Soft sensor development for mixed oil interface tracking in multi-product pipelines based on knowledge-informed semi-supervised Variational Bayesian Gaussian mixture regression

Sequential transportation of petroleum products in multi-product pipelines often lead to occurrence of mixed oil. The prediction of the arrival time of the mixed oil interface constitutes crucial data for the scheduling of treatment actions. However, existing soft sensors, like Gaussian mixture regression (GMR), may face challenges due to limited size of labeled data and numerical issues, leading to performance degradation or even training failure. To tackle these issues, we propose a Knowledge-informed Semi-supervised Variational Bayesian Gaussian mixture model (KI-SSVBGMR). It employs a semi-supervised fully Bayesian structure designed to address the constraints arising from the potential matrix singularity issues and shortage of labeled samples. Subsequently, we determine the crucial regression variable and establish its prior distribution based on industrial knowledge to improve model generalization. Finally, a learning procedure grounded in the Variational Inference algorithm is developed to train the KI-SSVBGMR. Through case studies, including numerical examples and real industrial datasets, our method demonstrates the effectiveness and reliability of the proposed soft sensor development method. This research can aid operators in improving mixed oil section management and provides valuable insights for integrating machine learning with industrial knowledge.