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

Abstract

This paper presents the theoretical back ground for a new measurement system for the monitoring of possible road subsidence and its verification with exper imental 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 measure ments. The correct functionality of the measurement system was verified.

Simultaneous Approximation of Measurement Values and Derivative Data using Discrete Orthogonal Polynomials

“…Clearly, this introduces covariance weighting on the residual and thus a metric between value and derivative domain is established as stated in [18] and [22]. Substituting W dy and minimizing Eqn.…”

“…The idea of including a covariance weighting on the residuals to get a valid metric between the value and derivative domain is introduced in [18] and extended to higher order derivatives in [22].…”

High Accurate Mathematical Tools to Estimate the Gravity Direction Using Two Non-Orthogonal Inclinometers

“…The monitoring of possible road subsidence is proposed using a combination of theodolite measurements and inclinometers [ 21 ] to detect ground motion near critical infrastructure during excavation in the vicinity. The proposed method, validated by Monte Carlo simulation, is formulated as a covariance weighted Hermite approximation problem.…”