Regularised kernel density estimation for clustered process data

Abstract

Process systems often present multiple operating regions, for example as a result of grade changes, and some systems produce data with very small variation. In both cases, the training data sets would be discretely clustered, which causes great difficulties in extracting the probability density function (PDF) for process condition monitoring. To overcome this obstacle, a regularisation method is suggested which adds some carefully designed noise into the training data set to stabilise the procedure of a non-parametric algorithm. A deconvolution method is employed to recover the PDF of the original data set. The kernel density estimation (KDE) method is chosen as the non-parametric algorithm to extract the PDF and confidence intervals of the training data sets. Three case studies show that it is a pragmatic method for dealing with real industrial process data.