Forming an Advanced Proper Orthogonal Decomposition-Based Data Science Framework for Advanced Diagnostics of Practical Multi-Body Systems: SHM Challenges in Complex Structures-and-Flexible Machinery

Abstract

In an attempt to tackle science-challenging SHM issues in complex multi-body structural and machinery systems, we are developing a methodology that exploits the principles of continuum mechanics (theoretical-computational-experimental) along with optimum reduction analysis to lay data science aspects for data-driven mechanics. The focus is on damage diagnostics in the presence of structural complexity: domain geometry and nonlinearity distribution. Simultaneous ensembles of accelerations form basic datasets to be augmented properly. We introduce two fundamental augmentations of a dataset. The first, referred to as the Simultaneous Three-Point Observation (S3PO), is the augmentation of a dataset with another two similar datasets. The second, referred to as the Spatial Differential Form (SDF), is the augmentation of a dataset with its spatial differential forms of order-1,2. The APOD resolution interpretation of the S3PO datasets of composite beam structures reveals coherence among the individual datasets forming the augmentation: they intersect along modal physics-carrying POD modes. The diametrically opposite is revealed for the rotor structure, modified with holes: the datasets do not intersect at all. This is clearly due to the fact that the dynamics are infested with a great degree of uncertainty due to the phenomenon of chaotic wave scattering. The APOD resolution of the SDF dataset of composite beams extracts the actual bending curvature distribution, indicating directly the structural health state footprint imposed by the thermodynamical manufacturing process. The introduced data augmentation operations and the physics extraction by the APOD reduction analysis constitute the basis for a sound data science in engineering mechanics-physics with impact on SHM.