Monitoring of batch processes with non-linear modeling methods

Multiway principal components analysis (MPCA) is a linear model in nature, thus, limited when it is applied to batch process. In this paper, the linear model MPCA was complemented with an auto associative neural network model in order to generate nonlinear principal components. The network´s bottleneck layer outputs (nonlinear principal components) were made orthogonal. A method to estimate confidence limits based on a kernel probability density function was proposed since the nonlinear scores are not normally distributed. A statistic-like parameter (D_NL) was proposed to evaluate on-line scores for new runs using the density estimated confidence bounds and replacing the T² statistic. The proposed method was applied to monitoring fed-batch streptomycete production, and the simulation results show that the nonlinear scores obtained with the auto associative neural networks capture more process data variance than if obtained with a linear method and the density estimation method proved to be more reliable