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ni3019
2026-02-05 21:29:20 +01:00
parent f75672ec36
commit e894c7089a
1 changed files with 45 additions and 40 deletions
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85
GHA_triaxial/gha1_ES.py
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@@ -117,26 +117,27 @@ def azimuth_at_ESpoint(P_prev: NDArray, P_curr: NDArray, E_hat_curr: NDArray, N_
return wrap_to_pi(float(np.arctan2(sE, sN)))
def optimize_next_point(beta_i: float, omega_i: float, alpha_target: float, ds: float, gamma0: float,
ell: EllipsoidTriaxial, maxSegLen: float = 1000.0, sigma0: float = None) -> Tuple[float, float, NDArray, float]:
def optimize_next_point(beta_i: float, omega_i: float, alpha_i: float, ds: float, gamma0: float,
ell: EllipsoidTriaxial, maxSegLen: float = 1000.0, sigma0: float = None) -> Tuple[float, float, NDArray, float]:
"""
:param beta_i:
:param omega_i:
:param alpha_target:
:param ds:
:param gamma0:
:param ell:
:param maxSegLen:
Berechnung der 1. GHA mithilfe der CMA-ES.
Die CMA-ES optimiert sukzessive einen Punkt, der maxSegLen vom vorherigen Punkt entfernt und zusätzlich auf der
geodätischen Linien liegt. Somit entsteht ein Geodäten ähnlicher Polygonzug auf der Oberfläche des dreiachsigen Ellipsoids.
:param beta_i: Beta Koordinate am Punkt i
:param omega_i: Omega Koordinate am Punkt i
:param alpha_i: Azimut am Punkt i
:param ds: Gesamtlänge
:param gamma0: Jacobi-Konstante am Startpunkt
:param ell: Ellipsoid
:param maxSegLen: maximale Segmentlänge
:param sigma0:
:return:
"""
# Startbasis (für Predictor + optionales alpha_start)
# Startbasis
E_i, N_i, U_i, En_i, Nn_i, P_i = ENU_beta_omega(beta_i, omega_i, ell)
# Predictor: dβ ≈ ds cosα / |N|, dω ≈ ds sinα / |E|
d_beta = ds * float(np.cos(alpha_target)) / Nn_i
d_omega = ds * float(np.sin(alpha_target)) / En_i
# Prediktor: dβ ≈ ds cosα / |N|, dω ≈ ds sinα / |E|
d_beta = ds * float(np.cos(alpha_i)) / Nn_i
d_omega = ds * float(np.sin(alpha_i)) / En_i
beta_pred = beta_i + d_beta
omega_pred = wrap_to_pi(omega_i + d_omega)
@@ -144,36 +145,44 @@ def optimize_next_point(beta_i: float, omega_i: float, alpha_target: float, ds:
if sigma0 is None:
R0 = (ell.ax + ell.ay + ell.b) / 3
sigma0 = 1e-3 * (ds / R0)
sigma0 = 1e-5 * (ds / R0)
def fitness(x: NDArray) -> float:
"""
Fitnessfunktion: Fitnesscheck erfolgt anhand der Segmentlänge und der Jacobi-Konstante.
Die Segmentlänge muss möglichst gut zum Sollwert passen. Die Jacobi-Konstante am Punkt x muss zur
Jacobi-Konstanten am Startpunkt passen, damit der Polygonzug auf derselben geodätischen Linie bleibt.
:param x: Koordinate in beta, lambda aus der CMA-ES
:return: Fitnesswert (f)
"""
beta = x[0]
omega = wrap_to_pi(x[1])
P = ell.ell2cart(beta, omega)
d = float(np.linalg.norm(P - P_i))
P = ell.ell2cart(beta, omega) # in kartesischer Koordinaten
d = float(np.linalg.norm(P - P_i)) # Distanz zwischen
# length penalty
# maxSegLen einhalten
J_len = ((d - ds) / ds) ** 2
if d > maxSegLen * 1.02:
J_len += 1e3 * ((d / maxSegLen) - 1.02) ** 2
w_len = 1.0
# alpha at end, computed using previous point (for Jacobi gamma)
# Azimut für Jacobi-Konstante
E_j, N_j, U_j, _, _, _ = ENU_beta_omega(beta, omega, ell)
alpha_end = azimuth_at_ESpoint(P_i, P, E_j, N_j, U_j)
# Jacobi gamma at candidate/end
# Jacobi-Konstante
g_end = jacobi_konstante(beta, omega, alpha_end, ell)
J_gamma = (g_end - gamma0) ** 2
w_gamma = 10
return float(w_len * J_len + w_gamma * J_gamma)
f = float(w_len * J_len + w_gamma * J_gamma)
return f
xb = escma(fitness, N=2, xmean=xmean, sigma=sigma0) # Aufruf CMA-ES
beta_best = float(np.clip(float(xb[0]), -0.499999 * np.pi, 0.499999 * np.pi))
omega_best = wrap_to_pi(float(xb[1]))
beta_best = xb[0]
omega_best = wrap_to_pi(xb[1])
P_best = ell.ell2cart(beta_best, omega_best)
E_j, N_j, U_j, _, _, _ = ENU_beta_omega(beta_best, omega_best, ell)
alpha_end = azimuth_at_ESpoint(P_i, P_best, E_j, N_j, U_j)
@@ -181,17 +190,16 @@ def optimize_next_point(beta_i: float, omega_i: float, alpha_target: float, ds:
return beta_best, omega_best, P_best, alpha_end
def gha1_ES(ell: EllipsoidTriaxial, beta0: float, omega0: float, alpha0: float, s_total: float, maxSegLen: float = 1000):
"""
:param ell:
:param beta0:
:param omega0:
:param alpha0:
:param s_total:
:param maxSegLen:
:return:
Aufruf der 1. GHA mittels CMA-ES
:param ell: Ellipsoid
:param beta0: Beta Startkoordinate
:param omega0: Omega Startkoordinate
:param alpha0: Azimut Startkoordinate
:param s_total: Gesamtstrecke
:param maxSegLen: maximale Segmentlänge
:return: Zielpunkt Pk und Azimut am Zielpunkt
"""
beta = float(beta0)
omega = wrap_to_pi(float(omega0))
@@ -205,15 +213,13 @@ def gha1_ES(ell: EllipsoidTriaxial, beta0: float, omega0: float, alpha0: float,
s_acc = 0.0
step = 0
nsteps_est = int(np.ceil(s_total / maxSegLen))
while s_acc < s_total - 1e-9:
step += 1
ds = min(maxSegLen, s_total - s_acc)
print(f"[GHA1-ES] Step {step}/{nsteps_est} ds={ds:.3f} m s_acc={s_acc:.3f} m beta={beta:.6f} omega={omega:.6f} alpha={alpha:.6f}")
beta, omega, P, alpha = optimize_next_point(beta_i=beta, omega_i=omega, alpha_target=alpha, ds=ds, gamma0=gamma0,
ell=ell, maxSegLen=maxSegLen)
beta, omega, P, alpha = optimize_next_point(beta_i=beta, omega_i=omega, alpha_i=alpha, ds=ds, gamma0=gamma0,
ell=ell, maxSegLen=maxSegLen)
s_acc += ds
points.append(P)
alpha_end.append(alpha)
@@ -225,7 +231,6 @@ def gha1_ES(ell: EllipsoidTriaxial, beta0: float, omega0: float, alpha0: float,
return Pk, alpha1
if __name__ == "__main__":
ell = EllipsoidTriaxial.init_name("BursaSima1980round")
s = 188891.650873