Least Squares Polynomial Chaos Regression for Stochastic Analysis of Transmission Lines Without and With Noise

Abstract

Stochastic transmission line (TL) analysis is often challenging due to the difficulty of fully identifying the probability distributions of all randomly varying parameters, especially in the presence of noise. These problems cannot be directly addressed by the existing polynomial chaos expansion (PCE) framework. To overcome the limitations, this paper proposes an improved PCE method for analyzing the stochastic TL model with noise. A regression-based non-intrusive approach termed least squares polynomial chaos regression (LSPCR) is employed to determine the PCE coefficients. Six algorithms for LSPCR are developed by respectively combining three sampling strategies, i.e., standard sampling (SS), asymptotic sampling (AS), and coherence-optimal sampling (COS), with two types of norm problems: the least-squares optimization problem (LSO) and the l1-minimum problem (l1-M). Numerical experiments are conducted on noiseless and noisy problems. The results reveal that the LSO-based algorithms (LSOs) are much faster than the l1-M-based algorithms (l1-Ms), regardless of the sampling strategy. In the absence of noise, these six algorithms require only a relatively small number of samples to achieve higher accuracy in solution moments compared to the Stochastic Galerkin (SG) method. When the sample size is large, the AS-based algorithms (ASs) and the COS-based algorithms (COSs) yield more accurate results than the SS-based algorithms (SSs), regardless of the norm problems. In the presence of noise, the LSOs outperform the l1-Ms for small sample sizes. However, no evident differences are observed among the six algorithms with large sample sizes.