Tournemenne Robin, Petiot Jean-François, Talgorn Bastien, Gilbert Joël, Kokkolaras Michael
Magique 3D Team, Inria Bordeaux Sud Ouest, 200 avenue de la vieille tour, 33405 Talence Cedex, France.
École Centrale de Nantes, LS2N, UMR CNRS 6004, 1 rue de la Noë, 44321 Nantes Cedex 3, France.
J Acoust Soc Am. 2019 Jun;145(6):3795. doi: 10.1121/1.5111346.
A method for optimizing the inner shape of brass instruments using sound simulations is presented. This study considers different objective functions and constraints (representative of both the intonation and the spectrum of the instrument) for a relatively large number of design variables. A complete physics-based model, taking into account the instrument and the musician's embouchure, is used to simulate steady regimes of sounds by means of the harmonic balance technique, the instrument being represented by its input impedance. The design optimization variables are related to the geometrical dimensions of the resonator. The embouchure's parameters are varied during the optimization procedure to obtain an average behavior of the instrument. The objective and constraint functions of the optimization problem are evaluated using the physics-based simulation model, which is computationally expensive. Moreover, the gradients of the objective and constraint functions can be discontinuous, unavailable, or hard to approximate reliably. Therefore, a surrogate-assisted derivative-free optimization strategy using the mesh adaptive direct search algorithm was employed. One example of a B♭ trumpet's bore is used to demonstrate the effectiveness of the design optimization approach: the obtained results improve previously reported objective function values significantly.
本文提出了一种利用声音模拟优化铜管乐器内部形状的方法。本研究针对相对大量的设计变量，考虑了不同的目标函数和约束条件（代表乐器的音准和频谱）。采用一个完整的基于物理的模型，该模型考虑了乐器和演奏者的口型，通过谐波平衡技术来模拟声音的稳定状态，乐器由其输入阻抗表示。设计优化变量与共鸣器的几何尺寸相关。在优化过程中改变口型参数以获得乐器的平均性能。优化问题的目标函数和约束函数使用基于物理的模拟模型进行评估，该模型计算成本高昂。此外，目标函数和约束函数的梯度可能是不连续的、不可用的或难以可靠近似的。因此，采用了一种使用网格自适应直接搜索算法的代理辅助无导数优化策略。以降B调小号的号管为例，证明了设计优化方法的有效性：所得结果显著提高了先前报道的目标函数值。
