Impedance fitting stops picking a circuit first: PCA nearest neighbours supply both candidates and starting values, matching manual fits within 1%
Synopsis
Equivalent-circuit fitting of electrochemical impedance spectra has depended on a human choosing a circuit topology and starting values, even though different topologies can produce nearly identical spectra. A University of Zagreb team expanded a few manually fitted spectra into a synthetic reference library, projected it into principal-component space, and used nearest-neighbour retrieval to shortlist topologies and supply physically plausible starting values at once, then refined each candidate by complex nonlinear least squares and chose by fit quality. Against independent manual fits, most parameters agreed within 1%, reduced chi-squared was lower in every case, and one spectrum took about 5 to 6 seconds.
Interpretation
Automated fitting no longer locks in a single circuit topology before fit quality is evaluated; several candidates are each refined and then compared. Most earlier automated methods predict one topology from spectral features and hand it to a downstream fit, separating topology choice from the assessment of fit quality. On three known measured spectra the automated pipeline selected the same topology as manual fitting, with parameters agreeing to 0.4%, 0.7% and 0.9%, and reduced chi-squared lower than the manual fit in every case.
Candidate topologies and each topology's starting parameters come from a single retrieval step in a reduced spectral space. Principal component analysis compresses log impedance magnitude and phase angle into the first five components, which together explain 97.62% of the variance. Five manually fitted spectra served as seeds for more than fifty thousand synthetic spectra generated by parameter perturbation; each test spectrum retrieves 400 nearest neighbours, and every topology among them is refined by complex nonlinear least squares from the parameters of its five nearest neighbours.
Regions the reference library does not cover produce outright wrong fits, and adding one representative spectrum restores them. A spectrum with normalized log impedance magnitude near 1.2, outside the [0,1] calibration range, was initially fitted to the wrong topology. After adding two manual fits of that spectrum and their synthetic neighbourhoods, bringing the database to 70,579 entries, the same test spectrum was correctly identified as 2TC_PAR with reduced chi-squared 0.000265, and all parameters except the statistically undetermined solution resistance agreed within 2.3%.
Perspective
The demonstration covers five equivalent-circuit topologies, the series and nested variants with one, two and three time constants, seeded from three measured spectra recorded on a PalmSens4 instrument at five points per decade from 10⁵ to 10⁻² Hz. Input frequencies must coincide exactly with points on the reference library's fixed grid and form an unbroken subrange. Reliable coverage is limited to the parameter envelope spanned by the seed spectra, and spectra outside it require a representative seed to be added.
When time constants nearly coincide, the associated parameters carry large uncertainty in both manual and automated fits, which the authors attribute to non-uniqueness inherent to complex nonlinear least squares and which more starting points or database coverage cannot remove. When a low-frequency plateau falls outside the measured window, a parameter can only be bounded from below. The neighbour pool size and the number of multistart points are tunable per spectrum and were set here by post hoc inspection, with no general rule yet for choosing them in advance. Quantitative resolution limits for parameters and for the minimum time-constant separation would need a dedicated sensitivity analysis, which the authors leave to future work.