A Framework for the Evaluation of Inclinometer Data in the Measurement of Structures
A Framework for the Evaluation of Inclinometer Data in the Measurement of Structures
复制标题
结构测量中测斜仪数据评估框架
DOI：
10.1109/tim.2011.2180969
复制
发表时间：
2012
影响因子：
5.6
通讯作者：
M. Harker
中科院分区：
文献类型：
--
作者：
P. O’Leary;M. Harker
本文提出了一种新的代数框架，用于结构建模和计算从局部导数重构曲线。这是使用测斜仪测量结构变形背后的根本问题。一个坚实的理论背景，与推导，提供了一个真实的和实际的测量问题的解决方案。重建问题的解决使用矩阵代数技术应用于变分。吉洪诺夫，频谱，和一个新的正则化技术的基础上截断约束基函数的实现。证明了通过基函数求解微分方程对应于计算关于所使用的基函数的弯曲模式的谱。这种见解产生了一种方法，确定基于谱紧性的基函数的最佳设置。提出了一种计算线性微分算子并产生全局估计量的全新方法。该方法也被扩展到产生一个正则化的线性微分算子。方法进行了验证，并提出了大量的数值模拟，包括蒙特卡罗模拟，以验证的敏感性的解决方案，噪声证实的索赔。该方法也适用于一个真实的测量问题，确定轨道附近的轨道施工期间的沉降。同时重建和时间滤波实现。
This paper presents a new algebraic framework for modeling structures and computing the reconstruction of curves from local derivatives. This is the fundamental problem behind the use of inclinometers to measure the deformation of structures. A solid theoretical background, with derivations, is provided for the solution of a real and practical measurement problem. The reconstruction problem is solved using matrix algebraic techniques applied to variational calculus. Tikhonov, spectral, and a new regularization technique based on truncated constrained basis functions are implemented. It is proved that the solution of differential equations via basis functions corresponds to computing the spectra of the bending modes with respect to the basis functions used. This insight yields a method of determining the optimal set of basis functions based on spectral compactness. A completely new approach to computing a linear differential operator which yields a global estimator is presented. The method is also extended to yield a regularizing linear differential operator. The methods are verified, and the claims made substantiated by extensive numerical simulations including Monte Carlo simulations to verify the susceptibility of the solution to noise. The methods are also applied to a real measurement problem of determining the subsidence of rail track during construction in the vicinity of the track. Simultaneous reconstruction and temporal filtering is implemented.