Threshold Effect in the Fiedler Eigenvalue Used as Collapse Signal for a Masonry Building During a Seismic Test

A masonry building was tested on the shaking table till the collapse, and during the experiment a digital video was taken. The video was motion magnified, then each frame was translated into a graph, in order to be analyzed by means of the graph centrality parameters. Some parameters underwent a significant variations in their value along the video frames, before the beginning of the collapse. Therefore, they showed the potential to predict the collapse of the structure, though of just a couple of seconds in advance. In particular, the Fiedler eigenvalue was the most promising. The time-series of the Fiedler eigenvalue could be a signal amenable to a direct analysis for an early warning system, provided we are able to extract a sufficiently clear collapse pattern. Of course, this is not a trivial task. Here we show how, exploiting the particular conditions of the seismic experiment and the peculiar characteristic of the Fiedler eigenvalue, it is possible to accomplish the task, even quite simply. The recognition problem of the collapse pattern is solved using the graph topological invariants capability to capture the dynamic of the building displacement time series, both in the time and frequency domain. Moreover, the initial multi-sensors and multidimensional “virtual sensors” issue is reduced to the analysis of a mono-dimensional parameter. This approach, firstly proposed for the manufacturing monitoring processes, represents a novelty for the building structural health.