论文标题
具有随机数据和顺序数据的广义概率监测模型
A Generalized Probabilistic Monitoring Model with Both Random and Sequential Data
论文作者
论文摘要
近几十年来，已经采用了许多多元统计分析方法及其相应的概率对应物来开发过程监测模型。但是，很少研究它们之间的有见地的联系。在这项研究中，通过随机数据和顺序数据开发了广义概率监测模型（GPMM）。由于在特定限制下可以将GPMM简化为各种概率线性模型，因此采用它来分析不同监测方法之间的连接。使用预期最大化（EM）算法，估计GPMM的参数在随机情况和顺序情况下估计。基于获得的模型参数，统计数据旨在监视过程系统的不同方面。此外，这些统计数据的分布是严格得出和证明的，因此可以相应地计算控制限制。在此之后，提出了贡献分析方法，用于识别一旦检测到过程异常的错误变量。最后，进一步研究了基于经典多元方法及其相应概率图形模型的监测模型之间的等价性。这项研究的结论是使用数值示例和田纳西·伊士曼（TE TE）过程验证的。实验结果表明，所提出的监视统计量受其相应分布的约束，并且在特定限制下的经典确定性模型中等同于统计。
Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful connections between them have rarely been studied. In this study, a generalized probabilistic monitoring model (GPMM) is developed with both random and sequential data. Since GPMM can be reduced to various probabilistic linear models under specific restrictions, it is adopted to analyze the connections between different monitoring methods. Using expectation maximization (EM) algorithm, the parameters of GPMM are estimated for both random and sequential cases. Based on the obtained model parameters, statistics are designed for monitoring different aspects of the process system. Besides, the distributions of these statistics are rigorously derived and proved, so that the control limits can be calculated accordingly. After that, contribution analysis methods are presented for identifying faulty variables once the process anomalies are detected. Finally, the equivalence between monitoring models based on classical multivariate methods and their corresponding probabilistic graphic models is further investigated. The conclusions of this study are verified using a numerical example and the Tennessee Eastman (TE) process. Experimental results illustrate that the proposed monitoring statistics are subject to their corresponding distributions, and they are equivalent to statistics in classical deterministic models under specific restrictions.
