An Adaptive Multi-Element Probabilistic Collocation Method for Statistical EMC/EMI Characterization

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IEEE Transactions on Electromagnetic Compatibility, ISSN: 0018-9375, Vol: 55, Issue: 6, Page: 1154-1168

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Yücel, Abdulkadir C.; Bagci, Hakan; Michielssen, Eric
Institute of Electrical and Electronics Engineers (IEEE); Institute of Electrical and Electronics Engineers
Physics and Astronomy; Engineering; Adaptive algorithm; Electromagnetic compatibility and interference (EMC/EMI); Generalized polynomial chaos (gPC); Multi-dimensional integral; Multi-element (ME); Probabilistic collocation (PC); Sparse grid (SG); Tensor product (TP); Tolerance analysis; Uncertainty quantification
article description
An adaptive multi-element probabilistic collocation (ME-PC) method for quantifying uncertainties in electromagnetic compatibility and interference phenomena involving electrically large, multi-scale, and complex platforms is presented. The method permits the efficient and accurate statistical characterization of observables (i.e., quantities of interest such as coupled voltages) that potentially vary rapidly and/or are discontinuous in the random variables (i.e., parameters that characterize uncertainty in a system's geometry, configuration, or excitation). The method achieves its efficiency and accuracy by recursively and adaptively dividing the domain of the random variables into subdomains using as a guide the decay rate of relative error in a polynomial chaos expansion of the observables. While constructing local polynomial expansions on each subdomain, a fast integral-equation-based deterministic field-cable-circuit simulator is used to compute the observable values at the collocation/integration points determined by the adaptive ME-PC scheme. The adaptive ME-PC scheme requires far fewer (computationally costly) deterministic simulations than traditional polynomial chaos collocation and Monte Carlo methods for computing averages, standard deviations, and probability density functions of rapidly varying observables. The efficiency and accuracy of the method are demonstrated via its applications to the statistical characterization of voltages in shielded/unshielded microwave amplifiers and magnetic fields induced on car tire pressure sensors. © 2013 IEEE.