Handling uncertainties in process optimization

Resumo

Optimization is a powerful tool to be applied in the process industry. It allows obtaining comparative improvements of a given facility finding the operational point that maximizes the profit. In spite of the different applications that concern the use of this tool, the management of uncertainty is a critical issue in order to propose optimal and feasible solutions. In this thesis, we present the study and application of techniques able to handle the uncertainties from the point of view of random behavior of process variables and errors in the models to be used in the optimization. Concerning with the random behavior of the process variables, we have focused our study in Stochastic Optimization as a tool to be applied in processes. In particular we have tested the Two-Stage Optimization and Chance Constrained Optimization methods in a process example from a hydrodesulfuration unit. Applying these techniques, the idea is to propose an optimal and feasible policy to be implemented when there is a change in the load to be treated despite the expected uncertainties. The implementation of these strategies is founded in the fact that both the raw materials and the quality of the product to be transformed are not completely known, and only their probability distribution functions are available. Regarding the two-stage optimization, we have solved a discrete equivalent problem using a scenario realization of the original probability distribution function, using the scenario aggregation methodology to take into account the nonanticipativity constraint, solving the dynamic optimization problem using a sequential approach. On the other hand, the chance constrained optimization has been solved using the inverse mapping technique to estimate the probability of the constraints, calculating the equivalent limit on the random variable solving a parameter estimation problem over the entire prediction horizon with the single shooting methodology. Because of the large computational times observed in the resolution of both methods, we have presented an open loop implementation that has been a tested using Montecarlo simulations. Because of the discretization applied in the two-stage approach, we have proposed a generalization method based in the interpolation of the outcomes of the second-stage, to apply this policy in open loop with the original probability distribution function. The results show that using the implementations described before, we can obtain an optimal trajectory for the load change problem in the hydrodesulfuration process that ensures a given degree of feasibility. About the management of the modeling errors, we have worked with Real Time Optimization, in order to find the stationary point that optimizes the process in an iterative way. In particular we have focused our attention in the Modifier-Adaptation Methodology as a technique to get over the modeling mismatch produced because of the partial knowledge of the system. Using previous information from literature and a simulation example, we have detected three challenges to be addressed in this methodology: infeasible operations produced in intermediate points, problems with the experimental gradient estimation and the possibility of using modifiers in dynamic optimization. Each of these topics were studied. We have proposed an intermediate layer between the RTO and the control one that uses a non-model based controller to modify the value suggested by the RTO algorithm when a violation on the process constraints is detected. If the experimental gradient is calculated using the dual control optimization approach, we have implemented a second controller (the dual one) to manage the excitation level of the process. With respect to the gradient estimation, we have proposed another way to see the modifier adaptation algorithm, with a methodology that intuitively finds a KKT point of the process directly in the space of the gradient modifiers: the Nested-Modifier Adaptation method. In our proposal the decision variables to be applied in the process must be calculated as the outcomes of an inner modified optimization with the same structure as the one solved in the original modifier-adaptation scheme. Nevertheless, the update law of the modifiers is implemented in an upper optimization layer that uses directly the performance index measured from the process as a cost function. At last we have presented some preliminary ideas about the implementation of the modifiers to solve dynamic optimization problem in a receding horizon implementation, modifying the NLP equivalent of the problem. As a result of the implementations proposed in the modifier-adaptation approach, we can say that for the steady-state case it has been increased the field of application of this method for those problems where the process gradient is difficult to obtain (or is not available) or when the measurements are contaminated with noise, detecting the real optimum of the process with an erroneous model. With this, we are able to converge in a feasible and robust path to the real optimum. On the other hand, in the dynamic case we have shown that correcting the process measurements with the natural response of system, it is possible to deal with modeling mismatch using the modifiers, provided the objective function can be measured at the end of the prediction horizon.