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.