I am trying to estimate 4 parameters (kdoc1, kdoc2, S1, S2), using GEKKO to solve a system of algebraic ordinary equations, minimizing the sum of the squares of the residual error between the observed and predicted values. I am not getting a good adjustment between the measured and the predicted data, do you have any suggestion about what am I doing wrong in the code?
Moreover, I am also trying to add another data set of measurement data. I want the model to do the estimation of the parameters using two measured data sets, I need to minimize the sum of residuals using the two data sets. Have you got any idea on how to do it in the code?
I already add additional points to help the solver converge using the suggestion python - Infrequent measurements in Gekko with extra simulation points - Stack Overflow
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import math as math
import pandas as pd
#TOC=5.93 mg/L
#M2 C1 5mg/L
#time: [0,0.08333,0.5,1,4,22.61667]; C2 measured: [0,9.33e-5,8.55e-5,8.55e-5,7.77e-5,7.00e-5]
#M4 C1 20mg/l
#time: [0,0.08333,0.5,1,4,22.61667]; C2 measured: [0,2.92e-4,2.72e-4,2.92e-4,2.72e-4,2.14e-4]
#measurements
t_data = [0.08333,0.5,1,4,22.61667]
x_data = [9.33e-5,8.55e-5,8.55e-5,7.77e-5,7.00e-5]
#x_data2 = [2.92e-4,2.72e-4,2.92e-4,2.72e-4,2.14e-4]
df1 = pd.DataFrame({'time':t_data,'x':x_data})
df1.set_index('time', inplace=True)
# simulation time points
df2 = pd.DataFrame({'time':np.linspace(0,25,51)}) #(0,25,51)
df2.set_index('time', inplace=True)
# merge dataframes
df = df2.join(df1,how='outer')
# get True (1) or False (0) for measurement
df['meas'] = (df['x'].values==df['x'].values).astype(int)
# replace NaN with zeros
df0 = df.fillna(value=0)
#Estimator Model
m = GEKKO()
m.time = df.index.values
# adjustable parameters
kdoc1 = m.FV() #m-1h-1
kdoc2 = m.FV() #m-1h-1
S1 = m.FV()
S2 = m.FV()
#State variables
# M (mol/L)
C0 = m.Var(value=8.00e-5)
C1 = m.Var(value=1.36e-3)
C2 = m.Var(value=x_data[0])
C2m = m.Param(df0['x'].values)
meas = m.Param(df0['meas'].values)
m.Minimize(meas*(C2-C2m)**2)
C3 = m.Var(value=0)
C4 = m.Var(value=3.16e-8)
C5 = m.Var(value=3.83e-7)
C6 = m.Var(value=0)
C7 = m.Var(value=0)
C8 = m.Var(value=0)
C9 = m.Var(value=0)
C10 = m.Var(value=0)
C11 = m.Var(value=0)
C12 = m.Var(value=3.21e-3)
TOC = m.Var(value=5.93)#mg-C/L
cC1 = m.Var(value=0)
cC2 = m.Var(value=0)
#temperature ºC
T = 20
#Rate constants
k1 = 2040000000*math.exp(-1887/(273.15+T))*3600
k2 = 138000000*math.exp(-8800/(273.15+T))*3600
k3 = 300000*math.exp(-2010/(273.15+T))*3600
k4 = 0.00000065*3600
k6 = 26700*3600
k7 = 167*3600
k8 = 27700*3600
k9 = 8300*3600
k10 = 0
k5 = 37800000000*math.exp(-2169/(273.15+T))*C4+2.52e25*math.exp(-16860/(273.15+T))*C10+0.87*math.exp(-503/(273.15+T))*C9
r1 = k1 * C0 * C1
r2 = k2 * C2
r3 = k3 * C0 * C2
r4 = k4 * C3
r5 = k5 * C2 * C2
r6 = k6 * C3 * C1* C4
r7 = k7 * C3 * C5
r8 = k8 * C6 * C3
r9 = k9 * C6 * C2
r10 = k10 * C2 * C3
r11 = kdoc1*S1*TOC*C2/12000
r12 = kdoc2*S2*TOC*C0/12000
t = m.Param(value=m.time)
m.Equation(C0.dt()== -r1 + r2 - r3 + r4 + r8 - r12)
m.Equation(C1.dt()== -r1 + r2 + r5 - r6 + r11)
m.Equation(C2.dt()== r1 - r2 - r3 + r4 - r5 + r6 - r9 - r10 - r11)
m.Equation(C3.dt()== r3 - r4 + r5 - r6 - r7 - r8 - r10)
m.Equation(C4.dt()== 0)
m.Equation(C5 == 1e-14/C4)
m.Equation(C6.dt()== r7 - r8 - r9)
m.Equation(C7 == (3.16e-8*C0)/C4)
m.Equation(C1 == (5.01e-10*C8)/C4)
m.Equation(C11 == (5.01e-11*C10)/C4)
m.Equation(C9 == (5.01e-7*C9)/C4)
m.Equation(C10 == C12 - 2*C11 - C5 + C4)
m.Equation(C12.dt()== 0)
m.Equation(TOC.dt()== 0)
m.Equation(cC1 == 17000*C1)
m.Equation(cC2 == 51500*C2)
#Application options
m.options.SOLVER = 1 #APOPT solver
m.options.IMODE = 5 #Dynamic Simultaneous - estimation
m.options.EV_TYPE = 2 #absolute error
m.options.NODES = 5 #collocation nodes (2,5)
if True:
kdoc1.STATUS=1
kdoc2.STATUS=1
S1.STATUS=1
S2.STATUS=1
#Solve
m.solve(disp=False)
#Results
data={'Time (h)':t,'C0 (M)':C0.value,'C1 (M)':C1.value, 'C2 (M)':C2.value,'C3 (M)':C3.value,'C4 (M)':C4.value,'C5 (M)':C5.value,'C6 (M)':C6.value,'C7 (M)':C7.value,'C8 (M)':C8.value,'C9 (M)':C9.value,'C10 (M)':C10.value,'C11 (M)':C11.value,'c12 (M)':C12.value}
dfr = pd.DataFrame(data, columns=['Time (h)','C0 (M)','C1 (M)','C2 (M)','C3 (M)','C4 (M)','C5 (M)','C6 (M)','C7 (M)','C8 (M)','C9 (M)','C10 (M)','C11 (M)','C12 (M)'])
#dfr.to_csv(r'C:\dfestimation.csv', index = False)
print('Solution')
print('kdoc1 = ' + str(kdoc1.value[0]))
print('kdoc2 = ' + str(kdoc2.value[0]))
print('S1 = ' + str(S1.value[0]))
print('S2 = ' + str(S2.value[0]))
plt.figure(1,figsize=(12,8))
plt.subplot(3,1,1)
plt.plot(m.time,C2.value,'bo',label='Predicted')
plt.plot(m.time,df['x'].values,'rs',label='Meas')
plt.plot(m.time,C2.value,label ='C2')
plt.legend(loc='best')
plt.subplot(3,1,2)
plt.plot(m.time,cC2.value,label ='C2')
plt.plot(m.time,cC1.value,label ='C1')
plt.legend(loc='best')
plt.subplot(3,1,3)
plt.plot(m.time,C0.value,label ='C0')
plt.plot(m.time,C1.value,label ='C1')
plt.plot(m.time,C3.value,label ='C3')
plt.plot(m.time,C4.value,label ='C4')
plt.plot(m.time,C5.value,label ='C5')
plt.plot(m.time,C6.value,label ='C6')
plt.plot(m.time,C7.value,label ='C7-')
plt.plot(m.time,C8.value,label ='C8')
plt.plot(m.time,C9.value,label ='C9')
plt.plot(m.time,C10.value,label ='C10')
plt.plot(m.time,C11.value,label ='C11')
plt.plot(m.time,C12.value,label ='C12')
plt.xlabel('time (h)')
plt.ylabel('Concentration (mol/L)')
plt.legend(loc='best')
