彭開(kāi)香 馬 亮 張 凱

復(fù)雜工業(yè)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)綜述

彭開(kāi)香1,2馬 亮1,2張 凱1,2

質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)是保證安全生產(chǎn)及獲得可靠產(chǎn)品質(zhì)量的有效手段,是當(dāng)前國(guó)際過(guò)程控制領(lǐng)域的研究熱點(diǎn).首先,梳理了質(zhì)量相關(guān)的故障檢測(cè)技術(shù)中典型方法的基本思想和改進(jìn)過(guò)程;其次,概述了質(zhì)量相關(guān)的故障診斷技術(shù)中常用的貢獻(xiàn)圖法及其相關(guān)改進(jìn)方法之間的聯(lián)系,并通過(guò)帶鋼熱連軋過(guò)程(Hot strip mill process,HSMP)案例比較了各種典型方法在質(zhì)量相關(guān)的故障檢測(cè)與診斷性能上的異同;最后,面向復(fù)雜工業(yè)過(guò)程運(yùn)行數(shù)據(jù)的主要特性,評(píng)析了質(zhì)量相關(guān)的故障檢測(cè)與診斷方法的研究現(xiàn)狀,并指出了該研究領(lǐng)域亟需解決的問(wèn)題和未來(lái)的發(fā)展方向.

質(zhì)量相關(guān),故障檢測(cè),故障診斷,偏最小二乘,貢獻(xiàn)圖

為了適應(yīng)市場(chǎng)對(duì)多品種、多規(guī)格、高附加值產(chǎn)品的需求,現(xiàn)代工業(yè)過(guò)程正朝著高效、大型和集成化方向發(fā)展.隨著生產(chǎn)規(guī)模的擴(kuò)大及復(fù)雜性的增加,采用合理的質(zhì)量相關(guān)的故障檢測(cè)與診斷方法來(lái)保障復(fù)雜工業(yè)過(guò)程的安全穩(wěn)定運(yùn)行及連續(xù)穩(wěn)定的產(chǎn)品質(zhì)量已經(jīng)逐漸成為過(guò)程控制領(lǐng)域的首要任務(wù).

復(fù)雜工業(yè)過(guò)程與生俱來(lái)的非線性、動(dòng)態(tài)、多模態(tài)、多時(shí)段、高維度、間歇等特性,使得傳統(tǒng)的基于過(guò)程機(jī)理模型的過(guò)程監(jiān)控方法很難適應(yīng)實(shí)際工業(yè)過(guò)程的復(fù)雜程度;而隨著大量的新型儀表、網(wǎng)絡(luò)化儀表和傳感技術(shù)應(yīng)用于生產(chǎn)制造全流程中,大量的過(guò)程數(shù)據(jù)被采集并存儲(chǔ)下來(lái),使得基于數(shù)據(jù)驅(qū)動(dòng)的故障檢測(cè)與診斷方法成為了當(dāng)今過(guò)程監(jiān)控領(lǐng)域的主流技術(shù),已成功應(yīng)用于化工、醫(yī)藥、鋼鐵冶金、高分子聚合物、微電子制造等生產(chǎn)過(guò)程中[1?6].

在基于數(shù)據(jù)驅(qū)動(dòng)的故障檢測(cè)與診斷的眾多方法中,研究論文和應(yīng)用案例數(shù)量最多的是多元統(tǒng)計(jì)過(guò)程監(jiān)控(Multivariate statistical process monitoring,MSPM)方法,其依托的主要理論是以主元分析(Principle component analysis,PCA)、偏最小二乘(Partial least squares,PLS)、規(guī)范變量分析(Canonical variable analysis,CVA)等為核心的投影降維方法.雖然基于PCA的故障檢測(cè)與診斷技術(shù)能夠有效地監(jiān)測(cè)過(guò)程變量的波動(dòng)和異常狀況,但是企業(yè)管理人員和工程師們可能更加關(guān)心的是由過(guò)程變量引起的故障是否會(huì)導(dǎo)致最終產(chǎn)品質(zhì)量和產(chǎn)量的變化[7].因此,我們更需要探尋易測(cè)的過(guò)程變量與難以測(cè)量的質(zhì)量變量間的相關(guān)關(guān)系,以通過(guò)過(guò)程變量的變化來(lái)監(jiān)測(cè)質(zhì)量指標(biāo)的波動(dòng)情況.

為了獲取過(guò)程變量與質(zhì)量變量之間的約束關(guān)系,國(guó)內(nèi)外的研究學(xué)者已經(jīng)發(fā)表和出版了大量的學(xué)術(shù)論文及著作,主要研究方向包括基于多元線性回歸 (Multiple linear regression, MLR)[8?11]、PLS[12?14]、CVA[15?18]等方法的質(zhì)量相關(guān)的過(guò)程監(jiān)測(cè)技術(shù).MLR方法主要通過(guò)研究過(guò)程變量軌跡的變化來(lái)分析并在線監(jiān)測(cè)最終產(chǎn)品的質(zhì)量情況;而基于PLS與基于CVA的過(guò)程監(jiān)測(cè)方法類似,主要區(qū)別是在獲取投影方向時(shí),前者立足于兩組變量之間的協(xié)方差最大化,而后者立足于兩組變量之間的相關(guān)系數(shù)最大化;從三者之間的關(guān)系來(lái)看, CVA是PLS的基礎(chǔ),MLR是CVA的特例,PLS是MLR的擴(kuò)展,PLS可以實(shí)現(xiàn)多種數(shù)據(jù)分析方法的綜合應(yīng)用,可以集MLR、CVA與PCA的基本功能于一體[19?20].同時(shí),從近年來(lái)質(zhì)量相關(guān)的過(guò)程監(jiān)測(cè)技術(shù)已取得的研究成果來(lái)看,基于PLS及其相關(guān)擴(kuò)展模型的質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)是最常用的方法[12,14,21?22],已逐漸成為過(guò)程和質(zhì)量工程師的得力助手.此外,針對(duì)不同的監(jiān)控指標(biāo)和應(yīng)用對(duì)象,CVA及MLR方法中的典型代表主元回歸(Principle component regression,PCR)[23]方法等也在不同應(yīng)用領(lǐng)域具有相應(yīng)的優(yōu)勢(shì).

本文針對(duì)復(fù)雜工業(yè)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)的研究現(xiàn)狀進(jìn)行綜述,結(jié)構(gòu)如下:首先,對(duì)質(zhì)量相關(guān)的故障檢測(cè)技術(shù)中常用的PLS及其擴(kuò)展模型、PCR模型、CVA模型的基本思想做一梳理總結(jié),重點(diǎn)介紹各模型的改進(jìn)過(guò)程及思路,并用帶鋼熱連軋生產(chǎn)過(guò)程案例對(duì)比仿真分析各種模型在質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)故障檢測(cè)應(yīng)用上的有效性;然后,概述了質(zhì)量相關(guān)的故障診斷技術(shù)中常用的貢獻(xiàn)圖法及其相關(guān)改進(jìn)方法之間的聯(lián)系,并用帶鋼熱連軋生產(chǎn)過(guò)程案例對(duì)比仿真分析各種方法在質(zhì)量相關(guān)的故障診斷應(yīng)用性能上的異同;最后,對(duì)復(fù)雜工業(yè)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷方法的研究現(xiàn)狀進(jìn)行評(píng)析,并指出未來(lái)該領(lǐng)域中的熱點(diǎn)研究方向.

1 質(zhì)量相關(guān)的故障檢測(cè)技術(shù)

為了更好地關(guān)注真正有用的質(zhì)量相關(guān)信息,有必要采取適當(dāng)?shù)氖侄螌?duì)過(guò)程測(cè)量數(shù)據(jù)進(jìn)行預(yù)處理,剔除冗余信息的干擾.針對(duì)這一問(wèn)題,變量選擇技術(shù)[24?25]及正交信號(hào)修正(Orthogonal signal correction,OSC)技術(shù)[26?27]是兩種發(fā)展比較成熟且常用的預(yù)處理手段,它們分別從變量濾波及特征濾波兩個(gè)不同的角度去除非質(zhì)量相關(guān)信息,最終都是為了增強(qiáng)過(guò)程變量與質(zhì)量變量之間的相關(guān)關(guān)系,但是這些方法都不是為了過(guò)程監(jiān)測(cè)而提出的.基于此,近十多年來(lái),國(guó)內(nèi)外的研究學(xué)者提出了一些基于PLS、PCR、CVA等模型的過(guò)程監(jiān)測(cè)技術(shù).

1.1 基于PLS模型的方法

假設(shè)對(duì)某生產(chǎn)過(guò)程的m 個(gè)過(guò)程變量和p個(gè)質(zhì)量變量進(jìn)行n次采樣,得到過(guò)程變量矩陣X (X∈Rn×m)和質(zhì)量變量矩陣Y(Y∈Rn×p).基于PLS模型的方法將數(shù)據(jù)矩陣[X,Y]投影到一個(gè)由較少潛變量[t1,···,tA](A為PLS主元個(gè)數(shù))所張成的低維空間中:

令W=[w1,···,wA]為計(jì)算得分向量的權(quán)重矩陣,由于不能直接由原始測(cè)量數(shù)據(jù)矩陣X直接得到T,所以引入權(quán)重矩陣R=[r1,···,rA],滿足T=XR,且有:

進(jìn)一步可得:

同時(shí)滿足:PTR=RTP=WTW=IA.

PLS方法將過(guò)程變量空間分解為兩個(gè)斜交投影的子空間:得分子空間,即質(zhì)量相關(guān)子空間;殘差子空間,即質(zhì)量無(wú)關(guān)子空間.傳統(tǒng)的故障檢測(cè)方法是利用T2統(tǒng)計(jì)量及Q統(tǒng)計(jì)量分別對(duì)得分子空間及殘差子空間進(jìn)行監(jiān)測(cè)[14].

在線監(jiān)測(cè)中,對(duì)于一個(gè)新測(cè)量樣本xnew,PLS模型的得分和殘差部分可以計(jì)算如下:

基于PLS模型的質(zhì)量相關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下[1]:

相關(guān)統(tǒng)計(jì)量控制限的計(jì)算可以參見(jiàn)文獻(xiàn)[12,28].

1.2 基于PLS擴(kuò)展模型的方法

雖然基于PLS的質(zhì)量相關(guān)的故障檢測(cè)技術(shù)已經(jīng)在化工及制藥等生產(chǎn)過(guò)程中得到廣泛應(yīng)用,但是仍然存在兩方面問(wèn)題:1)PLS模型需要選擇較多的主元來(lái)描述與質(zhì)量相關(guān)的變化,使得模型的解釋非常困難,而且這些主元中依然含有一些和質(zhì)量變量正交的成分,對(duì)預(yù)測(cè)產(chǎn)品質(zhì)量沒(méi)有幫助;2)PLS模型并沒(méi)有按照過(guò)程變量矩陣中方差大小的順序來(lái)抽取主元,使得用Q統(tǒng)計(jì)量監(jiān)測(cè)殘差子空間并不合適[29].基于此,為了改進(jìn)質(zhì)量相關(guān)的過(guò)程監(jiān)測(cè)效果,國(guó)內(nèi)外的研究學(xué)者在基本PLS模型的基礎(chǔ)上,進(jìn)一步提出了一些基于其擴(kuò)展模型的過(guò)程監(jiān)測(cè)方法.

1.2.1 基于全潛結(jié)構(gòu)投影(T-PLS)模型的方法

Zhou等[29]將PCA方法去除變量間相關(guān)性的優(yōu)勢(shì)與PLS方法抽取過(guò)程變量中與質(zhì)量相關(guān)空間的優(yōu)勢(shì)有效結(jié)合,構(gòu)建了T-PLS模型,其將主元空間再次分解為與質(zhì)量相關(guān)的子空間Xy和與質(zhì)量無(wú)關(guān)的子空間Xo,將殘差空間再次分解為含較大方差變化的子空間Xr和僅包含噪聲的殘差子空間Er,該模型僅通過(guò)檢測(cè)Xy和Er便可知生產(chǎn)過(guò)程中是否有質(zhì)量相關(guān)的故障發(fā)生.

通過(guò)T-PLS方法,可以對(duì)X和Y建模如下:

在線監(jiān)測(cè)中,對(duì)于一個(gè)新測(cè)量樣本xnew,相應(yīng)的得分和殘差部分可以計(jì)算如下:

基于T-PLS模型的質(zhì)量相關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下:

式中,Λo、Λr分別為to、tr的協(xié)方差矩陣.

相關(guān)統(tǒng)計(jì)量控制限的計(jì)算可以參見(jiàn)文獻(xiàn)[30].

進(jìn)一步地,Li等[31]研究了T-PLS模型的故障可檢測(cè)性問(wèn)題,提出了質(zhì)量相關(guān)故障檢測(cè)方法的聯(lián)合監(jiān)測(cè)指標(biāo);Zhao等[32]提出了T-PLS模型的多空間分解形式,并將具有不同來(lái)源特征的多組過(guò)程變量中與質(zhì)量相關(guān)的子空間和與質(zhì)量無(wú)關(guān)的子空間進(jìn)一步分解,有效地提高了質(zhì)量變量對(duì)過(guò)程變量的解釋能力及實(shí)時(shí)監(jiān)測(cè)的性能.

1.2.2 基于并發(fā)潛結(jié)構(gòu)投影(C-PLS)模型的方法

T-PLS模型在實(shí)際的應(yīng)用中存在兩個(gè)明顯的缺陷:1)沒(méi)有明確地解釋導(dǎo)致PLS模型主元空間中包含與質(zhì)量無(wú)關(guān)變化的原因;2)主元空間沒(méi)有必要分解為4個(gè)子空間,完全可以分解為與質(zhì)量相關(guān)的子空間和與輸入相關(guān)的子空間.基于此,Qin等[7]從對(duì)質(zhì)量變量全局監(jiān)控的角度,構(gòu)建了C-PLS模型,簡(jiǎn)化了T-PLS模型的結(jié)構(gòu).

通過(guò)C-PLS方法,可以將X和Y建模如下:

式中,Uc為輸入中與可預(yù)測(cè)的質(zhì)量相關(guān)的協(xié)方差部分,Tx為輸入中與可預(yù)測(cè)的質(zhì)量無(wú)關(guān)的方差部分, Ty為不能被輸入預(yù)測(cè)的質(zhì)量中的方差部分,?X為與Y正交的子空間.

在線監(jiān)測(cè)中,對(duì)于一個(gè)新測(cè)量樣本xnew,基于C-PLS模型的質(zhì)量相關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下:

相關(guān)統(tǒng)計(jì)量控制限的計(jì)算可以參見(jiàn)文獻(xiàn)[7].

1.2.3 基于改進(jìn)潛結(jié)構(gòu)投影(M-PLS)模型的方法

與T-PLS模型相同,C-PLS模型并沒(méi)有改變基本PLS模型對(duì)質(zhì)量變量的預(yù)測(cè)能力,而是根據(jù)質(zhì)量變量空間進(jìn)一步分解了測(cè)量變量空間,在計(jì)算量上還是有些復(fù)雜.基于此,Ding等[10]和Yin等[10,33]構(gòu)建了M-PLS模型,將過(guò)程變量空間分解為兩個(gè)子空間,但要求主元子空間不包含與質(zhì)量變量正交的成分,對(duì)預(yù)測(cè)產(chǎn)品質(zhì)量有全部貢獻(xiàn),而殘差空間對(duì)其預(yù)測(cè)沒(méi)有任何貢獻(xiàn).

通過(guò)M-PLS方法,可以將X和Y建模如下:

在線監(jiān)測(cè)中,對(duì)于一個(gè)新測(cè)量樣本xnew,基于M-PLS模型的質(zhì)量相關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下:

質(zhì)量無(wú)關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下:

相關(guān)統(tǒng)計(jì)量控制限的計(jì)算可以參見(jiàn)文獻(xiàn)[10].

1.2.4 基于高效潛結(jié)構(gòu)投影(E-PLS)模型的方法

M-PLS模型避免了C-PLS模型在實(shí)際應(yīng)用中復(fù)雜的迭代計(jì)算過(guò)程,很巧妙地利用SVD產(chǎn)生了兩個(gè)正交的子空間;而在殘差子空間中,雖然對(duì)預(yù)測(cè)產(chǎn)品質(zhì)量沒(méi)有幫助,但其中的變化仍有可能影響產(chǎn)品質(zhì)量.基于此,為了保證空間分解的完備性,Peng等[34]在M-PLS模型的基礎(chǔ)上,對(duì)進(jìn)一步主元分析,產(chǎn)生了兩個(gè)正交的子空間,構(gòu)建了E-PLS模型.

通過(guò)E-PLS方法,可以將X和Y建模如下:

在線監(jiān)測(cè)中,對(duì)于一個(gè)新測(cè)量樣本xnew,基于E-PLS模型的質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以參照式(18)和(13)計(jì)算.

E-PLS模型的相關(guān)統(tǒng)計(jì)量控制限的計(jì)算可以參見(jiàn)文獻(xiàn)[7,10,34].

1.3 基于PCR模型的方法

在利用PLS方法進(jìn)行質(zhì)量相關(guān)的故障檢測(cè)時(shí),過(guò)程變量之間常會(huì)存在多重共線問(wèn)題,會(huì)使回歸系數(shù)的估計(jì)受到嚴(yán)重影響,回歸模型的穩(wěn)定性變差,影響過(guò)程變量與質(zhì)量變量間的回歸分析效果.基于此, Peng等[23]在傳統(tǒng)MLR方法[8?11]的基礎(chǔ)上,受T-PLS與C-PLS的啟發(fā),提出了基于PCR模型的質(zhì)量相關(guān)的故障檢測(cè)方法,彌補(bǔ)了傳統(tǒng)PLS方法的不足,提高了質(zhì)量相關(guān)故障的檢測(cè)能力.

對(duì)X進(jìn)行PCA分解得:

式中,Tpc和Tres分別為主元得分矩陣及殘差得分矩陣,Ppc和Pres分別為主元載荷矩陣及殘差載荷矩陣.

計(jì)算線性回歸系數(shù)得:

對(duì)CPCR進(jìn)行QR分解得:

則將X投影到兩個(gè)正交的子空間:

對(duì)X?y和X?y⊥分別進(jìn)行PCA分解得:

在線監(jiān)測(cè)中,對(duì)于一個(gè)新測(cè)量樣本xnew,基于PCR模型的質(zhì)量相關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下:

質(zhì)量無(wú)關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下:

PCR模型的相關(guān)統(tǒng)計(jì)量控制限的計(jì)算可以參見(jiàn)文獻(xiàn)[12,23,28].

1.4 基于CVA模型的方法

CVA方法是一種直接從生產(chǎn)過(guò)程數(shù)據(jù)中產(chǎn)生狀態(tài)空間方程的子空間辨識(shí)方法,它與PCA和PLS有著緊密的聯(lián)系,這種聯(lián)系促進(jìn)了基于CVA的方法向具有序列相關(guān)性的故障檢測(cè)方向偏移,使得基于CVA的故障檢測(cè)技術(shù)在化工和制造業(yè)等領(lǐng)域得到成功應(yīng)用[15?18].

CVA方法的核心思想是在過(guò)程變量和質(zhì)量變量間尋找最優(yōu)的投影方向a和b,使得投影aTx和bTy之間的相關(guān)性最大,其目標(biāo)最大化準(zhǔn)則函數(shù)為

式中,Cxx=E(XXT),Cyy=E(YYT)分別為X和Y的自協(xié)方差矩陣,Cxy=E(XYT)為X和Y之間的互協(xié)方差矩陣,且有Cyx=E(YXT)=Cxy.

上述的優(yōu)化問(wèn)題可以通過(guò)如下的SVD實(shí)現(xiàn):

在線監(jiān)測(cè)中,對(duì)于一個(gè)新測(cè)量樣本xnew,基于CVA模型的質(zhì)量相關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下:

式中,p為選取的典型相關(guān)維數(shù).

質(zhì)量無(wú)關(guān)故障的統(tǒng)計(jì)監(jiān)測(cè)指標(biāo)可以計(jì)算如下:

式中,q為噪聲空間維數(shù).

CVA模型的相關(guān)統(tǒng)計(jì)量控制限的計(jì)算可以參見(jiàn)文獻(xiàn)[15].

1.5 對(duì)比總結(jié)

以上對(duì)基于PLS及其擴(kuò)展模型、PCR、CVA模型的質(zhì)量相關(guān)的故障檢測(cè)方法的基本思想進(jìn)行了詳細(xì)地梳理,下面從計(jì)算復(fù)雜度、空間投影結(jié)構(gòu)、子空間分解個(gè)數(shù)、統(tǒng)計(jì)量個(gè)數(shù)上對(duì)以上7種模型進(jìn)行對(duì)比總結(jié),如表1所示,其中a為經(jīng)過(guò)交叉檢驗(yàn)得到的主元個(gè)數(shù).

以上7種方法將測(cè)量變量空間分解為不同的子空間,而故障檢測(cè)就是利用相關(guān)統(tǒng)計(jì)量對(duì)各子空間分別進(jìn)行監(jiān)測(cè).如果相關(guān)統(tǒng)計(jì)量均在相應(yīng)的控制限內(nèi),那么認(rèn)為生產(chǎn)過(guò)程中沒(méi)有發(fā)生質(zhì)量相關(guān)或質(zhì)量無(wú)關(guān)的故障;反之,生產(chǎn)過(guò)程中則有質(zhì)量相關(guān)或質(zhì)量無(wú)關(guān)的故障發(fā)生.下面對(duì)基于以上7種模型的質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)故障的相關(guān)監(jiān)測(cè)統(tǒng)計(jì)量進(jìn)行概括總結(jié),如表2所示.

表1 對(duì)比結(jié)果Table 1 Comparison results

表2 監(jiān)測(cè)統(tǒng)計(jì)量總結(jié)Table 2 Summary of monitoring statistics

1.6 對(duì)比仿真研究

為了驗(yàn)證以上7種模型在質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)故障檢測(cè)應(yīng)用上的有效性,這里用帶鋼熱連軋過(guò)程案例來(lái)對(duì)比仿真研究.

帶鋼熱連軋過(guò)程是一個(gè)極其復(fù)雜的工業(yè)過(guò)程,其設(shè)備布置圖如圖1所示.精軋機(jī)組一般由6～7個(gè)機(jī)架組成,每臺(tái)機(jī)架主要由一對(duì)工作輥、一對(duì)支撐輥和相應(yīng)的液壓壓下裝置等部分構(gòu)成.在軋機(jī)的下支撐輥下部一般裝有軋制力檢測(cè)裝置,用于測(cè)量帶鋼軋制力,每臺(tái)軋機(jī)的驅(qū)動(dòng)一般由一臺(tái)大型的交流電機(jī)完成.上、下工作輥之間的輥縫主要由高精度的液壓伺服控制系統(tǒng)完成,以保證一定厚度的帶鋼經(jīng)該機(jī)架軋制后得到相應(yīng)的出口厚度.

軋機(jī)控制系統(tǒng)一般配備自動(dòng)厚度控制 (Automatic gauge control,AGC)、精軋溫度控制(Finishing temperature control,FTC)、自動(dòng)板型控制 (Automatic slab control,ASC)等控制器,以保證帶鋼出口厚度、溫度、板型等達(dá)到相應(yīng)要求.在精軋機(jī)組出口處一般裝有測(cè)厚儀、測(cè)溫儀、測(cè)寬儀和板型儀等各類儀表及傳感器,記錄并存儲(chǔ)了大量的現(xiàn)場(chǎng)數(shù)據(jù),為基于數(shù)據(jù)驅(qū)動(dòng)的故障檢測(cè)與診斷方法提供了大量的資源.

整個(gè)帶鋼熱連軋過(guò)程,我們關(guān)心的質(zhì)量變量為厚度、寬度及出口溫度等,尤其是出口厚度,是直接影響產(chǎn)品質(zhì)量的關(guān)鍵因素.出口厚度是由X射線測(cè)厚儀在最后一個(gè)機(jī)架的出口處測(cè)量,發(fā)生在前面機(jī)架的故障要等到X射線測(cè)厚儀測(cè)量到異常的厚度值,才能針對(duì)該故障進(jìn)行診斷,由此產(chǎn)生一個(gè)明顯的滯后延遲,給實(shí)際的生產(chǎn)運(yùn)行維護(hù)帶來(lái)了很多不便.因此,采用正確的質(zhì)量相關(guān)的故障檢測(cè)與診斷方法對(duì)保證帶鋼厚度符合要求具有重要的現(xiàn)實(shí)意義.

本文以某鋼鐵公司1700mm帶鋼熱連軋生產(chǎn)線為研究背景,利用以上7種模型對(duì)現(xiàn)場(chǎng)采集的兩組數(shù)據(jù)進(jìn)行質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)故障的檢測(cè).過(guò)程變量考慮為7機(jī)架的輥縫、軋制力、彎輥力(第一機(jī)架無(wú)彎輥)共20個(gè)變量,質(zhì)量變量考慮為精軋末機(jī)架的出口厚度.精軋機(jī)軋制過(guò)程變量及質(zhì)量變量分配情況如表3所示.

圖1 帶鋼熱連軋機(jī)布置圖Fig.1 Schematic layout of the hot strip mill

表3 過(guò)程及質(zhì)量變量分配表Table 3 Assignment table of process and quality variables

首先,考慮的故障為精軋機(jī)軋制過(guò)程中時(shí)常發(fā)生的第2、3機(jī)架之間冷卻水控制閥的執(zhí)行器故障,其不能按設(shè)定模式關(guān)閉,會(huì)對(duì)第3及之后機(jī)架的軋制力造成影響.由于機(jī)架本身AGC的作用,輥縫也相應(yīng)地發(fā)生變化,從而導(dǎo)致出口帶鋼厚度產(chǎn)生正向偏差,影響最終的產(chǎn)品質(zhì)量,故該故障為質(zhì)量相關(guān)的故障.該故障從第10s開(kāi)始,持續(xù)10s,在第20s左右結(jié)束,采樣間隔為10ms.

然后,考慮的故障為第5機(jī)架的彎輥力采樣值發(fā)生故障,其是一種階躍跳變故障.當(dāng)該故障發(fā)生時(shí),變量18會(huì)突然增大,而隨著AGC的反饋調(diào)節(jié)作用,后面兩個(gè)機(jī)架彎輥力的值也會(huì)發(fā)生相應(yīng)變化.但是,該故障只會(huì)引起帶鋼板型變化,對(duì)出口帶鋼厚度影響很小,故為質(zhì)量無(wú)關(guān)的故障.

按照表2中總結(jié)的質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)故障的監(jiān)測(cè)統(tǒng)計(jì)量,利用以上7種模型對(duì)現(xiàn)場(chǎng)采集的兩組能夠反映精軋機(jī)軋制過(guò)程的質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)故障樣本數(shù)據(jù)進(jìn)行檢測(cè),檢測(cè)結(jié)果如圖2及圖3所示.

通過(guò)圖2和圖3可以看出,對(duì)于帶鋼熱連軋生產(chǎn)過(guò)程中發(fā)生的質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)的故障,7種模型均可以給出明顯的報(bào)警.在故障報(bào)警率(Fault alarm rate,FAR)及故障檢測(cè)率(Fault detection rate,FDR)方面,對(duì)比結(jié)果如表4所示.

表4 故障報(bào)警率及故障檢測(cè)率對(duì)比結(jié)果Table 4 FAR and FDR comparison results

從表4的FAR和FDR對(duì)比情況來(lái)看,針對(duì)帶鋼熱連軋生產(chǎn)過(guò)程中發(fā)生的質(zhì)量相關(guān)的故障,雖然7種模型的FAR基本相似,但是FDR卻不盡相同,與另外5種模型相比,C-PLS和E-PLS模型具有更高的FDR;而對(duì)于帶鋼熱連軋生產(chǎn)過(guò)程中發(fā)生的質(zhì)量無(wú)關(guān)的故障,7種模型的FAR和FDR差別卻很小,其主要與本文所選擇案例的質(zhì)量變量較少,僅為精軋末機(jī)架出口厚度有關(guān).

從仿真結(jié)果來(lái)看,以上7種模型都使用了相關(guān)統(tǒng)計(jì)量對(duì)不同的子空間進(jìn)行質(zhì)量相關(guān)及質(zhì)量無(wú)關(guān)故障的檢測(cè).因此,未來(lái)的工作有必要進(jìn)一步深入分析空間分解對(duì)質(zhì)量相關(guān)故障檢測(cè)能力的影響問(wèn)題,進(jìn)而研究如何獲得過(guò)程變量與質(zhì)量變量之間精確的回歸系數(shù)以改善質(zhì)量相關(guān)故障的檢測(cè)性能.

圖2 質(zhì)量相關(guān)的故障檢測(cè)結(jié)果Fig.2 Quality-related fault detection results

圖3 質(zhì)量無(wú)關(guān)的故障檢測(cè)結(jié)果Fig.3 Quality-unrelated fault detection results

2 基于貢獻(xiàn)圖的質(zhì)量相關(guān)的故障診斷技術(shù)

當(dāng)常用的多元統(tǒng)計(jì)指標(biāo)T2及Q統(tǒng)計(jì)量超過(guò)了控制限,相關(guān)的基于PCR、PLS、CVA等方法的監(jiān)測(cè)模型可以給出明顯報(bào)警,提示生產(chǎn)過(guò)程出現(xiàn)異常狀況,但卻不能明確地提供與質(zhì)量相關(guān)的故障變量和故障種類.為了解決以上問(wèn)題,大量的基于多元統(tǒng)計(jì)的故障診斷方法涌現(xiàn)出來(lái),主要包括判別分析法[35?36]、基于相異因子的模式匹配方法[37?38]、基于結(jié)構(gòu)殘差的方法[39?41]、基于貢獻(xiàn)圖[42?45]及貢獻(xiàn)率[46?47]的方法等.在眾多的方法中,貢獻(xiàn)圖法及其相關(guān)改進(jìn)方法以其不需要對(duì)系統(tǒng)的結(jié)構(gòu)、原理及故障信息有深入的了解,近年來(lái)在與質(zhì)量相關(guān)的故障診斷中得到了廣泛應(yīng)用,被學(xué)術(shù)界和工業(yè)界廣泛研究和推廣.基于此,本部分將重點(diǎn)對(duì)質(zhì)量相關(guān)的故障診斷技術(shù)中常用的貢獻(xiàn)圖及其相關(guān)改進(jìn)方法進(jìn)行梳理總結(jié).

2.1 基于貢獻(xiàn)圖的方法

貢獻(xiàn)圖法的核心思想是當(dāng)與質(zhì)量相關(guān)的故障發(fā)生后,通過(guò)計(jì)算每一個(gè)變量對(duì)平方預(yù)報(bào)誤差(Squared prediction error,SPE)(也稱Q統(tǒng)計(jì)量)和T2統(tǒng)計(jì)量的貢獻(xiàn)進(jìn)行故障識(shí)別,具有較大貢獻(xiàn)的變量很可能是質(zhì)量相關(guān)的故障變量,但最終的故障原因還需要利用相關(guān)過(guò)程知識(shí)進(jìn)一步分析和確定.MacGregor等[48]最先提出了貢獻(xiàn)圖法;Miller等[49]嘗試將該方法應(yīng)用于過(guò)程質(zhì)量控制中;Louwerse等[50]將該方法應(yīng)用于基于PLS模型的批次過(guò)程判別分析中;李鋼等[51]提出了基于T-PLS模型的貢獻(xiàn)圖方法,并用統(tǒng)一的方式描述了所有變量對(duì)Qr,T2y,T2r,T2o的貢獻(xiàn)圖;Westerhuis等[52]和Conlin等[53]相繼討論了貢獻(xiàn)圖的控制限問(wèn)題,希望以此提高貢獻(xiàn)圖的故障診斷性能.

基于SPE統(tǒng)計(jì)量的貢獻(xiàn)圖法定義式如下:

基于T2統(tǒng)計(jì)量的貢獻(xiàn)圖法定義式如下:

2.2 基于重構(gòu)貢獻(xiàn)圖的方法

雖然貢獻(xiàn)圖法在實(shí)際的應(yīng)用中可以有效地診斷出對(duì)產(chǎn)品質(zhì)量影響比較大的故障變量,但由于實(shí)際的故障與征兆之間存在非單一的映射關(guān)系,使得利用該方法解釋故障的原因比較困難.基于此,Alcala等[54?55]提出了重構(gòu)貢獻(xiàn)圖(Reconstruction-based contribution,RBC)法,其利用沿著某一特定變量方向進(jìn)行重構(gòu)的故障檢測(cè)指數(shù)之和作為該變量的貢獻(xiàn)值.

按照

Dunia等[56]給出了基于SPE的沿任意方向的重構(gòu)形式;Yue等[57]給出了基于T2的重構(gòu)形式.將這兩種統(tǒng)計(jì)量表示成統(tǒng)一形式,則故障重構(gòu)指標(biāo)可以表示為

重構(gòu)的任務(wù)就是找到合適的fi使Index(zi)最小,從而找到準(zhǔn)確的故障辨識(shí)方向 ξi.對(duì)式(36)求偏導(dǎo)數(shù)并令其為0,可解得:

將式(37)代入式(38)可得:

式中, ξi可以是任意方向的故障,也可以是多維的故障矩陣.

RBC法在應(yīng)用中,當(dāng)故障幅值較大時(shí),能從理論上保證正確的診斷結(jié)果,較傳統(tǒng)的貢獻(xiàn)圖法更具有一般性,但該方法計(jì)算量相對(duì)較大,所闡述的物理意義不夠明確.基于此,Li等[58]將RBC法擴(kuò)展到更一般情況,提出了基于T-PLS模型的廣義RBC法,該方法既可以診斷傳感器故障,又可以分離帶有已知故障方向的過(guò)程故障.

根據(jù)故障重構(gòu)的結(jié)果,針對(duì)所有可能的故障類別Ξi,廣義RBC法定義式如下:

式中,?為Yue等[57]提出的由T2和SPE統(tǒng)計(jì)量合成的指標(biāo).

廣義RBC法利用一種新的質(zhì)量相關(guān)的故障檢測(cè)指標(biāo)?,將傳統(tǒng)的貢獻(xiàn)圖法與重構(gòu)的故障診斷思想相結(jié)合,提高了與質(zhì)量相關(guān)故障診斷的正確率,但該方法需要故障方向矩陣,限制了其廣泛應(yīng)用.基于此,Li等[59]提出了多向RBC法,該方法不需要故障方向矩陣,比傳統(tǒng)的RBC法的候選變量少很多,減小了計(jì)算復(fù)雜度,且對(duì)于單傳感器故障則完全退化為傳統(tǒng)的RBC法,具有較強(qiáng)的兼容性.

2.3 基于相對(duì)貢獻(xiàn)圖的方法

相對(duì)貢獻(xiàn)圖的概念最早是由Westerhuis等[52]提出的,在傳統(tǒng)貢獻(xiàn)圖法的基礎(chǔ)上引入了貢獻(xiàn)圖期望值的概念并將其作為比例因子.在實(shí)際的應(yīng)用中,由于計(jì)算期望值比控制限容易,所以使用基于期望值的相對(duì)貢獻(xiàn)圖法更簡(jiǎn)單,更適用于復(fù)雜工業(yè)過(guò)程的故障診斷.

式中,S=E[xxT].

同理,由式(39)和式(41)可得:

由式(43)和式(44)可以看出:盡管傳統(tǒng)貢獻(xiàn)圖法和RBC法的貢獻(xiàn)值表達(dá)形式不同,但它們的相對(duì)貢獻(xiàn)值的表達(dá)形式卻完全相同.

2.4 對(duì)比仿真研究

為了更清晰地了解傳統(tǒng)貢獻(xiàn)圖法、RBC法及相對(duì)貢獻(xiàn)圖法在質(zhì)量相關(guān)的故障診斷應(yīng)用中的有效性,仍然采用第1.6節(jié)中的帶鋼熱連軋過(guò)程案例對(duì)比仿真研究.故障診斷結(jié)果如圖4所示,符號(hào)“o”表示每個(gè)時(shí)間點(diǎn)所對(duì)應(yīng)的每個(gè)變量的診斷結(jié)果.

從圖4中可以看出,圖4(a)中只有故障變量3被診斷出來(lái),與實(shí)際情況不符;而圖4(b)和4(c)中故障變量3和故障變量10均被診斷出來(lái),與實(shí)際情況相符.隨著故障的傳播,其他的故障變量也被診斷出來(lái),診斷結(jié)果很好地反應(yīng)了實(shí)際的質(zhì)量相關(guān)故障的診斷過(guò)程,但相對(duì)貢獻(xiàn)圖法的計(jì)算量要比RBC法小很多.綜合來(lái)看,針對(duì)在精軋機(jī)軋制過(guò)程中質(zhì)量相關(guān)故障診斷的應(yīng)用性能上,相對(duì)貢獻(xiàn)圖法要好于RBC法及傳統(tǒng)的貢獻(xiàn)圖法.

圖4 質(zhì)量相關(guān)的故障診斷結(jié)果Fig.4 Quality-related fault diagnosis results

3 復(fù)雜工業(yè)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)研究現(xiàn)狀

復(fù)雜工業(yè)過(guò)程結(jié)構(gòu)龐大,生產(chǎn)過(guò)程內(nèi)部機(jī)理繁雜,運(yùn)行數(shù)據(jù)在記錄、傳輸過(guò)程中不可避免地含有各種噪聲、測(cè)量誤差及數(shù)據(jù)缺失等情況,導(dǎo)致了研究人員獲得的現(xiàn)場(chǎng)數(shù)據(jù)結(jié)構(gòu)復(fù)雜、品質(zhì)良莠不齊,難以尋找到合理的統(tǒng)計(jì)規(guī)律,即便經(jīng)過(guò)預(yù)處理之后的數(shù)據(jù)仍可能含有復(fù)雜特性,而當(dāng)前的質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)的研究主要集中在處理這些復(fù)雜工業(yè)過(guò)程運(yùn)行數(shù)據(jù)的特性上.基于此,本部分將面向復(fù)雜工業(yè)過(guò)程運(yùn)行數(shù)據(jù)的動(dòng)態(tài)、非線性、多模態(tài)、間歇等主要特性,對(duì)復(fù)雜工業(yè)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷方法的研究現(xiàn)狀進(jìn)行評(píng)述分析.

3.1 面向復(fù)雜工業(yè)過(guò)程的動(dòng)態(tài)特性

實(shí)際的工業(yè)生產(chǎn)過(guò)程并不完全處于穩(wěn)態(tài),而基本都是一個(gè)動(dòng)態(tài)的過(guò)程,雖然穩(wěn)態(tài)數(shù)據(jù)的協(xié)調(diào)方法和變量聚類較為簡(jiǎn)單,但并不符合工業(yè)現(xiàn)場(chǎng)的實(shí)際情況,無(wú)較大的應(yīng)用價(jià)值,因此必須利用動(dòng)態(tài)的理論思想對(duì)工業(yè)生產(chǎn)過(guò)程進(jìn)行分析.

傳統(tǒng)的PLS及其擴(kuò)展模型是基于穩(wěn)態(tài)數(shù)據(jù)建立的純代數(shù)結(jié)構(gòu),并不適合于描述動(dòng)態(tài)過(guò)程.為了描述實(shí)際工業(yè)過(guò)程的動(dòng)態(tài)特性,先后有多個(gè)學(xué)者提出了PLS及其擴(kuò)展模型的動(dòng)態(tài)改進(jìn)方法,這些方法大致可以分為三類:1)加入動(dòng)態(tài)濾波器的方法,如Kaspar等[60]提出的先利用動(dòng)態(tài)濾波器對(duì)輸入數(shù)據(jù)進(jìn)行預(yù)處理,再利用傳統(tǒng)的穩(wěn)態(tài)PLS方法回歸建模;2)與動(dòng)態(tài)模型相結(jié)合的方法,如Kaspar等[61]及Lakshminarayanan等[62]將外生變量自回歸(Auto-regressive exogenous,ARX)模型與PLS模型結(jié)合來(lái)刻畫生產(chǎn)過(guò)程的動(dòng)態(tài)特性;3)將生產(chǎn)過(guò)程的過(guò)去信息嵌入輸入數(shù)據(jù)矩陣中.

在以上三類動(dòng)態(tài)改進(jìn)方法中,第三類方法在基于PLS的質(zhì)量相關(guān)的故障檢測(cè)與診斷應(yīng)用中占大部分.Ricker[63]通過(guò)在輸入數(shù)據(jù)矩陣中增加歷史輸入信息,提出了一種基于有限脈沖響應(yīng)(Finite impulse response,FIR)的動(dòng)態(tài)PLS方法;Qin等[64]則將過(guò)去輸入、輸出信息同時(shí)嵌入數(shù)據(jù)矩陣中,提出了基于多變量滑動(dòng)自回歸(Auto-regressive moving average,ARMA)模型的動(dòng)態(tài)PLS方法,然而這些方法都不同程度上增加了輸入數(shù)據(jù)矩陣的維數(shù),難以應(yīng)用于實(shí)際的工業(yè)過(guò)程監(jiān)控.基于此,Chen等[65]提出了動(dòng)態(tài)PLS方法,并將其應(yīng)用于間歇過(guò)程的在線監(jiān)控中;Lee等[66]提出了基于動(dòng)態(tài)PLS的多重故障診斷方法;Fletcher等[67]提出了局部動(dòng)態(tài)PLS方法,并將其應(yīng)用于間歇過(guò)程建模中;Li等[58]和Liu等[68]先后將動(dòng)態(tài)T-PLS方法及動(dòng)態(tài)C-PLS方法應(yīng)用于動(dòng)態(tài)過(guò)程的質(zhì)量相關(guān)的過(guò)程監(jiān)測(cè)及故障診斷中;Jiao等[69]提出了基于自動(dòng)回歸滑動(dòng)平均模型(Auto-regressive moving average exogenous, ARMAX)的動(dòng)態(tài)最小二乘方法,并將其應(yīng)用于動(dòng)態(tài)輸入、靜態(tài)輸出過(guò)程的質(zhì)量相關(guān)的故障檢測(cè)中,取得了良好的效果.

同時(shí),在動(dòng)態(tài)PLS方法中,PLS及其擴(kuò)展模型的更新也是近年來(lái)一個(gè)值得關(guān)注的話題.Helland等[70]利用新數(shù)據(jù)和原模型參數(shù)進(jìn)行模型更新提出了遞推偏最小二乘(Recursive partial least squares, RPLS)算法;Qin[71]對(duì)該方法進(jìn)行補(bǔ)充,提出了分塊RPLS算法和兩種數(shù)據(jù)更新方法:移動(dòng)窗口法和遺忘因子法;Dong等[72]在前人研究工作的基礎(chǔ)上,將自適應(yīng)技術(shù)與T-PLS模型結(jié)合,提出了遞推T-PLS(Recursive total projection to latent structures,RTPLS)方法,實(shí)現(xiàn)了時(shí)變、動(dòng)態(tài)過(guò)程質(zhì)量相關(guān)的故障診斷,能夠很好地跟蹤過(guò)程的動(dòng)態(tài)變化,解決了傳統(tǒng)PLS模型確定之后,無(wú)法對(duì)工況變化做出反應(yīng)的缺陷.

此外,由于基于CVA的子空間方法能有效地對(duì)動(dòng)態(tài)系統(tǒng)辨識(shí),所以在監(jiān)控含有自相關(guān)的生產(chǎn)過(guò)程時(shí),能從根本上消除自相關(guān)對(duì)監(jiān)控指標(biāo)的影響. Wang等[73]率先嘗試將CVA方法應(yīng)用于連續(xù)生產(chǎn)過(guò)程監(jiān)控中;與此同時(shí),Negiz等[15]將基于CVA的狀態(tài)變化量與相關(guān)統(tǒng)計(jì)量相結(jié)合,應(yīng)用于牛奶巴氏殺菌過(guò)程監(jiān)控中,取得了良好的監(jiān)控效果.基于此,Russell等[16]將CVA方法應(yīng)用于TE(Tennessee eastman)過(guò)程的過(guò)程監(jiān)控中,并與PCA、動(dòng)態(tài)PCA(Dynamic principal component analysis, DPCA)的監(jiān)控效果做一對(duì)比,證明了CVA方法的優(yōu)越性;Jiang等[74]將CVA方法與貢獻(xiàn)圖法有效結(jié)合,應(yīng)用于TE過(guò)程的故障辨識(shí)中;曹玉蘋等[75]在傳統(tǒng)CVA方法的基礎(chǔ)上,進(jìn)一步地將過(guò)程數(shù)據(jù)和質(zhì)量數(shù)據(jù)空間精細(xì)化分解,使監(jiān)控系統(tǒng)在檢測(cè)故障的同時(shí),能夠有效地分析過(guò)程故障與產(chǎn)品質(zhì)量的關(guān)系,對(duì)實(shí)際工業(yè)應(yīng)用具有重要價(jià)值.

3.2 面向復(fù)雜工業(yè)過(guò)程的非線性特性

從嚴(yán)格意義上講,絕大多數(shù)的復(fù)雜工業(yè)過(guò)程變量之間、過(guò)程變量與質(zhì)量變量之間的相關(guān)關(guān)系都是非線性的,且隨著如半導(dǎo)體制造、生物發(fā)酵等工業(yè)過(guò)程的復(fù)雜化,數(shù)據(jù)的非線性特性變得尤為明顯,使得傳統(tǒng)的線性方法往往無(wú)法獲得滿意的效果.基于此,大量的PLS及其擴(kuò)展模型的非線性改進(jìn)方法涌現(xiàn)出來(lái),這些方法大多是針對(duì)基本模型的內(nèi)模型或外模型進(jìn)行改進(jìn).

非線性PLS方法最早由Wold等提出[76];Qin等[77]、Malthouse等[78]先后將神經(jīng)網(wǎng)絡(luò)技術(shù)引入到PLS建模體系中;Lindgren等[79]提出了核PLS (Kernel projection to latent structures,KPLS)方法,該方法通過(guò)核函數(shù)將原始變量的低維空間映射到高維空間,再用線性的PLS方法建模,由于該方法無(wú)需非線性優(yōu)化,模型訓(xùn)練較為容易,成為了面向非線性數(shù)據(jù)特性的質(zhì)量相關(guān)的故障診斷領(lǐng)域的主流方法.基于此,Zhang等[80]提出了基于多模塊的核PLS(Multi-block kernel partial least squares,MBKPLS)方法,并將其應(yīng)用于大規(guī)模生產(chǎn)過(guò)程的分散式故障診斷中;Peng等[81]提出了全核PLS(Total kernel projection to latent structures,T-KPLS)方法,并將其應(yīng)用于帶鋼熱連軋生產(chǎn)過(guò)程(Hot strip mill process,HSPM)質(zhì)量相關(guān)的故障診斷中;Zhao等[82]將全局函數(shù)與局部函數(shù)結(jié)合,提出了混合核T-PLS方法,并將其應(yīng)用于化工過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與辨識(shí)中;Mori等[83]提出了多向核PLS(Multiway kernel partial least squares,MKPLS)方法,并將其應(yīng)用于非線性間歇過(guò)程質(zhì)量相關(guān)的性能監(jiān)控中;Zhang等[84]提出了基于核C-PLS(Kernel concurrent projection to latent structures,KCPLS)的重構(gòu)方法,并將其應(yīng)用于非線性的青霉素發(fā)酵生產(chǎn)過(guò)程的故障診斷中;此外,該課題組[85]還提出了定向的核PLS(Directional kernel partial least squares,DKPLS)方法,建立了更直接的過(guò)程變量與質(zhì)量變量間的關(guān)系模型,并將其應(yīng)用于重?zé)V的生產(chǎn)過(guò)程監(jiān)控中;Luo等[86]提出了多線性PLS方法,并將其應(yīng)用于間歇過(guò)程的質(zhì)量預(yù)測(cè)及質(zhì)量相關(guān)的過(guò)程監(jiān)控中,取得了良好的效果.

同時(shí),面向具有非線性及動(dòng)態(tài)多重特性數(shù)據(jù)的工業(yè)過(guò)程,Liu等[87]提出了動(dòng)態(tài)全核PLS(Dynamic total kernel projection to latent structures, DT-KPLS)方法,并將其應(yīng)用于非線性動(dòng)態(tài)系統(tǒng)的質(zhì)量相關(guān)的過(guò)程監(jiān)控中;Jia等[88]通過(guò)在傳統(tǒng)的KPLS模型中引入遺忘因子,提出了動(dòng)態(tài)核PLS (Dynamic kernel partial least squares,D-KPLS)方法,并將其應(yīng)用于質(zhì)量相關(guān)的故障檢測(cè)中;鄧曉剛等[89]提出了基于核CVA(Kernel canonical variate analysis,KCVA)的故障診斷方法,其利用核函數(shù)完成了非線性空間到高維線性空間的映射,并在線性空間中使用CVA方法來(lái)辨識(shí)狀態(tài)空間模型,實(shí)現(xiàn)了具有非線性及動(dòng)態(tài)特性的連續(xù)攪拌反應(yīng)釜(Continuous stirred tank reactor,CSTR)系統(tǒng)的過(guò)程監(jiān)控;Tan等[90]將KCVA方法與獨(dú)立成分分析(Independent component analysis,ICA)方法有效結(jié)合,應(yīng)用于連續(xù)退火生產(chǎn)線的故障檢測(cè)與診斷中;Samuel等[91]將核密度估計(jì)方法與傳統(tǒng)的CVA方法有效結(jié)合,提出了一種新的KCVA方法,并利用TE過(guò)程仿真說(shuō)明了該方法在對(duì)具有非線性及動(dòng)態(tài)多重特性的工業(yè)過(guò)程進(jìn)行過(guò)程監(jiān)測(cè)的優(yōu)勢(shì).

3.3 面向復(fù)雜工業(yè)過(guò)程的多模態(tài)特性

復(fù)雜工業(yè)生產(chǎn)過(guò)程方案的變動(dòng)、產(chǎn)品類型的改變、外界環(huán)境的變化、原料和組分的變更等均會(huì)導(dǎo)致生產(chǎn)過(guò)程具有不同潛在過(guò)程特性的多種模態(tài),使得面向多模態(tài)生產(chǎn)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷問(wèn)題的研究面臨著較大的挑戰(zhàn).

針對(duì)多模態(tài)生產(chǎn)過(guò)程的質(zhì)量相關(guān)的故障檢測(cè)與診斷問(wèn)題,一些學(xué)者如 Hwang等[92]、Lane等[93]、Zhao等[94]在傳統(tǒng) PLS模型的基礎(chǔ)上提出了整體建模方法,但是這種方法所建立的模型無(wú)法準(zhǔn)確地刻畫所有的運(yùn)行模態(tài);而通過(guò)每種模態(tài)分別建模及分析的方法則需要根據(jù)各子模態(tài)間的相似度指標(biāo)分析或是利用聚類算法實(shí)現(xiàn)子模態(tài)之間的遷移,雖然可以獲取更多單一模態(tài)的獨(dú)立信息,但是很多有用的過(guò)程特性沒(méi)有得到深入的挖掘和理解,且當(dāng)模型結(jié)構(gòu)較為復(fù)雜時(shí),增加了在線實(shí)施的難度[94].

對(duì)于高斯混合模型(Gaussian mixture model, GMM)的多模態(tài)過(guò)程監(jiān)控方法,能夠監(jiān)控多操作條件及非線性的生產(chǎn)過(guò)程,近年來(lái)引起了不少學(xué)者如Yue等[95]、Yu等[96]、Qin等[95?96]、Yoo等[97]的關(guān)注,但在實(shí)際應(yīng)用中很難決定其局部模型的數(shù)量,且模型的訓(xùn)練較為復(fù)雜.針對(duì)該問(wèn)題,Peng等[98]將GMM法與傳統(tǒng)的PLS方法有效結(jié)合,提出了一種新的多重PLS方法和質(zhì)量相關(guān)的故障概率指標(biāo),并將其應(yīng)用于具有多模態(tài)特性的帶鋼熱連軋生產(chǎn)過(guò)程的質(zhì)量預(yù)測(cè)及故障監(jiān)測(cè)中,為多模態(tài)生產(chǎn)過(guò)程的過(guò)程監(jiān)控提供了一種新方法.

3.4 面向復(fù)雜工業(yè)過(guò)程的間歇特性

與連續(xù)生產(chǎn)過(guò)程相比,間歇過(guò)程具有過(guò)程機(jī)理復(fù)雜、規(guī)模龐大、工況多變、運(yùn)行環(huán)境惡劣、操作條件漂移、邊界條件模糊等特性,使得間歇過(guò)程的質(zhì)量相關(guān)的故障檢測(cè)與診斷問(wèn)題顯得更加復(fù)雜.針對(duì)該問(wèn)題,Nomikos等和Koori等的研究小組[99?100]率先在間歇過(guò)程的監(jiān)測(cè)及故障診斷中引入PLS方法,提出了多向PLS方法,其基本思想是將三維歷史數(shù)據(jù)展開(kāi)成二維數(shù)據(jù),再用傳統(tǒng)的PLS方法對(duì)間歇生產(chǎn)過(guò)程進(jìn)行監(jiān)控.基于此,Chen等[101]提出了間歇?jiǎng)討B(tài)PLS(Batch dynamic partial least squares, BDPLS)方法,并將其應(yīng)用于間歇過(guò)程的在線監(jiān)測(cè)中;¨Undey等[102]提出了間歇及半間歇過(guò)程的性能監(jiān)測(cè)及故障診斷框架;Facco等[103]提出了移動(dòng)平均PLS軟測(cè)量方法,并將其應(yīng)用于間歇過(guò)程的質(zhì)量評(píng)價(jià)中;Wang[104]提出了基于PLS的魯棒數(shù)據(jù)驅(qū)動(dòng)模型,并將其應(yīng)用于間歇過(guò)程的產(chǎn)品質(zhì)量預(yù)測(cè)中; Stubbs等[105]提出了多向間隔PLS方法,并將其應(yīng)用于間歇過(guò)程的性能監(jiān)測(cè)中;Peng等[23]提出了一種新的PCR方法,并將其應(yīng)用于具有多規(guī)格及多批次間歇特性的帶鋼熱連軋生產(chǎn)過(guò)程的質(zhì)量相關(guān)的故障檢測(cè)與診斷中;該課題組[106]還針對(duì)擁有多模態(tài)操作環(huán)境的間歇過(guò)程,提出了質(zhì)量相關(guān)的故障檢測(cè)與診斷框架,為間歇過(guò)程的過(guò)程監(jiān)控提供了一套新技術(shù)和解決方案.

同時(shí),基于時(shí)段的間歇過(guò)程統(tǒng)計(jì)建模方法得到了 Kesavan等[107]、¨Undey等[108]、Zhao等[109?111]、Lu等[112]研究人員的重視.該方法將多時(shí)段間歇過(guò)程劃分為若干個(gè)子時(shí)段,建立了基于子時(shí)段的統(tǒng)計(jì)分析模型并用于過(guò)程監(jiān)測(cè),克服了傳統(tǒng)多向統(tǒng)計(jì)分析方法在多時(shí)段間歇過(guò)程應(yīng)用中的難點(diǎn),提高了在線故障檢測(cè)的精度和靈敏度,促進(jìn)了對(duì)復(fù)雜工業(yè)過(guò)程的了解[111].然而,該方法在應(yīng)用中控制決策點(diǎn)的選取依然取決于對(duì)相關(guān)具體過(guò)程機(jī)理的深入了解和認(rèn)識(shí).基于此,Russell等[113]提出了更為一般的數(shù)據(jù)驅(qū)動(dòng)方法,該方法可以在任一過(guò)程時(shí)刻通過(guò)遞歸方式對(duì)產(chǎn)品質(zhì)量進(jìn)行在線監(jiān)控;Pan等[114]將該方法在甲基丙烯酸甲酯聚合過(guò)程中成功加以應(yīng)用,并獲得了較好的質(zhì)量監(jiān)控效果;Kaistha等[115]提出了一種基于處方的質(zhì)量改進(jìn)策略,并將其應(yīng)用于尼龍–66過(guò)程,減少了最終產(chǎn)品質(zhì)量的波動(dòng).

此外,復(fù)雜間歇過(guò)程生產(chǎn)線上經(jīng)常生產(chǎn)不同規(guī)格的產(chǎn)品,傳統(tǒng)的多元統(tǒng)計(jì)方法往往難以在新產(chǎn)品生產(chǎn)的初期進(jìn)行正常地監(jiān)測(cè),其原因在于只有當(dāng)生產(chǎn)過(guò)程數(shù)據(jù)存儲(chǔ)到一定數(shù)量時(shí),才能建立新產(chǎn)品的監(jiān)測(cè)模型,從而導(dǎo)致了大量的原材料消耗、不合格產(chǎn)品或事故的發(fā)生.因此,針對(duì)復(fù)雜間歇過(guò)程,能夠提出一種基于產(chǎn)品需求改變驅(qū)動(dòng)的監(jiān)測(cè)模型移植技術(shù)具有重要的工程意義.

復(fù)雜工業(yè)過(guò)程除了具有上述特性外,強(qiáng)耦合性、多批次、非高斯、分頻等也是其重要特性.從已獲得的研究成果來(lái)看,當(dāng)前質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)主要面向的是復(fù)雜工業(yè)過(guò)程的動(dòng)態(tài)及非線性特性,而對(duì)于多模態(tài)及間歇特性的研究成果還很少,更缺乏對(duì)復(fù)合特性的考慮,回避了該研究領(lǐng)域的本質(zhì)難點(diǎn).因此,有必要針對(duì)復(fù)雜工業(yè)過(guò)程的復(fù)合特性及復(fù)雜工況進(jìn)行綜合研究,突破復(fù)雜工業(yè)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)的關(guān)鍵問(wèn)題具有重要的研究?jī)r(jià)值.

4 總結(jié)與展望

本文對(duì)復(fù)雜工業(yè)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)的研究現(xiàn)狀進(jìn)行了較為全面的綜述,對(duì)相關(guān)的研究成果進(jìn)行了分類和評(píng)析,并通過(guò)帶鋼熱連軋過(guò)程案例對(duì)比分析了經(jīng)典方法在質(zhì)量相關(guān)的故障檢測(cè)與診斷上的不同性能.與傳統(tǒng)的故障檢測(cè)與診斷方法的研究狀況相比,質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)的研究還處于一個(gè)相對(duì)初步的探索階段,現(xiàn)有的方法大多是基于PLS及其擴(kuò)展模型的方法,且大多數(shù)方法是針對(duì)某一特定工況或應(yīng)用對(duì)象下的系統(tǒng),缺乏較為系統(tǒng)性的研究和分析.因此,有必要進(jìn)一步深入分析實(shí)際工業(yè)過(guò)程的復(fù)雜工況,研究新的質(zhì)量相關(guān)的故障檢測(cè)與診斷方法必將成為未來(lái)過(guò)程控制領(lǐng)域重要的研究方向.具體可以從以下幾個(gè)方向開(kāi)展研究工作:

1)統(tǒng)計(jì)過(guò)程監(jiān)測(cè)與過(guò)程知識(shí)相結(jié)合的質(zhì)量相關(guān)監(jiān)測(cè)模型建立問(wèn)題.基于數(shù)據(jù)驅(qū)動(dòng)的MSPM方法盡管在質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)中具有很強(qiáng)的通用性,但復(fù)雜工業(yè)生產(chǎn)過(guò)程內(nèi)部的機(jī)理和經(jīng)驗(yàn)知識(shí)的缺乏可能會(huì)導(dǎo)致質(zhì)量監(jiān)控信息的不準(zhǔn)確,如果能將監(jiān)控系統(tǒng)的模型、過(guò)程內(nèi)部機(jī)理和經(jīng)驗(yàn)知識(shí)相結(jié)合,使得不同的方法間優(yōu)勢(shì)互補(bǔ),可以提高過(guò)程監(jiān)測(cè)的性能,保證產(chǎn)品的質(zhì)量.

2)復(fù)雜間歇過(guò)程中過(guò)渡過(guò)程的質(zhì)量監(jiān)控問(wèn)題.針對(duì)復(fù)雜間歇過(guò)程中多時(shí)段特性及時(shí)段間的模糊過(guò)渡行為,深入研究潛在的過(guò)渡過(guò)程的相關(guān)特性與產(chǎn)品質(zhì)量間的關(guān)系很有必要,能有效地降低故障誤報(bào)率,提高產(chǎn)品的合格率.

3)質(zhì)量相關(guān)故障的傳播路徑跟蹤及故障定位問(wèn)題.復(fù)雜工業(yè)過(guò)程由成千上萬(wàn)個(gè)控制回路構(gòu)成,由于物料、能量及信息間的傳遞和反饋控制作用的存在,使得設(shè)備本身或外部擾動(dòng)等引起的故障很容易在回路間傳播,對(duì)生產(chǎn)過(guò)程的穩(wěn)定運(yùn)行和產(chǎn)品的質(zhì)量造成嚴(yán)重影響.因此,如何跟蹤質(zhì)量相關(guān)故障在回路間的傳播路徑,從而定位故障源并排除故障具有重要意義.

4)復(fù)雜動(dòng)態(tài)工業(yè)過(guò)程的多故障診斷問(wèn)題.當(dāng)復(fù)雜動(dòng)態(tài)工業(yè)過(guò)程同時(shí)發(fā)生多個(gè)故障時(shí),故障之間通常會(huì)表現(xiàn)出傳播特性,即異常狀態(tài)不僅可以使所在設(shè)備或子系統(tǒng)發(fā)生故障,而且還可能導(dǎo)致其他相關(guān)設(shè)備或子系統(tǒng)發(fā)生故障;此外,故障與原因之間的非單一映射關(guān)系使得復(fù)雜動(dòng)態(tài)工業(yè)過(guò)程的多故障診斷成為一個(gè)綜合而又復(fù)雜的問(wèn)題.因此,提出解決多故障診斷問(wèn)題的整體方案,突破復(fù)雜動(dòng)態(tài)工業(yè)過(guò)程多故障診斷領(lǐng)域的關(guān)鍵問(wèn)題,形成一套多故障診斷的綜合方法,不僅具有重要的學(xué)術(shù)價(jià)值,也是大量復(fù)雜動(dòng)態(tài)工業(yè)過(guò)程生產(chǎn)和運(yùn)行的迫切需求.

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Review of Quality-related Fault Detection and Diagnosis Techniques for Complex Industrial Processes

PENG Kai-Xiang1,2MA Liang1,2ZHANG Kai1,2

Quality-related fault detection and diagnosis techniques have been extensively applied to the process control fi eld to guarantee production safety and product quality,which,thus,have recently become an active area of research both in academia and industry.Firstly,the basic idea and improvements of typical methods for quality-related fault detection techniques are introduced in this paper.Then,quality-related fault diagnosis techniques are revisited,with special case study attention on the contribution plot based methods and their improved methods,in which on a hot strip mill process(HSMP)is used to show their di ff erent performances.Finally,the state-of-the-art research of quality-related fault detection and diagnosis methods for main characteristics of complex industrial process operation data are reviewed, and open problems,challenges and perspectives for future research are presented as well.

Quality-related,fault detection,fault diagnosis,partial least squares(PLS),contribution plot

彭開(kāi)香 北京科技大學(xué)自動(dòng)化學(xué)院教授. 2007年獲得北京科技大學(xué)控制科學(xué)與工程博士學(xué)位.主要研究方向?yàn)閺?fù)雜工業(yè)系統(tǒng)故障診斷與容錯(cuò)控制.E-mail:kaixiang@ustb.edu.cn(PENGKai-Xiang Professor at the School of Automation and Electrical Engineering,University of Science and Technology Beijing.He received his Ph.D.degree in control science and engineering from University of Science and Technology Beijing in 2007.His research interest covers fault diagnosis and fault-tolerant control for complex industrial system.)

馬 亮 北京科技大學(xué)自動(dòng)化學(xué)院博士研究生.2012年獲得華北理工大學(xué)控制理論與控制工程碩士學(xué)位.主要研究方向?yàn)閿?shù)據(jù)驅(qū)動(dòng)的故障診斷與容錯(cuò)控制.本文通信作者.E-mail:mlypplover@sina.com(MA Liang Ph.D.candidate at the School of Automation and Electrical Engineering,University of Science and Technology Beijing. He received his master degree in control theory and control engineering from North China University of Science and Technology in 2012.His research interest covers data-based fault diagnosis and fault-tolerant control.Corresponding author of this paper.)

張 凱 北京科技大學(xué)自動(dòng)化學(xué)院博士后,2016年獲得德國(guó)杜伊斯堡–艾森大學(xué)博士學(xué)位.主要研究方向?yàn)閿?shù)據(jù)驅(qū)動(dòng)故障診斷,統(tǒng)計(jì)過(guò)程監(jiān)控,診斷方法性能評(píng)估.E-mail:kai.zhang@uni-due.de(ZHANG KaiPostdoctoratthe School of Automation and Electrical Engineering,University of Science and Technology Beijing.He received his Ph.D.degree from the Institute of Automatic Control and Complex Systems,University of Duisburg-Essen,Germany in 2016.His research interest covers data-based fault diagnosis,statistical process monitoring,and performance assessment for fault diagnosis methods.)

彭開(kāi)香,馬亮,張凱.復(fù)雜工業(yè)過(guò)程質(zhì)量相關(guān)的故障檢測(cè)與診斷技術(shù)綜述.自動(dòng)化學(xué)報(bào),2017,43(3):349?365

Peng Kai-Xiang,Ma Liang,Zhang Kai.Review of quality-related fault detection and diagnosis techniques for complex industrial processes.Acta Automatica Sinica,2017,43(3):349?365

2016-06-03 錄用日期2016-10-14

Manuscript received June 3,2016;accepted October 14,2016國(guó)家自然科學(xué)基金(61473033)資助

Supported by National Natural Science Foundation of China (61473033)

本文責(zé)任編委胡昌華

Recommended by Associate Editor HU Chang-Hua

1.北京科技大學(xué)自動(dòng)化學(xué)院北京100083 2.鋼鐵流程先進(jìn)控制教育部重點(diǎn)實(shí)驗(yàn)室北京100083

1.School of Automation and Electrical Engineering,University of Science and Technology Beijing,Beijing 100083 2.Key Laboratory for Advanced Control of Iron and Steel Process of Ministry of Education,Beijing 100083

DOI10.16383/j.aas.2017.c160427