Modeling for output fiber length distribution of refining process using wavelet neural networks trained by NSGA II and gradient based two-stage hybrid algorithm

The chemi-thermo-mechanical pulping (CTMP) is an important process that produces fibers for paper-making, whose output fiber length distribution (FLD) directly determines the energy consumption and product quality of the subsequent papermaking production. Therefore, study on modeling and control of the output FLD is essential for improving pulp quality and saving energy in refining process. However, the output FLD of refining process has non-Gaussian stochastic distribution property, making it difficult to use conventional methods to establish the output FLD model effectively. Under the framework of stochastic distribution control theory, this paper presents a novel modeling approach for output probability density function (PDF) of fiber length in CTMP by combining with the improved wavelet neural network (WNN). In this context, the square root B-spline approximation principle is firstly adopted to extract the B-spline weights of fiber length PDF shape as the target outputs for the WNN based B-spline weights model. Secondly, a novel two-stage hybrid learning algorithm is proposed to establish the parameters system for the WNN based weighs model by defining a multi-objective evaluation index for modeling accuracy in advance. This learning algorithm integrates multi-objective NSGA II algorithm in the first stage for better initial solutions at a global scope, and gradient descent method is employed in the second stage for accurate solutions of WNN model parameters inside a local range. As a result, the final output PDF of fiber length is reconstructed by the estimated B-spline weights using the B-spline approximation principle again. Experiments using actual industrial data have demonstrated the superiority and practicability of the proposed method.