(486j) Simple Approaches for Robust Data Reconciliation

Data reconciliation and parameter estimation are important issues for real time optimization of chemical industries. As the presence of gross errors can severely bias both reconciled measurements and the estimates of parameters and unmeasured variables, several strategies have been developed to reduce the effects of gross errors (Romagnoli and Sánchez, 2000).

Recently data reconciliation methodologies based on robust estimators are devised. The robust approach to statistical modeling and data analysis aims at deriving methods that produce reliable estimates, and associated tests and confidence intervals, 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).

A critical review of robust data reconciliation literature reveals some adaptive strategies have been developed that achieve a high efficiency of the estimator even when the error probability distribution presents heavy tails. However, both theoretical and numerical results in Robust Statistics indicate that the increase in computational effort required by adaptive estimates does not yield a real improvement in performance.

In this work we present new methodologies for robust data reconciliation that combine the strengths of both monotone and redescending M-estimators. Monotone M-estimators have unique solutions. In contrast, redescending ones are more robust because they present a higher break-down point and are more efficient when the error model is satisfied but it corresponds to a heavy tailed distribution. Among the different types of redescending M-estimators the bisquare family of functions is selected.

The devised techniques are applied to estimate the value of measured and unmeasured variables and also to identify outliers. A specific study is conducted related with the effect of the measurement redundancy index on the identification capabilities of the strategies.

The performance of the proposed methodologies and their comparison with other existing approaches are illustrated through chemical engineering examples. Performance measures are the Mean Square Error, the Average Number of Type I Error and the Overall Performance.

References

Maronna R., Martin R.D. and V. Yohai, Robust Statistic: Theory and Methods, John Wiley and Sons Ltd., Chichester, 2006.

Romagnoli J. and M. Sánchez, Data Processing and Reconciliation for Chemical Process Operations, Academic Press, San Diego, 2000.