I want to use two inputs or more to create a more precise estimation of a variable. I already estimated it using only one input and one FOPDT equation, but when I try to add one more input and the respective k, tau and theta, along with another equation, i get "Solution Not Found" error. Can I create a system of equations this way?
More details about the solver output below. Even though I added more variables than equations to use more than one input, this made my problem have negative degrees of freedom.
--------- APM Model Size ------------
Each time step contains
Objects : 2
Constants : 0
Variables : 15
Intermediates: 0
Connections : 4
Equations : 6
Residuals : 6
Number of state variables: 1918
Number of total equations: - 2151
Number of slack variables: - 0
---------------------------------------
Degrees of freedom : -233
* Warning: DOF <= 0
**********************************************
Dynamic Estimation with Interior Point Solver
**********************************************
Info: Exact Hessian
******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************
This is Ipopt version 3.12.10, running with linear solver ma57.
Number of nonzeros in equality constraint Jacobian...: 6451
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 1673
Exception of type: TOO_FEW_DOF in file "IpIpoptApplication.cpp" at line 891:
Exception message: status != TOO_FEW_DEGREES_OF_FREEDOM evaluated false: Too few degrees of freedom (rethrown)!
EXIT: Problem has too few degrees of freedom.
An error occured.
The error code is -10
---------------------------------------------------
Solver : IPOPT (v3.12)
Solution time : 2.279999999154825E-002 sec
Objective : 0.000000000000000E+000
Unsuccessful with error code 0
---------------------------------------------------
Creating file: infeasibilities.txt
Use command apm_get(server,app,'infeasibilities.txt') to retrieve file
@error: Solution Not Found
And here's the code
from gekko import GEKKO
import numpy as np
import pandas as pd
import plotly.express as px
d19jc = d19jc.dropna()
d19jcSlice = d19jc.loc['2019-10-22 05:30:00':'2019-10-22 09:30:00'] #jc22
d19jcSlice.index = pd.to_datetime(d19jcSlice.index)
d19jcSliceGroupMin = d19jcSlice.groupby(pd.Grouper(freq='T')).mean()
data = d19jcSliceGroupMin.dropna()
xdf1 = data['Cond_PID_SP']
xdf2 = data['Front_PID_SP']
ydf1 = data['Cond_Center_Top_TC']
xms1 = pd.Series(xdf1)
xm1 = np.array(xms1)
xms2 = pd.Series(xdf2)
xm2 = np.array(xms2)
yms = pd.Series(ydf1)
ym = np.array(yms)
xm_r = len(xm1)
tm = np.linspace(0,xm_r-1,xm_r)
m = GEKKO()
m.options.IMODE=5
m.time = tm; time = m.Var(0); m.Equation(time.dt()==1)
k1 = m.FV(lb=0.1,ub=5); k1.STATUS=1
tau1 = m.FV(lb=1,ub=300); tau1.STATUS=1
theta1 = m.FV(lb=0,ub=30); theta1.STATUS=1
k2 = m.FV(lb=0.1,ub=5); k2.STATUS=1
tau2 = m.FV(lb=1,ub=300); tau2.STATUS=1
theta2 = m.FV(lb=0,ub=30); theta2.STATUS=1
# create cubic spline with t versus u
uc1 = m.Var(xm1); tc1 = m.Var(tm); m.Equation(tc1==time-theta1)
m.cspline(tc1,uc1,tm,xm1,bound_x=False)
# create cubic spline with t versus u
uc2 = m.Var(xm2); tc2 = m.Var(tm); m.Equation(tc2==time-theta2)
m.cspline(tc2,uc2,tm,xm2,bound_x=False)
x1 = m.Param(value=xm1)
x2 = m.Param(value=xm2)
y = m.Var(value=ym)
yObj = m.Param(value=ym)
m.Equation(tau1*y.dt()+(y-ym[0])==k1 * (uc1-xm1[0]))
m.Equation(tau2*y.dt()+(y-ym[0])==k2 * (uc2-xm2[0]))
m.Minimize((y-yObj)**2)
m.options.EV_TYPE=2
print('solve start')
m.solve(disp=True)
print('k1: ', k1.value[0])
print('tau1: ', tau1.value[0])
print('theta1: ', theta1.value[0])
print('k2: ', k2.value[0])
print('tau2: ', tau2.value[0])
print('theta2: ', theta2.value[0])
df_plot = pd.DataFrame({'DateTime' : data.index,
'Cond_Center_Top_TC' : np.array(yObj),
'Fit Cond_Center_Top_TC - Train' : np.array(y),
figGekko = px.line(df_plot,
x='DateTime',
y=['Cond_Center_Top_TC','Fit Cond_Center_Top_TC - Train'],
labels={"value": "Degrees Celsius"},
title = "(Cond_PID_SP & Front_PID_SP) -> Cond_Center_Top_TC JC only - Train")
figGekko.update_layout(legend_title_text='')
figGekko.show()
