Session: 07-17-01: Machine Learning and Artificial Intelligence in Dynamics, Vibrations and Control

Paper Number: 146107

146107 - Laying Sound Mechanics Foundations for Data-Driven Nonlinear Dynamics Enhanced With Machine Learning Aspects: Unbiased Extraction of the Laws of Motion of Flexible Solids as Geometric Features of Sensor Datasets 

Com     Computational mechanics and metrology science and technology have paved the road to advance classical mechanics to the level of datasets.  This calls for research to establish the foundations of a framework of data science for computational and experimental mechanics (sources of datasets landscapes). This need is intensively fueled by the computational paradigms of machine learning and artificial intelligence. In view of the need for foundations for data science, we pose the following fundamental question: what types of sensor datasets are appropriate to create for unbiased extraction of features expressing the physics laws of motion of the generic flexible solid continuum. Among other factors, this physics information is essential for informing deep learning neural networks in the process of training. The so-called physics-informed neural networks are informed directly by the analytic statements of the motions of equation. Here given a generic physical complex (multi-physics multibody structural-mechanical) system, we would like to learn its behavior by informing an algorithm with those features in datasets that represent aspects of the laws of motion.  

Guided by the fact that distributed structural systems response in characteristic modes of free vibrations-as a result of the coherence imposed by the laws of motion, we have conducted a systematic structural dynamics experimental exploration, where ensembles of acceleration response signals were collected at several fixed locations while a flexible structure was excited by an ensemble of random force pulses applied over a grid of spatial points. We find that simultaneous acceleration response ensembles associated with at least three distant material points of the structure intersect, as data-point clouds, over a set of dominant proper orthogonal decomposition modes. This intersection of datasets identifies invariants of motion of a physical system. We claim that this mode intersection is a pure data level-expressed manifestation of the laws of motion in the force-acceleration space. Moreover, we find that the acceleration ensemble of signals at a point due to another ensemble of excitation force at a different point is dominated by a single proper orthogonal decomposition mode: its shape is linearly distributed over a restricted domain of the force magnitude. This fact forms the basis of the Linearity-Nonlinearity Diagnostic Test we have introduced to sample and identify the spatial dependence of geometric nonlinearity in a flexible continuum.

The above experiment is pivotal for establishing a sound foundation of data science to support systematic data-driven mechanics with machine learning aspects: Just as the observation and measurements of the free fall of objects in the gravitation field lead to the discovery of the linear law relating the moving force and the induced acceleration, the restriction of random forces in a small width zone leads to the extraction from ensembles of acceleration-collected simultaneously at different points-of the laws of motion in the form of shapes of POD modes. The impact of this discovery resides into the fact that the complexity of the geometry of the structure is not an issue any mode. Sensor provided information for impulsie-induced motions contains features of the geometric complexcity of the systems thanks to the physics process of wave propagation and diffusion, and its interaction with anomalies in the domain of the system.

The above results were obtained by processing large volume ensembles of sensor signals in flexible structures of simple and quite complicated geometries by advanced proper orthogonal decomposition-projection tools. The POD processing of datasets is completely unbiased. POD reduction is axiomatic and stems from the geometry topology formed by the data-point clouds as high-dimensional geometric objects of the seed 2D matrix dataset. The proper orthogonal decomposition as a data processing computational procedure is not limited to datasets stemming from a linear process. The POD modes can be correlated to natural modes of vibration computed by the Experimental Modal Analysis if the dataset is stemming from the structure response in the very weak nonlinear regime.  

In fact, our explorative experimental exploration of complex multibody structural-mechanical systems indicates that generation of impulse force (random single and multiple pulses)-induced datasets (tensor-structured) of tri-axial acclelerations over local and global spanning regions and its data reduction by advanced POD tools qualifies as the most elementary ground zero unsupervised machine learning procedure. This leads to the most comprehensive and optimal newral networks for advanced computations-predictions-diagnostics.

Presenting Author: Ioannis Georgiou National Technical University of Athens, NTUA

Presenting Author Biography: Dr. Ioannis T. Georgiou is a Professor with the School of Naval Architecture & Marine Engineering,
National Technical University of Athens, and an Adjunct Professor with the School of Mechanical Engineering,
Purdue University, West Lafayette, Indiana.
His current research focus on nonlinear multi-physics dynamics-chaos-bifurcations & Identification
and Diagnostics-Prognostics of Complex Structural & Material Systems.

Authors:

Ioannis Georgiou National Technical University of Athens, NTUA