Data-driven, Wavelet-based Identification and Reduced-order Modeling of Linear Systems with Closely Spaced Modes

This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical damping distribution. Traditional Fourier-based methods often fail to reliably identify closely spaced modes or accurately capture modal interactions and complexities. To address these limitations, we propose a methodology leveraging the enhanced time -frequency resolution capabilities of the continuous wavelet transform (CWT). By selecting appropriate harmonic regions within the wavelet spectra, we effectively isolate modes, and then invert them back in the temporal domain by applying the inverse CWT (ICWT). In this way we reconstruct the corresponding modal dynamics in the time domain. Using the Hilbert transform, instantaneous phases are extracted for each identified mode, enabling the introduction of a complexified modal matrix which robustly characterizes the system's modal properties, even under challenging perturbations such as noise and uncertainties due to modal interference and unmodeled effects. The identified modal parameters are utilized to reconstruct the frequency response functions (FRFs) of the system and to develop a reduced-order model (ROM) that captures accurately the system's dominant dynamical behavior valid in a specified frequency range.. Validation of the methodology is conducted both with a numerical non-classical damping and an experimental testbed representing a model of an airplane structure. Results demonstrate the effectiveness of the proposed approach in resolving intricate modal interactions and accurately reproducing the dynamic response of complex structural systems.

Physics-Informed Machine Learning for the Inverse Design of Wave Scattering Clusters

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward scattering problem may be readily analyzed, the inverse problem is very challenging as it is ill-posed, high-dimensional, and known to admit non-unique solutions. Therefore, the inverse design of multiple scattering fields and remote sensing of scattering elements remains a topic of great interest. Motivated by recent advances in physics-informed machine learning, we develop a deep neural network that is capable of predicting the locations of scatterers by evaluating the patterns of a target wavefield. We present a modeling and training formulation to optimize the multi-functional nature of our network in the context of inverse design, remote sensing, and wavefield engineering. Namely, we develop a multi-stage training routine with customized physics-based loss functions to optimize models to detect the locations of scatterers and predict cluster configurations that are physically consistent with the target wavefield. We demonstrate the efficacy of our model as a remote sensing and inverse design tool for three scattering problem types, and we subsequently applicability for designing clusters that direct waves along preferred paths or localize wave energy. Hence, we present an effective model for multiple scattering inverse design which may have diverse applications such as wavefield imaging or passive wave energy control.

Machine Learning Extreme Acoustic Non-reciprocity in a Linear Waveguide with Multiple Nonlinear Asymmetric Gates

This work is a study of acoustic non-reciprocity exhibited by a passive one-dimensional linear waveguide incorporating two local strongly nonlinear, asymmetric gates. Two local nonlinear gates break the symmetry and linearity of the waveguide, yielding strong global non-reciprocal acoustics, in the way that extremely different acoustical responses occur depending on the side of application of harmonic excitation. To the authors' best knowledge that the present two-gated waveguide is capable of extremely high acoustic non-reciprocity, at a much higher level to what is reported by active or passive devices in the current literature; moreover, this extreme performance combines with acceptable levels of transmissibility in the desired direction of wave propagation. Machine learning is utilized for predictive design of this gated waveguide in terms of the measures of transmissibility and non-reciprocity, with the aim of reducing the required computational time for high-dimensional parameter space analysis. The study sheds new light into the physics of these media and considers the advantages and limitations of using neural networks to analyze this type of physical problems. In the predicted desirable parameter space for intense non-reciprocity, the maximum transmissibility reaches as much as 40%, and the transmitted energy from upstream to downstream varies up to nine orders of magnitude, depending on the direction of wave transmission. The machine learning tools along with the numerical methods of this work can inform predictive designs of practical non-reciprocal waveguides and acoustic metamaterials that incorporate local nonlinear gates. The current paper shows that combinations of nonlinear gates can lead to extremely high non-reciprocity while maintaining desired levels of transmissibility.