Transducer Array Acoustic Field Control Using Eigenvector Phasing
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Solution Overview
Problem
Existing systems for producing an acoustic field using multiple control points are limited by slow and unpredictable solution times, making it difficult to support a large number of control points and control acoustic fields of larger volumes.
Innovation Solution
The method involves defining control points with known spatial relationships, computing a matrix to determine eigenvectors and eigenvalues, and using eigenproblems to find valid phases and amplitudes for transducer arrays, allowing for faster and more predictable control of acoustic fields with a higher number of control points.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Area of stationary object
If a large number of control points are used to control acoustic fields of larger volumes, then the coverage area and control precision are improved, but the computation time increases and becomes unpredictable
Solution Approach 1:
The patent changes the mathematical approach from iterative methods to eigenvalue decomposition of a matrix derived from the acoustic field model. This parameter change in the computational method transforms the unpredictable iterative convergence into a deterministic O(N²) algorithm, enabling reliable real-time control of large acoustic fields with many control points
Solution Approach 2:
The patent replaces the mechanical iterative adjustment process with a mathematical eigenvalue-based solution. By substituting the iterative computational mechanism with a direct matrix decomposition approach, the system achieves faster and more predictable solution times while maintaining the ability to control large numbers of control points
2Measurement precision
If a large number of control points are used to increase acoustic field volume control, then the spatial resolution is improved, but the system complexity increases
Solution Approach 1:
The patent transforms the system from an iterative optimization problem to a linear algebra eigenvalue problem. This mathematical transformation provides a direct computational pathway that scales predictably with the number of control points, maintaining high spatial resolution control precision while managing system complexity through established numerical linear algebra techniques
3Ease of operation
If known methods are used to control acoustic fields, then the basic functionality is achieved, but the solution time is slow and unpredictable
Solution Approach 1:
The patent substitutes the iterative computational mechanism with a direct eigenvalue decomposition approach. This replacement transforms the slow and unpredictable iterative convergence into a deterministic algorithm with O(N²) complexity, significantly improving solution speed while preserving the ease of acoustic field control capability
Solution Approach 2:
The patent pre-computes the matrix representation of the acoustic field model based on the transducer array geometry and acoustic propagation characteristics. This preliminary action allows the actual control calculation to proceed through a direct eigenvalue decomposition rather than iterative adjustment, dramatically improving solution speed for real-time control applications
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
This approach enables real-time updating and efficient control of larger acoustic fields with a higher number of control points, improving power output efficiency and suitability for applications like haptic feedback and manufacturing.
Implementation Method 1
operating the transducer array to cause one or more of the transducers to output an acoustic wave each having an initial amplitude and phase
Implementation Method 2
the distance between adjacent control points should be sufficient to enable the sound waves of the acoustic field to phase shift from one of the control points to match the next control point
Implementation Method 3
The eigenvalues represent scaling factors, some of which will be relatively high and some of which will be relatively low, in relation to each other
Data Source
AI summary
A plurality of control points are defined have a known spatial relationship relative to an array of transducers. An amplitude is assigned to each control point. A matrix is produced containing elements which represent, for each of the control points, the effect that producing a modeled acoustic field having the assigned amplitude with a particular phase at the control point has on the consequential amplitude and phase of the modeled acoustic field at the other control points. Eigenvectors of the matrix are determined, each eigenvector representing a set of phases and relative amplitudes of the modeled acoustic field at the control points. One of the sets is selected and the transducer array is operated to cause one or more of the transducers to output an acoustic wave each having an initial amplitude and phase such that the phases and amplitudes of the resultant acoustic field at the control points correspond to the phases and relative amplitudes of the selected set.