Figure 9.15:

Model fit to a single adsorption experiment.

Code for Figure 9.15

Text of the GNU GPL.

main.py

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
from paresto import Paresto
from misc import octave_save
import numpy as np
import matplotlib.pyplot as plt
import os
plt.ion()

# Define the data arrays
Hgas1 = np.array([2.659, 27.590, 141.038, 332.613, 546.857, 608.583,
                   875.353, 991.072, 1080.134, 1142.782, 1203.178,
                   1256.244])

Hads1 = np.array([32.31, 40.02, 45.40, 48.49, 50.19, 53.86, 52.77,
                   53.19, 53.67, 54.15, 54.51, 54.73])

Hgas2 = np.array([3.755, 36.331, 189.904, 413.881, 624.665, 817.592])

Hads2 = np.array([33.17, 40.90, 45.59, 47.72, 48.74, 49.43])

Hgas3 = np.array([12.794, 119.331, 339.917, 545.227, 735.746, 890.642])

Hads3 = np.array([36.91, 42.90, 45.65, 47.00, 47.82, 48.60])

Hgas4 = np.array([7.424, 73.312, 251.177, 491.691, 707.806, 873.926])

Hads4 = np.array([39.11, 46.06, 49.87, 51.57, 52.48, 53.18])

Hgas5 = np.array([9.176, 72.065, 259.002, 475.250, 670.034, 818.669])

Hads5 = np.array([39.52, 46.06, 49.92, 51.86, 52.96, 53.88])

Hgas6 = np.array([2.962, 34.350, 176.860, 405.233, 607.476, 799.723, 946.765])

Hads6 = np.array([32.70, 40.11, 44.92, 47.40, 48.62, 49.50, 50.12])

Hgas7 = np.array([3.159, 38.528, 200.877, 433.924, 647.630, 820.673])

Hads7 = np.array([32.42, 39.81, 44.51, 46.79, 48.14, 48.95])

Hgas8 = np.array([34.127, 172.316, 385.633, 616.149, 812.932, 961.191,
                   1061.967, 1155.829, 1219.299])

Hads8 = np.array([43.79, 48.97, 51.57, 53.09, 54.05, 54.67, 55.20,
                   55.60, 55.93])

# Choose a dataset or datasets to fit
cgmeas = Hgas4
cadsmeas = Hads4

Ks0 = 2
cms0 = 40
cmp0 = 0

# Define a model (this is an example using a simple function)
def alg_model(t, y, p):
    return [
        y.cads - p.cmp - (p.cms * p.sqKs * np.sqrt(y.cgmeas)) / (1 + p.sqKs * np.sqrt(y.cg)),
        y.cg - y.cgmeas
    ]

def lsq(t, y, p):
    return [y.cadsmeas - y.cads]

# Create an instance of the Paresto class with the model
pe = Paresto()
pe.transcription = "shooting"
pe.nlp_solver_options = {'sens_linsol_options': {'eps': 0}}

pe.z = ['cg', 'cads']
pe.p = ['sqKs', 'cms', 'cmp']
pe.d = ['cgmeas', 'cadsmeas']
pe.alg = alg_model
pe.lsq = lsq
pe.tout = np.arange(1, cgmeas.shape[0] + 1)

pe.initialize()

pe.ic.sqKs = np.sqrt(Ks0)
pe.ic.cms = cms0
pe.ic.cmp = cmp0
pe.ic.cg = 100
pe.ic.cads = 30

pe.lb_ub()
pe.lb.sqKs = np.sqrt(1e-3)
pe.lb.cms = 10
pe.lb.cmp = 0
pe.lb.cg = pe.ic.cg
pe.lb.cads = pe.ic.cads

pe.ub.sqKs = np.sqrt(5)
pe.ub.cms = 200
pe.ub.cmp = 100
pe.ub.cg = pe.ic.cg
pe.ub.cads = pe.ic.cads

# Perform optimization
est, yy, pp = pe.optimize(np.vstack([cgmeas, cadsmeas]).reshape(2, len(pe.tout), 1))

# Calculate confidence intervals
conf = pe.confidence(est, 0.95)

# Display results
print('Estimated parameters')
print('\n'.join(f'{k}: {float(v)}' for k, v in est.theta.items()))

print('Bounding box intervals')
print('\n'.join(f'{k}: {float(v)}' for k, v in conf.bbox.items()))


# Set up plotting values
nplot = 100
Xplot = np.linspace(0, 1.05 * np.max(cgmeas), nplot)
sqKs = est.theta.sqKs
cms = est.theta.cms
cmp = est.theta.cmp
Yplot = cms * sqKs * np.sqrt(Xplot) / (1 + sqKs * np.sqrt(Xplot)) + cmp

# Combine plot data
table1 = np.column_stack((Xplot, Yplot))
table2 = np.column_stack((cgmeas, cadsmeas))

octave_save('adsone.dat',
    ('table1', table1),
    ('table2', table2),
)

# Check the environment variable for plotting
if not os.getenv('OMIT_PLOTS') == 'true':
    plt.figure()
    plt.plot(table1[:, 0], table1[:, 1], label='Table 1', color = 'b')
    plt.plot(table2[:, 0], table2[:, 1], label='Table 2', marker='+', linestyle='None')
    plt.legend()
    if not os.getenv('OMIT_PLOTS') == 'true':
        plt.show()