应用数学
核(代数)
残余物
常微分方程
偏微分方程
计算机科学
有限元法
算法
数学
数学优化
微分方程
离散数学
数学分析
工程类
结构工程
作者
Jie Dong,Qiang Wang,Mengyuan Wang,Kaixiang Peng
出处
期刊:IEEE Access
[Institute of Electrical and Electronics Engineers]
日期:2018-01-01
卷期号:6: 16646-16654
被引量:12
标识
DOI:10.1109/access.2018.2812919
摘要
Distributed parameter systems (DPS) widely exist in the large-scale industrial production industry. Techniques developed for DPS can further demonstrate the complexity of the industrial process, such as the hot-rolled strip laminar cooling (HSLC) process. Due to the infinite dimensional of states variables and manipulated variables, it is a challenging work to model and monitor for DPS in practice. In this paper, a data-driven approach for process modeling and quality monitoring of DPS is obtained. A second-order partial differential equation (PDE) is transformed into finite-dimensional model of ordinary differential equation (ODE) with finite element method (FEM) and Galerkin method. Then, this model is described by state space with time-space separation. To realize the proposed scheme by the data-driven approach, we use the industrial process data to estimate the parameters in the model and basic functions by recursive least squares method. Based on this model, a kernel representation of DPS for residual generation is obtained in the statistical framework. $T^{2}$ statistic is employed to evaluate the residual and the threshold is determined by the use of noncentral $\chi ^{2}$ -distribution. Finally, the effectiveness of the proposed scheme is demonstrated by conducting a simulation on the production process of HSLC.
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