Optimization of absorption placement using geometrical acoustic models and least squares

Area of Science:

• Acoustics
• Room Acoustics
• Computational Acoustics

Background:

• Optimizing acoustic absorption in spaces to achieve a target impulse response is typically a nonlinear problem.
• Existing nonlinear optimization methods can be computationally expensive and complex.
• A need exists for efficient and direct methods for acoustic absorption assignment.

Purpose of the Study:

• To reformulate the nonlinear problem of optimal absorption placement as a constrained linear least-squares problem.
• To develop a direct and computationally efficient method for distributing acoustic absorption.
• To accommodate multiple frequency bands, sources, receivers, and placement constraints.

Main Methods:

• Reformulation of absorption assignment as a constrained linear least-squares problem.
• Application of regularized solutions for direct absorption distribution.
• Integration with a beam tracing model for demonstration.

Main Results:

• The proposed method provides a direct distribution of acoustic absorption.
• The approach successfully handles multiple frequency bands, sources, and receivers.
• Optimal absorption placement on walls and ceiling was demonstrated in a classroom model.

Conclusions:

• The constrained linear least-squares approach offers an efficient alternative to nonlinear optimization for acoustic absorption placement.
• The method allows for flexible and direct control over sound absorption distribution.
• This technique is applicable to various room acoustics scenarios, including classroom design.