A Probabilistic Quality-Relevant Monitoring Method With Gaussian Mixture Model

Process uncertainty, which is usually caused by various factors, is generally subject to unknown complex distribution. However, many existing monitoring methods are established with a single distribution, and thus they may not accurately reflect the uncertainty within process systems. In this study, a probabilistic quality- relevant monitoring (PQM-GMM) is proposed with the Gaussian mixture model to address the aforementioned issue. Different from conventional monitoring methods, the proposed method measures the process uncertainty using multiple Gaussian distributions, which can be used to approximate any unknown complex distribution. Then, the optimization problem of the proposed PQM-GMM model is solved using the expectation maximization (EM) algorithm, which includes an augmented Lagrange multiplier in the M-step for model parameter estimation. Using the obtained results, a quality-relevant monitoring model is established with three statistics. It is noted that the proposed model can also be extended to many existing methods since they share a similar structure. Besides, the detailed information such as initial value selection, missing data problem, computation complexity is discussed. The effectiveness and superiority of the proposed method are tested using a numerical simulation example and a real low-pressure heater application. In comparison with some commonly used quality-relevant methods, the proposed model can be robustly established in the presence of corrupted data, and has a better detection sensitivity for the process anomalies in both process and quality variables. Note to Practitioners - A quality-relevant monitoring method is proposed in this study with Gaussian mixture model (GMM) for detecting the abnormal conditions of industrial processes under harsh environment. Since GMM can be used to approximate any unknown complex distribution, the process uncertainty within the collected data can be meticulously measured using the proposed PQM-GMM model. Besides, the quality-independent faults and quality-related faults can also be effectively distinguished using the designed monitoring statistics.