Abstract
Deformation and displacement monitoring of arch dams is usually conducted by measurement methods that gained widespread acceptance. Mostly pointwise measurements acquired within different epochs serve as the basis for deformation analysis. The uncertainty information of these observations is generally established. When referring to surface-based deformation monitoring, terrestrial laser scanning (TLS) is intensively hyped up. Nevertheless, current knowledge about stochastic modelling of TLS observations is scarce and very often reduced to a diagonal variance-covariance matrix (VCM). This neglects the exiting correlations within the point clouds. Aiming to fill the gap, this paper shows one possibility of obtaining a fully populated variance-covariance matrix using the elementary error model (EEM). Previous publications on this topic described the application of EEM for the Leica HDS 7000 laser scanner and showed results on simulated data for laboratory objects. Within this paper instrumental errors of the same scanner are modeled differently, according to recent work. A real scan of the arch dam Kops in Austria highlights influences on the variances, covariances and correlations of points within the point cloud for two instrument error models. Findings show that the model choice does not bring a notable change in the error of positions, but influences the correlation coefficients up to a level of Δρ = 0.2.
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References
ICOLD (2018) Dam Surveillance Guide, Bulletin 158, pp. 107–108.
Heunecke, O.; Kuhlmann, H.; Welsch, W.; Eichhorn, A.; Neuner, H. (2013) Handbuch Ingenieurgeodäsie-Auswertung geodätischer Überwachungsmessungenm, Chapter 15, in Möser, M.; Müller, G.; Schlemmer, H. (Ed.) 2nd edition, Wichmann, Berlin, Germany.
Wunderlich, T.; Niemeier, W.; Wujanz, D.; Holst, C.; Neitzel, F.; Kuhlmann, H. (2016) Areal Deformation Analysis from TLS Point Clouds–the Challenge, Allgemeine Vermessungsnachrichten, Vol. 123, no. 11–12.
Kuhlmann, H.; Holst, C. (2018) Flächenhafte Abtastung mit Laserscanning-Messtechnik, flächenhafte Modellierung und aktuelle Entwicklungen im Bereich des terrestrischen Laserscanning, pp. 168–207. In: Ingenieurgeodäsie-Handbuch der Geodäsie, ed. W. Schwarz, Springer-Verlag, Berlin, Germany.
Gordon, S.J.; Lichti, D.D. (2007) Modeling Terrestrial Laser Scanner Data for Precise Structural Deformation Measurement, Journal of Surveying Engineering Vol. 133, No.22.
Grimm-Pitzinger, A.; Rudig, S. (2005) Laserscannerdaten für flächenhafte Deformationsanalysen, Proceedings of 13th Internationale Geodätischen Woche, Obergurgl, Austria.
Alba, M.; L. Fregonese, F. Prandi, M. Scaioni, P. Valgoi (2006) Structural Monitoring Of A Large Dam By Terrestrial Laser Scanning, IAPRS & SIS, 36(5), pp. 6–12.
Heine, E.; Reiner, H.; Weinold, T. (2009) Deformationsmessungen mit terrestrischen Laserscannern am Beispiel der Kops Staumauer, Chesi G., Weinold T. (Ed.): 15. Internationale Geodätische Woche Obergurgl, Herbert Wichmann Verlag.
Eling, D. (2009) Terrestrisches Laserscanning für die Bauwerksüberwachung, In: Wissenschaftliche Arbeiten der Fachrichtung Geodäsie und Geoinformatik der Leibniz Universität Hannover, Nr. 282.
Neuner, H.; Holst, C.; Kuhlmann, H. (2016) Overview on Current Modelling Strategies of Point Clouds for Deformation Analysis, Allgemeine Vermessungsnachrichten, Vol. 123, no. 11–12.
Kauker, S. & Schwieger, V. (2017) A synthetic covariance matrix for monitoring by terrestrial laser scanning. Journal of Applied Geodesy, 11(2), pp. 77–87.
Kauker, S.; Harmening, C.; Neuner, H.; Schwieger, V. (2017) Modellierung und Auswirkung von Korrelationen bei der Schätzung von Deformationsparametern beim terrestrischen Laserscanning. In: Lienhart, W. [Ed.], Proceedings of 18. Internationalen Ingenieurvermessungskurs, Graz, 2017, Wichmann Verlag, Berlin, pp. 321–336.
Ogundare, J. O. (2016) Precision Surveying: The Principles and Geoamtics Practice, John Wiley & Sons, Inc., New Jersey, pp. 300–301.
Niemeier, W. (2008) Ausgleichungsrechnung, 2nd edition, Walter de Gruyter, Berlin, Germany.
Harmening, C.; Neuner, H. (2015) Continous modelling of point clouds by means of freefrom surfaces, Österreichische Zeitschrift für Vermessung und Geoinformation (VGI),103.
Harmening, C.; Kauker, S.; Neuner, H-B.; Schwieger, V. (2016) Terrestrial Laserscanning-Modeling of Correlations and Point Clouds for Deformation Analysis, FIG Working Week 2–6 May 2016 Christchurch, New Zealand.
Zhao, X.; Kermarrec, G.; Kargoll, B.; Alkhatib, H.; Neumann, I. (2019) Influence of the simplified stochastic model of TLS measurements on geometry-based deformation analysis. J. of Applied Geodesy, 13(3), pp. 199–214.
Jurek, T.; Kuhlmann, H. & Holst, C. (2017) Impact of spatial correlations on the surface estimation based on terrestrial laser scanning. J. of Applied Geodesy, 11(3), pp. 143–155.
Schwieger, V. (1999) Ein Elementarfehlermodell für GPS Überwachungsmessungen, Schriftenreihe der Fachrichtung Vermessungswesen der Universität Hannover, Vol. 231.
Kirkup, L.; Frenkel, B. (2006) An Introduction to Uncertainty in Measurement: Using the GUM. Cambridge University Press.
Metropolis, N.; Ulam, S. (1949) The Monte Carlo Method. Journal of the Americal Statistical Association, Vol. 44, No. 247, pp. 335–341.
Soudarissanane, S. S. (2016) The Geometry of Terrestrial Laser Scanning-identification of errors, modeling and mitigation of scanning geometry, retrieved from: repository.tudelft.nl, last accessed on 20.01.2020.
Zámečníková, M.; Neuner, H.; Pegritz, S.; Sonnleitner, R. (2015) Investigation on the influence of the incidence angle on the reflectorless distance measurement of a terrestrial laser scanner. Österr. Z. Vermess. Geoinform 2015, 103, 208–218
Leica Geosystem AG (2011) Datasheet HDS 7000 Laser Scanner. Retrieved from http://w3.leica-geosystems.com/downloads123/hds/hds/HDS7000/brochures-datasheet/HDS7000_DAT_en.pdf, last accessed on 20.01.2020.
Neitzel, F. (2006) Gemeinsame Bestimmung von Ziel-, Kippachsfehler und Exzentrizität der Zielachse am Beispiel des Zoller + FröhlichImager 5003, Luhmann/Müller(Ed.)–Photogrammetrie-Laserscanning-Optische 3D-Messtechnik, Proceedings oft he Oldenburger 3D-Tage 2006, Wichman, Berlin, Germany.
Strahlberg, C (1997) Eine vektorielle Darstellung des Einflusses von Ziel-und Kippachsfehler auf die Winkelmessung, Zeitschrift für Vermessungswesen, Vol. 5/1997, pp. 225–235.
Neitzel, F. (2006b) Untersuchung des Achssystems und des Taumelfehlers terrestrischer Laserscanner mit tachymetrischem Messprinzip. In: Proceedings of the 72. DVW-Seminar Terrestrial Laserscanning 2006 in Fulda, Volume 51, Wißner, Augsburg, pp. 15–34.
Muralikrishnan, B.; Ferrucci, M.; Sawyer, D.; Gerner, G.; Lee, V.; Blackburn, C.; Phillips, S.; Petrov, P.; Yakovlev, Y.; Astrelin, A.; Milligan, S.; Palmateer, J. (2015) Volumetric Performance Evaluation of a Laser Scanner Based on Geometric Error Model, Precise Engineering, Vol. 40, p. 139–150.
Medić, T.; Holst, C.; Kuhlmann, H. (2017) Towards System Calibration of Panoramic Laser Scanners from a Single Station, Sensors, Vol. 17, No. 5.
Medić, T.; Holst, C.; Kuhlmann, H. (2019) Sensitivity Analysis and Minimal Measurement Geometry for Target-Based Calibration of High-End Panoramic Terrestrial Laser Scanners Remote Sensing, Vol. 11, no. 1519.
Holst, C.; Medić, T.; Kuhlmann, H. (2018). Dealing with systematic laser scanner errors due to misalignment at area-based deformation analyses. J. of Applied Geodesy, 12(2), pp. 169–185.
Holst, C.; Medić, T.; Blome, M.; Kuhlmann, H. (2019) TLS-Kalibrierung: in-situ und/oder a priori?, 184th DVW-Seminar, Terrestrisches Laserscanning 2019, Fulda, Germany.
Chow, J. C. K.; Lichti, D. D.; Glennie, C.; Hartzell, P. (2013) Improvements to and Comparison of Static Terrestial LiDAR Self-Calibration Methods Sensors 2013, 13.
Ganser O. (1975) Staumauer Kops, Anlage der Drainagebohrungen, Auswirkung Dieser Massnahmen auf die Höhe des Bergwasserspiegels und die Grösse des Sohlenwasserdruckes. In: 12. Talsperrenkongreß in Mexiko 1976. Die Talsperren Österreichs, vol 22. Springer, Vienna, Austria.
Illwerke vkw AG (2020) Website: https://www.illwerkevkw.at/kopssee.htm, last accseed on 22.01.2020.
36. Suchocki, C. (2020) Comparison of Time-of-Flight and Phase-Shift TLS Intensity Data for the Diagnostics Measurements of Buildings. In: Materials 2020, 13, pp. 353.
Girardeau-Montaut, D. (2019) Point processing with Cloud Compare, Presentation of Point Cloud Processing Workshop 2019 Stuttgart, retrieved from: pcp2019.ifp.uni-stuttgart.de/presentations/04-CloudCompare_PCP_2019_public.pdf, last accessed 24.01.2020.
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The authors cordially thank DFG (Deutsche Forschungsgemeinschaft) for funding the investigations of the IMKAD II Project under the sign SCHW 838/7-3.
We also want to express our gratitude to Illwerke vkv AG, especially to Dr.-Ing. Ralf Laufer for allowing and supporting the measurement campaign in 2019.
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Kerekes, G., Schwieger, V. (2021). Determining Variance-Covariance Matrices for Terrestrial Laser Scans: A Case Study of the Arch Dam Kops. In: Kopáčik, A., Kyrinovič, P., Erdélyi, J., Paar, R., Marendić, A. (eds) Contributions to International Conferences on Engineering Surveying. Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-51953-7_5
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