## IGPE – Incremental Global Parameter Estimation

IGPE is a novel pseudo-deterministic method fort he global estimation of parameters in dynamical systems.

The method is described in detail in [1] and this web page contains additional material to ease the application of the method.

The basic idea of IGPE is to estimate state derivatives based on measurement data, thereby transforming the originally dynamic parameter estimation to an algebraic one. The algebraic problem can next be solved to its global optimum using readily (and freely) available software as for instance BARON (which can be used free of charge via the NEOS optimization server).

Finally a local dynamic parameter estimation problem is solved using the estimates obtained in the previous step as initial guess. This last step is necessary since a bias is inevitably introduced in the first step, the estimation of state derivatives, and guarantees that the final estimates are optimal in a statistical sense.

Our experience is that this heuristic procedure typically yields the global optimum to the original problem, although no guarantee can be given.

In [1] seven case studies and an investigation on the effect of measurement noise are treated. The following files contain:

1.) The measurement data for all test cases

2.) Some matlab routines to estimate the derivatives of the state measurements

3.) The GAMS models to solve the global algebraic parameter estimation problem

4.) The GPROMS models to solve the local dynamic parameter estimation problem. If you like to receive a copy of [1] or have further questions, please contact EDVSupport.pt@avt.rwth-aachen.de. Please note that no support on the provided routines and models can be given.

1.) Measurement data:

Test Problem 7_1 (first experiment)

Test Problem 7_2 (second experiment)

Test Problem 7_3 (third experiment)

Test Problem 7_4 (fourth experiment)

Noise Study, low frequency, 0% noise

Noise Study, low frequency, 10% noise 1

Noise Study, low frequency, 10% noise 2

Noise Study, low frequency, 10% noise 3

Noise Study, low frequency, 20% noise 1

Noise Study, low frequency, 20% noise 2

Noise Study, low frequency, 20% noise 3

Noise Study, high frequency, 0% noise 1

Noise Study, high frequency, 10% noise 1

Noise Study, high frequency, 10% noise 2

Noise Study, high frequency, 10% noise 3

Noise Study, high frequency, 20% noise 1

Noise Study, high frequency, 20% noise 2

Noise Study, high frequency, 20% noise 3

2.) Matlab code:

Call in the following form:

[vectorOfSmoothData, vectorOfEstimatedDerivatives] = smooth(vectorOfMeasurementTimes, vectorOfMeasurements)

3.) GAMS model files:

The examples can be solved to the global optimum using BARON free of charge via the NEOS server for optimization at:

http://www-neos.mcs.anl.gov/neos/solvers/go:BARON/GAMS.html

Example_7_1.gms (to estimate the first two parameters)

Example_7_2.gms (to estimate the remaining 6 parameters)

Example_1_HighResNoise00_1 (high resolution, 0% noise)

Example_1_HighResNoise01_1 (high resolution, 10% noise)

Example_1_HighResNoise01_2 (high resolution, 10% noise)

Example_1_HighResNoise01_3 (high resolution, 10% noise)

Example_1_HighResNoise02_1 (high resolution, 20% noise)

Example_1_HighResNoise02_2 (high resolution, 20% noise)

Example_1_HighResNoise02_3 (high resolution, 20% noise)

Example_1_LowResNoise00_1 (high resolution, 0% noise)

Example_1_LowResNoise01_1 (high resolution, 10% noise)

Example_1_LowResNoise01_2 (high resolution, 10% noise)

Example_1_LowResNoise01_3 (high resolution, 10% noise)

Example_1_LowResNoise02_1 (high resolution, 20% noise)

Example_1_LowResNoise02_2 (high resolution, 20% noise)

Example_1_LowResNoise02_3 (high resolution, 20% noise)

4.) gPROMS model file containing all test cases:

5.) Download all files as zip-file

Allfiles.zip

References:

[1] Michalik, C., Chachuat, B., Marquardt, W., 2008. Incremental Global Parameter Estimation in Dynamical Systems, submitted