A KPI-Based Probabilistic Soft Sensor Development Approach that Maximizes the Coefficient of Determination

Advanced technology for process monitoring and fault diagnosis is widely used in complex industrial processes. An important issue that needs to be considered is the ability to monitor key performance indicators (KPIs), which often cannot be measured sufficiently quickly or accurately. This paper proposes a data-driven approach based on maximizing the coefficient of determination for probabilistic soft sensor development when data are missing. Firstly, the problem of missing data in the training sample set is solved using the expectation maximization (EM) algorithm. Then, by maximizing the coefficient of determination, a probability model between secondary variables and the KPIs is developed. Finally, a Gaussian mixture model (GMM) is used to estimate the joint probability distribution in the probabilistic soft sensor model, whose parameters are estimated using the EM algorithm. An experimental case study on the alumina concentration in the aluminum electrolysis industry is investigated to demonstrate the advantages and the performance of the proposed approach.