemic uncertainty quantification of carbon nanotube interconnects”, in Proc. IEEE Symp. Electromagn. Compatibility and Signal Integrity, Aug 2017, pp. 108-111
[11] A. K. Prasad and S. Roy, “Mixed Epistemic-Aleatory Uncertainty Quantification using Reduced Dimensional Polynomial Chaos and Parametric ANOVA (PANOVA)” in 24th IEEE Conference on Electrical Performance of Electronic Packaging, Oct. 2017
[12] Weinmeister, J., Xie, N., Gao, X., Prasad, A., and Roy, S., “Analysis of a Polynomial Chaos-Kriging Metamodel for Uncertainty Quantification in Aerospace Applications”, in 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, January 8-12, 2018, Kissimmee, Florida
[13] A.K. Prasad and S. Roy, ”Multi-Fidelity Approach for Polynomial Chaos based Statistical Analysis of Microwave Networks”, accepted for presentation in Applied Computational Electromagnetic Society Conference, Denver, March 2018



Program of Study:
CS 575
ECE 554
CS 545
ECE 641
ECE 581A5
ECE 795
ECE 799
N/A