Application of Splines Supported by Kriging for Precise Shape Analysis of Incompletely Measured Structures

Abstract

The creation of precise models of engineering structures constructed with splines requires that a relatively regular set of observations be supplied. The presence of door and window openings in such structures, and covering caused by other elements while performing the measurements, often results in gaps in the observation sets. Because the splines tend to minimize the total curvature, model flattening occurs at the areas without observations, which leads to deformation in the adjoining areas. Spline models in such areas offer, as a rule, insufficient approximation accuracy. The solution of the problem, presented in the paper, involves filling the gaps in an incomplete set of observations with artificially generated pseudo-observations. This will allow reducing surface deformations in the areas adjoining to the immeasurable locations. The kriging method was chosen to perform such task. To verify the effectiveness of the solution proposed, several variants of models were constructed and analyzed afterwards. The paper provides the theoretical assumptions as to the method, remarks regarding the properties of test models, and the results of analyses performed, together with conclusions to evaluate the usefulness of the method described.