What do numerical instability (ill-condition) warnings indicate?
Answer: Numerical instability warnings indicate that digits of accuracy were lost during computation. CSI software performs computation with 16 digits of accuracy, some of which may be lost when analysis involves systems of significantly different stiffness, in which lower-order values are truncated to suit operations with higher-order values. When this warning occurs, ETABS reports the location of the occurrence such that the user may edit the model if necessary.
Reviewing animation of deformation for gravity self weight case , and first mode of vibration to make sure they are as expected can help determine problematic areas. Some situations where numerical instability may occur include:
- When the rigid-diaphragm assumption is applied to a slab with flexible interconnecting objects.
- When multiple releases are assigned to a joint, causing joint DOF to become orphaned (without stiffness). In this instance, numerical instability warnings indicate a modeling problem which should be corrected.
- Orphan nodes or elements which are not correctly attached to the rest of the structure, or laterally unbraced . Reviewing deformation animation under gravity cases and modal cases usually helps locate these orphan elements which will be deflecting large amounts and completely out of phase with rest of the structure
A model should always be checked for ill-conditions without P-delta iterative analysis first, if the ill-conditions occur only when activating P-delta analysis, please refer to information below.
P-Delta FAQ and troubleshooting
Depending on the number of digits lost, actions which result include the following:
- Less than 6 does not generate a response in that values and solution are sufficiently accurate.
- Between 6 and 11 lost digits of accuracy may or may not create numerical problems, therefore warning message is reported which reads: The results of the analysis may still be acceptable but the user should carefully check the results, especially the global sums of loads.
- Over 11 digits lost causes an Ill-condition warning at the end of the analysis and results may not be sufficiently accurate. ETABS indicates the location of the numerical problem, in this case the user needs to check and revise the model.
ETABS 2013 and above, offers different options for equation solvers, when getting an ill-condition message while running Advanced or Multi-threaded solver, the user must re-run analysis using standard solver (Analyze>Advanced Sap fire), to get complete information about numerical issues, including location coordinates within the model(default coordinates are inches or mm), then check for instabilities as indicated above at these coordinates.
Another source of numerical issues including ill-conditions is an auto-merge tolerance that is too small, the program default's is 0.1in and rarely needs to be changed you can review this via Options>Tolerances
Recommendations for Large Models
In the case of very large models, running the standard solver can take an impractical amount of time , in this case we recommend:
- Make a copy of the model, and add unit mass to ALL 6 DOF at every joint, Rotational inertial is necessary to pick up torsional modes for frame elements.
- Make sure the mass source is defined as from self-weigh and additional masses and not lumped at stories
- Run an Eigen analysis. Any solver will do for this, so use the fastest. A dozen modes is enough to detect problems
- Loss of accuracy more than 11 digits usually represents a rigid-body mode or mechanism, and the eigen modes usually pick these up as having large periods
- It is also good to look for the report on the number of eigen-values below the shift, as this may pick up problems due to P-delta that may not be near zero-frequency (large period)
- The standard-solver is a good way to pick up problems like 6 to 10 digits lost due to large stiffness differences that cause inaccuracy but as indicated above this are not necessarily instabilities.