(246h) Probabilistic Process Design Under Uncertainty Via Dynamic Optimization
In its most general form, the problem of optimization under uncertainty involves uncertain parameters drawn from continuous probability distributions and is infinite-dimensional. Solution approaches generally rely on the discretization of the stochastic variables and the creation of multiple scenarios, to approximate the expected value of the objective function  . In the case of many uncertain parameters or when a fine discretization is desired, scenario-based approaches can quickly grow computationally intractable. To some extent, this has been mitigated by reformulating scenario-based problems as dynamic optimization programs, whereby scenarios are arranged chronologically in a pseudo-time domain rather than solved simultaneously  . These âsequentialâ methods have been shown to have significant memory usage benefits compared to âsimultaneousâ multi-scenario approaches, as well as to present practical benefits in terms of reducing the number of flowsheet initialization calculations.
In this work, we propose abandoning the scenario-based approach altogether, instead treating the uncertain parameters of a process flowsheet as time-varying disturbance variables acting on a (static or pseudo-transient ) process model over a pseudo-time domain. The parameter uncertainty space is then mapped using the intersections of continuous parameter trajectories, rather than via a finite set of discrete scenarios. We illustrate the significant computational benefits of the proposed strategy with two case studies: a dimethyl ether plant and the Williams-Otto process.
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