Investigation of Electrochemical Processes in Solid Oxide Fuel Cells by Modified Levenberg–Marquardt Algorithm: A New Automatic Update Limit Strategy

Mark Žic,Iztok Fajfar,Matevž Kunaver,Vanja Subotić,Sergei Pereverzyev

doi:10.3390/pr9010108

Abstract

Identification of ongoing processes in solid oxide fuel cells (SOFC) enables both optimizing the operating environment and prolonging the lifetime of SOFC. The Levenberg–Marquardt algorithm (LMA) is commonly used in the characterization of unknown electrochemical processes within SOFC by extracting equivalent electrical circuit (EEC) parameter values from electrochemical impedance spectroscopy (EIS) data. LMA is an iteration optimization algorithm regularly applied to solve complex nonlinear least square (CNLS) problems. The LMA convergence can be boosted by the application of an ordinary limit strategy, which avoids the occurrence of off-limit values during the fit. However, to additionally improve LMA descent properties and to discard the problem of a poor initial parameters choice, it is necessary to modify the ordinary limit strategy. In this work, we designed a new automatic update (i.e., adaptive) limit strategy whose purpose is to reduce the impact of a poor initial parameter choice. Consequently, the adaptive limit strategy was embedded in a newly developed EIS fitting engine. To demonstrate that the new adaptive (vs. ordinary) limit strategy is superior, we used it to solve several CNLS problems. The applicability of the adaptive limit strategy was also validated by analyzing experimental EIS data collected by using industrial-scale SOFCs.

Highlights

Electrochemical power sources, e.g., solid oxide fuel cells (SOFC) [1], are gaining an increasing interest due to new generation of SOFC devices that are more environmentallyfriendly and highly-efficient
In order to study the impact of different limit strategies (Table 1) on Levenberg–Marquardt algorithm (LMA) convergence properties, the ZARC data were fitted by EECR(QR)(QR)(QR)
The new strategy was put to the test by solving several complex nonlinear leastsquare (CNLS) problems

Summary

Introduction

Electrochemical power sources, e.g., solid oxide fuel cells (SOFC) [1], are gaining an increasing interest due to new generation of SOFC devices that are more environmentallyfriendly and highly-efficient. When employing appropriate diagnostic tools, degradation can be limited or even prevented, prolonging the SOFC lifetime. Numerous electrochemical processes that take place in SOFC can be characterized by EIS and examined in more detail by using diagnostic tools such as electrical equivalent circuit(s) (EEC) [4], the distribution of relaxation times [3,5] (DRT), and the distribution of diffusion times [6,7] (DDT). The EEC approach demands a specification of the EEC model, an initial parameters choice [8], and a selection of the appropriate optimization algorithm [9]. When investigating electrochemical processes in SOFC by using EEC, the initial parameter choice is one of the most important steps since it impacts the accuracy of the final result

Objectives

Results

Conclusion