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    Journal of Process Control 32 (2015) 109116

    Contents lists available at ScienceDirect

    Journal of Process Control

    j ourna l ho me pa ge: www.elsev ier .com/ locate / jprocont

    anonical variate analysis-based monitoring of process correlationtructure using causal feature representation

    enben Jianga,b, Xiaoxiang Zhub, Dexian Huanga, Richard D. Braatzb,

    Department of Automation, Tsinghua University and Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, ChinaDepartment of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

    r t i c l e i n f o

    rticle history:eceived 3 February 2015eceived in revised form 21 May 2015ccepted 26 May 2015vailable online 17 June 2015

    eywords:ault monitoringorrelation structural fault

    a b s t r a c t

    Although the monitoring of process variables has been extensively studied, techniques for monitoringfaults in the process correlation structures have not yet been fully investigated. The typical methodsbased on the covariance matrix of the process data for process monitoring have limited capability toeffectively monitor underlying structural changes. This paper proposes a canonical variate analysis (CVA)approach based on the feature representation of causal dependency (CD) for the monitoring of faults asso-ciated with changes in process structures, which employs CD for pretreating the data and subsequentlyutilizes CVA for quantifying dissimilarity. Apart from the improved performance of capturing the under-lying connective structure information, the utilization of the CD feature in the first step provides more

    ausal mapimensionality reduction techniqueanonical variate analysis

    application-dependent representations compared with the original data, as well as decreased degree ofredundancy in the feature space by incorporating causal information. The effectiveness of the proposedCD-based approach for the monitoring of structural changes is demonstrated for both single faults andmultiple faults in simulation studies of a networked system. In the simulation results, the CD-basedmethod performs the best, followed by correlation-based and then variable-based methods.

    2015 Elsevier Ltd. All rights reserved.

    . Introduction

    As manufacturing facilities become increasingly integrated andarge scale, the potential for faults to dynamically propagate in non-ntuitive ways to produce significant harm to equipment, life, andhe environment has increased. The rapid detection of faults andssociated identification of their causes are, therefore, of outmostmportance, which has attracted the interest of many researchersnd practitioners. However, most of the process monitoring meth-ds developed so far, including the multivariate statistical controlhart approaches [13], dimensionality reduction techniques [48],nd time-series or state-space methods [9,10], focus on the moni-oring of process variable faults [11,12].

    Compared with the achievements in the monitoring of processariable faults, limited exploration has been done on the impor-ant complementary problem of monitoring the faults of process

    orrelation structures [13]. With the emerging big data concept,he monitoring of correlation structures has become of increasednterest [14]. The explosive growth of process data along with the

    Corresponding author at: 77 Massachusetts Avenue, Room E19-551, Cambridge,A 02139, USA. Tel.: +1 617 253 3112; fax: +1 617 258 0546.

    E-mail address: [email protected] (R.D. Braatz).

    ttp://dx.doi.org/10.1016/j.jprocont.2015.05.004959-1524/ 2015 Elsevier Ltd. All rights reserved.

    increasingly large-scale industries provides a valuable resource forthe analysis and operations of industrial processes. This paper aimsto develop a new approach for monitoring changes in the processstructure.

    Typical approaches adopted for monitoring the process cor-relations are based on the process information described by thecovariance matrix. Example approaches include the generalizedvariance [15,16,18], the conditional entropy [17], and the likelihoodratio test (LRT) [19,20]. The covariance-based methods experienceinherent limitations in the detection of local anomalies as well asthe subsequent identification of the fault origins. In other words,the inherent structure of the process is not explicitly taken intoaccount in the covariance-based methods. For instance, two vari-ables, x and y, can be connected in several different ways such as (i)direct connection x y, (ii) indirect connection x z y or (iii)co-regulated by a third variable z (z x and z y). In all thesecases, the variability between x and y may be similar, and a devi-ation on their underlying causal relationship may pass undetectedand undiscerned by only monitoring the covariance. In order toaccess and use the underlying information of the process corre-

    lation structure, alternative measures of structural relationshipsshould be adopted in the process monitoring procedures.

    An efficient way to explore the relationship for the under-lying structure amongst variables is using causal information. A

    dx.doi.org/10.1016/j.jprocont.2015.05.004http://www.sciencedirect.com/science/journal/09591524http://www.elsevier.com/locate/jproconthttp://crossmark.crossref.org/dialog/?doi=10.1016/j.jprocont.2015.05.004&domain=pdfmailto:[email protected]/10.1016/j.jprocont.2015.05.004

  • 110 B. Jiang et al. / Journal of Process C

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    Fig. 1. Causal linkage of the variables x, y, and z.

    ausal map can clearly reflect the directional linkages betweenny two variables. In addition, the information of causal connec-ivity can be used to reduce the correlated degree for the featurepace of correlation, thereby enhancing the performance of faultonitoring. It was shown in [21] that the monitoring performanceas more sensitive in a space of uncorrelated features. For exam-le, in Fig. 1, without considering the causal connectivity amonghe three variables, the feature representation of correlation con-ains three components, i.e., rx,y, ry,z, and rx,z. From the causalinks in Fig. 1, rx,z is redundant with (rx,y, ry,z). In other words,he inclusion of rx,z in the feature representation of correlationoes not provide more information but increases the degree oforrelation.

    It is important to note that the directional connectivity of theomponents within the plant can play a significant role in faultonitoring [2224]. Several papers describe the construction of the

    ausal map from a process flow diagram or piping and instrumen-ation diagram [23,25,40]. Their results showed that data-drivenechniques in combination with cause-and-effect relationshipsmong process variables can lead to efficient monitoring of faults.he linkage of data-driven analysis with a causal relationship ofhe process has been identified as a promising approach to fault

    onitoring [22,23,25].Previously, the authors introduced a feature representation

    f causal dependency (CD) to incorporate the data-driven tech-iques in conjunction with the causal information [2628]. TheD is utilized to quantify the similarity between the relation-hip of two causally related variables under current operatingonditions and historical operating conditions. It was reported in29] that better fault monitoring results are achieved for featureshat are more application-dependent. In terms of application-ependence in process facilities, the CD is an appropriate featureo represent deviations in the process structure. In this article,n approach based on the CD feature representation is proposedor the monitoring of process structural faults. The proposedD-based approach can potentially facilitate to detect processtructural faults and to identify the root causes, owing to thener description of the underlying structure and the less cor-elated feature space of the CD by utilizing causal information.ifferent from the previous work [27] and [28] which focusedn the monitoring of process variable faults, this article investi-ates the monitoring of process correlation structures. In addition,his work incorporates a dimensionality reduction step based onanonical Variate Analysis (CVA), which generates dynamic state-pace models from the process data to improve the monitoringroficiency.

    The rest of this paper is organized as follows. Section 2 brieflyeviews the traditional CVA-based data-driven monitoring method.ection 3 describes the CD-based approach for monitoring pro-ess structural faults. The effectiveness of the proposed methods demonstrated by a gene network system in Section 4. Section 5ummarizes the conclusions.

    . Canonical variate analysis

    The Canonical Variate Analysis (CVA) method, which serves as

    he technique in the step of dissimilarity quantification, is brieflyeviewed in this section. More details of CVA can be found in30,31].

    ontrol 32 (2015) 109116

    2.1. CVA theorem

    CVA is a dimensionality reduction technique in multivariatestatistical analysis which maximizes the correlation between twoselected sets of variables. Consider vectors of process variablesx Rm and y Rn with covariance matrices xx and yy and cross-covariance matrix xy . The orthogonal basis is chosen as thoselinear combinations of a variable set x that are more correlatedwith the linear combinations of another variable set y in the CVAapproach, where these linear combi

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