Charles Acquah

Chemical process design under uncertainty has received considerable attention in recent years, and has led to the development of several modeling and solution approaches. These approaches are broadly categorized under stochastic formulations (model uncertain parameters with probability distributions), multiperiod formulations (where uncertain parameters are discretized into a number of deterministic realizations) and parametric programming formulations. The vast majority of work done in the area of design under uncertainty has focused on systems in which the cost function is analytic and continuous. On the other hand, uncertainty considerations in systems where the cost function and constraints are non-analytic (differential-algebraic equations, DAE) in nature remain largely unexplored. Two application areas which fall under this domain are the pultrusion process for the fabrication of polymer-matrix composites and optical fiber drawing process.

These are thermal manufacturing processes which are governed by a highly non-linear system of partial differential-algebraic equations. Additionally, carrying out optimization on such systems can be computationally intensive. With growing demands on bandwidth for transmitting large volumes of information faster, cheaper, and more efficiently, quality manufacturing of optical fibers at high production speeds, and reliability in the performance of optical fibers are of high importance. In the optical fiber manufacturing process, high draw speeds result in large temperature gradients which often lead to inferior quality fiber with poor optical and mechanical properties. On the other hand, low draw speeds lead to superior quality fiber with better optical and mechanical properties. Here, quality is achieved at the expense of production throughput. Therefore, the realization of good quality fiber without unduly compromising production throughput becomes an optimization problem. The objective is to maximize the fiber draw speed subject to constraints on fiber mechanical properties (e.g. defects, residual stress and drawing tension) and fiber transmission properties (e.g. refractive index profile). The problem becomes even more challenging when uncertainties in process and model parameters are incorporated in an optimization endeavor.

In this research, the pultrusion and optical fiber drawing problems have been cast as deterministic multiperiod one-stage optimization problems (OSOP) and solved using uncertainty analysis algorithm and software previously developed in our computing laboratory. As a means of validation, the deterministic OSOP solution was systematically compared with a stochastic sampling-based approach in terms of solution quality and computational time. This comparison was carried out using the pultrusion process employed in the fabrication of polymer-matrix composites. Results show that the OSOP method was computationally faster than the sampling-based method, although the OSOP method resulted in slightly more conservative solutions. However, for all practical purposes, the solutions were observed to be reasonably close. This constituted the first case study. these satisfactory results, the OSOP method was then directly applied to the second case study which was the optical fiber optimization problem under uncertainty. Typical CPU time required for solving the fiber drawing problem is of the order of weeks. The use of high-speed super-computing resources (NCSA) significantly reduced the computational burden.

Publications

• J-06-03: C. Acquah, I. Datskov, A. Mawardi, F. Zhang, L.E.K. Achenie, R. Pitchumani, and E. Santos, "Optimization Under Uncertainty of a Composite Fabrication Process Using a Deterministic One-Stage Approach," Computers and Chemical Engineering, 30, pp. 947-960, 2006.
• J-06-07: C. Acquah, I. Datskov, A. Mawardi, F. Zhang, L.E.K. Achenie, R. Pitchumani, and E. Santos, "Optimization of an Optical Fiber Drawing Process Under Uncertainty," Industrial and Engineering Chemistry Research, 45, pp. 8475-8483, 2006