Brass Instruments Design Using Physics-Based Sound Simulation Models and Surrogate-Assisted Derivative-Free Optimization

Abstract

This paper presents a method for design optimization of brass wind instruments. The shape of a trumpet’s bore is optimized to improve intonation using a physics-based sound simulation model. This physics-based model consists of an acoustic model of the resonator (input impedance), a mechanical model of the excitator (the lips of a virtual musician) and a model of the coupling between the excitator and the resonator. The harmonic balance technique allows the computation of sounds in a permanent regime, representative of the shape of the resonator according to control parameters of the virtual musician. An optimization problem is formulated, in which the objective function to be minimized is the overall quality of the intonation of the different notes played by the instrument (deviation from the equal-tempered scale). The design variables are the physical dimensions of the resonator. Given the computationally expensive function evaluation and the unavailability of gradients, a surrogate-assisted optimization framework is implemented using the mesh adaptive direct search algorithm (MADS). Surrogate models are used both to obtain promising candidates in the search step of MADS and to rank-order additional candidates generated by the poll step of MADS. The physics-based model is then used to determine the next design iterate. Two examples (with two and five design optimization variables, respectively) are presented to demonstrate the approach. Results show that significant improvement of intonation can be achieved at reasonable computational cost. The implementation of this method for computer-aided instrument design is discussed, considering different objective functions or constraints based on intonation but also on the timbre of the instrument.