A recursive Nonlinear PLS algorithm for adaptive nonlinear process modeling

Partial least squares (PLS) regression has been shown to be a powerful multivariate linear regression method for problems where the data are noisy and highly correlated. However, in many practical situations, the processes being modeled exhibit nonlinear behavior, which cannot be reliably modeled by linear regression methods. Furthermore, the processes often experience time-varying changes. In this paper, a recursive nonlinear PLS (RNPLS) algorithm is proposed to deal with this problem. First, a nonlinear PLS (NLPLS) model is built by performing PLS regression on the extended input matrix and the output matrix, where the extension of the input matrix includes the outputs of the hidden nodes of an RBF network and a constant column with all elements being one. When new data cannot be described by the old model in the sense that the model performance on a moving window of data is not satisfactory, the recursive algorithm is then used to modify the structure and parameters of the model to adapt process changes. Applications of this RNPLS algorithm to a simulated pH neutralization process and an industrial propylene polymerization process are presented and the results demonstrate that this algorithm adapts the process changes effectively and gives satisfactory prediction results.