基于LASSO回归的R-vine copula模型构建及其在化工过程故障检测中的应用

Vine copula模型在描述高维数据间的非线性、非高斯特性相依关系问题上提供了一种新的思路，在化工过程建模领域受到越来越多关注。笔者将LASSO(least absolute shrinkage and selection operator)回归引入R-vine copula(LASSO-R-vine copula, LRVC),根据变量间联系的强弱程度确定变量在R-vine矩阵中的位置，利用回归分析正则化路径选择R-vine copula矩阵结构，遵循R-vine矩阵构建规则和回归过程确定R-vine结构矩阵模型，以获得一个与变量独立性有关的稀疏矩阵模型。该方法构建的矩阵结构独立于copula函数类型和参数，在处理高维度复杂工业过程数据时，利用稀疏模型和惩罚力度简化copula函数类型选择过程，缩短了建模时间，使统计建模具有更强的灵活性。该方法在TE(Tennessee Eastman)和醋酸脱水过程故障监测中表现出较好的预测效果，证明了提出的方法在非线性、非高斯过程的有效性。

Model of R-vine copula based on LASSO regression and its application in chemical process fault detection

The vine copula model provides a new way to describe the nonlinear and non-Gaussian dependence of high-dimensional data and has attracted more and more attention in the field of chemical process modeling. In this article, a novel chemical process fault detection method, LASSO-R-vine copula (LRVC), is proposed by introducing LASSO (least absolute shrinkage and selection operator) regression into R-vine copula. LRVC determines the position of the variables in the R-vine matrix according to the strength of the relationship between the variables, using regression to analyze the regularization path and select the R-vine copula matrix structure. The R-vine structure matrix model is determined to obtain a sparse matrix model related to variables'' independence by following the R-vine matrix construction rules and regression process. The matrix structure constructed by this method is independent of the copula function type and parameters. When dealing with high-dimensional complex industrial process data, sparse models and penalties could simplify the copula function type''s selection process, shorten the modeling time, and make the statistical modeling more flexible. This method shows an excellent predictive effect in TE and the acetic acid dehydration process fault monitoring, proving its effectiveness in nonlinear and non-Gaussian processes.