Vision-based techniques are frequently used to compute the dynamic deflections of bridges but they are rather computationally complicated and require demanding instrumentation. In this article, we show that it is possible to reconstruct the 2-D kinematics of flexible bridges using a simplified algorithm to analyze common video imagery. The only requirements are that the movement of the control points is clearly visible on the images and that next to each control point, there exist vertical and horizontal bridge elements defining the image scale. We applied this technique during controlled, forced excitations of a timber bridge that was stiff in the vertical but very flexible in the lateral axis because of cumulated damage. We used videos from low-cost cameras, in which the changes of the pixel coordinates of several control points during excitation events and their attenuation were clear. These videos were obtained during two annual structural health monitoring surveys using numerous sensors (Global Navigation Satellite Systems (GNSS), robotic total station (RTS), accelerometers), and hence the output of the video analysis was fully controlled. Because of various errors, the transformation of the video image coordinates into bridge coordinates yielded spurious deflections along the main axis of the bridge, which were used to control the uncertainty of our results. We found that the computed lateral deflections (i) were statistically significant, (ii) satisfied structural constraints, and (iii) were consistent with structural estimates derived from other sensors. Additionally, they provided accurate estimates of the natural frequency and the damping factor of the bridge. This approach can be applied in other cases of monitoring of flexible structures if the requirements for planar deformation, pixel resolution and scale definition are satisfied.
Summary Variable slip models of seismic faults represent ill-posed (or under-determined) problems with infinity of solutions; a single solution is typically obtained using constraints imposed by the L-curve theory, through an experimentally derived coefficient which optimizes the trade-off between fault roughness (smoothness, mean slip gradient) and mean misfit of observations to the fault model. However, in some cases, diverse Variable Slip Fault Models (VSFM) have been presented, even using the same data sets. In this article we investigate the problem of stability (sensitivity) of VSFM to input geodetic (GNSS/GPS, INSAR) ground slip measurements, based on statistics of synthetic data: statistically similar sets of synthetic ground displacements were the only degree of freedom in an analysis leading to comparable VSFM, regarded as images of slip amplitude and of rake. Differences of synthetic models from the reference fault model for different levels of noise, both for filtered and for PCA-filtered were examined, and results were summarized in images depicting the differences and the variability (standard deviation) of each fault slip patch, both for slip and rake. From this ‘truth’-based approach, it was found that an increase in observations noise is reflected in increase of variability (instability) of fault models, especially away from the fault center, higher for slip than in rake. Analysis with a different virtual observations system indicates that stations above the fault tend to show spurious stress concentration areas on the fault surface, in agreement with previous studies. Analysis with synthetic data appears as a promising strategy to validate a VSFM based on geodetic data.
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