Journal of Civil Structural Health Monitoring

, Volume 9, Issue 1, pp 21–36 | Cite as

The use of inverse methods for response estimation of long-span suspension bridges with uncertain wind loading conditions

Practical implementation and results for the Hardanger Bridge
  • Øyvind Wiig PetersenEmail author
  • Ole Øiseth
  • Eliz-Mari Lourens
Original Paper


Structural health monitoring seeks to assess the condition or behavior of the structure from measurement data, which for long-span bridges typically are wind velocities and/or structural vibrations. However, in the assessment of the wind-induced response effects, models for the loads must be adopted, which introduces uncertainties. An alternative is to apply model-based inverse methods that consider the actual input forces unknown, and estimate these forces jointly together with the system states using limited vibration data. This article presents a case study of implementing Kalman-type inverse methods to a long-span suspension bridge in complex terrain, with the objective of estimating the full-field response. Previous studies have shown the local wind field is complicated, leading to uncertain load effects. We discuss the key challenges faced in the use of the methodology for the long-span bridges and present the results for a 6 h storm event. The analysis show that the dynamic response contribution from the 14 lowermost bridge modes (up to 3 rad/s or 0.5 Hz) can be reconstructed with decent accuracy. The estimated response magnitude differs from the predicted response from design specifications, pointing to load-related uncertainties that can be reduced to give greater confidence in the assessment of wind-induced fatigue, wind-resistant performance and other response effects.


Suspension bridge Structural monitoring Inverse methods Response estimation 



This work was financially supported by the Norwegian Public Roads Administration, the E39 Coastal Highway Route project. We are grateful for the constructive comments of the anonymous reviewers that improved the paper significantly.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Øyvind Wiig Petersen
    • 1
    Email author
  • Ole Øiseth
    • 1
  • Eliz-Mari Lourens
    • 2
  1. 1.NTNU, Norwegian University of Science and TechnologyTrondheimNorway
  2. 2.Delft University of TechnologyDelftThe Netherlands

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