Implement under-relaxation for the tight-coupling iterative solver#3300
Implement under-relaxation for the tight-coupling iterative solver#3300luwang00 wants to merge 36 commits intoOpenFAST:devfrom
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Release 5.0.0
SeaState: Logic for near-surface current
Update docs for 5.0.0 release, including missing api changes
MD: standardize input file header text to match docs
* Previously, olaf wake propagation did not consider wave velocity. * A similar bug was found in the SetSectAvgInflow subroutine. * The optional BoxExceedAllow flag for IfW_FlowField_GetVelAcc was not passed correctly through the SeaState WaveField subroutine for AD.
Minor documentation bugs
Various bug fixes for AeroDyn when modeling MHK turbines
Temporary fix for HydroDyn rectangular member visualization
Previously, the self-weight of the reaction node(s) is missing. This is now added back along with any cable loads on the reaction node(s) just in case.
FVW: Fix notification about wake extent
Fix SubDyn reaction load output
OLAF FVW stability issue when simulating multiple rotors
… improve numerical stability
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Dear @luwang00, Thanks for this addition. Should it be that the relaxation factor reduces with each iteration of the nonlinear solve, and after convergence, the factor gets reset back to unity for the next time step? This is what we did within the nonlinear solve for the old quasi-static mooring module of FAST; I believe MAP++ does something similar. Perhaps with this method, the additional user input is not needed. Best regards, |
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Changing this to a dynamic relaxation factor could be really useful. Perhaps later. |
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| ! Relax - Under-relaxation factor for the iterative solver (-) [>0 and <=1] | ||
| CALL ReadVar( UnIn, InputFile, p%Relax, "Relax", "Under-relaxation factor for the iterative solver (-) [>0 and <=1]", ErrStat2, ErrMsg2, UnEc) |
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could we change this to a ReadVarWDefault and use a default value of 1.0?
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I think a constant default should be around 0.8. Alternatively, we can make the default the adaptive option.
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Hi @jjonkman, thanks for the comment. I think typically the relaxation factors should be smaller, i.e., take smaller steps, for the first few iterations when the solution is far from convergence and the correction step is large. This is where there is the greatest danger of overshooting and divergence. As we approach a converged solution, the corrections are smaller, and we can gradually increase the underrelaxation factor safely to some maximum value. I want to see if I can implement a simple adaptive underrelaxation based on the change in residual, but even then, I think it would be nice to give the user some control over this (with default settings), like a fixed underrelaxation factor or a max and a min value for adaptive underrelaxation. Different models can have very different characteristics. For some models, proper under-relaxation can be critical, and it is hard to have some thing that is one size fit all. I also added some example results in the PR message above. |
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Thanks for the addition insight and example results, @luwang00. I see your point about wanting to increase the relaxation factor with successive iterations. If I recall from past quasi-static mooring work, we chose the opposite because our starting point was the converged solution from the previous time step and only small changes are expected between time steps. So, divergence was not really a concern and reducing the relaxation factor with iteration helped ensure that convergence was reached for the few cases where the solution did start to diverge. I suspect the same is true for tight coupling solver. Regardless, a bit more testing with different models will probably help identify the best solution. |
…esidual between iterations
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I'll be curious how much of a difference the auto-relax makes.
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Merge this to |
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Feature or improvement description
This PR adds under-relaxation for the tight-coupling iterative solver to address occasional solution divergence. Using an under-relaxation factor less than 1 can potentially improve the stability of numerically challenging models. It can also improve simulation time by avoiding oscillatory convergence and reducing the number of times the Jacobian needs to be updated. The under-relaxation is only applied to the input corrections and not the state corrections. This appears to be adequate.
The user can either provide a constant under-relaxation factor or enable adaptive adjustment of the relaxation factor. With the latter, the user still needs to provide an initial under-relaxation factor to be used during the first iteration of each predictor or corrector step if enabled.
Using a constant under-relaxation factor of 1 removes the under-relaxation and recovers the previous behavior. However, based on limited testing, setting an under-relaxation factor above 0.8 is usually detrimental to convergence and performance and is not recommended. (Note that to avoid changes to r-test results, the r-test input files will be updated to use a constant factor of 1, even though that is likely not optimal.)
The adaptive under-relaxation uses a simple delayed correction approach to avoid having to save duplicated states and inputs for backtracking. With this approach, the first iteration of each predictor step (or corrector step if enabled) uses the initial under-relaxation factor provided by the user. From the second iteration onward, the under-relaxation factor is
To minimize the chance of solution diverging from the first iteration, a smaller initial under-relaxation factor is suggested with this approach. Based on limited testing, the adaptive under-relaxation method does not provide significant performance improvement over a reasonable constant under-relaxation factor for a typical convergence tolerance of 1e-4. However, it does reduce the number of iterations in each step significantly for smaller tolerances such as 1e-5. In practice, any improvement is likely sensitive to the characteristics of the model and the tolerance requested.
To support the added functionality, two new inputs are inserted in the main
fstinput file on line 14 and line 15:The
defaultkeyword can be used with both as indicated in the input descriptions above.Example results
The following example results are based on a very challenging model of a floating twin-rotor MHK turbine system with flexible blades (with added mass) and support structures and OLAF FVW model.
Without under-relaxation, the simulation diverges after about 22 s. In contrast, the simulation proceeds without issue with a constant under-relaxation factor of 0.3 (higher value not tested). Before the simulation diverges without under-relaxation, the two simulations give consistent results. See example output channels below:
The numbers of iterations at each time step are compared below. Interestingly, simulating with under-relaxation requires comparable or fewer iterations, suggesting very poor convergence without. This is also obvious from the fact that when simulating without under-relaxation, OpenFAST needs to recompute the Jacobian frequently, as indicated by the spikes in the number of iterations in the figure below. In contrast, the simulation with under-relaxation does not require any Jacobian update after initialization.
Impacted areas of the software
Glue-code, docs, r-test
Test results, if applicable
r-test input files needed to be updated with the new under-relaxation input. Results should not change if the under-relaxation factor is set to 1 with adaptive relaxation turned off.
To-Dos