Stochastic Modal Appropriation (SMA)

Abstract

All available modal identification algorithms (for example SSI, FDD, ARMA) are based on the principle of subspaces in the sense that the pole is identified which characterizes the signal subspace and the noise subspace is taken automatically as its orthogonal complement. This is a response type characterization. For structural dynamics applications however, one is interested in different subspaces, namely the non-conservative subspace and the conservative subspace. The only currently available method that does this is the force appropriation method for in-laboratory testing. In this work, we propose an In-Operation structural identification algorithm based on a different principle, namely the anti-symmetry principle. The idea is as follows: Consider the response of a structure. Construct the anti-symmetric response depending on a certain unknown parameter and consider the resultant of both. This introduces a rotation to the original signal. By varying the parameter, one spans a lot of different subspaces and by proper (mathematically derived) operations on these subspaces and the original one it is possible to cancel out one subspace leaving the data in a single subspace from which the proper parameters can be estimated. This idea is formulated mathematically for a SDOF system subject to unmeasured white noise excitation and it is shown that it provides highly accurate modal parameter estimates.