A novel dynamic nonlinear partial least squares based on the cascade structure

For the collinearity problem of input variables in actual industrial process modeling, a novel dynamic nonlinear partial least squares (PLS) approach is presented to solve this problem. In the proposed method, a novel cascade structure which is composed of an autoregressive exogenous model and a radial basis function neural network is introduced as the inner model of the conventional PLS method, so that the newly established PLS method has both dynamic and nonlinear characteristics. In this improvement, an external model for extracting the latent variables of input and output is established through the original PLS model, which eliminates the collinearity between original dependent variables, and then the aforementioned cascade framework is employed to describe the dynamic and nonlinear relationships between the input and output score variables. Furthermore, in order to estimate the unknown parameters of the established dynamic nonlinear inner model, a stochastic gradient algorithm and a forgetting factor stochastic gradient algorithm are presented. Additionally, a simple cross validation method is used to determine the orders of the inner model. Finally, a numerical simulation example and an application example are given to demonstrate the effectiveness of the proposed approach.