Automatic mode tracking for flight dynamic analysis using a spanning algorithm

Identifying and tracking dynamic modes in a multi-dimensional parameter space is a problem that presents itself in many engineering disciplines. In a flight dynamics context, the dynamic modes refer to the modes of motion obtained from a linearisation of the aircraft system about a known operating point. Typically dynamic results derived from these linear models are unsorted, where mode indices are unrelated from one operating point to the next. When varying the parameters, or in this case operating point, difficulties in automating the process of relating modes from a linear system derived at one parameter set to the next exists. This paper builds on the work in tracking modes in a structural context, using the Modal Assurance Criterion (MAC) to numerically relate modes from two comparable linear systems. The (MAC) is deployed within a spanning algorithm to discover and identify all modes within all conditions, with their relationship to adjacent/neighbouring conditions. This is tested on a 1-, 2- and 3-dimensional parameter space, twelve state system.