Mau -4 years ago 302
Python Question

# Python Pyomo: parameter estimation in an ODE system

I am new using Pyomo, so I apologize in advance if this is a basic question. Well, I am working with kinetic models and my aim is to estimate kinetic parameters. I started with a 'toy model' for understanding better Pyomo before trying my complicated one.

So, my toy model is a simple ODE system of 3 equations:

``````dX1/dt = -k1*X1
dX2/dt =  k1*X1 - k2*X2
dX3/dt =  k2*X2
``````

My aim is to estimate parameters k1 and k2. I slightly changed the code from this tutorial and is the following:

``````from pyomo.environ import *
from pyomo.dae import *

model = AbstractModel()
model.t = ContinuousSet()
model.MEAS_t = Set(within=model.t)
model.x1_meas = Param(model.MEAS_t)
model.x2_meas = Param(model.MEAS_t)
model.x3_meas = Param(model.MEAS_t)

model.x1 = Var(model.t)
model.x2 = Var(model.t)
model.x3 = Var(model.t)

model.k1 = Var(bounds=(0,3))
model.k2 = Var(bounds=(0,3))

model.x1dot = DerivativeVar(model.x1,wrt=model.t)
model.x2dot = DerivativeVar(model.x2,wrt=model.t)
model.x3dot = DerivativeVar(model.x3,wrt=model.t)

def _x1dot(model,i):
return model.x1dot[i] == -model.k1*model.x1[i]
model.x1dotcon = Constraint(model.t, rule=_x1dot)

def _x2dot(model,i):
return model.x2dot[i] == model.k1*model.x1[i]-model.k2*model.x2[i]
model.x2dotcon = Constraint(model.t, rule=_x2dot)

def _x3dot(model,i):
return model.x3dot[i] == model.k2*model.x2[i]
model.x3dotcon = Constraint(model.t, rule=_x3dot)

def _obj(model):
return sum((model.x1[i]-model.x1_meas[i])**2+(model.x2[i]-model.x2_meas[i])**2+(model.x3[i]-model.x3_meas)**2 for i in model.MEAS_t)
model.obj = Objective(rule=_obj)

model.pprint()

instance = model.create_instance('data2.dat')
instance.t.pprint()

discretizer = TransformationFactory('dae.collocation')
discretizer.apply_to(instance,nfe=8,ncp=5)

solver=SolverFactory('ipopt')

results = solver.solve(instance,tee=True)

instance.k1.pprint()
instance.k2.pprint()
``````

Once I run this code, I got the following message:

``````TypeError: Cannot convert object of type 'IndexedParam' (value = x3_meas) to a numeric value.
``````

However, when I erase all the lines corresponding to x3_meas in my code, as well as the data in my .dat file, it works perfectly.

Does anyone know what is the problem?

My data looks like:

``````set t := 0.00 0.66 1.33 2.00 2.66 3.33 4.00 4.66 5.33 6.00 ;
set MEAS_t := 0.00 0.66 1.33 2.00 2.66 3.33 4.00 4.66 5.33 6.00 ;
param x1_meas :=
0.00 1.000000
0.66 0.263597
1.33 0.069483
2.00 0.018316
2.66 0.004828
3.33 0.001273
4.00 0.000335
4.66 0.000088
5.33 0.000023
6.00 0.000006
;
param x2_meas :=
0.00 0.000000
0.66 0.499640
1.33 0.388227
2.00 0.234039
2.66 0.129311
3.33 0.068803
4.00 0.035960
4.66 0.018630
5.33 0.009609
6.00 0.004945
;
param x3_meas :=
0.00 0.000000
0.66 0.236763
1.33 0.542289
2.00 0.747645
2.66 0.865861
3.33 0.929925
4.00 0.963704
4.66 0.981281
5.33 0.990367
6.00 0.995049
;
``````

``````def _obj(model):