Enhanced DRT estimation using prior knowledge

In recent decades, the analysis of impedance data by their numerical transformation into the domain of relaxation times to yield distributions of uncorrelated relaxation times (DRT) has gained widespread popularity for characterising electrochemical power and conversion devices such as batteries, capacitors, electrolysis and fuel cells. Information acquired by DRT analysis supplements the information known from measurements and the physical and electrochemical characteristics of the studied device. Various pre-compiled numerical tools for the inversion of the underlying integral equation of the DRT impedance are nowadays readily available to estimate the DRT from measured (or modelled) data. The only significant effort in such DRT estimation is yet to adjust one or another tuning parameter especially when employing regularisation methods. Virtually all these tools assume the DRT is real valued, which is unfortunately not the case when the data are not exactly of the same nature as that of the employed integral kernel. This is regrettably a fact little known even among those familiar and well versed with DRT analysis. The use of prior knowledge that is, valid information independent of the data, is rarely utilised to full extent for constraining numerically the solution space of the resulting DRT