Modifica di Asse Trasversale Cerniera (sezione)

====Script Python: Errore localizzazione HA da corda <math>s</math> e sagitta <math>h</math>====

<syntaxhighlight lang="python">
import numpy as np
import matplotlib.pyplot as plt

# Constants
r = 90.7  # Radius in mm
s = 12.02  # Length of Arc in mm
alpha = s / r  # Angle in radians
r_var = 26.33  # Distance from the hinge axis in mm

# Calculate start and end points
p_start = np.array([r_var, 0])
p_end = np.array([r_var * np.cos(alpha), r_var * np.sin(alpha)])

# Calculate reference values
s_ref = np.sqrt((p_end[0] - p_start[0])**2 + (p_end[1] - p_start[1])**2)
h_ref = s_ref / 2 * np.tan(alpha / 4)
scale_noise = 0.01  # Reduced noise in mm
samples = 1000  # number of Gaussian samples
noise = scale_noise * np.random.randn(5, samples)

# Add noise to points
pn_start = np.array([p_start[0] + noise[0, :], p_start[1] + noise[1, :]])
pn_end = np.array([p_end[0] + noise[2, :], p_end[1] + noise[3, :]])

# Calculate length of the chord (s) and sagitta (height) (h_noise)
s = np.sqrt((pn_end[0, :] - pn_start[0, :])**2 + (pn_end[1, :] - pn_start[1, :])**2)
h_noise = h_ref + noise[4, :]
r_noise = (4 * h_noise**2 + s**2) / (8 * h_noise)
delta_r_noise = np.abs(r_noise - r_var)

# Calculate the 72nd quantile of the error
error_quantile_reduced_noise = np.quantile(delta_r_noise, 0.72)
print(f'Errore (72° percentile) con rumore ridotto: {error_quantile_reduced_noise:.2f} mm')

# Optional: Plot the distribution of errors
plt.hist(delta_r_noise, bins=30, edgecolor='k', alpha=0.7)
plt.axvline(error_quantile_reduced_noise, color='r', linestyle='dashed', linewidth=1)
plt.title('Distribuzione degli errori di misurazione')
plt.xlabel('Errore (mm)')
plt.ylabel('Frequenza')
plt.show()
</syntaxhighlight>