Accuracy and robustness of sparse reconstruction techniques for azimuthal mode analysis of in-duct sound fields

Abstract

Sparse reconstruction techniques enable the detection of the dominant azimuthal mode content in ducts with a limited number of sensors. This is of great importance in various fields of application, such as fan noise analyses. The analysis of weaker azimuthal modes has hardly been considered or looked at, although they can contribute considerably to the total sound field and can provide important information on sound propagation effects. To address this shortcoming, the Enhanced Orthogonal Matching Pursuit (EOMP) algorithm presented in this paper was developed. It is based on the established Compressed Sensing Orthogonal Matching Pursuit (OMP) algorithm, which is used to reliably detect the dominant azimuthal modes. In an extension step, the weaker modes are determined by applying a Least Squares Fit or a Discrete Fourier Transform to the deconvolved measurement vector. The capabilities and limitations of the different versions of the EOMP algorithm are tested on experimental data of multiple rotor-coherent sound field components generated by a fan stage. Furthermore, the EOMP algorithm is explored in detail for typical practical application scenarios using Monte-Carlo simulations. In both cases, the performance is compared with an alternative method, the Basis Pursuit Denoising (BPDN) algorithm. Within the Monte-Carlo framework, extensive parameter variations for the signal-to-noise ratio, mode sparsity (number of dominant modes) and mode field sparsity-level (magnitude ratio of dominant modes to weak modes), are performed over a wide frequency range. These Monte-Carlo simulations allow the comprehensive evaluation of the accuracy of the algorithms under investigation. Sensor ring designs and the considered analysis mode ranges can have a large impact on the overall reconstruction accuracy. Therefore, both aspects are also addressed in the presented study to provide helpful insights for future applications of the azimuthal mode analysis. Additionally, the EOMP algorithm is further improved by a regularised Least Squares Fit for the enhanced step and is shown to provide the best accuracy and robustness among the investigated algorithms.