Joint Diagnosis of High-dimensional Process Mean and Covariance Matrix based on Bayesian Model Selection

Apart from the quick detection of abnormal changes in a process, it is also critical to pinpoint faulty variables after an out-of-control signal. The existing diagnostic procedures mainly focus on the diagnosis of changes in the process mean. This paper investigates the joint diagnosis of high-dimensional process mean and covariance matrix based on Bayesian model selection with nonlocal priors. The proposed procedure enjoys two promising features. First, in addition to the isolation of shifted components, it can also provide a probability that the identified components are true, which is very useful for elimination of root causes of abnormal changes. Second, it possesses the model consistency property in the sense that the probability of identifying the true components with shifts approaches one as the sample size increases. The performance comparisons favor the proposed procedure. A real example based on the urban waste water treatment process is provided to illustrate the implementation of the proposed method.

除了快速检测过程中的异常变化之外，在接收到失控信号（out-of-control signal）后精准定位故障变量，同样至关重要。现有诊断流程主要聚焦于过程均值偏移的诊断。本文针对基于贝叶斯模型选择（Bayesian model selection）与非局部先验（nonlocal priors）的高维过程均值与协方差矩阵（high-dimensional process mean and covariance matrix）联合诊断问题展开研究。所提出的诊断流程具备两项优异特性：其一，除了能够分离出发生偏移的分量之外，还可给出所识别分量为真实故障分量的概率，这对于排查异常变化的根本原因极具实用价值；其二，该方法具备模型一致性（model consistency）性质，即随着样本量增大，识别出真实偏移分量的概率将趋近于1。性能对比结果均表明所提方法更具优势。文末辅以基于城市污水处理过程的实际案例，以展示所提方法的具体实施流程。