A risk evaluation method for deformation monitoring systems

S. Zaminpardaz, P.J.G. Teunissen*, C.C.J.M. Tiberius

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)
135 Downloads (Pure)


In this contribution, we propose a method for statistically evaluating the risk in a deformation monitoring system. When the structure under monitoring moves beyond tolerance, the monitor system should issue an alert. Only a very small probability is acceptable of the system telling us that no change beyond a critical threshold has taken place, while in reality it has. This probability is referred to as integrity risk. We provide a formulation of integrity risk where the interaction between estimation and testing is taken into account, implying the use of conditional probabilities. In doing so, we assumed different scenarios with the alerts being dependent on both the identified hypothesis and the threat that the estimated size of deformations entails. It is hereby highlighted that a correct risk evaluation requires estimation and testing being considered together, as they are typically intimately linked. In practice, one may, however, find it simpler computation-wise to neglect the estimation–testing link. For this case, we provide an approximation of the integrity risk. This approximation may provide a too optimistic or pessimistic description of the integrity risk depending on the testing procedure and tolerances of the structure at hand. Monitoring systems, besides issuing timely alerts, are also required to provide threat estimates together with their corresponding probabilistic properties. As the testing outcome determines how the threat gets estimated, the threat estimator will then inherit the statistical properties of both estimation and testing. We derive the threat estimator b¯ j and its probability density function, taking the contributions from combined estimation and testing into account. It is highlighted that although the threat estimator under the identified hypothesis Hj, i.e., b^ j, is normally distributed, the estimator b¯ j is not. It is explained that working with b^ j instead of b¯ j, thus ignoring the estimation–testing link, may provide a too optimistic description of the threat estimator’s quality. The presented method is illustrated by means of two simple deformation examples.

Original languageEnglish
Article number28
Number of pages15
JournalJournal of Geodesy
Issue number3
Publication statusPublished - 2020


  • Conditional distribution
  • Deformation
  • Integrity risk
  • Monitoring system
  • Statistical testing
  • Threat estimation


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