Evolutionary strategy to optimize sonic black hole profiles in duct terminations

Sonic black holes (SBH) at duct ends constitute a particular type of anechoic termination. Acoustic waves get slowed down by means of a set of rings separated by cavities, whose inner radii diminish following a power law. Ideally, such design produces no wave reflection. In practice, however, this is not possible though the reflection coefficient remains low for a broadband frequency range. In this work, an evolutionary strategy (ES) is used to optimize the shape of SBH profiles and to try to improve the results of the standard power-law design. We test several cost functions for the reflection coefficient and impose constraints on the radii to fasten convergence. Different optimization problems are addressed. The first one is to determine the optimum exponent for the classical power-law profile. In the second one, the inner ring radii are only imposed to be monotonically decreasing from the SBH entrance. This results in new designs that overcome the performance of the optimum power-law profile at almost all frequencies. To perform the computations, we use a transfer matrix method for the SBH and resort to a derandomized ES with covariance matrix adaptation, which can easily deal with multiobjective optimization at a very reasonable computational cost.