PERFOMANCE COMPARISON OF NEW STRATEGIES FOR ROBUST DATA RECONCILIATION

1

Claudia E. LLanos1 , Mabel C. Sánchez

1

2

and Ricardo A. Maronna

Planta Piloto de Ingeniería Química (UNS-CONICET), Bahía Blanca 8000, Argentina

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Dpto. de Matemática - Facultad de Ciencias Exactas â??Universidad Nacional de La Plata,

La Plata 1900, Argentina

ID 387486
PASWORD 390380
Keyword: Data Reconciliation, Robust Statistic, Outliers. Abstract
The operation of today´s chemical plants is characterized by the stringent need to introduce fast and low-cost changes to improve their performance. The decision-making process about possible modifications in a system requires knowledge about its actual state. This is determined by the values of the process variables contained in the model chosen to represent plant operation. In general this model is constituted by the equations of conservation of mass and energy.
The numerical values resulting from the observations do not provide consistent information because they contain some type of error that avoids the conservation equations to be satisfied exactly. Therefore, it is a common practice to incorporate the application of data reconciliation procedures that provide adjusted measurementsâ?? values, which are consistent with the corresponding balance equations (Romagnoli and Sánchez, 2000).
Different approaches are proposed for the simultaneous treatment of random and gross errors in data reconciliation problems. Simultaneous approaches based on the concepts of Robust Statistic have been devised since the last two decades. Robust strategies produce reliable estimates not only when data follow a given distribution exactly, but also when this happens only approximately due to the presence of outliers (Maronna et al., 2006).
Different types of M-estimators, which are generalizations of the Maximum Likelihood Estimator, were used as objective function of the data reconciliation problem instead of the weighted least square estimator. Ozyurt and Pike (2004) presented a comprehensive performance analysis of six robust objective functions and three gross error detection criteria for simulated and industrial case studies operating at steady state. Special attention was given to the concept of tuning the loss functions to obtain the same efficiency at the ideal condition. This proves necessary for a comparative study of different methods. Furthermore an outlier rejection rule, which only depends on the observation residuals after the application of the data reconciliation procedure, is introduced. They concluded that
methods based on the Cauchy distribution and Hampelâ??s redescending M-estimator gave promising results with less computation.
A performance analysis of distinct robust M-estimators was also performed by Prata et al. (2008) for dynamic systems who concluded that the Welsch M-estimator shows better performance. The Quasi Weighted Least Square estimator was proposed by Zhang et al. (2010), and its behavior was compared with respect to the performances of Huber and Hampel estimators for linear systems. Chen et al. (2013) used the correntropy as an optimality criterion in the estimation problems. By properly adjusting its kernel width, the effectiveness of this estimator is tuned. The optimal kernel width value is chosen by minimizing Aikake information criterion. Its behavior is mainly analyzed in relation with that shown by the quasi-weight least squares estimator for the same type of linear systems.
In this work a comparative performance analysis is presented regarding the robust estimation and gross error detection capabilities of the robust data reconciliation strategies that have been presented in the last decade. The comparison is conducted by tuning all loss functions to obtain the same efficiency at the ideal condition. With this purpose, approximate finite sample variances and relative efficiencies are calculated by simulation and Monte Carlo studies. Furthermore, an outlier rejection rule that does not have a loss function dependent cut point is considered in this study. Linear case studies of incremental size, extracted from the literature, are used for the analysis. Performance measures are the Mean Square Error, the Average Number of Type I Error and the Overall Performance.

References

Chen, J., Peng, Y., Munoz, J. Correntropy estimator for data reconciliation. Chemical Engineering
Science, 2013, 104, 1019â??1027.
Maronna, R., Martin, R., Yohai, V. Robust Statistic: Theory and Methods, John Wiley and Sons Ltd., Chichester, 2006.
Ã?zyurt, D., Pike, R. Theory and practice of simultaneous data reconciliation and gross error detection for chemical process. Computers and Chemical Engineering, 2004, 28, 381-402.
Prata, D., Pinto, J., Lima, E. Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data
Reconciliation. Computer-Aided Chemical Engineering, 2008, 25, 501-506.
Romagnoli, J., Sánchez, M. Data Processing and Reconciliation for Chemical Process Operations, Academic Press, San Diego, 2000.
Zhang, Z., Shao, Z., Chen, X., Wang, K., Qian, J. Quasi-weighted least square estimator for data reconciliation. Computers and Chemical Engineering, 2010, 34, 154â??162.