(765g) Design of Experiments Based On Computational Singular Perturbation

Parameter estimation for large-scale systems has always been a difficult task, because of identifiability constraints on such systems in the vast majority of cases. Hence, preliminary sensitivity analysis and model reduction is inevitable in such systems. In order to derive reduced models, the conventional method used for kinetic systems is a criterion based on quasi-steady state (QSS) analysis, by using net rates of production/consumption of species, and identifying and removing the QSS species. In earlier work [1], we have investigated alternate methods of model reduction for kinetic systems such as singular value decomposition (SVD) and parameter clustering-based approaches; these were applied to steady-state data and models. In this contribution, we develop a method based on transient analysis of models of large-scale kinetic and catalytic systems that combines model reduction and the design of experiments.

Using computational singular perturbation (CSP), we separate the model of our system into dynamic modes and contributing reactions in a rigorous automated manner, and use this to build a reduced-order model at every instant. This reduced model is obtained by performing the modal decomposition, and separating the dynamic modes into active, exhausted and dormant modes. The exhausted and dormant modes do not contribute to the current dynamics of the process in a significant manner, and their contribution can be neglected; this provides us with a reduced-order model. This reduced model provides us with a subset of significant parameters that need to be estimated, i.e., the parameters of the reactions that contribute significantly to the active modes. Optimal input sequences are then designed (based on D optimal analysis) that provide the maximum sensitivity of the measured system outputs (outlet species concentrations and partial pressures) to these significant parameters, subject to identifiability constraints for the reduced order system. A sequential design protocol is devised to apply the model reduction and experiment design steps iteratively, until an acceptable model has been identified. Robustness of the modal decomposition and the experiment design to parametric uncertainty is achieved by including a stochastic optimization approach to obtaining the D optimal experimental design. The method is demonstrated for two catalytic systems, the decomposition of ammonia on ruthenium catalyst to produce hydrogen, and the preferential oxidation of carbon monoxide on platinum catalyst.

References:

[1] Kumar, S.  Narasimhan, K.  Patwardhan, S.C.  Prasad, V. , 'Experiment design, identification and control in large-scale chemical processes', Proceedings of the 2010 International Conference on Modelling, Identification and Control (ICMIC)