Abstract: A probabilistic kernel principal component analysis mixture model (PKPCAM) based on Bayesian inference was proposed to detect and diagnose the fault in the nonlinear and multimode processes. In PKPCAM, each operating mode was characterized by a local probabilistic kernel principal component, leading to a series of components corresponding to multiple operation conditions. Firstly, process data were projected from the original measurement space into the high-dimensional feature space. Then the probabilistic kernel principal component analysis mixture model was estimated in the feature space and used to characterize the multiple local components from the viewpoint of probability. Finally, utilizing the posterior probability of the monitored sample in kernel subspace, according to Mahalanobis distance within the local mode, the Bayesian reference based global probability index was proposed for fault detection. And meantime, using the relative contribution of variable within mode, global contribution index was derived to perform diagnosis. Comparing to the two methods based on the sub-principal component analysis using k-means clustering and the kernel principal component analysis, the feasibility and effectiveness by the proposed Bayesian inference based PKPCAM method for fault detection and diagnosis in nonlinear and multimode process was validated on Tennessee Eastman process.

Key words: nonlinear and multimode process, probabilistic kernel principal component analysis mixture model, Bayesian inference, fault detection, fault diagnosis

摘要： 针对一类非线性多模态的化工过程,提出一种基于概率核主元的混合模型(PKPCAM),并利用贝叶斯推理策略进行过程监控与故障诊断.在提出的模型中, 每个操作模态由一个局部化的概率核主元分量描述,从而构建的一系列分量对应了不同的操作模态.首先,将过程数据从原始的度量空间投影到高维特征空间;其次,在该特征空间建立概率主元混合模型,从概率角度刻画数据集的多个局部分量特征;最后,在提取的核主元分量内获得测试样本的后验概率,结合模态内的马氏距离贡献度,提出基于贝叶斯推理的全局概率指标进行故障检测,同时利用模态内变量的相对贡献度,基于全局贡献度指标进行故障诊断.利用TEP仿真平台,与基于k均值聚类的次级主元分析和核主元分析的方法进行了对比分析,验证了提出的贝叶斯推理的PKPCAM方法对非线性多模态过程进行故障检测与诊断的可行性和有效性.

关键词: 非线性多模态过程, 概率核主元混合模型, 贝叶斯推理, 故障检测, 故障诊断