A great mechanics-dynamics challenge for a realistic mechanical structure of complex geometry is the physics interpretation-and-exploitation of high fidelity-precision sensory signals of elastic wave propagation dynamical processes. It is at the current frontier of the state-of-the-art of scientific research in structural health monitoring, particularly in damage detection where guided waves are created. Multiple scales of geometric features of the complex structure are reflected as-difficult to isolate and characterize (the challenge) properties-in the time evolution of the initially elastic wave motion settling down, after unknown interactions, to the long term free vibration motion. These properties, except a few classical ones (isolated resonant frequencies), cannot be extracted-resolved over a spatial domain when available signals are treated separately and not as a block of information over the whole time of evolution. We need the spatial dimension to resolve the complicated sensory signals over their entire time horizon. Thus we are introducing the spatial dimension by the canonical eight-dimensional data cloud (Canonical 8D-Data Cloud) concept to build methods to explore the impact-induced free dynamics of complex mechanical structures. The complex structure in this study is a large scale aluminum alloy plate stiffened by a frame made of T-section beams. The Canonical 8D-Data Cloud is identified with the simultaneous acceleration measurements by eight piezoelectric sensors equally spaced and attached on the periphery of a circular material curve drawn on the uniform surface of the stiffened plate. This approach views the dynamics within the intrinsic complexity of the physical structure simply because simultaneous spatial information is obtained by an array of sensors.  In mathematical-physics terms,  this is a projection of the dynamics into a finite-dimensional space, where the Data Cloud is formed. We have the following results: The free dynamics induced by a nondestructive point impact are-over the initial transient free wave and wave-defect interaction phase-very sensitive to the magnitude of the impacting point force. In the absence of defects and interactions with the boundaries the wave motion would be approximated a linear dynamical process and the sensitivity would be null. But this is not the case. We have some sources related to the structural geometry complexity of the stiffened plate that causes uncertainty. This uncertainty is quantified at multiple spatial scales by the essential low-dimensional modal dynamics extracted by Advanced Proper Orthogonal Decomposition (POD) analysis of the Canonical 8D Data Cloud. The physics behind the uncertainty is the scattering, and possible other interactions, of elastic waves impinging on a visible site of a structural anomaly, left during the assembly of the stiffened plate. The other remarkable result is the fact that the long term free vibration dynamics-the attractor in terms of nonlinear dynamics language-is not sensitive to the initial conditions inferred by the impact. However, spatial characteristics on the shapes of the POD modes reflect the influence of the assembly defect on the shapes of the normal modes of vibration. These results are obtained thanks to the sensor array-graph geometry furnishing the Canonical 8D-Data Cloud and the computation-identification of its intrinsic data-geometry by the unparalleled Advanced Proper Orthogonal Decomposition transform. This is what we mean by machine learning. The Canonical 8D-Data Cloud is potentially the seed for a systematic machine learning approach to tackle the challenge of the complicated elastic wave propagation-free dynamics processes in complex mechanical structures.


Forming Canonical 8D Data Clouds to Explore the Transient Dynamics of Physical Stiffened Plates: A Machine Learning Approach for Complex Mechanical Structures

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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