Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Abstract

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.

Published by IEEE Trans CAD in May 2014

References in corpus (2)

• Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos
• Efficient Uncertainty Quantification for the Periodic Steady State of Forced and Autonomous Circuits

Cited by in corpus (4)

• Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition
• Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques
• High-Dimensional Uncertainty Quantification of Electronic and Photonic IC with Non-Gaussian Correlated Process Variations
• Chance-Constrained and Yield-aware Optimization of Photonic ICs with Non-Gaussian Correlated Process Variations