A mathematical algorithm for dimensional control of tunnels using topographic profiles

Abstract

We propose a new method to study the geometry of tunnels based on comparing topographic profiles considered as curves instead of sets of discrete points. Two different approaches were used to compare the profiles: one based on the notion of functional depth, which is a measure of the centrality of a set of curves, and the other based on ordering the scores of principal component decomposition. The proposed methodology was used to analyse the geometric quality of a tunnel by comparing a set of cross-sections of the tunnel measured using a RIEGL LMS-Z390i terrestrial laser scanner. The results obtained demonstrate the usefulness of the method based on principal component decomposition in detecting significant differences of the geometry along the tunnel.

Keywords:

• functional outliers
• functional depth
• functional high density region
• tunnel inspection
• laser scanner

2010 AMS Subject Classifications::

• 62-07
• 68U05

Acknowledgements

This work is funded by project BIA2011-26915 of the Spanish Ministry of Science and Innovation.