Nonlinear processes and non-Gaussian properties are challenging subjects for soft sensor modeling of chemical processes. In this paper, we propose a D-vine copula regression method based on a Hamiltonian Monte Carlo (HMC) sampling strategy (HMCCR). In the data pretreatment process, the rolling pin monotonic transformation method is used to ensure that the data have a monotonic relationship. Subsequently, a D-vine copula model is established to obtain the conditional probability density of the key variables based on the auxiliary variables. The expected value, the variance, and the prediction uncertainty of the query data set are calculated using the HMC method. The proposed regression method can successfully approximate the nonlinear and non-Gaussian relationship between the output and input variables using the vine copula function. In addition, we also propose a supplementary sampling strategy based on the HMCCR model to remind operators to supplement the manual analysis. The validity and performance of the proposed method are demonstrated using two industrial examples.

中文翻译：

---

基于哈密顿蒙特卡罗的D型藤Copula回归模型，用于复杂化学过程的软传感器建模

对于化学过程的软传感器建模，非线性过程和非高斯性质是具有挑战性的主题。在本文中，我们提出了一种基于哈密顿蒙特卡洛（HMC）采样策略（HMCCR）的D-vine copula回归方法。在数据预处理过程中，使用the面杖单调变换方法来确保数据具有单调关系。随后，建立D-vine copula模型以基于辅助变量获得关键变量的条件概率密度。使用HMC方法计算查询数据集的期望值，方差和预测不确定性。所提出的回归方法可以使用藤蔓copula函数成功地近似输出和输入变量之间的非线性和非高斯关系。此外，我们还建议基于HMCCR模型的补充抽样策略，以提醒操作员补充人工分析。通过两个工业实例证明了该方法的有效性和性能。