Investigation of electrochemical processes in solid oxide fuel cells by modified Levenberg–Marquardt algorithm: A new automatic update limit strategy

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.