Optimisation of hydrophone placement: a dynamical systems approach

Abstract

Tools from equivariant bifurcation theory are applied to the problem of the optimisation of horizontal planar arrays to minimise array noise gain in a 2D isotropic noise field. We specifically use the performance measure derived in the paper by Hayward [3], which is invariant under suitable actions of the symmetry group ${\bf S}_n\times{\bf O}(2)$ , although we would expect most suitable measures to inherit such a symmetry due to the physical properties of the array. An analysis of bifurcations in the presence of this symmetry provides a list of array configurations which one would expect to (locally) optimise performance. This analysis provides a systematic way to search through $2n$ -dimensional phase-space, via low dimensional searches, for solutions. We provide an example of the technique for an array with seven hydrophones and a maximum aperture size of $3m$ .