Fredrik Lingvall

Licentiate Thesis, Signals and Systems, Uppsala University, March 2000.

Paper copies of the thesis can be obtained from Ylva Johansson, Signals and Systems Group, Uppsala University, Box 534, SE-75121 Uppsala, Sweden.

Abstract:

Efficient data representation and choice of suitable basis (representation) are the main issues addressed in the thesis. Three separate applications are presented: two are in the field of non-destructive testing, while in the third methods for reconstructing room temperature distributions based on ultrasonic measurements are considered.

The need for compact representation arises from the limited amount of data available for the classification of material defects and for temperature estimation, respectively. The main goal that was common for the first two projects was developing software tools of self-learning type, suitable for automatic classification of defects in multi-layer aluminum aircraft structures and welds in steel material, respectively. Different NDT methods were used in both cases, eddy current for the aircraft structures and ultrasonics for welds.

A compact data representation was necessary in both cases, due to the low number of examples available for training the classifiers. This was accomplished by compressing the high dimensional data vector, obtained from the measurements, using various truncated bases, such as: wavelets, Fourier, and principal component bases.

Efficient data representation was also a crucial part of the third project. The aim was to reconstruct a 2D-temperature distribution in many points of a room, based on a limited number of measurements (time of flight of an ultrasonic wave). To achieve a satisfactory performance strong prior knowledge regarding the reconstructed surface was necessary. The prior knowledge was incorporated by expressing the temperature distribution using suitable base functions. Computer simulations revealed that the principal component basis (specific for the measured data) clearly outperformed other more general base function sets (for instance, wavelets), which confirmed the importance of a suitable data representation.