Dominant Modes of Mechanical Systems

To obtain a reduced model of a mechanical system, we can identify the dominant modes and retain those as the reduced model. Two widely used schemes for selection of dominant modes we Modal Cost Analysis (MCA) and balancing, but neither of the methods guarantees that the model error is small, where model error measures the difference between the output of the full model and the output of the reduced model. We introduce a set of coordinates called Pseudo Uncorrelated modal coordinates (PUnc) that we can use in conjunction with Component Cost Analysis (CCA) to select dominant modes yielding a reduced model with minimum model error. Furthermore, unlike MCA and balancing, the accuracy of the reduced model (the model error) in PUnc coordinates can be evaluated before reduction.