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MDO formulations for a toy example in aerostructure¶
from __future__ import annotations
from gemseo import configure_logger
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo import generate_n2_plot
from gemseo.problems.aerostructure.aerostructure_design_space import (
AerostructureDesignSpace,
)
configure_logger()
algo_options = {
"xtol_rel": 1e-8,
"xtol_abs": 1e-8,
"ftol_rel": 1e-8,
"ftol_abs": 1e-8,
"ineq_tolerance": 1e-5,
"eq_tolerance": 1e-3,
}
Traceback (most recent call last):
File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/checkouts/develop/doc_src/_examples/mdo/plot_aerostructure.py", line 31, in <module>
from gemseo.problems.aerostructure.aerostructure_design_space import (
ModuleNotFoundError: No module named 'gemseo.problems.aerostructure'
Create discipline¶
First, we create disciplines (aero, structure, mission) with dummy formulas
using the AnalyticDiscipline
class.
aero_formulas = {
"drag": "0.1*((sweep/360)**2 + 200 + thick_airfoils**2-thick_airfoils -4*displ)",
"forces": "10*sweep + 0.2*thick_airfoils-0.2*displ",
"lift": "(sweep + 0.2*thick_airfoils-2.*displ)/3000.",
}
aerodynamics = create_discipline(
"AnalyticDiscipline", name="Aerodynamics", expressions=aero_formulas
)
struc_formulas = {
"mass": "4000*(sweep/360)**3 + 200000 + 100*thick_panels +200.0*forces",
"reserve_fact": "-3*sweep -6*thick_panels+0.1*forces+55",
"displ": "2*sweep + 3*thick_panels-2.*forces",
}
structure = create_discipline(
"AnalyticDiscipline", name="Structure", expressions=struc_formulas
)
mission_formulas = {"range": "8e11*lift/(mass*drag)"}
mission = create_discipline(
"AnalyticDiscipline", name="Mission", expressions=mission_formulas
)
disciplines = [aerodynamics, structure, mission]
We can see that structure and aerodynamics are strongly coupled:
generate_n2_plot(disciplines, save=False, show=True)
Create an MDO scenario with MDF formulation¶
Then, we create an MDO scenario based on the MDF formulation
design_space = AerostructureDesignSpace()
scenario = create_scenario(
disciplines,
"MDF",
"range",
design_space,
maximize_objective=True,
)
scenario.add_constraint("reserve_fact", constraint_type="ineq", value=0.5)
scenario.add_constraint("lift", value=0.5)
scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 10, "algo_options": algo_options})
scenario.post_process("OptHistoryView", save=False, show=True)
Create an MDO scenario with bilevel formulation¶
Then, we create an MDO scenario based on the bilevel formulation
sub_scenario_options = {
"max_iter": 5,
"algo": "NLOPT_SLSQP",
"algo_options": algo_options,
}
design_space_ref = AerostructureDesignSpace()
Create the aeronautics sub-scenario¶
For this purpose, we create a first sub-scenario to maximize the range with respect to the thick airfoils, based on the aerodynamics discipline.
aero_scenario = create_scenario(
[aerodynamics, mission],
"DisciplinaryOpt",
"range",
design_space_ref.filter(["thick_airfoils"], copy=True),
maximize_objective=True,
)
aero_scenario.default_inputs = sub_scenario_options
Create the structure sub-scenario¶
We create a second sub-scenario to maximize the range with respect to the thick panels, based on the structure discipline.
struct_scenario = create_scenario(
[structure, mission],
"DisciplinaryOpt",
"range",
design_space_ref.filter(["thick_panels"], copy=True),
maximize_objective=True,
)
struct_scenario.default_inputs = sub_scenario_options
Create the system scenario¶
Lastly, we build a system scenario to maximize the range with respect to the sweep, which is a shared variable, based on the previous sub-scenarios.
design_space_system = design_space_ref.filter(["sweep"], copy=True)
system_scenario = create_scenario(
[aero_scenario, struct_scenario, mission],
"BiLevel",
"range",
design_space_system,
maximize_objective=True,
inner_mda_name="MDAJacobi",
tolerance=1e-8,
)
system_scenario.add_constraint("reserve_fact", constraint_type="ineq", value=0.5)
system_scenario.add_constraint("lift", value=0.5)
system_scenario.execute({
"algo": "NLOPT_COBYLA",
"max_iter": 7,
"algo_options": algo_options,
})
system_scenario.post_process("OptHistoryView", save=False, show=True)
Total running time of the script: (0 minutes 0.001 seconds)