Maximum-likelihood estimation of kinetic parameters via the extent-based incremental approach

Abstract

For lumped homogeneous reaction systems, this paper presents a kinetic model identification scheme that provides maximum-likelihood parameter estimates and guarantees convergence to global optimality. The use of the extent-based incremental approach allows one to (i) identify each reaction individually, and (ii) reduce the number of parameters to be identified via optimization to the ones that appear nonlinearly in the investigated rate law. The approach results in maximum-likelihood parameter estimation if the experimental extents are uncorrelated and the rate estimates used to compute the modeled extents are unbiased. Furthermore, the identification problem can be rearranged via Taylor series expansion as a polynomial optimization problem. This optimization problem is then reformulated as a convex optimization problem that can be solved efficiently to global optimality. Different aspects of the approach are demonstrated via simulated examples.