Uncertainty Quantification of Bandgaps in Acoustic Metamaterials with Stochastic Geometric Defects and Material Properties

TL;DR

This paper applies spectral projection and polynomial chaos expansion to efficiently quantify uncertainty in acoustic metamaterials' bandgaps caused by stochastic defects and material variations, significantly reducing sampling requirements.

Contribution

It introduces a novel, interpretable encoding of geometric defects and demonstrates substantial sampling reduction while accurately capturing output distributions.

Findings

Achieved up to 100-fold sampling reduction in 1D scenarios.

Maintained accurate probability distributions with combined sampling techniques.

Validated effectiveness in both low and high-dimensional input spaces.

Abstract

This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given stochastic material properties and geometric defects. A novel method of encoding geometric defects in an interpretable, resolution independent is showcased in the formation of input space probability distributions. Orders of magnitude sampling reductions down to $\sim10^0$ and $\sim10^1$ are achieved in the 1D and 7D input space scenarios respectively while maintaining accurate output space probability distributions through combining Monte Carlo, quadrature rule, and sparse grid sampling with surrogate model fitting.