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

Area of Science:

• Acoustics and Vibrations
• Signal Processing
• Computational Mechanics

Background:

• Near-field acoustical holography (NAH) is crucial for vibro-acoustic system analysis.
• High accuracy in NAH often requires overdetermined hologram data, limiting practical applications.
• Overdetermined data can lead to rank deficiency issues, compromising accuracy and stability.

Purpose of the Study:

• To determine optimal hologram point selection and regularization methods for accurate NAH with underdetermined data.
• To compare different data-sorting and regularization techniques for inverse conditioning in NAH.
• To validate a best practice for inverting underdetermined NAH data through simulation and experimentation.

Main Methods:

• Compared three data selection methods: iterative discarding, singular value monitoring, and zero padding.
• Evaluated Tikhonov regularization, Bayesian regularization, and data compression for inverse conditioning.
• Utilized the inverse equivalent source method with a point-excited thin plate for numerical testing.

Main Results:

• Effective independence method for hologram point selection combined with compressed sensing regularization significantly reduced reconstruction error.
• The integrated approach enhanced the modal assurance criterion (MAC) value, indicating improved mode identification.
• Simulation and experimental results confirmed the efficacy of the proposed best practice.

Conclusions:

• The combination of effective independence data selection and compressed sensing regularization is optimal for underdetermined NAH.
• This integrated technique improves the accuracy and stability of vibro-acoustic system analysis.
• The findings provide a practical guideline for applying NAH with limited measurement points.