How Significant Are Differences Obtained by Neglecting Correlations When Testing for Deformation: A Real Case Study...

Area of Science:

• Geodesy
• Geomatics Engineering
• Computational Geometry

Background:

• B-spline surfaces offer high continuity and local support, valuable for surface fitting in engineering geodesy.
• Least-square (LS) fitting of 3D point clouds from terrestrial laser scanners (TLS) enables rigorous deformation analysis.
• Standard software often limits deformation analysis to distance maps, hindering robust statistical testing.

Purpose of the Study:

• To investigate the impact of mathematical correlations, arising from error propagation, on deformation test statistics.
• To assess the consequences of misspecifying the stochastic model in B-spline surface fitting for TLS data.
• To determine if simplifications in the stochastic model affect deformation test decisions.

Main Methods:

• Utilizing B-spline surface fitting for 3D point clouds from terrestrial laser scanners (TLS).
• Transforming the variance-covariance matrix (VCM) of TLS measurements using the error propagation law.
• Applying adapted bootstrapping for computing p-values due to intractable test distributions.
• Comparing test statistics from real TLS and laser tracker (LT) data from a bridge under load.

Main Results:

• Mathematical correlations induced by error propagation significantly affect deformation test statistics.
• Misspecification of the stochastic model can lead to incorrect rejection of the null hypothesis (no-deformation).
• The study quantifies the impact of heteroscedasticity and correlations on test decisions.

Conclusions:

• Accurate stochastic modeling is crucial for reliable deformation analysis and risk management in engineering geodesy.
• Neglecting induced mathematical correlations can lead to costly errors in structural health monitoring.
• The findings support potential simplifications in stochastic modeling based on the intensity model without compromising test decisions.