hydroflask_water_mode_analysis.py

# %%
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

# %%
mode_data = np.loadtxt('hydroflask_water_modes.csv', dtype=np.complex128)

# %%
x = np.linspace(0, 1, 7)
x_long = np.linspace(0, 1, 100)

def rev_sigmoid(x, a, b, c, d):
    return c * (1.0 - (1.0 / (1.0 + np.exp(-b*(x-a))))) + d

# %%
plt.figure()
mode_freqs = np.flip(np.abs(mode_data[:,0]))
plt.scatter(x, mode_freqs, marker='x', color='r', label='Measured')

popt, pcov = curve_fit(rev_sigmoid, x, mode_freqs, bounds=([0, 1, -100, -200], [1, 100, 100, 200]))
plt.plot(x_long, rev_sigmoid(x_long, *popt), label='Model')
print(popt)

# plt.title('First mode frequency vs water amount')
plt.ylabel('Frequency [Hz]')
plt.xlabel('Water as fraction of bottle volume')
plt.xticks(x, ['0', '1/32', '1/16', '1/8', '1/4', '1/2', '1'])
plt.legend()
plt.grid()
plt.savefig('Figures/Water_Freq.png')

# %%
plt.figure()
colors = ['r', 'k']
for i in range(2):
    mode_damps = np.abs(mode_data[:,40+i])
    tau_gains = np.exp(-1.0 / mode_damps)
    t60s = np.log(0.001) / (48000 * np.log(tau_gains))
    plt.scatter(x, t60s, label='Mode #{}'.format(i+1), marker='x', color=colors[i])

mode_damps1 = np.mean(np.abs(mode_data[:,40:41]), axis=1)
mode_damps2 = np.mean(np.abs(mode_data[:,41:42]), axis=1)
mode_damps_avg = np.mean(np.abs(mode_data[:,40:42]), axis=1)
# # plt.plot(x, mode_damps, label='Avg')

def model_mode_damp(mode_damps, label, order=4):
    z_damp = np.polyfit(x, mode_damps, order)
    p_damp = np.poly1d(z_damp)
    tau_gains = np.exp(-1.0 / p_damp(x_long))
    t60s = np.log(0.001) / (48000 * np.log(tau_gains))
    plt.plot(x_long, t60s, label=label)
    # print('Damp function:')
    # print(p_damp)

model_mode_damp(mode_damps1, 'Mode 1 Model', 5)
model_mode_damp(mode_damps2, 'Mode 2 Model', 5)
# model_mode_damp(mode_damps_avg, 'Avg Model')

plt.legend()
# plt.title('First 2 modes damping vs water amount')
plt.ylabel(r'$T_{60}$ [seconds]')
plt.xlabel('Water as fraction of bottle volume')
plt.xticks(x, ['0', '1/32', '1/16', '1/8', '1/4', '1/2', '1'])
plt.grid()
plt.savefig('Figures/Water_Damping.png')

# %%
plt.show()