ve1001
Reputation: 183
Equation Definition Error (Equation without an equality or inequality) while using GEKKO MHE
I'm currently trying out the GEKKO MHE mode. I have two specified manipulated variables and controlled variables in the model, and one parameter that I'm looking to estimate via MHE. When I currently run the model, I get an equation definition error, saying that
Equation without an equality (=) or inequality (>,<) -267.25544516-267.28925105-267.21324717-267.21191109-264.56454462 STOPPING...
The model was initialized as:
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
n = 17
m = GEKKO(remote=False)
m.time = np.linspace(0,8,n)
c1_in_arr = np.load('c1_in_arr.npy')
c2_in_arr = np.load('c2_in_arr.npy')
V1_measured = np.load('V1_measured.npy')
V2_measured = np.load('V2_measured.npy')
#mmanipulated variables, feeding in the arrays for them
m.C1_in = m.MV(value=c1_in_arr)
m.C2_in = m.MV(value=c2_in_arr)
#estimated variables, feeding in the upper and lower bounds for them
m.C1_eff = m.FV(value = 0.98, lb = 0.95, ub = 1.0)
#controlled variables, feeding in the measurements for them
m.V1 = m.CV(value=V1_measured)
m.V2 = m.CV(value=V2_measured)
mdot_1 = m.Var()
mdot_2 = m.Var()
m.Equation(mdot_1== 1.52*m.C1_eff*m.C1_in)
m.Equation(mdot_2==-0.668*mdot_1 + 1.33*m.C1_eff*m.C2_in)
df_c = pd.read_csv('Values_C.csv',index_col=0)
Hhat_C1 = m.Var()
Hhat_C1 = m.Var()
M_m = 125
mdot_m = 75
mdot_s = 46
m.Equations([Hhat_C1 == -0.606 + 0.0057 * mdot_1,
Hhat_C2 == -3.933 + 0.00096 * mdot_1])
C1_m = m.Var(value = 200)
C2_m = m.Var(value = 150)
m.Equations([C1_m.dt() == mdot_1 - C1_m/M_m*mdot_m,
C2_m.dt() == mdot_2 - C2_m/M_s*mdot_s)
m.Equation(m.V1==0.8*C1_m/M_m)
m.Equation(m.V2 == 0.78*C1_m/C2_m)
m.options.IMODE = 5
#setting the solver settings to MHE
m.options.EV_TYPE = 1
#setting the solver for the MHE to calculate the parameters based on the sum of absolute errors
m.C1_in.STATUS = 0
m.C2_in.STATUS = 0
m.SiO2_in.STATUS = 0
m.C1_eff.STATUS = 1
m.V1.STATUS = 1
m.V2.STATUS = 1
m.C1_in.FSTATUS = 1
m.C2_in.FSTATUS = 1
m.C1_eff.FSTATUS = 0
m.V1.FSTATUS = 1
m.V2.FSTATUS = 1
m.C1_eff.DMAX = 1.0
m.V1.MEAS_GAP = 0.001
m.V2.MEAS_GAP = 0.001
m.open_folder()
m.solve(disp = False)
When I open the GEKKO folder prior to solving, the infeasibilities file is also not present in the folder.
The model is able to run without error when the MVs and CVs are initialized as just the first variable of the "measurement" array
ex. m.C1_in = m.MV(value=c1_in_arr[0])
however, the provided parameter estimate is then incorrect.
I think that this error may be due to the way my MVs and CVs are being treated within the model. Is there a way to pinpoint which equation is causing this error, or if it's due to the MV/CV initialization?
Thank you!
Upvotes: 2
Views: 550
Answers (1)
John Hedengren
Reputation: 14321
The problem is likely with using a Numpy array or Pandas dataframe in a Gekko equation such as:
# incorrect
df_c = pd.read_csv('Values_C.csv',index_col=0)
m.Equation(m.C1_in==df_c)
You can resolve this error by instead creating an input Parameter such as:
# correct
df_c = pd.read_csv('Values_C.csv',index_col=0)
df_c = m.Param(df_c)
m.Equation(m.C1_in==df_c)
I don't have your .npy files so I can't reproduce your error. However, I did replace those with random array inputs of length n to get a successful solution. There were also parameters such as M_s that are undefined so I included some sample values. Your definition of MVs and CVs is good. The error is likely due to other input parameters that need to be converted to Gekko type Parameters before using them in an equation.
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
n = 17
m = GEKKO(remote=False)
m.time = np.linspace(0,8,n)
c1_in_arr = np.random.rand(n)
c2_in_arr = np.random.rand(n)
V1_measured = np.random.rand(n)
V2_measured = np.random.rand(n)
#mmanipulated variables, feeding in the arrays for them
m.C1_in = m.MV(value=c1_in_arr)
m.C2_in = m.MV(value=c2_in_arr)
#estimated variables, feeding in the upper and lower bounds for them
m.C1_eff = m.FV(value = 0.98, lb = 0.95, ub = 1.0)
#controlled variables, feeding in the measurements for them
m.V1 = m.CV(value=V1_measured)
m.V2 = m.CV(value=V2_measured)
mdot_1 = m.Var()
mdot_2 = m.Var()
m.Equation(mdot_1== 1.52*m.C1_eff*m.C1_in)
m.Equation(mdot_2==-0.668*mdot_1 + 1.33*m.C1_eff*m.C2_in)
Hhat_C1 = m.Var()
Hhat_C2 = m.Var()
M_m = 125
M_s = 125
mdot_m = 75
mdot_s = 46
m.Equations([Hhat_C1 == -0.606 + 0.0057 * mdot_1,
Hhat_C2 == -3.933 + 0.00096 * mdot_1])
C1_m = m.Var(value = 200)
C2_m = m.Var(value = 150)
m.Equations([C1_m.dt() == mdot_1 - C1_m/M_m*mdot_m,
C2_m.dt() == mdot_2 - C2_m/M_s*mdot_s])
m.Equation(m.V1==0.8*C1_m/M_m)
m.Equation(m.V2 == 0.78*C1_m/C2_m)
m.options.IMODE = 5
#setting the solver settings to MHE
m.options.EV_TYPE = 1
#setting the solver for the MHE to calculate the
#parameters based on the sum of absolute errors
m.C1_in.STATUS = 0
m.C2_in.STATUS = 0
m.C1_eff.STATUS = 1
m.V1.STATUS = 1
m.V2.STATUS = 1
m.C1_in.FSTATUS = 1
m.C2_in.FSTATUS = 1
m.C1_eff.FSTATUS = 0
m.V1.FSTATUS = 1
m.V2.FSTATUS = 1
m.C1_eff.DMAX = 1.0
m.V1.MEAS_GAP = 0.001
m.V2.MEAS_GAP = 0.001
m.open_folder()
m.solve(disp = True)
The file infeasibilities.txt won't be created if there is a model error that prevents the solver from running or if there is a successful solution. With the random input values, there is a successful solution.
----------------------------------------------------------------
APMonitor, Version 0.9.2
APMonitor Optimization Suite
----------------------------------------------------------------
--------- APM Model Size ------------
Each time step contains
Objects : 0
Constants : 0
Variables : 11
Intermediates: 0
Connections : 0
Equations : 8
Residuals : 8
Warning: CV( 1 ) on at cycle 1 with no MVs on
Warning: CV( 2 ) on at cycle 1 with no MVs on
Number of state variables: 417
Number of total equations: - 416
Number of slack variables: - 0
---------------------------------------
Degrees of freedom : 1
**********************************************
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 3.10.2, running with linear solver mumps.
Number of nonzeros in equality constraint Jacobian...: 510
Number of nonzeros in inequality constraint Jacobian.: 384
Number of nonzeros in Lagrangian Hessian.............: 32
Total number of variables............................: 417
variables with only lower bounds: 192
variables with lower and upper bounds: 33
variables with only upper bounds: 0
Total number of equality constraints.................: 224
Total number of inequality constraints...............: 192
inequality constraints with only lower bounds: 192
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 1.4079997e+001 1.20e+002 9.00e+000 0.0 0.00e+000 - 0.00e+000 0.00e+000 0
1 2.2358394e+002 1.20e+002 9.95e+000 11.0 1.03e+011 - 1.05e-010 1.45e-012f 1
2 3.0439837e+004 1.20e+002 2.27e+005 12.1 1.14e+012 - 2.78e-013 1.89e-011f 1
3 3.0621616e+006 1.20e+002 2.44e+006 11.4 4.33e+010 - 1.00e+000 4.98e-008f 1
4 3.0621722e+006 6.66e-001 2.49e+004 4.6 3.93e+000 - 9.90e-001 1.00e+000f 1
5 3.0609833e+006 1.78e-014 2.55e+002 2.6 1.28e+000 - 9.90e-001 1.00e+000f 1
6 2.9460876e+006 1.42e-014 2.55e+000 0.6 8.89e+001 - 9.90e-001 1.00e+000f 1
7 7.0161757e+005 2.84e-014 2.55e-002 -1.3 1.69e+003 - 9.90e-001 1.00e+000f 1
8 1.1625511e+004 2.84e-014 2.57e-004 -2.7 1.48e+003 - 9.90e-001 9.91e-001f 1
9 1.0176844e+003 6.17e-009 5.69e-002 -0.1 3.45e+003 - 1.00e+000 9.32e-001f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 4.7702371e+002 1.77e-008 3.10e+000 -0.8 8.48e+003 - 1.00e+000 6.38e-001f 1
11 2.8271410e+002 2.82e-007 1.44e+000 -1.0 5.55e+003 - 1.00e+000 7.81e-001f 1
12 2.3676481e+002 8.50e-008 1.67e+000 -1.9 1.06e+004 - 1.00e+000 7.37e-001f 1
13 2.2794093e+002 1.98e-007 1.82e+000 -3.0 6.91e+003 - 9.98e-001 7.00e-001f 1
14 2.2582143e+002 7.63e-008 9.56e-001 -3.2 2.35e+003 - 1.00e+000 7.47e-001f 1
15 2.2529511e+002 2.39e-008 2.72e-001 -4.0 7.00e+002 - 1.00e+000 7.20e-001f 1
16 2.2508076e+002 5.09e-010 2.51e-004 -4.6 2.10e+002 - 1.00e+000 1.00e+000f 1
17 2.2507517e+002 7.65e-011 2.25e-004 -6.7 5.16e+000 - 1.00e+000 8.51e-001f 1
18 2.2507454e+002 1.43e-011 3.79e-005 -6.2 6.63e-001 - 1.00e+000 8.13e-001f 1
19 2.2507438e+002 3.69e-012 1.75e-005 -7.0 1.68e-001 - 1.00e+000 7.43e-001f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 2.2507434e+002 9.33e-013 5.66e-006 -8.2 4.29e-002 - 1.00e+000 7.47e-001f 1
21 2.2507433e+002 2.36e-013 1.64e-006 -8.6 1.09e-002 - 1.00e+000 7.47e-001f 1
22 2.2507432e+002 6.01e-014 1.33e-006 -9.3 2.23e-003 - 1.00e+000 7.45e-001f 1
23 2.2507432e+002 1.42e-014 9.06e-014 -11.0 2.74e-004 - 1.00e+000 1.00e+000h 1
Number of Iterations....: 23
(scaled) (unscaled)
Objective...............: 2.2507432359796402e+002 2.2507432359796402e+002
Dual infeasibility......: 9.0594198809412774e-014 9.0594198809412774e-014
Constraint violation....: 9.4739031434680035e-015 1.4210854715202004e-014
Complementarity.........: 1.2089838737827345e-011 1.2089838737827345e-011
Overall NLP error.......: 1.2089838737827345e-011 1.2089838737827345e-011
Number of objective function evaluations = 24
Number of objective gradient evaluations = 24
Number of equality constraint evaluations = 24
Number of inequality constraint evaluations = 24
Number of equality constraint Jacobian evaluations = 24
Number of inequality constraint Jacobian evaluations = 24
Number of Lagrangian Hessian evaluations = 23
Total CPU secs in IPOPT (w/o function evaluations) = 0.163
Total CPU secs in NLP function evaluations = 0.083
EXIT: Optimal Solution Found.
The solution was found.
The final value of the objective function is 225.07432359796402
---------------------------------------------------
Solver : IPOPT (v3.12)
Solution time : 0.2523 sec
Objective : 225.07433063732404
Successful solution
---------------------------------------------------
Upvotes: 1
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