Multivariate monitoring of fermentation processes with non-linear modelling methods

Multiway principal components analysis (MPCA) and parallel factor analysis (PARAFAC) are widely used in exploratory data analysis and multivariate statistical process control (MSPC). These models are linear in nature, thus, limited when non-linear relations are present in the data. Principal component analysis (PCA) can be extended to non-linear principal components analysis using autoassociative neural networks. In this paper, the network’s bottleneck layer outputs (non-linear components) were made orthogonal. A method to estimate confidence limits based on a kernel probability density function was proposed since these limits do not assume that the non-linear scores are normally distributed. A measure for the non-linear scores (DNL) was presented here to monitor on-line the process replacing the well known Hotelling’s T2 statistic. One hundred and two industrial fermentation runs were used to evaluate the performance of a non-linear technique for multivariate process statistical monitoring. Three process runs with faults were used to compare the error detection performance using a statistic for the non-linear scores and the residuals statistic (SPE).