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.

用于过程监测和故障诊断的先进技术在复杂工业过程中得到了广泛应用。需要考虑的一个重要问题是监测关键性能指标（KPI）的能力，这些指标往往无法足够快速或准确地测量。本文提出了一种数据驱动的方法，用于在数据缺失的情况下基于最大化决定系数来开发概率软测量器。首先，使用期望最大化（EM）算法解决训练样本集中的数据缺失问题。然后，通过最大化决定系数，建立二次变量与关键性能指标之间的概率模型。最后，使用高斯混合模型（GMM）来估计概率软测量模型中的联合概率分布，其参数使用EM算法进行估计。通过对铝电解行业中氧化铝浓度的实验案例研究，展示了所提方法的优势和性能。