(669b) A Novel Feasible-Path Approach to Designs of Process Systems With Uncertainty

Authors: 
Wang, S., University of Texas at Austin
Baldea, M., The University of Texas at Austin


A Novel Feasible-Path Approach to Designs of Process Systems with Uncertainty

Siyun Wang and Michael Baldea

Department of Chemical Engineering

The University of Texas at Austin, 1 University Station C0400, Austin, TX 78712

email: mbaldea@che.utexas.edu

Fluctuating market conditions and the need for switching between an increasingly diverse portfolio of conventional and renewable feedstock are at the origin increased uncertainty in the operation of chemical and energy generation processes. This translates into fluctuations in process variables such as flow rate, pressure, temperature, and product quality of the entire process system[1]. Accounting for such uncertainties in at the process design stage is therefore an increasingly important need.

A broadly used approach for optimizing dynamical systems under uncertainty relies on computing the objective function as the average over several realizations (scenarios) of the uncertain variables, sampled from their respective distributions. Such scenario-based approaches are computationally intensive, and quickly become intractable as the number of uncertain variables or scenarios increases [2]. Moreover, typical scenarios involve single changes in the uncertain variables (e.g., step changes) and neglect the overall, real-world transient behavior of the system, which consist of sequences of such events.

In this work, we propose to eschew the traditional scenario-based strategy for optimization of under uncertainty. Rather, we proceed by solving the design problem as a deterministic dynamic optimization problem using a feasible-path approach. To this end, we represent the uncertain variables as pseudo-random multi-level signals (PRMS), which are imposed on the system dynamics during each iteration (time integration step) of the optimization. PRMS are constructed from random sequences defined on a Galois field[3] , in a way that each level of the signal occurs with a desired probability. Additionally, the frequency content of the signal can be manipulated to excite specific modes of the process in order to obtain an optimal design with a well-defined bandwidth.

 We illustrate the proposed approach through two case studies concerning a lumped-parameter system and distributed-parameter system. We show that the optima derived using the proposed approach are very close to the results obtained with scenario-based algorithms for optimization under uncertainty available in the open literature, but are obtained at a significantly lower computational cost (defined in terms of CPU time and memory requirements).

Reference

[1] E.N. Pistikopoulos. Uncertainty in process design and operations. Comput. Chen. Eng.,

[2] L.T. Biegler and I.E. Grossmann. Retrospective on optimization. Comput. Chem. Eng., 28(8):1169-1192, 2004.

[3] H.A. Barker. Primitive maximum-length sequences and pseudo-random signals. Transactions of the Institute of Measurement and Control, 26(4):339-348, 2004.