Dynamic data reconciliation nonlinear

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 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. 

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. 

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. 

Several researchers [e.g., Tjoa and Biegler (1992) and Robertson et al. (1996)] have demonstrated advantages of using nonlinear programming (NLP) techniques over such traditional data reconciliation methods as successive linearization for steady-state or dynamic processes. Through the inclusion of variable bounds and a more robust treatment of the nonlinear algebraic constraints, improved reconciliation performance can be realized. 

Liebman, M. J. T. F. Edgar and L. S. Lasdon. Efficient Data Reconciliation and Estimation for Dynamic Processes Using Nonlinear Programming Techniques. Comput Chem Eng 16(10/11) 963-986 (1992). 

In this chapter, the general problem of joint parameter estimation and data reconciliation was discussed. First, the typical parameter estimation problem was analyzed, in which the independent variables are error-free, and aspects related to the sequential processing of the information were considered. Later, the more general formulation in terms of the error-in-variable method (EVM), where measurement errors in all variables are considered in the parameter estimation problem, was stated. Alternative solution techniques were briefly discussed. Finally, joint parameter-state estimation in dynamic processes was considered and two different approaches, based on filtering techniques and nonlinear programming techniques, were discussed. 

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