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

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

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

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

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

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

November 13, 2018

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

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

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

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)

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 1 ------------------------------------------------------------------------------------ 0.06 0.00029042 20714 0.06 0.0001 22857 0.06 0.00029042 22857 0.06 0 25000 0.06 0.0001 25000 0.06 0.00029042 25000 Cluster 2 ------------------------------------------------------------------------------------ 0.02066 0.00084343 18571 Cluster 3 ------------------------------------------------------------------------------------ 0.02066 0.00029042 20714 0.02066 0.0001 22857 0.02066 0.00029042 22857 0.02066 0 25000 0.02066 0.0001 25000 0.02066 0.00029042 25000 Cluster 4 ------------------------------------------------------------------------------------ 0.06 0.00084343 16429 0.06 0.00084343 18571 Rotational stiffness of the interior bearings Rotational stiffness of the exterior bearings

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 …