Removal of the effects of outliers in batch process data through maximum correntropy estimator

In some batch processes, the control of a variable of interest is done by controlling another variable. The relationship between the variable of interest and the controlled variable is established by an empirical process model which should be built from reliable data. The presence of outliers in the variable of interest affects the reliability of the data which can result in erroneous interpretations concerning the variable of interest. In this paper, a novel method, referred to as the maximum correntropy estimator (MCE), of removing the effects of outliers by the use of a robust estimator that maximizes correntropy is proposed. The effectiveness of MCE is dependent on the proper selection of kernel width which is a parameter that specifies the minimum magnitude of error arising from an outlier which will be excluded by the estimator in approximating the trend of the majority of the values of the variable of interest with time. An initial set of outliers is determined by a preliminary detection method and from these outliers, the minimum value of error is estimated for the kernel width. The trend which is an unknown function is fitted by a linear combination of scaling functions of a given resolution and its coefficients are determined by MCE. Given the unknown function, the remaining outliers are identified on a proposed error cut-off value. The values of all the outliers are replaced with estimates from the unknown function so that the batch data set is now free of outliers and can then be used in building a reliable process model. The advantages of the proposed method, data from a chemical batch reactor, are presented to help readers delve into the matter.

► Preliminary outlier detection method (PODM) can decide the minimum outlier error.
► PODM can handle multiple sets of batch dynamic data.
► Maximum correntropy estimator (MCE) is a robust parameter estimation method.
► The kernel width of MCE can be estimated by the minimum error from an outlier.
► PODM and MCE are applied to the data with outliers from a real batch plant.