Regularized Linear Kramers-Kronig Transform for Consistency Check of Noisy Impedance Spectra with Logarithmic Frequency Distribution

Abstract

Measured impedance spectra can be noisy or can be affected by artifacts due to system nonlinearity or instability. Methods, such as the Linear Kramers-Kronig help to check consistency of measurements, but have massive problems with noisy spectra. Filtering or averaging, which are often used for noise reduction, are not always efficient. They lead, in some cases, in impedance spectra, which are still noisy or having blurred features or oscillating due to over-correction. In this paper, we propose a Tikhonov regularized linear Kramers-Kronig transform (LKK) for checking consistency and correct noisy impedance spectra. The proposed method introduces damped weights bias [1] to regularize the inverse problem related to the parameter extraction for the Voigt model building the basis for the LKK. This results in a Kramers-Kronig-compliant, corrected, impedance spectrum with significantly reduced noise effects. Applied on a measured noisy RC impedance spectrum, as example, and and an impedance spectrum of lithium-ion battery. The proposed method reduces measurement deviation from a RMSE of $35\ \Omega$ to a RMSE of $14\ \Omega$.