Abstract
The determination of acoustic material parameters using ultrasonic transmission measurements can mathematically be described as an inverse problem. The question concerning the influence of uncertainties on the problem's solution can be answered using a statistical approach. Therefore, the sources of uncertainty have to be identified statistically. A method for linearising the model function using the Guide to the expression of uncertainty in measurement is introduced for inverse problems. The statistical inversion of the model is executed by means of two different approaches, that are compared and interpreted exemplarily.
Zusammenfassung
Die Bestimmung akustischer Materialparameter mittels Ultraschall-Transmissionsmessung kann mathematisch durch ein inverses Problem beschrieben werden. Die Frage nach dem Einfluss von Unsicherheiten der Lösung dieses inversen Problems kann mit Hilfe statistischer Ansätze beantwortet werden. Zunächst wird daher eine Modellierung von Unsicherheitsquellen vorgenommen. Ein Verfahren zur Linearisierung im Sinne des Guide to the expression of uncertainty in measurement für inverse Probleme wird vorgestellt. Die statistische Inversion wird mittels zweier unterschiedlicher Verfahren durchgeführt, die beispielhaft verglichen und interpretiert werden.
About the authors
Nadine Feldmann, M. Sc. is a research associate at the measurement engineering group at the faculty of electrical engineering, computer science and mathematics at Paderborn University. Her field of research includes the statistical description of inverse problems and the modelling of measurement uncertainties.
Paderborn University, Measurement Engineering Group, Warburger Straße 100, 33098 Paderborn, Germany
Dr.-Ing. Fabian Bause was a research associate at the measurement engineering group at the faculty of electrical engineering, computer science and mathematics at Paderborn University until 2015. His field of research included the simulation of ultrasonic measurement systems and the determination of acoustic material properties.
Paderborn University, Measurement Engineering Group, Warburger Straße 100, 33098 Paderborn, Germany
Univ.-Prof. Dr.-Ing. Bernd Henning is the head of the measurement engineering group at the faculty of electrical engineering, computer science and mathematics at Paderborn University. His main field of research includes acoustic measurement systems, ultrasonic, optical and biomedical metrology.
Paderborn University, Measurement Engineering Group, Warburger Straße 100, 33098 Paderborn, Germany
Acknowledgement
The authors would like to thank the German Research Foundation (DFG) for financial support of the research projects HE 2897/3-1 (determination of acoustic material properties) and HE 2897/6-1 (evaluation of hydrothermal aging of continuous-fiber reinforced thermoplastics and development of an ultrasonic measurement system for non-destructive characterization of the state of aging for structural health monitoring and remaining life-time predictions).
©2016 Walter de Gruyter Berlin/Boston
