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

如今，几乎所有较大的公共活动都是通过电声放大和扬声器系统进行的。在以前的一个项目中，基于伴随欧拉方程的时间域优化可以识别整个系统的单个扬声器的最佳位置和最优控制，以产生所需的声场，并考虑到空气流动和温度分层等非均匀环境条件。本项目的目的是在这个过程中考虑复阻抗边界条件。为此，在该方法中加入了表示壁阻抗的体积惩罚方法，并使之适用于实验数据。作为驱动函数的优化问题，体积惩罚的优化是一个高维优化问题，可采用基于伴随的方法进行求解。结果表明，该方法可以处理复杂的几何构型和边界条件。开发了一种方法，该方法不仅可以用来优化扩声系统关于单个扬声器的定位和控制，而且可以用来优化边界条件，即关于房间的二级声学结构的处理。通过模拟中激励信号的随机变化，可以直接以能量衰减曲线为目标函数或由其导出的参数(如混响时间或清晰度)来优化电声和室内声环境。与现有方法相比，开发的方法可以考虑基于波的声音传播现象，如绕射和散射，以及气流和温度分层，这些现象在露天场景中特别重要。通过在高性能计算机上的实现，扬声器驱动功能和墙阻抗将针对中等复杂性的真实扩声场景同时被优化，从而为该方法提供概念验证；还将证明，利用当前可用的计算能力已经可以优化到4 kHz的频率。

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.