Spatiotemporal compressive sensing of full-field Lagrangian continuous displacement response from optical flow of edge: Identification of full-field dynamic modes

Abstract The present state of condition monitoring of civil infrastructure involves the application of a large number of contact-based vibration sensors at different locations of the structures. The traditional vibration sensors, such as accelerometers or strain gauges, require considerable effort in laying out the connection wires. Also, their cost of maintenance is quite high considering the harsh environment they are exposed to. In recent times, there is a growing urge in developing contactless, vision-based vibration sensors that potentially alleviate the previously mentioned drawbacks. In a previous paper, the authors proposed a framework of acquiring full-field spatiotemporal Lagrangian displacement response of a continuous vibrating edge from its video by computing the optical-flow of the edge using d’Alembertian of Gaussian filter. Such spatially dense measurements are required to compute full-field mode shapes. But, from the perspective of condition monitoring of large infrastructures, such spatially dense measurements record a large amount of high dimensional data over the whole period of acquisition time. It poses a considerable challenge in the form of an increase in storage and data transmission capacity. In this paper, such drawbacks are addressed by suggesting a computational strategy of spatiotemporal compressive sensing of the full-field Lagrangian displacement response from the video of the vibrating structure with unknown geometric properties and boundary conditions. The non-uniformly sampled data, simultaneously both in the spatial and temporal dimension, still retains the low order dynamics of the system from which the full-field and high dimensional displacement responses are reconstructed. Subsequently, the modal parameters and full-field mode shapes are estimated from the reconstructed full-field Lagrangian displacement response. The experimental validation of the proposed method satisfactorily reconstructs the dense full-field displacement response along with estimating full-field dynamic modes from the low-dimensional spatiotemporal sub-sampled measurement data for a three-story steel frame and an aluminum cantilever beam for different compression ratios. The applicability of the proposed method is demonstrated on a simulated wind turbine tower model with unknown geometry or boundary conditions. The full-field displacement response and mode shapes of the non-prismatic wind turbine tower with a concentrated mass at the top are successfully reconstructed from the noise-induced sub-sampled data.