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Typical challenges of simulation-based design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima, and the failure of the analysis to return a value to the optimizer. One possible remedy to alleviate these issues is to use surrogate models in lieu of the computational models or simulations and derivative-free optimization algorithms. In this work, we use the R dynaTree package to build statistical surrogates of the blackboxes and the direct search method for derivative-free optimization. We present different formulations for the surrogate problem (SP) considered at each search step of the mesh adaptive direct search (MADS) algorithm using a surrogate management framework. The proposed formulations are tested on 20 analytical benchmark problems and two simulation-based multidisciplinary design optimization (MDO) problems. Numerical results confirm that the use of statistical surrogates in MADS improves the efficiency of the optimization algorithm.

Various constrained problem formulations for the optimization of an electro-thermal wing anti-icing system in both running-wet and evaporative regimes are presented. The numerical simulation of the system is performed by solving the conjugate heat transfer problem between the fluid and solid domains. The optimization goal is to reduce the energy use and power demand of the anti-icing system while ensuring a safe protection. The formulations are carefully proposed from the physical and mathematical viewpoints; their performance is assessed by means of several numerical test cases to discern the most promising for each regime. The design optimization is conducted using the mesh adaptive direct search algorithm using quadratic and statistical surrogate models in the search step. The influence of the models on the convergence speed and the quality of the obtained design solutions is investigated.

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.

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.

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