Matrix operations using parameters modified through moving horizon estimation

Question

I've recently started trying out moving horizon estimation with GEKKO. My specified manipulated variables are used in a heat balance equation within my model, and I am having some issues with the matrix operations in the model.

Example code:

from gekko import GEKKO
import numpy as np

#creating a sample array of input values
nt = 51
u_meas = np.zeros(nt)
u_meas[3:10] = 1.0
u_meas[10:20] = 2.0
u_meas[20:40] = 0.5
u_meas[40:] = 3.0

p = GEKKO(remote=False)
p.time = np.linspace(0,10,nt)

n = 1 #process model order

#designating u as my input, and that I'm going to be using these measurements to estimate my parameters with MHE
p.u = p.MV(value=u_meas)
p.u.FSTATUS=1

#parameters I'm looking to modulate
p.K = p.FV(value=1, lb = 1, ub = 3) #gain
p.tau = p.FV(value=5, lb = 1, ub = 10) #time constant

p.x = [p.Intermediate(p.u)]

#constants within the model that do not change
X_O2 = 0.5
X_SiO2 = 0.25
X_N2 = 0.1
m_feed = 100

#creating an array with my feed separated into components. This creates a 1D array with the individual feed streams of my components. 
mdot_F_i = (np.tile(m_feed,3)*np.array([X_O2, X_SiO2, X_N2])

#at this point, I want to add my MV values to the end of my component feed array for later heat and mass balance equations. Normally, in my previous model without MHE, I would put

mdot_c_i = np.concatenate(mdot_F_i, x, (other MV variables after))

However, now that u is a specified MV in GEKKO, and not a set value, I get an error at the mdot_c_i line that says that the array at index 0 has 1 dimension, and the array at index 1 has 2 dimensions.

I'm guessing that I have to specify mdot_c_i as an intermediate variable within Gekko. I've tried a couple different variations, alternately specifying mdot_c_i as an intermediate and trying to use only the values of the MV; however, I keep getting that error.

Has anyone experiences similar issues to this?

Thank you!

John Hedengren John Hedengren · Accepted Answer · 2020-08-25T21:06:24

You can resolve this by using np.append() instead of np.concatenate(). Try something like:

mdot_c_i = np.append(mdot_F_i, p.u)

Here is a minimum and complete example if you'd like to try it.

import numpy as np
from gekko import GEKKO
m = GEKKO(remote=False)
x = m.Array(m.Var,3,lb=-10,ub=10)
y = m.Var(5,lb=-5,ub=5)
z = np.append(x,y)
m.Minimize(np.dot([1,1,-1,1],z))
m.solve(disp=False)
print([zi.value[0] for zi in z])
# solution: [-10.0, -10.0, 10.0, -5.0]

Gekko variables need to be stored as objects, not as numerical values. The error may be because the np.concatenate() function is trying to access the length of the Gekko manipulated variable data p.u.value to concatenate those values instead of concatenating p.u as an object.

Matrix operations using parameters modified through moving horizon estimation

1 Answers