Nonlinear Monitoring and Prediction Model in an Industrial Environmental Process

Abstract

A new nonlinear process monitoring and quality prediction technique based on kernel partial least squares (PLS) has been developed and applied to a biological wastewater treatment system. The calculation step that makes kernel PLS (KPLS) different from other linear and non-linear PLS techniques is the mapping of the data set from its original space into a hyper-dimensional space before the extraction of the principal components in the feature space. Suggestions are provided for a nonlinear monitoring measure on the KPLS space, as well as guidelines to select the number of eigenvalues in the feature space. Eleven process and manipulated variables (X-block) were used to model three process output variables (Y-block) in the industrial plant: the sludge volume index, cyanide reduction and COD reduction. The prediction results show that the KPLS-based model is superior to other models: it has the smallest mean squared error (MSE) of 5.04% while other PLS models (linear PLS, quadratic PLS, spline PLS) of the input space, as well as the other kernel regression methods, such as the kernel principal component regression and ridge regression, have relatively large modeling error values between 5.8 and 8.5%. Additionally, KPLS gives better fault detection performance when compared to other linear and nonlinear methods, where abnormal process variations are relevant to the microbial treatment and to the settling capability, which affect sludge volume index (SVI), chemical oxygen demand (COD), and cyanide (CN) reduction. These results indicate that the KPLS technique is able to accurately model the nonlinear processes under complex operating conditions, and can supervise process faults in industrial plants, since it can effectively capture the nonlinear causal relationships in the treatment process.