Deformation monitoring and the maximum number of stable points method

Abstract

Abstract. The question of determination of displacements in control networks with two or more measuring epochs is a well-known problem with broad applications to different fields of science and engineering. The standard procedure, which is computed by means of the pseudoinverse matrix, however, makes an implicit assumption that may be not convenient for the network at hand: it distributes the noticed displacement among the majority of the network points. The present paper develops what it has been named as the maximum number of stable points hypothesis and builds from the corresponding theoretical framework an applicable computation procedure. Application to a particular example will confirm its clear advantages versus the standard procedure for deformation determination in the cases where a single large deformation may be suspected.

Adaptive Stochastic Resonance Method Based on Quantum Genetic Algorithm and its Application in Dynamic Characteristic Identification of Bridge GNSS Monitoring Data

“…The reason is that the accelerometer has some shortcomings, such as integral accumulation error, insensitivity to low-frequency vibration, and others [61]. Therefore, growing number of studies have focused on corresponding data processing methods, such as linear analysis-based methods [64,65], wavelet transform [66][67][68][69][70][71][72], principal component analysis [73,74], empirical mode decomposition (EMD) and its derivative method [72,[75][76][77][78][79][80][81][82][83], to extract the vibration features of bridges. Compared with difficulties in simulating and estimating the displacement error in accelerometer monitoring, a certain rule exists to address for the noise in 3D coordinate time series of bridge monitoring deformation from GNSS [84][85][86][87].…”

Deformation Monitoring of the Submillimetric UPV Calibration Baseline

“…As it was previously demonstrated [2], this involves the underlying assumption that displacements, provided they occur, are expected to be small shifts (the least possible) affecting all points. This may sound as a very sensible working assumption.…”

“…This may be especially the case of quite unexpected, considerably large displacements where the suspicion leads to a possible movement of a single or few pillars due to unfortunate circumstances. A method to obtain the solution most compatible with the hypothesis of stability of the majority of pillars and possible large displacements in the least number of them was presented in Baselga et al [2] and named the maximum number of stable points method. In a nutshell, for a pair of campaigns the method solves the over-determined rank where ( ) + denotes the pseudoinverse, I is the identity matrix and y is a real-valued vector the same size as x that will be determined by an optimization procedure under the condition…”

Squared Msplit(q) S-transformation of control network deformations

“…An erroneous identification leads to erroneous defining of datum for estimated object deformations and, in consequence, to disinformation. The identification of mutually stable points is the only serious problem in congruence models, and it is still the subject of interest for surveyors and geodesists (Baselga and García-Asenjo 2016;Amiri-Simkooei et al 2016;Aydin 2017).…”