def inv_sigmoid(x):
return cas.log(1 / x - 1)
def test_gpkit_style_solve():
"""
Here, the problem is formulated *exactly* as it is in the GPKit paper.
This isn't how you would actually want to solve this problem (lots of redundant variables here...), but
this test just confirms that it's a valid mathematical formulation and still works.
Also note that all constraints and the objective are log-transformed, so under the hood, this is basically
exactly a geometric program (and should be convex, yay).
"""
opti = asb.Opti() # initialize an optimization environment
### Variables
D = opti.variable(init_guess=1e3,
log_transform=True) # total drag force [N]
A = opti.variable(init_guess=1e1, log_transform=True) # aspect ratio
S = opti.variable(init_guess=1e2,
log_transform=True) # total wing area [m^2]
V = opti.variable(init_guess=1e2,
log_transform=True) # cruising speed [m/s]
W = opti.variable(init_guess=8e3,
log_transform=True) # total aircraft weight [N]
Re = opti.variable(init_guess=5e6,
log_transform=True) # Reynolds number [-]
C_D = opti.variable(init_guess=3e-2,
log_transform=True) # Drag coefficient of wing [-]
C_L = opti.variable(init_guess=1,
log_transform=True) # Lift coefficient of wing [-]
C_f = opti.variable(init_guess=1e-2,
log_transform=True) # Skin friction coefficient [-]
W_w = opti.variable(init_guess=3e3, log_transform=True) # Wing weight [N]
### Constraints
# Drag model
C_D_fuse = CDA0 / S
C_D_wpar = k * C_f * S_wetratio
C_D_ind = C_L**2 / (pi * A * e)
opti.subject_to(cas.log(C_D) >= cas.log(C_D_fuse + C_D_wpar + C_D_ind))
# Wing weight model
W_w_strc = W_W_coeff1 * (N_ult * A**1.5 * (W_0 * W * S)**0.5) / tau
W_w_surf = W_W_coeff2 * S
opti.subject_to(cas.log(W_w) >= cas.log(W_w_surf + W_w_strc))
# Other models
opti.subject_to([
cas.log(D) >= cas.log(0.5 * rho * S * C_D * V**2),
cas.log(Re) <= cas.log((rho / mu) * V * (S / A)**0.5),
cas.log(C_f) >= cas.log(0.074 / Re**0.2),
cas.log(W) <= cas.log(0.5 * rho * S * C_L * V**2),
cas.log(W) <= cas.log(0.5 * rho * S * C_Lmax * V_min**2),
cas.log(W) >= cas.log(W_0 + W_w),
])
# Objective
opti.minimize(cas.log(D))
sol = opti.solve()
assert sol.value(D) == pytest.approx(303.1, abs=0.1)
error = model(machs_to_fit, fit_params) - beta(machs_to_fit)
error = np.array(error)
machs_to_plot = np.linspace(-0.5, 1.5, 500)
fig, ax = plt.subplots(1, 1, figsize=(8, 7), dpi=200)
plt.subplot("221")
plt.plot(machs_to_plot, beta(machs_to_plot), ".", label="")
plt.plot(machs_to_plot, model(machs_to_plot, fit_params))
plt.ylim(-0.05, 1.05)
plt.title("Fit: Normal Space")
plt.xlabel(r"Mach $M$ [-]")
plt.ylabel(r"$\beta = \sqrt{1-M^2}$")
plt.subplot("222")
plt.plot(machs_to_plot, inv_sigmoid(beta(machs_to_plot)), ".", label="")
plt.plot(machs_to_plot, inv_sigmoid(model(machs_to_plot, fit_params)))
plt.ylim(-15, 5)
plt.title("Fit: Inverse Sigmoid Space")
plt.xlabel(r"Mach $M$ [-]")
plt.ylabel(r"$\sigma^{-1}\left(\beta\right)$")
plt.subplot("223")
plt.plot(machs_to_plot, cas.log(beta(machs_to_plot)), ".", label="")
plt.plot(machs_to_plot, cas.log(model(machs_to_plot, fit_params)))
plt.ylim(-2.5, 0.5)
plt.title("Fit: Log Space")
plt.xlabel(r"Mach $M$ [-]")
plt.ylabel(r"$\ln(\beta)$")
plt.subplot("224")
plt.plot(machs_to_fit, error)
plt.title("Error in Fit range")
plt.savefig("machfitting.png")
def test_original_gpkit_like_solve():
opti = asb.Opti() # initialize an optimization environment
### Variables
D = opti.variable(log_transform=True, init_guess=1000, scale=1e3) # total drag force [N]
A = opti.variable(log_transform=True, init_guess=10, scale=1e1) # aspect ratio
S = opti.variable(log_transform=True, init_guess=100, scale=1e2) # total wing area [m^2]
V = opti.variable(log_transform=True, init_guess=100, scale=1e2) # cruising speed [m/s]
W = opti.variable(log_transform=True, init_guess=8e3, scale=1e4) # total aircraft weight [N]
Re = opti.variable(log_transform=True, init_guess=5e6, scale=1e6) # Reynolds number [-]
C_D = opti.variable(log_transform=True, init_guess=0.03, scale=1e-2) # Drag coefficient of wing [-]
C_L = opti.variable(log_transform=True, init_guess=1, scale=1e-1) # Lift coefficient of wing [-]
C_f = opti.variable(log_transform=True, init_guess=0.01, scale=1e-2) # Skin friction coefficient [-]
W_w = opti.variable(log_transform=True, init_guess=3e3, scale=1e3) # Wing weight [N]
### Constraints
# Drag model
C_D_fuse = CDA0 / S
C_D_wpar = k * C_f * S_wetratio
C_D_ind = C_L ** 2 / (pi * A * e)
opti.subject_to(cas.log(C_D) >= cas.log(C_D_fuse + C_D_wpar + C_D_ind))
# Wing weight model
W_w_strc = W_W_coeff1 * (N_ult * A ** 1.5 * (W_0 * W * S) ** 0.5) / tau
W_w_surf = W_W_coeff2 * S
opti.subject_to(cas.log(W_w) >= cas.log(W_w_surf + W_w_strc))
# Other models
opti.subject_to([
cas.log(D) >= cas.log(0.5 * rho * S * C_D * V ** 2),
cas.log(Re) <= cas.log((rho / mu) * V * (S / A) ** 0.5),
cas.log(C_f) >= cas.log(0.074 / Re ** 0.2),
cas.log(W) <= cas.log(0.5 * rho * S * C_L * V ** 2),
cas.log(W) <= cas.log(0.5 * rho * S * C_Lmax * V_min ** 2),
cas.log(W) >= cas.log(W_0 + W_w),
])
# Objective
opti.minimize(cas.log(D))
sol = opti.solve()
assert sol.value(D) == pytest.approx(303.1, abs=0.1)