Network robustness measures based on responses to undetectable observation errors

• Autorzy: Prószyński W. , Parzyński Z.
• Języki publikacji: EN

Abstrakty

EN

The examination of the concept of network robustness to observation gross errors based on the reliability and strain analysis (see Vanicek et al 2001), has revealed some disadvantages due to a discrete nature of the network's structure. The weak sides of the strain analogy shown in (Gambin et al. 2008), specially for small networks, speak in favour of finding a non-tensor replacement for network robustness measures. One of the possible approaches, applicable to all types of geodetic networks with uncorrelated observations and sufficient for most practical purposes, could be the use of traditional concepts of internal and external reliability for assessing network robustness to observation gross crrors. Such a proposal, maintaining the maximum undetectable error in an individual observation as a source of network deformations (as in Vanicek et al. 2001), and analyzing the resulting node displacements and element deformations, is discussed and illustrated on a simple numerical example. The proposal provides a direct Iink between the robustness and the accuracy analysis of a network, and has a clear onterpretation in terms of mechanical strength analogy. As a theoretical support, deformation-oriented properties of the reliability matrix and the properties of network responses to undetectable observation errors are analyzed.

Słowa kluczowe

EN

network robustness; undetectable observation errors; mechanical strength analogy; reliability matrix; node displacements; element deformations

PL

niezawodność sieci; niewykrywalne błędy obserwacji; analogia mechaniczna wytrzymałości; niezawodność macierzy; przemieszczenie węzłów; odkształcenia elementu

• Wydawca: Wydział Geodezji i Kartografii Politechniki Warszawskiej
• Czasopismo: Reports on Geodesy
• Rocznik: 2009
• Tom: z. 2/87
• Strony: 343--352
• Opis fizyczny: Bibliogr. 9 poz., tab., wykr.

Twórcy

autor

Prószyński W.

autor

Parzyński Z.

• Faculty of Geodesy and Cartography, Warsaw University of Technology

Bibliografia

• [1] Baarda W. (1968) A testing procedure for use in geodetic netwerks, Publications on Geodesy, New Series, Netherlands Geodetic Commission, vol. 2, No. 5, Delft.
• [2] Chatterjee S., Hadi A.S. (1988) Sensitivity analysis in linear regression, Wiley, New York.
• [3] Gambin W., Parzyński Z., Prószyński W. (2008) The concept of network robustness based on strain analogy as seen in the light of continuum mechanics, Proceedings of the 13th FIG Symposium on Deformation Measurements, Lisbon.
• [4] Gruendig L.,Bahndorf J. (1985) Sequential optimisation of geodetic networks with respect to accuracy and reliability, Proceedings of 7th International Symposium on Geodetic Computations, Kraków, Poland.
• [5] Prószyński W (1994) Criteria for internal reliability of linear least squares models, Bull. Géodésique 68: 162 – 167.
• [6] Prószyński W (1997) Measuring the robustness potential of linear least squares models; geodetic illustration, J. Geod., Vol. 71, pp. 652 – 659.
• [7] Rao C.R. (1982) Linear statistical inference and its applications (in Polish), PWN, Warszawa.
• [8] Seemkooei A.A. (2001) Comparison of reliability and geometrical strength criteria, Journal of Geodesy 75: 227 – 233.
• [9] Vaniček P, Craymer MR, Krakiwsky EJ (2001) Robustness analysis of geodetic horizontal networks, Journal of Geodesy 75: 199 – 209.