Parameter Estimation of Complex Systems from Sparse and Noisy Data

Mathematical modeling is a key component of various disciplines in science andengineering. A mathematical model which represents important behavior of a realsystem can be used as a substitute for the real process for many analysis and synthesistasks. The performance of model based techniques, e.g. system analysis, computersimulation, 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 availableexperimental data.Parameter estimation is usually formulated as an optimization problem where theparameter estimate is computed by minimizing the discrepancy between the modelprediction and the experimental data. If a simple model and a large amount of data areavailable then the estimation problem is frequently well-posed and a small error in datafitting 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 estimationproblem is often ill-conditioned and good data fitting does not ensure accurate modelpredictions. Many challenges that can often be neglected for estimation involving simplemodels need to be carefully considered for estimation problems involving complexmodels.To obtain a reliable and accurate estimate from sparse and noisy data, a set oftechniques is developed by addressing the challenges encountered in estimation ofcomplex models, including (1) model analysis and simplification which identifies the important sources of uncertainty and reduces the model complexity; (2) experimentaldesign for collecting information-rich data by setting optimal experimental conditions;(3) regularization of estimation problem which solves the ill-conditioned large-scaleoptimization problem by reducing the number of parameters; (4) nonlinear estimationand filtering which fits the data by various estimation and filtering algorithms; (5) modelverification by applying statistical hypothesis test to the prediction error.The developed methods are applied to different types of models ranging from modelsfound in the process industries to biochemical networks, some of which are described byordinary differential equations with dozens of state variables and more than a hundredparameters.