1. Real-time optimization via a multiple model approach
- Author
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Speakman, Alasdair Jack, Gerogiorgis, Dimitrios, and Francois, Gregory
- Subjects
Real-time Optimization ,Multiple Model Approach ,Industrial processes ,modifier adaptation ,directional Hessian modifier adaptation - Abstract
Industrial processes are run with a set of operating conditions which determine the profitability and safety of the plant. Therefore, it is important to optimize the process to find the best operating conditions which improves performance, reduces waste and ensures safety. Typical model-based optimization approaches cannot handle a mismatch between the plant and model, resulting in sub-optimal performance. One approach to account for this difference is to quantify the degree of mismatch into a known uncertainty, and account for it in the optimization scheme. Alternatively, real-time optimization (RTO) attempts to rectify the mismatch by using measurements directly from the plant. Several approaches to RTO have been suggested, and the one of interest in this thesis, known as modifier adaptation (MA), uses the measurements to directly modify the model such that the gradients and value of the model characteristic functions match the values estimated from the plant. The primary advantage of this is that the first-order conditions of optimality are met by the plant if the MA scheme converges. The vast majority of RTO schemes discard the known uncertainty in the model infavor of the real-time measurements. This thesis investigates how an RTO scheme can be formulated using this known uncertainty to formulate multiple models. The reason that multi-model approaches have not been used in MA, and not widely used in other RTO methods, could be due to several different factors. The first is that using the model uncertainty and using real-time measurements both try to account for the plant-model mismatch, therefore using both is not necessary. Another reason is that the main issue of MA (of requiring accurate gradient estimates of the plant) is not directly dealt with by using a multi-model approach, which is where the main focus of research has been for the MA field. Finally, using multi-model approaches requires longer solving times which is especially undesirable for real-time optimization. The potential advantages of using multi-model methods is an increase in the feasibility of the iterations, reducing the chance of breaking the constraints before convergence. This can also allow for the scheme to be more aggressive with the filtering, thereby providing faster improvement to the objective and faster convergence to the plant optimum. Also, the required properties of the model which allow for convergence to occur can be less restrictive for the proposed methods, improving the chance of converging to the plant optimum. Two distinct categories of multiple model approaches have been defined, namely multiple solution and single solution approaches. Using the multiple solution approach, the model uncertainty is used to formulate a set of different programs, and each of these will produce a potential solution, which are used to find the next RTO iteration. A framework has been formulated which encompasses how a multiple solution approach can be applied to RTO, and from this three recommended approaches are proposed. Each of these are developed around a specific advantage, including limiting the increase in computation time, or guaranteeing model adequacy conditions. All three methods are shown to have improvements when applied to several different case studies, allowing for fast convergence to the plant optimum. Using the single solution approach, the model uncertainty is taken into the optimization scheme to formulate a single program to be solved. Two different approaches using a single solution approach have been formulated and discussed in full. The first of which is known as robust modifier adaptation, and combines a common method to handling model uncertainty in model-based optimization, with the standard MA scheme. Three different methods are proposed using these robust methods, and the resulting approach produces more robust iterates at the cost of simulating more models. The other approach is known as directional Hessian modifier adaptation (DHMA), and constitutes of using the uncertainty in the model to formulate a new model which has the same second directional derivative as the maximum observed by the models in the uncertainty set at a given direction and location in the input space. This approach can guarantee the feasibility of all iterates if at least one of the models in the uncertainty set upper-bounds the unknown plant second directional derivative. All of the approaches developed as part of this thesis have worked off the same basis, of using the known uncertainty in the model to formulate an RTO approach using multiple models, therefore the performance, applicability, and similarities of these approaches is comprehensively investigated and compared. Overall, the proposed multi-model RTO approaches allow for the feasibility of the iterates to be improved, reducing the chance of unsafe operation and ensuring that the product specifications are met. Additionally, the rate of improvement to the objective function is provided which reduces one of the primary issues of MA of a slow rate of improvement in regards to the number of steady-state measurements required. This comes at the cost of increased computation time to solve the RTO solution. In the end, there is a trade-off between the number of models used (i.e. the increase in computation time) and the benefit gained which needs to be considered, as if solving the RTO solution constitutes a large portion of the iteration time, then the improvement may not be worthwhile. However, if data collection is the bulk of the iteration time, then ensuring the best improvement is found is worth the additional computation time.
- Published
- 2023
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