Non-destructive Testing of Concrete by Interpreting Ultrasound Signals via Linear Optimization

This thesis presents some mathematical models to represent ultrasound measurements in an attempt to automatically interpret ultrasound measurements. It is a multidisciplinary work mixing ultrasound non-destructive testing and linear optimization. Assumptions on the specimen are formulated, modeled and finally verified using linear optimization. The formulated assumptions include position, size and certain types of reflecting surfaces, and are modeled such that they can be fitted to a measurement using the linear optimization technique column generation. For the fit, a reference signal is used to find reflectors in the measurement and to simulate a set of reflectors with different strengths of reflection. Some parameters, like position and size of the reflectors, are optimized and determined during the fit. Finally, after the fit is obtained, the fitted simulation of the reflectors is compared to the measurement, and the L1-distance between both is used to verify or dismiss the assumptions in the model. If, e.g., a surface-like reflector was able to be fitted at the right position in the specimen, then the L1- distance will be reduced as the amount of non-explainable signal is shrunk by the found reflector. Otherwise, the reflector will be discarded from the fit and the L1-distance will be unchanged due to the unchanged amount of non-explainable signal. While the reference signal is crucial for the fit, it is usually not available on real measurements. Three different parametrized approximation-techniques will be developed and compared. The first one consists of a part cut from the measurement and the two other ones will model the reference signal, once as a Gaussian wave and once from the Fourier transform. Parameters to the references will be obtained using tools like Levenberg-Marquardt algorithm or linear regression.