Optimization under uncertainty of a composite fabrication process using a deterministic one-stage approach

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 parameters with probability distributions), multiperiod formulations (where uncertain parameters are discretized into a number of deterministic realizations), and parametric programming formulations. This paper presents an application of the one-stage optimization problem (OSOP), a multiperiod method, to find optimal cure temperature cycle design under uncertainty for polymer-matrix composites fabrication using the pultrusion process. The process is governed by a highly non-linear system of partial differential-algebraic equations.The OSOP method is also systematically compared with a sampling-based approach in terms of computational efficiency and solution quality. Most work done so far using such deterministic methods has focused on problems where the performance objective function (often cost) and process constraints are analytic/algebraic in nature. In contrast, in materials processing simulations, evaluation of the objective function and the process constraints are based on the solution of differential-algebraic equations (DAE).