def test_par_est(self):
"""
Test parameter estimation.
"""
cost_ref = 1.1109779e-2
u_norm_ref = 0.556018602
model = self.model_illust
op = self.op_illust_est_automatic
# Simulate with nominal parameters
n_meas = 16
sim_res = model.simulate(input=('u', lambda t: -0.2 + N.sin(t)),
final_time=4.,
options={
'ncp': n_meas,
'CVode_options': {
'rtol': 1e-10
}
})
# Assemble external data by adding noise to simulation
Q = N.diag([1., 1.])
N.random.seed(1)
t_meas = sim_res['time']
sigma = 0.05
x1_meas = sim_res['x1'] + sigma * N.random.randn(n_meas + 1)
x2_meas = sim_res['x2'] + sigma * N.random.randn(n_meas + 1)
u_meas = sim_res['u']
data_x1 = N.vstack([t_meas, x1_meas])
data_x2 = N.vstack([t_meas, x2_meas])
data_u1 = N.vstack([t_meas, u_meas])
quad_pen = OrderedDict()
quad_pen['x1'] = data_x1
quad_pen['x2'] = data_x2
eliminated = OrderedDict()
eliminated['u'] = data_u1
external_data = ExternalData(Q=Q,
quad_pen=quad_pen,
eliminated=eliminated)
# Eliminate
blt_op = BLTOptimizationProblem(op)
# Check remaining variables
alg_vars = sorted([
var.getName() for var in blt_op.getVariables(blt_op.REAL_ALGEBRAIC)
if not var.isAlias()
])
assert len(alg_vars) == 3
# Set up options
dae_opts = op.optimize_options()
dae_opts['init_traj'] = sim_res
dae_opts['nominal_traj'] = sim_res
dae_opts['external_data'] = external_data
blt_opts = blt_op.optimize_options()
blt_opts['init_traj'] = sim_res
blt_opts['nominal_traj'] = sim_res
blt_opts['external_data'] = external_data
# Optimize and check result
res_dae = op.optimize(options=dae_opts)
res_blt = blt_op.optimize(options=blt_opts)
assert_results(res_dae, cost_ref, u_norm_ref, u_norm_rtol=1e-2)
assert_results(res_blt, cost_ref, u_norm_ref, u_norm_rtol=1e-2)
N.testing.assert_allclose([res_dae['p1'][0], res_dae['p3'][0]],
[2.022765, 0.992965],
rtol=2e-3)
N.testing.assert_allclose([res_blt['p1'][0], res_blt['p3'][0]],
[2.022765, 0.992965],
rtol=2e-3)
def run_demo(with_plots=True):
"""
This example solves the optimization problem from pyjmi.examples.ccpp using the Python-based symbolic elimination.
"""
# Load initial gues
init_path = os.path.join(get_files_path(), "ccpp_init.txt")
init_res = LocalDAECollocationAlgResult(
result_data=ResultDymolaTextual(init_path))
# Compile model
class_name = "CombinedCycleStartup.Startup6"
file_paths = (os.path.join(get_files_path(), "CombinedCycle.mo"),
os.path.join(get_files_path(), "CombinedCycleStartup.mop"))
compiler_options = {'equation_sorting': True, 'automatic_tearing': True}
op = transfer_optimization_problem("CombinedCycleStartup.Startup6",
file_paths, compiler_options)
# Set elimination options
elim_opts = EliminationOptions()
elim_opts['ineliminable'] = ['plant.sigma']
if with_plots:
elim_opts['draw_blt'] = True
# Eliminate algebraic variables
op = BLTOptimizationProblem(op, elim_opts)
# Set collocation options
opt_opts = op.optimize_options()
opt_opts['init_traj'] = init_res
opt_opts['nominal_traj'] = init_res
# Solve the optimal control problem
opt_res = op.optimize(options=opt_opts)
# Extract variable profiles
opt_plant_p = opt_res['plant.p']
opt_plant_sigma = opt_res['plant.sigma']
opt_plant_load = opt_res['plant.load']
opt_time = opt_res['time']
# Plot the optimized trajectories
if with_plots:
plt.close(2)
plt.figure(2)
plt.subplot(3, 1, 1)
plt.plot(opt_time, opt_plant_p * 1e-6)
plt.ylabel('evaporator pressure [MPa]')
plt.grid(True)
plt.title('Optimized trajectories')
plt.subplot(3, 1, 2)
plt.plot(opt_time, opt_plant_sigma * 1e-6)
plt.grid(True)
plt.ylabel('turbine thermal stress [MPa]')
plt.subplot(3, 1, 3)
plt.plot(opt_time, opt_plant_load)
plt.grid(True)
plt.ylabel('input load [1]')
plt.xlabel('time [s]')
# Verify solution for testing purposes
try:
import casadi
except:
pass
else:
cost = float(opt_res.solver.solver_object.getOutput('f'))
N.testing.assert_allclose(cost, 17492.465548193624, rtol=1e-5)