Determining the shape of the surface of shell structures using splines and alternative methods: Kriging and Fourier series

Abstract

Shell structures belong to a characteristic group of objects for which it is essential to know the magnitude and distribution of local deformations of the coat. Deformations may be important both in terms of stability, as well as special functions performed by these objects. While survey instruments usually ensure the required accuracy of the measurements, the methods for providing a mathematical description of the shape of shells do not always allow for a correct detection of deformations. This paper compares several methods of approximation potentially useful for making a precise description of the shape of a given shell object. Spline functions, as the most versatile tool in terms of description of objects shape, were adopted as the base method. For comparison purposes, according to the shape of the object in question, kriging and Fourier series methods were selected. Particular attention has been paid to the accuracy aspect, which has enabled deformations to be determined within centimeter or subcentimeter accuracy. Results of the study revealed the greatest overall accuracy of spline functions. This accuracy however decreases quickly when the observations become more irregular. Both, the past and future studies of the authors focus on integrating the best features of the described methods in order to ensure a high accuracy of the created models. The results may be useful not only in surveying but also in other fields associated with the approximation of surfaces based on measurement data.