Traditional angle-of-arrival (AoA) measurements rely on time-of-flight calculation or finding maximum signal strength during antenna rotation, and their precision is limited especially when strong noise is present. In this work, we introduce the use of eigen-spectrum of a micro-structured medium for such application and exploit the sensitive nature of this new candidate for the purpose of AoA estimation. A periodic array of phononic crystals (PC) is used as the sensor medium to collect signals of oblique stress waves. The 2D wavenumber band structure of the phononic crystal is pre-calculated in an eigenvalue analysis and is related to incident angles through Snell’s law. This eigenvalue problem allows one to express the reflected/transmitted scattering signal at the interface as a weighted sum of the eigenvectors. Therefore, the spectral topology of the band structure will affect the measured signal. Multiple branch points exist in the band structure. The first type of branch points are related to the critical angles (CA), where one wavenumber solution transitions from purely real to imaginary (or vice versa). The second type of branch points are the exceptional points (EP), which are spectral singularities in non-Hermitian systems. Both of the two types of branch points have angle-sensitive nature and are the spectral boundaries between propagating modes and evanescent modes. The branch points associated with the critical angles have zero wavenumber component normal to the boundary, which leads to total internal reflection for these modes. At the angles associated with the exceptional points, the angle-dependent wavenumber solutions will coalesce, and the eigen-basis (mode shapes) will become defective. Consequently, sudden jumps in the scattering energy can be observed when the wave sweeps through the EP-related angles. Abrupt signal discontinuities can be observed at both the CA-related and EP-related angles, which can be easily measured during sensor rotation. Consequently, the scattering signal will undergo topological phase transitions at these angles. Therefore, these topological branch points mark the wavenumber thresholds which separate the signals into different clusters. Such a property is particularly suitable for incorporation with machine learning methods. We demonstrate the sensing potential of the angle-dependent topology of phononic band structure using a signal classification approach. Principal component analysis is performed on the mode shapes to determine optimal sensor locations, so that the number of sensors needed is minimal and signal variance is maintained. Using a supervised machine learning method, any incident signal (after proper normalization) can be classified into a small range of incident angles, corresponding to a wavenumber range between two branch points in the band structure. With relatively small number of sensors needed, this method is shown to be robust under low SNR conditions. The proposed application of micro-structured media highlights the physical importance of band structure topology for sensing purposes, adds extra strength to the existing AoA estimation methods, and can be easily enhanced with the fast-growing data-driven techniques.


Scattering Signal Classification Based on Topological Phase Transitions in Phononic Crystals

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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