Adjoint-based optimization of sound reinforcement including non-uniform flow

Abstract

The determination of optimal geometric arrangements and electronic drives of loudspeaker arrays in sound reinforcement applications is an ill-posed inverse problem. This paper introduces an innovative method to determine complex driving functions, also considering complex environmental conditions. As an alternative to common frequency domain methods, the authors present an adjoint-based approach in the time domain: Acoustic sources are optimized in order to generate a given target sound field. Instead of the Helmholtz equation, the full non-linear Euler equations are considered. This enables an easier treatment of non-uniform flow and boundary conditions. As proof of concept, a circular and a linear monopole array are examined. For the latter, the environmental conditions include wind and thermal stratification. For all examples, the method is able to provide appropriate driving functions.

Approximate Acoustic Boundary Conditions in the Time-Domain using Volume Penalization

“…Time-domain simulations can be based on the wave equation [14], the non-linear Euler equations [31,32] or the acoustic equations as its linearized form. A variety of numerical methods has been utilized, like the finitedifference (FD) [4], the finite element (FEM) [5], the finite volume (FVM) [2] or the discontinuous Galerkin method (DG) [25].…”

Finite‐difference‐based simulation and adjoint optimization of gas networks

“…Besides, they are used for data assimilation tasks 13,14 and for analyzing and optimizing reactive flow configurations 15,16 . Furthermore, the adjoint approach is used in the field of aeroacoustics 17,18 …”

“…15,16 Furthermore, the adjoint approach is used in the field of aeroacoustics. 17,18 Also in the context of gas networks, the adjoint approach is already established. It has been used to make decisions in hierarchical models, 19 error estimations 20 and for optimizing gas networks 21,22 using a finite volume discretization.…”

Directional sound source modeling using the adjoint Euler equations in a finite-difference time-domain approach

“…This generalized form allows one to model the behavior of acoustic sources in situations with complex background flow and thermal stratification, relevant for applications such as ventilation systems with thermal gradients, sound reinforcement in open spaces such as train stations or sports stadiums, or noise pollution in urban environments. In a previous study (Stein et al, 2019) we have demonstrated how to model and optimize sound sources, for example, for open-air concerts with a non-uniform velocity and temperature background. While in that study only idealized spherical sources with uniform directivity were used, the present study shows that the adjoint FDTD a) Electronic mail: stein@cfd.tu-berlin.de, ORCID: 0000-0002-4298-2001. approach is also capable of synthesizing realistic sound sources with arbitrary directivity.…”