A Hierarchical Approach to Dimensionality Reduction and Nonparametric Problems in the Polynomial Chaos Simulation of Transmission Lines

2020 ◽  
Vol 62 (3) ◽  
pp. 736-745
Author(s):  
Paolo Manfredi
Keyword(s):  
Dimensionality Reduction ◽  
Transmission Lines ◽  
Polynomial Chaos ◽  
Hierarchical Approach

scholarly journals Efficient Uncertainty Assessment in EM Problems via Dimensionality Reduction of Polynomial-Chaos Expansions

Technologies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 37
Author(s):  
Christos Salis ◽  
Nikolaos Kantartzis ◽  
Theodoros Zygiridis
Keyword(s):  
Dimensionality Reduction ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Uncertainty Assessment ◽  
Test Cases ◽  
Stochastic Inputs ◽  
Dimensionality Reduction Technique ◽  
Sensitivity Analysis Method ◽  
Polynomial Chaos Expansions ◽  
Involved Field

The uncertainties in various Electromagnetic (EM) problems may present a significant effect on the properties of the involved field components, and thus, they must be taken into consideration. However, there are cases when a number of stochastic inputs may feature a low influence on the variability of the outputs of interest. Having this in mind, a dimensionality reduction of the Polynomial Chaos (PC) technique is performed, by firstly applying a sensitivity analysis method to the stochastic inputs of multi-dimensional random problems. Therefore, the computational cost of the PC method is reduced, making it more efficient, as only a trivial accuracy loss is observed. We demonstrate numerical results about EM wave propagation in two test cases and a patch antenna problem. Comparisons with the Monte Carlo and the standard PC techniques prove that satisfying outcomes can be extracted with the proposed dimensionality-reduction technique.

Radiated Susceptibility Analysis of Multiconductor Transmission Lines Based on Polynomial Chaos

2021 ◽  
Vol 35 (12) ◽  
pp. 1556-1566
Author(s):  
Tianhao Wang ◽  
Quanyi Yu ◽  
Xianli Yu ◽  
Le Gao ◽  
Huanyu Zhao
Keyword(s):  
Transmission Lines ◽  
Polynomial Chaos ◽  
Elevation Angle ◽  
Polarization Angle ◽  
Random Input ◽  
Multiconductor Transmission Lines ◽  
Sparse Polynomial ◽  
Calculation Results ◽  
Line Theory ◽  
Input Variables

To address the uncertainties of the radiated susceptibility of multiconductor transmission lines (MTLs), a surrogate model of the MTLs radiated susceptibility is established based on generalized polynomial chaos (gPC), and the gPC is made sparser by combining the adaptive hyperbolic truncation (AHT) scheme and the least angle regression (LAR) method. The uncertainties of the radiated susceptibility of transmission lines are calculated using the adaptive-sparse polynomial chaos (AS-PC) scheme. The parameters related to the incident field, such as elevation angle theta, azimuth angle psi, polarization angle eta, and field amplitude E, are inevitably random. Therefore, these four variables are taken as random input variables, and each of them is subject to different variable distributions. The MTLs model with infinite ground as the reference conductor is adopted, different impedances are used and the AS-PC scheme is combined with transmission line theory to calculate the average, standard deviation and probability distribution of the radiated susceptibility of MTLs. Sobol global sensitivity analysis based on variance decomposition is adopted to calculate the influence of random input variables on the MTLs radiated susceptibility model. The calculation results are compared with the results of the Monte Carlo (MC) method, proving that the proposed method is correct and feasible.

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