# On Data Selection and Regularization for Underdetermined Vibro-Acoustic Source Identification

## TL;DR

This paper explores how to improve vibro-acoustic source identification using fewer measurement points and better regularization techniques.

## Contribution

The study introduces a best practice combining data selection and regularization methods for underdetermined acoustical holography.

## Key findings

- Using the effective independence method for data selection reduces reconstruction errors.
- Regularization via compressed sensing improves the accuracy of underdetermined holography.
- Experimental results confirm the effectiveness of the proposed data selection and regularization integration.

## Abstract

The number of hologram points in near-field acoustical holography (NAH) for a vibro-acoustic system plays a vital role in conditioning the transfer function between the source and measuring points. The requirement for many overdetermined hologram points for extended sources to obtain high accuracy poses a problem for the practical applications of NAH. Furthermore, overdetermination does not generally ensure enhanced accuracy, stability, and convergence, owing to the problem of rank deficiency. To achieve satisfactory reconstruction accuracy with underdetermined hologram data, the best practice for choosing hologram points and regularization methods is determined by comparing cross-linked sets of data-sorting and regularization methods. Three typical data selection and treatment methods are compared: iterative discarding of the most dependent data, monitoring singular value changes during the data reduction process, and zero padding in the patch holography technique. To test the regularization method for inverse conditioning, which is used together with the data selection method, the Tikhonov method, Bayesian regularization, and the data compression method are compared. The inverse equivalent source method is chosen as the holography method, and a numerical test is conducted with a point-excited thin plate. The simulation results show that selecting hologram points using the effective independence method, combined with regularization via compressed sensing, significantly reduces the reconstruction error and enhances the modal assurance criterion value. The experimental results also support the proposed best practice for inverting underdetermined hologram data by integrating the NAH data selection and regularization techniques.