Modeling and optimization of sound reinforcement scenarios with impedance affected boundaries in the time domain

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Nowadays, almost all larger public events are carried out with electroacoustic amplification and loudspeaker systems. In a previous project, it was shown that an optimization based on the adjoint Euler equations in the time domain can identify an optimal position and optimal control of individual loudspeakers of an overall system to generate a desired sound field, also taking into account non-homogeneous environmental conditions such as air flows and temperature stratification. The present project aims to consider complex impedance boundary conditions in this process. For this purpose, a volume-penalization approach for the representation of wall impedances is added to the method and adapted to experimental data. As the optimization of driving functions, the optimization of volume penalization is a high-dimensional optimization problem, which can be solved by means of an adjoint-based approach. It will be shown that complex geometric configurations and boundary conditions can be handled by this method. A method is developed that can be used to optimize not only a sound reinforcement system with respect to the positioning and control of individual loudspeakers but also the boundary conditions, i.e. the treatment of the room with respect to its secondary acoustic structure. Through a stochastic variation of excitation signals in the simulation, the electroacoustic and room acoustic environment can be optimized directly with respect to an energy decay curve as the objective function or parameters derived from it, such as the reverberation time or clarity. In contrast to existing methods, the developed method can take into account wave-based phenomena of sound propagation such as diffraction and scattering as well as airflow and temperature stratification, which are of particular importance in open-air scenarios. By implementation on a high-performance computer, loudspeaker driving functions and wall impedances are to be optimized simultaneously for a real sound reinforcement scenario of intermediate complexity, thus providing a proof-of-concept for the method; it is also to be demonstrated that optimization up to a frequency of 4 kHz is already possible with currently available computing power.