(434d) Partial Modifier Adaptation for Economic Optimization of Process Systems Under Frequent Disturbances and Structural Model Uncertainty

Uncertainty is inherent to process models because of unmodelled phenomena and modelling assumptions. This is especially the case for industrial models, where parsimony and computational efficiency are prioritized over fidelity. Owing to this uncertainty, the use of process models for economic optimization techniques can be ineffective as the model is an inaccurate representation of the true plant. To this end, various schemes aimed to address the effects of uncertainty for process economic optimization have been proposed in the literature including robust optimization [1], stochastic optimization [2], and model adaptation [3].

Model adaptation is particularly appealing as it attempts to remove the model uncertainty rather than sacrificing performance for robust solutions (i.e., those that work well for all potential uncertainty realizations). Models are commonly adapted via their parameters but can also be adapted through their constraints and objective function when performing model-based optimization. The latter approach, which is commonly referred to as modifier adaptation [4], is superior to parameter adaptation in models with significant plant-model mismatch. This method has been proven to match the Karush-Kuhn-Tucker (KKT) conditions of the plant and the model [4], thereby ensuring that both the plant and the process model optimum matches and resulting in truly optimal decisions.

The modifiers used for adaptation are computed by using plant measurements and model predictions of the process cost and constraints, whereby the difference between the model and plant are reconciled using bias terms and gradient corrections with respect to the model inputs. While the bias terms are relatively easy to estimate assuming that the plant is measurable, the gradient terms are considerably harder to estimate. Plant gradients are commonly acquired by perturbing the plant inputs and waiting for the desired variables to reach their new perturbed state [4]. However, this perturbation process can be computationally costly as transient times in processes may be lengthy [5]. This issue is further amplified for multiple-input systems whereby many perturbations must be imposed on the system. Owing to the nonlinearity of most real chemical plants, gradients obtained before a disturbance occurs are no longer accurate in a post-disturbance state, thus the gradient-acquisition process can be interrupted if disturbance are high-frequency.

In this work, we present a modifier adaptation methodology whereby speed is prioritized in the gradient-computation framework such that the system may reach an operating point in the neighbourhood of the true optimum despite the presence of high-frequency disturbances. This is achieved through adaptation of gradients only with respect to some (as opposed to all) process inputs. The proposed work includes an algorithm to choose which inputs to use for gradient adaptation such that they will have the most significant effect on the plant-model mismatch. This is achieved by comparing the cost predictions under different partial adaptations assumptions and choosing the input adaptations that results in the most favourable predicted economics. In this way, the partial modifiers are continually refined and can be activated/disactivated such that the optimization decisions lead to both quick and economic actions. The change between partial adaptation is resolved using first-order filters, such that the scheme switches operating conditions smoothly.

This study presents the first “fast” modifier adaptation approach whereby the traditional perturbation methods can be used for gradient calculation under high-frequency disturbances. The proposed scheme is tested against the traditional modifier adaptation scheme for the Williams-Otto plant [6] as well as a 5x5 synthetic system, both subject to high disturbance frequencies. Through these cases, the proposed scheme is shown to reduce the gradient-computation time by up to 50% and 80%, respectively. In doing so, the proposed scheme enables quick operating point changes to occur before the systems are disturbed resulting in up to 25% economic improvement (i.e., increased profits or abated losses). This novelty broadens the applicability of modifier adaptation to systems with slow dynamics (thus, slow gradient-computation) and frequent disturbances.

References

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[2] Zhang Y, Monder D, Forbes FJ. Real-time optimization under parametric uncertainty: a probability constrained approach. J. Process Control. 2002; 12: 373–389. https://doi.org/10.1016/S0959-1524(01)00047-6.

[3] Chachuat B, Srinivasan B, Bonvin D. Adaptation strategies for real-time optimization. Comput. Chem. Eng. 2009; 33(10): 1557–1567. https://doi.org/10.1016/j.compchemeng.2009.04.014.

[4] Marchetti A, Chachuat B, Bonvin D. Modifier-Adaptation Methodology for Real-Time Optimization. Ind. Eng. Chem. Res. 2009; 48(13): 6022–6033. https://doi.org/10.1021/ie801352x.

[5] Marchetti AG, François G, Faulwasser T, Bonvin D. Modifier Adaptation for Real-Time Optimization–Methods and Applications. Processes. 2016; 4(4): 55. https://doi.org/10.3390/pr4040055.

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