Combined State Order and Model Order Formulations in the Unified Matrix Polynomial Method (UMPA)

The unified matrix polynomial (coefficient) method (UMPA) has been used by the authors to provide a single, educational framework that encompasses most commercial and research methods used to estimate modal parameters from measured input-output data (normally frequency response functions). In past publications of this methodology, the issue of state order has not clearly been identified in the formulation of the UMPA model. State order refers to the order of the base vector that is an elementary part of the basic UMPA model and has been a part of the modal parameter estimation development since the Ibrahim Time Domain methods in the mid 1970s. The UMPA model is restated to clearly identify the role of base vector order and the relationship between base vector (state) order and polynomial model order. This relationship provides a mechanism for explaining a number of modal parameter estimation methods that have not previously been identified and helps to explain the sensitivity of different modal parameter estimation methods to noise.