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Analyse und Optimierung geodätischer Netze nach spektralen Kriterien und mechanische Analogien / R. Jäger (1988)

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Titre :	Analyse und Optimierung geodätischer Netze nach spektralen Kriterien und mechanische Analogien
Titre original :	[Analyse et optimisation des réseaux géodésiques d'après des critères spectraux et des analogies mécaniques]
Type de document :	Thèse/HDR
Auteurs :	R. Jäger, Auteur
Editeur :	Munich : Bayerische Akademie der Wissenschaften
Année de publication :	1988
Collection :	DGK - C
Sous-collection :	Dissertationen num. 342
Importance :	135 p.
Format :	21 x 30 cm
ISBN/ISSN/EAN :	978-3-7696-9390-4
Note générale :	Bibliographie
Langues :	Allemand (ger)
Descripteur :	[Vedettes matières IGN] Systèmes de référence et réseaux [Termes IGN] élasticité [Termes IGN] matrice [Termes IGN] méthode des éléments finis [Termes IGN] optimisation (mathématiques) [Termes IGN] quantité discrète [Termes IGN] réseau géodésique [Termes IGN] valeur propre
Index. décimale :	30.10 Systèmes de référence et réseaux géodésiques
Résumé :	(Auteur) According to the expression 'spectral criterions' this thesis is dealing - within the analysis and optimisation of geodetic networks - with mathematical models describable as eigenvalue problems connected with the variance-covariance matrix of network-coordinates. The eigenvalues and eigenvectors serve as spectral criterions for network analysis and as spectral target functions for network optimisation respectively. A first network analysis model consists in the comparison of the appropriate variance-covariance matrix with an ideal criterion-matrix, and is based on the general eigenvalue problem of these matrices. Theoretical investigations concerning thereby the problem of choice of datum lead to a unification of hitherto existing approaches in form of a datum-invariant substitutive eigenvalue problem. A second consideration is due to the simple eigenvalue-problem of the variance-covariance matrix of the network-coordinates itself. A therefore developed filter model includes the influence of a weak datum on the spectral criterions as well as a separation between the inner geometry of the regarded network and its absolute foundation. The theoretical studies are completed and further extended by network examples. The analysis of geodetic networks by means of the simple eigenvalue problem of its variance-covariance matrix of coordinates is closely linked to the kinetics, especially to the eigen-vibrations of elastic mechanical structures. Proceeding from the elastic continuum, the complete foundation of analogies between elastomechanics and geodetic network-compensation by least squares can be carried out in the step of its finite-element-discretisation, being based fundamentally ('fundamental analogies') on equivalent principles, of variations. The well-known analogies between particular corresponding finite elements and geodetic observational types are thereby included and resulting as a special case (denoted as 'direct analogies') of the so cal-led 'principal analogies', which are not at all depending on special types of elements. The principal analogies are forming the central kernel of the treated concept of analogy-foundation. In the sense of a complete analogy-foundation the very principal analogies at the same time represent the link to the way back to the differential equations of the adjoint continuum structures. The differential equations are traced back to their dependence to network-design (pattern), the observational types/elements and their weight-parameterisation). For the purpose of a general derivation of differential equations of regularly designed geodetic networks, there is developed a procedure with an algorithmic nature which is also be applicable to mechanical structures. The mechanical analogies in the matrix equations and differential equations turn out to be useful for the interpretation of the eigenvector-shapes and the eigenvalue-spectrum within the above mentioned geodetic network analysis. For geodetic networks of high density the spectral analysis can advantageously be performed directly by the solution of the differential equations of the (elastic) continuum. The theoretical parts of this chapter are underpinned by appropriate examples. As inversion of the network analysis with spectral criterions this thesis is (to its second main part) further on dealing with the optimisation on spectral target functions. The chapters of optimisation are introduced by preliminary theoretical research concerning the influence of single observations on the spectral characteristics of a network and with the possibilities of modifying the eigenvalue-spectrum and the eigenvectors by changing observation-weights, design (graph) and nodal point-positions respectively within the network. As for the spectral optimisation concerning 2nd/3rd Order Design and 1st Order Design of point observations, this theoretical framework turns out that the aims of these optimisation-designs can be achieved by target functions limited to the eigenvalues of the above-mentioned eigenvalue problems. The concept of optimisation leads - mathematically spoken - to the problem of solving different associated inverse eigenvalue problems with respect to prescribed target-spectra. For all interesting eigenvalue problems and intended optimisation problems of the above-mentioned designs there can be found a unified iterative solution procedure referring to the normal equations as kernel. The particular eigenvalue problem of optimisation as well as partly required datum-changes are realized by specific transformations within this iteration procedure. As concerns the final representation of some results of the spectral estimation method, a first attention is - above mechanical aspects - paid to the theoretically founded accordance between the results obtained by classical optimisation and those of spectral optimisation in 2nd/3rd Order Design of classical observation types (applying thereby the corresponding model of the general eigenvalue problem due to a criterion matrix). The second point of interest is mainly dedicated to the results and network examples concerning 1st Order Design appearing as the problem of determining optimum supporting-point observations in geodetic networks; this is quite a dual problem between pure 1st Order Design (optimum positions of these points) and 2nd/3rd Order Design (optimum weights of these point-observations). The optimisation concerning point observations is representing a new component within geodetic network optimisation. Besides the problem of ideal positions for linking free networks (for ex-ample railway network-chains) to points of the superior network, this kind of optimisation is actually getting more and more important with regard to the quest/ion of finding out best positions for supporting classical terrestrial networks by GPS-point-positioning.
Numéro de notice :	28104
Affiliation des auteurs :	non IGN
Thématique :	POSITIONNEMENT
Nature :	Thèse étrangère
Permalink :	https://documentation.ensg.eu/index.php?lvl=notice_display&id=63451

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
28104-01	30.10	Livre	Centre de documentation	Géodésie	Disponible
28104-02	30.10	Livre	Centre de documentation	Géodésie	Disponible

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