Fix constraints and objective output

[jefalon]

Purpose

Fixes two bugs. First, by splitting up_k during the update step of ControlUpdater(), u_k and p_k update allowing for computation of objective values and constraints during optimization. Second, replacing assignment of control to creation of new Constants() in WindFarmManager restore taylor_test convergence of order 2.

Type of change

Select the appropriate type(s) that describe this PR

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (non-backwards-compatible fix or feature)
• Code style update (formatting, renaming)
• Refactoring (no functional changes, no API changes)
• Documentation update
• Maintenance update
• Other (please describe)

Testing

In order to properly test the Taylor test, we would need to setup a regression test for each objective. That might be too much.

Checklist

Put an x in the boxes that apply.

• I have run existing tests which pass locally with my changes
• I have added new tests or examples that prove my fix is effective or that my feature works
• I have added necessary documentation

[jefalon]

@johnjasa, one test I'd like to do to feel perfectly comfortable with the constraints is the prob.check_totals() from OpenMDAO to see if the gradients of the constraints are working. Unfortunately, I am unable to get that to work as it gets stuck during the prob.run_model() step. Any suggestions?

Edit: nevermind I just had too many turbines which made run_model take forever. Reducing the test to 2 turbines resulted in the desired output

[johnjasa]

Nice, great resolution, @jefalon! Did the computed gradients match the FD well?

[jefalon]

not exactly:

-------------------------
Group: Group 'Full Model'
-------------------------
  Full Model: 'cons_comp_0.con_0' wrt 'DVs'
    Analytic Magnitude : 1.354340e+05
          Fd Magnitude : 7.174046e+04 (fd:None)
    Absolute Error (Jan - Jfd) : 2.069118e+05 *

    Relative Error (Jan - Jfd) / Jfd : 2.884172e+00 *

    Raw Analytic Derivative (Jfor)
[[  85131.02062371   -3775.04290323 -105205.2978261    -3559.38237232]]

    Raw FD Derivative (Jfd)
[[-39681.2109375  -1354.7109375  59744.4375       928.1484375]]

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  Full Model: 'obj_comp.obj' wrt 'DVs'
    Analytic Magnitude : 1.032296e-04
          Fd Magnitude : 1.032261e-04 (fd:None)
    Absolute Error (Jan - Jfd) : 1.428940e-08

    Relative Error (Jan - Jfd) / Jfd : 1.384282e-04 *

    Raw Analytic Derivative (Jfor)
[[-3.84775201e-05 -1.73090123e-05  9.38306753e-05  8.48712344e-06]]

    Raw FD Derivative (Jfd)
[[-3.84859741e-05 -1.73160806e-05  9.38223675e-05  8.48341733e-06]]

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The gradient of the objective function seem right, but the power constraints seem very wrong. That said, it seems like OpenMDAO is only using a 1e-6 perturbation.

|    |    |    x_0: 0.0
|    |    |    y_0: -1537.0
|    |    |    x_1: 1e-06
|    |    |    y_1: 1537.0

Since these are in meters, that is like shifting the turbine by a micrometer and expecting a good response. Seem off

[johnjasa]

Oh yes, those are quite wrong for the constraint, the top section. Is that with the power constraint, not the spacing constraint? I think we have more digging to do. There's a chance the FD is wrong, but I wouldn't expect the computed gradients to be of opposite sign like we're seeing.

[jefalon]

I just updated my comment to include more information. Additionally, the min_dist constraint seems to work flawlessly (I just turned it off to emphasize the power constraint)

[johnjasa]

Right on, I hear what you're saying about the step size. We could try a few different step sizes to see if the computed power constraint is correct.

I guess what we're stepping towards is that the power objective has correct gradients, right? But the power constraint doesn't. So we need to find out the implementation difference.

[johnjasa]

Great fixes here, Jeff! All good to merge on my end.