Spatio-temporal decomposition of 2D travelling waves from video measurements

Abstract

Video-based techniques have become of increasing interest for identifying the dynamic properties of infrastructures with arbitrary complexity. Most applications rely on frame-by-frame tracking of fixed targets to derive time-varying physical parameters. Although these techniques can estimate different kinds of motion, the need for speckle patterns or high-contrast markers imposes serious limitations for real-world monitoring scenarios. Moreover, the frame-based paradigm may hide important temporal patterns which can only be observed when considering full-field temporal processing. Recent works have demonstrated that the spatial-only context can derive numerous drawbacks if the main goals are to maintain security and reliability of a given structure. Considering the aforementioned issues, this work proposes a novel formulation for video-based dynamics monitoring by posing the problem in the context of a blind source separation paradigm using nonnegative matrix factorization. This approach can be implemented in an efficient and autonomous manner, without the need of structural surface preparation nor supervision or camera calibration. We demonstrate that considering each pixel as an individual sensor measuring local changes allows to accurately analyze their time-varying content and to reconstruct each specific video motion in an output-only manner. Our main interest is to monitor amorphous structures, such as melted pools commonly seen in industrial processes. The application on simulated and experimental data shows the effectiveness to identify, separate and reconstruct independent motions from video measurements only without human intervention and prior knowledge.