Mathematical modeling is a key component of various disciplines in science and
engineering. A mathematical model which represents important behavior of a real
system can be used as a substitute for the real process for many analysis and synthesis
tasks. The performance of model based techniques, e.g. system analysis, computer
simulation, controller design, sensor development, state filtering, product monitoring,
and process optimization, is highly dependent on the quality of the model used.
Therefore, it is very important to be able to develop an accurate model from available
experimental data.
Parameter estimation is usually formulated as an optimization problem where the
parameter estimate is computed by minimizing the discrepancy between the model
prediction and the experimental data. If a simple model and a large amount of data are
available then the estimation problem is frequently well-posed and a small error in data
fitting automatically results in an accurate model. However, this is not always the case.
If the model is complex and only sparse and noisy data are available, then the estimation
problem is often ill-conditioned and good data fitting does not ensure accurate model
predictions. Many challenges that can often be neglected for estimation involving simple
models need to be carefully considered for estimation problems involving complex
models.
To obtain a reliable and accurate estimate from sparse and noisy data, a set of
techniques is developed by addressing the challenges encountered in estimation of
complex models, including (1) model analysis and simplification which identifies the important sources of uncertainty and reduces the model complexity; (2) experimental
design for collecting information-rich data by setting optimal experimental conditions;
(3) regularization of estimation problem which solves the ill-conditioned large-scale
optimization problem by reducing the number of parameters; (4) nonlinear estimation
and filtering which fits the data by various estimation and filtering algorithms; (5) model
verification by applying statistical hypothesis test to the prediction error.
The developed methods are applied to different types of models ranging from models
found in the process industries to biochemical networks, some of which are described by
ordinary differential equations with dozens of state variables and more than a hundred
parameters.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-12-8691 |
| Date | 2010 December 1900 |
| Creators | Chu, Yunfei |
| Contributors | Hahn, Juergen |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | application/pdf |
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