Physical Only Modes Identification Using the Stochastic Modal Appropriation Algorithm

Many operational modal analysis (OMA) algorithms such as SSI, FDD, IV, ... are conceptually based on the separation of the signal subspace and the noise subspace of a certain data matrix. Although this is a trivial problem in theory, in the practice of OMA, this is a troublesome problem. Errors, such as truncation errors, measurement noise, modeling errors, estimation errors make the separation difficult if not impossible. This leads to the appearance of nonphysical modes, and their separation from physical modes is difficult. An engineering solution to this problem is based on the so-called stability diagram which shows alignments for physical modes. This still does not solve the problem since it is rare to find modes stable in the same order. Moreover, nonphysical modes may also stabilize. Recently, the stochastic modal appropriation (SMA) algorithm was introduced as a valid competitor for existing OMA algorithms. This algorithm is based on isolating the modes mode by mode with the advantage that the modal parameters are identified simultaneously in a single step for a given mode. This is conceptually similar to ground vibration testing (GVT). SMA is based on the data correlation sequence which enjoys a special physical structure making the identification of nonphysical modes impossible under the isolating conditions. After elaborating the theory behind SMA, we illustrate these advantages on a simulated system as well as on an experimental case.