Experimental Verification of Simulated Spectral Fluctuations of Unintended Electromagnetic Emissions from Electric Vehicles

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J. Electromagn. Eng. Sci. 2026;26(3):325-327

doi : https://doi.org/10.26866/jees.2026.3.l.30

Jun-Mo Park^a, Il-Suek Koh^b

Department of Electrical and Computer Engineering, Inha University, Incheon, Korea

^*Corresponding Author: Il-Suek Koh (e-mail: ikoh@inha.ac.kr)

ahttps://orcid.org/0009-0008-9213-7771

bhttps://orcid.org/0000-0003-0014-2466

Received 2025 May 27; Revised 2025 August 29; Accepted 2025 November 21.

Abstract

I. Introduction

Electric vehicles (EVs) contain numerous electronic components that produce unintended electromagnetic emissions (UEE) across a broad frequency range, resulting in a complex spectrum. Traditionally, these emissions have been measured to assess their suitability for electromagnetic compatibility (EMC)/electromagnetic interference (EMI) applications [1]. However, for vehicle classification based on UEE measurements, data collected for EMC/EMI applications are generally insufficient to train a classifier. Therefore, data augmentation is required.

Since the measured data pertaining to military objects are usually confidential, a simulation method must be implemented to generate the necessary data. In this letter, we investigate the feasibility of using such a simulation to estimate a key parameter of the UEE. We assume that the emission spectrum can be hypothesized as a Gaussian process—a theory grounded in the central limit theorem—given that the spectrum depends on many vehicle components whose states change in time. To verify this hypothesis, we examine the normality and standard deviation of spectrum fluctuations based on both simulated and experimental EMC/EMI data from both EVs and diesel vehicles (DVs).

Section II of this letter describes the simulation setup and the Monte Carlo (MC) method employed for data generation. In Section III, fluctuations in the simulation and measurement data are estimated and compared. Finally, Section IV presents the conclusion.

II. Simulation Data

The detailed simulation procedure and configurations for generating the UEE spectra of three vehicle types—compact car, sport utility vehicle (SUV), and truck—have been described in [2]. For the simulation, three common UEE sources located inside the vehicles were considered: the battery management system (BMS), the DC–DC converter, and the DC motor [1]. UEEs were computed over the 30–800 MHz frequency range outside the vehicles using a CST time solver. A total of 7,776 spectra were generated by combining eight source locations, three emission source orientations, and 108 observation points [2]. Notably, the observation points were positioned 10 m away from the vehicles. Furthermore, the azimuth (φ) and elevation (θ) angles were varied from 0° to 330° at 30° intervals and from 0° to 80° at 10° intervals, respectively. In this context, let j denote an emission source; the simulated spectrum generated by source j is then expressed as spnj(f), where j ∈ {1,2,3} denotes the BMS, DC–DC converter, and DC motor, respectively; p ∈ {x, y, z} denotes the orientation of the source; and n ∈ {1,2, …,108} denotes the observation point index.

To expand the dataset, the source location was randomly chosen, and its orientation was assumed to be random as well. Consequently, the spectrum can be formulated as follows:

where i denotes the index for the MC simulation trial. The coefficients a_i, b_i and c_i are random weights, which are independent uniform random variables over [−1, 1] satisfying |a_i| + |b_i| + |c_i| = 1. Finally, the spectrum of UEE at the observation point (n) can be calculated as Sni(f)=Σj=13Snij(f).

The simulated data were obtained by averaging, in a manner analogous to that used for the experimental data, as follows:

where N = 10⁶, denotes the total trial number of the MC simulation. Fig. 1 illustrates the SUV’s simulation spectra S̄_n (f), with 108 spectra plotted at each frequency point.

Fig. 1

S̄_n (f) of the SUV over the entire frequency range.

III. Fluctuation Estimation and Comparison

The experimental spectra of four EVs (Fig. 2), obtained at an observation point 10 m from the EVs in accordance with the KS C 9990 standard (matching the 10-m distance of the simulation setup), exhibited greater fluctuations than the simulated spectra (Fig. 1). This was expected, since the simulation accounted for only three emission components, whereas a real vehicle contains many more. Nonetheless, the overall fluctuation levels were comparable. The original experimental data contained many deterministic line spectra, which were removed using MATLAB’s filloutliers function. Although these spectra cannot be eliminated completely, their impact on fluctuation estimation was reduced.

Fig. 2

Experimental spectra of the four EVs.

The experimental spectrum was modeled as a random process whose value fluctuates about its mean at each frequency. However, the scarcity of data hindered precise estimation of the fluctuation. Therefore, to quantify fluctuations based on variance, the spectrum was assumed to be a variance-ergodic process. In other words, for the experimental case, the variance at a frequency point was computed from the fluctuation over the entire frequency band. In contrast, for the simulation, the variance at each frequency was computed from the 108 samples obtained from different observation points.

The spectrum in Fig. 2 was assumed to follow a Gaussian process, implying that the fluctuation at each frequency point follows a Gaussian probability density function (PDF). To verify this assumption, experimental data pertaining to the four EVs and an additional 30 DVs were considered. Since emission sources in DVs differ from those in EVs, a direct comparison with the current simulation was not possible.

First, the mean of the spectra was calculated using the moving average method with a 20% window size. Subsequently, fluctuation samples were collected after removing the mean from the spectra. The normality of these samples was examined using Q–Q plots.

Fig. 3 presents three Q–Q plots: one for simulation and two for experimental data (from four EVs and two selected DVs). To evaluate the deviation from a Gaussian PDF, a metric D, defined as the vertical distance between the data and the reference line in the Q–Q plot, was used. Only 0.17% of the simulation samples (Fig. 3(a)) and less than 1.7% of the experimental samples (Fig. 3(b) and (c)) exceeded a distance of unity (i.e., D > 1 dBμV/m), implying that a Gaussian PDF accurately models both the simulation and experimental fluctuations, except at the extremes. Two DV datasets were selected based on the maximum (DV 1) and minimum (DV 2) D values.

Fig. 3

Q–Q plots for testing the normality of fluctuation distribution of (a) the simulation data, (b) experimental data (EVs), and (c) experimental data (DVs).

To completely characterize the Gaussian process, the mean, standard deviation (σ(f)), and frequency correlation were calculated. Among these three parameters, the standard deviation is the most challenging to estimate.

Table 1 summarizes the standard deviations of the simulation and experimental spectrum fluctuations. The standard deviation of the simulation data was estimated by averaging σ(f) over all frequencies. Although the number of emission components differed significantly between the simulation and experiment, the order of σ was the same. Table 1 shows that the difference in σ is small for EVs and slightly larger for DVs, as expected.

Table 1

Standard deviations of the simulation and experimental spectrum fluctuations (unit: dBμV/m)

Table 2 summarizes the variation of σ as the moving average window size is varied from 10% to 30%. The effect of window size on σ estimation is negligible. Therefore, the proposed simulation scheme can effectively predict spectral fluctuations.

Table 2

Standard deviations of the experimental spectrum fluctuations for different moving average window sizes (unit: dBμV/m)

The frequency correlation estimated from experimental data was assumed to follow an exponential function. The average frequency lag was 9.9 MHz for EVs and 12.7 MHz for DVs at a correlation coefficient of 0.2.

After estimating the fluctuation, random spectra were synthesized. Fig. 4 shows three spectra generated for EV 2 assuming proper mean, standard deviation, and correlation.

Fig. 4

Examples of synthesized spectra for EV 2.

IV. Conclusion

The experimental results of this study demonstrate that the UEE spectrum can be accurately modeled as a Gaussian process. The standard deviations of the simulation and experimental data for EVs showed good agreement, indicating the simulation’s predictive capability for this statistical measure. Similar behavior was observed for DVs. Therefore, the proposed UEE spectrum generation scheme for vehicles is well suited for machine learning applications.

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