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.

中文翻译：

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精炼过程中纤维长度随机分布整形的数据驱动预测概率密度函数控制

纸浆是造纸工业中最重要的原材料，其纤维长度随机分布（FLSD）成形直接决定后续造纸过程的能耗和纸张质量。但是，均值和方差不足以描述显示非高斯分布特性的FLSD整形。因此，传统的基于纤维长度均值和方差的控制方法很难有效地控制FLSD的成形。在本文中，提出了一种新颖的数据驱动预测概率密度函数（PDF）控制方法，用于精炼过程中的FLSD整形。首先，通过径向基函数神经网络（RBF-NN）对FLSD成形的PDF进行近似，并使用迭代学习定律来调整每个RBF基函数的参数。第二，基于随机矢量功能链接网络（RVFLN）的数据驱动建模方法构建了权重矢量的预测模型。因此，在精炼过程中，基于所构建的FLSD成形PDF模型设计了预测控制器，并讨论了所得闭环系统的稳定性问题。利用工业数据进行的实验说明了该方法的有效性。执业者注意 —精制过程中的纸浆质量控制在制浆和造纸过程中产品质量的优化和节能方面起着至关重要的作用。与基于纤维长度均值和方差的常规控制方法不同，针对纤维长度的非高斯随机分布动态特性，提出了一种新的数据驱动的预测PDF控制方法，该方法用于实现所需的PDF纤维长度分布的整形。这种新颖的控制方法在某种意义上包括了对光纤长度的传统均值和方差的控制，并且具有更广泛的应用。