Machine learning approach for impedance locus uncertainties
-
Luca Bifano
,
Markus Michel
Abstract
This work deals with the determination of the uncertainty of measurement data, determined by electrical impedance spectroscopy. Four different types of sand were measured impedimetrically in a measuring cell designed as a plate capacitor in a frequency range from 20 Hz to 1 MHz. The measuring cell was filled ten times with each sand and 20 impedance spectra were recorded for each filling. The uncertainty at each frequency was determined from the measurement data. It was found that the measurement data variance with a given measuring-cell filling was negligibly small. However, it increased by a factor of up to 100 when the measuring cell was repeatedly emptied and re-filled with the same material. We propose a way to estimate a continuous approximation of the uncertainty band of the impedance locus in the complex plane from the discrete uncertainties at each frequency. It uses a Support Vector Machine (SVM) to generate a regression curve using the discrete uncertainties. The result of the regression was used to estimate the uncertainties of an average impedance locus. The said machine learning tool can handle large amounts of data, classes, and influencing variables. In this manner, it can help to identify cause-effect relationships. Furthermore, at the end of this work a possibility to estimate a continuous uncertainty band along the impedance locus curve via SVM regression is shown. This is an extension to the common methodology in literature, where the uncertainty is only determined at selected individual points of the impedance spectrum.
Kurzfassung
Diese Arbeit befasst sich mit der Unsicherheitsbestimmung von Messdaten, die mittels elektrischer Impedanzspektroskopie generiert wurden. Vier verschiedene Sandsorten wurden in einer als Plattenkondensator ausgelegten Messzelle in einem Frequenzbereich von 20 Hz bis 1 MHz impedimetrisch vermessen. Die Messzelle wurde zehnmal mit jedem Sand gefüllt und für jede Füllung wurden 20 Impedanzspektren aufgenommen. Die Unsicherheit bei jeder Frequenz wurde aus den Messdaten ermittelt. Es zeigte sich, dass die Varianz der Messdaten bei einer bestimmten Messzellenfüllung vernachlässigbar klein war. Sie nahm jedoch um einen Faktor von bis zu 100 zu, wenn die Messzelle wiederholt geleert und mit demselben Material neu gefüllt wurde. Wir stellen eine Möglichkeit vor, um eine Annäherung an ein kontinuierliches Unsicherheitsband der Nyquist-Ortskurve in der komplexen Ebene aus den diskreten Unsicherheiten bei jeder Frequenz zu schätzen. Dabei wird eine Support Vector Machine (SVM) verwendet, um eine Regressionskurve mithilfe der diskreten Unsicherheiten zu erstellen. Das Ergebnis der Regression wurde verwendet, um die Unsicherheiten der mittleren Nyquist-Ortskurve zu schätzen. Die SVM kann große Datenmengen, Klassen und Einflussvariablen verarbeiten. So kann sie helfen, Ursache-Wirkungs-Beziehungen zu identifizieren. Darüber hinaus wird am Ende dieser Arbeit eine Möglichkeit aufgezeigt, ein kontinuierliches Unsicherheitsband entlang der Nyquist-Ortskurve mittels SVM-Regression zu schätzen. Dies ist eine Erweiterung der in der Literatur üblichen Methodik, bei der die Unsicherheit nur an ausgewählten einzelnen Punkten des Impedanzspektrums bestimmt wird.
About the authors
Luca Bifano received the M.Sc. degree from the University of Bayreuth, Germany in 2018. He joined the Department of Measurement and Control Engineering at the University of Bayreuth in 2018. His current research interests include electrical impedance measurement systems and their applications in the field of bulk solids with the foundry industry as a focus.
Markus Michel received the M.S. in mechatronics and automotive engineering from the University of Bayreuth, Germany, in 2022. He joined the Department of Measurement and Control Engineering at the University of Bayreuth in 2021. His research interest includes electrical impedance measurement systems and their applications in the field of bulk solids with the foundry industry as a focus in particular with respect to machine learning methods.
Max Weidl received the M.Sc. degree in mechatronics and automotive engineering from the University of Bayreuth, Bayreuth, Germany, in 2023. He joined the Department of Measurement and Control Engineering at the University of Bayreuth in 2023. His current research interest includes modeling, design and characterization of surface-acoustic-wave components at the Department of Measurement and Control Engineering at the University of Bayreuth.
Dipl.-Ing. (univ.) Alice Fischerauer works since 2004 as a senior research and teaching associate with the Chair of Measurement and Control Systems at the University of Bayreuth. Her main research interests are on impedance spectroscopy and electrical capacitance tomography with focus on modelling and signal processing.
Gerhard Fischerauer received his Dipl.-Ing. and Dr.-Ing. degrees from the Technical University of Munich, Germany, in 1989 and 1996, respectively. From 1990 to 2001, he worked in microacoustics, Siemens Corporate Technology and Epcos, Munich, and then moved to Siemens Matsushita (later: Epcos), Munich. Since 2001, he has held the Chair of Measurement and Control Engineering at the University of Bayreuth, Germany. His research areas include measurement technology in general, sensor systems, microsensors and non-destructive condition monitoring.
-
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] L. Bifano, A. Fischerauer, and G. Fischerauer, “Investigation of complex permittivity spectra of foundry sands,” Tech. Mess., vol. 87, no. 5, pp. 372–380, 2020. https://doi.org/10.1515/teme-2019-0121.Search in Google Scholar
[2] O. Kanoun, Impedance Spectroscopy Advanced Applications; Battery Research, Bioimpedance, System Design, Berlin, Boston, De Gruyter, 2018.10.1515/9783110558920Search in Google Scholar
[3] M. Paluszek and S. Thomas, MATLAB Machine Learning Recipes : A Problem-Solution Approach, New York, NY, Apress, 2019.10.1007/978-1-4842-3916-2Search in Google Scholar
[4] N. N., “Evaluation of measurement data – guide to the expression of uncertainty in measurement,” 2008.Search in Google Scholar
[5] N. N., “Grundlagen der Messtechnik, Teil 3: Auswertung von Messungen einer einzelnen Messgröße, Messunsicherheit,” DIN 1319-3, 1996.Search in Google Scholar
[6] N. N., “Grundlagen der Messtechnik, Teil 4: Auswertung von Messungen, Messunsicherheit,” DIN 1319-4, 1999.Search in Google Scholar
[7] L. Paradowski, “Uncertainty ellipses and their application to interval estimation of emitter position,” IEEE Trans. Aero. Electron. Syst., vol. 33, no. 1, pp. 126–133, 1997. https://doi.org/10.1109/7.570715.Search in Google Scholar
[8] P. M. Ramos, F. M. Janeiro, and P. S. Girão, “Uncertainty evaluation of multivariate quantities: a case study on electrical impedance,” Measurement, vol. 78, pp. 397–411, 2016. https://doi.org/10.1016/j.measurement.2015.08.043.Search in Google Scholar
[9] H. Working and H. Hotelling, “Applications of the theory of error to the interpretation of trends,” J. Am. Stat. Assoc., vol. 24, no. 165A, pp. 73–85, 1929. https://doi.org/10.1080/01621459.1929.10506274.Search in Google Scholar
[10] R. L. Winkler and W. L. Hays, Statistics – Probability, Inference, and Decision, New York, Holt, Rinehart and Winston, 1975.Search in Google Scholar
[11] F. Jiang, Y. Lu, Y. Chen, D. Cai, and G. Li, “Image recognition of four rice leaf diseases based on deep learning and support vector machine,” Comput. Electron. Agric., vol. 179, p. 105824, 2020. https://doi.org/10.1016/j.compag.2020.105824.Search in Google Scholar
[12] S.-C. Du, D.-L. Huang, and H. Wang, “An adaptive support vector machine-based workpiece surface classification system using high-definition metrology,” IEEE Trans. Instrum. Meas., vol. 64, no. 10, pp. 2590–2604, 2015. https://doi.org/10.1109/TIM.2015.2418684.Search in Google Scholar
[13] S. P. Rana, M. Dey, G. Tiberi, et al.., “Machine learning approaches for automated lesion detection in microwave breast imaging clinical data,” Nature, vol. 9, no. 10510, pp. 1–12, 2019. https://doi.org/10.1038/s41598-019-46974-3.Search in Google Scholar PubMed PubMed Central
[14] I. Steinwart and A. Christmann, Support Vector Machines, New York, Springer, 2008.Search in Google Scholar
[15] R. G. Brereton and G. R. Lloyd, “Support vector machines for classification and regression,” Analyst, vol. 135, pp. 230–267, 2010. https://doi.org/10.1039/b918972f.Search in Google Scholar PubMed
[16] L. Bifano, A. Fischerauer, A. Liedtke, and G. Fischerauer, “Characterization of sand and sand–binder systems from the foundry industry with electrical impedance spectroscopy,” J. Sens. Sens. Syst., vol. 10, no. 1, pp. 43–51, 2021. https://doi.org/10.5194/jsss-10-43-2021.Search in Google Scholar
[17] L. Bifano and G. Fischerauer, “Unsicherheit der elektrischen Impedanzspektroskopie bei Schüttgütern (Uncertainty of electrical impedance spectroscopy in bulk solids, in German),” Tech. Mess., vol. 89, no. S1, pp. 2–7, 2022. https://doi.org/10.1515/teme-2022-0053.Search in Google Scholar
[18] N. N., “Agilent E4980A Precision LCR Meter User’s Guide”, 2013.Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Editorial
- XXXVI. Messtechnisches Symposium des AHMT in Magdeburg
- Research Articles
- Studying the effects of siloxane poisoning on a SnO2 metal oxide semiconductor gas sensor in temperature cycled operation enabling self-monitoring and self-compensation
- Investigations on terthiophene as an electrically conductive polymer for UV laser lithography
- Properties and special phenomena of strain sensors made of carbon particle-filled elastomers
- Machine learning approach for impedance locus uncertainties
- Investigation of cross-sensitivities of the potential drop method for structural health monitoring of civil structures
- Modular Direct Laser Writing setup for high precision nanostructuring
Articles in the same Issue
- Frontmatter
- Editorial
- XXXVI. Messtechnisches Symposium des AHMT in Magdeburg
- Research Articles
- Studying the effects of siloxane poisoning on a SnO2 metal oxide semiconductor gas sensor in temperature cycled operation enabling self-monitoring and self-compensation
- Investigations on terthiophene as an electrically conductive polymer for UV laser lithography
- Properties and special phenomena of strain sensors made of carbon particle-filled elastomers
- Machine learning approach for impedance locus uncertainties
- Investigation of cross-sensitivities of the potential drop method for structural health monitoring of civil structures
- Modular Direct Laser Writing setup for high precision nanostructuring
