(184c) Globally Optimal Parameter Identification for ODE Models with Discontinuities

This work applies a previously-developed globally optimal method of determining parameters from experimental data to ODE/DAE models in which the state variable trajectories can potentially exhibit discontinuities. Typical non-linear regression techniques used for ODE/DAE models with no analytical integral solution do not guarantee global optimality of the solution, and fail to ascertain validity of the proposed problem parameterization for the given data. To address these shortcomings, our method employs finite-dimensional global optimization techniques, and is guaranteed to identify the global optimum of the corresponding non-linear regression problem that employs a numerical approximation of the ODE model. The method employs two phases employing interval analysis, relaxation strategies for identifying efficient over and underestimators.

            The aforementioned two-stage method will be employed in a case study involving a non-isothermal reaction/diffusion model which can potentially exhibit ignition/extinction phenomena. A comparison to the behavior of an isothermal reaction/diffusion model will be carried out. The identifiability of model parameters from gas concentration data will also be discussed.