A missing data imputation method for industrial soft sensor modeling

Data on complex industrial processes are often missing, due to sensor or equipment malfunctions; this poses challenges for the prediction of important quality variables and soft sensor applications, and may have a significant impact on production processes and equipment maintenance. Traditional missing data imputation methods face challenges in terms of acquiring data distributions, structures, etc., and are detached from the downstream soft sensor tasks, as they do not consider the close connections and synergistic relationships between missing data imputation and soft sensors. This affects the filling results for important quality variables, and thus reduces the prediction accuracy of the downstream soft sensors. To address these issues, a missing data imputation method for industrial soft sensor modeling, called PFIDM, is proposed that can realize a customized data imputation process with a progressive feedback strategy. The loss function of the improved diffusion model (IDDPM) is rationally designed to introduce KL dispersion between the noise addition process and the data distribution corresponding to the generation process into the next step of noise prediction, which involves predicting and correcting the noise of the current data state. In addition, a dynamic step decay factor related to the noise intensity is defined in the sampling process, and the sampling step span is adaptively adjusted to reduce the number of sampling steps and to accelerate the sampling time. The superiority of the proposed method is verified by comparing several typical methods and instantiating a dataset.