BATCH PROCESSES MONITORING: IDENTIFICATION STAGE

Marco V. Cedeño1, Leandro P.F. Rodríguez Aguilar1, Mabel C. Sánchez1

1Planta Piloto de Ingeniería Química (Universidad Nacional del Sur-CONICET),

ID: 385840

Password: 506699

Keywords

Multivariable Statistical Process Control, Hotelling Statistic, Fault Identification, Clusters, Fermentation.

Abstract

Batch processes are mainly involved in the production of high-added value products. These processes are characterized by the fact that small variations of operation conditions may have a substantial impact on the final product quality. Therefore a large amount of variables and non-linear relations among them should be quickly and unambiguously taken into account to monitor product quality with the purpose of ensuring a safe and profitable operation.
Many successful applications of Multivariate Statistical Process Control for the monitoring and diagnosis of batch processes have been presented. In general, the batch progress is monitored by exploiting the information contained in a historical database of successful batches using projection techniques.
Monitoring approaches that work in the original measurements space have been successfully applied for batch processes if the number of variables involved is not extremely high and there exist strong non-linear relationships among them that prevent the measurements from being linear combinations. For these cases, original space strategies can perform as well as, or even better than some projection-based techniques (Alvarez et al., 2010). They apply only the Hotelling statistic for detecting the faulty state. If that statistic exceeds its critical value for a given number of consecutive observations, the faulty state is declared and, all the effort must be oriented towards finding what the root cause of the deviation is. The identification of the variables that signal the abnormal behavior is frequently performed by calculating the variable contributions to the inflated statistic.
Recently, a new approach to identify the suspicious measurements when the Hotelling statistic exceeds its critical value was proposed (Cedeño et al., 2012). The methodology
consists in finding the Nearest In-Control Neighbour (NICN) of the observation point by solving a minimization problem. The distance between these points is used to evaluate the relative influence of each measured variable on the Hotelling statistic value. Those variables whose distance measures exceed a certain threshold help to isolate the root cause of the fault.
To determine the threshold for each variable, its contribution to the inflated statistic for a set of simulated fault cases, in which that variable is not faulty, are evaluated. Then the empirical cumulative distribution function of that variable contribution is obtained. The control limit is selected as the variable-contribution value for which the cumulative probability is (1-α), where α is the probability of wrongly identifying a variable as faulty.
For batch processes, the aforementioned procedure for calculating the variable-contributions control limits requires a large amount of simulations for each observation time interval. A straightforward solution to this problem came from cluster analysis. This is a procedure devoted to explain different behaviors of a data set by grouping them on high-density regions. It is an iterative multi-objective optimization strategy that characterizes an observation by analogous pattern descriptions. A clustering technique can be implemented to divide the variable-contributions of batch processes into two groups. One of them corresponds to the measurements that signal the abnormal situation, the other one is associated to the observations which are in control.
In this work the monitoring strategy presented by Cedeño et al. (2012), is extended to tackle batch processes. The technique uses only the Hotelling statistics for detection purposes. The identification of the faulty set of observations is performed by applying the NICN concept to calculate the variable contributions to the inflated statistic, and then using cluster theory to point out the suspicious measurements. It avoids the setting of empirical parameters. A fed- batch penicillin fermentation benchmark (Birol et al., 2002) is used to analyze the performance of the presented strategy, which is compared with the most commonly used statistical monitoring strategies.

References

Alvarez R.A., Brandolin A., Sánchez M. Batch process monitoring in the original measurementâ??s space. J. of Process Control 2010; 20: 716-725.
Birol G, Ã?ndey C, Ã?inar A. A Modular Simulation Package for Fed-Batch Fermentation: Penicillin Production. Comp. Chem. Eng. 2002; 26: 1553-1565.
Cedeño M.V., Rodriguez L.P., Alvarez C.R., Sánchez M.C. A new approach to estimate variable contributions to Hotellingâ??s statistic. Chem. & Intell. Lab. Sys. 2012; 118: 120-126.