A Systematic Grey-Box Modeling Methodology via Data Reconciliation and SOS Constrained Regression

Abstract

Developing the so-called grey box or hybrid models of limited complexity for process systems is the cornerstone in advanced control and real-time optimization routines. These models must be based on fundamental principles and customized with sub-models obtained from process experimental data. This allows the engineer to transfer the available process knowledge into a model. However, there is still a lack of a flexible but systematic methodology for grey-box modeling which ensures certain coherence of the experimental sub-models with the process physics. This paper proposes such a methodology based in data reconciliation (DR) and polynomial constrained regression. A nonlinear optimization of limited complexity is to be solved in the DR stage, whereas the proposed constrained regression is based in sum-of-squares (SOS) convex programming. It is shown how several desirable features on the polynomial regressors can be naturally enforced in this optimization framework. The goodnesses of the proposed methodology are illustrated through: (1) an academic example and (2) an industrial evaporation plant with real experimental data.

Gray-box Soft Sensors in Process Industry: Current Practice, and Future Prospects in Era of Big Data

“…ANN and GA were integrated with the first-principle model of the reactor to efficiently predict and control the reactor temperature and the flow rate of the component. Pitarc et al [53] proposed a serial GB model for prediction of overall heat transfer coefficient of heat exchangers in an evaporation plant. Data reconciliation (DR) and polynomial constrained regression approaches were used as BB models.…”

“…Industry Application Category Process GB Type Target BB Type [32][33][34][35][36]92] Iron and steelmaking estimation and control "pickling process", "continuous casting", "hot strip mill" "serial", "parallel", "combined" "concentration of hydrochloric acid", "tundish temperature", "scale breaker entry temperature", "drying rate" "Taylor series", "PLS and RF", "ANN" [37][38][39] Food industry estimation and control 'fish drying process", "milk drying process", "whey separation" serial "drying rate", "moisture contents", "membrane fouling" "ANN", "exponential static membrane resistance function" [45][46][47][48][49][50][51][52][53][54]93] Chemical, biochemical, and pharmaceutical "estimation and optimization", "estimation and control" "fermentation extraction", "twin screw extruder ", "extrusion", "mold cooling", "acetone-butanol ethanol fermentation process", "MP fermentation", "fed-batch fermentation", "evaporation plant"…”

Real-time optimisation for a heat-recovery section with equipment degradation

“…This technique is based on the concept of redundancy (duplicated sensors or algebraic constraints) in order to satisfy physical laws [7]. In this case, the constraints of the optimisation problem for the data reconciliation are (4)- (5), and the objective is to minimise the error between the decision variables that fulfil the constraints (T in c , T in h , T out c , T out h , F c , F h ) and their respectively measured data.…”

“…In this paper we present and describe the approach and a prototypical tool for the optimisation of the hot-source distribution in such heat-recovery system. For such a task, greybox models for the heat exchangers have been obtained using data reconciliation (in order to correct measurements and estimate the heat-transfer coefficient) and constrained regression (to build up an experimental model for the heat-transfer coefficient) [5].…”

Special Issue on “Process Modelling and Simulation”

“…The special issue brings together fourteen contributions on topics ranging from the process systems [1-3] and (bio)chemical engineering [4,5] fields, to software development [6] and applications in heat and power systems [7,8]. Moreover, the hot topic of data mining and machine learning is also discussed from a process engineering perspective in [9,10]. This conveys the broadness of use and impact that models will have (and already have) for industrial decision support in the approaching digital era.Process models are the foundation that other applications (sensitivity analysis, predictive simulation, real-time optimization, etc.)…”