def test_betz_derivatives(self):
import openmdao.api as om
from openmdao.test_suite.test_examples.test_betz_limit import ActuatorDisc
prob = om.Problem()
prob.model.add_subsystem('a_disk', ActuatorDisc())
prob.setup()
prob.check_partials(compact_print=True)
def problem_init():
prob = Problem()
indeps = prob.model.add_subsystem("indeps", IndepVarComp(), promotes=["*"])
indeps.add_output("a", 0.5)
indeps.add_output("Area", 10.0, units="m**2")
indeps.add_output("rho", 1.225, units="kg/m**3")
indeps.add_output("Vu", 10.0, units="m/s")
prob.model.add_subsystem("a_disk", ActuatorDisc(), promotes=["*"])
# setup the optimization
prob.driver = ScipyOptimizeDriver()
prob.driver.options["optimizer"] = "SLSQP"
prob.model.add_design_var("a", lower=0.0, upper=1.0)
prob.model.add_design_var("Area", lower=0.0, upper=1.0)
# negative one so we maximize the objective
prob.model.add_objective("Cp", scaler=-1)
prob.setup()
prob.final_setup()
return prob
def test_model_viewer_has_correct_data_from_optimization_problem(self):
"""
Verify that the correct model structure data exists when stored as compared
to the expected structure, using the ActuatorDisc model.
"""
# build the model
prob = Problem()
indeps = prob.model.add_subsystem('indeps',
IndepVarComp(),
promotes=['*'])
indeps.add_output('a', .5)
indeps.add_output('Area', 10.0, units='m**2')
indeps.add_output('rho', 1.225, units='kg/m**3')
indeps.add_output('Vu', 10.0, units='m/s')
prob.model.add_subsystem('a_disk',
ActuatorDisc(),
promotes_inputs=['a', 'Area', 'rho', 'Vu'])
# setup the optimization
prob.driver = ScipyOptimizeDriver()
prob.driver.options['optimizer'] = 'SLSQP'
prob.model.add_design_var('a', lower=0., upper=1.)
prob.model.add_design_var('Area', lower=0., upper=1.)
# negative one so we maximize the objective
prob.model.add_objective('a_disk.Cp', scaler=-1)
prob.setup()
prob.final_setup()
model_viewer_data = _get_viewer_data(prob)
expected_tree_betz = json.loads("""
{"name": "root", "type": "root", "class": "Group", "component_type": null,
"subsystem_type": "group", "is_parallel": false, "linear_solver": "LN: RUNONCE",
"nonlinear_solver": "NL: RUNONCE", "children": [
{"name": "indeps", "type": "subsystem", "class": "IndepVarComp",
"subsystem_type": "component", "is_parallel": false, "component_type": "indep",
"linear_solver": "", "nonlinear_solver": "", "children": [
{"name": "a", "type": "unknown", "implicit": false, "dtype": "ndarray"},
{"name": "Area", "type": "unknown", "implicit": false, "dtype": "ndarray"},
{"name": "rho", "type": "unknown", "implicit": false, "dtype": "ndarray"},
{"name": "Vu", "type": "unknown", "implicit": false, "dtype": "ndarray"}]},
{"name": "a_disk", "type": "subsystem", "class": "ActuatorDisc",
"subsystem_type": "component", "is_parallel": false, "component_type": "explicit",
"linear_solver": "", "nonlinear_solver": "",
"children": [{"name": "a", "type": "param", "dtype": "ndarray"},
{"name": "Area", "type": "param", "dtype": "ndarray"},
{"name": "rho", "type": "param", "dtype": "ndarray"},
{"name": "Vu", "type": "param", "dtype": "ndarray"},
{"name": "Vr", "type": "unknown", "implicit": false,
"dtype": "ndarray"},
{"name": "Vd", "type": "unknown", "implicit": false,
"dtype": "ndarray"},
{"name": "Ct", "type": "unknown", "implicit": false,
"dtype": "ndarray"},
{"name": "thrust", "type": "unknown", "implicit": false,
"dtype": "ndarray"},
{"name": "Cp", "type": "unknown", "implicit": false,
"dtype": "ndarray"},
{"name": "power", "type": "unknown", "implicit": false,
"dtype": "ndarray"}]}]}
""")
expected_pathnames_betz = json.loads('[]')
expected_conns_betz = json.loads("""
[{"src": "indeps.a", "tgt": "a_disk.a"}, {"src": "indeps.Area", "tgt": "a_disk.Area"},
{"src": "indeps.rho", "tgt": "a_disk.rho"}, {"src": "indeps.Vu", "tgt": "a_disk.Vu"}]
""")
expected_abs2prom_betz = json.loads("""
{"input": {"a_disk.a": "a", "a_disk.Area": "Area", "a_disk.rho": "rho", "a_disk.Vu": "Vu"},
"output": {"indeps.a": "a", "indeps.Area": "Area", "indeps.rho": "rho", "indeps.Vu": "Vu",
"a_disk.Vr": "a_disk.Vr", "a_disk.Vd": "a_disk.Vd", "a_disk.Ct": "a_disk.Ct",
"a_disk.thrust": "a_disk.thrust", "a_disk.Cp": "a_disk.Cp",
"a_disk.power": "a_disk.power"}}
""")
expected_declare_partials_betz = json.loads("""
["indeps.a > indeps.a", "indeps.Area > indeps.Area", "indeps.rho > indeps.rho", "indeps.Vu > indeps.Vu", "a_disk.Vr > a_disk.a", "a_disk.Vr > a_disk.Vu", "a_disk.Vd > a_disk.a", "a_disk.Ct > a_disk.a", "a_disk.thrust > a_disk.a", "a_disk.thrust > a_disk.Area", "a_disk.thrust > a_disk.rho", "a_disk.thrust > a_disk.Vu", "a_disk.Cp > a_disk.a", "a_disk.power > a_disk.a", "a_disk.power > a_disk.Area", "a_disk.power > a_disk.rho", "a_disk.power > a_disk.Vu", "a_disk.Vr > a_disk.Vr", "a_disk.Vd > a_disk.Vd", "a_disk.Ct > a_disk.Ct", "a_disk.thrust > a_disk.thrust", "a_disk.Cp > a_disk.Cp", "a_disk.power > a_disk.power"]
""")
expected_driver_name = 'ScipyOptimizeDriver'
expected_design_vars_names = ['indeps.a', 'indeps.Area']
expected_responses_names = [
'a_disk.Cp',
]
# check expected model tree
self.check_model_viewer_data(
model_viewer_data,
expected_tree_betz,
expected_pathnames_betz,
expected_conns_betz,
expected_abs2prom_betz,
expected_declare_partials_betz,
expected_driver_name,
expected_design_vars_names,
expected_responses_names,
)
def test_betz(self):
from openmdao.api import Problem, ScipyOptimizeDriver, IndepVarComp, ExplicitComponent
class ActuatorDisc(ExplicitComponent):
"""Simple wind turbine model based on actuator disc theory"""
def setup(self):
# Inputs
self.add_input('a', 0.5, desc="Induced Velocity Factor")
self.add_input('Area', 10.0, units="m**2", desc="Rotor disc area")
self.add_input('rho', 1.225, units="kg/m**3", desc="air density")
self.add_input('Vu', 10.0, units="m/s", desc="Freestream air velocity, upstream of rotor")
# Outputs
self.add_output('Vr', 0.0, units="m/s",
desc="Air velocity at rotor exit plane")
self.add_output('Vd', 0.0, units="m/s",
desc="Slipstream air velocity, downstream of rotor")
self.add_output('Ct', 0.0, desc="Thrust Coefficient")
self.add_output('thrust', 0.0, units="N",
desc="Thrust produced by the rotor")
self.add_output('Cp', 0.0, desc="Power Coefficient")
self.add_output('power', 0.0, units="W", desc="Power produced by the rotor")
self.declare_partials('Vr', ['a', 'Vu'])
self.declare_partials('Vd', 'a')
self.declare_partials('Ct', 'a')
self.declare_partials('thrust', ['a', 'Area', 'rho', 'Vu'])
self.declare_partials('Cp', 'a')
self.declare_partials('power', ['a', 'Area', 'rho', 'Vu'])
def compute(self, inputs, outputs):
""" Considering the entire rotor as a single disc that extracts
velocity uniformly from the incoming flow and converts it to
power."""
a = inputs['a']
Vu = inputs['Vu']
qA = .5 * inputs['rho'] * inputs['Area'] * Vu ** 2
outputs['Vd'] = Vd = Vu * (1 - 2 * a)
outputs['Vr'] = .5 * (Vu + Vd)
outputs['Ct'] = Ct = 4 * a * (1 - a)
outputs['thrust'] = Ct * qA
outputs['Cp'] = Cp = Ct * (1 - a)
outputs['power'] = Cp * qA * Vu
def compute_partials(self, inputs, J):
""" Jacobian of partial derivatives."""
a = inputs['a']
Vu = inputs['Vu']
Area = inputs['Area']
rho = inputs['rho']
# pre-compute commonly needed quantities
a_times_area = a * Area
one_minus_a = 1.0 - a
a_area_rho_vu = a_times_area * rho * Vu
J['Vr', 'a'] = -Vu
J['Vr', 'Vu'] = one_minus_a
J['Vd', 'a'] = -2.0 * Vu
J['Ct', 'a'] = 4.0 - 8.0 * a
J['thrust', 'a'] = .5 * rho * Vu**2 * Area * J['Ct', 'a']
J['thrust', 'Area'] = 2.0 * Vu**2 * a * rho * one_minus_a
J['thrust', 'rho'] = 2.0 * a_times_area * Vu ** 2 * (one_minus_a)
J['thrust', 'Vu'] = 4.0 * a_area_rho_vu * (one_minus_a)
J['Cp', 'a'] = 4.0 * a * (2.0 * a - 2.0) + 4.0 * (one_minus_a)**2
J['power', 'a'] = 2.0 * Area * Vu**3 * a * rho * (
2.0 * a - 2.0) + 2.0 * Area * Vu**3 * rho * one_minus_a ** 2
J['power', 'Area'] = 2.0 * Vu**3 * a * rho * one_minus_a ** 2
J['power', 'rho'] = 2.0 * a_times_area * Vu ** 3 * (one_minus_a)**2
J['power', 'Vu'] = 6.0 * Area * Vu**2 * a * rho * one_minus_a**2
# build the model
prob = Problem()
indeps = prob.model.add_subsystem('indeps', IndepVarComp(), promotes=['*'])
indeps.add_output('a', .5)
indeps.add_output('Area', 10.0, units='m**2')
indeps.add_output('rho', 1.225, units='kg/m**3')
indeps.add_output('Vu', 10.0, units='m/s')
prob.model.add_subsystem('a_disk', ActuatorDisc(),
promotes_inputs=['a', 'Area', 'rho', 'Vu'])
# setup the optimization
prob.driver = ScipyOptimizeDriver()
prob.driver.options['optimizer'] = 'SLSQP'
prob.model.add_design_var('a', lower=0., upper=1.)
prob.model.add_design_var('Area', lower=0., upper=1.)
# negative one so we maximize the objective
prob.model.add_objective('a_disk.Cp', scaler=-1)
prob.setup()
prob.run_driver()
# minimum value
assert_rel_error(self, prob['a_disk.Cp'], 16./27., 1e-4)
assert_rel_error(self, prob['a'], 0.33333, 1e-4)
def test_model_viewer_has_correct_data_from_optimization_problem(self):
"""
Verify that the correct model structure data exists when stored as compared
to the expected structure, using the ActuatorDisc model.
"""
# build the model
prob = om.Problem()
indeps = prob.model.add_subsystem('indeps',
om.IndepVarComp(),
promotes=['*'])
indeps.add_output('a', .5)
indeps.add_output('Area', 10.0, units='m**2')
indeps.add_output('rho', 1.225, units='kg/m**3')
indeps.add_output('Vu', 10.0, units='m/s')
prob.model.add_subsystem('a_disk',
ActuatorDisc(),
promotes_inputs=['a', 'Area', 'rho', 'Vu'])
# setup the optimization
prob.driver = om.ScipyOptimizeDriver()
prob.driver.options['optimizer'] = 'SLSQP'
prob.model.add_design_var('a', lower=0., upper=1.)
prob.model.add_design_var('Area', lower=0., upper=1.)
# negative one so we maximize the objective
prob.model.add_objective('a_disk.Cp', scaler=-1)
prob.setup()
prob.final_setup()
model_viewer_data = _get_viewer_data(prob)
# To generate the reference JSON file, use this code
# from openmdao.utils.testing_utils import _ModelViewerDataTreeEncoder
# with open('betz_tree_new.json', 'w') as outfile:
# json.dump(model_viewer_data['tree'], outfile,cls=_ModelViewerDataTreeEncoder, indent=4)
with open(os.path.join(self.parent_dir,
'betz_tree.json')) as json_file:
expected_tree_betz = json.load(json_file)
expected_pathnames_betz = json.loads('[]')
expected_conns_betz = json.loads("""
[{"src": "indeps.a", "tgt": "a_disk.a"}, {"src": "indeps.Area", "tgt": "a_disk.Area"},
{"src": "indeps.rho", "tgt": "a_disk.rho"}, {"src": "indeps.Vu", "tgt": "a_disk.Vu"}]
""")
expected_abs2prom_betz = json.loads("""
{"input": {"a_disk.a": "a", "a_disk.Area": "Area", "a_disk.rho": "rho", "a_disk.Vu": "Vu"},
"output": {"indeps.a": "a", "indeps.Area": "Area", "indeps.rho": "rho", "indeps.Vu": "Vu",
"a_disk.Vr": "a_disk.Vr", "a_disk.Vd": "a_disk.Vd", "a_disk.Ct": "a_disk.Ct",
"a_disk.thrust": "a_disk.thrust", "a_disk.Cp": "a_disk.Cp",
"a_disk.power": "a_disk.power"}}
""")
expected_declare_partials_betz = json.loads("""
["a_disk.Vr > a_disk.a", "a_disk.Vr > a_disk.Vu", "a_disk.Vd > a_disk.a", "a_disk.Ct > a_disk.a", "a_disk.thrust > a_disk.a", "a_disk.thrust > a_disk.Area", "a_disk.thrust > a_disk.rho", "a_disk.thrust > a_disk.Vu", "a_disk.Cp > a_disk.a", "a_disk.power > a_disk.a", "a_disk.power > a_disk.Area", "a_disk.power > a_disk.rho", "a_disk.power > a_disk.Vu"]
""")
expected_driver_name = 'ScipyOptimizeDriver'
expected_design_vars_names = ['indeps.a', 'indeps.Area']
expected_responses_names = [
'a_disk.Cp',
]
# check expected model tree
self.check_model_viewer_data(
model_viewer_data,
expected_tree_betz,
expected_pathnames_betz,
expected_conns_betz,
expected_abs2prom_betz,
expected_declare_partials_betz,
expected_driver_name,
expected_design_vars_names,
expected_responses_names,
)