Uncertainties estimation in surveying measurands: application to volumes.

Volume represents a measurand of great interest in civil engineering and construction works. The estimation of this measurand is a problem already solved by surveying engineering, but the quantification of its uncertainty has been overlooked. As a result, the inaccurate estimation of the volume can lead to significant deviations in the execution costs of earthworks. Moreover, it is not possible to comply with the internationally accepted requirements concerning the expression of measures with an indication of its uncertainty, i.e., the guidelines of the BIPM (Bureau International des Poids et Mesures). In this context, this paper presents a methodology for the quantification of uncertainty in the surveying measurement of volumes, which is generally carried out through digital terrain models processed by CAD or specific surveying software. Two methods for volume estimation are presented and the variance-covariance propagation laws are applied to each of them, leading to the computation of volume uncertainty from measures of position coordinates for which uncertainties are known. Then, the developed methods for uncertainty estimation are successfully tested in different scenarios. The conceptual and mathematical developments for the uncertainty quantification in the computation of volumes resulted in closed-form algorithms implemented in MATLAB that can be potentially incorporated into commercial surveying software.