(642g) Accurate Model Identification for Non-Invertible Mimo Sandwich Block-Oriented Processes

A continuous-time, semi-empirical modeling method proposed by Rollins et al. (1998) provided an exact solution to the Hammerstein system and as is known as H-BEST (Hammerstein Block-Oriented Exact Solution Technique). Rollins et al. (2003) and Bhandari and Rollins (2003) extended this work to multiple input, multiple output (MIMO) Hammerstein and Wiener (W-BEST) systems, respectively. The purpose of this work is to extend this approach to more complicated block-oriented systems, namely a Hammerstein-Wiener process.

According to Brillinger (1977), Greblicki and Pawlak (1991), and Pearson and Ogunnaike (1997), the Hammerstein-Wiener process is a specific type of “sandwich model” and in this particular case the linear dynamic block is “sandwiched” between two static nonlinearities models. Thus, both Hammerstein and Wiener processes are also special cases of sandwich systems. For this class of systems, most of the work in system identification has consisted of discrete-time modeling. To avoid modeling complexities and inherent drawbacks, Lee et al. (2004) introduced a special test signal so that the linear dynamic model and output nonlinear static function can be estimated separately from the input nonlinear static function. Park et al. (2006) later modified this special test signal to identify these structures separately, making it a simpler identification problem.

By exploiting a closed form solution, the method that we propose has the major advantages of being simplier to build and implement the model, and does not require a complex algorithm or solution to a difficult optimization problem. We evaluate the performance of this method on the three case studies in Park et al. (2006) and compare our results to their results. Even with sampling at 1/10 the rate, the proposed method is shown to provide a higher level of predictive accuracy. We also demonstrate the ability of the proposed method to treat non-invertible processes and present a MIMO case study with non-invertible, static, nonlinear blocks.

References:

[1] Rollins, D. K.; Smith, P. and Liang, J. (1998). Accurate simplistic predictive modeling of nonlinear dynamic processes. ISA Transactions, 36, pp. 293-303.

[2] Rollins, D. K., Bhandari, N., Bassily, A. M., Colver, G. M. and Chin, S. (2003). A continuous-time nonlinear dynamic predictive modeling method for Hammerstein processes. Ind. & Eng. Chem. Rsch., 42(4), pp. 860-872.

[3] Bhandari, N.; Rollins, D. K. (2003). A continuous-time MIMO Wiener modeling method. Ind. & Eng. Chem. Rsch., 42, pp. 5583.

[4] Brillinger, D. R. (1977). The identification of a particular nonlinear time series system, Biometrika, 64, pp. 509-515.

[5] Greblicki, W. and Pawlak, M. (1991). Nonparametric identification of nonlinear block-oriented systems. Preprints, 9th IFAC/IFORS Symposium, Budapest, Hungary, pp. 720-724.

[6] Pearson, R. K. and Ogunnaike, B. A. (1997). Nonlinear Process Identification. In Nonlinear Process Control; Henson, M. A., Seborg, D. E., Eds.; Prentice Hall: Upper Saddle River, NJ.

[7] Lee, Y. L.; Sung, S. W.; Park, S. and Park, S. (2004). Input test signal design and parameter estimation method for the Hammerstein-Wiener processes. Ind. Eng. Chem. Res., 43, pp. 7521-7530.

[8] Park, H. C.; Sung, S. W.; Lee, J. (2006). Modeling of Hammerstein-Wiener processes with special input test signals. Ind. Eng. Chem. Res., 45, pp. 1029-1038.

[9] Rollins, D. K.; Pacheco, L. and Bhandari, N. (2005). A Quantitative Measure to Evaluate Competing Designs for Non-linear Dynamic Process Identification, accepted by the Canadian Journal of Chemical Engineering.