Reliable high-performance computing strategies for chemical process modeling: Nonlinear parameter estimation

We present here a new methodology for reliably finding all solutions to a system of nonlinear equations or computing globally optimal solutions to nonconvex nonlinear programs, such as arising in chemical process modeling. The method is based on interval analysis and branch and bound scheme, in particular an interval Newton/generalized bisection (IN/GB) algorithm. For global optimization problems, such as nonlinear parameter estimation, this approach is deterministic and provides a mathematical and computational guarantee that the global optimum in the parameter estimation problem is found. The technique used is general-purpose and was applied here to a diverse set of applications. The method applying a new hybrid pre-conditioning strategy, in which a simple pivoting pre-conditioner is used in combination with the standard inverse-midpoint method, is presented, as is a new scheme for selection of the real point used in formulating the interval-Newton equation. Tests on a variety of problems arising in chemical process modeling have shown that the new methodologies lead to substantial reductions in computation time requirements, in many cases by multiple orders of magnitude.; In addition, we also present high performance computing (HPC) strategies to further enhance the computing performance of IN/GB in use of distributed parallel processing resources. We discuss issues of load balancing and work scheduling that arise in the implementation of parallel branch and bound, and describe and analyze techniques for this purpose. Results show that a consistently high efficiency can be achieved in solving nonlinear equations, providing excellent scalability. The effectiveness of the approach used is also demonstrated in the consistent superlinear speedup observed in performing global optimization.; Ultimately, this reliable HPC technology, including interval analysis and parallel processing, provides opportunities to solve nonlinear parameter estimation and data reconciliation problems faster and more reliably than ever before. In applying to several chemical process modeling problems, we demonstrate the importance of obtaining and using globally optimal, as opposed to locally optimal, parameters in terms of superior model prediction and statistical significance.