Optimizing with OpenMDAO¶
If you don't already have OpenMDAO, you can install it with pip install OpenMDAO
OpenMDAO doesn't actually do any of the optimization, it is simply a convenient framework for forming models for optimization. It installs SciPy along with its optimizer as a dependency during the installation process. If you want access to additional optimizers, I recommend the pyOptSparse library.
Adding OptVL to a model¶
OptVL comes with OpenMDAO components to make it simple to include it into an OpenMDAO model. All the hard/tedious work of specifying how the gradient functions should be called is already done for you in this group. Simply import the group and add it to your model.
import openmdao.api as om
from optvl import OVLGroup
model = om.Group()
model.add_subsystem("ovlsolver", OVLGroup(geom_file="aircraft.avl", mass_file="aircraft.mass"))
alpha and beta are automatically exposed as inputs to the group.
The geometric variables of each surface are added as inputs of the form <surface name>:<geo variable>.
To turn on other inputs such as the reference values and case parameters, use the "input_param_vals" and "input_ref_vals" keywords to the group, respectively.
model.add_subsystem("ovlsolver", OVLGroup(geom_file="aircraft.avl",input_param_vals=True, input_ref_vals=True))
CL, CD, and CM are automatically added as outputs.
To add stability derivatives or control surface derivatives as outputs, just use the output_stability_derivs and output_con_surf_derivs keyword arguments to the group to turn them on.
model.add_subsystem("ovlsolver", OVLGroup(geom_file="aircraft.avl", output_stability_derivs=True, output_con_surf_derivs=True))
Output options¶
To write out the AVL geometry and the TecPlot surface CP file at every time step, use the option write_grid=True.
Additionally, if you are not interested in viewing the files in ParaView and instead only want to use TecPlot 360, then I also recommend adding write_grid_sol_time=True.
model.add_subsystem("ovlsolver", OVLGroup(geom_file="aircraft.avl", write_grid=True))
# for easier postprocessing in TecPlot 360 (not compatible with ParaView)
model.add_subsystem("ovlsolver", OVLGroup(geom_file="aircraft.avl", write_grid=True, write_grid_sol_time=True ))
Setting design variables¶
For simple optimization problems, the inputs and outputs can be directly added as design variables, objective functions, and constraints.
# directly setting the inputs as design variables
model.add_design_var("ovlsolver.Wing:aincs", lower=-10, upper=10)
model.add_design_var("ovlsolver.Elevator", lower=-10, upper=10)
# the outputs of OptVL can be used as constraints
model.add_constraint("ovlsolver.CL", equals=1.5)
model.add_constraint("ovlsolver.CM", equals=0.0, scaler=1e3)
# the scaler values bring the objective function to ~ order 1 for the optimizer
model.add_objective("ovlsolver.CD", scaler=1e3)
Setting Optimizer options and running¶
After you have set up your model you will have to apply a driver. In our case our driver is the SLSQP optimizer of SciPy, but you could also apply other drivers to the model such as the DOE driver.
The next step is to tell OpenMDAO we are done with our problem, and it can be set up with prob.setup(mode='rev')
Warning
When using the OptVL group we must setup the problem with mode='rev'.
OptVL uses reverse mode derivatives because in general we will have more geometric variables than output functions of interest.
The line with om.n2 creates an N2 diagram, which is helpful for examining our model.
See this page for more information on the N2 diagram.
prob = om.Problem(model)
prob.driver = om.ScipyOptimizeDriver()
prob.driver.options['optimizer'] = 'SLSQP'
prob.driver.options['debug_print'] = ["desvars", "ln_cons", "nl_cons", "objs"]
prob.driver.options['tol'] = 1e-6
prob.driver.options['disp'] = True
prob.setup(mode='rev')
om.n2(prob, show_browser=False, outfile="vlm_opt.html")
prob.run_driver()
Example script¶
Below is an OpenMDAO script analogous to the SciPy-based example.
"""A openmdao based optimization for an aicraft using optvl"""
import openmdao.api as om
from optvl import OVLGroup
model = om.Group()
model.add_subsystem("ovlsolver", OVLGroup(geom_file="aircraft.avl"))
# look at vlm_opt.html to see all the design variables and add them here
model.add_design_var("ovlsolver.Wing:aincs", lower=-15, upper=15)
model.add_design_var("ovlsolver.Elevator", lower=-10, upper=10)
# the outputs of OptVL can be used as contraints
model.add_constraint("ovlsolver.CL", equals=1.5)
model.add_constraint("ovlsolver.CM", equals=0.0, scaler=1e3)
# the scaler values bring the objective functinon to ~ order 1 for the optimizer
model.add_objective("ovlsolver.CD", scaler=1e3)
prob = om.Problem(model)
prob.driver = om.ScipyOptimizeDriver()
prob.driver.options['optimizer'] = 'SLSQP'
prob.driver.options['debug_print'] = ["desvars", "ln_cons", "nl_cons", "objs"]
prob.driver.options['tol'] = 1e-10
prob.driver.options['disp'] = True
prob.setup(mode='rev')
# this causes and error with OpenMDAO 3.38 (https://github.com/OpenMDAO/OpenMDAO/issues/3521)
# om.n2(prob, show_browser=False, outfile="vlm_opt.html")
prob.run_driver()
om.n2(prob, show_browser=False, outfile="vlm_opt.html")
del_ele = prob.get_val('ovlsolver.Elevator')
print(f'ovlsolver.Elevator {del_ele}')
aincs = prob.get_val('ovlsolver.Wing:aincs')
print(f'ovlsolver.Wing:aincs {aincs}')
cd = prob.get_val('ovlsolver.CD')
print(f'ovlsolver.CD {cd}')
# do this instead if you want to check derivatives
# prob.run_model()
# prob.check_totals()
Optimization terminated successfully (Exit mode 0)
Current function value: 85.54669279688602
Iterations: 19
Function evaluations: 19
Gradient evaluations: 19
Optimization Complete
-----------------------------------
ovlsolver.Elevator [0.10802368]
ovlsolver.Wing:aincs [11.46493221 1.92748591 2.14445549 2.27131259 -4.81944669]
ovlsolver.CD [0.08554669]