(371af) Simultaneous Model Structure Identification, Parameter Estimation and Process Optimization Via Output Modifier Adaptation

In model-based optimization schemes, a mathematical model is used for predicting the plant behavior. Typically, this model is determined once for all and is adapted to the process via parameter estimation [2]. However, given that the plant often varies with time and/or is operated in a different manner (e.g. distinct campaigns of a batch reactor), estimating the parameters may not be sufficient for readapting the model to the plant behavior. The process model may also need maintenance. In this case, the model structure should be allowed to evolve with time and not be fixed at the model deployment [1].

The aim of our work is to proposed an online model maintenance method via output modifier adaptation (MAy) [3]. MAy is a variant of real-time optimization (RTO) methods that applies input-affine correction terms (also known as modifiers) to the model outputs in such a way that the optimum calculated via the modified model optimization problem matches the actual process optimum. In our method, the modifiers are used not only for optimizing the plant but also as a criterion for model structure selection. This set-up leads to a two-level optimization problem structure.

In the first level, the modifiers are applied to solve an identification problem, which selects the best model structure in the available model set, while simultaneously performing parameter estimation. In order to determine the available model set, we divide the process model into blocks, each individual block representing a part of the process to be modeled. Next, several candidate sub-models are proposed to describe each block. Different candidates are constituted by different sets of equations. Depending on the sub-models that are chosen for each block, the process model, which now can be seen as a combination of sub-models, has a different shape (gradients) and prediction capacity. These differences are quantified by the modifiers of MAy that, in this context, represent the mismatch between the process model and the plant. By minimizing their norm, we are able to choose the sub-model combination that best describes the plant behavior (i.e. minimum mismatch).

In the second level of the two-level optimization problem structure, the updated model is used to optimize the process in a more classical MAy framework. By combining these two optimization problems, we are able to choose the best model structure in the available model set while optimizing the process. Also, we are able to keep the nice MAy property that guarantees convergence to the plant optimum given that the process model is adequate (i.e. it is locally convex in the vicinity of the plant optimal inputs) [3]. Our approach is demonstrated on a case study, a continuous stirred tank reactor, in which the best model structure with readapted parameters is chosen among several candidates and the plant optimum is reached without constraint violations.

[1] Bonvin, D.; Georgakis, C.; Pantelides, C.; Barolo, M.; Grover, M.; Rodrigues, D.; Schneider, R.; Dochain, D. “Linking models and experiments”. Industrial & Engineering Chemistry Research 2016,55, 6891–6903

[2] Quelhas, A. D.; de Jesus, N. J. C.; Pinto, J. C.. “Common vulnerabilities of RTO implementations in real chemical processes”. The Canadian Journal of Chemical Engineering 2013, 91(4), 652-668.

[3] Marchetti, A.; Chachuat, B.; Bonvin, D. “Modifier-adaptation methodology for real-time optimization”. Industrial & engineering chemistry research 2009,48, 6022–6033