Parameter estimation for nonlinear dynamic systems with significant uncertainties

Abstract

The parameter estimation problem can be formulated as an optimization problem which minimizes the norm of the discrepancy between data and model simulation while constraining the parameters within a reasonable range. A more generalized structure of parameter estimation problem, which is different from the traditional formulation, is given by optimizing certain performance indices rather than minimizing the fitting error, while determining certain parameters of the process. One advantage of defining a generalized structure for parameter estimation problem is that existing approaches for parameter estimation can be used to solve optimization problems of similar structure.

In order to overcome the above challenges, this dissertation presents (i) a framework for generalized parameter estimation problems where a wide range of optimization problems with similar structure can be formulated and solved; (ii) a novel parameter set selection method which can handle significant parametric uncertainty; and (iii) an application of the framework and the presented parameter set selection method to an industrial ethanol production process, two signal transduction pathway models, and an inverse problem involving a fluorescent protein reporter system.

However, before any estimation is performed, it is also important to determine if all of the parameters are numerically identifiable. If not, then what subset of parameters that can be uniquely and accurately estimated? A systematic scheme for parameter set selection is based on optimality criteria computed from the Fisher information matrix which is closely related to the parameter-output sensitivity matrix. Unfortunately, existing sensitivity analysis techniques cannot effectively handle parametric uncertainty, since local techniques depends on the parameter values that are not known prior to estimation, while the global techniques do not rely on the concept of sensitivity matrix.

Mathematical models composed of ordinary differential equations (ODEs) are widely used to describe the behavior of dynamic systems, ranging from power systems, chemical processes to biochemical reaction networks. The accuracy of the models are not only dependent on the structure of the model which is determined by the physics, chemistry, or biology of the system, but also relies on adjustable parameters of the model, many of which need to be re-estimated from experiment data.