  In many contexts the modal properties of a structure change, either due to
the impact of a changing environment, fatigue, or due to the presence of
structural damage. For example during flight, an aircraft's modal properties
are known to change with both altitude and velocity. It is thus important to
quantify these changes given only a truncated set of modal data, which is
usually the case experimentally. This procedure is formally known as the
generalised inverse eigenvalue problem. In this paper we experimentally show
that first-order gradient-based methods that optimise objective functions
defined over a modal are prohibitive due to the required small step sizes. This
in turn leads to the justification of using a non-gradient, black box optimiser
in the form of particle swarm optimisation. We further show how it is possible
to solve such inverse eigenvalue problems in a lower dimensional space by the
use of random projections, which in many cases reduces the total dimensionality
of the optimisation problem by 80% to 99%. Two example problems are explored
involving a ten-dimensional mass-stiffness toy problem, and a one-dimensional
finite element mass-stiffness approximation for a Boeing 737-300 aircraft.
