In this paper, the multivariate Laplace distribution (also called L1 distribution) is adopted to construct a robust probabilistic principal component regression model (MRPPCR‐L1) under multiple operating modes. In the practical industrial chemistry process, outliers exist due to incorrect recording, disturbances, and process noises and might result in modelling distortion. To address this problem, Laplace distribution, instead of the Gaussian distribution in traditional methods, is introduced to reduce the negative influence of outliers. Moreover, probabilistic principal component regression is employed for dealing with the mixture modelling problem owing to its probabilistic property to determine the operating modes. The formulation of this approach is derived with the expectation maximum algorithm and the soft sensing model is also developed for prediction. Compared to the conventional method, a numerical example and the Tennessee Eastman process are used to demonstrate the robust modelling performance of the proposed method.

中文翻译：

---

混合鲁棒L1概率主成分回归和软传感器应用

本文采用多元Laplace分布（也称为L1分布）构建了多种操作模式下的鲁棒概率主成分回归模型（MRPPCR-L1）。在实际的工业化学过程中，异常记录是由于记录不正确，干扰和过程噪声而引起的，并可能导致建模失真。为了解决这个问题，引入拉普拉斯分布而不是传统方法中的高斯分布，以减少离群值的负面影响。此外，由于概率主成分回归具有确定操作模式的概率特性，因此它被用于处理混合建模问题。该方法的公式是通过期望最大值算法得出的，并且还开发了用于预测的软传感模型。与常规方法相比，通过算例和田纳西州伊士曼过程证明了该方法的鲁棒建模性能。