Calibration of Wideband Frequency-Domain Data using Bayesian Model Calibration
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Since the mid-2010s, automotive industry has been constantly shifting towards sustainable, electric passenger transport, with 20% of cars sold in 2024 being electric [1]. This change requires power electronics to be efficient and power-dense [2]. Electromagnetic compatibility (EMC) is strongly linked to efficiency and power density. To obtain road approval in the EU, standards such as CISPR 25 [3] must be met, like the EURO 6 & 7 [4,5] exhaust limits for combustion engines. We use simulation-based methods to predict electric vehicle emissions before laboratory EMC tests, enabling early detection of failure. These predictions rely on parametric circuit and surrogate models like Wideband Kriging (WBK) [6] for spectral emissions. Because large simulation models contain unknown and tolerance-affected parameters, repeated calibration on hardware prototypes is required. We address this using a Bayesian calibration framework [7], which combines WBK models with Hamiltonian Markov Chain Monte Carlo [8] with No-U-Turn Sampler [9,10], along with a neutralizing scheme for “bad distribution geometries” [11], but without a systematic model-discrepancy term [12]. The calibration routine is applied to an electromagnetic interference (EMI) filter (see Figure 1), which consists of 3 functional and 7 parasitic parameters. The 10D filter problem reflects typical features such as abrupt changes and the behavior of vector-valued information contained in EMC spectra. A calibration result for this filter on simulated data with additive white Gaussian noise is shown in Figure 2. Figure 2a presents WBK-based filter response predictions for 400 design parameter samples from a non-informative 10D uniform prior, while Figure 2b shows the expected calibrated response and its confidence interval resulting from posterior sampling. The calibration shows good agreement with noisy simulation data, demonstrating the potential to calibrate parametric circuit models using observations like frequency-domain measurements. The framework aims for future vehicle powertrain simulation calibration with several 100 degrees of freedom.
