Six algorithms are included in TAMKIT for selecting DOF to retain for a TAM reduction. These are all implemented in Nastran and are all designed to develop an accurate static (Guyan) TAM. Of the three methods, only the Grid Point Kinetic Energy (GPKE) method does not require any preliminary selection of DOF. It can be used as a preliminary guideline for selecting DOF, though it is rarely sufficient on its own. The Residual Kinetic Energy (RKE) method requires the selection of an initial set of DOF that will be a subset of the final set. The RKE method provides guidance in which DOF to add to this set, but it is not an iterative algorithm that automatically adds DOF. The Iterative Residual Kinetic Energy (IRKE) algorithm applies the RKE algorithm iteratively, redistributing the mass using a Guyan reduction at each step. The Iterative Guyan Reduction (IGR) method requires the selection of an initial large candidate set of DOF that will be a superset of the final set. For most practical problems this initial set must be selected by the user, though for small problems that is not necessary since the complete set of DOF in the model can be used as a starting point. The Effective Independence (EI) algorithm iteratively removes DOF based on maximizing the norm of the Fisher Information Matrix (FIM). Even though this method does allow for the pre-weighting of the mode shapes by the mass matrix, it does not perform any reduction and therefore can be applied to much larger candidate sets than the IGR algorithm. The Mass Weighted Effective Independence (MWEI) algorithm combines the IGR and EI algorithms, performing a mass reduction at each step, but using a mass-weighted effective independence measure to choose which DOF to eliminate.
None of these methods can completely replace engineering judgment, though they can provide excellent guidance in selecting DOF. There are two automated paths for optimally selecting DOF. One is to start with a small initial set, and use the IRKE algorithm to add DOF until satisfactory orthogonality error norms are achieved. This can be followed by an IGR or MWEI algorithm to eliminate DOF without significantly increasing error norms. Another path would be to apply the EI algorithm to a set of all accessible locations on the model to select a number of DOF that are practical for application of the IGR or MWEI algorithms. We have seen situations where the IGR algorithm out performs the MWEI algorithm and visa-versa. It is usually best to apply both algorithms and choose the best solution.
None of the iterative algorithms are optimal in the sense of finding the set of DOF that minimizes any particular error norm. The only algorithm that we have found that will generate an “optimal” solution is a Genetic Algorithm. This algorithm has been implemented in MATLAB and is packaged along with TAMKIT in the IMAT+TestKit.