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REVIEW 3 major objections 5 minor 66 references

Multisine electrochemical impedance spectroscopy for Li-ion battery characterisation

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Multisine EIS matches single-sine in steady state and reads impedance during battery operation.

desk verdict A careful, honest methods paper: steady-state multisine vs. single-sine equivalence is nailed, but the operando results lean on an unvalidated drift-removal step and a single cell, so accept conditionally. read the letter →

arxiv 2607.17832 v1 pith:JGLEAEWM submitted 2026-07-20 eess.SY cond-mat.mtrl-scics.SY

Noël Hallemans , Heiko Seel-Mayer , Peter Keil , Stephen R. Duncan , David A. Howey This is my paper · ORCID
classification eess.SYcond-mat.mtrl-scics.SY
keywords multisineexcitationelectrochemicalimpedancespectroscopyoperandoEISlithium-ionbatteryButler-VolmerkineticslinearitystationarityverificationKramers-Kronigtrendremoval
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a carefully designed multisine excitation—a short sum of many sine waves applied at once—measures exactly the same steady-state impedance of a lithium-ion cell as the standard sequential single-sine method, while cutting measurement time from about 976 s to 200 s. Its more consequential claim is that multisine bursts can do something single-sines cannot: extract credible impedance while the battery is charging, discharging, relaxing, or changing temperature, because all frequencies see the same operating condition simultaneously. Using such operando measurements, the paper finds that charge-transfer resistance is lower during cycling than at rest, and that charge and discharge do not give the same impedance even at equal state of charge and temperature. The paper interprets this asymmetry as the signature of Butler-Volmer reaction kinetics linearised around a non-zero current—information that steady-state EIS cannot provide. If correct, this turns multisine EIS into a practical tool for parameterising battery models and quantifying reaction heat during real operation.

What carries the argument

The engine of the method is the odd random-phase multisine: a sum of sine waves at odd-integer multiples of a 20 mHz fundamental (40 excited frequencies spanning 20 mHz–1 kHz), with randomised phases that keep the crest factor near the single-sine value. Exciting only odd harmonics and leaving every seventh odd harmonic unexcited creates spectral 'traps' where even and odd nonlinear distortions land, so linearity and stationarity can be read directly from the current and voltage spectra. Impedance is the ratio of DFT voltage to DFT current at excited harmonics; several periods yield a variance estimate and confidence circles. For operando bursts, the prior trend-removal method fits basis fun

What would settle it

Repeat the C/3 charge and discharge multisine bursts on the same cell at several C-rates and on at least one fresh cell, and compare the charge/discharge asymmetry at equal SOC and temperature with an independently parametrised Butler-Volmer prediction (from DC pulses or nonlinear EIS). If the asymmetry disappears when the trend-removal basis-function order is changed, or fails to follow the predicted C-rate scaling, the paper's separation of drift from dynamics and its kinetic-asymmetry claim would both collapse.

Watch

Extended reading notes

Core claim

The central discovery, on the paper's own terms, is that an odd random-phase multisine signal delivered through a modified commercial potentiostat yields the same impedance spectra as single-sine excitation when the cell is linear and stationary, and that this equivalence is what makes operando impedance measurement legitimate: because all excited frequencies overlap in time, each frequency is evaluated at the same drift, the same state of charge, and the same temperature. After removing slow trends and transients with the authors' basis-function method, the resulting impedance during C/3 charge and discharge satisfies Kramers-Kronig compliance where single-sine operando data fails, and reve

Load-bearing premise

The operando conclusions rest on the assumption that the trend-removal method—which fits basis functions to the slow evolution of the spectra and is specified in a cited prior paper, not re-derived here—cleanly separates drift and transients from the true impedance without leaking into the reported spectra; Kramers-Kronig compliance alone cannot certify this because the paper itself notes that it is insensitive to nonstationarity.

Editorial extensions

If this is right

  • Multisine bursts cut impedance characterisation from about 976 s to 200 s while giving the same steady-state result as single-sines at equal rms current.
  • Operando impedance during C/3 charging and discharging is measurably lower than steady-state impedance in the charge-transfer frequency range, and charge and discharge differ even at matched SOC and temperature.
  • The charge/discharge asymmetry is a linearised Butler-Volmer effect around non-zero current, so operando EIS can probe kinetic asymmetry that classical steady-state EIS cannot see.
  • Impedance measured in short bursts during relaxation and temperature ramps tracks the growth of the charge-transfer arc and the Arrhenius-like temperature dependence of exchange current, supporting use as a thermal and state diagnostic.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable corollary: repeating the same multisine bursts on multiple cells, C-rates, and repeated runs would establish whether the charge/discharge asymmetry is a general kinetic property or partly a single-cell artefact—the paper does not claim to settle cell-to-cell variation.
  • If the drift/trend-separation assumption holds, operando impedance at non-zero current could feed physics-based battery models with parameters valid under load, which would change how reaction-heat and overpotential estimates are derived from standard impedance data.
  • The trap-harmonic design generalises: choosing different harmonic-excitation patterns could separate nonlinearity order from drift, and might allow time-varying nonlinear models—not just linearised averages—to be identified from the same bursts.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper presents a practical demonstration of multisine electrochemical impedance spectroscopy (EIS) on a modified commercial potentiostat, applied to a commercial Li-ion cell over 20 mHz–1 kHz. It compares single-sine and multisine impedance under steady-state conditions at several SOCs, showing overlap, and verifies linearity/stationarity using non-excited spectral bins, Lissajous plots, and an external measurement-model/Kramers-Kronig tool. It then presents operando multisine measurements during C/3 charge/discharge, relaxation, and a temperature ramp, using a drift/transient-removal procedure from an earlier paper, and interprets the resulting spectra in terms of Butler-Volmer linearization around nonzero current, relaxation dynamics, and thermal activation. The paper argues that multisine excitation resolves the erroneous low-frequency impedance produced by sequential single-sine excitation during operation.

Significance. If the operando results are valid, the paper would be a valuable practical demonstration that broadband multisine EIS on commercial hardware can characterize battery dynamics away from steady state, with direct time-series validation of linearity and stationarity. The steady-state leg is the strongest part: the comparison uses rms-matched excitations, the spectra show non-excited bins at the noise floor, the Kramers-Kronig check is done with an external measurement-model tool, the 1 kHz point is transparently excluded, and Appendix B provides a period-to-period variance estimate. These are concrete strengths. The operando leg is weaker: it depends on a trend-removal method that is only cited, not specified or revalidated here, and the reported physical conclusions derive from a single cell and single run.

major comments (3)
  1. [Section 4.3, Figs 10–13] The operando impedance data in Figs 10–13 are obtained by ‘modelling a linear time-variation and removing the drifts and transients using the method of Hallemans et al. [38,60]’. This basis-function procedure is not specified in this paper, no sensitivity analysis is shown, and no independent validation is provided. The only reported check is Kramers-Kronig compliance through the measurement model, yet Section 4.2 itself states (citing You et al. [59]) that Kramers-Kronig analysis is insensitive to the type of nonstationarity seen as ‘skirts’ in Figs 10 and 13. The central operando claim therefore currently rests on an unvalidated, model-dependent step. Please specify the trend-removal model and demonstrate, e.g. with synthetic time-varying impedance or an independent benchmark, that the drift/transient basis does not partially absorb the evolving low-frequency or charge-transfer respons
  2. [Section 4.3, Figs 11–13] The physical conclusions — charge/discharge asymmetry at equal SOC, growth of the charge-transfer arc during relaxation, and the temperature trend — are all derived from a single cell with a single repetition. With one cell and one run order, the observed asymmetries and trends cannot be separated from cell-to-cell variability or run-order effects. This is load-bearing for the claim that the charge/discharge asymmetry is a genuine kinetic effect (Butler-Volmer linearization around nonzero current). Please add replicate measurements, at minimum repeated runs on the same cell for the charge/discharge comparison, and report scatter or confidence intervals; ideally use multiple cells.
  3. [Section 4.3, Fig. 10] The comparison between single-sine and multisine operando data is not fully on equal footing: the single-sine impedance is computed directly from the spectra without drift removal, while the multisine impedance is computed after drift/transient removal. The text says that even after drift removal the single-sine data still fail Kramers-Kronig, but the corresponding processed single-sine spectra are not shown. To support the claim that ‘multisine excitation resolves this issue’, please display single-sine operando impedance after the same or an equivalent drift-removal treatment (or explain quantitatively why the same treatment cannot be applied), so the comparison isolates the benefit of simultaneous excitation from the benefit of postprocessing.
minor comments (5)
  1. [Section 2, Eqs (3)–(4)] Please define T_transients(f_m) explicitly; currently it appears in both expressions without a formal definition.
  2. [Section 3.2] The anti-aliasing filter is stated to have cut-off 65 kHz while the sampling frequency is 15.625 kHz (Nyquist ≈7.8 kHz). The wording is imprecise; if the signal bandwidth is limited by the 1.6 kHz reconstruction filter, say so explicitly, otherwise readers may question the anti-aliasing design.
  3. [Fig. 11] The legend labels ‘C/3 charge’ and ‘C/3 discharge’ plus ‘Steady-state’ are clear, but the corresponding symbols for charge vs discharge are difficult to distinguish in the printed Nyquist plot; please increase marker differentiation or use separate panels.
  4. [Appendix B, Eq. (15)] The variance formula is stated without derivation. A brief explanation of the noise assumptions (stationary, zero-mean, independent of signal) and why the covariance term enters with this sign would help readers apply the result.
  5. [Section 4.1] The low-frequency increase in the voltage spectrum is attributed to ‘a small drift signal’. This is acknowledged, but it would be useful to state whether that drift is quantitatively negligible for the impedance estimate, given that non-excited bins are otherwise at the noise floor.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central steady-state equivalence is a direct external benchmark, and the operando processing is a cited prior method rather than a prediction reduced to its own inputs.

full rationale

The paper's central steady-state claim is supported by direct comparison between multisine and single-sine impedance measurements (Fig. 6, Eq. 9), i.e. an external benchmark, so it is not a fitted parameter renamed as a prediction. The operando results rely on the trend-removal/basis-function method of Hallemans et al. [60] and the BLTVA framework of [23], but the paper does not define the reported operando impedance as that method's output by construction; it presents it as an estimated average impedance and separately shows raw spectra, drift 'skirts', and current/voltage time series. Section 4.2 explicitly acknowledges that Kramers-Kronig and measurement-model checks are insensitive to nonstationarity, so the reported KK compliance is a weak validation rather than a circular proof. The lack of a re-derivation of [60] and the use of a single cell are validation and generality limitations, not instances of prediction-by-construction. No equation or fitted parameter in the paper is shown to be equivalent to its own input, and no load-bearing uniqueness theorem or ansatz is imported via self-citation. Therefore no significant circularity is identified.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper's central claims rest on standard EIS definitions plus three domain assumptions that carry most of the weight: (i) non-excited spectral bins at the noise floor certify linearity/stationarity; (ii) KK/measurement-model compliance certifies data validity (which the paper itself notes is insufficient for nonlinear and nonstationary data); (iii) the drift/trend-removal method of the authors' prior work [60] returns the true time-varying impedance. No new physical entities are introduced; the 'best linear time-varying approximation' concept is imported from the authors' prior literature [23, 50]. The free parameters are a hand-chosen excitation amplitude (standard SNR/linearity trade-off), the measurement-model Voigt elements (validation only), and the unspecified basis functions of the drift-removal model, which directly determine the operando impedance values and therefore the paper's headline physical observations.

free parameters (3)
  • Excitation rms amplitude = 70.5 mA rms (multisine); 100 mA amplitude (single-sine)
    Hand-chosen trade-off between SNR and linearity (Section 3, 'Amplitudes'); linearity is then verified from the spectra, so this is not a hidden fit to the impedance claim.
  • Voigt measurement-model elements = 6 for multisine, 7 for single-sine at 50% SOC
    Fitted to each impedance dataset using Orazem's software [57] purely for KK/validity checking (Fig. 7); they certify the data rather than enter the reported impedance.
  • Drift/trend-removal basis functions (method of Hallemans et al. [60]) = unspecified in this paper
    The operando impedance values are exactly the output of this fitted model; its form and degrees of freedom are defined only in the cited reference, so the operando numbers cannot be reconstructed from this paper alone.
assumptions (5)
  • standard math Impedance is defined by Z(omega)=V(k)/I(k) at excited harmonics, per Eq. (9)
    Definition under the linear-time-invariant interpretation; the paper then attempts to verify that interpretation.
  • domain assumption Non-excited frequency bins sitting at the noise floor certify linearity and stationarity (Fig. 5; Section 4.2)
    The paper uses this as its primary validity evidence; it presumes stationary noise and no unmodeled drift, which Section 4.3 shows is violated in operando (skirts).
  • domain assumption Kramers-Kronig compliance via a Voigt measurement model implies valid (linear, stationary) EIS data
    Section 4.2 adopts this common test while explicitly acknowledging (citing You et al. [59]) that KK is insensitive to nonlinearity and that nonstationary multisine data can pass.
  • domain assumption The trend-removal method of Hallemans et al. [60] separates drift/transients from the true time-varying impedance
    Section 4.3: basis functions are fitted to the slow spectral evolution; every operando result inherits this model, which is not re-validated or specified here.
  • domain assumption The reduced charge-transfer impedance during charge/discharge is caused by Butler-Volmer kinetics linearized around a non-zero current
    Section 4.3 interpretation; temperature drift is ruled out (<0.4 degC) but alternative mechanisms (concentration/SEI changes) are not quantified, and the experiment is single-cell.

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Cite this review

Pith. "Pith review of Multisine electrochemical impedance spectroscopy for Li-ion battery characterisation." pith.science (2026). https://pith.science/paper/JGLEAEWM

@misc{pith2026260717832,
  author       = {Pith},
  title        = {Pith review of: Multisine electrochemical impedance spectroscopy for Li-ion battery characterisation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JGLEAEWM}},
  note         = {Machine review of arXiv:2607.17832}
}
read the original abstract

Electrochemical impedance spectroscopy (EIS) is a valuable tool for non-invasive battery characterisation as it provides a compact data representation of physical processes over a wide range of time scales. Commonly, sinusoids at different frequencies are injected sequentially (single-sines). Alternatively, a multisine excitation (a sum of sines) is advantageous for reducing experiment time and allowing impedance to be measured during operational conditions (e.g.\ charging, discharging, relaxation, and during temperature changes). In this work, we demonstrate high-fidelity multisine EIS measurements on Li-ion cells over a wide frequency range (20 mHz to 1 kHz) taken with a commercial potentiostat, and compare these to single-sine EIS, discussing the advantages of both techniques and how to verify the conditions of linearity and stationarity. We also measure broadband multisine impedance at different operating conditions (during charging/discharging, relaxation, and temperature changes), showing how this tool gives new insights into battery dynamics, material properties, charge transfer processes, and thermal performance.

Figures

Figures reproduced from arXiv: 2607.17832 by the authors.

Figure 1
Figure 1. Single-sine and multisine current excitation signals for bat [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Odd random-phase multisine signal. The grey signals are [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Potentiostat generation and measurement stages for multisine impedance. A reference current is applied to the battery and the current [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Relaxation voltage for 4 h before steady-state EIS measure [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Signals, spectra, and impedance at linear and stationary conditions at 50% SOC. Time-domain signals were subsampled 125 times for [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Comparison of single-sine and multisine impedance at lin [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 8
Figure 8. Figure 8: Multisine current and voltage spectra at 10% SOC for a [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 7
Figure 7. Figure 7: Measurement model residuals (real and imaginary) and [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 9
Figure 9. Figure 9: Single-sines at 20 mHz at 50% SOC in linear and stationary conditions measured for four periods of which we discarded the first one. [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: Operando impedance measurements during C/ [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: Multisine EIS spectra at steady-state, charge, and dis [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 14
Figure 14. Figure 14: Comparison of single-sine and multisine impedance data at [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]
Figure 13
Figure 13. Figure 13: Operando impedance during heating at 50% SOC. Three [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]
Figure 15
Figure 15. Figure 15: Variation of SOC for single-sine vs. multisine at equivalent [PITH_FULL_IMAGE:figures/full_fig_p012_15.png]

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Pith tools

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