Optimization of brass wind instruments based on sound simulations

This paper exploits a new optimization method of the inner shape of brass instruments using sound simulations to derive objective functions. The novelties are the obtention of optimal bores for objective functions representative of the intonation but also of the spectrum of the instrument, and the possibility to include constraints in the optimization problem. A complete physics-based model, taking into account the instrument and the musician’s embouchure, is used, in order to simulate sounds’ permanent regimes using the harmonic balance technique. The instrument is modeled by its input impedance computed with the transfer matrix method under plane wave propagation and visco-thermal losses. Some embouchure’s parameters remain variable during the optimization procedure in order to get the average behavior of the instrument. The design variables are the geometrical 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). Two optimization examples of a B[trumpets bore (with two and ten design optimization variables) demonstrate the effectiveness of the approach. Results show that solvers can deal flawlessly with high dimensional problems, under constraints, improving significantly the value of the objective functions.