def test_remote_voi(self):
prob = Problem()
prob.model.add_subsystem('par', ParallelGroup())
prob.model.par.add_subsystem('G1', Mygroup())
prob.model.par.add_subsystem('G2', Mygroup())
prob.model.add_subsystem('Obj', ExecComp('obj=y1+y2'))
prob.model.connect('par.G1.y', 'Obj.y1')
prob.model.connect('par.G2.y', 'Obj.y2')
prob.model.add_objective('Obj.obj')
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SLSQP'
prob.setup(vector_class=PETScVector)
prob.run_driver()
J = prob.compute_totals(of=['Obj.obj', 'par.G1.c', 'par.G2.c'],
wrt=['par.G1.x', 'par.G2.x'])
assert_rel_error(self, J['Obj.obj', 'par.G1.x'], np.array([[2.0]]), 1e-6)
assert_rel_error(self, J['Obj.obj', 'par.G2.x'], np.array([[2.0]]), 1e-6)
assert_rel_error(self, J['par.G1.c', 'par.G1.x'], np.array([[1.0]]), 1e-6)
assert_rel_error(self, J['par.G1.c', 'par.G2.x'], np.array([[0.0]]), 1e-6)
assert_rel_error(self, J['par.G2.c', 'par.G1.x'], np.array([[0.0]]), 1e-6)
assert_rel_error(self, J['par.G2.c', 'par.G2.x'], np.array([[1.0]]), 1e-6)
def set_optimizer(self, optStr):
assert type(optStr) == type(''), 'Input optimizer must be a string'
self.optimizer = optStr.upper()
# Reset all design variables and constraints
self.design_variables = []
self.constraints = []
self.objective = None
# Establish the optimization driver
if self.optimizer in ['SOGA','SOPSO','NM','SUBPLEX']:
from openmdao.api import HeuristicDriverParallel
self.prob.driver = HeuristicDriverParallel()
#elif self.optimizer in ['SUBPLEX']:
#from openmdao.api import HeuristicDriver
#self.prob.driver = HeuristicDriver()
elif self.optimizer in ['COBYLA','SLSQP']:
self.prob.driver = ScipyOptimizer()
elif self.optimizer in ['CONMIN', 'PSQP','SNOPT','NSGA2','ALPSO']:
from openmdao.api import pyOptSparseDriver
self.prob.driver = pyOptSparseDriver()
else:
raise ValueError('Unknown or unworking optimizer. '+self.optimizer)
# Set default options
self.prob.driver.options['optimizer'] = self.optimizer
if self.optimizer == 'CONMIN':
self.prob.driver.opt_settings['ITMAX'] = 1000
elif self.optimizer in ['PSQP']:
self.prob.driver.opt_settings['MIT'] = 1000
elif self.optimizer in ['SOGA','SOPSO','NM','SUBPLEX']:
self.prob.driver.options['population'] = 50
self.prob.driver.options['generations'] = 500
elif self.optimizer in ['NSGA2']:
self.prob.driver.opt_settings['PopSize'] = 200
self.prob.driver.opt_settings['maxGen'] = 500
elif self.optimizer in ['SNOPT']:
self.prob.driver.opt_settings['Iterations limit'] = 500
self.prob.driver.opt_settings['Major optimality tolerance'] = 1e-4
self.prob.driver.opt_settings['Major feasibility tolerance'] = 1e-6
self.prob.driver.opt_settings['Minor feasibility tolerance'] = 1e-6
self.prob.driver.opt_settings['Function precision'] = 1e-8
elif self.optimizer in ['COBYLA','SLSQP']:
self.prob.driver.options['tol'] = 1e-6
self.prob.driver.options['maxiter'] = 1000
def benchmark_mppt(self):
model = MPPT_MDP()
model.add_design_var('pt0.param.CP_Isetpt', lower=0., upper=0.4)
model.add_design_var('pt1.param.CP_Isetpt', lower=0., upper=0.4)
model.add_objective('perf.result')
# create problem and add optimizer
prob = Problem(model)
prob.driver = pyOptSparseDriver(optimizer='SNOPT')
prob.driver.opt_settings = {
'Major optimality tolerance': 1e-3,
'Major feasibility tolerance': 1.0e-5,
'Iterations limit': 500000000,
'New basis file': 10
}
prob.setup()
prob.run_driver()
assert_rel_error(self, prob['perf.result'], -9.4308562238E+03, 1e-6)
# prob = Problem(model)
# prob.setup()
# prob.run_model()
# print(prob['paraboloid.mean_QoI'])
# print(prob['paraboloid.mean_xi'])
#------------ Run optimization using SNOPT
prob = Problem()
indeps = prob.model.add_subsystem('indeps', IndepVarComp(), promotes=['*'])
indeps.add_output('mean_xi', 10 * np.ones(3))
prob.model.add_subsystem('paraboloid',
Paraboloid(),
promotes_inputs=['mean_xi'])
# Set up the Optimization
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.driver.opt_settings['Major optimality tolerance'] = 3e-7
prob.driver.opt_settings['Major feasibility tolerance'] = 3e-7
prob.driver.opt_settings['Major iterations limit'] = 1000
prob.driver.opt_settings['Verify level'] = -1
prob.model.add_design_var('mean_xi',
lower=-20 * np.ones(3),
upper=20 * np.ones(3))
prob.model.add_objective('paraboloid.mean_QoI')
prob.setup()
prob.run_driver()
print(prob['paraboloid.mean_QoI'])
print(prob['paraboloid.mean_xi'])
def test_brachistochrone_for_docs_coloring_demo_solve_segments(self):
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.plotting import plot_results
from dymos.examples.brachistochrone import BrachistochroneODE
from openmdao.utils.general_utils import set_pyoptsparse_opt
#
# Initialize the Problem and the optimization driver
#
p = om.Problem(model=om.Group())
_, optimizer = set_pyoptsparse_opt('IPOPT', fallback=True)
p.driver = om.pyOptSparseDriver(optimizer=optimizer)
p.driver.opt_settings['print_level'] = 4
# p.driver.declare_coloring()
#
# Create a trajectory and add a phase to it
#
traj = p.model.add_subsystem('traj', dm.Trajectory())
#
# In this case the phase has many segments to demonstrate the impact of coloring.
#
phase = traj.add_phase('phase0',
dm.Phase(ode_class=BrachistochroneODE,
transcription=dm.Radau(num_segments=100,
solve_segments='forward')))
#
# Set the variables
#
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10))
phase.add_state('x', fix_initial=True)
phase.add_state('y', fix_initial=True)
phase.add_state('v', fix_initial=True)
phase.add_control('theta', continuity=True, rate_continuity=True,
units='deg', lower=0.01, upper=179.9)
phase.add_parameter('g', units='m/s**2', val=9.80665)
#
# Replace state terminal bounds with nonlinear constraints
#
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
#
# Minimize time at the end of the phase
#
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
#
# Setup the Problem
#
p.setup()
#
# Set the initial values
#
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 2.0
p['traj.phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input')
p['traj.phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input')
p['traj.phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input')
#
# Solve for the optimal trajectory
#
dm.run_problem(p)
# Test the results
assert_near_equal(p.get_val('traj.phase0.timeseries.time')[-1], 1.8016,
tolerance=1.0E-3)
# Generate the explicitly simulated trajectory
exp_out = traj.simulate()
plot_results([('traj.phase0.timeseries.states:x', 'traj.phase0.timeseries.states:y',
'x (m)', 'y (m)'),
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.controls:theta',
'time (s)', 'theta (deg)')],
title='Brachistochrone Solution\nRadau Pseudospectral Method',
p_sol=p, p_sim=exp_out)
plt.show()
def min_time_climb(optimizer='SLSQP', num_seg=3, transcription='gauss-lobatto',
transcription_order=3, force_alloc_complex=False):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.declare_coloring()
if optimizer == 'SNOPT':
p.driver.opt_settings['Major iterations limit'] = 1000
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings['Function precision'] = 1.0E-12
p.driver.opt_settings['Linesearch tolerance'] = 0.1
p.driver.opt_settings['Major step limit'] = 0.5
t = {'gauss-lobatto': dm.GaussLobatto(num_segments=num_seg, order=transcription_order),
'radau-ps': dm.Radau(num_segments=num_seg, order=transcription_order),
'runge-kutta': dm.RungeKutta(num_segments=num_seg)}
traj = dm.Trajectory()
phase = dm.Phase(ode_class=MinTimeClimbODE, transcription=t[transcription])
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj', traj)
phase.set_time_options(fix_initial=True, duration_bounds=(50, 400),
duration_ref=100.0)
phase.add_state('r', fix_initial=True, lower=0, upper=1.0E6,
ref=1.0E3, defect_ref=1.0E3, units='m',
rate_source='flight_dynamics.r_dot')
phase.add_state('h', fix_initial=True, lower=0, upper=20000.0,
ref=1.0E2, defect_ref=1.0E2, units='m',
rate_source='flight_dynamics.h_dot', targets=['h'])
phase.add_state('v', fix_initial=True, lower=10.0,
ref=1.0E2, defect_ref=1.0E2, units='m/s',
rate_source='flight_dynamics.v_dot', targets=['v'])
phase.add_state('gam', fix_initial=True, lower=-1.5, upper=1.5,
ref=1.0, defect_ref=1.0, units='rad',
rate_source='flight_dynamics.gam_dot', targets=['gam'])
phase.add_state('m', fix_initial=True, lower=10.0, upper=1.0E5,
ref=1.0E3, defect_ref=1.0E3, units='kg',
rate_source='prop.m_dot', targets=['m'])
phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0,
rate_continuity=True, rate_continuity_scaler=100.0,
rate2_continuity=False, targets=['alpha'])
phase.add_parameter('S', val=49.2386, units='m**2', opt=False, targets=['S'])
phase.add_parameter('Isp', val=1600.0, units='s', opt=False, targets=['Isp'])
phase.add_parameter('throttle', val=1.0, opt=False, targets=['throttle'])
phase.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3, units='m')
phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0)
phase.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad')
phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
# Unnecessary but included to test capability
phase.add_path_constraint(name='alpha', units='deg', lower=-8, upper=8)
phase.add_path_constraint(name='time', lower=0, upper=400)
phase.add_path_constraint(name='time_phase', lower=0, upper=400)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', ref=1.0)
# test mixing wildcard ODE variable expansion and unit overrides
phase.add_timeseries_output(['aero.*', 'prop.thrust', 'prop.m_dot'],
units={'aero.f_lift': 'lbf', 'prop.thrust': 'lbf'})
p.model.linear_solver = om.DirectSolver()
p.setup(check=True, force_alloc_complex=force_alloc_complex)
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 300.0
p['traj.phase0.states:r'] = phase.interpolate(ys=[0.0, 111319.54], nodes='state_input')
p['traj.phase0.states:h'] = phase.interpolate(ys=[100.0, 20000.0], nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[135.964, 283.159], nodes='state_input')
p['traj.phase0.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='state_input')
p['traj.phase0.states:m'] = phase.interpolate(ys=[19030.468, 16841.431], nodes='state_input')
p['traj.phase0.controls:alpha'] = phase.interpolate(ys=[0.0, 0.0], nodes='control_input')
p.run_driver()
return p
def test_ex_double_integrator_input_times(self, compressed=True):
"""
Tests that externally connected t_initial and t_duration function as expected.
"""
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring()
times_ivc = p.model.add_subsystem('times_ivc',
om.IndepVarComp(),
promotes_outputs=['t0', 'tp'])
times_ivc.add_output(name='t0', val=0.0, units='s')
times_ivc.add_output(name='tp', val=1.0, units='s')
transcription = dm.Radau(num_segments=20,
order=3,
compressed=compressed)
phase = dm.Phase(ode_class=DoubleIntegratorODE,
transcription=transcription)
p.model.add_subsystem('phase0', phase)
p.model.connect('t0', 'phase0.t_initial')
p.model.connect('tp', 'phase0.t_duration')
phase.set_time_options(input_initial=True,
input_duration=True,
units='s')
phase.add_state('x', fix_initial=True, rate_source='v', units='m')
phase.add_state('v',
fix_initial=True,
fix_final=True,
rate_source='u',
units='m/s')
phase.add_control('u',
units='m/s**2',
scaler=0.01,
continuity=False,
rate_continuity=False,
rate2_continuity=False,
lower=-1.0,
upper=1.0)
# Maximize distance travelled in one second.
phase.add_objective('x', loc='final', scaler=-1)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['t0'] = 0.0
p['tp'] = 1.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 0.25],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 0],
nodes='state_input')
p['phase0.controls:u'] = phase.interpolate(ys=[1, -1],
nodes='control_input')
p.run_driver()
def two_burn_orbit_raise_problem(transcription='gauss-lobatto', optimizer='SLSQP', r_target=3.0,
transcription_order=3, compressed=False,
show_output=True):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.declare_coloring()
if optimizer == 'SNOPT':
p.driver.opt_settings['Major iterations limit'] = 100
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
if show_output:
p.driver.opt_settings['iSumm'] = 6
elif optimizer == 'IPOPT':
p.driver.opt_settings['hessian_approximation'] = 'limited-memory'
p.driver.opt_settings['nlp_scaling_method'] = 'gradient-based'
p.driver.opt_settings['print_level'] = 4
p.driver.opt_settings['linear_solver'] = 'mumps'
p.driver.opt_settings['mu_strategy'] = 'adaptive'
# p.driver.opt_settings['derivative_test'] = 'first-order'
traj = make_traj(transcription=transcription, transcription_order=transcription_order,
compressed=compressed)
p.model.add_subsystem('traj', subsys=traj)
# Needed to move the direct solver down into the phases for use with MPI.
# - After moving down, used fewer iterations (about 30 less)
p.setup(check=True)
# Set Initial Guesses
p.set_val('traj.parameters:c', value=1.5, units='DU/TU')
burn1 = p.model.traj.phases.burn1
burn2 = p.model.traj.phases.burn2
coast = p.model.traj.phases.coast
if burn1 in p.model.traj.phases._subsystems_myproc:
p.set_val('traj.burn1.t_initial', value=0.0)
p.set_val('traj.burn1.t_duration', value=2.25)
p.set_val('traj.burn1.states:r', value=burn1.interpolate(ys=[1, 1.5],
nodes='state_input'))
p.set_val('traj.burn1.states:theta', value=burn1.interpolate(ys=[0, 1.7],
nodes='state_input'))
p.set_val('traj.burn1.states:vr', value=burn1.interpolate(ys=[0, 0],
nodes='state_input'))
p.set_val('traj.burn1.states:vt', value=burn1.interpolate(ys=[1, 1],
nodes='state_input'))
p.set_val('traj.burn1.states:accel', value=burn1.interpolate(ys=[0.1, 0],
nodes='state_input'))
p.set_val('traj.burn1.states:deltav', value=burn1.interpolate(ys=[0, 0.1],
nodes='state_input'))
p.set_val('traj.burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0], nodes='control_input'))
if coast in p.model.traj.phases._subsystems_myproc:
p.set_val('traj.coast.t_initial', value=2.25)
p.set_val('traj.coast.t_duration', value=3.0)
p.set_val('traj.coast.states:r', value=coast.interpolate(ys=[1.3, 1.5],
nodes='state_input'))
p.set_val('traj.coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7], nodes='state_input'))
p.set_val('traj.coast.states:vr', value=coast.interpolate(ys=[0.3285, 0],
nodes='state_input'))
p.set_val('traj.coast.states:vt', value=coast.interpolate(ys=[0.97, 1],
nodes='state_input'))
p.set_val('traj.coast.states:accel', value=coast.interpolate(ys=[0, 0],
nodes='state_input'))
if burn2 in p.model.traj.phases._subsystems_myproc:
p.set_val('traj.burn2.t_initial', value=5.25)
p.set_val('traj.burn2.t_duration', value=1.75)
p.set_val('traj.burn2.states:r', value=burn2.interpolate(ys=[1, r_target],
nodes='state_input'))
p.set_val('traj.burn2.states:theta', value=burn2.interpolate(ys=[0, 4.0],
nodes='state_input'))
p.set_val('traj.burn2.states:vr', value=burn2.interpolate(ys=[0, 0],
nodes='state_input'))
p.set_val('traj.burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / r_target)],
nodes='state_input'))
p.set_val('traj.burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('traj.burn2.states:accel', value=burn2.interpolate(ys=[0.1, 0],
nodes='state_input'))
p.set_val('traj.burn2.controls:u1', value=burn2.interpolate(ys=[0, 0],
nodes='control_input'))
dm.run_problem(p, run_driver=False, simulate=True, make_plots=True)
return p
def test_two_burn_orbit_raise_for_docs(self):
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, pyOptSparseDriver, DirectSolver, SqliteRecorder
from openmdao.utils.assert_utils import assert_rel_error
from openmdao.utils.general_utils import set_pyoptsparse_opt
from dymos import Phase, Trajectory
from dymos.examples.finite_burn_orbit_raise.finite_burn_eom import FiniteBurnODE
traj = Trajectory()
p = Problem(model=traj)
p.driver = pyOptSparseDriver()
_, optimizer = set_pyoptsparse_opt('SNOPT', fallback=False)
p.driver.options['optimizer'] = 'SNOPT'
p.driver.options['dynamic_simul_derivs'] = True
traj.add_design_parameter('c', opt=False, val=1.5)
# First Phase (burn)
burn1 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('theta',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-30,
upper=30)
# Second Phase (Coast)
coast = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
duration_ref=10)
coast.set_state_options('r',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vr',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vt',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
# Third Phase (burn)
burn2 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
initial_ref=10)
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-30,
upper=30)
burn2.add_objective('deltav', loc='final', scaler=1.0)
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.driver.add_recorder(
SqliteRecorder('two_burn_orbit_raise_example_for_docs.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('design_parameters:c', value=1.5)
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val(
'burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'),
)
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0],
nodes='control_input'))
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7],
nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.run_driver()
assert_rel_error(self,
traj.get_values('deltav', flat=True)[-1],
0.3995,
tolerance=2.0E-3)
# Plot results
exp_out = traj.simulate(times=50, num_procs=3)
fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)
span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)
ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')
ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)
ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)
t_sol = traj.get_values('time')
x_sol = traj.get_values('pos_x')
y_sol = traj.get_values('pos_y')
dv_sol = traj.get_values('deltav')
u1_sol = traj.get_values('u1', units='deg')
t_exp = exp_out.get_values('time')
x_exp = exp_out.get_values('pos_x')
y_exp = exp_out.get_values('pos_y')
dv_exp = exp_out.get_values('deltav')
u1_exp = exp_out.get_values('u1', units='deg')
for phase_name in ['burn1', 'coast', 'burn2']:
ax_u1.plot(t_sol[phase_name], u1_sol[phase_name], 'ro', ms=3)
ax_u1.plot(t_exp[phase_name], u1_exp[phase_name], 'b-')
ax_deltav.plot(t_sol[phase_name], dv_sol[phase_name], 'ro', ms=3)
ax_deltav.plot(t_exp[phase_name], dv_exp[phase_name], 'b-')
ax_xy.plot(x_sol[phase_name],
y_sol[phase_name],
'ro',
ms=3,
label='implicit' if phase_name == 'burn1' else None)
ax_xy.plot(x_exp[phase_name],
y_exp[phase_name],
'b-',
label='explicit' if phase_name == 'burn1' else None)
plt.show()
def setUp(self):
# --- geometry ----
# --- geometry ----
z_param = np.array([0.0, 43.8, 87.6])
d_param = np.array([6.0, 4.935, 3.87])
t_param = np.array([0.027*1.3, 0.023*1.3, 0.019*1.3])
n = 15
z_full = np.linspace(0.0, 87.6, n)
L_reinforced = 30.0*np.ones(n) # [m] buckling length
theta_stress = 0.0*np.ones(n)
yaw = 0.0
# --- material props ---
E = 210e9*np.ones(n)
G = 80.8e9*np.ones(n)
rho = 8500.0*np.ones(n)
sigma_y = 450.0e6*np.ones(n)
# --- spring reaction data. Use float('inf') for rigid constraints. ---
kidx = np.array([0], dtype=int) # applied at base
kx = np.array([float('inf')])
ky = np.array([float('inf')])
kz = np.array([float('inf')])
ktx = np.array([float('inf')])
kty = np.array([float('inf')])
ktz = np.array([float('inf')])
nK = len(kidx)
# --- extra mass ----
midx = np.array([n-1], dtype=int) # RNA mass at top
m = np.array([285598.8])
mIxx = np.array([1.14930678e+08])
mIyy = np.array([2.20354030e+07])
mIzz = np.array([1.87597425e+07])
mIxy = np.array([0.00000000e+00])
mIxz = np.array([5.03710467e+05])
mIyz = np.array([0.00000000e+00])
mrhox = np.array([-1.13197635])
mrhoy = np.array([0.])
mrhoz = np.array([0.50875268])
nMass = len(midx)
addGravityLoadForExtraMass = True
# -----------
# --- wind ---
wind_zref = 90.0
wind_z0 = 0.0
shearExp = 0.2
# ---------------
# if addGravityLoadForExtraMass=True be sure not to double count by adding those force here also
# # --- loading case 1: max Thrust ---
wind_Uref1 = 11.73732
plidx1 = np.array([n-1], dtype=int) # at top
Fx1 = np.array([1284744.19620519])
Fy1 = np.array([0.])
Fz1 = np.array([-2914124.84400512])
Mxx1 = np.array([3963732.76208099])
Myy1 = np.array([-2275104.79420872])
Mzz1 = np.array([-346781.68192839])
nPL = len(plidx1)
# # ---------------
# # --- loading case 2: max wind speed ---
wind_Uref2 = 70.0
plidx2 = np.array([n-1], dtype=int) # at top
Fx2 = np.array([930198.60063279])
Fy2 = np.array([0.])
Fz2 = np.array([-2883106.12368949])
Mxx2 = np.array([-1683669.22411597])
Myy2 = np.array([-2522475.34625363])
Mzz2 = np.array([147301.97023764])
# # ---------------
# --- safety factors ---
gamma_f = 1.35
gamma_m = 1.3
gamma_n = 1.0
gamma_b = 1.1
# ---------------
# --- fatigue ---
z_DEL = np.array([0.000, 1.327, 3.982, 6.636, 9.291, 11.945, 14.600, 17.255, 19.909, 22.564, 25.218, 27.873, 30.527, 33.182, 35.836, 38.491, 41.145, 43.800, 46.455, 49.109, 51.764, 54.418, 57.073, 59.727, 62.382, 65.036, 67.691, 70.345, 73.000, 75.655, 78.309, 80.964, 83.618, 86.273, 87.600])
M_DEL = 1e3*np.array([8.2940E+003, 8.1518E+003, 7.8831E+003, 7.6099E+003, 7.3359E+003, 7.0577E+003, 6.7821E+003, 6.5119E+003, 6.2391E+003, 5.9707E+003, 5.7070E+003, 5.4500E+003, 5.2015E+003, 4.9588E+003, 4.7202E+003, 4.4884E+003, 4.2577E+003, 4.0246E+003, 3.7942E+003, 3.5664E+003, 3.3406E+003, 3.1184E+003, 2.8977E+003, 2.6811E+003, 2.4719E+003, 2.2663E+003, 2.0673E+003, 1.8769E+003, 1.7017E+003, 1.5479E+003, 1.4207E+003, 1.3304E+003, 1.2780E+003, 1.2673E+003, 1.2761E+003])
nDEL = len(z_DEL)
gamma_fatigue = 1.35*1.3*1.0
life = 20.0
m_SN = 4
# ---------------
# --- constraints ---
min_d_to_t = 120.0
min_taper = 0.4
# ---------------
# # V_max = 80.0 # tip speed
# # D = 126.0
# # .freq1p = V_max / (D/2) / (2*pi) # convert to Hz
nPoints = len(z_param)
nFull = len(z_full)
wind = 'PowerWind'
prob = Problem()
root = prob.root = Group()
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.driver.opt_settings['Major iterations limit'] = 1000
root.add('z_param', IndepVarComp('z_param', z_param))
root.add('d_param', IndepVarComp('d_param', d_param))
root.add('t_param', IndepVarComp('t_param', t_param))
root.add('TowerSE', TowerSE(nPoints, nFull, nK, nMass, nPL, nDEL, wind=wind))
prob.driver.add_objective('TowerSE.tower1.mass', scaler=1E-6)
prob.driver.add_desvar('z_param.z_param', lower=np.zeros(nPoints), upper=np.ones(nPoints)*1000., scaler=1E-2)
prob.driver.add_desvar('t_param.t_param', lower=np.ones(nPoints)*0.001, upper=np.ones(nPoints)*1000., scaler=1E-6)
prob.driver.add_desvar('d_param.d_param', np.array([2,2.1,2.2]), upper=np.ones(nPoints)*1000., scaler=1E-6)
prob.root.connect('z_param.z_param', 'TowerSE.z_param')
prob.root.connect('d_param.d_param', 'TowerSE.d_param')
prob.root.connect('t_param.t_param', 'TowerSE.t_param')
prob.driver.add_constraint('TowerSE.tower1.stress', upper=np.ones(n))
prob.driver.add_constraint('TowerSE.tower2.stress', upper=np.ones(n))
prob.driver.add_constraint('TowerSE.tower1.global_buckling', upper=np.ones(n))
prob.driver.add_constraint('TowerSE.tower2.global_buckling', upper=np.ones(n))
prob.driver.add_constraint('TowerSE.tower1.shell_buckling', upper=np.ones(n))
prob.driver.add_constraint('TowerSE.tower2.shell_buckling', upper=np.ones(n))
prob.driver.add_constraint('TowerSE.tower1.damage', upper=np.ones(n)*0.8)
prob.driver.add_constraint('TowerSE.gc.weldability', upper=np.zeros(n))
prob.driver.add_constraint('TowerSE.gc.manufacturability', upper=np.zeros(n))
freq1p = 0.2 # 1P freq in Hz
prob.driver.add_constraint('TowerSE.tower1.f1', lower=1.1*freq1p)
prob.driver.add_constraint('TowerSE.tower2.f1', lower=1.1*freq1p)
prob.setup()
if wind=='PowerWind':
prob['TowerSE.wind1.shearExp'] = shearExp
prob['TowerSE.wind2.shearExp'] = shearExp
# assign values to params
# --- geometry ----
#prob['TowerSE.z_param'] = z_param
#prob['TowerSE.d_param'] = d_param
#prob['TowerSE.t_param'] = t_param
prob['TowerSE.z_full'] = z_full
prob['TowerSE.tower1.L_reinforced'] = L_reinforced
prob['TowerSE.distLoads1.yaw'] = yaw
# --- material props ---
prob['TowerSE.tower1.E'] = E
prob['TowerSE.tower1.G'] = G
prob['TowerSE.tower1.rho'] = rho
prob['TowerSE.tower1.sigma_y'] = sigma_y
# --- spring reaction data. Use float('inf') for rigid constraints. ---
prob['TowerSE.tower1.kidx'] = kidx
prob['TowerSE.tower1.kx'] = kx
prob['TowerSE.tower1.ky'] = ky
prob['TowerSE.tower1.kz'] = kz
prob['TowerSE.tower1.ktx'] = ktx
prob['TowerSE.tower1.kty'] = kty
prob['TowerSE.tower1.ktz'] = ktz
# --- extra mass ----
prob['TowerSE.tower1.midx'] = midx
prob['TowerSE.tower1.m'] = m
prob['TowerSE.tower1.mIxx'] = mIxx
prob['TowerSE.tower1.mIyy'] = mIyy
prob['TowerSE.tower1.mIzz'] = mIzz
prob['TowerSE.tower1.mIxy'] = mIxy
prob['TowerSE.tower1.mIxz'] = mIxz
prob['TowerSE.tower1.mIyz'] = mIyz
prob['TowerSE.tower1.mrhox'] = mrhox
prob['TowerSE.tower1.mrhoy'] = mrhoy
prob['TowerSE.tower1.mrhoz'] = mrhoz
prob['TowerSE.tower1.addGravityLoadForExtraMass'] = addGravityLoadForExtraMass
# -----------
# --- wind ---
prob['TowerSE.wind1.zref'] = wind_zref
prob['TowerSE.wind1.z0'] = wind_z0
# ---------------
# # --- loading case 1: max Thrust ---
prob['TowerSE.wind1.Uref'] = wind_Uref1
prob['TowerSE.tower1.plidx'] = plidx1
prob['TowerSE.tower1.Fx'] = Fx1
prob['TowerSE.tower1.Fy'] = Fy1
prob['TowerSE.tower1.Fz'] = Fz1
prob['TowerSE.tower1.Mxx'] = Mxx1
prob['TowerSE.tower1.Myy'] = Myy1
prob['TowerSE.tower1.Mzz'] = Mzz1
# # ---------------
# # --- loading case 2: max Wind Speed ---
prob['TowerSE.wind2.Uref'] = wind_Uref2
prob['TowerSE.tower2.plidx'] = plidx2
prob['TowerSE.tower2.Fx'] = Fx2
prob['TowerSE.tower2.Fy'] = Fy2
prob['TowerSE.tower2.Fz'] = Fz2
prob['TowerSE.tower2.Mxx'] = Mxx2
prob['TowerSE.tower2.Myy'] = Myy2
prob['TowerSE.tower2.Mzz'] = Mzz2
# # ---------------
# --- safety factors ---
prob['TowerSE.tower1.gamma_f'] = gamma_f
prob['TowerSE.tower1.gamma_m'] = gamma_m
prob['TowerSE.tower1.gamma_n'] = gamma_n
prob['TowerSE.tower1.gamma_b'] = gamma_b
# ---------------
# --- fatigue ---
prob['TowerSE.tower1.z_DEL'] = z_DEL
prob['TowerSE.tower1.M_DEL'] = M_DEL
prob['TowerSE.tower1.gamma_fatigue'] = gamma_fatigue
prob['TowerSE.tower1.life'] = life
prob['TowerSE.tower1.m_SN'] = m_SN
# ---------------
# --- constraints ---
prob['TowerSE.gc.min_d_to_t'] = min_d_to_t
prob['TowerSE.gc.min_taper'] = min_taper
# ---------------
# # --- run ---
prob.run()
print prob['TowerSE.gc.weldability']
print prob['TowerSE.gc.manufacturability']
self.J = prob.check_total_derivatives(out_stream=None)
"""
def _test_integrate_polynomial_control_rate2(self, transcription):
#
# Define the OpenMDAO problem
#
p = om.Problem(model=om.Group())
#
# Define a Trajectory object
#
traj = dm.Trajectory()
p.model.add_subsystem('traj', subsys=traj)
#
# Define a Dymos Phase object with GaussLobatto Transcription
#
phase = dm.Phase(ode_class=BrachistochroneODE,
transcription=transcription(num_segments=20, order=3))
traj.add_phase(name='phase0', phase=phase)
#
# Set the time options
# Time has no targets in our ODE.
# We fix the initial time so that the it is not a design variable in the optimization.
# The duration of the phase is allowed to be optimized, but is bounded on [0.5, 10].
#
phase.set_time_options(fix_initial=True,
duration_bounds=(1.0, 10.0),
units='s')
#
# Set the time options
# Initial values of positions and velocity are all fixed.
# The final value of position are fixed, but the final velocity is a free variable.
# The equations of motion are not functions of position, so 'x' and 'y' have no targets.
# The rate source points to the output in the ODE which provides the time derivative of the
# given state.
phase.add_state('x', fix_initial=True, fix_final=True)
phase.add_state('y', fix_initial=True, fix_final=True)
phase.add_state('v', fix_initial=True)
phase.add_state('int_theta_dot',
fix_initial=False,
rate_source='theta_rate2')
phase.add_state('int_theta',
fix_initial=False,
rate_source='int_theta_dot',
targets=['theta'])
# Define theta as a control.
phase.add_polynomial_control(name='theta',
order=11,
units='rad',
shape=(1, ),
targets=None)
# Force the initial value of the theta polynomial control to equal the initial value of the theta state.
traj.add_linkage_constraint(phase_a='phase0',
phase_b='phase0',
var_a='theta',
var_b='int_theta',
loc_a='initial',
loc_b='initial')
traj.add_linkage_constraint(phase_a='phase0',
phase_b='phase0',
var_a='int_theta_dot',
var_b='theta_rate',
loc_a='initial',
loc_b='initial',
units='rad/s')
# Minimize final time.
phase.add_objective('time', loc='final')
# Set the driver.
p.driver = om.pyOptSparseDriver(optimizer='SLSQP')
# Allow OpenMDAO to automatically determine our sparsity pattern.
# Doing so can significant speed up the execution of Dymos.
p.driver.declare_coloring()
# Setup the problem
p.setup(check=True)
# Now that the OpenMDAO problem is setup, we can set the values of the states.
p.set_val('traj.phase0.t_initial', 0.0, units='s')
p.set_val('traj.phase0.t_duration', 5.0, units='s')
p.set_val('traj.phase0.states:x',
phase.interp('x', [0, 10]),
units='m')
p.set_val('traj.phase0.states:y',
phase.interp('y', [10, 5]),
units='m')
p.set_val('traj.phase0.states:v',
phase.interp('v', [0, 5]),
units='m/s')
p.set_val('traj.phase0.states:int_theta',
phase.interp('int_theta', [0.1, 45]),
units='deg')
p.set_val('traj.phase0.states:int_theta_dot',
phase.interp('int_theta_dot', [0, 0]),
units='deg/s')
p.set_val('traj.phase0.polynomial_controls:theta', 45.0, units='deg')
# Run the driver to solve the problem
dm.run_problem(p, simulate=True, make_plots=True)
sol = om.CaseReader('dymos_solution.db').get_case('final')
sim = om.CaseReader('dymos_simulation.db').get_case('final')
t_sol = sol.get_val('traj.phase0.timeseries.time')
t_sim = sim.get_val('traj.phase0.timeseries.time')
x_sol = sol.get_val('traj.phase0.timeseries.states:x')
x_sim = sim.get_val('traj.phase0.timeseries.states:x')
y_sol = sol.get_val('traj.phase0.timeseries.states:y')
y_sim = sim.get_val('traj.phase0.timeseries.states:y')
v_sol = sol.get_val('traj.phase0.timeseries.states:v')
v_sim = sim.get_val('traj.phase0.timeseries.states:v')
int_theta_sol = sol.get_val('traj.phase0.timeseries.states:int_theta')
int_theta_sim = sim.get_val('traj.phase0.timeseries.states:int_theta')
theta_sol = sol.get_val(
'traj.phase0.timeseries.polynomial_controls:theta')
theta_sim = sim.get_val(
'traj.phase0.timeseries.polynomial_controls:theta')
assert_timeseries_near_equal(t_sol,
x_sol,
t_sim,
x_sim,
tolerance=1.0E-2)
assert_timeseries_near_equal(t_sol,
y_sol,
t_sim,
y_sim,
tolerance=1.0E-2)
assert_timeseries_near_equal(t_sol,
v_sol,
t_sim,
v_sim,
tolerance=1.0E-2)
assert_timeseries_near_equal(t_sol,
int_theta_sol,
t_sim,
int_theta_sim,
tolerance=1.0E-2)
def hp_transient(transcription='gauss-lobatto',
num_segments=5,
transcription_order=3,
compressed=False,
optimizer='SLSQP',
run_driver=True,
force_alloc_complex=True,
solve_segments=False,
show_plots=False,
save=True,
Tf_final=370):
p = om.Problem(model=om.Group())
model = p.model
nn = 1
p.driver = om.ScipyOptimizeDriver()
p.driver = om.pyOptSparseDriver(optimizer=optimizer)
p.driver.declare_coloring()
traj = p.model.add_subsystem('traj', dm.Trajectory())
phase = traj.add_phase(
'phase',
dm.Phase(ode_class=HeatPipeRun,
transcription=dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)))
phase.set_time_options(fix_initial=True,
fix_duration=False,
duration_bounds=(1., 3200.))
phase.add_state(
'T_cond',
rate_source='cond.Tdot',
targets='cond.T',
units='K', # ref=333.15, defect_ref=333.15,
fix_initial=True,
fix_final=False,
solve_segments=solve_segments)
phase.add_state(
'T_cond2',
rate_source='cond2.Tdot',
targets='cond2.T',
units='K', # ref=333.15, defect_ref=333.15,
fix_initial=True,
fix_final=False,
solve_segments=solve_segments)
phase.add_control('T_evap', targets='evap.Rex.T_in', units='K', opt=False)
phase.add_boundary_constraint('T_cond', loc='final', equals=Tf_final)
phase.add_objective('time', loc='final', ref=1)
phase.add_timeseries_output('evap_bridge.Rv.q',
output_name='eRvq',
units='W')
phase.add_timeseries_output('evap_bridge.Rwa.q',
output_name='eRwaq',
units='W')
phase.add_timeseries_output('evap_bridge.Rwka.q',
output_name='eRwkq',
units='W')
phase.add_timeseries_output('cond_bridge.Rv.q',
output_name='cRvq',
units='W')
phase.add_timeseries_output('cond_bridge.Rwa.q',
output_name='cRwaq',
units='W')
phase.add_timeseries_output('cond_bridge.Rwka.q',
output_name='cRwkq',
units='W')
phase.add_timeseries_output('evap.pcm.PS', output_name='ePS', units=None)
phase.add_timeseries_output('cond.pcm.PS', output_name='cPS', units=None)
phase.add_timeseries_output('cond2.pcm.PS', output_name='c2PS', units=None)
p.model.linear_solver = om.DirectSolver()
p.setup(force_alloc_complex=force_alloc_complex)
p['traj.phase.t_initial'] = 0.0
p['traj.phase.t_duration'] = 195.
p['traj.phase.states:T_cond'] = phase.interpolate(ys=[293.15, 333.15],
nodes='state_input')
p['traj.phase.states:T_cond2'] = phase.interpolate(ys=[293.15, 333.15],
nodes='state_input')
p['traj.phase.controls:T_evap'] = phase.interpolate(ys=[333., 338.],
nodes='control_input')
p.run_model()
opt = p.run_driver()
# sim = traj.simulate(times_per_seg=10)
print('********************************')
# save_csv(p, sim, '../../output/output.csv',
# y_name=['parameters:T_evap', 'states:T_cond', 'states:T_cond2',
# 'eRvq', 'eRwaq', 'eRwkq', 'cRvq', 'cRwaq', 'cRwkq'],
# y_units=['K', 'K', 'K', 'W', 'W', 'W', 'W', 'W', 'W'])
if show_plots:
import matplotlib.pyplot as plt
# time = sim.get_val('traj.phase.timeseries.time', units='s')
time_opt = p.get_val('traj.phase.timeseries.time', units='s')
# T_cond = sim.get_val('traj.phase.timeseries.states:T_cond', units='K')
T_cond_opt = p.get_val('traj.phase.timeseries.states:T_cond',
units='K')
# T_cond2 = sim.get_val('traj.phase.timeseries.states:T_cond2', units='K')
T_cond2_opt = p.get_val('traj.phase.timeseries.states:T_cond2',
units='K')
# T_evap = sim.get_val('traj.phase.timeseries.controls:T_evap', units='K')
T_evap_opt = p.get_val('traj.phase.timeseries.controls:T_evap',
units='K')
ePS_opt = p.get_val('traj.phase.timeseries.ePS')
cPS_opt = p.get_val('traj.phase.timeseries.cPS')
c2PS_opt = p.get_val('traj.phase.timeseries.c2PS')
plt.plot(time_opt, T_cond_opt)
# plt.plot(time, T_cond)
plt.plot(time_opt, T_cond2_opt)
# plt.plot(time, T_cond2)
plt.plot(time_opt, T_evap_opt)
# plt.plot(time, T_evap)
plt.xlabel('time, s')
plt.ylabel('T_cond, K')
plt.show()
plt.plot(time_opt, cPS_opt)
# plt.plot(time, EPS)
plt.plot(time_opt, c2PS_opt)
# plt.plot(time, T_cond2)
plt.plot(time_opt, ePS_opt)
# plt.plot(time, T_evap)
plt.xlabel('time, s')
plt.ylabel('percent solid')
plt.show()
return p
def _run_transcription(self, transcription):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
#
# First Phase: Standard Brachistochrone
#
num_segments = 10
transcription_order = 3
compressed = False
if transcription == 'gauss-lobatto':
tx0 = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
tx1 = dm.GaussLobatto(num_segments=num_segments * 2,
order=transcription_order * 3,
compressed=compressed)
elif transcription == 'radau-ps':
tx0 = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
tx1 = dm.Radau(num_segments=num_segments * 2,
order=transcription_order * 3,
compressed=compressed)
phase0 = dm.Phase(ode_class=BrachistochroneODE, transcription=tx0)
p.model.add_subsystem('phase0', phase0)
phase0.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase0.add_state('x', fix_initial=True, fix_final=False)
phase0.add_state('y', fix_initial=True, fix_final=False)
phase0.add_state('v', fix_initial=True)
phase0.add_parameter('g', units='m/s**2', val=9.80665)
phase0.add_control('theta',
units='deg',
rate_continuity=False,
lower=0.01,
upper=179.9)
phase0.add_boundary_constraint('x', loc='final', equals=10)
phase0.add_boundary_constraint('y', loc='final', equals=5)
# Add alternative timeseries output to provide control inputs for the next phase
phase0.add_timeseries('timeseries2',
transcription=tx1,
subset='control_input')
#
# Second Phase: Integration of ArcLength
#
phase1 = dm.Phase(ode_class=BrachistochroneArclengthODE,
transcription=tx1)
p.model.add_subsystem('phase1', phase1)
phase1.set_time_options(fix_initial=True, input_duration=True)
phase1.add_state('S',
fix_initial=True,
fix_final=False,
rate_source='Sdot')
phase1.add_control('theta', opt=False, units='deg', targets=['theta'])
phase1.add_control('v', opt=False, units='m/s', targets=['v'])
#
# Connect the two phases
#
p.model.connect('phase0.t_duration', 'phase1.t_duration')
p.model.connect('phase0.timeseries2.controls:theta',
'phase1.controls:theta')
p.model.connect('phase0.timeseries2.states:v', 'phase1.controls:v')
# Minimize time at the end of the phase
# phase1.add_objective('time', loc='final', scaler=1)
# phase1.add_boundary_constraint('S', loc='final', upper=12)
phase1.add_objective('S', loc='final', ref=1)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase0.interpolate(ys=[0, 10],
nodes='state_input')
p['phase0.states:y'] = phase0.interpolate(ys=[10, 5],
nodes='state_input')
p['phase0.states:v'] = phase0.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase0.interpolate(ys=[5, 100],
nodes='control_input')
p['phase0.parameters:g'] = 9.80665
p['phase1.states:S'] = 0.0
p.run_driver()
expected = np.sqrt((10 - 0)**2 + (10 - 5)**2)
assert_near_equal(p['phase1.timeseries.states:S'][-1],
expected,
tolerance=1.0E-3)
def test_doc_ssto_linear_tangent_guidance(self):
import numpy as np
import matplotlib.pyplot as plt
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.plotting import plot_results
g = 1.61544 # lunar gravity, m/s**2
class LaunchVehicle2DEOM(om.ExplicitComponent):
"""
Simple 2D Cartesian Equations of Motion for a launch vehicle subject to thrust and drag.
"""
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('vx',
val=np.zeros(nn),
desc='x velocity',
units='m/s')
self.add_input('vy',
val=np.zeros(nn),
desc='y velocity',
units='m/s')
self.add_input('m', val=np.zeros(nn), desc='mass', units='kg')
self.add_input('theta',
val=np.zeros(nn),
desc='pitch angle',
units='rad')
self.add_input('thrust',
val=2100000 * np.ones(nn),
desc='thrust',
units='N')
self.add_input('Isp',
val=265.2 * np.ones(nn),
desc='specific impulse',
units='s')
# Outputs
self.add_output('xdot',
val=np.zeros(nn),
desc='velocity component in x',
units='m/s')
self.add_output('ydot',
val=np.zeros(nn),
desc='velocity component in y',
units='m/s')
self.add_output('vxdot',
val=np.zeros(nn),
desc='x acceleration magnitude',
units='m/s**2')
self.add_output('vydot',
val=np.zeros(nn),
desc='y acceleration magnitude',
units='m/s**2')
self.add_output('mdot',
val=np.zeros(nn),
desc='mass rate of change',
units='kg/s')
# Setup partials
ar = np.arange(self.options['num_nodes'])
self.declare_partials(of='xdot',
wrt='vx',
rows=ar,
cols=ar,
val=1.0)
self.declare_partials(of='ydot',
wrt='vy',
rows=ar,
cols=ar,
val=1.0)
self.declare_partials(of='vxdot', wrt='vx', rows=ar, cols=ar)
self.declare_partials(of='vxdot', wrt='m', rows=ar, cols=ar)
self.declare_partials(of='vxdot',
wrt='theta',
rows=ar,
cols=ar)
self.declare_partials(of='vxdot',
wrt='thrust',
rows=ar,
cols=ar)
self.declare_partials(of='vydot', wrt='m', rows=ar, cols=ar)
self.declare_partials(of='vydot',
wrt='theta',
rows=ar,
cols=ar)
self.declare_partials(of='vydot', wrt='vy', rows=ar, cols=ar)
self.declare_partials(of='vydot',
wrt='thrust',
rows=ar,
cols=ar)
self.declare_partials(of='mdot',
wrt='thrust',
rows=ar,
cols=ar)
self.declare_partials(of='mdot', wrt='Isp', rows=ar, cols=ar)
def compute(self, inputs, outputs):
theta = inputs['theta']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
vx = inputs['vx']
vy = inputs['vy']
m = inputs['m']
F_T = inputs['thrust']
Isp = inputs['Isp']
outputs['xdot'] = vx
outputs['ydot'] = vy
outputs['vxdot'] = F_T * cos_theta / m
outputs['vydot'] = F_T * sin_theta / m - g
outputs['mdot'] = -F_T / (g * Isp)
def compute_partials(self, inputs, jacobian):
theta = inputs['theta']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
m = inputs['m']
F_T = inputs['thrust']
Isp = inputs['Isp']
# jacobian['vxdot', 'vx'] = -CDA * rho * vx / m
jacobian['vxdot', 'm'] = -(F_T * cos_theta) / m**2
jacobian['vxdot', 'theta'] = -(F_T / m) * sin_theta
jacobian['vxdot', 'thrust'] = cos_theta / m
# jacobian['vydot', 'vy'] = -CDA * rho * vy / m
jacobian['vydot', 'm'] = -(F_T * sin_theta) / m**2
jacobian['vydot', 'theta'] = (F_T / m) * cos_theta
jacobian['vydot', 'thrust'] = sin_theta / m
jacobian['mdot', 'thrust'] = -1.0 / (g * Isp)
jacobian['mdot', 'Isp'] = F_T / (g * Isp**2)
class LinearTangentGuidanceComp(om.ExplicitComponent):
""" Compute pitch angle from static controls governing linear expression for
pitch angle tangent as function of time.
"""
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
self.add_input('a_ctrl',
val=np.zeros(nn),
desc='linear tangent slope',
units='1/s')
self.add_input('b_ctrl',
val=np.zeros(nn),
desc='tangent of theta at t=0',
units=None)
self.add_input('time_phase',
val=np.zeros(nn),
desc='time',
units='s')
self.add_output('theta',
val=np.zeros(nn),
desc='pitch angle',
units='rad')
# Setup partials
arange = np.arange(self.options['num_nodes'])
self.declare_partials(of='theta',
wrt='a_ctrl',
rows=arange,
cols=arange,
val=1.0)
self.declare_partials(of='theta',
wrt='b_ctrl',
rows=arange,
cols=arange,
val=1.0)
self.declare_partials(of='theta',
wrt='time_phase',
rows=arange,
cols=arange,
val=1.0)
def compute(self, inputs, outputs):
a = inputs['a_ctrl']
b = inputs['b_ctrl']
t = inputs['time_phase']
outputs['theta'] = np.arctan(a * t + b)
def compute_partials(self, inputs, jacobian):
a = inputs['a_ctrl']
b = inputs['b_ctrl']
t = inputs['time_phase']
x = a * t + b
denom = x**2 + 1.0
jacobian['theta', 'a_ctrl'] = t / denom
jacobian['theta', 'b_ctrl'] = 1.0 / denom
jacobian['theta', 'time_phase'] = a / denom
class LaunchVehicleLinearTangentODE(om.Group):
"""
The LaunchVehicleLinearTangentODE for this case consists of a guidance component and
the EOM. Guidance is simply an OpenMDAO ExecComp which computes the arctangent of the
tan_theta variable.
"""
def initialize(self):
self.options.declare(
'num_nodes',
types=int,
desc='Number of nodes to be evaluated in the RHS')
def setup(self):
nn = self.options['num_nodes']
self.add_subsystem('guidance',
LinearTangentGuidanceComp(num_nodes=nn))
self.add_subsystem('eom', LaunchVehicle2DEOM(num_nodes=nn))
self.connect('guidance.theta', 'eom.theta')
#
# Setup and solve the optimal control problem
#
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring()
traj = dm.Trajectory()
p.model.add_subsystem('traj', traj)
phase = dm.Phase(ode_class=LaunchVehicleLinearTangentODE,
transcription=dm.GaussLobatto(num_segments=10,
order=5,
compressed=True))
traj.add_phase('phase0', phase)
phase.set_time_options(fix_initial=True,
duration_bounds=(10, 1000),
targets=['guidance.time_phase'])
phase.add_state('x',
fix_initial=True,
lower=0,
rate_source='eom.xdot',
units='m')
phase.add_state('y',
fix_initial=True,
lower=0,
rate_source='eom.ydot',
units='m')
phase.add_state('vx',
fix_initial=True,
lower=0,
rate_source='eom.vxdot',
targets=['eom.vx'],
units='m/s')
phase.add_state('vy',
fix_initial=True,
rate_source='eom.vydot',
targets=['eom.vy'],
units='m/s')
phase.add_state('m',
fix_initial=True,
rate_source='eom.mdot',
targets=['eom.m'],
units='kg')
phase.add_boundary_constraint('y',
loc='final',
equals=1.85E5,
linear=True)
phase.add_boundary_constraint('vx', loc='final', equals=1627.0)
phase.add_boundary_constraint('vy', loc='final', equals=0)
phase.add_parameter('a_ctrl',
units='1/s',
opt=True,
targets=['guidance.a_ctrl'])
phase.add_parameter('b_ctrl',
units=None,
opt=True,
targets=['guidance.b_ctrl'])
phase.add_parameter('thrust',
units='N',
opt=False,
val=3.0 * 50000.0 * 1.61544,
targets=['eom.thrust'])
phase.add_parameter('Isp',
units='s',
opt=False,
val=1.0E6,
targets=['eom.Isp'])
phase.add_objective('time', index=-1, scaler=0.01)
p.model.linear_solver = om.DirectSolver()
phase.add_timeseries_output('guidance.theta', units='deg')
p.setup(check=True)
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 500.0
p['traj.phase0.states:x'] = phase.interpolate(ys=[0, 350000.0],
nodes='state_input')
p['traj.phase0.states:y'] = phase.interpolate(ys=[0, 185000.0],
nodes='state_input')
p['traj.phase0.states:vx'] = phase.interpolate(ys=[0, 1627.0],
nodes='state_input')
p['traj.phase0.states:vy'] = phase.interpolate(ys=[1.0E-6, 0],
nodes='state_input')
p['traj.phase0.states:m'] = phase.interpolate(ys=[50000, 50000],
nodes='state_input')
p['traj.phase0.parameters:a_ctrl'] = -0.01
p['traj.phase0.parameters:b_ctrl'] = 3.0
dm.run_problem(p)
#
# Check the results.
#
assert_near_equal(p.get_val('traj.phase0.timeseries.time')[-1],
481,
tolerance=0.01)
#
# Get the explitly simulated results
#
exp_out = traj.simulate()
#
# Plot the results
#
plot_results(
[('traj.phase0.timeseries.states:x',
'traj.phase0.timeseries.states:y', 'range (m)', 'altitude (m)'),
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.theta',
'range (m)', 'altitude (m)')],
title=
'Single Stage to Orbit Solution Using Linear Tangent Guidance',
p_sol=p,
p_sim=exp_out)
plt.show()
def test_tandem_phases_for_docs(self):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
#
# First Phase: Standard Brachistochrone
#
num_segments = 10
transcription_order = 3
compressed = False
tx0 = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
tx1 = dm.Radau(num_segments=num_segments * 2,
order=transcription_order * 3,
compressed=compressed)
phase0 = dm.Phase(ode_class=BrachistochroneODE, transcription=tx0)
p.model.add_subsystem('phase0', phase0)
phase0.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase0.add_state(
'x',
rate_source=BrachistochroneODE.states['x']['rate_source'],
units=BrachistochroneODE.states['x']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase0.add_state(
'y',
rate_source=BrachistochroneODE.states['y']['rate_source'],
units=BrachistochroneODE.states['y']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase0.add_state(
'v',
rate_source=BrachistochroneODE.states['v']['rate_source'],
targets=BrachistochroneODE.states['v']['targets'],
units=BrachistochroneODE.states['v']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase0.add_control(
'theta',
continuity=True,
rate_continuity=True,
targets=BrachistochroneODE.parameters['theta']['targets'],
units='deg',
lower=0.01,
upper=179.9)
phase0.add_input_parameter(
'g',
targets=BrachistochroneODE.parameters['g']['targets'],
units='m/s**2',
val=9.80665)
phase0.add_boundary_constraint('x', loc='final', equals=10)
phase0.add_boundary_constraint('y', loc='final', equals=5)
# Add alternative timeseries output to provide control inputs for the next phase
phase0.add_timeseries('timeseries2',
transcription=tx1,
subset='control_input')
#
# Second Phase: Integration of ArcLength
#
phase1 = dm.Phase(ode_class=BrachistochroneArclengthODE,
transcription=tx1)
p.model.add_subsystem('phase1', phase1)
phase1.set_time_options(fix_initial=True, input_duration=True)
phase1.add_state('S',
fix_initial=True,
fix_final=False,
rate_source='Sdot',
units='m')
phase1.add_control('theta', opt=False, units='deg', targets='theta')
phase1.add_control('v', opt=False, units='m/s', targets='v')
#
# Connect the two phases
#
p.model.connect('phase0.t_duration', 'phase1.t_duration')
p.model.connect('phase0.timeseries2.controls:theta',
'phase1.controls:theta')
p.model.connect('phase0.timeseries2.states:v', 'phase1.controls:v')
# Minimize time at the end of the phase
# phase1.add_objective('time', loc='final', scaler=1)
# phase1.add_boundary_constraint('S', loc='final', upper=12)
phase1.add_objective('S', loc='final', ref=1)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase0.interpolate(ys=[0, 10],
nodes='state_input')
p['phase0.states:y'] = phase0.interpolate(ys=[10, 5],
nodes='state_input')
p['phase0.states:v'] = phase0.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase0.interpolate(ys=[5, 100],
nodes='control_input')
p['phase0.input_parameters:g'] = 9.80665
p['phase1.states:S'] = 0.0
p.run_driver()
expected = np.sqrt((10 - 0)**2 + (10 - 5)**2)
assert_rel_error(self,
p['phase1.timeseries.states:S'][-1],
expected,
tolerance=1.0E-3)
fig, (ax0, ax1) = plt.subplots(2, 1)
fig.tight_layout()
ax0.plot(p.get_val('phase0.timeseries.states:x'),
p.get_val('phase0.timeseries.states:y'), '.')
ax0.set_xlabel('x (m)')
ax0.set_ylabel('y (m)')
ax1.plot(p.get_val('phase1.timeseries.time'),
p.get_val('phase1.timeseries.states:S'), '+')
ax1.set_xlabel('t (s)')
ax1.set_ylabel('S (m)')
plt.show()
def _make_problem(transcription='gauss-lobatto', num_segments=8, transcription_order=3,
compressed=True, optimizer='SLSQP', force_alloc_complex=False,
solve_segments=False, y_bounds=None):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
if optimizer == 'SNOPT':
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Verify level'] = 3
elif optimizer == 'IPOPT':
p.driver.opt_settings['mu_init'] = 1e-3
p.driver.opt_settings['max_iter'] = 500
p.driver.opt_settings['print_level'] = 5
p.driver.opt_settings['nlp_scaling_method'] = 'gradient-based' # for faster convergence
p.driver.opt_settings['alpha_for_y'] = 'safer-min-dual-infeas'
p.driver.opt_settings['mu_strategy'] = 'monotone'
p.driver.declare_coloring(tol=1.0E-12)
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
t = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
traj = dm.Trajectory()
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=t)
p.model.add_subsystem('traj0', traj)
traj.add_phase('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.add_state('x', fix_initial=False, fix_final=False, solve_segments=solve_segments)
phase.add_state('y', fix_initial=False, fix_final=False, solve_segments=solve_segments)
if y_bounds is not None:
phase.set_state_options('y', lower=y_bounds[0], upper=y_bounds[1])
# Note that by omitting the targets here Dymos will automatically attempt to connect
# to a top-level input named 'v' in the ODE, and connect to nothing if it's not found.
phase.add_state('v', fix_initial=False, fix_final=False, solve_segments=solve_segments)
phase.add_control('theta',
continuity=True, rate_continuity=True,
units='deg', lower=0.01, upper=179.9)
phase.add_parameter('g', targets=['g'], units='m/s**2')
phase.add_boundary_constraint('x', loc='initial', equals=0)
phase.add_boundary_constraint('y', loc='initial', equals=10)
phase.add_boundary_constraint('v', loc='initial', equals=0)
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.set_solver_print(0)
p.setup(check=['unconnected_inputs'], force_alloc_complex=force_alloc_complex)
p['traj0.phase0.t_initial'] = 0.0
p['traj0.phase0.t_duration'] = 1.5
p['traj0.phase0.states:x'] = phase.interp('x', [0, 10])
p['traj0.phase0.states:y'] = phase.interp('y', [10, 5])
p['traj0.phase0.states:v'] = phase.interp('v', [0, 9.9])
p['traj0.phase0.controls:theta'] = phase.interp('theta', [5, 100])
p['traj0.phase0.parameters:g'] = 9.80665
return p
def make_problem(self, transcription=Radau, optimizer='SLSQP', numseg=30):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.declare_coloring()
OPT, OPTIMIZER = set_pyoptsparse_opt(optimizer, fallback=False)
p.driver.options['optimizer'] = OPTIMIZER
if OPTIMIZER == 'SNOPT':
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Verify level'] = 3
elif OPTIMIZER == 'IPOPT':
p.driver.opt_settings['nlp_scaling_method'] = 'gradient-based'
p.driver.opt_settings['max_iter'] = 500
p.driver.opt_settings['print_level'] = 5
traj = p.model.add_subsystem('traj', Trajectory())
phase = traj.add_phase(
'phase',
Phase(ode_class=RobotArmODE,
transcription=transcription(num_segments=numseg, order=3)))
phase.set_time_options(fix_initial=True, fix_duration=False)
phase.add_state('x0',
fix_initial=True,
fix_final=True,
rate_source='x0_dot',
units='m')
phase.add_state('x1',
fix_initial=True,
fix_final=True,
rate_source='x1_dot',
units='rad')
phase.add_state('x2',
fix_initial=True,
fix_final=True,
rate_source='x2_dot',
units='rad')
phase.add_state('x3',
fix_initial=True,
fix_final=True,
rate_source='x3_dot',
units='m/s')
phase.add_state('x4',
fix_initial=True,
fix_final=True,
rate_source='x4_dot',
units='rad/s')
phase.add_state('x5',
fix_initial=True,
fix_final=True,
rate_source='x5_dot',
units='rad/s')
phase.add_control('u0',
opt=True,
lower=-1,
upper=1,
scaler=0.1,
units='m**2/s**2',
continuity=False,
rate_continuity=False)
phase.add_control('u1',
opt=True,
lower=-1,
upper=1,
scaler=0.1,
units='m**3*rad/s**2',
continuity=False,
rate_continuity=False)
phase.add_control('u2',
opt=True,
lower=-1,
upper=1,
scaler=0.1,
units='m**3*rad/s**2',
continuity=False,
rate_continuity=False)
phase.add_path_constraint('u0',
lower=-1,
upper=1,
scaler=0.1,
units='m**2/s**2')
phase.add_path_constraint('u1',
lower=-1,
upper=1,
scaler=0.1,
units='m**3*rad/s**2')
phase.add_path_constraint('u2',
lower=-1,
upper=1,
scaler=0.1,
units='m**3*rad/s**2')
phase.add_objective('time', ref=0.1)
phase.set_refine_options(refine=True, tol=1e-5, smoothness_factor=1.2)
p.setup(check=True, force_alloc_complex=False, mode='auto')
p.set_val('traj.phase.t_initial', 0)
p.set_val('traj.phase.t_duration', 10)
p.set_val('traj.phase.states:x0',
phase.interpolate(ys=[4.5, 4.5], nodes='state_input'))
p.set_val(
'traj.phase.states:x1',
phase.interpolate(ys=[0.0, 2 * np.pi / 3], nodes='state_input'))
p.set_val(
'traj.phase.states:x2',
phase.interpolate(ys=[np.pi / 4, np.pi / 4], nodes='state_input'))
p.set_val('traj.phase.states:x3',
phase.interpolate(ys=[0.0, 0.0], nodes='state_input'))
p.set_val('traj.phase.states:x4',
phase.interpolate(ys=[0.0, 0.0], nodes='state_input'))
p.set_val('traj.phase.states:x5',
phase.interpolate(ys=[0.0, 0.0], nodes='state_input'))
return p
def test_discs(self):
OPT, OPTIMIZER = set_pyoptsparse_opt('SNOPT')
if OPTIMIZER is not 'SNOPT':
raise unittest.SkipTest("pyoptsparse is not providing SNOPT or SLSQP")
# So we compare the same starting locations.
np.random.seed(123)
radius = 1.0
pin = 15.0
n_disc = 7
prob = Problem()
prob.root = root = Group()
from openmdao.api import pyOptSparseDriver
driver = prob.driver = pyOptSparseDriver()
driver.options['optimizer'] = 'SNOPT'
driver.options['print_results'] = False
# Note, active tolerance requires relevance reduction to work.
root.ln_solver.options['single_voi_relevance_reduction'] = True
# Also, need to be in adjoint
root.ln_solver.options['mode'] = 'rev'
obj_expr = 'obj = '
sep = ''
for i in range(n_disc):
dist = "dist_%d" % i
x1var = 'x_%d' % i
# First disc is pinned
if i == 0:
root.add('p_%d' % i, IndepVarComp(x1var, pin), promotes=(x1var, ))
# The rest are design variables for the optimizer.
else:
init_val = 5.0*np.random.random() - 5.0 + pin
root.add('p_%d' % i, IndepVarComp(x1var, init_val), promotes=(x1var, ))
driver.add_desvar(x1var)
for j in range(i):
x2var = 'x_%d' % j
yvar = 'y_%d_%d' % (i, j)
name = dist + "_%d" % j
expr = '%s= (%s - %s)**2' % (yvar, x1var, x2var)
root.add(name, ExecComp(expr), promotes = (x1var, x2var, yvar))
# Constraint (you can experiment with turning on/off the active_tol)
#driver.add_constraint(yvar, lower=radius)
driver.add_constraint(yvar, lower=radius, active_tol=radius*3.0)
# This pair's contribution to objective
obj_expr += sep + yvar
sep = ' + '
root.add('sum_dist', ExecComp(obj_expr), promotes=('*', ))
driver.add_objective('obj')
prob.setup(check=False)
prob.run()
def setup_problem(
trans=dm.GaussLobatto(num_segments=10), polynomial_control=False):
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
from dymos.transcriptions.runge_kutta.runge_kutta import RungeKutta
p = om.Problem(model=om.Group())
if isinstance(trans, RungeKutta):
p.driver = om.pyOptSparseDriver()
else:
p.driver = om.ScipyOptimizeDriver()
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=trans)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10))
phase.add_state('x',
fix_initial=True,
fix_final=not isinstance(trans, RungeKutta))
phase.add_state('y',
fix_initial=True,
fix_final=not isinstance(trans, RungeKutta))
phase.add_state('v', fix_initial=True)
if not polynomial_control:
phase.add_control('theta',
units='deg',
rate_continuity=False,
lower=0.01,
upper=179.9)
else:
phase.add_polynomial_control('theta',
order=1,
units='deg',
lower=0.01,
upper=179.9)
phase.add_parameter('g', units='m/s**2', opt=False, val=9.80665)
if isinstance(trans, RungeKutta):
phase.add_timeseries_output('check', units='m/s', shape=(1, ))
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input')
p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input')
if not polynomial_control:
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5],
nodes='control_input')
else:
p['phase0.polynomial_controls:theta'][:] = 5.0
return p
model.add_constraint('%s.ConS1' % name, upper=0.0, parallel_deriv_color='con4')
model.add_constraint('%s_con5.val' % name, equals=0.0)
# Add broadcast parameters
model.add_design_var('bp.cellInstd', lower=0., upper=1.0)
model.add_design_var('bp.finAngle', lower=0., upper=np.pi/2.)
model.add_design_var('bp.antAngle', lower=-np.pi/4, upper=np.pi/4)
# Add objective
model.add_objective('obj.val')
# Instantiate Problem with driver (SNOPT) and recorder
prob = Problem(model)
if 'nopt' not in argv:
prob.driver = pyOptSparseDriver(optimizer='SNOPT')
prob.driver.opt_settings = {
'Major optimality tolerance': 1e-3,
'Major feasibility tolerance': 1.0e-5,
'Iterations limit': 500000000
}
if 'record' in argv:
if MPI:
print('recording not supported for parallel runs.')
else:
prob.driver.add_recorder(SqliteRecorder('data.sql'))
prob.setup()
# For Parallel execution, we must use KSP or LinearGS
def test_double_integrator_for_docs(self):
import matplotlib.pyplot as plt
import openmdao.api as om
from openmdao.utils.assert_utils import assert_rel_error
import dymos as dm
from dymos.examples.plotting import plot_results
from dymos.examples.double_integrator.double_integrator_ode import DoubleIntegratorODE
# Initialize the problem and assign the driver
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
# Setup the trajectory and its phase
traj = p.model.add_subsystem('traj', dm.Trajectory())
transcription = dm.Radau(num_segments=30, order=3, compressed=False)
phase = traj.add_phase(
'phase0',
dm.Phase(ode_class=DoubleIntegratorODE,
transcription=transcription))
#
# Set the options for our variables.
#
phase.set_time_options(fix_initial=True, fix_duration=True, units='s')
phase.add_state('x', fix_initial=True, rate_source='v', units='m')
phase.add_state('v',
fix_initial=True,
fix_final=True,
rate_source='u',
units='m/s')
phase.add_control('u',
units='m/s**2',
scaler=0.01,
continuity=False,
rate_continuity=False,
rate2_continuity=False,
lower=-1.0,
upper=1.0)
#
# Maximize distance travelled.
#
phase.add_objective('x', loc='final', scaler=-1)
p.model.linear_solver = om.DirectSolver()
#
# Setup the problem and set our initial values.
#
p.setup(check=True)
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 1.0
p['traj.phase0.states:x'] = phase.interpolate(ys=[0, 0.25],
nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[0, 0],
nodes='state_input')
p['traj.phase0.controls:u'] = phase.interpolate(ys=[1, -1],
nodes='control_input')
#
# Solve the problem.
#
p.run_driver()
#
# Verify that the results are correct.
#
x = p.get_val('traj.phase0.timeseries.states:x')
v = p.get_val('traj.phase0.timeseries.states:v')
assert_rel_error(self, x[0], 0.0, tolerance=1.0E-4)
assert_rel_error(self, x[-1], 0.25, tolerance=1.0E-4)
assert_rel_error(self, v[0], 0.0, tolerance=1.0E-4)
assert_rel_error(self, v[-1], 0.0, tolerance=1.0E-4)
#
# Simulate the explicit solution and plot the results.
#
exp_out = traj.simulate()
plot_results(
[('traj.phase0.timeseries.time', 'traj.phase0.timeseries.states:x',
'time (s)', 'x $(m)$'),
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.states:v',
'time (s)', 'v $(m/s)$'),
('traj.phase0.timeseries.time',
'traj.phase0.timeseries.controls:u', 'time (s)', 'u $(m/s^2)$')],
title='Double Integrator Solution\nRadau Pseudospectral Method',
p_sol=p,
p_sim=exp_out)
plt.show()
def flying_robot_direct_collocation(transcription='gauss-lobatto',
compressed=True):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(num_segments=8, order=5, compressed=compressed)
elif transcription == "radau-ps":
t = dm.Radau(num_segments=8, order=5, compressed=compressed)
else:
raise ValueError('invalid transcription')
traj = p.model.add_subsystem('traj', dm.Trajectory())
phase = traj.add_phase('phase0',
dm.Phase(ode_class=FlyingRobotODE, transcription=t))
phase.set_time_options(fix_initial=True,
fix_duration=False,
duration_bounds=(0.1, 1E4),
units='s')
phase.add_state('x',
shape=(2, ),
fix_initial=True,
fix_final=True,
rate_source='v',
units='m')
phase.add_state('v',
shape=(2, ),
fix_initial=True,
fix_final=True,
rate_source='u',
units='m/s')
phase.add_state('J',
fix_initial=True,
fix_final=False,
rate_source='u_mag2',
units='m**2/s**3')
phase.add_control('u',
units='m/s**2',
shape=(2, ),
scaler=0.01,
continuity=False,
rate_continuity=False,
rate2_continuity=False,
lower=-1,
upper=1)
# Minimize the control effort
phase.add_objective('time', loc='final')
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 1.0
p['traj.phase0.states:x'] = phase.interpolate(ys=[[0.0, 0.0],
[-100.0, 100.0]],
nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[[0.0, 0.0], [0.0, 0.0]],
nodes='state_input')
p['traj.phase0.controls:u'] = phase.interpolate(ys=[[1, 1], [-1, -1]],
nodes='control_input')
p.run_driver()
return p
def ex_aircraft_steady_flight(optimizer='SLSQP',
solve_segments=False,
use_boundary_constraints=False,
compressed=False):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
_, optimizer = set_pyoptsparse_opt(optimizer, fallback=False)
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
if optimizer == 'SNOPT':
p.driver.opt_settings['Major iterations limit'] = 20
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings["Linesearch tolerance"] = 0.10
p.driver.opt_settings['iSumm'] = 6
if optimizer == 'SLSQP':
p.driver.opt_settings['MAXIT'] = 50
num_seg = 15
seg_ends, _ = lgl(num_seg + 1)
phase = dm.Phase(ode_class=AircraftODE,
transcription=dm.Radau(num_segments=num_seg,
segment_ends=seg_ends,
order=3,
compressed=compressed,
solve_segments=solve_segments))
# Pass Reference Area from an external source
assumptions = p.model.add_subsystem('assumptions', IndepVarComp())
assumptions.add_output('S', val=427.8, units='m**2')
assumptions.add_output('mass_empty', val=1.0, units='kg')
assumptions.add_output('mass_payload', val=1.0, units='kg')
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0),
duration_bounds=(300, 10000),
duration_ref=5600)
fix_final = True
if use_boundary_constraints:
fix_final = False
phase.add_boundary_constraint('mass_fuel',
loc='final',
units='lbm',
equals=1e-3,
linear=False)
phase.add_boundary_constraint('alt',
loc='final',
units='kft',
equals=10.0,
linear=False)
phase.set_state_options('range',
units='NM',
fix_initial=True,
fix_final=False,
ref=1e-3,
defect_ref=1e-3,
lower=0,
upper=2000)
phase.set_state_options('mass_fuel',
units='lbm',
fix_initial=True,
fix_final=fix_final,
upper=1.5E5,
lower=0.0,
ref=1e2,
defect_ref=1e2)
phase.set_state_options('alt',
units='kft',
fix_initial=True,
fix_final=fix_final,
lower=0.0,
upper=60,
ref=1e-3,
defect_ref=1e-3)
phase.add_control('climb_rate',
units='ft/min',
opt=True,
lower=-3000,
upper=3000,
rate_continuity=True,
rate2_continuity=False)
phase.add_control('mach', units=None, opt=False)
phase.add_input_parameter('S', units='m**2')
phase.add_input_parameter('mass_empty', units='kg')
phase.add_input_parameter('mass_payload', units='kg')
phase.add_path_constraint('propulsion.tau',
lower=0.01,
upper=2.0,
shape=(1, ))
p.model.connect('assumptions.S', 'phase0.input_parameters:S')
p.model.connect('assumptions.mass_empty',
'phase0.input_parameters:mass_empty')
p.model.connect('assumptions.mass_payload',
'phase0.input_parameters:mass_payload')
phase.add_objective('range', loc='final', ref=-1.0e-4)
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 3600.0
p['phase0.states:range'][:] = phase.interpolate(ys=(0, 724.0),
nodes='state_input')
p['phase0.states:mass_fuel'][:] = phase.interpolate(ys=(30000, 1e-3),
nodes='state_input')
p['phase0.states:alt'][:] = 10.0
p['phase0.controls:mach'][:] = 0.8
p['assumptions.S'] = 427.8
p['assumptions.mass_empty'] = 0.15E6
p['assumptions.mass_payload'] = 84.02869 * 400
p.run_driver()
return p
def EESG_Opt_example():
opt_problem=Problem(root=EESG_Opt())
#Example optimization of an EESG for costs on a 5 MW reference turbine
# add optimizer and set-up problem (using user defined input on objective function)
#
opt_problem.driver=pyOptSparseDriver()
opt_problem.driver.options['optimizer'] = 'CONMIN'
opt_problem.driver.add_objective('Costs') # Define Objective
opt_problem.driver.opt_settings['IPRINT'] = 4
opt_problem.driver.opt_settings['ITRM'] = 3
opt_problem.driver.opt_settings['ITMAX'] = 10
opt_problem.driver.opt_settings['DELFUN'] = 1e-3
opt_problem.driver.opt_settings['DABFUN'] = 1e-3
opt_problem.driver.opt_settings['IFILE'] = 'CONMIN_EESG.out'
opt_problem.root.deriv_options['type']='fd'
# Specificiency target efficiency(%)
Eta_Target = 93.0
# Set bounds for design variables for an EESG designed for a 5MW turbine
opt_problem.driver.add_desvar('r_s',lower=0.5,upper=9.0)
opt_problem.driver.add_desvar('l_s', lower=0.5, upper=2.5)
opt_problem.driver.add_desvar('h_s', lower=0.06, upper=0.15)
opt_problem.driver.add_desvar('tau_p', lower=0.04, upper=0.2)
opt_problem.driver.add_desvar('N_f', lower=10, upper=300)
opt_problem.driver.add_desvar('I_f', lower=1, upper=500)
opt_problem.driver.add_desvar('n_r', lower=5.0, upper=15.0)
opt_problem.driver.add_desvar('h_yr', lower=0.01, upper=0.25)
opt_problem.driver.add_desvar('h_ys', lower=0.01, upper=0.25)
opt_problem.driver.add_desvar('b_r', lower=0.1, upper=1.5)
opt_problem.driver.add_desvar('d_r', lower=0.1, upper=1.5)
opt_problem.driver.add_desvar('t_wr', lower=0.001, upper=0.2)
opt_problem.driver.add_desvar('n_s', lower=5.0, upper=15.0)
opt_problem.driver.add_desvar('b_st', lower=0.1, upper=1.5)
opt_problem.driver.add_desvar('d_s', lower=0.1, upper=1.5)
opt_problem.driver.add_desvar('t_ws', lower=0.001, upper=0.2)
# set up constraints for the PMSG_arms generator
opt_problem.driver.add_constraint('B_symax',upper=2.0-1.0e-6) #1
opt_problem.driver.add_constraint('B_rymax',upper=2.0-1.0e-6) #2
opt_problem.driver.add_constraint('B_tmax',upper=2.0-1.0e-6) #3
opt_problem.driver.add_constraint('B_gfm',lower=0.617031,upper=1.057768) #4
opt_problem.driver.add_constraint('B_g',lower=0.7,upper=1.2) #5
opt_problem.driver.add_constraint('B_pc',upper=2.0) #6
opt_problem.driver.add_constraint('E_s',lower=500.0,upper=5000.0) #7
opt_problem.driver.add_constraint('con_uAs',lower=0.0+1.0e-6) #8
opt_problem.driver.add_constraint('con_zAs',lower=0.0+1.0e-6) #9
opt_problem.driver.add_constraint('con_yAs',lower=0.0+1.0e-6) #10
opt_problem.driver.add_constraint('con_uAr',lower=0.0+1.0e-6) #11
opt_problem.driver.add_constraint('con_zAr',lower=0.0+1.0e-6) #12
opt_problem.driver.add_constraint('con_yAr',lower=0.0+1.0e-6) #13
opt_problem.driver.add_constraint('con_TC2',lower=0.0+1.0e-6) #14
opt_problem.driver.add_constraint('con_TC3',lower=0.0+1e-6) #15
opt_problem.driver.add_constraint('con_br',lower=0.0+1e-6) #16
opt_problem.driver.add_constraint('con_bst',lower=0.0-1e-6) #17
opt_problem.driver.add_constraint('A_1',upper=60000.0-1e-6) #18
opt_problem.driver.add_constraint('J_s',upper=6.0) #19
opt_problem.driver.add_constraint('J_f',upper=6.0) #20
opt_problem.driver.add_constraint('A_Cuscalc',lower=5.0,upper=300) #22
opt_problem.driver.add_constraint('A_Curcalc',lower=10,upper=300) #23
opt_problem.driver.add_constraint('K_rad',lower=0.2+1e-6,upper=0.27) #24
opt_problem.driver.add_constraint('Slot_aspect_ratio',lower=4.0,upper=10.0)#25
opt_problem.driver.add_constraint('gen_eff',lower=Eta_Target) #26
opt_problem.driver.add_constraint('n_brushes',upper=6) #27
opt_problem.driver.add_constraint('Power_ratio',upper=2-1.0e-6) #28
opt_problem.setup()
# Specify Target machine parameters
opt_problem['machine_rating']=5000000.0
opt_problem['Torque']=4.143289e6
opt_problem['n_nom']=12.1
# Initial design variables
opt_problem['r_s']=3.2
opt_problem['l_s']=1.4
opt_problem['h_s']= 0.060
opt_problem['tau_p']= 0.170
opt_problem['I_f']= 69
opt_problem['N_f']= 100
opt_problem['h_ys']= 0.130
opt_problem['h_yr']= 0.120
opt_problem['n_s']= 5
opt_problem['b_st']= 0.470
opt_problem['n_r']=5
opt_problem['b_r']= 0.480
opt_problem['d_r']= 0.510
opt_problem['d_s']= 0.400
opt_problem['t_wr']=0.140
opt_problem['t_ws']=0.070
opt_problem['R_o']=0.43 #10MW: 0.523950817,#5MW: 0.43, #3MW:0.363882632 #1.5MW: 0.2775 0.75MW: 0.17625
# Costs
opt_problem['C_Cu']=4.786
opt_problem['C_Fe']= 0.556
opt_problem['C_Fes']=0.50139
#Material properties
opt_problem['rho_Fe']= 7700 #Magnetic Steel/iron density
opt_problem['rho_Fes']= 7850 #structural Steel density
opt_problem['rho_Copper']=8900 # Kg/m3 copper density
opt_problem['main_shaft_cm']=np.array([0.0, 0.0, 0.0])
opt_problem['main_shaft_length'] =2.0
#Run optimization
opt_problem.run()
"""Uncomment to print solution to screen/an excel file
def setup_energy_opt(num_seg,
order,
Q_env=0.,
Q_sink=0.,
Q_out=0.,
m_flow=0.1,
m_burn=0.,
opt_m_flow=False,
opt_m_burn=False):
"""
Helper function to set up and return a problem instance for an energy minimization
of a simple thermal system.
Parameters
----------
num_seg : int
The number of ODE segments to use when discretizing the problem.
order : int
The order for the polynomial interpolation for the collocation methods.
"""
# Instantiate the problem and set the optimizer
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SNOPT'
p.driver.opt_settings['Major iterations limit'] = 2000
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-7
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-7
p.driver.opt_settings['Verify level'] = -1
# Set up the phase for the defined ODE function, can be LGR or LGL
phase = Phase('gauss-lobatto',
ode_class=TankAloneODE,
ode_init_kwargs={},
num_segments=num_seg,
transcription_order=order,
compressed=True)
# Do not allow the time to vary during the optimization
phase.set_time_options(opt_initial=False, opt_duration=False)
# Set the state options for mass, temperature, and energy.
phase.set_state_options('m', lower=1., upper=10., fix_initial=False)
phase.set_state_options('T', fix_initial=True)
phase.set_state_options('energy', fix_initial=True)
# Minimize the energy used to pump the fuel
# phase.add_objective('energy', loc='final')
# phase.add_objective('m', loc='initial')
phase.add_objective('time', loc='final')
# Allow the optimizer to vary the fuel flow
if opt_m_flow:
phase.add_control('m_flow',
val=m_flow,
lower=0.01,
opt=True,
rate_continuity=True)
else:
phase.add_control('m_flow', val=m_flow, opt=False)
if opt_m_burn:
phase.add_control('m_burn',
val=m_burn,
lower=0.01,
opt=True,
rate_continuity=True)
else:
phase.add_control('m_burn', val=m_burn, opt=False)
phase.add_control('Q_env', val=Q_env, dynamic=False, opt=False)
phase.add_control('Q_sink', val=Q_sink, dynamic=False, opt=False)
phase.add_control('Q_out', val=Q_out, dynamic=False, opt=False)
# Constrain the temperature, 2nd derivative of fuel mass in the tank, and make
# sure that the amount recirculated is at least 0, otherwise we'd burn
# more fuel than we pumped.
if opt_m_flow:
phase.add_path_constraint('T', upper=1.)
phase.add_path_constraint('m_flow_rate', upper=0.)
phase.add_path_constraint('m_recirculated', lower=0.)
phase.add_path_constraint('m_flow', upper=3.)
# Add the phase to the problem and set it up
p.model.add_subsystem('phase', phase)
p.driver.add_recorder(SqliteRecorder('out.db'))
p.setup(check=True, force_alloc_complex=True, mode='fwd')
# Give initial values for the phase states, controls, and time
p['phase.states:m'] = 2.
p['phase.states:T'] = 1.
p['phase.states:energy'] = 0.
p['phase.t_initial'] = 0.
p['phase.t_duration'] = 10.
p.set_solver_print(level=-1)
return p
num_inputs = nn
elif 'bandwidth' in varied_term:
bandwidth = nn
print(
f'Running {num_repeats} cases of {num_inputs} num_inputs, {num_outputs} num_outputs, {bandwidth} bandwidth'
)
prob = om.Problem()
prob.model = MatrixGroup(comp_type=MatrixComp,
num_inputs=num_inputs,
num_outputs=num_outputs,
bandwidth=bandwidth,
random_seed=random_seed)
prob.driver = om.pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.driver.opt_settings['Major optimality tolerance'] = 1e-8
prob.driver.opt_settings['Major print level'] = 0
prob.driver.opt_settings['Minor print level'] = 0
prob.driver.opt_settings['iPrint'] = 0
prob.model.add_design_var('x', lower=-10, upper=10)
prob.model.add_objective('obj')
if 'inputs' in varied_term or 'bandwidth' in varied_term:
prob.setup(mode='rev')
else:
prob.setup(mode='fwd')
prob['x'][:] = 2.
def test_ssto_simulate_root_trajectory(self):
"""
Tests that we can properly simulate a trajectory even if the trajectory is the root
group of the model. In this case the name of the trajectory in the output will
be 'sim_traj'.
"""
import numpy as np
import matplotlib.pyplot as plt
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
g = 1.61544 # lunar gravity, m/s**2
class LaunchVehicle2DEOM(om.ExplicitComponent):
"""
Simple 2D Cartesian Equations of Motion for a launch vehicle subject to thrust and drag.
"""
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('vx',
val=np.zeros(nn),
desc='x velocity',
units='m/s')
self.add_input('vy',
val=np.zeros(nn),
desc='y velocity',
units='m/s')
self.add_input('m', val=np.zeros(nn), desc='mass', units='kg')
self.add_input('theta',
val=np.zeros(nn),
desc='pitch angle',
units='rad')
self.add_input('thrust',
val=2100000 * np.ones(nn),
desc='thrust',
units='N')
self.add_input('Isp',
val=265.2 * np.ones(nn),
desc='specific impulse',
units='s')
# Outputs
self.add_output('xdot',
val=np.zeros(nn),
desc='velocity component in x',
units='m/s')
self.add_output('ydot',
val=np.zeros(nn),
desc='velocity component in y',
units='m/s')
self.add_output('vxdot',
val=np.zeros(nn),
desc='x acceleration magnitude',
units='m/s**2')
self.add_output('vydot',
val=np.zeros(nn),
desc='y acceleration magnitude',
units='m/s**2')
self.add_output('mdot',
val=np.zeros(nn),
desc='mass rate of change',
units='kg/s')
# Setup partials
ar = np.arange(self.options['num_nodes'])
self.declare_partials(of='xdot',
wrt='vx',
rows=ar,
cols=ar,
val=1.0)
self.declare_partials(of='ydot',
wrt='vy',
rows=ar,
cols=ar,
val=1.0)
self.declare_partials(of='vxdot', wrt='vx', rows=ar, cols=ar)
self.declare_partials(of='vxdot', wrt='m', rows=ar, cols=ar)
self.declare_partials(of='vxdot',
wrt='theta',
rows=ar,
cols=ar)
self.declare_partials(of='vxdot',
wrt='thrust',
rows=ar,
cols=ar)
self.declare_partials(of='vydot', wrt='m', rows=ar, cols=ar)
self.declare_partials(of='vydot',
wrt='theta',
rows=ar,
cols=ar)
self.declare_partials(of='vydot', wrt='vy', rows=ar, cols=ar)
self.declare_partials(of='vydot',
wrt='thrust',
rows=ar,
cols=ar)
self.declare_partials(of='mdot',
wrt='thrust',
rows=ar,
cols=ar)
self.declare_partials(of='mdot', wrt='Isp', rows=ar, cols=ar)
def compute(self, inputs, outputs):
theta = inputs['theta']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
vx = inputs['vx']
vy = inputs['vy']
m = inputs['m']
F_T = inputs['thrust']
Isp = inputs['Isp']
outputs['xdot'] = vx
outputs['ydot'] = vy
outputs['vxdot'] = F_T * cos_theta / m
outputs['vydot'] = F_T * sin_theta / m - g
outputs['mdot'] = -F_T / (g * Isp)
def compute_partials(self, inputs, jacobian):
theta = inputs['theta']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
m = inputs['m']
F_T = inputs['thrust']
Isp = inputs['Isp']
# jacobian['vxdot', 'vx'] = -CDA * rho * vx / m
jacobian['vxdot', 'm'] = -(F_T * cos_theta) / m**2
jacobian['vxdot', 'theta'] = -(F_T / m) * sin_theta
jacobian['vxdot', 'thrust'] = cos_theta / m
# jacobian['vydot', 'vy'] = -CDA * rho * vy / m
jacobian['vydot', 'm'] = -(F_T * sin_theta) / m**2
jacobian['vydot', 'theta'] = (F_T / m) * cos_theta
jacobian['vydot', 'thrust'] = sin_theta / m
jacobian['mdot', 'thrust'] = -1.0 / (g * Isp)
jacobian['mdot', 'Isp'] = F_T / (g * Isp**2)
class LaunchVehicleLinearTangentODE(om.Group):
"""
The LaunchVehicleLinearTangentODE for this case consists of a guidance component and
the EOM. Guidance is simply an OpenMDAO ExecComp which computes the arctangent of the
tan_theta variable.
"""
def initialize(self):
self.options.declare(
'num_nodes',
types=int,
desc='Number of nodes to be evaluated in the RHS')
def setup(self):
nn = self.options['num_nodes']
self.add_subsystem(
'guidance',
om.ExecComp('theta=arctan(tan_theta)',
theta={
'value': np.ones(nn),
'units': 'rad'
},
tan_theta={'value': np.ones(nn)}))
self.add_subsystem('eom', LaunchVehicle2DEOM(num_nodes=nn))
self.connect('guidance.theta', 'eom.theta')
#
# Setup and solve the optimal control problem
#
traj = dm.Trajectory()
p = om.Problem(model=traj)
phase = dm.Phase(ode_class=LaunchVehicleLinearTangentODE,
transcription=dm.Radau(num_segments=20,
order=3,
compressed=False))
traj.add_phase('phase0', phase)
phase.set_time_options(fix_initial=True,
duration_bounds=(10, 1000),
units='s')
#
# Set the state options. We include rate_source, units, and targets here since the ODE
# is not decorated with their default values.
#
phase.add_state('x', fix_initial=True, lower=0, rate_source='eom.xdot')
phase.add_state('y', fix_initial=True, lower=0, rate_source='eom.ydot')
phase.add_state('vx',
fix_initial=True,
lower=0,
rate_source='eom.vxdot',
units='m/s',
targets=['eom.vx'])
phase.add_state('vy',
fix_initial=True,
rate_source='eom.vydot',
units='m/s',
targets=['eom.vy'])
phase.add_state('m',
fix_initial=True,
rate_source='eom.mdot',
units='kg',
targets=['eom.m'])
#
# The tangent of theta is modeled as a linear polynomial over the duration of the phase.
#
phase.add_polynomial_control('tan_theta',
order=1,
units=None,
opt=True,
targets=['guidance.tan_theta'])
#
# Parameters values for thrust and specific impulse are design parameters. They are
# provided by an IndepVarComp in the phase, but with opt=False their values are not
# design variables in the optimization problem.
#
phase.add_parameter('thrust',
units='N',
opt=False,
val=3.0 * 50000.0 * 1.61544,
targets=['eom.thrust'])
phase.add_parameter('Isp',
units='s',
opt=False,
val=1.0E6,
targets=['eom.Isp'])
#
# Set the boundary constraints. These are all states which could also be handled
# by setting fix_final=True and including the correct final value in the initial guess.
#
phase.add_boundary_constraint('y',
loc='final',
equals=1.85E5,
linear=True)
phase.add_boundary_constraint('vx', loc='final', equals=1627.0)
phase.add_boundary_constraint('vy', loc='final', equals=0)
phase.add_objective('time', index=-1, scaler=0.01)
#
# Add theta as a timeseries output since it's not included by default.
#
phase.add_timeseries_output('guidance.theta', units='deg')
#
# Set the optimizer
#
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
#
# We don't strictly need to define a linear solver here since our problem is entirely
# feed-forward with no iterative loops. It's good practice to add one, however, since
# failing to do so can cause incorrect derivatives if iterative processes are ever
# introduced to the system.
#
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
#
# Assign initial guesses for the independent variables in the problem.
#
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 500.0
p['phase0.states:x'] = phase.interp('x', [0, 350000.0])
p['phase0.states:y'] = phase.interp('y', [0, 185000.0])
p['phase0.states:vx'] = phase.interp('vx', [0, 1627.0])
p['phase0.states:vy'] = phase.interp('vy', [1.0E-6, 0])
p['phase0.states:m'] = phase.interp('m', [50000, 50000])
p['phase0.polynomial_controls:tan_theta'] = [[0.5 * np.pi], [0.0]]
#
# Solve the problem.
#
p.run_driver()
#
# Check the results.
#
assert_near_equal(p.get_val('phase0.timeseries.time')[-1],
481,
tolerance=0.01)
#
# Get the explitly simulated results
#
exp_out = traj.simulate()
#
# Plot the results
#
fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(10, 8))
axes[0].plot(p.get_val('phase0.timeseries.states:x'),
p.get_val('phase0.timeseries.states:y'),
marker='o',
ms=4,
linestyle='None',
label='solution')
axes[0].plot(exp_out.get_val('sim_traj.phase0.timeseries.states:x'),
exp_out.get_val('sim_traj.phase0.timeseries.states:y'),
marker=None,
linestyle='-',
label='simulation')
axes[0].set_xlabel('range (m)')
axes[0].set_ylabel('altitude (m)')
axes[0].set_aspect('equal')
axes[1].plot(p.get_val('phase0.timeseries.time'),
p.get_val('phase0.timeseries.theta'),
marker='o',
ms=4,
linestyle='None')
axes[1].plot(exp_out.get_val('sim_traj.phase0.timeseries.time'),
exp_out.get_val('sim_traj.phase0.timeseries.theta'),
linestyle='-',
marker=None)
axes[1].set_xlabel('time (s)')
axes[1].set_ylabel('theta (deg)')
plt.suptitle(
'Single Stage to Orbit Solution Using Polynomial Controls')
fig.legend(loc='lower center', ncol=2)
plt.show()
def test_static_parameter_connections_radau(self):
class TrajectoryODE(om.Group):
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
self.add_subsystem(
'sum',
om.ExecComp('m_tot = sum(m)',
m={
'val': np.zeros((2, 2)),
'units': 'kg'
},
m_tot={
'val': np.zeros(nn),
'units': 'kg'
}))
self.add_subsystem('eom', FlightPathEOM2D(num_nodes=nn))
self.connect('sum.m_tot', 'eom.m')
optimizer = 'SLSQP'
num_segments = 1
transcription_order = 5
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.declare_coloring()
seg_ends, _ = lgl(num_segments + 1)
phase = dm.Phase(ode_class=TrajectoryODE,
transcription=dm.Radau(num_segments=num_segments,
order=transcription_order,
segment_ends=seg_ends))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0.0, 100.0),
duration_bounds=(0., 100.))
phase.add_state('h',
fix_initial=True,
fix_final=True,
lower=0.0,
units='m',
rate_source='eom.h_dot')
phase.add_state('v',
fix_initial=True,
fix_final=False,
units='m/s',
rate_source='eom.v_dot')
phase.add_parameter('m',
val=[[1, 2], [3, 4]],
units='kg',
targets='sum.m',
static_target=True)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True, force_alloc_complex=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 100.0
p['phase0.states:h'] = phase.interp('h', [20, 0])
p['phase0.states:v'] = phase.interp('v', [0, -5])
p.run_model()
expected = np.array([[1, 2], [3, 4]])
assert_near_equal(p.get_val('phase0.rhs_all.sum.m'), expected)
def test_steady_aircraft_for_docs(self):
import matplotlib.pyplot as plt
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.aircraft_steady_flight.aircraft_ode import AircraftODE
from dymos.examples.plotting import plot_results
from dymos.utils.lgl import lgl
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
num_seg = 15
seg_ends, _ = lgl(num_seg + 1)
traj = p.model.add_subsystem('traj', dm.Trajectory())
phase = traj.add_phase(
'phase0',
dm.Phase(ode_class=AircraftODE,
transcription=dm.Radau(num_segments=num_seg,
segment_ends=seg_ends,
order=3,
compressed=False)))
# Pass Reference Area from an external source
assumptions = p.model.add_subsystem('assumptions', om.IndepVarComp())
assumptions.add_output('S', val=427.8, units='m**2')
assumptions.add_output('mass_empty', val=1.0, units='kg')
assumptions.add_output('mass_payload', val=1.0, units='kg')
phase.set_time_options(fix_initial=True,
duration_bounds=(300, 10000),
duration_ref=5600)
phase.add_state('range',
units='NM',
rate_source='range_rate_comp.dXdt:range',
fix_initial=True,
fix_final=False,
ref=1e-3,
defect_ref=1e-3,
lower=0,
upper=2000)
phase.add_state('mass_fuel',
units='lbm',
rate_source='propulsion.dXdt:mass_fuel',
fix_initial=True,
fix_final=True,
upper=1.5E5,
lower=0.0,
ref=1e2,
defect_ref=1e2)
phase.add_state('alt',
units='kft',
rate_source='climb_rate',
fix_initial=True,
fix_final=True,
lower=0.0,
upper=60,
ref=1e-3,
defect_ref=1e-3)
phase.add_control('climb_rate',
units='ft/min',
opt=True,
lower=-3000,
upper=3000,
targets=['gam_comp.climb_rate'],
rate_continuity=True,
rate2_continuity=False)
phase.add_control('mach',
targets=['tas_comp.mach', 'aero.mach'],
units=None,
opt=False)
phase.add_parameter(
'S',
targets=['aero.S', 'flight_equilibrium.S', 'propulsion.S'],
units='m**2')
phase.add_parameter('mass_empty',
targets=['mass_comp.mass_empty'],
units='kg')
phase.add_parameter('mass_payload',
targets=['mass_comp.mass_payload'],
units='kg')
phase.add_path_constraint('propulsion.tau',
lower=0.01,
upper=2.0,
shape=(1, ))
p.model.connect('assumptions.S', 'traj.phase0.parameters:S')
p.model.connect('assumptions.mass_empty',
'traj.phase0.parameters:mass_empty')
p.model.connect('assumptions.mass_payload',
'traj.phase0.parameters:mass_payload')
phase.add_objective('range', loc='final', ref=-1.0e-4)
phase.add_timeseries_output('aero.CL', units=None, shape=(1, ))
phase.add_timeseries_output('aero.CD', units=None, shape=(1, ))
p.setup()
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 3600.0
p['traj.phase0.states:range'][:] = phase.interpolate(
ys=(0, 724.0), nodes='state_input')
p['traj.phase0.states:mass_fuel'][:] = phase.interpolate(
ys=(30000, 1e-3), nodes='state_input')
p['traj.phase0.states:alt'][:] = 10.0
p['traj.phase0.controls:mach'][:] = 0.8
p['assumptions.S'] = 427.8
p['assumptions.mass_empty'] = 0.15E6
p['assumptions.mass_payload'] = 84.02869 * 400
dm.run_problem(p)
assert_near_equal(p.get_val('traj.phase0.timeseries.states:range',
units='NM')[-1],
726.85,
tolerance=1.0E-2)
exp_out = traj.simulate()
plot_results(
[('traj.phase0.timeseries.states:range',
'traj.phase0.timeseries.states:alt', 'range (NM)',
'altitude (kft)'),
('traj.phase0.timeseries.time',
'traj.phase0.timeseries.states:mass_fuel', 'time (s)',
'fuel mass (lbm)'),
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.CL',
'time (s)', 'lift coefficient'),
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.CD',
'time (s)', 'drag coefficient')],
title='Commercial Aircraft Optimization',
p_sol=p,
p_sim=exp_out)
plt.show()
def test_min_time_climb_for_docs_partial_coloring(self):
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.min_time_climb.doc.min_time_climb_ode_partial_coloring import MinTimeClimbODE
for fd in (False, True):
if fd:
pc_options = (False, True)
else:
pc_options = (False, )
for pc in pc_options:
with self.subTest(
f'Finite Differencing: {fd} Partial Coloring: {pc}'):
print(f'Finite Differencing: {fd} Partial Coloring: {pc}')
#
# Instantiate the problem and configure the optimization driver
#
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'IPOPT'
p.driver.declare_coloring(tol=1.0E-12)
p.driver.opt_settings['max_iter'] = 500
p.driver.opt_settings[
'alpha_for_y'] = 'safer-min-dual-infeas'
#
# Instantiate the trajectory and phase
#
traj = dm.Trajectory()
phase = dm.Phase(
ode_class=MinTimeClimbODE,
ode_init_kwargs={
'fd': fd,
'partial_coloring': pc
},
transcription=dm.GaussLobatto(num_segments=30))
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj', traj)
#
# Set the options on the optimization variables
#
phase.set_time_options(fix_initial=True,
duration_bounds=(50, 400),
duration_ref=100.0)
phase.add_state('r',
fix_initial=True,
lower=0,
upper=1.0E6,
ref=1.0E3,
defect_ref=1.0E3,
units='m',
rate_source='flight_dynamics.r_dot')
phase.add_state('h',
fix_initial=True,
lower=0,
upper=20000.0,
ref=1.0E2,
defect_ref=1.0E2,
units='m',
rate_source='flight_dynamics.h_dot')
phase.add_state('v',
fix_initial=True,
lower=10.0,
ref=1.0E2,
defect_ref=1.0E2,
units='m/s',
rate_source='flight_dynamics.v_dot')
phase.add_state('gam',
fix_initial=True,
lower=-1.5,
upper=1.5,
ref=1.0,
defect_ref=1.0,
units='rad',
rate_source='flight_dynamics.gam_dot')
phase.add_state('m',
fix_initial=True,
lower=10.0,
upper=1.0E5,
ref=1.0E3,
defect_ref=1.0E3,
units='kg',
rate_source='prop.m_dot')
phase.add_control('alpha',
units='deg',
lower=-8.0,
upper=8.0,
scaler=1.0,
rate_continuity=True,
rate_continuity_scaler=100.0,
rate2_continuity=False,
targets=['alpha'])
phase.add_parameter('S',
val=49.2386,
units='m**2',
opt=False,
targets=['S'])
phase.add_parameter('Isp',
val=1600.0,
units='s',
opt=False,
targets=['Isp'])
phase.add_parameter('throttle',
val=1.0,
opt=False,
targets=['throttle'])
#
# Setup the boundary and path constraints
#
phase.add_boundary_constraint('h',
loc='final',
equals=20000,
scaler=1.0E-3)
phase.add_boundary_constraint('aero.mach',
loc='final',
equals=1.0)
phase.add_boundary_constraint('gam',
loc='final',
equals=0.0)
phase.add_path_constraint(name='h',
lower=100.0,
upper=20000,
ref=20000)
phase.add_path_constraint(name='aero.mach',
lower=0.1,
upper=1.8)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', ref=100.0)
p.model.linear_solver = om.DirectSolver()
#
# Setup the problem and set the initial guess
#
p.setup()
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 500
p['traj.phase0.states:r'] = phase.interp(
'r', [0.0, 50000.0])
p['traj.phase0.states:h'] = phase.interp(
'h', [100.0, 20000.0])
p['traj.phase0.states:v'] = phase.interp(
'v', [135.964, 283.159])
p['traj.phase0.states:gam'] = phase.interp(
'gam', [0.0, 0.0])
p['traj.phase0.states:m'] = phase.interp(
'm', [19030.468, 10000.])
p['traj.phase0.controls:alpha'] = phase.interp(
'alpha', [0.0, 0.0])
#
# Solve for the optimal trajectory
#
dm.run_problem(p)
#
# This code is intended to save the coloring plots for the documentation.
# In practice, use the command line interface to view these files instead:
# `openmdao view_coloring coloring_files/total_coloring.pkl --view`
#
stfd = '_fd' if fd else ''
stpc = '_pc' if pc else ''
coloring_dir = f'coloring_files{stfd}{stpc}'
if fd or pc:
if os.path.exists(coloring_dir):
shutil.rmtree(coloring_dir)
shutil.move('coloring_files', coloring_dir)
_view_coloring(
os.path.join(coloring_dir, 'total_coloring.pkl'))
#
# Test the results
#
assert_near_equal(p.get_val('traj.phase0.t_duration'),
321.0,
tolerance=1.0E-1)
def setUp(self):
solver = 'SLSQP'
num_seg = 10
seg_ncn = 2
rel_lengths = 'lgl'
# Instantiate a problem and set it's root to an empty Trajectory
prob = Problem()
prob.add_traj(Trajectory("traj0"))
if solver == 'SNOPT' and pyOptSparseDriver is not None:
driver = pyOptSparseDriver()
driver.options['optimizer'] = solver
driver.opt_settings['Major iterations limit'] = 1000
driver.opt_settings['iSumm'] = 6
driver.opt_settings['Major step limit'] = 0.5
driver.opt_settings["Major feasibility tolerance"] = 1.0E-5
driver.opt_settings["Major optimality tolerance"] = 1.0E-5
driver.opt_settings["Minor feasibility tolerance"] = 1.0E-4
driver.opt_settings['Verify level'] = 3
else:
driver = ScipyOptimizer()
driver.options['tol'] = 1.0E-6
driver.options['disp'] = True
driver.options['maxiter'] = 500
prob.driver = driver
dynamic_controls = [{'name': 'theta', 'units': 'rad'},
{'name': 'psi', 'units': 'rad'}]
static_controls = [{'name': 'mass', 'units': 'kg'},
{'name': 'g', 'units': 'm/s/s'},
{'name': 'Cd', 'units': 'unitless'},
{'name': 'D_magnetic', 'units': 'N'},
{'name': 'R', 'units': 'J/(kg*K)'},
{'name': 'S', 'units': 'm**2'},
{'name': 'T_ambient', 'units': 'K'},
{'name': 'p_tube', 'units': 'Pa'}]
phase0 = CollocationPhase(name='phase0', rhs_class=MagnePlaneRHS,
num_seg=num_seg, seg_ncn=seg_ncn,
rel_lengths=rel_lengths,
dynamic_controls=dynamic_controls,
static_controls=static_controls)
prob.trajectories["traj0"].add_phase(phase0)
phase0.set_state_options('x', lower=0, upper=100,
ic_val=0, ic_fix=True,
fc_val=10, fc_fix=True,
scaler=10.0, defect_scaler=0.1)
phase0.set_state_options('y', lower=0, upper=0,
ic_val=0, ic_fix=True,
fc_val=0, fc_fix=True,
scaler=10.0, defect_scaler=0.1)
phase0.set_state_options('z', lower=-10, upper=10,
ic_val=-10, ic_fix=True,
fc_val=-5, fc_fix=True,
scaler=10.0, defect_scaler=0.1)
phase0.set_state_options('v', lower=0, upper=np.inf,
ic_val=0.0, ic_fix=True,
fc_val=10.0, fc_fix=False,
scaler=10.0, defect_scaler=0.1)
phase0.set_dynamic_control_options('theta', ic_val=-1.57, fc_val=0.2,
opt=True, lower=-1.58, upper=1.58,
scaler=0.01)
phase0.set_dynamic_control_options('psi', ic_val=0.0, fc_val=0.0,
opt=True, lower=0.0, upper=0.0,
scaler=0.01)
phase0.set_static_control_options(name='g', val=9.80665, opt=False)
phase0.set_static_control_options(name='mass', val=1200, opt=False)
phase0.set_static_control_options(name='Cd', val=0.0, opt=False)
phase0.set_static_control_options(name='S', val=0.0, opt=False)
phase0.set_static_control_options(name='p_tube', val=0.0, opt=False)
phase0.set_static_control_options(name='T_ambient', val=298.0,
opt=False)
phase0.set_static_control_options(name='R', val=287.0, opt=False)
# Set D_magnetic equal to the thrust value for now, no net forces
# on the pod except gravity.
phase0.set_static_control_options(name='D_magnetic', val=30000.0,
opt=False)
phase0.set_time_options(t0_val=0, t0_lower=0, t0_upper=0, tp_val=1.81,
tp_lower=0.5, tp_upper=10.0)
prob.trajectories["traj0"].add_objective(name="t", phase="phase0",
place="end", scaler=1.0)
# Do top-level FD
prob.root.deriv_options['type'] = 'fd'
self.prob = prob
if __name__ == '__main__':
# Setup and run the model.
from openmdao.core.problem import Problem
from openmdao.drivers.scipy_optimizer import ScipyOptimizer
from openmdao.api import pyOptSparseDriver
from openmdao.api import SqliteRecorder
top = Problem()
top.root = SellarDerivatives()
# top.driver = ScipyOptimizer()
# top.driver.options['optimizer'] = 'SLSQP'
# top.driver.options['tol'] = 1.0e-8
top.driver = pyOptSparseDriver()
top.driver.options['optimizer'] = 'SNOPT'
top.driver.add_desvar('z', lower=np.array([-10.0, 0.0]),
upper=np.array([10.0, 10.0]))
top.driver.add_desvar('x', lower=0.0, upper=10.0)
top.driver.add_objective('obj')
top.driver.add_constraint('con1', upper=0.0)
top.driver.add_constraint('con2', upper=0.0)
rec = SqliteRecorder('sellar_snopt.db')
top.driver.add_recorder(rec)
rec.options['record_derivs'] = True
top.setup()
def test_discs(self):
OPT, OPTIMIZER = set_pyoptsparse_opt('SNOPT')
if OPTIMIZER is not 'SNOPT':
raise unittest.SkipTest("pyoptsparse is not providing SNOPT or SLSQP")
# So we compare the same starting locations.
np.random.seed(123)
radius = 1.0
pin = 15.0
n_disc = 7
prob = Problem()
prob.root = root = Group()
from openmdao.api import pyOptSparseDriver
driver = prob.driver = pyOptSparseDriver()
driver.options['optimizer'] = 'SNOPT'
driver.options['print_results'] = False
# Note, active tolerance requires relevance reduction to work.
root.ln_solver.options['single_voi_relevance_reduction'] = True
# Also, need to be in adjoint
root.ln_solver.options['mode'] = 'rev'
obj_expr = 'obj = '
sep = ''
for i in range(n_disc):
dist = "dist_%d" % i
x1var = 'x_%d' % i
# First disc is pinned
if i == 0:
root.add('p_%d' % i, IndepVarComp(x1var, pin), promotes=(x1var, ))
# The rest are design variables for the optimizer.
else:
init_val = 5.0*np.random.random() - 5.0 + pin
root.add('p_%d' % i, IndepVarComp(x1var, init_val), promotes=(x1var, ))
driver.add_desvar(x1var)
for j in range(i):
x2var = 'x_%d' % j
yvar = 'y_%d_%d' % (i, j)
name = dist + "_%d" % j
expr = '%s= (%s - %s)**2' % (yvar, x1var, x2var)
root.add(name, ExecComp(expr), promotes = (x1var, x2var, yvar))
# Constraint (you can experiment with turning on/off the active_tol)
#driver.add_constraint(yvar, lower=radius)
driver.add_constraint(yvar, lower=radius, active_tol=radius*3.0)
# This pair's contribution to objective
obj_expr += sep + yvar
sep = ' + '
root.add('sum_dist', ExecComp(obj_expr), promotes=('*', ))
driver.add_objective('obj')
prob.setup(check=False)
prob.run()
def test_simple_no_exception(self):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
transcription = dm.GaussLobatto(num_segments=3,
order=3,
compressed=True,
solve_segments='forward')
fix_final = True
traj = dm.Trajectory()
phase = dm.Phase(ode_class=BrachistochroneVectorStatesODE,
transcription=transcription)
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj0', traj)
phase.set_time_options(fix_initial=True,
duration_bounds=(.5, 10),
units='s')
# can't fix final position if you're solving the segments
phase.add_state('pos',
rate_source='pos_dot',
units='m',
fix_initial=True)
# test add_boundary_constraint with arrays:
expected = np.array([10, 5])
phase.add_boundary_constraint(name='pos',
loc='final',
lower=expected - 1)
phase.add_boundary_constraint(name='pos',
loc='final',
upper=expected + 1)
phase.add_boundary_constraint(name='pos', loc='final', equals=expected)
phase.add_state('v',
rate_source='vdot',
units='m/s',
fix_initial=True,
fix_final=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_parameter('g', units='m/s**2', val=9.80665, opt=False)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True, force_alloc_complex=True)
p.final_setup()
p['traj0.phase0.t_initial'] = 0.0
p['traj0.phase0.t_duration'] = 1.8016
pos0 = [0, 10]
posf = [10, 5]
p['traj0.phase0.states:pos'] = phase.interpolate(ys=[pos0, posf],
nodes='state_input')
p['traj0.phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['traj0.phase0.controls:theta'] = phase.interpolate(
ys=[5, 100], nodes='control_input')
p['traj0.phase0.parameters:g'] = 9.80665
p.run_driver()
def test_radau(self):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
t = dm.Radau(num_segments=20, order=[3, 5] * 10, compressed=True)
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=t)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.add_state(
'x',
rate_source=BrachistochroneODE.states['x']['rate_source'],
units=BrachistochroneODE.states['x']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state(
'y',
rate_source=BrachistochroneODE.states['y']['rate_source'],
units=BrachistochroneODE.states['y']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state(
'v',
rate_source=BrachistochroneODE.states['v']['rate_source'],
targets=BrachistochroneODE.states['v']['targets'],
units=BrachistochroneODE.states['v']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_control(
'theta',
targets=BrachistochroneODE.parameters['theta']['targets'],
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_input_parameter(
'g',
targets=BrachistochroneODE.parameters['g']['targets'],
units='m/s**2',
val=9.80665)
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100],
nodes='control_input')
p['phase0.input_parameters:g'] = 9.80665
p.run_driver()
exp_out = phase.simulate()
t_initial = p.get_val('phase0.timeseries.time')[0]
tf = p.get_val('phase0.timeseries.time')[-1]
x0 = p.get_val('phase0.timeseries.states:x')[0]
xf = p.get_val('phase0.timeseries.states:x')[-1]
y0 = p.get_val('phase0.timeseries.states:y')[0]
yf = p.get_val('phase0.timeseries.states:y')[-1]
v0 = p.get_val('phase0.timeseries.states:v')[0]
vf = p.get_val('phase0.timeseries.states:v')[-1]
g = p.get_val('phase0.timeseries.input_parameters:g')[0]
thetaf = exp_out.get_val('phase0.timeseries.controls:theta')[-1]
assert_almost_equal(t_initial, 0.0)
assert_almost_equal(x0, 0.0)
assert_almost_equal(y0, 10.0)
assert_almost_equal(v0, 0.0)
assert_almost_equal(tf, 1.8016, decimal=3)
assert_almost_equal(xf, 10.0, decimal=3)
assert_almost_equal(yf, 5.0, decimal=3)
assert_almost_equal(vf, 9.902, decimal=3)
assert_almost_equal(g, 9.80665, decimal=3)
assert_almost_equal(thetaf, 100.12, decimal=0)
def min_time_climb(optimizer='SLSQP', num_seg=3, transcription='gauss-lobatto',
transcription_order=3, top_level_jacobian='csc', simul_derivs=True,
force_alloc_complex=False):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
if simul_derivs:
p.driver.options['dynamic_simul_derivs'] = True
if optimizer == 'SNOPT':
p.driver.opt_settings['Major iterations limit'] = 1000
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings['Function precision'] = 1.0E-6
p.driver.opt_settings['Linesearch tolerance'] = 0.10
p.driver.opt_settings['Major step limit'] = 0.5
# p.driver.opt_settings['Verify level'] = 3
phase = Phase(transcription,
ode_class=MinTimeClimbODE,
num_segments=num_seg,
compressed=True,
transcription_order=transcription_order)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(50, 400),
duration_ref=100.0)
phase.set_state_options('r', fix_initial=True, lower=0, upper=1.0E6,
scaler=1.0E-3, defect_scaler=1.0E-2, units='m')
phase.set_state_options('h', fix_initial=True, lower=0, upper=20000.0,
scaler=1.0E-3, defect_scaler=1.0E-3, units='m')
phase.set_state_options('v', fix_initial=True, lower=10.0,
scaler=1.0E-2, defect_scaler=1.0E-2, units='m/s')
phase.set_state_options('gam', fix_initial=True, lower=-1.5, upper=1.5,
ref=1.0, defect_scaler=1.0, units='rad')
phase.set_state_options('m', fix_initial=True, lower=10.0, upper=1.0E5,
scaler=1.0E-3, defect_scaler=1.0E-3)
phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0,
continuity=True, rate_continuity=True, rate2_continuity=False)
phase.add_design_parameter('S', val=49.2386, units='m**2', opt=False)
phase.add_design_parameter('Isp', val=1600.0, units='s', opt=False)
phase.add_design_parameter('throttle', val=1.0, opt=False)
phase.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3, units='m')
phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0, units=None)
phase.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad')
phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
phase.add_path_constraint(name='alpha', lower=-8, upper=8)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final')
p.model.options['assembled_jac_type'] = top_level_jacobian.lower()
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.setup(check=True, force_alloc_complex=force_alloc_complex)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 298.46902
p['phase0.states:r'] = phase.interpolate(ys=[0.0, 111319.54], nodes='state_input')
p['phase0.states:h'] = phase.interpolate(ys=[100.0, 20000.0], nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[135.964, 283.159], nodes='state_input')
p['phase0.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='state_input')
p['phase0.states:m'] = phase.interpolate(ys=[19030.468, 16841.431], nodes='state_input')
p['phase0.controls:alpha'] = phase.interpolate(ys=[0.0, 0.0], nodes='control_input')
p.run_driver()
if SHOW_PLOTS:
exp_out = phase.simulate(times=np.linspace(0, p['phase0.t_duration'], 100))
import matplotlib.pyplot as plt
plt.plot(phase.get_values('time'), phase.get_values('h'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('h'), 'b-')
plt.xlabel('time (s)')
plt.ylabel('altitude (m)')
plt.figure()
plt.plot(phase.get_values('v'), phase.get_values('h'), 'ro')
plt.plot(exp_out.get_values('v'), exp_out.get_values('h'), 'b-')
plt.xlabel('airspeed (m/s)')
plt.ylabel('altitude (m)')
plt.figure()
plt.plot(phase.get_values('time'), phase.get_values('alpha'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('alpha'), 'b-')
plt.xlabel('time (s)')
plt.ylabel('alpha (rad)')
plt.figure()
plt.plot(phase.get_values('time'), phase.get_values('prop.thrust', units='lbf'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('prop.thrust', units='lbf'), 'b-')
plt.xlabel('time (s)')
plt.ylabel('thrust (lbf)')
plt.show()
return p
import openmdao.api as om
from testbed_components import simple_1D_low, simple_1D_high
np.random.seed(314)
mm = om.MultiFiMetaModelUnStructuredComp(nfi=2)
mm.add_input("x", np.zeros((1, )))
mm.add_output("y", np.zeros((1, )))
# Surrrogate model that implements the multifidelity cokriging method.
mm.options["default_surrogate"] = om.MultiFiCoKrigingSurrogate(normalize=False)
prob = om.Problem()
prob.model.add_subsystem("mm", mm, promotes=["*"])
prob.driver = om.pyOptSparseDriver() # om.ScipyOptimizeDriver() #
prob.driver.options["optimizer"] = "SNOPT"
# prob.driver.opt_settings['Verify level'] = -1
# --- Objective ---
prob.model.add_objective("y")
prob.model.add_design_var("x", lower=0.0, upper=1.0)
prob.setup()
prob["x"] = 0.8
s = time()
num_high = 5
def test(self):
from openaerostruct.geometry.utils import generate_mesh, write_FFD_file
from openaerostruct.geometry.geometry_group import Geometry
from openaerostruct.transfer.displacement_transfer import DisplacementTransfer
from openaerostruct.aerodynamics.aero_groups import AeroPoint
from openaerostruct.integration.multipoint_comps import MultiCD
from openmdao.api import IndepVarComp, Problem, Group, NewtonSolver, ScipyIterativeSolver, LinearBlockGS, NonlinearBlockGS, DirectSolver, LinearBlockGS, PetscKSP, ScipyOptimizeDriver, ExplicitComponent# TODO, SqliteRecorder, CaseReader, profile
from openmdao.devtools import iprofile
from openmdao.api import view_model
from openmdao.utils.assert_utils import assert_check_partials
from pygeo import DVGeometry
# Create a dictionary to store options about the surface
mesh_dict = {'num_y' : 5,
'num_x' : 3,
'wing_type' : 'CRM',
'symmetry' : True,
'num_twist_cp' : 5,
'span_cos_spacing' : 0.}
mesh, _ = generate_mesh(mesh_dict)
surf_dict = {
# Wing definition
'name' : 'wing', # name of the surface
'type' : 'aero',
'symmetry' : True, # if true, model one half of wing
# reflected across the plane y = 0
'S_ref_type' : 'wetted', # how we compute the wing area,
# can be 'wetted' or 'projected'
'fem_model_type' : 'tube',
'mesh' : mesh,
'mx' : 2,
'my' : 3,
'geom_manipulator' : 'FFD',
# Aerodynamic performance of the lifting surface at
# an angle of attack of 0 (alpha=0).
# These CL0 and CD0 values are added to the CL and CD
# obtained from aerodynamic analysis of the surface to get
# the total CL and CD.
# These CL0 and CD0 values do not vary wrt alpha.
'CL0' : 0.0, # CL of the surface at alpha=0
'CD0' : 0.015, # CD of the surface at alpha=0
# Airfoil properties for viscous drag calculation
'k_lam' : 0.05, # percentage of chord with laminar
# flow, used for viscous drag
't_over_c_cp' : np.array([0.15]), # thickness over chord ratio (NACA0015)
'c_max_t' : .303, # chordwise location of maximum (NACA0015)
# thickness
'with_viscous' : True, # if true, compute viscous drag
'with_wave' : False, # if true, compute wave drag
}
surfaces = [surf_dict]
n_points = 2
# Create the problem and the model group
prob = Problem()
indep_var_comp = IndepVarComp()
indep_var_comp.add_output('v', val=248.136, units='m/s')
indep_var_comp.add_output('alpha', val=np.ones(n_points)*6.64, units='deg')
indep_var_comp.add_output('M', val=0.84)
indep_var_comp.add_output('re', val=1.e6, units='1/m')
indep_var_comp.add_output('rho', val=0.38, units='kg/m**3')
indep_var_comp.add_output('cg', val=np.zeros((3)), units='m')
prob.model.add_subsystem('prob_vars',
indep_var_comp,
promotes=['*'])
# Loop through and add a certain number of aero points
for i in range(n_points):
# Create the aero point group and add it to the model
aero_group = AeroPoint(surfaces=surfaces)
point_name = 'aero_point_{}'.format(i)
prob.model.add_subsystem(point_name, aero_group)
# Connect flow properties to the analysis point
prob.model.connect('v', point_name + '.v')
prob.model.connect('alpha', point_name + '.alpha', src_indices=[i])
prob.model.connect('M', point_name + '.M')
prob.model.connect('re', point_name + '.re')
prob.model.connect('rho', point_name + '.rho')
prob.model.connect('cg', point_name + '.cg')
# Connect the parameters within the model for each aero point
for surface in surfaces:
filename = write_FFD_file(surface, surface['mx'], surface['my'])
DVGeo = DVGeometry(filename)
geom_group = Geometry(surface=surface, DVGeo=DVGeo)
# Add tmp_group to the problem as the name of the surface.
# Note that is a group and performance group for each
# individual surface.
aero_group.add_subsystem(surface['name'] + '_geom', geom_group)
name = surface['name']
prob.model.connect(point_name + '.CD', 'multi_CD.' + str(i) + '_CD')
# Connect the mesh from the geometry component to the analysis point
prob.model.connect(point_name + '.' + name + '_geom.mesh', point_name + '.' + name + '.def_mesh')
# Perform the connections with the modified names within the
# 'aero_states' group.
prob.model.connect(point_name + '.' + name + '_geom.mesh', point_name + '.aero_states.' + name + '_def_mesh')
prob.model.connect(point_name + '.' + name + '_geom.t_over_c', point_name + '.' + name + '_perf.' + 't_over_c')
prob.model.add_subsystem('multi_CD', MultiCD(n_points=n_points), promotes_outputs=['CD'])
from openmdao.api import pyOptSparseDriver
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = "SNOPT"
prob.driver.opt_settings = {'Major optimality tolerance': 1.0e-5,
'Major feasibility tolerance': 1.0e-5}
# # Setup problem and add design variables, constraint, and objective
prob.model.add_design_var('alpha', lower=-15, upper=15)
prob.model.add_design_var('aero_point_0.wing_geom.shape', lower=-3, upper=2)
prob.model.add_constraint('aero_point_0.wing_perf.CL', equals=0.45)
prob.model.add_design_var('aero_point_1.wing_geom.shape', lower=-3, upper=2)
prob.model.add_constraint('aero_point_1.wing_perf.CL', equals=0.5)
prob.model.add_objective('CD', scaler=1e4)
# Set up the problem
prob.setup()
prob.run_model()
# Check the partials at this point in the design space
data = prob.check_partials(compact_print=True, out_stream=None, method='cs', step=1e-40)
assert_check_partials(data, atol=1e20, rtol=1e-6)
def test_min_time_climb_for_docs_gauss_lobatto(self):
import matplotlib.pyplot as plt
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.min_time_climb.min_time_climb_ode import MinTimeClimbODE
from dymos.examples.plotting import plot_results
#
# Instantiate the problem and configure the optimization driver
#
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
#
# Instantiate the trajectory and phase
#
traj = dm.Trajectory()
phase = dm.Phase(ode_class=MinTimeClimbODE,
transcription=dm.GaussLobatto(num_segments=15,
compressed=False))
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj', traj)
#
# Set the options on the optimization variables
# Note the use of explicit state units here since much of the ODE uses imperial units
# and we prefer to solve this problem using metric units.
#
phase.set_time_options(fix_initial=True,
duration_bounds=(50, 400),
duration_ref=100.0)
phase.add_state('r',
fix_initial=True,
lower=0,
upper=1.0E6,
units='m',
ref=1.0E3,
defect_ref=1.0E3,
rate_source='flight_dynamics.r_dot')
phase.add_state('h',
fix_initial=True,
lower=0,
upper=20000.0,
units='m',
ref=1.0E2,
defect_ref=1.0E2,
rate_source='flight_dynamics.h_dot')
phase.add_state('v',
fix_initial=True,
lower=10.0,
units='m/s',
ref=1.0E2,
defect_ref=1.0E2,
rate_source='flight_dynamics.v_dot')
phase.add_state('gam',
fix_initial=True,
lower=-1.5,
upper=1.5,
units='rad',
ref=1.0,
defect_ref=1.0,
rate_source='flight_dynamics.gam_dot')
phase.add_state('m',
fix_initial=True,
lower=10.0,
upper=1.0E5,
units='kg',
ref=1.0E3,
defect_ref=1.0E3,
rate_source='prop.m_dot')
phase.add_control('alpha',
units='deg',
lower=-8.0,
upper=8.0,
scaler=1.0,
rate_continuity=True,
rate_continuity_scaler=100.0,
rate2_continuity=False)
phase.add_parameter('S',
val=49.2386,
units='m**2',
opt=False,
targets=['S'])
phase.add_parameter('Isp',
val=1600.0,
units='s',
opt=False,
targets=['Isp'])
phase.add_parameter('throttle',
val=1.0,
opt=False,
targets=['throttle'])
#
# Setup the boundary and path constraints
#
phase.add_boundary_constraint('h',
loc='final',
equals=20000,
scaler=1.0E-3)
phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0)
phase.add_boundary_constraint('gam', loc='final', equals=0.0)
phase.add_path_constraint(name='h',
lower=100.0,
upper=20000,
ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', ref=1.0)
p.model.linear_solver = om.DirectSolver()
#
# Setup the problem and set the initial guess
#
p.setup(check=True)
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 500
p.set_val('traj.phase0.states:r', phase.interp('r', [0.0, 50000.0]))
p.set_val('traj.phase0.states:h', phase.interp('h', [100.0, 20000.0]))
p.set_val('traj.phase0.states:v', phase.interp('v',
[135.964, 283.159]))
p.set_val('traj.phase0.states:gam', phase.interp('gam', [0.0, 0.0]))
p.set_val('traj.phase0.states:m', phase.interp('m',
[19030.468, 10000.]))
p.set_val('traj.phase0.controls:alpha',
phase.interp('alpha', [0.0, 0.0]))
#
# Solve for the optimal trajectory
#
dm.run_problem(p)
#
# Test the results
#
assert_near_equal(p.get_val('traj.phase0.t_duration'),
321.0,
tolerance=1.0E-1)
#
# Get the explicitly simulated solution and plot the results
#
exp_out = traj.simulate()
plot_results(
[('traj.phase0.timeseries.time', 'traj.phase0.timeseries.states:h',
'time (s)', 'altitude (m)'),
('traj.phase0.timeseries.time',
'traj.phase0.timeseries.controls:alpha', 'time (s)',
'alpha (deg)')],
title='Supersonic Minimum Time-to-Climb Solution',
p_sol=p,
p_sim=exp_out)
plt.show()
params_IdepVar_func=add_floris_params_IndepVarComps,
params_IndepVar_args={}))
jensen_prob = Problem(root=OptAEP(nTurbines=nTurbines, nDirections=nDirections, use_rotor_components=False,
wake_model=jensen_wrapper, wake_model_options={'variant': 'CosineYaw_1R',
'radius multiplier': 1.0}, datasize=0,
params_IdepVar_func=add_jensen_params_IndepVarComps,
params_IndepVar_args={'use_angle': True}))
probs = [gauss_prob, floris_prob, jensen_prob]
names = ['gauss', 'floris', 'jensen']
for indx, prob in enumerate(probs):
# set up optimizer
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.driver.add_objective('obj', scaler=1E-5)
# set optimizer options
prob.driver.opt_settings['Verify level'] = 3
prob.driver.opt_settings['Print file'] = 'SNOPT_print_exampleOptYaw_%s.out' % names[indx]
prob.driver.opt_settings['Summary file'] = 'SNOPT_summary_exampleOptYaw_%s.out' % names[indx]
prob.driver.opt_settings['Major iterations limit'] = 1000
# select design variables
for direction_id in range(0, nDirections):
prob.driver.add_desvar('yaw%i' % direction_id, lower=-30.0, upper=30.0, scaler=1)
prob.setup()
def setup_prob(self):
"""
Short method to select the optimizer. Uses pyOptSparse if available,
or Scipy's SLSQP otherwise.
"""
try: # Use pyOptSparse optimizer if installed
from openmdao.api import pyOptSparseDriver
self.prob.driver = pyOptSparseDriver()
if self.prob_dict['optimizer'] == 'SNOPT':
self.prob.driver.options['optimizer'] = "SNOPT"
self.prob.driver.opt_settings = {'Major optimality tolerance': 1.0e-8,
'Major feasibility tolerance': 1.0e-8,
'Major iterations limit':400,
'Minor iterations limit':2000,
'Iterations limit':1000
}
elif self.prob_dict['optimizer'] == 'ALPSO':
self.prob.driver.options['optimizer'] = 'ALPSO'
self.prob.driver.opt_settings = {'SwarmSize': 40,
'maxOuterIter': 200,
'maxInnerIter': 6,
'rtol': 1e-5,
'atol': 1e-5,
'dtol': 1e-5,
'printOuterIters': 1
}
elif self.prob_dict['optimizer'] == 'NOMAD':
self.prob.driver.options['optimizer'] = 'NOMAD'
self.prob.driver.opt_settings = {'maxiter':1000,
'minmeshsize':1e-12,
'minpollsize':1e-12,
'displaydegree':0,
'printfile':1
}
elif self.prob_dict['optimizer'] == 'SLSQP':
self.prob.driver.options['optimizer'] = 'SLSQP'
self.prob.driver.opt_settings = {'ACC' : 1e-10
}
except: # Use Scipy SLSQP optimizer if pyOptSparse not installed
self.prob.driver = ScipyOptimizer()
self.prob.driver.options['optimizer'] = 'SLSQP'
self.prob.driver.options['disp'] = True
self.prob.driver.options['tol'] = 1.0e-10
# Actually call the OpenMDAO functions to add the design variables,
# constraints, and objective.
for desvar_name, desvar_data in iteritems(self.desvars):
self.prob.driver.add_desvar(desvar_name, **desvar_data)
for con_name, con_data in iteritems(self.constraints):
self.prob.driver.add_constraint(con_name, **con_data)
for obj_name, obj_data in iteritems(self.objective):
self.prob.driver.add_objective(obj_name, **obj_data)
# Use finite differences over the entire model if user selected it
if self.prob_dict['force_fd']:
self.prob.root.deriv_options['type'] = 'fd'
# Record optimization history to a database.
# Data saved here can be examined using `plot_all.py` or `OptView.py`
if self.prob_dict['record_db']:
recorder = SqliteRecorder(self.prob_dict['prob_name']+".db")
recorder.options['record_params'] = True
recorder.options['record_derivs'] = True
self.prob.driver.add_recorder(recorder)
# Profile (time) the problem
if self.prob_dict['profile']:
profile.setup(self.prob)
profile.start()
# Set up the problem
self.prob.setup()
# Use warm start from previous db file if desired.
# Note that we only have access to the unknowns, not the gradient history.
if self.prob_dict['previous_case_db'] is not None:
# Open the previous case and start from the last iteration.
# Change the -1 value in get_case() if you want to select a different iteration.
cr = CaseReader(self.prob_dict['previous_case_db'])
case = cr.get_case(-1)
# Loop through the unknowns and set them for this problem.
for param_name, param_data in iteritems(case.unknowns):
self.prob[param_name] = param_data
