Automatic initial value generation procedure for nonlinear process models by interval arithmetic based cutting and splitting

Abstract

To solve large nonlinear equation systems, we present a hybrid method based on interval arithmetic and real-valued root-finding. The proposed approach includes two new interval arithmetic based methods, the so-called cutting and a special kind of bisection of consistent variable spaces. Applied to three examples from chemical engineering, it is shown that the approach is now able to find all system solutions within a variable space as well as only one process-relevant solution in much less time thanks to the built-in root-finding step. For the latter, a conventional Newton method as well as IPOPT have been examined. The hybrid approach no longer needs a well-estimated initial point to converge to a solution, only rough initial variable bounds are required.