| Problems in estimating parameters in models of dynamic systems characterized by sets of non-linear ordinary differential equations (ODEs) have been investigated using techniques based on maximum likelihood and quasilinearization. Emphasis is on system models characterized by stiff ODEs, by multiple operating regimes governed by mutually exclusive sets of parameters, and by model parameter correlation. These system characteristics may lead to such estimation algorithm failures as parameter estimates that converge towards extreme or physically meaningless values, or numerical difficulties during solution of model or parameter update equations. These types of algorithm failures have been found to be caused by lack of information content in system observations, insensitivity of model response in certain operating regimes to one or more model parameters, model characteristics such as parameter dependency or model degeneracy, and numerical difficulties including lack of machine precision or accuracy in solution of model equations.; Techniques have been developed to identify situations and system characteristics that lead to difficulties in parameter estimation, and to carry out estimation calculations when difficulties are encountered. Central to several techniques is the Fisher information matrix, used as a measure of system observation information content for a given system model and parameter set, and as a basis for modifying parameter update vectors. Information matrix eigenvalues and eigenvectors are interpreted as defining a hypervolume representing the uncertainty associated with model parameters, and in turn, parameter update vectors. Certain parameter update difficulties can be avoided by modifying the shape of this hypervolume through use of various scaling techniques and spectral factorization.; When system observations contain insufficient information for estimation of a complete set of system parameters, algorithms incorporating rank-deficient updates and stage-wise updating of subsets of the full parameter vector have been developed and shown to be successful when applied to experimental systems exhibiting parameter dependency and unknown measurement noise characteristics. Guidelines have been developed to select appropriate solution techniques when difficulties are encountered in practical parameter estimation problems. Solution techniques that have been developed are incorporated into a flexible suite of integrated software components that run in an interactive graphics-based workstation environment. |
