Dynamic data reconciliation

Extended Kalman filtering has been a popular method used in the literature to solve the dynamic data reconciliation problem (Muske and Edgar, 1998). As an alternative, the nonlinear dynamic data reconciliation problem with a weighted least squares objective function can be expressed as a moving horizon problem (Liebman et al., 1992), similar to that used for model predictive control discussed earlier. 

Dynamic Data Reconciliation Using Nonlinear Programming Techniques 148... 

In this chapter, the data reconciliation problem for dynamic/quasi-steady-state evolving processes is considered. The problem of measurement bias is extended to consider dynamic situations. Finally in this chapter, an alternative approach for nonlinear dynamic data reconciliation using nonlinear programming techniques will be discussed. 

DYNAMIC DATA RECONCILIATION A FILTERING APPROACH 8.2.1. Problem Statement... 

DYNAMIC DATA RECONCILIATION USING NONLINEAR PROGRAMMING TECHNIQUES... 

If the most recent available measurements are at time step c, then a history horizon HAt can be defined from (tc — HAt) to tc, where At is the time step size. In order to obtain enough redundant information about the process, it is important to choose a horizon length appropriate to the dynamic of the specific system (Liebman et al., 1992). As shown in Fig. 5, only data measurements within the horizon will be reconciled during the nonlinear dynamic data reconciliation run. 

Albuquerque and Biegler (1996) followed a different approach to incorporating bias into the dynamic data reconciliation, by taking into account the presence of a bias from the very beginning through the use of contaminated error distributions. This approach is fully discussed in Chapter 11. 

Finally, an approach for nonlinear dynamic data reconciliation using nonlinear programming techniques was discussed. This formulation involves the optimization of an objective function through the adjustment of estimate functions constrained by differential and algebraic equalities and inequalities. 

Figueroa, J. L., and Romagnoli, J. A. (1994). A strategy for dynamic data reconciliation within Matlab environment. Australas. Chem. Eng. Conf. 22nd, Perth, Australia, pp. 819-826. 

Jang, S. S., Josepth, B and Mukai, H. (1986). Comparison of two approaches to on-line parameter and state estimation problem of non-linear systems. Ind. Eng. Chem. Process Des. Dev. 25, 809-814. Jazwinski, A. H. (1970). Stochastic Processes and Filtering Theory. Academic Press, New York. Liebman, M. J., Edgar, T. F., and Lasdon, L. S. (1992). Efficient data reconciliation and estimation for dynamic process using non-linear programming techniques. Comput. Chem. Eng. 16, 963-986. McBrayer, K. F., and Edgar, T. F. (1995). Bias detection and estimation on dynamic data reconciliation. J Proc. Control 15, 285-289. 

In this section the extension of the use of nonlinear programming techniques to solve the dynamic joint data reconciliation and parameter estimation problem is briefly discussed. As shown in Chapter 8, the general nonlinear dynamic data reconciliation (NDDR) formulation can be written as ... 

Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation... 

Keywords Nonlinear dynamic data reconciliation, robust estimation and gross error. 

This work presents a comparative performance analysis among some robust estimators (all estimators reported by Ozyurt and Pike, 2004, and Welsch estimator) for nonlinear dynamic data reconciliation (NDDR in the presence of gross errors. 

In this work a comparative analysis of the capacity of robust estimators to reduce the negative effect of gross errors on nonlinear dynamic data reconciliation was accomplished. The results obtained have shown that among the studied cases the Welsch and Lorentzian robust estimators produced better reconciled values, but they also have shown that, although the robust estimators were more efficient in reducing the effect of biases, this problem still deserves more investigation. 

Benqlilou C., Bagajewicz, M.J., Espuna, A. and Puigjaner, L., 2002, A Comparative Study of Linear Dynamic Data Reconciliation Techniques, 9th Mediterranean Congress of Chemical Engineering. Barcelona, Nov. 26-30. 

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