def traj_optim_static(paths, tree):
path, envs, modes, mnps = paths
guard_index = [0]
n = len(modes)
v_init = np.zeros((n, 3))
for i in range(1, n):
if not np.all(modes[i] == modes[i - 1]):
guard_index.append(i)
elif len(envs[i]) != 0:
if not envs[i][0].is_same(envs[i - 1][0]):
guard_index.append(i)
elif not (mnps[i][0].is_same(mnps[i - 1][0])
and mnps[i][1].is_same(mnps[i - 1][1])):
# manipulator change
guard_index.append(i)
g_v = np.identity(3)
g_v[0:2, 0:2] = config2trans(path[i - 1])[0:2, 0:2]
v_init[i - 1] = np.dot(g_v.T,
np.array(path[i]) - np.array(path[i - 1]))
#guard_index.append(len(modes)-1)
guard_index = np.unique(guard_index)
Gs = dict()
hs = dict()
As = dict()
bs = dict()
for i in range(len(path)):
G, h, A, b = contact_mode_constraints(path[i], mnps[i], envs[i],
modes[i], tree.world,
tree.mnp_mu, tree.env_mu,
tree.mnp_fn_max)
gid = np.any(G[:, 0:3], axis=1)
aid = np.any(A[:, 0:3], axis=1)
Gs[i] = G[gid, 0:3]
hs[i] = h[gid].flatten()
As[i] = A[aid, 0:3]
bs[i] = b[aid].flatten()
modeconstraints = (Gs, hs, As, bs)
q_goal = np.array(tree.x_goal)
opt_prob = Optimization('Trajectory Optimization', obj_fun)
x_init = np.hstack((np.array(path).flatten(), v_init.flatten()))
cs = constraints(x_init, path, Gs, hs, As, bs, guard_index)
opt_prob.addVarGroup('x', n * 6, 'c', value=x_init, lower=-10, upper=10)
opt_prob.addObj('f')
opt_prob.addConGroup('g', len(cs), 'i', lower=0.0, upper=10000.0)
print(opt_prob)
slsqp = SLSQP()
#slsqp.setOption('IPRINT', -1)
slsqp(opt_prob,
sens_type='FD',
goal=q_goal,
path=path,
modecons=modeconstraints,
guard_index=guard_index)
print(opt_prob.solution(0))
qs = [opt_prob.solution(0)._variables[i].value for i in range(n * 3)]
return qs
def solveOpt(int_domain,J,x,model,u0):
def objfun(u,**kwargs):
# 1) extract paraeters
int_domain = kwargs['int_domain']
J = kwargs['J']
x = kwargs['x']
model = kwargs['model']
# 2) define objective function
f = np.trapz(int_domain,J * model.pf(int_domain,u,x))
g = [0]*2
# 3) budget constraint
g[1] = u.sum() - 1
# 4) VaR constarint
W = model.W
sigmaMax = model.VaR / norm.ppf(1-model.alpha)
g[0] = -sigmaMax + np.sqrt(W.dot(u).dot(u))
fail = 0
return f,g,fail
opt_prob = Optimization('test problem',objfun)
opt_prob.addObj('f')
opt_prob.addCon('budget const','e')
opt_prob.addCon('VaR const','i')
opt_prob.addVarGroup('u',model.M,'c',lower=np.zeros(model.M),
upper=np.ones(model.M),value=u0)
print opt_prob
slsqp = SLSQP()
slsqp.setOption('IPRINT',-1)
slsqp(opt_prob,sens_type='FD',int_domain=int_domain,J=J,x=x,model=model)
print opt_prob.solution(0)
def solveOpt(int_domain, J, a, model, u0, sign):
'''
INPUT:
int_domain =
J =
a =
model =
u0 =
sign =
OUTPUT:
opt_prob =
'''
def objfun(u, **kwargs):
'''objfun defines the objective function and the constraints (equality
and inequality) of the optiization problem'''
# 1) extract paraeters
int_domain = kwargs['int_domain']
J = kwargs['J']
x = kwargs['a']
model = kwargs['model']
sign = kwargs['sign']
# 2) define objective function
funz = np.trapz(x=int_domain, y=J * model.pf(int_domain, u, x))
g = [0] * 2
# 3) budget constraint
g[0] = u.sum() - 1
# 4) VaR constarint
W = model.W
sigmaMax = model.VaR / norm.ppf(1 - model.alpha)
g[1] = -sigmaMax + np.sqrt(W.dot(u).dot(u))
fail = 0
return sign * funz, g, fail
opt_prob = Optimization('ODAA problem', objfun)
opt_prob.addObj('funz')
opt_prob.addCon('budget const', 'e')
opt_prob.addCon('VaR const', 'i')
slsqp = SLSQP() # instantiate Optimizer
slsqp.setOption('IPRINT', -1)
opt_prob.addVarGroup('u',
model.M,
'c',
lower=np.zeros(model.M),
upper=np.ones(model.M),
value=u0)
#print opt_prob # print optimization problem
slsqp(opt_prob,
sens_type='FD',
int_domain=int_domain,
J=J,
a=a,
model=model,
sign=sign)
#print opt_prob.solution(0) # print solution
return opt_prob
def get_pyopt_optimization(f, g_f, con, g_con, x0, T):
opt_prob = Optimization('stoc planner', obj_fun(f, con))
opt_prob.addObj('f')
opt_prob.addVarGroup('flat_plan',
x0.size,
type='c',
value = x0,
lower = 0.,
upper = 1.0)
opt_prob.addConGroup('g', T, 'e')
# opt = SLSQP()
# opt = pySNOPT.SNOPT()
# opt = PSQP()
# opt = CONMIN()
opt = ALGENCAN()
return opt_prob, opt
def main():
###########################################
# Define some values
###########################################
n_blades = 2
n_elements = 10
radius = unit_conversion.in2m(9.6) / 2
root_cutout = 0.1 * radius
dy = float(radius - root_cutout) / n_elements
dr = float(1) / n_elements
y = root_cutout + dy * np.arange(1, n_elements + 1)
r = y / radius
pitch = 0.0
airfoils = (('SDA1075_494p', 0.0, 1.0), )
allowable_Re = [
1000000., 500000., 250000., 100000., 90000., 80000., 70000., 60000.,
50000., 40000., 30000., 20000., 10000.
]
vehicle_weight = 12.455
max_chord = 0.3
max_chord_tip = 5.
alt = 0
tip_loss = True
mach_corr = False
# Forward flight parameters
v_inf = 4. # m/s
alpha0 = 0.0454 # Starting guess for trimmed alpha in radians
n_azi_elements = 5
# Mission times
time_in_hover = 300. # Time in seconds
time_in_ff = 500.
mission_time = [time_in_hover, time_in_ff]
Cl_tables = {}
Cd_tables = {}
Clmax = {}
# Get lookup tables
if any(airfoil[0] != 'simple' for airfoil in airfoils):
for airfoil in airfoils:
Cl_table, Cd_table, Clmax = aero_coeffs.create_Cl_Cd_table(
airfoil[0])
Cl_tables[airfoil[0]] = Cl_table
Cd_tables[airfoil[0]] = Cd_table
Clmax[airfoil[0]] = Clmax
# Create list of Cl functions. One for each Reynolds number. Cl_tables (and Cd_tables) will be empty for the
# 'simple' case, therefore this will be skipped for the simple case. For the full table lookup case this will be
# skipped because allowable_Re will be empty.
Cl_funs = {}
Cd_funs = {}
lift_curve_info_dict = {}
if Cl_tables and allowable_Re:
Cl_funs = dict(
zip(allowable_Re, [
aero_coeffs.get_Cl_fun(Re, Cl_tables[airfoils[0][0]],
Clmax[airfoils[0][0]][Re])
for Re in allowable_Re
]))
Cd_funs = dict(
zip(allowable_Re, [
aero_coeffs.get_Cd_fun(Re, Cd_tables[airfoils[0][0]])
for Re in allowable_Re
]))
lift_curve_info_dict = aero_coeffs.create_liftCurveInfoDict(
allowable_Re, Cl_tables[airfoils[0][0]])
###########################################
# Set design variable bounds
###########################################
# Hover opt 500 gen, 1000 pop, 12.455 N weight, 9.6 in prop
chord = np.array([
0.11923604, 0.2168746, 0.31540216, 0.39822882, 0.42919, 0.35039799,
0.3457828, 0.28567224, 0.23418368, 0.13502483
])
twist = np.array([
0.45316866, 0.38457724, 0.38225075, 0.34671967, 0.33151445, 0.28719111,
0.25679667, 0.25099005, 0.19400679, 0.10926302
])
omega = 3811.03596674 * 2 * np.pi / 60
original = (omega, chord, twist)
dtwist = np.array(
[twist[i + 1] - twist[i] for i in xrange(len(twist) - 1)])
dchord = np.array(
[chord[i + 1] - chord[i] for i in xrange(len(chord) - 1)])
twist0 = twist[0]
chord0 = chord[0]
omega_start = omega
dtwist_start = dtwist
dchord_start = dchord
twist0_start = twist0
chord0_start = chord0
omega_lower = 2000 * 2 * np.pi / 60
omega_upper = 8000.0 * 2 * np.pi / 60
twist0_lower = 0. * 2 * np.pi / 360
twist0_upper = 60. * 2 * np.pi / 360
chord0_upper = 0.1198
chord0_lower = 0.05
dtwist_lower = -10.0 * 2 * np.pi / 360
dtwist_upper = 10.0 * 2 * np.pi / 360
dchord_lower = -0.1
dchord_upper = 0.1
opt_prob = Optimization('Mission Simulator', objfun)
opt_prob.addVar('omega_h',
'c',
value=omega_start,
lower=omega_lower,
upper=omega_upper)
opt_prob.addVar('twist0',
'c',
value=twist0_start,
lower=twist0_lower,
upper=twist0_upper)
opt_prob.addVar('chord0',
'c',
value=chord0_start,
lower=chord0_lower,
upper=chord0_upper)
opt_prob.addVarGroup('dtwist',
n_elements - 1,
'c',
value=dtwist_start,
lower=dtwist_lower,
upper=dtwist_upper)
opt_prob.addVarGroup('dchord',
n_elements - 1,
'c',
value=dchord_start,
lower=dchord_lower,
upper=dchord_upper)
opt_prob.addObj('f')
opt_prob.addCon('thrust', 'i')
opt_prob.addCon('c_tip', 'i')
opt_prob.addConGroup('c_lower', n_elements, 'i')
opt_prob.addConGroup('c_upper', n_elements, 'i')
print opt_prob
slsqp = SLSQP()
slsqp.setOption('IPRINT', 1)
slsqp.setOption('MAXIT', 1000)
slsqp.setOption('ACC', 1e-8)
fstr, xstr, inform = slsqp(opt_prob,
sens_type='FD',
n_blades=n_blades,
radius=radius,
dy=dy,
dr=dr,
y=y,
r=r,
pitch=pitch,
airfoils=airfoils,
vehicle_weight=vehicle_weight,
max_chord=max_chord,
tip_loss=tip_loss,
mach_corr=mach_corr,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
Cl_tables=Cl_tables,
Cd_tables=Cd_tables,
allowable_Re=allowable_Re,
alt=alt,
v_inf=v_inf,
alpha0=alpha0,
mission_time=mission_time,
n_azi_elements=n_azi_elements,
lift_curve_info_dict=lift_curve_info_dict,
max_chord_tip=max_chord_tip)
print opt_prob.solution(0)
# pop_size = 300
# max_gen = 500
# opt_method = 'nograd'
# nsga2 = NSGA2()
# nsga2.setOption('PrintOut', 2)
# nsga2.setOption('PopSize', pop_size)
# nsga2.setOption('maxGen', max_gen)
# nsga2.setOption('pCross_real', 0.85)
# nsga2.setOption('xinit', 1)
# fstr, xstr, inform = nsga2(opt_prob, n_blades=n_blades, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch,
# airfoils=airfoils, vehicle_weight=vehicle_weight, max_chord=max_chord, tip_loss=tip_loss,
# mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs, Cl_tables=Cl_tables,
# Cd_tables=Cd_tables, allowable_Re=allowable_Re, opt_method=opt_method, alt=alt,
# v_inf=v_inf, alpha0=alpha0, mission_time=mission_time, n_azi_elements=n_azi_elements,
# pop_size=pop_size, max_gen=max_gen, lift_curve_info_dict=lift_curve_info_dict,
# max_chord_tip=max_chord_tip)
# print opt_prob.solution(0)
# opt_method = 'nograd'
# xstart_alpso = np.concatenate((np.array([omega_start, twist0_start, chord0_start]), dtwist_start, dchord_start))
# alpso = ALPSO()
# alpso.setOption('xinit', 0)
# alpso.setOption('SwarmSize', 200)
# alpso.setOption('maxOuterIter', 100)
# alpso.setOption('stopCriteria', 0)
# fstr, xstr, inform = alpso(opt_prob, xstart=xstart_alpso, n_blades=n_blades, n_elements=n_elements,
# root_cutout=root_cutout, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch,
# airfoils=airfoils, thrust=thrust, max_chord=max_chord, tip_loss=tip_loss,
# mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs, Cl_tables=Cl_tables,
# Cd_tables=Cd_tables, allowable_Re=allowable_Re, opt_method=opt_method)
# print opt_prob.solution(0)
def get_performance(o, c, t):
chord_meters = c * radius
prop = propeller.Propeller(t,
chord_meters,
radius,
n_blades,
r,
y,
dr,
dy,
airfoils=airfoils,
Cl_tables=Cl_tables,
Cd_tables=Cd_tables)
quad = quadrotor.Quadrotor(prop, vehicle_weight)
ff_kwargs = {
'propeller': prop,
'pitch': pitch,
'n_azi_elements': n_azi_elements,
'allowable_Re': allowable_Re,
'Cl_funs': Cl_funs,
'Cd_funs': Cd_funs,
'tip_loss': tip_loss,
'mach_corr': mach_corr,
'alt': alt,
'lift_curve_info_dict': lift_curve_info_dict
}
trim0 = np.array([alpha0, o])
alpha_trim, omega_trim, converged = trim.trim(quad, v_inf, trim0,
ff_kwargs)
T_ff, H_ff, P_ff = bemt.bemt_forward_flight(
quad,
pitch,
omega_trim,
alpha_trim,
v_inf,
n_azi_elements,
alt=alt,
tip_loss=tip_loss,
mach_corr=mach_corr,
allowable_Re=allowable_Re,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
lift_curve_info_dict=lift_curve_info_dict)
dT_h, P_h = bemt.bemt_axial(prop,
pitch,
o,
allowable_Re=allowable_Re,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
tip_loss=tip_loss,
mach_corr=mach_corr,
alt=alt)
return sum(dT_h), P_h, T_ff, P_ff, alpha_trim, omega_trim
omega = xstr[0]
twist0 = xstr[1]
chord0 = xstr[2]
dtwist = xstr[3:3 + len(r) - 1]
dchord = xstr[3 + len(r) - 1:]
twist = calc_twist_dist(twist0, dtwist)
chord = calc_chord_dist(chord0, dchord)
print "chord = " + repr(chord)
print "twist = " + repr(twist)
# twist_base = calc_twist_dist(twist0_base, dtwist_base)
# chord_base = calc_chord_dist(chord0_base, dchord_base)
perf_opt = get_performance(omega, chord, twist)
perf_orig = get_performance(original[0], original[1], original[2])
print "omega_orig = " + str(original[0])
print "Hover Thrust of original = " + str(perf_orig[0])
print "Hover Power of original = " + str(perf_orig[1])
print "FF Thrust of original = " + str(perf_orig[2])
print "FF Power of original = " + str(perf_orig[3])
print "Trim original (alpha, omega) = (%f, %f)" % (perf_orig[4],
perf_orig[5])
print "omega = " + str(omega * 60 / 2 / np.pi)
print "Hover Thrust of optimized = " + str(perf_opt[0])
print "Hover Power of optimized = " + str(perf_opt[1])
print "FF Thrust of optimized = " + str(perf_opt[2])
print "FF Power of optimized = " + str(perf_opt[3])
print "Trim optimized (alpha, omega) = (%f, %f)" % (perf_opt[4],
perf_opt[5])
# print "Omega base = " + str(omega_start*60/2/np.pi)
# print "Thrust of base = " + str(sum(perf_base[0]))
# print "Power of base = " + str(sum(perf_base[1]))
#
plt.figure(1)
plt.plot(r, original[1], '-b')
plt.plot(r, chord, '-r')
plt.xlabel('radial location')
plt.ylabel('c/R')
plt.legend(['start', 'opt'])
plt.figure(2)
plt.plot(r, original[2] * 180 / np.pi, '-b')
plt.plot(r, twist * 180 / np.pi, '-r')
plt.xlabel('radial location')
plt.ylabel('twist')
plt.legend(['start', 'opt'])
plt.show()
g = [0.0]*2
g[0] = 3 - x0
g[1] = 2 - x1
fail = 0
return f,g,fail
# =============================================================================
#
# =============================================================================
# Instantiate Optimization Problem
opt_prob = Optimization('TOY Constrained Problem',objfunc,use_groups=True)
opt_prob.addVarGroup('a',2,'c',value=1.0, lower=0.0, upper=10)
opt_prob.delVarGroup('a')
opt_prob.addVar('x','c',value=1.0, lower=0.0, upper=10)
opt_prob.addVarGroup('y',2,'c',value=1.0, lower=0.0, upper=10)
opt_prob.delVarGroup('y')
opt_prob.addVarGroup('z',1,'c',value=1.0, lower=0.0, upper=10)
opt_prob.addVarGroup('b',5,'c',value=3.0, lower=0.0, upper=10)
opt_prob.delVarGroup('b')
opt_prob.addObj('f')
opt_prob.addCon('g1','i')
opt_prob.addCon('g2','i')
print(opt_prob)
# Instantiate Optimizer (SLSQP) & Solve Problem
slsqp = SLSQP()
slsqp(opt_prob)
g = [0.0] * 2
g[0] = 3 - x0
g[1] = 2 - x1
fail = 0
return f, g, fail
# =============================================================================
#
# =============================================================================
# Instantiate Optimization Problem
opt_prob = Optimization('TOY Constraint Problem', objfunc, use_groups=True)
opt_prob.addVarGroup('a', 2, 'c', value=1.0, lower=0.0, upper=10)
opt_prob.delVarGroup('a')
opt_prob.addVar('x', 'c', value=1.0, lower=0.0, upper=10)
opt_prob.addVarGroup('y', 2, 'c', value=1.0, lower=0.0, upper=10)
opt_prob.delVarGroup('y')
opt_prob.addVarGroup('z', 1, 'c', value=1.0, lower=0.0, upper=10)
opt_prob.addVarGroup('b', 5, 'c', value=3.0, lower=0.0, upper=10)
opt_prob.delVarGroup('b')
opt_prob.addObj('f')
opt_prob.addCon('g1', 'i')
opt_prob.addCon('g2', 'i')
print opt_prob
# Instantiate Optimizer (PSQP) & Solve Problem
slsqp = SLSQP()
slsqp(opt_prob)
g = g1 + g2 + g3
fail = 0
return f, g, fail
# =============================================================================
# Run the NSGA Optimizer
# =============================================================================
#Define the lower and upper bounds for R
LB = [500] * nvar
UB = [9000] * nvar
InitR = []
for i in range(nvar):
InitR.append(random.randint(1500, 9000))
opt_prob = Optimization('Reservoir Operations Optimization', benefit)
opt_prob.addVarGroup('x', nvar, 'c', lower=LB, upper=UB, value=InitR)
opt_prob.addObj('f')
opt_prob.addConGroup('g', nvar * 3,
'i') # 3 inequality constraints Smin, Smax, Hmin
# Instantiate Optimizer (NSGA2) & Solve Problem
nsga2 = NSGA2()
nsga2.setOption('PrintOut', 0)
nsga2.setOption('PopSize', 1000)
nsga2.setOption('maxGen', 150)
nsga2.setOption('pMut_real', 0.075)
nsga2(opt_prob)
print "Optimization Completed Successfully!"
a = opt_prob.solution(0)
print a
def optimize_twist(**k):
omega = k['omega']
omega_lower = k['omega_lower']
omega_upper = k['omega_upper']
twist0 = k['twist0']
twist0_lower = k['twist0_lower']
twist0_upper = k['twist0_upper']
n_elements = k['n_elements']
dtwist = k['dtwist']
dtwist_lower = k['dtwist_lower']
dtwist_upper = k['dtwist_upper']
opt_prob_fc = Optimization('Rotor in Hover w/ Fixed Chord',
objfun_optimize_twist)
opt_prob_fc.addVar('omega',
'c',
value=omega,
lower=omega_lower,
upper=omega_upper)
opt_prob_fc.addVar('twist0',
'c',
value=twist0,
lower=twist0_lower,
upper=twist0_upper)
opt_prob_fc.addVarGroup('dtwist',
n_elements - 1,
'c',
value=dtwist,
lower=dtwist_lower,
upper=dtwist_upper)
opt_prob_fc.addObj('f')
opt_prob_fc.addCon('thrust', 'i')
n_blades = k['n_blades']
root_cutout = k['root_cutout']
radius = k['radius']
dy = k['dy']
dr = k['dr']
y = k['y']
r = k['r']
pitch = k['pitch']
airfoils = k['airfoils']
thrust = k['thrust']
chord = k['chord']
allowable_Re = k['allowable_Re']
Cl_tables = k['Cl_tables']
Cd_tables = k['Cd_tables']
Cl_funs = k['Cl_funs']
Cd_funs = k['Cd_funs']
tip_loss = k['tip_loss']
mach_corr = k['mach_corr']
alt = k['alt']
# Routine for optimizing twist with a constant chord
slsqp2 = SLSQP()
slsqp2.setOption('IPRINT', 1)
slsqp2.setOption('MAXIT', 200)
slsqp2.setOption('ACC', 1e-7)
fstr, xstr, inform = slsqp2(opt_prob_fc,
sens_type='FD',
n_blades=n_blades,
n_elements=n_elements,
root_cutout=root_cutout,
radius=radius,
dy=dy,
dr=dr,
y=y,
r=r,
pitch=pitch,
airfoils=airfoils,
thrust=thrust,
tip_loss=tip_loss,
mach_corr=mach_corr,
omega=omega,
chord=chord,
allowable_Re=allowable_Re,
Cl_tables=Cl_tables,
Cd_tables=Cd_tables,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
alt=alt)
return fstr, xstr
import numpy as np
def objfun(x, **kwargs):
W = kwargs['W']
a = kwargs['a']
f = a * W.dot(x).dot(x)
g = [x.sum() - 1]
fail = 0
return f, g, fail
opt_prob = Optimization('test problem', objfun)
opt_prob.addVarGroup('x',
3,
'c',
lower=np.zeros(3),
upper=np.ones(3),
value=[1, 0, 0])
opt_prob.addObj('f')
opt_prob.addCon('g1', 'i')
print opt_prob
W = np.eye(3)
# Instantiate Optimizer (SLSQP) & Solve Problem
slsqp = SLSQP()
slsqp.setOption('IPRINT', -1)
slsqp(opt_prob, sens_type='FD', W=W, a=10)
print opt_prob.solution(0)
def main():
###########################################
# Define some values
###########################################
n_blades = 2
n_elements = 10
radius = unit_conversion.in2m(9.6) / 2
root_cutout = 0.1 * radius
dy = float(radius - root_cutout) / n_elements
dr = float(1) / n_elements
y = root_cutout + dy * np.arange(1, n_elements + 1)
r = y / radius
pitch = 0.0
airfoils = (('SDA1075_494p', 0.0, 1.0), )
#allowable_Re = []
allowable_Re = [
1000000., 500000., 250000., 100000., 90000., 80000., 70000., 60000.,
50000., 40000., 30000., 20000., 10000.
]
vehicle_weight = 12.455
max_chord = 0.6
max_chord_tip = 5.
alt = 0
tip_loss = True
mach_corr = False
# Forward flight parameters
v_inf = 4. # m/s
alpha0 = 0.0454 # Starting guess for trimmed alpha in radians
n_azi_elements = 5
# Mission times
time_in_hover = 0. # Time in seconds
time_in_ff = 500.
mission_time = [time_in_hover, time_in_ff]
Cl_tables = {}
Cd_tables = {}
Clmax = {}
# Get lookup tables
if any(airfoil[0] != 'simple' for airfoil in airfoils):
for airfoil in airfoils:
Cl_table, Cd_table, Clmax = aero_coeffs.create_Cl_Cd_table(
airfoil[0])
Cl_tables[airfoil[0]] = Cl_table
Cd_tables[airfoil[0]] = Cd_table
Clmax[airfoil[0]] = Clmax
# Create list of Cl functions. One for each Reynolds number. Cl_tables (and Cd_tables) will be empty for the
# 'simple' case, therefore this will be skipped for the simple case. For the full table lookup case this will be
# skipped because allowable_Re will be empty.
Cl_funs = {}
Cd_funs = {}
lift_curve_info_dict = {}
if Cl_tables and allowable_Re:
Cl_funs = dict(
zip(allowable_Re, [
aero_coeffs.get_Cl_fun(Re, Cl_tables[airfoils[0][0]],
Clmax[airfoils[0][0]][Re])
for Re in allowable_Re
]))
Cd_funs = dict(
zip(allowable_Re, [
aero_coeffs.get_Cd_fun(Re, Cd_tables[airfoils[0][0]])
for Re in allowable_Re
]))
lift_curve_info_dict = aero_coeffs.create_liftCurveInfoDict(
allowable_Re, Cl_tables[airfoils[0][0]])
###########################################
# Set design variable bounds
###########################################
omega_start = 4250. * 2 * np.pi / 60
# These are c/R values for the DA4002 propeller given at the UIUC propeller database
chord_base = np.array([
0.1198, 0.1128, 0.1436, 0.1689, 0.1775, 0.1782, 0.1773, 0.1782, 0.1790,
0.1787, 0.1787, 0.1786, 0.1785, 0.1790, 0.1792, 0.1792, 0.1692, 0.0154
])
chord_base = np.array(
[chord_base[i] for i in [0, 2, 4, 6, 8, 10, 12, 14, 15, 17]])
twist_base = np.array([
42.481, 44.647, 41.154, 37.475, 34.027, 30.549, 27.875, 25.831, 23.996,
22.396, 21.009, 19.814, 18.786, 17.957, 17.245, 16.657, 13.973, 2.117
]) * 2 * np.pi / 360
twist_base = np.array(
[twist_base[i] for i in [0, 2, 4, 6, 8, 10, 12, 14, 15, 17]])
dtwist_base = np.array([
twist_base[i + 1] - twist_base[i] for i in xrange(len(twist_base) - 1)
])
dchord_base = np.array([
chord_base[i + 1] - chord_base[i] for i in xrange(len(chord_base) - 1)
])
twist0_base = twist_base[0]
chord0_base = chord_base[0]
chord_start = chord_base
twist_start = twist_base
dtwist_start = dtwist_base
dchord_start = dchord_base
twist0_start = twist0_base
chord0_start = chord0_base
print "chord0_start = " + str(chord0_start)
omega_lower = 2000 * 2 * np.pi / 60
omega_upper = 8000.0 * 2 * np.pi / 60
twist0_lower = 0. * 2 * np.pi / 360
twist0_upper = 60. * 2 * np.pi / 360
chord0_upper = 0.1198
chord0_lower = 0.05
dtwist_lower = -10.0 * 2 * np.pi / 360
dtwist_upper = 10.0 * 2 * np.pi / 360
dchord_lower = -0.1
dchord_upper = 0.1
opt_prob = Optimization('Mission Simulator', objfun)
opt_prob.addVar('omega_h',
'c',
value=omega_start,
lower=omega_lower,
upper=omega_upper)
opt_prob.addVar('twist0',
'c',
value=twist0_start,
lower=twist0_lower,
upper=twist0_upper)
opt_prob.addVar('chord0',
'c',
value=chord0_start,
lower=chord0_lower,
upper=chord0_upper)
opt_prob.addVarGroup('dtwist',
n_elements - 1,
'c',
value=dtwist_start,
lower=dtwist_lower,
upper=dtwist_upper)
opt_prob.addVarGroup('dchord',
n_elements - 1,
'c',
value=dchord_start,
lower=dchord_lower,
upper=dchord_upper)
opt_prob.addObj('f')
opt_prob.addCon('thrust', 'i')
opt_prob.addCon('c_tip', 'i')
opt_prob.addConGroup('c_lower', n_elements, 'i')
opt_prob.addConGroup('c_upper', n_elements, 'i')
print opt_prob
pop_size = 300
max_gen = 1100
opt_method = 'nograd'
nsga2 = NSGA2()
nsga2.setOption('PrintOut', 2)
nsga2.setOption('PopSize', pop_size)
nsga2.setOption('maxGen', max_gen)
nsga2.setOption('pCross_real', 0.85)
nsga2.setOption('pMut_real', 0.2)
nsga2.setOption('xinit', 1)
fstr, xstr, inform = nsga2(opt_prob,
n_blades=n_blades,
radius=radius,
dy=dy,
dr=dr,
y=y,
r=r,
pitch=pitch,
airfoils=airfoils,
vehicle_weight=vehicle_weight,
max_chord=max_chord,
tip_loss=tip_loss,
mach_corr=mach_corr,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
Cl_tables=Cl_tables,
Cd_tables=Cd_tables,
allowable_Re=allowable_Re,
opt_method=opt_method,
alt=alt,
v_inf=v_inf,
alpha0=alpha0,
mission_time=mission_time,
n_azi_elements=n_azi_elements,
pop_size=pop_size,
max_gen=max_gen,
lift_curve_info_dict=lift_curve_info_dict,
max_chord_tip=max_chord_tip)
print opt_prob.solution(0)
# opt_method = 'nograd'
# xstart_alpso = np.concatenate((np.array([omega_start, twist0_start, chord0_start]), dtwist_start, dchord_start))
# alpso = ALPSO()
# alpso.setOption('xinit', 0)
# alpso.setOption('SwarmSize', 200)
# alpso.setOption('maxOuterIter', 100)
# alpso.setOption('stopCriteria', 0)
# fstr, xstr, inform = alpso(opt_prob, xstart=xstart_alpso, n_blades=n_blades, n_elements=n_elements,
# root_cutout=root_cutout, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch,
# airfoils=airfoils, thrust=thrust, max_chord=max_chord, tip_loss=tip_loss,
# mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs, Cl_tables=Cl_tables,
# Cd_tables=Cd_tables, allowable_Re=allowable_Re, opt_method=opt_method)
# print opt_prob.solution(0)
# opt_method = 'grad'
# slsqp = SLSQP()
# slsqp.setOption('IPRINT', 1)
# slsqp.setOption('MAXIT', 1000)
# slsqp.setOption('ACC', 1e-7)
# fstr, xstr, inform = slsqp(opt_prob, sens_type='FD', n_blades=n_blades, n_elements=n_elements,
# root_cutout=root_cutout, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch,
# airfoils=airfoils, thrust=thrust, max_chord=max_chord,
# tip_loss=tip_loss, mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs,
# Cl_tables=Cl_tables, Cd_tables=Cd_tables, allowable_Re=allowable_Re,
# opt_method=opt_method, alt=alt)
# print opt_prob.solution(0)
def get_performance(o, c, t):
chord_meters = c * radius
prop = propeller.Propeller(t,
chord_meters,
radius,
n_blades,
r,
y,
dr,
dy,
airfoils=airfoils,
Cl_tables=Cl_tables,
Cd_tables=Cd_tables)
quad = quadrotor.Quadrotor(prop, vehicle_weight)
ff_kwargs = {
'propeller': prop,
'pitch': pitch,
'n_azi_elements': n_azi_elements,
'allowable_Re': allowable_Re,
'Cl_funs': Cl_funs,
'Cd_funs': Cd_funs,
'tip_loss': tip_loss,
'mach_corr': mach_corr,
'alt': alt,
'lift_curve_info_dict': lift_curve_info_dict
}
trim0 = np.array([alpha0, o])
alpha_trim, omega_trim, converged = trim.trim(quad, v_inf, trim0,
ff_kwargs)
T_ff, H_ff, P_ff = bemt.bemt_forward_flight(
quad,
pitch,
omega_trim,
alpha_trim,
v_inf,
n_azi_elements,
alt=alt,
tip_loss=tip_loss,
mach_corr=mach_corr,
allowable_Re=allowable_Re,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
lift_curve_info_dict=lift_curve_info_dict)
dT_h, P_h = bemt.bemt_axial(prop,
pitch,
o,
allowable_Re=allowable_Re,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
tip_loss=tip_loss,
mach_corr=mach_corr,
alt=alt)
return sum(dT_h), P_h, T_ff, P_ff, alpha_trim, omega_trim
omega = xstr[0]
twist0 = xstr[1]
chord0 = xstr[2]
dtwist = xstr[3:3 + len(r) - 1]
dchord = xstr[3 + len(r) - 1:]
twist = calc_twist_dist(twist0, dtwist)
chord = calc_chord_dist(chord0, dchord)
print "chord = " + repr(chord)
print "twist = " + repr(twist)
# twist_base = calc_twist_dist(twist0_base, dtwist_base)
# chord_base = calc_chord_dist(chord0_base, dchord_base)
perf_opt = get_performance(omega, chord, twist)
#perf_base = get_performance(omega_start, chord_base, twist_base)
print "omega = " + str(omega * 60 / 2 / np.pi)
print "Hover Thrust of optimized = " + str(perf_opt[0])
print "Hover Power of optimized = " + str(perf_opt[1])
print "FF Thrust of optimized = " + str(perf_opt[2])
print "FF Power of optimized = " + str(perf_opt[3])
print "Trim (alpha, omega) = (%f, %f)" % (perf_opt[4], perf_opt[5])
fail = 0
return -sum([
x[i] * sum([(1 + len(reachable_sets[i][u])) * y[i][u] - 0.5 * sum([
len(set(reachable_sets[i][u]) & set(reachable_sets[i][v])) *
y[i][u] * y[i][v] for v in users if v != u
]) for u in users]) for i in items
]), g, fail
#return -np.dot(x,(((1+reachable_sets_len)*y).sum(axis=1) - 0.5*(y*((y[:,:,None]*intersections).sum(axis=2))).sum(axis=1)))
# Initialize problem
opt_prob = Optimization('Algorithm A: Real-valued Relaxation',
objective,
use_groups=True)
opt_prob.addVarGroup('x', len(x), 'c', lower=0.0, upper=1.0, value=0.5)
opt_prob.addVarGroup('y',
len(y.flatten()),
'c',
lower=0.0,
upper=1.0,
value=0.5)
opt_prob.addObj('f')
opt_prob.addCon('g0', 'e')
#opt_prob.addConGroup('g1',len(users),'i')
print(opt_prob)
# Instantiate Optimizer (SLSQP) & Solve Problem
slsqp = SLSQP()
slsqp.setOption('IPRINT', -1)
slsqp(opt_prob, sens_type='FD')
def main():
###########################################
# Define some values
###########################################
n_blades = 2
n_elements = 10
radius = unit_conversion.in2m(9.6) / 2
#radius = 0.1397
root_cutout = 0.1 * radius
dy = float(radius - root_cutout) / n_elements
dr = float(1) / n_elements
y = root_cutout + dy * np.arange(1, n_elements + 1)
r = y / radius
pitch = 0.0
airfoils = (('SDA1075_494p', 0.0, 1.0), )
#allowable_Re = []
allowable_Re = [
1000000., 500000., 250000., 100000., 90000., 80000., 70000., 60000.,
50000., 40000., 30000., 20000., 10000.
]
vehicle_weight = 12.455
max_chord = 0.6
alt = 0
tip_loss = True
mach_corr = False
Cl_tables = {}
Cd_tables = {}
Clmax = {}
# Get lookup tables
if any(airfoil[0] != 'simple' for airfoil in airfoils):
for airfoil in airfoils:
Cl_table, Cd_table, Clmax = aero_coeffs.create_Cl_Cd_table(
airfoil[0])
Cl_tables[airfoil[0]] = Cl_table
Cd_tables[airfoil[0]] = Cd_table
Clmax[airfoil[0]] = Clmax
# Create list of Cl functions. One for each Reynolds number. Cl_tables (and Cd_tables) will be empty for the
# 'simple' case, therefore this will be skipped for the simple case. For the full table lookup case this will be
# skipped because allowable_Re will be empty.
Cl_funs = {}
Cd_funs = {}
lift_curve_info_dict = {}
if Cl_tables and allowable_Re:
Cl_funs = dict(
zip(allowable_Re, [
aero_coeffs.get_Cl_fun(Re, Cl_tables[airfoils[0][0]],
Clmax[airfoils[0][0]][Re])
for Re in allowable_Re
]))
Cd_funs = dict(
zip(allowable_Re, [
aero_coeffs.get_Cd_fun(Re, Cd_tables[airfoils[0][0]])
for Re in allowable_Re
]))
lift_curve_info_dict = aero_coeffs.create_liftCurveInfoDict(
allowable_Re, Cl_tables[airfoils[0][0]])
###########################################
# Set design variable bounds
###########################################
omega_start = 4250. * 2 * np.pi / 60
chord_base = np.array([
0.1198, 0.1128, 0.1436, 0.1689, 0.1775, 0.1782, 0.1773, 0.1782, 0.1790,
0.1787, 0.1787, 0.1786, 0.1785, 0.1790, 0.1792, 0.1792, 0.1692, 0.0154
])
chord_base = np.array(
[chord_base[i] for i in [0, 2, 4, 6, 8, 10, 12, 14, 15, 17]])
twist_base = np.array([
42.481, 44.647, 41.154, 37.475, 34.027, 30.549, 27.875, 25.831, 23.996,
22.396, 21.009, 19.814, 18.786, 17.957, 17.245, 16.657, 13.973, 2.117
]) * 2 * np.pi / 360
twist_base = np.array(
[twist_base[i] for i in [0, 2, 4, 6, 8, 10, 12, 14, 15, 17]])
dtwist_base = np.array([
twist_base[i + 1] - twist_base[i] for i in xrange(len(twist_base) - 1)
])
dchord_base = np.array([
chord_base[i + 1] - chord_base[i] for i in xrange(len(chord_base) - 1)
])
twist0_base = twist_base[0]
chord0_base = chord_base[0]
chord_start = chord_base
twist_start = twist_base
dtwist_start = dtwist_base
dchord_start = dchord_base
twist0_start = twist0_base
chord0_start = chord0_base
# chord = np.array([8.92386048e-02, 1.73000845e-01, 2.70523039e-01, 2.71542807e-01, 2.78749355e-01, 2.36866151e-01,
# 2.04103526e-01, 1.37456074e-01, 8.68094589e-02, 1.05601135e-04])
# twist = np.array([0.00161645, 0.15105685, 0.28791442, 0.31577392, 0.28644651, 0.27418749, 0.24854514, 0.21812646,
# 0.19802027, 0.14972058])
# omega_start = 3184.41320387 * 2*np.pi/60
# chord_start = chord
# twist_start = twist
# dchord_start = np.array([chord[i+1]-chord[i] for i in xrange(len(chord)-1)])
# dtwist_start = np.array([twist[i+1]-twist[i] for i in xrange(len(twist)-1)])
# twist0_start = twist[0]
# chord0_start = chord[0]
## Initialize everything to zeros
# dtwist_start = np.zeros(n_elements-1)
# dchord_start = np.zeros(n_elements-1)
# twist0_start = 0.0
# chord0_start = 0.0
omega_lower = 2000 * 2 * np.pi / 60
omega_upper = 8000.0 * 2 * np.pi / 60
twist0_lower = 0.0 * 2 * np.pi / 360
twist0_upper = 60. * 2 * np.pi / 360
chord0_upper = 0.1198
chord0_lower = 0.05
dtwist_lower = -10.0 * 2 * np.pi / 360
dtwist_upper = 10.0 * 2 * np.pi / 360
dchord_lower = -0.1
dchord_upper = 0.1
opt_prob = Optimization('Rotor in Hover', objfun)
opt_prob.addVar('omega',
'c',
value=omega_start,
lower=omega_lower,
upper=omega_upper)
opt_prob.addVar('twist0',
'c',
value=twist0_start,
lower=twist0_lower,
upper=twist0_upper)
opt_prob.addVar('chord0',
'c',
value=chord0_start,
lower=chord0_lower,
upper=chord0_upper)
opt_prob.addVarGroup('dtwist',
n_elements - 1,
'c',
value=dtwist_start,
lower=dtwist_lower,
upper=dtwist_upper)
opt_prob.addVarGroup('dchord',
n_elements - 1,
'c',
value=dchord_start,
lower=dchord_lower,
upper=dchord_upper)
opt_prob.addObj('f')
opt_prob.addCon('thrust', 'i')
opt_prob.addConGroup('c_lower', n_elements, 'i')
opt_prob.addConGroup('c_upper', n_elements, 'i')
print opt_prob
opt_method = 'nograd'
nsga2 = NSGA2()
nsga2.setOption('PrintOut', 2)
nsga2.setOption('PopSize', 300)
nsga2.setOption('maxGen', 1100)
nsga2.setOption('pCross_real', 0.85)
nsga2.setOption('xinit', 1)
fstr, xstr, inform = nsga2(opt_prob,
n_blades=n_blades,
n_elements=n_elements,
root_cutout=root_cutout,
radius=radius,
dy=dy,
dr=dr,
y=y,
r=r,
pitch=pitch,
airfoils=airfoils,
vehicle_weight=vehicle_weight,
max_chord=max_chord,
tip_loss=tip_loss,
mach_corr=mach_corr,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
Cl_tables=Cl_tables,
Cd_tables=Cd_tables,
allowable_Re=allowable_Re,
opt_method=opt_method,
alt=alt,
lift_curve_info_dict=lift_curve_info_dict)
print opt_prob.solution(0)
# opt_method = 'nograd'
# xstart_alpso = np.concatenate((np.array([omega_start, twist0_start, chord0_start]), dtwist_start, dchord_start))
# alpso = ALPSO()
# alpso.setOption('xinit', 0)
# alpso.setOption('SwarmSize', 200)
# alpso.setOption('maxOuterIter', 100)
# alpso.setOption('stopCriteria', 0)
# fstr, xstr, inform = alpso(opt_prob, xstart=xstart_alpso, n_blades=n_blades, n_elements=n_elements,
# root_cutout=root_cutout, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch,
# airfoils=airfoils, thrust=thrust, max_chord=max_chord, tip_loss=tip_loss,
# mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs, Cl_tables=Cl_tables,
# Cd_tables=Cd_tables, allowable_Re=allowable_Re, opt_method=opt_method)
# print opt_prob.solution(0)
# opt_method = 'grad'
# slsqp = SLSQP()
# slsqp.setOption('IPRINT', 1)
# slsqp.setOption('MAXIT', 1000)
# slsqp.setOption('ACC', 1e-7)
# fstr, xstr, inform = slsqp(opt_prob, sens_type='FD', n_blades=n_blades, n_elements=n_elements,
# root_cutout=root_cutout, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch,
# airfoils=airfoils, thrust=thrust, max_chord=max_chord,
# tip_loss=tip_loss, mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs,
# Cl_tables=Cl_tables, Cd_tables=Cd_tables, allowable_Re=allowable_Re,
# opt_method=opt_method, alt=alt)
# print opt_prob.solution(0)
def get_performance(o, c, t):
chord_meters = c * radius
prop = propeller.Propeller(t,
chord_meters,
radius,
n_blades,
r,
y,
dr,
dy,
airfoils=airfoils,
Cl_tables=Cl_tables,
Cd_tables=Cd_tables)
return bemt.bemt_axial(prop,
pitch,
o,
allowable_Re=allowable_Re,
Cl_funs=Cl_funs,
Cd_funs=Cd_funs,
tip_loss=tip_loss,
mach_corr=mach_corr,
output='long',
alt=alt)
omega = xstr[0]
twist0 = xstr[1]
chord0 = xstr[2]
dtwist = xstr[3:3 + len(r) - 1]
dchord = xstr[3 + len(r) - 1:]
twist = calc_twist_dist(twist0, dtwist)
chord = calc_chord_dist(chord0, dchord)
print "chord = " + repr(chord)
print "twist = " + repr(twist)
# twist_base = calc_twist_dist(twist0_base, dtwist_base)
# chord_base = calc_chord_dist(chord0_base, dchord_base)
perf_opt = get_performance(omega, chord, twist)
#perf_base = get_performance(omega_start, chord_base, twist_base)
print "omega = " + str(omega * 60 / 2 / np.pi)
print "Thrust of optimized = " + str(sum(perf_opt[0]))
print "Power of optimized = " + str(perf_opt[1])
# print "Omega base = " + str(omega_start*60/2/np.pi)
# print "Thrust of base = " + str(sum(perf_base[0]))
# print "Power of base = " + str(sum(perf_base[1]))
plt.figure(1)
plt.plot(r, chord_start, '-b')
plt.plot(r, chord, '-r')
plt.xlabel('radial location')
plt.ylabel('c/R')
plt.legend(['start', 'opt'])
plt.figure(2)
plt.plot(r, twist_start * 180 / np.pi, '-b')
plt.plot(r, twist * 180 / np.pi, '-r')
plt.xlabel('radial location')
plt.ylabel('twist')
plt.legend(['start', 'opt'])
plt.show()
from pyOpt import CONMIN
def obj_fun(x):
f = x[0]**2 - 5 * x[0] + x[1]**2 - 5 * x[1] + 2 * x[2]**2 - 21 * x[2] + x[
3]**2 + 7 * x[3] + 50
g = [0] * 3
g[0] = x[0]**2 + x[0] + x[1]**2 - x[1] + x[2]**2 + x[2] + x[3]**2 - x[3] - 8
g[1] = x[1]**2 - x[0] + 2 * x[1]**2 + x[2]**2 + 2 * x[3]**2 - x[3] - 10
g[2] = 2 * x[0]**2 + 2 * x[0] + x[1]**2 - x[1] + x[2]**2 - x[3] - 5
fail = 0
return f, g, fail
xinit = [1.0, 1.0, 1.0, 1.0]
opt_prob = Optimization('Rosen-Suzuki Constrained Minimization', obj_fun)
opt_prob.addVarGroup('x', 4, 'c', value=xinit)
opt_prob.addConGroup('g', 3, 'i')
opt_prob.addObj('f')
print opt_prob
conmin = CONMIN()
conmin.setOption('IPRINT', 1)
conmin(opt_prob)
print opt_prob.solution(0)
