Regularized Bayesian\nFusion for Multimodal Data Integration\nin Industrial Processes

The collection of data from multiple sources with distinct\nmodalities\nand varying levels of quality is pervasive in modern industry. Furthermore,\nassociated with each source are often different sampling rates, and\nsome sources may not even have a regular acquisition pattern. These\naspects pose significant challenges when developing machine learning\n(ML) models for predicting target variables, such as product properties,\nor process key performance indicators (KPIs). Data imputation schemes\nare a common solution but often require case-by-case analysis to mitigate\nthe risk of introducing unrealistic artifacts, complicating the analysis\npipeline and making the process more complex and less scalable. This\nwork introduces a flexible solution for combining redundant sources\nof information with respect to a target response, considering their\nassociated quality, while accommodating for different sampling rates\nand information quality. The proposed Regularized Bayesian Fusion\n(RegBF) approach aims to produce estimates of the target variable\nwith an expected smoothness level, being at the same time compatible\nwith the dominant dynamic mode of the industrial process. The methodology\nis scalable and flexible, as it can incorporate new data sources,\nat any time, in the form of either dynamic first-principle models,\ndata-driven ML models, or instrumental information sources (e.g.,\nonline or laboratory analytical instruments). The proposed approach\nis tested in two case studies: one from a Kamyr digester process and\nthe other from a wastewater treatment plant operation.