662e Performing Integrated Process and Control Design Using a Modified Polynomial Chaos Expansion (Mpce) in Optimisation under Uncertainty (Ouu)

C. Esther Van Cauwenberghe and J. Alberto Bandoni. PLAPIQUI-CONICET, Cno La Carrindanga Km 7, Bahía Blanca, 8000, Argentina

During the last 20 years new fundamental and significant advances have become the state-of-the-art in process systems engineering (Biegler and Grossmann, 1997). It is widely recognized that the ability to manage and control a system with uncertainty and disturbances strongly depends on the process design. In order to find economically optimal design, the interaction between process and control design should not be neglected. Although such methods are highly sophisticated and powerful, defining an accurate process model to be optimised remains a difficult task and involving uncertainties makes it even more difficult, since inherently the parameters associated have uncertainty. Thus, the specifications must state the dynamic scenarios under which the process will be operated as the dynamic behavior is optimised, in order to integrated process and control design (Bansal, 2000). Therefore, the scenario data will strongly affect the design and the robustness against uncertainty in scenarios should be hardly verified. At this point it is remarkable to state that optimisation under uncertainty (OUU) differs, on one hand, from the field of stochastic programming, since OUU problem formulations typically lack the specific mathematical structure often found in stochastic programming, so that OUU could be thought of as nonlinear programming under uncertainty, involving nonlinear implicit objective and constraint functions and, on the other hand, from traditional nonlinear programming in that OUU problems contain nondeterministic parameters as well as statistical measures in the objective function and/or constraint specifications. In this work, the use of a modified polynomial chaos expansion (MPCE) method in the OUU process is proposed. This is a fundamentally different approach than either the sampling-based or analytic reliability OUU methods (Walters, 2003; Field and Gregoriu, 2003). In the MPCE-based approach to OUU, the statistical properties of the uncertain parameters, u, are decomposed using spectral expansion methods. The MPCE decomposition process besides generates a large system of coupled state equations, whose solution can be obtained dynamically. Once this system is solved, the resulting data can be aggregated, using the MPCE basis functions, to produce statistical metrics on the response function, that are needed as objective/constraint data in the OUU problem. Fine-grain parallel computing and adaptive procedures can be also exploited, considering the number of terms of the polynomials (O(125 – 130)) and its sparcely. This paper studies formerly the process performance being affected for data uncertainty and the consequent design of both control and process structure, and it lattely discusses the use of a MPCE to faced the OUU problem. The issues are exemplified through a modified atmosphere packaging (MAP) process and control design previously developed by the authors.