(753a) A Hybrid Modelling Approach Integrating First Principles Modelling with Subspace Identification

Good models are integral to process systems engineering, often being the core around which control and optimization formulations are designed. First principles or mechanistic modeling refers to the type of modeling where explicit knowledge of the process mechanism is present and utilized. Often times, the fewer the assumptions made, the higher the number of model parameters and the more complex the model structure. The task of building and maintaining a first principles model [1-2] continues to involve significant effort.

Increased availability of data, along with improved computational capabilities have made the data driven methods of modeling very attractive. In these approaches, a model structure is chosen a priori, and parameters are identified using available data. In this direction several statistical based approaches exist, distinguished by the kinds of model stricture being utilized, including latent variable based methods and subspace identification algorithms.

Statistical methods of process modeling are very well recognized nowadays. Projection to latent spaces (PLS) is one such statistical latent variable method where measurement data of high dimension is projected to lower dimensional space to create simpler and effective models. Their usefulness to batch processes [3] have been extensively demonstrated with algorithms utilized to handle batches of non-uniform lengths. Another statistical based modeling approach is subspace identification, which enable identifying models having state-space representation and thus are very effective for prediction and control purposes. Usefulness of subspace identification scheme to batch processes [4] have been explored in great detail recently.

However, integration of these statistical modeling techniques in synergy with first principles models have not been demonstrated yet. There have been some examples in the past that utilize a priori process knowledge to create hybrid or grey-box models [5-6], but these have artificial neural networks (ANN) as the data driven model.

This presentation addresses the problem of synergizing first principles models with subspace identified models. This is achieved by building a hybrid model where the subspace model identification algorithm is used to create a model for the residuals (mismatch in the outputs generated by the first principles model and the plant output) rather than being used to create a dynamic model for the process outputs. A continuous stirred tank (CSTR) setup is used to illustrate the proposed approach on a continuous system. The further evaluate its efficacy, the proposed methodology is applied on a batch polymethyl methacrylate (PMMA) polymerization reactor and the predictions are compared with that of first principles modelling and data driven approach alone. The presentation demonstrates the improved modeling capability of the hybrid model over either of its components.

References:

[1] Pinto, J.; Ray, W. The dynamic behavior of continuous solution polymerization reactorsa .VII. Experimental study of a copolymerization reactor. Chemical Engineering Science 1995, 50, 715 _ 736.

[2] Poyton, A.; Varziri, M.; McAuley, K.; McLellan, P.; Ramsay, J. Parameter estimation in continuous-time dynamic models using principal differential analysis. Computers & Chemical Engineering 2006, 30, 698-708.

[3] Flores-Cerrillo, J.; MacGregor, J. F. Iterative Learning Control for Final Batch Product Quality Using Partial Least Squares Models. Industrial & Engineering Chemistry Research 2005, 44, 9146_9155.

[4] Corbett, B.; Mhaskar, P. Subspace identification for data-driven modeling and quality control of batch processes. AIChE Journal 62, 1581_1601.

[5] Su, H.-T.; Bhat, N.; Minderman, P.; McAvoy, T. Integrating Neural Networks with First Principles Models for Dynamic Modeling. IFAC Proceedings Volumes 1992, 25, 327 _332, 3rd IFAC Symposium on Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes (DYCORD+ '92), Maryland, USA, 26-29 April.

[6] Wilson, J.; Zorzetto, L. A generalised approach to process state estimation using hybrid artificial neural network mechanistic models. Computers & Chemical Engineering 1997, 21, 951-963