1. Physical-Model-Based Data Interpretation
Ian Smith and Romain Pasquier
EPFL – Swiss Federal Institute of Technology
Lausanne, Switzerland

3. Structural Performance Monitoring
Structural management tasks
Assessing reserve capacity
Retrofitting / Strengthening
Evaluating loading changes
Replacement decision making
(Damage detection)
Need good predictions.
Monitoring goal: Find reliable behavior models
November 13, 2018

4. Behavior-Model Predictions
Source: ANSYS
Unknown values
System identification
Prediction +
confidence interval ≠
November 13, 2018

5. System Identification (Traditional approaches)
Model-updating by residual minimization Predicted value - Measured value = 0
What are the conditions that make this a good objective function?
Complete models
No systematic errors
All dependencies between uncertainties are known
November 13, 2018

6. System Identification using thresholds
Comparison of observed and expected residuals Observed residual: predicted value – observed value Expected residual: uncertainties in model and measurements  Values of thresholds
Observed residual
(Candidate model)
Observed residual
(Rejected model)
Threshold
Residual
November 13, 2018

7. System Identification using thresholds
Comparison of measured value to several thousand models
November 13, 2018

8. November 13, 2018

9. IBS Model Solid elements Smeared concrete reinforcement Beam elements
Shell elements
Beam elements
Solid elements
Smeared concrete reinforcement
Fixed bearing devices modeling
Expansion bearing devices modeling
Steel girders and concrete deck modeled by shell elements for thin structures. Perfect composite action is provided by rigid links between each node of the girder top flange and the concrete deck.
Diaphragms, Wind braces and stiffeners modeled by beam elements and attached directly to the girder web.
Barriers and sidewalk were modeled by solid elements because of the irregular geometry.
Bearing devices were idealized by rigid links, attached to girder bottom flange. To take into account the friction of the pin between the plates of the bearings, a rotational spring is modeled. What is the value of its stiffness?
Rigid links
Rigid links
Pinned rigid link

10. Unknowns Corroded bearing devices Crack on the pier cap
Rotational stiffness
Crack on the pier cap
Vertical spring stiffness
The behavior of the structure has many unknowns. This unknowns can be identify as parameters values.
Exterior bearings are much more corroded than the interiors. Different rotational stiffness are applied to the exterior bearings.
The softness under the west girder could be modeled by a vertical spring and its stiffness becomes a parameter.
The Young’s modulus of concrete is also a parameter.
Material properties such as Young’s modulus of concrete

11. Preliminary study Load case of 3 full trucks at midspan
Measured value
Threshold (upper)
Threshold (lower)
Predicted and measured values [mm]
Load case of 3 full trucks at midspan
Load case of 6 full trucks at midspan
An initial model set is made by applying these varying parameters.
This figure shows the predictions of the models and the vertical displacement measured at the quarter of the span of the longest girder for the three static load case.
Up to down, the load increases. As we can see the model is stiffer for the heavier load case. The first load shows a suitable distribution of the predictions around the measurements.
Non linear behavior caused by the crack of pier cap or by the friction of the corroded bearing devices?
Influence of pier cap softness limited by the transverse stiffness of the bridge
Releasing of the bearing under the west girder for the load case of 6 full trucks

12. Model simplifications errors
±15% Model simplifications to obtain 7 Candidate models
Predicted and measured values [mm]
Threshold (lower)
Measured value
Threshold (upper)
-45% to +100% Model simplifications to obtain the entire set as Candidate models
Predicted and measured values [mm]
By releasing the rotation on west girder bearings and by roughly accounting for the barriers joints, we obtain a softer response on the west girder.
Threshold (lower)
Measured value
Threshold (upper)

13. Clusters of model parameter values
20% error : 15 candidate models
7 Candidate models
Young’s modulus of concrete [Mpa]
Cluster Representation
'Model Number' 'ALPHA_EXT' 'ALPHA_INT' 'EX_CONC'
Cluster
Cluster
Cluster
Cluster
Rotational stiffness of the interior bearings
Rotational stiffness of the exterior bearings

14. Conclusions Further study
With a 20% model simplifications error, 4 clusters of model parameter values are identified
The reduction of the initial model space is more than 99%
Non-linear behavior in the region of the west girder
Further study
Decrease the model simplifications by:
Modeling a non-linear rotational stiffness of the bearings
Accounting for the joints of the barriers
Further measurements:
Quantify non-linear behavior
Measure the deformations of the barriers to look for a soft connection with the concrete deck …