Joint Parameter Estimation-Data Reconciliation Problem

JOINT PARAMETER ESTIMATION-DATA RECONCILIATION PROBLEM 

In the error-in-variable method (EVM), measurement errors in all variables are treated in the parameter estimation problem. EVM provides both parameter estimates and reconciled data estimates that are consistent with respect to the model. The regression models are often implicit and undetermined (Tjoa and Biegler, 1992), that is. 

In experiments we observe the measurements values, z, of the variables, z, and allow for errors in all of them. Thus, 

Assuming that j are normally distributed and uncorrelated, with zero mean and known positive definite covariance matrix the parameter estimation problem can be formulated as minimizing with respect to Zj and 6  

In the following sections, different approaches to the solution of the preceding problem are briefly described. Special attention is devoted to the two-stage nonlinear EVM, and a method proposed by Valko and Vadja (1987) is described that allows the use of existing routines for data reconciliation, such as those used for successive linearization. 

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Joint Parameter Estimation-Data Reconciliation Problem 166... 

JOINT PARAMETER ESTIMATION-DATA RECONCILIATION PROBLEM... 

All of the previous ideas are developed further in Chapter 8, where the analysis of dynamic and quasi-steady-state processes is considered. Chapter 9 is devoted to the general problem of joint parameter estimation-data reconciliation, an important issue in assessing plant performance. In addition, some techniques for estimating the covariance matrix from the measurements are discussed in Chapter 10. New trends in this field are summarized in Chapter 11, and the last chapter is devoted to illustrations of the application of the previously presented techniques to various practical cases. 

Chapter 9 deals with the general problem of joint parameter estimation data reconciliation. Starting from the typical parameter estimation problem, the more general formulation in terms of the error-in-variable methods is described, where measurement errors in all variables are considered. Some solution techniques are also described here. 

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. 

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 ... 

Several related problems have been previously considered in the literature. In addition to the afore mentioned statistical approaches for structural change detection in data sets and their application for linear system identification [7], the joint problem of model structure determination and parameter estimation was addressed by [8-10]. A related approach was used by [11-13] in the context of data reconciliation. Additional aspects of model selection in chemical engineering are covered in [14]. Although the present problem shares common features with the all of the previous applications, it also presents unique characteristics that require a specific formulation. 

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