Alternatives to Kronig-Kramers transformation and testing, and estimation of distributions

Abstract

Two alternatives to Kronig-Kramers analysis of small-signal ac immittance data are discussed and illustrated using both synthetic and experimental data. The first, a derivative method of approximating imaginary-part response from real-part data, is found to be too approximate in regions where the imaginary-part varies appreciably with frequency. The second, a distribution of relaxation-times fitting method, is shown to be valuable for testing whether a data set satisfies the Kronig-Kramers relations and so is associated with a system whose properties are time-invariant. It also is valuable for estimating real-or imaginary-part response from the other part, usually with small error. Unlike Kronig-Kramers analysis, the second method usually requires no extrapolation outside the range of the measured data. Finally, this discrete-function method also allows one to estimate the distribution of relaxation times or activation energies associated with a given set of frequency-response data. This application is described and illustrated for both synthetic and experimental data and is shown to yield good but somewhat approximate results for the estimation of continuous distributions. It is particularly valuable for identifying response regions arising from a continuous distribution and distinguishing them from those associated with discrete time-constant response.

Kinetic Studies on State of the Art Solid Oxide Cells: A Comparison between Hydrogen/Steam and Reformate Fuels

“…To exclude contributions from the test set-up, the recorded spectra were corrected with a short-circuit measurement and lead inductance was removed through a procedure utilizing the Kramers-Kronig relations. 17,18 This procedure involves comparing the imaginary impedance generated from the measured real impedance, with the measured imaginary impedance, and the difference between these is used to determine the inductance.…”

“…23 Prior to the fitting and calculation of DRTs, adequate data quality was assured by checking the compliance of the data with Kramers-Kronig (KK) transforms 17,18 and the fit residuals and goodness of fit values were also carefully considered. All CNLS fits, DRT-and KK-transforms as well as simulations were done using the software RAVDAV.…”

“…38.90. 17 Downloaded on 2016-10-19 to IP Timmerman et al 8 have investigated and modelled methane reforming kinetics of an SOFC with Ni/YSZ fuel electrode for stationary as well as auxiliary power unit (APU) relevant fuel mixtures. The determined kinetic expression could adequately accommodate methane reforming as well as the reverse (methanation) reactions.…”

Comparison of Parametric and Nonparametric Methods for the Analysis and Inversion of Immittance Data: Critique of Earlier Work

“…The frequency-response data considered here may involve discrete lines only, a continuous distribution, or a combination of both. One of the two deconvolution methods involves the use of Tikhonov regulation [1], and the other uses complex nonlinear least-squares fitting (CNLS) of an appropriate model [2][3][4][5][6][7][8][9][10]. Recently Maier, Winterhalter, and their associates have published three papers [11][12][13] dealing with the analysis of admittance data by a nonlinear Tikhonov regularization method (NTRM): termed by them a nonparametric method.…”

Impedance study on the capacitance of silver electrode oxidised in alkaline electrolyte

“…The impedance spectra were fitted with a Voigttype circuit composed with a network of connected in series subcircuits, each of them containing a resistance and a capacitance connected in series (RC) [110][111][112]. Two examples are shown in Fig.…”