Data-Driven Predictive Probability Density Function Control of Fiber Length Stochastic Distribution Shaping in Refining Process

Pulp is the most important raw material in paper industries, whose fiber length stochastic distribution (FLSD) shaping directly determines the energy consumption and paper quality of the subsequent papermaking processes. However, the mean and variance are insufficient to describe the FLSD shaping, which displays non-Gaussian distributional properties. Therefore, the traditional control method based on the mean and variance of the fiber length is difficult to control the FLSD shaping effectively. In this article, a novel data-driven predictive probability density function (PDF) control method is proposed for the FLSD shaping in the refining process. First, the PDF of FLSD shaping is approximated by a radial basis function neural network (RBF-NN) and the parameters of each RBF basis function are tuned by using an iterative learning law. Second, the random vector functional link network (RVFLN)-based data-driven modeling method is employed to construct the prediction model of the weight vector. Consequently, the predictive controller is designed based on the constructed PDF model of the FLSD shaping in the refining process and the stability issue of the resulted closed-loop system is discussed. The experiments using industrial data are given to illustrate the effectiveness of the proposed method. Note to Practitioners —Pulp quality control in the refining process plays a critical role in the optimization of product quality and energy saving in the pulping and papermaking processes. Different from the conventional control method based on the mean and variance of the fiber length, a novel data-driven predictive PDF control method is proposed for the non-Gaussian stochastic distribution dynamic characteristics of the fiber length, which is used to achieve the desired PDF shaping of fiber length distribution. This kind of novel control method includes the control of the traditional mean and variance of the fiber length in some sense and has applications that are more extensive.