For efficient process control and monitoring, accurate real-time information of quality variables is essential. To predict these quality (or slow-rate) variables at a fast-rate, in the industry, inferential/soft sensors are often used. However, most of the conventional methods for soft sensors do not utilize prior process knowledge even if it is available. The prediction accuracy of these inferential sensors depends mainly on the quality of available data, which can be affected by significant noise and possible sensor failures. To address these issues, in this work, a generic Gaussian Bayesian network based soft-sensor framework is developed, which can account multiple hidden states and multirate/missing data. In the proposed framework, due to the presence of hidden variables and missing data, posterior probability of these variables in E-step of the EM algorithm is evaluated using Bayesian inference. Compared to the existing soft-sensors, the proposed approach will allow users to integrate prior knowledge into the BN structure. Moreover, due to the probabilistic nature of BNs, variances of measurement noises and disturbances between hidden states are simultaneously estimated. The proposed framework is generic and can be used for any multi-layered structure. Its performance is demonstrated for two different structures, two-layer and multilayered structures, on a benchmark flow-network problem and an industrial process. It is observed that the proposed Gaussian Bayesian network based soft sensors are able to give significantly better and more reliable estimates compared to the conventional approaches.

对于有效的过程控制和监测，质量变量的准确实时信息是必不可少的。为了快速预测这些质量（或慢速）变量，业界经常使用推理/软传感器。然而，大多数用于软传感器的传统方法即使可用也没有利用先验过程知识。这些推理传感器的预测精度主要取决于可用数据的质量，这可能会受到显着噪声和可能的传感器故障的影响。为了解决这些问题，在这项工作中，开发了一种基于通用高斯贝叶斯网络的软传感器框架，它可以考虑多个隐藏状态和多速率/缺失数据。在提出的框架中，由于存在隐藏变量和缺失数据，这些变量在 EM 算法的 E 步中的后验概率是使用贝叶斯推理来评估的。与现有的软传感器相比，所提出的方法将允许用户将先验知识整合到 BN 结构中。此外，由于 BN 的概率性质，测量噪声的方差和隐藏状态之间的干扰被同时估计。提议的框架是通用的，可用于任何多层结构。在基准流网络问题和工业过程中，针对两种不同的结构（两层和多层结构）证明了其性能。据观察，与传统方法相比，所提出的基于高斯贝叶斯网络的软传感器能够提供更好、更可靠的估计。