Unscented Kalman filter with parameter identifiability analysis for the estimation of multiple parameters in kinetic models

In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison

On the design of optimally informative dynamic experiments for model discrimination in multiresponse nonlinear situations

We present a new method for determining optimally informative dynamic experiments for the purpose of model discrimination among several rival multiresponse nonlinear structured dynamic models generally described by systems of differential and algebraic equations (DAEs). A robust and efficient algorithm based on an extension to the dynamic case of the discrimination criterion put forth by Buzzi-Ferraris and Forzatti (Chem. Eng. Sci. 1984,39, 81) is developed to calculate dynamic input trajectories by reformulation of the experiment design problem as an optimal control problem. We show that the new approach, by taking parametric uncertainty into account, can provide significant improvements in the ability to distinguish among a series of rival dynamic models over previous attempts to design dynamic experiments primarily based on parameter point estimates and thus maximizes the divergence of the model predictions without regard for uncertainty (Espie, D. M.; Macchietto, S. AIChE J. 1989, 35, 223). We illustrate the experiment design concepts with a relatively simple, but pedagogical example of the dynamic modeling of the fermentation of baker's yeast, although the methods are general enough to be applied in other modeling exercises

On the design of optimally informative experiments for dynamic crystallization process modeling

In this paper, we present the challenging application of now well-established general and systematic procedures for model development, statistical discrimination, and validation to a published large-scale dynamic crystallization process model. Because of the model's size, this represents, to our knowledge, the first application of such statistical methods to such a large-scale dynamic model. For completeness, a brief review of both the model development procedures and the dynamic model are included in the paper. In reviewing the model development procedures, we cover such methods as parametric identifiability testing (to determine whether the parameters, as they appear in the model, can in fact be identified), as well as optimal design of dynamic experiments for both model discrimination among three crystallization models (differing in their kinetics only) and parameter precision improvement within the single "best" dynamic model. Because of the relatively large scale of the model, an optimization-based approach is used for testing of model parameter identifiability that involves semi-infinite programming (SIP) to ensure that the entire control (or input) space has been explored. The problem of designing dynamic experiments is cast as an optimal control problem that enables the calculation of optimal sampling points, experiment durations, fixed and variable external control profiles, and initial conditions of a dynamic experiment subject to general constraints on inputs and outputs. Within this framework, methods are presented to provide experiment design robustness, accounting for parametric uncertainty and subsequently model prediction uncertainty. The paper details the progression of the three crystallization models through the model development procedures and shows the Gahn and Mersmann model (Chem. Eng. Sci. 1999, 54, 1273) to be superior to its competitors