MS20.1: Physics-enhanced machine learning and data-driven nonlinear dynamics

Deep learning algorithms can be employed to monitor and assess the actual conditions of civil and industrial structures before damage can cause detrimental effects on their safety or serviceability. Within this framework, the suitability of deep learning algorithms has been investigated for linear structures, while there is a lack of studies targeted at demonstrating their effectiveness for damage detection in nonlinear dynamical systems. In this perspective, the present study illustrates preliminary results concerning damage detection in a single-degree-of-freedom Duffing oscillator using a 1-dimensional convolutional autoencoder-based neural network architecture. The neural network training is carried out in an unsupervised manner to avoid the need for labeled databases. Numerical simulations demonstrate that the proposed computational strategy allows for the reliable identification of low damage levels in dynamical systems experiencing nonlinear behavior.

In this study, we investigate a Laval rotor dynamics scenario where the damping properties remain elusive. To address this challenge, we employ an artificial neural network to model the damping force, seamlessly integrating it into the governing equations of motion. Through direct time integration techniques, we analyse the system’s behaviour and delve into the frequency response function to elucidate the impact of incorporating data-driven models into simulations. This approach sheds light on the efficacy of leveraging neural networks to capture unknown physical phenomena, enhancing the accuracy and predictive capabilities of dynamics analyses. The case study showcases the potentials, but also pitfalls, of the direct integration of learning models into knowledge-based system descriptions.

Multiple-degree-of-freedom (MDOF) linear dynamical systems can be exactly decomposed into single-degree-of-freedom (SDOF) oscillators via proper orthogonal decomposition (POD); however, techniques based on linear mappings do not generalise to nonlinear systems. Machine learning approaches have been proposed as a means to decompose/decouple nonlinear systems via nonlinear transformations. Normalising flows (NFs) map complex distributions onto a simplified, user-defined latent space. The current work proposes an augmented linear state-space model as the target space, and uses continuous NFs to solve a neural ordinary differential equation (ODE) that defines the nonlinear map from the data distribution to the latent, decomposed space. This approach is demonstrated using a simulated two-degree-of-freedom (2DOF), lumped-mass system with a cubic spring.

This study deals with the design of distributed internal oscillators in a metastructure to achieve its beneficial low-frequency vibration performance. First, an analytical approach is taken in which all of them are equal mutually and tuned to the first resonance of the metastructure with blocked internal oscillators. As tuning to the second resonance frequency of the metastructure of this shape could not be achieved practically, a physics-based machine learning approach is developed to design absorbers of different size and distribution along the metastructure, targeting the widest possible low-frequency vibration attenuation regions around the first and second resonance simultaneously. Such metastructure is then fabricated and its beneficial performance is verified experimentally.

Over the past fifty years, Moore's Law has guided nanotechnology towards the miniaturization of components across all three dimensions: x, y, and z. As we near its limits in 2025, our laboratory is investigating a novel form of nanotechnology with components that extend over large distances in the x and y dimensions while maintaining nanoscale thickness in the z dimension. These extreme-aspect-ratio nanostructures possess a unique blend of macro- and nano-features, exhibiting properties absent in their smaller-scale equivalents. High-aspect-ratio mechanical resonators are crucial for precision sensing, ranging from macroscopic gravitational wave detectors to nanoscale acoustics. Nevertheless, fabrication difficulties and significant computational expenses have restricted the length-to-thickness ratio of these devices, leaving a substantial area in nano-engineering unexplored. We introduce, for the first time, nanomechanical resonators that extend several centimeters in length while maintaining nanometer-scale thickness. We investigate this novel design space using an optimization approach that strategically utilizes rapid millimeter-scale simulations to guide the more computationally demanding centimeter-scale design optimization. The combination of nanofabrication, machine learning-guided design optimization, and precision engineering paves the way for a solid-state approach to room temperature quality factors of 10 billion at kilohertz mechanical frequencies—comparable to the extreme performance of top cryogenic resonators and levitated nanospheres, even under much less stringent temperature and vacuum conditions. Advancing this nanotechnology will necessitate a convergence of new physics insights, innovative structural engineering, and advanced material science.