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Optimierung geodätischer Netze mit spektralen Zielfunktionen / H. Kaltenbach (1992)

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Titre :	Optimierung geodätischer Netze mit spektralen Zielfunktionen
Titre original :	[Optimisation des réseaux géodésiques par les fonctions spectrales recherchées]
Type de document :	Thèse/HDR
Auteurs :	H. Kaltenbach, Auteur
Editeur :	Munich : Bayerische Akademie der Wissenschaften
Année de publication :	1992
Collection :	DGK - C
Sous-collection :	Dissertationen num. 393
Importance :	116 p.
Format :	21 x 30 cm
ISBN/ISSN/EAN :	978-3-7696-9439-0
Note générale :	Bibliographie
Langues :	Allemand (ger)
Descripteur :	[Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] analyse spectrale [Termes IGN] canevas [Termes IGN] itération [Termes IGN] matrice de covariance [Termes IGN] mire parlante [Termes IGN] problème inverse [Termes IGN] réseau géodésique [Termes IGN] système de coordonnées [Termes IGN] système non linéaire [Termes IGN] valeur propre
Index. décimale :	30.10 Systèmes de référence et réseaux géodésiques
Résumé :	(Auteur) The following thesis deals with the optimization of geodetic networks based on spectral target functions. The spectral analysis and optimization is based on the decomposition of the normal equation matrix of the adjustment or on the covariance matrix of the coordinates in the system of eigenvalues and eigenvectors. Chapter two contains some important mathematical background knowledge from the field of direct and inverse eigenvalue problems and the iterative solution of nonlinear systems of equations. Especially some properties of the newton-procedure are discussed, because this method is generally used to solve inverse eigenvalue problems. To apply the Newton-procedure it is necessary to know the derivatives of the eigenvalues and vectors of the considered matrix with respect to the design parameters. The derivatives of an arbitrary (symmetric) matrix are summarized in this chapter. The spectral analysis of geodetic networks related to aspects of precision and reliability is the subject of chapter three. Some wellknown local and global measures for the precision are summarized shortly. Aspects concerned with the so-called inner geometry of a network and the definition of the coordinate system (datum problem) are mentioned and supplemented by examples. The optimization with target functions related to the eigenvalue spectrum is the main part of this thesis and the subject analyzed in detail in chapter four. Principally spoken the task is to determine the coordinates of the netpoints and the observation weights in such a manner that the resulting normal equation or covariance matrix has a special target spectrum. This is the definition of the inverse eigenvalue problem. Based on a given start design of a geodetic network the target function is formulated and the inverse eigenvalue problem is solved iteratively. As mentioned above it is necessary to know the derivatives of the eigenvalues with respect to the coordinates and the observation weights. The derivatives can be computed based on the eigenvalue problem for the normal equation matrix or the covariance matrix and furthermore it is necessary to calculate the derivatives of the elements of the normal equation matrix analytically. Problems arising in network optimization like handling the orientation unknowns in direction networks or the consideration of inner geometry and datum definition of a network are discussed. Examples show the effectiveness of the optimization procedure and show how the so-called weak form of geodetic networks can be reduced. The spectral network optimization is a useful tool for understanding properties and behaviour of geodetic networks. The spectral formulation with target eigenvalues allows the solution of first, second and third order design problems in the usual classification of network optimization. The examples are also used to investigate the properties of the iterative solution procedure, especially the rate of convergence or the definiteness of solutions. In analogy to the eigenvalues, one can define an inverse eigenvector problem : the task is to determine the design parameters -namely the coordinates and the observation weights - in such a way that the normal equation matrix has given eigenvectors. The formulation of solution procedures and the difficulties in formulating suitable target functions for eigenvectors is the topic of chapter five. One application of this topic is the field of deformation analysis, where the task is to achieve the components of the dominant eigenvector in such a manner that they are perpendicular to. the expected direction of the deformations. To make an algorithm for network optimization a suitable tool in network planning, it is inevitable to consider some practical aspects. In the first order design, namely the determination of the coordinates of the netpoints, it is obvious that the rate of displacement of the points is limited by the local topography. One cannot move the points arbitrarily without loosing connections between the points. Therefore it is obvious to introduce the possible rate of displacement of the points as restrictions into the optimization algorithm. The same is valid for the observation weigths in a weight optimization (second order design). To take into account aspects of reliability we have to formulate upper bounds for the weights because observations with very high weights compared with other observations usually have low redundancy. Therefore in the adjustment gross errors can be found with a low probability, but unknown errors can distort the results significantly. If we take into account these practical aspects within the iterative solution procedure of the inverse eigenvalue problem we get a problem of minimizing a certain target function with additional restrictions in the form of equations and unequations. There are several methods in optimization theory for solving such problems. Chapter six of the present thesis deals with this topic. Again examples are used to supplement the theoretical investigations.
Numéro de notice :	61414
Affiliation des auteurs :	non IGN
Thématique :	POSITIONNEMENT
Nature :	Thèse étrangère
Permalink :	https://documentation.ensg.eu/index.php?lvl=notice_display&id=60937

Exemplaires(2)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
61414-01	30.10	Livre	Centre de documentation	Géodésie	Disponible
61414-02	30.10	Livre	Centre de documentation	Géodésie	Disponible

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