Power of Global Test in Deformation Analysis
Publication: Journal of Surveying Engineering
Volume 138, Issue 2
Abstract
There are two kinds of global test procedures in deformation analysis; -test (CT) and -test (FT). This study discusses their power functions. The CT is more powerful than the other one in an analytical point of view. However, it requires an accurate knowledge on the a priori variance of unit weight. Therefore, in practice, the FT is mostly chosen. Despite its common usage, a -power function is considered in the sensitivity design of deformation networks. It is claimed in this study that the -distribution’s power function should be taken into account, if, in reality, the FT will be applied. Thereby, some boundary values deduced from the noncentral -distribution to be used in sensitivity analysis are computed and tabulated. Furthermore, a simulation for a monitoring network is designed, and it is shown that the mean success rates of the two testing procedures are identical with their own powers known beforehand. This numerical experiment depicts that one should consider the related power function in the design stage, and that each power function gives a realistic probability of how the corresponding test procedure is successful.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The mentioned code in this study has been written with Scilab 5.3.1, free and open source software (distributed under CeCILL license-GPL compatible) developed by the Scilab Consortium—Digiteo. The author thanks the editor, two anonymous reviewers, and Simay Atayer for helpful comments.
References
Abramowitz, M., and Stegun, I. A. (1968). Handbook of mathematical functions, Dover, New York.
Aydin, C., and Demirel, H. (2005). “Computation of Baarda’s lower bound of the non-centrality parameter.” J. Geodes.JOGEF8, 78(7–8), 437–441.
Aydin, C., and Demirel, H. (2007). “Effect of estimated variance components for different gravity meters on analysis of gravity changes.” Festschrift zum 65. Geburtstag von Prof. Dr.-Ing. Carl-Erhard Gerstenecker, Technische Universitaet Darmstadt, December 2007, (1–11), Darmstadt, Germany.
Baarda, W. (1968). A testing procedure for use in geodetic networks, Netherlands Geodetic Commission, Publications on Geodesy, 2/5, Delft, The Netherlands.
Cai, J., Grafarend, E. W., and Schaffrin, B. (2005). “Statistical inference of the eigenspace components of a two-dimensional, symmetric rank-two random tensor.” J. Geodes.JOGEF8, 78(7–8), 425–436.
Chen, Y. Q., and Chrzanowski, A. (1994). “An approach to separability of deformation models.” Zeitschrift für Vermessungswesen, 119(2), 96–103.
Cooper, M. A. R. (1987). Control surveys in civil engineering, Collins, London.
Even-Tzur, G. (2002). “GPS vector configuration design for monitoring deformation networks.” J. Geodes.JOGEF8, 76(8), 455–461.
Even-Tzur, G. (2004). “Variance factor estimation for two-step analysis of deformation networks.” J. Surv. Eng.JSUED2, 130(3), 113–118.
Even-Tzur, G. (2010). “More on sensitivity of a geodetic monitoring network.” J. Appl. Geodes., 4(1), 55–59.
Even-Tzur, G. (2011). “Deformation analysis by means of extended free network adjustment contraints.” J. Surv. Eng.JSUED2, 137(2), 47–52.
Gaida, W., and Koch, K. R. (1985). “Solving the cumulative distribution function of the noncentral F-distribution for the noncentrality parameter.” Scientific Bulletins of the Stanislaw Staszic Univ. of Mining and MetallurgyZASGDE, Geodesy b. 90, 1024, 35–43.
Hahn, M., Heck, B., Jaeger, R., and Scheuring, R. (1989). “Ein Verfahren zur Abstimmung der Signifikanzniveaus für allgemeine -verteilte Teststatistiken−Teil I: Theorie.” Zeitschrift für Vermessungswesen, 114(5), 234–248.
Hekimoglu, S., Demirel, H., and Aydin, C. (2002). “Reliability of conventional deformation analysis methods for vertical networks.” Proc. of FIG XXII International Congress (CD-ROM), International Federation of Surveyors Publications, Copenhagen, Denmark.
Hekimoglu, S., Erdogan, B., and Butterworth, S. (2010). “Increasing the efficacy of the conventional deformation analysis methods: Alternative strategy.” J. Surv. Eng.JSUED2, 136(2), 53–62.
Hekimoglu, S., and Koch, K. R. (1999). “How can reliability of robust methods be measured?” Third Turkish-German Joint Geodetic Days, Altan, M. O., and Gründig, L., eds., Vol. 1, 179–196.
Koch, K. R. (1999). Parameter estimation and hypothesis testing in linear models, Springer-Verlag, Berlin.
Kuang, S. (1991). “Optimization and design of deformation monitoring schemes.” Ph.D. thesis Tech Rep. 157, Dept. of Surveying Engineering, Univ. of New Brunswick, Fredericton, NB, Canada.
Kutterer, H. (1998). “Quality aspects of a GPS reference network in Antarctica—A simulation study.” J. Geodes.JOGEF8, 72(2), 51–63.
Marjetic, A., Ambrozic, T., Turk, G., Sterle, O., and Stopar, B. (2010). “Statistical properties of strain and rotation tensors in geodetic network.” J. Surv. Eng.JSUED2, 136(3), 102–110.
Neitzel, F. (2001). “Maximum correlation adjustment in geometrical deformation analysis.” Proc., 1st Int. Symp. on Robust Statistics and Fuzzy Techniques in Geodesy and GIS, Carosio, A. and Kutterer, H., eds., ETH, Institute of Geodesy and Photogrammetry, Zurich, Switzerland, 123–132.
Niemeier, W. (1982). “Principal component analysis and geodetic networks—Some basic considerations.” Proc., Survey Control Networks, Borre, K., and Welsch, W. M., eds., International Federation of Surveyors, Copenhagen, Denmark, 275–291.
Niemeier, W. (1985). “Anlage von Überwachungsnetzen.” Geodaetische netze in landes-und ingenieurvermessung II., Pelzer, H., ed., Verlag Konrad Wittwer, Stuttgart, Germany, 527–558 (in German).
Proszynski, W. (2003). “Is the minimum-trace datum definition theoretically correct as applied in computing 2D and 3D displacements?” Proc. of the FIG 11th Int. Symp. on Deformation Measurements (CD-ROM), International Federation of Surveyors Publication 2, Copenhagen, Denmark.
SciLab [5.3.0] [Computer software]. The SciLab Consortium, Le Chesnay, France.
Teunissen, P. J. G. (2000). Testing theory an introduction, Delft Univ., Delft, The Netherlands.
Welsch, W., and Heunecke, O. (2001). “Models and terminology for the analysis of geodetic monitoring observations.” Official Report of the Ad Hoc Committee of FIG Working Group 6.1, Proc. of FIG 10th Int. Symp. on Deformation Measurements., International Federation of Surveyors Publication 25, Copenhagen, Denmark, 1–23.
Wu, J. C., and Chen, Y. Q. (2002). “Improvement of the separability of survey scheme for monitoring crustal deformations in the area of an active fault.” J. Geodes.JOGEF8, 76(2), 77–81.
Information & Authors
Information
Published In
Copyright
© 2012. American Society of Civil Engineers.
History
Received: May 5, 2011
Accepted: Aug 4, 2011
Published online: Aug 6, 2011
Published in print: May 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.