Assessment of Adjustments Methods in Traverse Networks for Positioning

Various factors contribute to the degree of accuracy of the adjusted parameter (coordinate), one of which is the choice of adjustment model. Adjustment models seeks to eliminate (accounts) for the presence of random errors present in a given observations. The choice is critical for surveyors and other spatial analysts for optimal positioning and mapping projects since different adjustment models will yield different level of accuracy of spatial information generated irrespective of the quality of observations. For a traversing network, various adjustment models have been put forward which include; the Transit, the Bowditch, and the Crandels models. In spite of these models, internal consistency and reliability indicators of the network of positions are determined using the least squares adjustment model (observation equation and condition equation models). The aim of this work is to analyze the various traverse adjustment models. The approach deployed in this work was to compute the provisional coordinate of six traverse stations using the approximate methods of adjustment i.e., Bowditch and transit methods of traverse adjustment models. In addition, the least square adjustment models were deployed to minimize the propagation of residuals of the obtained values. The adjusted distances and directions were then compared with the observed distances and directions to obtain the residuals. The coordinate of positions was determined and the Root Mean Square Error (RMSE) associated with the traverse adjustment models are given as 0.128702264 and 0.008560954. Similarly, the RMSE of the adjusted values using the least square models are given as 0.007181432, and 0.005763969 for the observation and condition equation models respectively. The analysis of these results reveals that the traverse adjustment models are unique with capabilities embedded in the determination of the observables during data acquisition. However, for mapping and engineering survey of small locations, the transit method is more preferable to the Bowditch method.

Adjustment Of Single And Double Braced Quadrilateral Using Least Square Condition Equation

Quadrilateral is a single or double triangulation system consisting of figures with four corners stations. It consist of two known stations and a base line. Other corners of the triangles are measured using precise instrument. The systems is treated as the strongest with the best arranged triangular structure which provides adequate means of determining the lengths of other sides of the triangle whose length, bearings and positions are required. In this four sided polygon with four (4) points were established. The coordinate of two points (A and B) are known while the coordinates of points (C and D) are required. The purpose of the exercise was to use least square condition equation to determine and adjust coordinates of the two unknown points using the Angular measurements of quadrilateral. Two separate measurements were taken (observation 1 and observation 2) forming a network of a single and double braced quadrilateral respectively. After which, the data obtained were reduced and then adjusted using least square condition equation.

Implementation of Condition Equation Model in Geodetic Observation: A Case Study of Circular Reservoir Structure

In engineering projects involving the construction of aboveground storage tank big enough to retain and/or accommodate large quantities of petroleum products such as crude oil and condensate, mathematical reduction of obtained field data using condition equation method is always appropriate for an onward monitoring of those structures. This paper demonstrates how condition equation method can be used to adjust geodetic surveying measurements in relation to aboveground storage tank. Accuracy is in the order of σa = 5.66e-4 and σb = 1.113e-3 while σsmax and σsmin are 0.0522 and -0.0511 respectively. The results obtained revealed that the method can be satisfactorily implemented for aboveground circular reservoir storage tank structural modelling and monitoring for a similar scenario.

On the Effect of Thomson and Initial Stress in a Thermo-Porous Elastic Solid under G-N Electromagnetic Theory

The present work investigated the effect of Thomson and initial stress in a thermo-porous elastic solid under G-N electromagnetic theory. The Thomson coefficient affects the heat condition equation. A constant Thomson coefficient, instead of traditionally a constant Seebeck coefficient, is assumed. The charge density of the induced electric current is taken as a function of time. A normal mode method is proposed to analyze the problem and to obtain numerical solutions. The results that were obtained for all physical sizes are graphically illustrated and we offer a comparison between the type II G-N theory and the G-N theory of type III, both in the present case and in the absence of specific parameters, as initial stress, pores and the Thomson effect. Some particular cases are also discussed in the context of the problem. The results indicate that the effect of initial stress, Thomson coefficient effect, and magnetic field are very pronounced.

The New Approach to Identification of Parametric and Momentary Damages on the Basis of Lindeberg – Levy’s Model

The new approach for the assessment of reliability condition of the exploited system, based on the appropriate analysis of changes in the current parameters of technical condition aRb and the regulation condition aRc, determined from the compressed condition equation (1 and 2). While analyzing the course of momentary parameters for technical condition aRb and the regulation condition aRc, it was observed that the parametric and momentary damages can be identified on the basis of quantitative relations between momentary threshold value dpr and corresponding momentary permissible value dpr dop, which are calculated from equation (7, 8, 9) resulting from Lindeberg–Levy’s theorem. It is assumed that the damages are prevailing, when for the moment θi: >dpri> dpr dopi. With the number of damages (damage map), reliability parameters for each moment of exploitation of technical object (before the catastrophic damages will occur) can be determined. Parametric damages (expected lifetime E(T) and standard deviation of expected lifetime σE(T) provides the reasonable information for the appropriate planning of the servicing of exploitative objects.

Identification of Parametric and Momentary Damages on the Basis of Lindeberg-Levy’s Model

Article presents the innovative method for the assessment of reliability condition of the exploited system, based on the appropriate analysis of changes in the current parameters of technical condition aRb and the regulation condition aRc, determined from the compressed condition equation (1 and 2). While analyzing the course of momentary parameters for technical condition aRb and the regulation condition aRc, it was observed that the parametric and momentary damages can be identified on the basis of quantitative relations between momentary threshold value dpr and corresponding momentary permissible value dprdop, which are calculated from equation (7, 8, 9) resulting from Lindeberg-Levy’s theorem. It is assumed that the damages are prevailing, when for the moment θi: dpri>dpr dopi. With the number of damages (damage map), reliability parameters for each moment of exploitation of technical object (before the catastrophic damages will occur) can be determined. Parametric damages (expected lifetime E(T) and standard deviation of expected lifetime σE(T) provides the reasonable information for the appropriate planning of the servicing of exploitative objects.

A Sort of New Improved Algorithm For Total Least Square

Aim to blemish of total least square algorithm based on error equation of virtual observation, this paper put forward and deduced a sort of new improved algorithm which selects essential unknown parameters among designing matrix, and then, doesn’t consider condition equation of unknown parameters among designing matrix. So, this paper perfected and enriched algorithm, and sometimes, new method of this paper is better. Finally, the results of examples showed that new mothod is viable and valid.