Sparse Green’s Functions Estimation Using Orthogonal Matching Pursuit: Application to Aeroacoustic Beamforming

Abstract

The paper presents a new methodology for the numerical estimation of the Green's functions in complex external aeroacoustic configurations. Computational aeroacoustics is used to propagate multi-frequency signals from focus points to microphones. The method takes advantage of the sparsity of the Green's functions in the time-domain to minimize the simulation time. It leads to a complex sparse linear regression problem. To solve it, the Orthogonal MatchingPursuit algorithm is adapted. The method is first applied on the case of the diffraction by a rigid sphere. Results are studied both in terms of Green's function estimation and aeroacoustic beamforming. They show that the Green's functions are obtained with a good accuracy and enable to localize acoustic sources placed behind the diffracting object. The methodology is then applied on a NACA0012 2D wing in a potential flow for which the Green's function is not known analytically. The use of the reverse-flow reciprocity principle enables to reduce the complexity of the estimation problem when there are more scan points than microphones. It is shown that it is possible to take advantage of the presence of diffracting objects to improve the capability of detection of a sensor array.

Damage Identification of Semi-Rigid Joints in Frame Structures Based on Additional Virtual Mass Method

“…Substitute Equation ( 8) into the objective function (7) and the l 0 norm of the damage factor increment ∆µ = (µµ 0 ) is used as the constraint to construct the objective function for the sparse damage identification, as shown in Equation ( 9). An Orthogonal Matching Pursuit (OMP) algorithm [35] can be used to optimize the objective function to obtain sparse recognition results. However, the OMP algorithm relies on the iterative screening results of the previous step, and the final optimization result is usually a local optimal solution.…”

An accurate triangular spectral element method-based numerical simulation for acoustic problems in complex geometries

“…Application of high-order finite difference schemes can also be found in acoustic source localization with time-reversal and beamforming method. 7,8 However, one limitation of FDM is that schemes with different orders are constructed independently with each other. Therefore, increasing the order of FDM in calculation requires additional efforts to construct corresponding high-order scheme, especially corresponding schemes for points near the boundary, 4 which may lead to inefficiency when pursuing higher accuracy in CAA problems.…”