Direct Access to the Optimal Regularization Parameter in Distribution of Relaxation Times Analysis

Schlüter, Nicolas; Ernst, S.; Schröder, Uwe

doi:10.1002/celc.202000787

Cited by 31 publications

(20 citation statements)

References 38 publications

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“…Finally, the total number of time constants was generated by decupling the number of frequencies recognized in the DRT calculation. The selection of optimal regularization parameters for each deconvolution is based on our former work [36,38] and is presented more in detail in the supporting information. The confidence intervals of section 2.2 and the supporting information have been calculated based on a normal distribution of the respective DRT data for each time constant.…”

Section: Data Evaluationmentioning

confidence: 99%

“…For noisy data, on the other hand, higher regularization parameters are needed, which are accompanied by a decreased resolution. [36,38] Simultaneously, statistical noise also reduces resolution regardless of the l used. [39] Outliers in the impedance spectrum also have a strong influence on a DRT analysis result.…”

Section: Introductionmentioning

confidence: 99%

“…For high‐quality data,

λ

can be chosen exceedingly small, and thus the problem is only slightly regularized, yielding a high resolution in the resulting DRT spectrum. For noisy data, on the other hand, higher regularization parameters are needed, which are accompanied by a decreased resolution [36,38] . Simultaneously, statistical noise also reduces resolution regardless of the

λ

used [39] .…”

Section: Introductionmentioning

confidence: 99%

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Quality‐Indicator‐Based Preprocessing for the Distribution of Relaxation Times Method

et al. 2021

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The deconvolution of impedance data to their respective distribution of relaxation times (DRT) is accompanied by an increase in the resolution of the frequency domain and is, thus, advantageous. Yet, most of the techniques used for computing DRT spectra from experimental data are valid only for impedance spectra that solely show polarization processes. Therefore, most experimental electrochemical impedance spectra must be corrected from perturbing inductive, capacitive, or diffusive contributions. This preprocessing is time consuming, and its quality has an enormous impact on the obtained DRT spectra. It also prohibits using the DRT method within an automated impedance evaluation. In this work, we propose a software-aided approach for deriving optimal preprocessing. For this purpose, we first introduce a quality indicator that reflects the quality of a certain preprocessing. Based on this quality indicator, we furthermore introduce a new batch fitting approach for deriving the optimal equivalent electrical circuit within the preprocessing of experimental impedance spectra. Besides, the batch fitting displays the optimal frequency range for modeling the unwanted impedance fractions. Based on this information, the considered impedance data can finally be optimally corrected from any non-polarization processes. The new methods and their application are tested for simulated data and experimental impedance data of a lithium-ion cell.

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Section: Data Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…For high‐quality data,

λ

λ

used [39] .…”

Section: Introductionmentioning

confidence: 99%

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Quality‐Indicator‐Based Preprocessing for the Distribution of Relaxation Times Method

et al. 2021

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“…In the literature, different methods are used to obtain a suitable regularization parameter. In this study, the cross-validation test from Saccoccio et al [29] in combination with the variance test of Schlüter et al [30,31] was used to optimize the regularization parameter. This combination is presented and tested for synthetic and measured EIS for batteries [31].…”

Section: Electrochemical Characterizationmentioning

confidence: 99%

“…The polarization resistances of each cell dependent on the fuel composition and temperature were evaluated using the distribution function of the DRT analysis. An optimal regularization parameter was chosen based on the results of the EIS evaluation procedure from Schlüter et al [31]. The cross-validation and variance tests were applied to the three EIS after the CC measurement (see Figure 5).…”

Section: Evaluation Of the Polarization Resistancementioning

confidence: 99%

Femtosecond Laser-Induced Surface Modification of the Electrolyte in Solid Oxide Electrolysis Cells

et al. 2020

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Electrolyte-supported solid oxide cells are often used for steam electrolysis. Advantages are high mechanical stability and a low degradation rate. The aim of this proof of concept study was to use a femtosecond laser to process the electrolyte of an electrolyte-supported solid oxide cell and evaluate the effect of this laser treatment on the electrochemical performance. The femtosecond laser treatment induces a macroscopic and a superimposed microscopic structure. It can be proven that the electrolyte remains gas tight and the electrochemical performance increases independently of the laser parameters. The initial area-specific resistance degradation during a constant current measurement of 200 h was reduced from 7.9% for a non-treated reference cell to 3.2% for one of the laser-treated cells. Based on electrochemical impedance measurements, it was found that the high frequency resistance of the laser-treated cells was reduced by up to 20% with respect to the reference cell. The impedance spectra were evaluated by calculating the distribution of relaxation times, and in advance, a novel approach was used to approximate the gas concentration resistance, which was related to the test setup and not to the cell. It was found that the low frequency polarization resistance was increased for the laser-treated cells. In total, the area-specific resistance of the laser-treated cells was reduced by up to 14%.

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Introducing Alternative Algorithms for the Determination of the Distribution of Relaxation Times

Bergmann

Schlüter

2022

ChemPhysChem

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Impedance spectroscopy is a powerful characterization method to evaluate the performance of electrochemical systems. However, overlapping signals in the resulting impedance spectra oftentimes cause misinterpretation of the data. The distribution of relaxation times (DRT) method overcomes this problem by transferring the impedance data from the frequency domain into the time domain, which yields DRT spectra with an increased resolution. Unfortunately, the determination of the DRT is an ill-posed problem, and appropriate mathematical regularizations become inevitable to find suitable solutions.The Tikhonov algorithm is a widespread method for computing DRT data, but it leads to unlikely spectra due to necessary boundaries. Therefore, we introduce the application of three alternative algorithms (Gold, Richardson Lucy, Sparse Spike) for the determination of stable DRT solutions and compare their performances. As the promising Sparse Spike deconvolution has a limited scope when using one single regularization parameter, we furthermore replaced the scalar regularization parameter with a vector. The resulting method is able to calculate well-resolved DRT spectra.

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Direct Access to the Optimal Regularization Parameter in Distribution of Relaxation Times Analysis

Cited by 31 publications

References 38 publications

Quality‐Indicator‐Based Preprocessing for the Distribution of Relaxation Times Method

Quality‐Indicator‐Based Preprocessing for the Distribution of Relaxation Times Method

Femtosecond Laser-Induced Surface Modification of the Electrolyte in Solid Oxide Electrolysis Cells

Introducing Alternative Algorithms for the Determination of the Distribution of Relaxation Times

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