Title: Robust simulation and design using semi-infinite programs with implicit functions

Authors: Matthew D. Stuber, Paul I. Barton

Addresses: Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA. ' Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

Abstract: A method is presented for guaranteeing robust steady-state operation of chemical processes using a model-based approach, taking into account uncertainty in the model parameters and disturbances in the process inputs. Intractable constrained max–min optimisation formulations have been proposed for this problem in the past. A new approach is presented in which the equality constraints (process model equations) are solved numerically for the process variables as implicit functions of the uncertain parameters and controls. The problem is then formulated as a semi-infinite program (SIP) constrained only by the performance specifications as semi-infinite inequality constraints. A rigorous, finite ε-optimal convergent algorithm for solving such SIPs is proposed, making no assumptions on convexity, which makes use of the novel developments of parametric interval-Newton methods for bounding implicit functions, and novel developments in McCormick relaxations of algorithms.

Keywords: interval analysis; SIP; semi-infinite optimisation; global optimisation; McCormick relaxation; robust simulation; design under uncertainty; robust design; chemical processes; process model equations; model-based approaches.

DOI: 10.1504/IJRS.2011.041186

International Journal of Reliability and Safety, 2011 Vol.5 No.3/4, pp.378 - 397

Received: 25 May 2010
Accepted: 12 Oct 2010
Published online: 31 Mar 2015 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article