Several options controlling the algorithm stop criteria, error calculation methods, and DOF removal process are selected in the Solver Options region of the selectASET form.
The Goal text box indicates the stop criteria for the algorithm. If the goal is an integer greater than 1, it indicates the final number of DOF, or the final number of triaxes if the Triaxes box is checked. If the user enters a value less than 1, the goal is defined in terms of the maximum orthogonality error. When the iterative algorithm computes an error greater than or equal to the goal, the algorithm will stop. If the goal is set to 0, the algorithm will stop when the error exceeds the initial error.
If the Triaxes checkbox is selected, the algorithm will iteratively evaluate and remove triaxes (three translational DOF) at each iteration rather than nodes. In this case, if the Goal is an integer value, it indicates the final number of triaxes rather than DOF. Note that to use the triaxial selection method, the candidate set TAM loaded into selectASET must include all three translational DOF on all grids.
The Retain DOF button allows the user to specify a set of DOF or triaxes that should be retained in the final accelerometer set. There may be certain locations on the structure that are desirable to visualize mode shapes or may be desired for other reasons, and this button allows the user to ensure that the specified DOF/triax locations will be included in the final set. Conversely, the Exclude DOF button allows the user to specify a set of DOF/triaxes that should be removed from the candidate set before the algorithm starts iterating. Clicking either button will bring up the DOF selection form. Individual DOF/triaxes can be selected from the DOF selection form or they can be loaded from an ASCII file. Two types of files are supported: (1) a Nastran bulk data file containing ASET cards can be loaded to select the Retain/Exclude DOF or triaxes, or (2) a two-column delimited text file with columns of grid, DOF. The generic text file can use any standard delimiter (comma, semicolon, tab, etc.) and cannot contain any non-numeric characters. If grids or DOF that are not in the candidate set are present in the selected file, they will be ignored, and if the Triaxes checkbox is selected, only the grid IDs on the ASET cards or the first column of the text file will be read.
The final two solver options—the Scale modes checkbox and the Metric drop-down box—control how the error is computed. The orthogonality matrix, O, is calculated as shown below:
O = PHIT*M*PHI
where
PHI = FEM target modes, partitioned to the current DOF set
M = TAM mass matrix, statically reduced to the current DOF set
There are different schools of thought on whether the target modes, PHI, should be renormalized to the TAM mass matrix before computing the orthogonality. If the target modes are renormalized, the O matrix will have values of exactly 1.0 on the diagonal, with the magnitude of the off-diagonal terms indicating the degree of linear independence of the modes. If the modes are not renormalized, the diagonal terms will generally be less than 1.0, and the deviation from 1.0 on the diagonal and the deviation from 0.0 on the off-diagonal are used to infer the of the selected accelerometer set. Because both methods are valid and there is no “correct” way to compute the orthogonality, selectASET can accommodate either method.
Regardless of the status of the Scale modes checkbox, the orthogonality error matrix is computed the same way:
E = I – O
where:
E = error matrix
I = identity matrix
The method to reduce the error matrix into a scalar error value is dependent on the Metric drop-down box. If the drop-down box indicates MAX, the scalar error is computed by taking the maximum absolute value of the error matrix, E. If the drop-down box indicates RSS, the scalar error is computed by taking the square root of the sum of the squared terms of the entire error matrix E. As before, there is no “correct” error calculation method and a case can be made for either.