Principal component analysis for efficient characterization of stochastic electromagnetic fields

Abstract

The propagation of stochastic electromagnetic fields can be accurately modeled using the auto-and cross-correlation spectra of the field components. In this work, we introduce the framework of principal component analysis for reducing the computational cost of handling stochastic electromagnetic fields described by correlation matrices. We consider noisy electromagnetic fields originating from stationary random processes with Gaussian probability distribution. The amount of data obtained by 2-dimensional near-field measurements and by determining the autoand cross-correlation information of electromagnetic interference can become burdensome for further processing even for problems of moderate size. For obtaining the correlation data, 2 measurement probes have to scan a defined grid of measurement points. For each pair of points, the spatial correlations need to be calculated, and hence, the data obtained scales quadratically with the number of sampling points.To reduce the amount of data, we project the given data obtained by measurement or simulation onto directions of maximum variation, the so called principal components, and keep only those principal components which contribute most to the total variance. In this way, the memory demand for storage and further computation of stochastic electromagnetic fields can be reduced significantly. KEYWORDS electromagnetic interference, noisy electromagnetic fields, principal component analysis, stochastic electromagnetic fields Int J Numer Model. 2018;31:e2246.wileyonlinelibrary.com/journal/jnm

Cyclostationary Characterization of Radiated Emissions in Digital Electronic Devices

“…points. An efficient method for the reduction of reference points is the principal component analysis (PCA) for eigenvalue decomposition of the correlation matrix [29], [30]. Applying this method allows the reduction of the reference probe positions down to the number of principal eigenvalues.…”

An extension of the transverse wave formulation to model stochastic electromagnetic fields

“…whereS is the scattering operator built from the continuuity conditions of the tangential fields [2], [14]. Collecting all the incoming and outgoing waves in (8) and (10) of all the interfaces in the structure, the Hilbert space vectors of incident and reflected waves are built and the problem is settled in the form of coupled equations…”

“…Using this formalism we can analyze multilayer structures, where homogeneous layers of finite extension in z-direction alternate with thin structured layers. The structured layers are described by the surface admittance matrices Y ij (u, v) translated in scattering operators as presented in (10). From this formulation, we can describe multilayer structures consisting of thin layers, with structured metalization, resistive layers, and impressed voltage and current sources and thick homogeneous material.…”

“…Characterization of noisy fields using field-field correlations opens new perspectives on signal integrity, EMI analysis, for low noise energy sensing and EMI source imaging [6]- [8]. Evolution of correlation information of stationary noisy propagating EM fields and aspects for their analysis by principal components are addressed in [9], [10].…”

Differential form representation of stochastic electromagnetic fields

“…Free space electromagnetic field propagation considering field-field correlations has been addressed in . Near field measurements for radiated EMI is discussed in (Russer et al, 2015d), while analysis of measurement data by principal component analysis, critical for large data sets acquired in characterizing fields by correlation information, is discussed in (Arnaut and Obiekezie, 2014;Haider and Russer, 2017).…”