In the Poles module, the poles are selected from the stability diagram or selected autonomously. Information about the FRF dataset, references and responses sieve, polyreference model orders, and frequency range is displayed in the Poles Info panel. Hovering the mouse pointer over AFU Name will show some additional information about the data file
Selecting a plotted line with the mouse pointer and holding down the middle button will highlight that line and its corresponding entry in the plot legend. Selecting a line in the plot legend with the mouse pointer and holding down the middle button will highlight that line and the corresponding line in the plot axes (this feature is not available in Matlab R2014b or later). The name from the legend will be displayed in the message line at the bottom of the window.
Stability Diagram – The stability diagram is generated by comparing the computed poles and vectors for successive model orders. First, the two poles that are closest in frequency are found. If these poles are within the Frequency tolerance (as a percent difference), the Frequency is considered stable. If the damping of these two closest poles are within the Damping tolerance (as a percent difference), the Pole (frequency and damping) is considered stable. If the vectors associated with these two closest poles are within the Vector tolerance (as a MAC, or unity-length normalized vector inner-product), the Pole & Vector are considered stable. The vectors used for the stability comparison are the residues (i.e., 'solver' shapes) computed from the polyreference processing. These two poles are then removed from the sets of poles, and the process is repeated until all poles meeting the stability conditions are evaluated.
Pole picking is activated by selecting Pick Poles from the axes context menu or the Display menu for the Poles module, or pushing the Pick Poles icon on the toolbar. Ctrl+S is the hotkey shortcut to toggle pole picking on and off. Panning and pole picking are mutually exclusive, as only one can be active at a time, but switching directly between them is possible. The axes windowing hotkeys (Ctrl+X, Ctrl+Y, and Ctrl+N) are also operable while picking poles and panning. Cursors cannot be added, deleted, or moved while peak picking or panning is active.
Poles are selected from the stability diagram using a cross-hairs cursor with an open area at the center. The currently highlighted pole marker is outlined in red. How close to a pole marker the cursor must be to highlight it is determined by the Pick Pole Cursor Tolerance, which set in the Preferences dialog. Information about the highlighted pole (model order, frequency, and damping) is displayed in the white frame at the lower right corner of the module. The highlighted pole is selected or deselected by clicking the left mouse button. The selected poles are added to the Poles List, and deselected poles are removed from the Poles List. The pole marker is filled if the pole is in the Poles List, and empty if it is not in the Poles List. If a selected pole is highlighted, pressing the middle mouse button will animate that mode shape if a TDM has been imported. The poles selected autonomously are plotted on the top row of the stability diagram and the poles returned from SDOFit are plotted on the bottom row. The color and symbol of the pole markers are selected in the Preferences dialog.
Poles List – Selected poles are added to the Poles List, which is the table in the lower left side of the module listing the frequency and damping of the selected poles. The check boxes in the Poles List determine if a pole is enabled. Only the enabled (checked) poles are written to a file
Plot Function – Select the mode indicator functions to plot. The available MIFs are the same as for the Setup module. The colors of the MIFs plotted on the stability diagram are set in the Preferences dialog.
Plot Function : CMIF Order – Select the ordering of the CMIF and QMIF functions. If the CMIF Order is 'sorted', the CMIF and QMIF functions are sorted by decreasing magnitude at each spectral line. When CMIF Order is 'tracked', the CMIF and QMIF functions are sorted based on the similarity of the left singular vectors between adjacent spectral lines. The left singular vectors are compared by determining the maximum inner product for the vectors from adjacent spectral lines. The singular values are sorted accordingly.
Plot Function : Max MIF Order – Select the maximum order of the mode indicator functions that are plotted.
Plot Stability – Select stability conditions for which pole markers are plotted on the stability diagram. The symbol and color of the pole markers for the stability conditions are set in the Preferences dialog.
Stability – Enter the tolerance for stability criterion (Frequency, Damping, and Vector), as a percent.
Autonomous Pole Selection – The autonomous pole selection process implemented in AFPoly is based on the Common Statistical Subspace Autonomous Mode Identification (CSSAMI) method, which is explained in great detail in references [3-5]. This procedure evaluates the large set of poles and residue vectors produced by the modal parameter estimation algorithm for all model orders to identify clusters of consistent modes. The general process is outlined below.
1. Only the poles currently displayed on the stability diagram are evaluated.
2. The pole densities, which are a measure of the number of other poles near each pole on the complex plane, are computed and poles with a density less than the Minimum Pole Density are removed.
3. Pole weighted vectors are constructed for the remaining poles and vectors and the modal assurance criteria (MAC) matrix is computed for these state vectors. All poles corresponding to a value in the MAC matrix less than the Pole Weighted Vector MAC are excluded from further consideration.
4. The pole clusters are identified by the singular values of the MAC matrix that are greater than the Minimum Cluster Size. The poles included in each cluster must meet the Cluster Inclusion Threshold. Any clusters that have fewer poles than the Minimum Cluster Size after applying the Cluster Inclusion Threshold are discarded.
5. The median of the frequency and damping of the poles in the cluster are taken to the values that represent the frequency and damping of the pole cluster. The residue vector and modal participation factor for each pole cluster is computed from the singular value decomposition of the residues and participations, respectively, associated with the poles in the cluster.
6. The mean and standard deviation of the frequency and damping of the poles in each cluster and the normalized modal and state vector residuals are also computed.
7. The autonomously selected poles are displayed on the top row of the stability diagram and are added to the Poles List.
Autonomous Pole Selection : Minimum Pole Density – Enter the minimum density of poles that will be included in the autonomous pole selection process. Entry must be a positive integer. The density of each pole is determined using a frequency tolerance and a damping tolerance. The density of each pole is equal to the number of poles that lie within the rectangle defined by these tolerances. The frequency and damping tolerances used for the pole density evaluation are the same as those defined for the stability criterion.
Autonomous Pole Selection : Pole Weighted Vector Order – Enter the order of the pole weighted vector that is used in the autonomous pole selection process. Entry must be a positive integer. This state vector is constructed from the poles and associated residues generated from the polyreference processing.
Autonomous Pole Selection : Pole Weighted Vector MAC – Enter the minimum MAC value of the pole weighted vectors that are included in the cluster identification step of the autonomous pole selection process. Entry must be between 0 and 1.
Autonomous Pole Selection : Minimum Cluster Size – Enter the minimum size of the clusters retained in the autonomous pole selection process. Entry must be a positive integer.
Autonomous Pole Selection : Cluster Inclusion Threshold – Enter the threshold value for the poles to be included in a cluster. Entry must be between 0 and 1.
Tools > Poles > Send MIFS to UIPLOT – Computes (if necessary) and sends all MIFs to UIPLOT.
Tools > Poles > Send MIFS to IMAT Plot – Computes (if necessary) and sends the selected MIF to an IMAT plot figure.
Tools > Poles > Send Stability to MATLAB Plot – Sends a copy of the stability diagram to a MATLAB plot figure.
Tools > Poles > Pick Model Order – Opens a dialog GUI to select a model order from a list, as shown here. All poles plotted on the stability diagram for that model order are added to the Poles List.
Tools > Poles > List Autonomous Clusters – Lists statistical information from the autonomously selected pole clusters in a table dialog. Clicking on a column header sorts the table by that value. Listed in the table are the cluster size, which is the number of poles in the cluster, the median frequency of the cluster in Hz, and the median damping of the cluster in both percent critical and Hz. Also listed is the standard deviation of the frequency and damping of the poles in the clusters. The standard deviations are listed in the units of the associated value (Hz or %Cr) and as a percentage of the associated median values. The last four columns (NMVR1, NMVR2, NSVR1, and NSVR2) are the normalized modal and state vector residuals, which are measure of the consistency of the vectors associated with a cluster, with smaller values indicating greater consistency. Refer to references [3-5] for more information about these parameters.
The rows of the table can be selected with the mouse and this dialog also has some features similar to those on the Poles List panel. The Remove button will remove the poles selected in the table from the Poles List, which is equivalent to deselecting the pole markers in the stability diagram. The Select button will add the poles selected in the table to the Poles List, which is equivalent to selecting the pole markers in the stability diagram. The Animate button will send the selected pole cluster shapes to the animator. If the Animate Back-Expanded Shapes check box is checked, then the shapes will be back-expanded when sent to the animator.
Tools > Poles > Delete SDOFit Poles – Opens a dialog GUI that lists the frequency and damping of any poles that have been returned from SDOFit. Select the poles to remove from the Pole List and delete from the AFPoly stability diagram.
Tools > Poles > Auto Select Poles – This tool is provided as redundancy to the Auto Select Poles pushbutton on the Autonomous Pole Selection panel in case the height of the AFPoly figure is such that the Autonomous Pole Selection panel disappears.