468895 Robust Classification of Systematic Measurement Errors
Data Reconciliation (DR) is a well known methodology that considers the measurements and the model of the plant. This tool works in the sense that measurements and conservation equations have the less possible discrepancy. It consists in solving an optimization problem which minimizes a non linear function of the error subject to the satisfaction of a set of process constraints (Romagnoli and Sánchez, 2000).
Classical estimators provide optimal estimates when measurements follow exactly a probability distribution function, while robust estimator aims at giving goods results when the measurements recollected just make this approximately (Maronna et al., 2006). Many researchers have made comparisons between these families of estimators and reported results that verified the estimation quality of the robust ones (Ozyurt and Pike, 2004; Martinez Prata et al., 2010; Chen et al., 2013; Llanos et al., 2015).
The simultaneous presence of bias and outliers was treated by Chen et al. (2013). They applied the correntropy estimator to solve the DR problem and analyzed the results of performance's parameters. The reduction of gross errors effect was also studied by Nicholson et al. (2014). They employed the Hampel's redescending estimator plus an advanced step moving window for the resolution of the dynamic DR problem. Those authors considered that measurements are contaminated by outliers, biases and drifts.
Regarding the robust classification of systematic errors, Martinez Prata et al. (2010) addressed the simultaneous identification of bias and outliers using the Welsch estimator and a Particle Swam Optimization algorithm. Recently Zhang and Chen (2015) presented a robust strategy to distinguish among outliers, biases and drifts, which makes use of the Correntropy estimator.
In Llanos et al. (2015), a comparison of recently appeared robust methodologies was made taking into account performance parameters that measure the capacity of detection, the power of reconciliation and the computational requirement. It was concluded that one of their proposed approaches, called the Simple Method (SiM) is an efficient alternative for solving the type of problems in consideration. The procedure is made up of two steps. First, the robust median of the measurements contained in a moving window is calculated using the Bi-square function. Then an optimization problem is solved applying the Huber estimator and the solution of the previous step as initial point.
In this work, a new strategy for the robust classification of systematic measurements errors is presented. The DR stage is based on the SiM. The identification stage uses the Measurements Test (MT) to detect outliers or suspicious variables. When the MT is applied to the last two observations of the moving window, two cases may arise. If the statistical test of only the penultimate measurement is greater than its critical value, an outlier has been identified. In contrast if the statistical values of the two observations are greater than the critical ones, then the next measurements are saved to make a robust linear regression. The relation between the estimated slope and the variance of the observations allows distinguishing between biases and drifts.
Application results of the methodology for linear and nonlinear benchmarks, extracted from the literature, are used to evaluate its performance. Three cases are analyzed for different lengths of the data horizon. The first one involves the presence of outliers and biases; the second one considers that measurements may contain outliers and drifts, and the last one studies the possible existence of all the systematic observation errors. The performance of the proposed methodology is measured in terms of the Percentage of Right Classification for each type of systematic error and a global index. Results show that there is a window length which allows obtaining the best classification of the simulated errors.
1) Maronna, R. A.; Martin, R.D.; Yohai, V. Robust Statistics: Theory and Methods; John Wiley and Sons Ltd.: Chichester, 2006.
2) Özyurt, D. B.; Pike, R.W. Theory and Practice of Simultaneous Data Reconciliation and Gross Error Detection for Chemical Processes. Comput. Chem. Eng. 2004, 28, 381-402.
3) Romagnoli, J.; Sánchez, M. Data Processing and Reconciliation for Chemical Process Operations; Academic Press: San Diego, 2000.
4) Martinez Prata, D.; Schwaab, M.; Lima, E.L.; Pinto, J.C. Simultaneous Robust Data Reconciliation and Gross Error Detection through Particle Swarm Optimization for an Industrial Polypropylene Reactor. Chem. Eng. Sci. 2010, 65, 4943-4954.
5) Chen J, Peng Y, Munoz J. Correntropy Estimator for Data Reconciliation. Chem. Eng. Sci. 2013, 104, 10019-27.
6) Nicholson, B.; López-Negrete, R.; Biegler, L. T. On-line State Estimation of Nonlinear Dynamic Systems with Gross Errors. Comput. Chem. Eng. 2014, 70, 149-159.
7) Zhang, Z.; Chen, J. Correntropy Based Data Reconciliation and Gross Error Detection and Identification for Nonlinear Dynamic Processes. Comput. Chem. Eng. 2015, 75, 120-134.
8) Llanos C. E.; Sánchez, M. C.; Maronna, R. A. Robust estimator for Data Reconciliation. Ind. Eng. Chem. Res., 2015, 54 (18), pp 5096–5105