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Deformations Detection by a Bayesian Approach: Prior Information Representation and Testing Criteria Definition

  • A. Albertella
  • N. Cazzaniga
  • F. Sansò
  • F. Sacerdote
  • M. Crespi
  • L. Luzietti
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 131)

Abstract

It is well known that the classical testing procedures are not able to detect any significant deformation when the estimated displacements stemming from repeated surveys are small with respect to their precisions. This is true even if the displacements show some internal consistency (e.g. all the displacements have a common direction) or agree with prior hypotheses based on ancillary data (e.g. geological and geotechnical investigations about a landslide) or information derived by previous surveys.

In this paper we discuss an alternative (Bayesian) approach able to overcome this problem often rising in deformation monitoring and to establish a more powerful testing procedure by considering prior information about the displacements.

In details, we investigate the main problems related to the stochastic representation of the prior information by a suited covariance matrix and to the definition of a criterion for assessing the displacements significance. Finally the approach is checked on synthetic examples.

Keywords.

Deformation monitoring Bayes’ theorem displacements significance 

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References

  1. Betti B., Crespi M., Sansò F. (1998). Deformation Detection According to a Bayesian Approach. IV Hotine-Marussi Symposium on Mathematical Geodesy, Trento, September 14–17, pp. 83–88.Google Scholar
  2. Box G. E. P., Tiao G. C. (1992). Bayesian Inference in Statistical Analysis. Wiley Classics Library ed., New York Chichester Brisbane Toronto Singapore.Google Scholar
  3. Koch K. R. (1990). Bayesian Inference with Geodetic Applications. Number 31 in Lecture Notes in Earth Sciences. Springer, Berlin Heidelberg New York.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • A. Albertella
    • 1
  • N. Cazzaniga
    • 1
  • F. Sansò
    • 1
  • F. Sacerdote
    • 2
  • M. Crespi
    • 3
  • L. Luzietti
    • 3
  1. 1.DIIAR, Dipartimento di Ingegneria Idraulica Ambientale, Sezione RilevamentoPolitecnico di MilanoMilanItaly
  2. 2.DIC, Dipartimento di Ingegneria CivileUniversità di FirenzeFlorenceItaly
  3. 3.DITS, Dipartimento di Idraulica Trasporti e StradeArea di Geodesia e Geomatica Università di Roma “La Sapienza”RomeItaly

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