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, in this dissertation, 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. The accuracy and efficiency of the proposed approaches are validated through multiple numerical examples.

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

Publications:
[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”, accepted for publication in IEEE Trans. Microwave Theory Techn, Apr. 2017
[4] 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
[5] 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
[6] 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
[7] 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
[8] 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
[9] 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
[10] 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
[11] X. Gao, J. Weinmeister, N. Xie, S. Roy, and A. K. Prasad, “Combining a reduced polynomial chaos expansion approach with universal kriging”, accepted for presentation in AIAA Aviation and Aeronautics, June 5-9, 2017, Denver, Colorado
[12] 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”, accepted for presentation in IEEE Int. Conf. Numer. Electromagn. Multiphys. Modeling. Optim, May. 2017
[13] A. K. Prasad and S. Roy, “A novel dimension fusion based polynomial chaos approach for mixed aleatory-epistemic uncertainty quantification of carbon nanotube interconnects” accepted for presentation in IEEE Symp. Electromagn. Compatibility and Signal Integrity, Aug 2017

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