Factor analysis process monitoring method based on probabilistic information of variables

doi:10.11949/j.issn.0438-1157.20170057

Abstract

Abstract:

Factor analysis (FA), which noise factors are taken into consideration, can establish probabilistic generative model by the expectation maximum (EM) algorithm. However, traditional FA (ST) index may lead to missed fault alarms by utilizing only expectation information of variables and ignoring variance information of variables that is more representative of uncertainty. The drawback of FA (ST) index was revealed by probabilistic analysis of process variables. Another important part in the modeling process was to determine number of factors, which could preserve most useful process information in the meantime of dimension reducing. A negative log likelihood probability (NLLP) index, which integrated more comprehensive probabilistic information, was proposed to overcome dilemma of insufficient information of traditional monitoring index. For the determination of number of factors, a novel global-local method was introduced so that information explanation ratios of global factors and variables over process information reached convergence simultaneously. Numerical simulation and Tennessee Eastman (TE) process study illustrated effectiveness and superiority of the proposed method.

Key words: factor analysis, parameter estimation, process control, information explanation ratio, statistical analysis

摘要：

因子分析（factor analysis，FA）将噪声因素加入到建模过程中，可通过最大期望（expectation maximum，EM）算法建立模型。传统的FA（ST）指标仅利用了变量的期望信息而忽略了更能代表不确定性的方差信息，这可能会导致故障的漏报。通过对过程变量的概率分析，从本质上揭示了FA（ST）的这一缺陷。建模过程中的另一个重要因素是确定因子个数，使得在降维的同时能最大程度地保留对过程有用的信息。针对传统监控指标信息不足的问题，提出的负对数似然概率（negative log likelihood probability，NLLP）指标整合了更全面的概率信息；针对因子个数给定的问题，提出了一种整体-局部因子数确定法，使得因子和变量对于过程的信息解释率都达到收敛。最后通过数值例子和Tennessee Eastman（TE）过程验证了所提方法的有效性和优越性。

关键词: 因子分析, 参数估计, 过程控制, 信息解释率, 统计分析

CLC Number:

TP277

HU Tingting, WANG Fan, SHI Hongbo. Factor analysis process monitoring method based on probabilistic information of variables[J]. CIESC Journal, 2017, 68(7): 2844-2850.

胡婷婷, 王帆, 侍洪波. 基于变量概率信息的因子分析监控方法[J]. 化工学报, 2017, 68(7): 2844-2850.

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