Inverse boundary value problems with uncertain boundary values and their relevance to inclinometer measurements

Abstract

This paper presents the theoretical background for a new measurement system for the monitoring of possible road subsidence and its verification with experimental results. A combination of theodolite measurements and inclinometers are used to perform the monitoring of possible land subsidence. The aim is to detect ground motion near critical infrastructure during excavation is the vicinity. The required computation corresponds to an inverse boundary value problem with uncertain boundary values. The solution is formulated as a covariance weighted Hermite approximation problem. Additionally, a method of taking advantage of the properties of the over-constrained system to identify a defective sensor is presented. The correct functionality of the proposed method and its performance in terms of uncertainty is demonstrated with a Monte Carlo simulation. Additionally, tests were performed with a real monitoring system with reference measurements. The correct functionality of the measurement system was verified.