An inverse approach to the characterisation of material parameters of piezoelectric discs with triple-ring-electrodes

Feldmann, Nadine; Jurgelucks, Benjamin; Claes, Leander; Schulze, Veronika; Henning, Bernd; Walther, Andrea

doi:10.1515/teme-2018-0066

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…Setting F i = −v i Z m,i , this enables to solve equation ( 4) for the frequency-dependent electrical impedance Z el = u/i of the transducer model. In an inverse procedure, the parameters of the Mason model for a given ultrasonic transducer are identified by comparing the electrical impedance of the model Z el with the electrical impedance Z meas of a physical transducer [4]. As the physical transducer is to be used in an acoustic absorption measurement system based on an established system for sound velocity measurement (e.g.…”

Section: Transducer Modellingmentioning

confidence: 99%

“…Note that these results are only valid for the setup and transducer described before with an excitation signal voltage of 1 V. As a reference, the specific acoustic impedances and losses of several fluids at 293 K and 100 kPa are included in figure 3 as well [7]. The losses µ depicted are low estimates, as they only include the influence of shear viscosity and thermal conductivity (µ = 4 3 µ s + cp−cv cp•cv ν), omitting the additional loss caused by the relatively unexplored volume viscosity. Thus, in a physical setup, the difference between the minimal losses necessary for linear sound propagation and the actual losses in the respective fluid is expected to be more significant.…”

Section: Estimation Of Non-linearitymentioning

confidence: 99%

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Estimation of acoustic wave non-linearity in ultrasonic measurement systems

Claes¹,

Steidl²,

Hetkämper³

et al. 2020

Preprint

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Most measurement methods based on ultrasound, such as sound velocity, absorption or flow measurement systems, require that the acoustic wave propagation is linear. In many cases, linear wave propagation is assumed due to small signal amplitudes or verified, for example, by analysing the received signal spectra for the generation of harmonic frequency components. In this contribution, we present an approach to quantify occurrence of non-linear effects of acoustic wave propagation in ultrasonic measurement systems based on the evaluation of the acoustic Reynolds number. One parameter required for the determination of the acoustic Reynolds number is the particle velocity of the acoustic wave, which is not trivially obtained in most measurement systems. We thus present a model-based approach to estimate the particle velocity of an acoustic wave by identifying a Mason model from electrical impedance measurements of a given transducer. The Mason model is then used to determine the transducer's velocity output for a given electrical signal, allowing for an evaluation of the acoustic Reynolds number for different target media.

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Section: Transducer Modellingmentioning

confidence: 99%

Section: Estimation Of Non-linearitymentioning

confidence: 99%

Estimation of acoustic wave non-linearity in ultrasonic measurement systems

Claes¹,

Steidl²,

Hetkämper³

et al. 2020

Preprint

Self Cite

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“…For details regarding the inverse problem and optimization of sensitivities see e.g. [5], [7]. In order to design and analyse new piezoelectric devices, models are employed [14].…”

Section: Introductionmentioning

confidence: 99%

Existence, Uniqueness and Regularity of Piezoelectric Partial Differential Equations

Jurgelucks¹,

Lahmer²,

Schulze³

2019

Preprint

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Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into the practical simulation of piezoelectric ceramics there still remain open questions regarding the partial differential equations governing the piezoceramics.The piezoelectric behavior of many piezoceramics can be described by a second order coupled partial differential equation system. This consists of an equation of motion for the mechanical displacement in three dimensions and a coupled electrostatic equation for the electric potential. Furthermore, an additional Rayleigh damping approach makes sure that a more realistic model is considered.In this work we analyze existence, uniqueness and regularity of solutions to theses equations and give a result concerning the long-term behavior. The wellposedness of the initial boundary value problem in a bounded domain with sufficiently smooth boundary is proved by Galerkin approximation in the discretized weak version, followed by an energy estimation using Gronwall inequality and using the weak limit to show the results in the infinite dimensional space. Initial conditions are given for the mechanical displacement and the velocity.

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Neuronale Netze zur Startwertschätzung bei der Identifikation piezoelektrischer Materialparameter

Koch,

Claes,

Jurgelucks

et al. 2024

Tm - Technisches Messen

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Zusammenfassung In diesem Beitrag wird ein Ansatz zur Identifikation eines vollständigen Satzes piezoelektrischer Materialparameter basierend auf der Messung der elektrischen Impedanz anhand eines einzelnen Probekörpers durch Lösung eines inversen Problems vorgestellt. Vorangegangene Arbeiten zeigen, dass die Regularisierung des zur Lösung eingesetzten Optimierungsverfahrens aufgrund der großen Anzahl an zu bestimmenden Materialparametern anspruchsvoll ist. Darauf aufbauend wird vorgestellt, inwiefern datenbasierte Methoden des maschinellen Lernens zu einer robusteren und effizienteren Lösung des inversen Problems beitragen können. Insbesondere eine verbesserte Startwertschätzung für den gradientenbasierten Optimierungsprozess basierend auf einem neuronalen Netz steht im Mittelpunkt dieses Beitrags. Dieses Netz wird mithilfe synthetischer Daten trainiert und approximiert die Inverse eines Simulationsmodells für die elektrische Impedanz bei gegebenen piezoelektrischen Materialparametern. Die synthetischen Trainingsdaten werden generiert, indem ein klassisches Simulationsmodell, das auch für die Lösung des inversen Problems eingesetzt wird, ausreichend oft mit randomisierten Materialparametern ausgewertet wird. Mithilfe des neuronalen Netzes werden Werte für Materialparameter bestimmt, die, basierend auf einer Auswertung der Zielfunktion des inversen Problems, das physikalische Verhalten besser beschreiben als die in vorangegangenen Arbeiten verwendeten, analytisch ermittelten Werte. Dadurch kann die Komplexität und der Rechenaufwand des anschließenden Optimierungsverfahrens signifikant reduziert werden.

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An inverse approach to the characterisation of material parameters of piezoelectric discs with triple-ring-electrodes

Cited by 3 publications

References 12 publications

Estimation of acoustic wave non-linearity in ultrasonic measurement systems

Estimation of acoustic wave non-linearity in ultrasonic measurement systems

Existence, Uniqueness and Regularity of Piezoelectric Partial Differential Equations

Neuronale Netze zur Startwertschätzung bei der Identifikation piezoelektrischer Materialparameter

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