Balanced reduction of high-dimensional mechanical systems: a block-balancing approach

An efficient scheme for balanced reduction of high-dimensional models of lightly damped mechanical systems is developed. Given a modal realization, closed-form solutions of the reachability and observability Gramians exist that are only block-diagonalized by means of a subspace iteration. The subspace dimension is based on the Gramian diagonals. This iteration has rapid convergence for most lightly damped systems and gives accurate reduction results even for (almost) nonminimal systems. The block-balancing algorithm is especially suited for Hankel norm calculation.<>