Three-Dimensional Networks Are Horizontally Superior in Robustness: A Mathematical Reasoning

After least squares adjustment, the possible outliers among the observations are detected using a statistical test, such as Baarda’s data-snooping test. However, statistical tests do not guarantee that all of the incorrect observations will be detected. Robustness analysis is a technique that augments this classical approach with geometrical strength analysis using strain. The technique allows the effect of undetected errors among the observations to be portrayed. In this technical note, we will show that three-dimensional networks are usually horizontally superior in robustness by explaining mathematically why the magnitudes of the deformation measures in the $XZ$ and $YZ$ planes are many times larger than their $XY$ -plane counterparts.