## Main.ParameterFit History

November 04, 2019, at 12:54 PM by 136.36.211.159 -
Changed lines 101-103 from:
(:sourceend:)
to:
(:sourceend:)

November 04, 2019, at 12:48 PM by 136.36.211.159 -
Deleted lines 0-1:
!! Parameter Estimation
November 04, 2019, at 12:47 PM by 136.36.211.159 -
Changed line 7 from:
% MATLAB example
to:
% APM MATLAB example
Changed line 10 from:
# Python example
to:
# APM Python example

# Python Gekko example
m.options.IMODE = 2
November 04, 2019, at 12:46 PM by 136.36.211.159 -

(:html:)
<iframe width="560" height="315" src="https://www.youtube.com/embed/3ZVRstDL9A4" frameborder="0" allow="autoplay; encrypted-media" allowfullscreen></iframe>
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November 04, 2019, at 12:45 PM by 136.36.211.159 -
Changed lines 34-96 from:
Once the base-case is converged, a select number of parameters can be set free for the optimization problem.  The parameter is set to be fixed or calculated based on the DBS parameter ''STATUS''.  A value of ''1'' indicates that the parameter is to be calculated by the optimizer while a value of ''0'' indicates that the parameter is to remained fixed.
to:
Once the base-case is converged, a select number of parameters can be set free for the optimization problem.  The parameter is set to be fixed or calculated based on the DBS parameter ''STATUS''.  A value of ''1'' indicates that the parameter is to be calculated by the optimizer while a value of ''0'' indicates that the parameter is to remained fixed.

!!! Example: Nonlinear Regression

%width=550px%Attach:gekko_imode2_regression.png

(:source lang=python:)
import numpy as np
from gekko import GEKKO

xm = np.array([18.3447,79.86538,85.09788,10.5211,44.4556, \
69.567,8.960,86.197,66.857,16.875, \
52.2697,93.917,24.35,5.118,25.126, \
34.037,61.4445,42.704,39.531,29.988])

ym = np.array([5.072,7.1588,7.263,4.255,6.282, \
6.9118,4.044,7.2595,6.898,4.8744, \
6.5179,7.3434,5.4316,3.38,5.464, \
5.90,6.80,6.193,6.070,5.737])

# define GEKKO model
m = GEKKO()
# parameters and variables
a = m.FV(value=0)
b = m.FV(value=0)
c = m.FV(value=0,lb=-100,ub=100)
x = m.Param(value=xm)
ymeas = m.Param(value=ym)
ypred = m.Var()
# parameter and variable options
a.STATUS = 1 # available to optimizer
b.STATUS = 1 #  to minimize objective
c.STATUS = 1
# equation
m.Equation(ypred == a + b/x + c*m.log(x))
# objective
m.Obj(((ypred-ymeas)/ymeas)**2)
# application options
m.options.IMODE = 2  # regression mode
# solve
m.solve() # remote=False for local solve

# show final objective
print('Final SSE Objective: ' + str(m.options.objfcnval))

# print solution
print('Solution')
print('a = ' + str(a.value))
print('b = ' + str(b.value))
print('c = ' + str(c.value))

# plot solution
import matplotlib.pyplot as plt
plt.figure(1)
plt.plot(x,ymeas,'ro')
plt.plot(x,ypred,'bx');
plt.xlabel('x')
plt.ylabel('y')
plt.legend(['Measured','Predicted'],loc='best')
plt.savefig('results.png')
plt.show()
(:sourceend:)
June 09, 2017, at 12:58 AM by 10.5.113.159 -
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nlc.imode = 2
to:
apm.imode = 2
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apm_option(server,app,'nlc.imode',2);
to:
apm_option(server,app,'apm.imode',2);
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apm_option(server,app,'nlc.imode',2)
to:
apm_option(server,app,'apm.imode',2)
June 16, 2015, at 06:57 PM by 45.56.3.184 -
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June 16, 2015, at 06:57 PM by 45.56.3.184 -
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''NLC.imode = 2''

Parameter estimation with model parameter update
(MPU) is accomplished by solving a number of steady state conditions simultaneously.  The MPU cases are selected from a number of steady state operating conditions.  The objective is to minimize the difference between measured values and model states.

''objective =
minimize(meas-model)''
to:
nlc.imode = 2

% MATLAB example
apm_option
(server,app,'nlc.imode',2);

# Python example
apm_option(server,app,'nlc.imode',2)

Parameter estimation with model parameter update (MPU) is accomplished by solving a number of steady state conditions simultaneously.  The MPU cases are selected from a number of steady state operating conditions.  The objective is to
minimize the difference between measured values and model states such as a squared error.

''objective = minimize (meas-model)'^2^'
''
September 30, 2008, at 04:15 PM by 158.35.225.227 -
Changed lines 11-12 from:
Measurements are brought into the optimization problem via a Comma Separate Value (CSV) file.  The CSV file consists of columns of data for a unique measurement.  The rows of the CSV file are the measurement at various times that correspond to steady-state conditions.  If the data is not at steady-state, dynamic parameter estimation should be used instead.
to:
!!! CSV File Input

Measurements are brought into the optimization problem via a Comma Separate Value (
CSV) file.  The file must have the same name as the model file, but with the ''.csv'' extension.

The CSV file consists of columns of data for a unique measurement.  The column headings are the global variable names
.  The rows of the CSV file are the measurement at various times that correspond to steady-state conditions.  If the data is not at steady-state, dynamic parameter estimation should be used instead.

There is no limit to the number of data sets that may be included for MPU.  The only limitation is the amount of computational resources that are available to run the problem.

!!! Parameters

All parameters are generally set to OFF as a first simulation.  This creates a warm-start file ''mpu.t0'' and verifies that there are no spurious degrees of freedom.

Once the base-case is converged, a select number of parameters can be set free for the optimization problem.  The parameter is set to be fixed or calculated based on the DBS parameter ''STATUS''.  A value of ''1'' indicates that the parameter is to be calculated by the optimizer while a value of ''0'' indicates that the parameter is to remained fixed.
September 30, 2008, at 04:04 PM by 158.35.225.227 -
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to:
||border=1 width=50%
September 30, 2008, at 04:04 PM by 158.35.225.227 -
The DBS file parameter ''imode'' is used to control the simulation mode.  This option is set to ''2'' for model parameter update.

''NLC.imode = 2''

Changed lines 11-13 from:
The DBS file parameter ''imode'' is used to control the simulation mode.  This option is set to ''2'' for model parameter update.

''NLC.imode =
2''
to:
Measurements are brought into the optimization problem via a Comma Separate Value (CSV) file.  The CSV file consists of columns of data for a unique measurementThe rows of the CSV file are the measurement at various times that correspond to steady-state conditions.  If the data is not at steady-state, dynamic parameter estimation should be used instead.

||border=1 width=80%
||! Measurement #1 ||! Measurement #
2 ||! Measurement #3 ||
|| Time 1, Meas 1 || Time 1, Meas 2 || Time 1, Meas 3 ||
|| Time 2, Meas 1 || Time 2, Meas 2 || Time 2, Meas 3 ||
September 30, 2008, at 03:17 PM by 158.35.225.227 -
Changed lines 5-9 from:
''objective = minimize(meas-model)''
to:
''objective = minimize(meas-model)''

The DBS file parameter ''imode'' is used to control the simulation mode.  This option is set to ''2'' for model parameter update.

''NLC.imode = 2
''
September 29, 2008, at 06:50 PM by 158.35.225.229 -