Acoustic Field Reconstruction via Virtual Source Segmentation
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Solution Overview
Problem
Existing Near-field Acoustical Holography methods face challenges in reconstructing sound fields with non-spherical source surfaces and require large measurement areas or complex computational processes, leading to spatial windowing effects and inaccurate reconstructions.
Innovation Solution
A method that uses virtual source locations and scaled wave functions to compute acoustic quantities through a least-norm fit, allowing accurate reconstruction with a smaller number of measurements and lower computational cost, even for complex source geometries.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If spherical wave functions with a common origin are used to represent the sound field, then the sound field reconstruction can be performed, but errors are introduced in the reconstruction on non-spherical source surfaces
Solution Approach 1:
The patent divides the sound field representation into multiple localized spherical wave expansions, each centered at a different virtual source location. This segmentation allows the global sound field to be accurately represented even on non-spherical surfaces by combining multiple local spherical harmonics expansions
Solution Approach 2:
The patent introduces virtual source locations as intermediary points that are not physically present but mathematically constructed to optimize the spherical wave expansion. These virtual sources act as mediators between the actual sound sources and the measurement surface, enabling accurate reconstruction without requiring the measurement surface to be spherical
2Measurement precision
If a large number of measurement positions are used to obtain a sufficiently accurate model, then the reconstruction accuracy improves, but the computational cost and complexity increase
Solution Approach 1:
The patent uses a limited number of carefully selected virtual source locations and spherical wave functions to achieve accurate reconstruction. Rather than using excessive measurement positions, the method employs just enough spherical harmonics terms to capture the essential sound field characteristics, avoiding unnecessary computational complexity
Solution Approach 2:
The patent changes the parameters of the spherical wave expansion by optimizing the number of terms and the locations of virtual sources. This parameter optimization allows achieving high reconstruction accuracy with a reduced number of measurement positions by adjusting the mathematical model to better fit the specific sound field being measured
3Reliability
If traditional regularization methods like Tikhonov regularization are applied, then the solution can be stabilized, but they do not work properly for spherical wave expansions
Solution Approach 1:
The patent modifies the regularization approach by changing the parameter selection criteria for spherical wave expansion terms. Instead of using traditional Tikhonov regularization which doesn't work properly, the method implements a selective truncation strategy based on the decay of spherical harmonic coefficients, which is naturally compatible with the spherical wave expansion framework
4Productivity
If spatial DFT is used for NAH calculation, then the processing speed is very fast, but severe spatial windowing effects occur unless the measurement area fully covers the areas with high sound pressure
Solution Approach 1:
The patent replaces the spatial DFT mechanical processing system with a spherical wave expansion-based computational approach. This substitution eliminates the severe spatial windowing effects inherent in DFT methods while maintaining computational efficiency through the use of closed-form spherical harmonic solutions and optimized virtual source configurations
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables accurate sound field reconstruction on non-planar surfaces with fewer measurements and reduced computational demands, effectively handling underdetermined estimation problems and improving regularization schemes for optimal filtering.
Implementation Method 1
computing a second acoustic quantity at a target location from a superposition of the set of wave functions multiplied by respective expansion coefficients
Data Source
AI summary
Disclosed herein is a method of reconstructing a sound field. The method comprises receiving measured values indicative of a first acoustic quantity measured at a set of measurement locations; defining a set of virtual source locations; and computing a second acoustic quantity for at least one target location from one or more wave functions each representative of a respective sound field originating from a respective one of the defined set of virtual source locations; wherein the one or more wave functions are weighted by respective one or more weighting factors, and wherein computing comprises determining the one or more weighting factors from a least-norm fit of the one or more wave functions to the received measured values.