基于MKPCA的間歇過(guò)程故障檢測(cè)終

1、基于MKPCA的間歇過(guò)程故障檢測(cè)終 作者： 日期：2 個(gè)人收集整理 勿做商業(yè)用途基于多向核主元分析的啤酒發(fā)酵過(guò)程故障診斷模型摘要：針對(duì)主元分析故障診斷模型在非線性時(shí)變過(guò)程中應(yīng)用的局限性,基于間歇過(guò)程的周期性特點(diǎn)，將核變換理論引入非線性空間的數(shù)據(jù)特征提取中，提出了一種改進(jìn)的多向核主元分析故障診斷模型，有效地解決了過(guò)程數(shù)據(jù)的非線性問(wèn)題，保證數(shù)據(jù)信息抽取的完整性。通過(guò)與其他方法的對(duì)比實(shí)驗(yàn)，結(jié)果表明所提出的方法對(duì)緩慢時(shí)變的間歇過(guò)程具有良好的實(shí)時(shí)性和準(zhǔn)確性。關(guān)鍵詞：間歇過(guò)程 故障檢測(cè) 多向核主元分析 1 引言間歇過(guò)程是批次生產(chǎn)的重復(fù)過(guò)程，廣泛應(yīng)用于生物制藥、化工原料、食品等行業(yè)，其具有生產(chǎn)過(guò)程重復(fù)性高、

2、動(dòng)態(tài)特性變化快、建模困難等特點(diǎn),這導(dǎo)致傳統(tǒng)的故障診斷方法難以得到較好的應(yīng)用效果1。主元分析(principal component analysis, PCA)是多元統(tǒng)計(jì)過(guò)程監(jiān)測(cè)(multivariate statistical process monitoring， MSPM)的重要方法之一，但是PCA在過(guò)程建模時(shí)假定過(guò)程是線性的，這導(dǎo)致在具有強(qiáng)非線性生產(chǎn)過(guò)程的在線監(jiān)測(cè)中存在誤報(bào)率過(guò)高的現(xiàn)象2.近年來(lái)針對(duì)間歇過(guò)程提出的多向主元分析(MPCA)方法得到了較多的研究，然而MPCA實(shí)質(zhì)上仍是一種線性化建模方法,對(duì)復(fù)雜的非線性過(guò)程在線監(jiān)控的可靠性和實(shí)時(shí)性往往也難以保證3。針對(duì)非線性過(guò)程監(jiān)測(cè)的建模問(wèn)題

3、，Scholkopf等人將核函數(shù)理論引入到統(tǒng)計(jì)過(guò)程監(jiān)控中，將主元分析（PCA）方法推廣到代表非線性領(lǐng)域的高維特征空間，據(jù)此發(fā)展的KPCA模型可以從數(shù)據(jù)樣本中提取出非線性特征，與PCA算法相比,該方法表現(xiàn)出更優(yōu)的監(jiān)測(cè)性能4。本文針對(duì)間歇過(guò)程特點(diǎn)，將核函數(shù)理論應(yīng)用于多向主元分析中，提出一種改進(jìn)的多向核主元分析（MKPCA）過(guò)程故障監(jiān)測(cè)算法,并通過(guò)啤酒發(fā)酵過(guò)程的故障檢測(cè)實(shí)驗(yàn)對(duì)算法性能進(jìn)行了驗(yàn)證。個(gè)人收集整理，勿做商業(yè)用途本文為互聯(lián)網(wǎng)收集,請(qǐng)勿用作商業(yè)用途2 核主元分析（KPCA） 核主元分析通過(guò)非線性映射將輸入集合映射到一個(gè)高維特征空間，使數(shù)據(jù)具有更好的可分性,再對(duì)高維空間的映射數(shù)據(jù)進(jìn)行PCA處理，

4、得到非線性主元.KPCA不直接計(jì)算特征向量,而是將其轉(zhuǎn)化為求核矩陣的特征值和特征向量,避免了在特征空間求特征向量,而數(shù)據(jù)在特征向量上的投影轉(zhuǎn)換為求核函數(shù)的線性組合，大大簡(jiǎn)化了計(jì)算量5。首先通過(guò)非線性映射函數(shù)：，將輸入空間，k= 1, 2, , M映射到特征空間F：，k= 1, 2, ., M中,然后在該特征空間中對(duì)式(1)的協(xié)方差矩陣進(jìn)行線性主元分析。 （1）在特征空間中計(jì)算主元，可通過(guò)求解式(2）中的特征值和特征向量得到： （2）將每個(gè)樣本與式(2)作內(nèi)積，可得式(3)。 （3)因?yàn)槭剑?）的所有解均在張成的子空間內(nèi),所以存在系數(shù)使得式(4）成立。 （4)對(duì)式（2)、（3)和(4)進(jìn)行合并，

5、得式（5）. (5）取作為核函數(shù)，可得到式（6）. （6）式中，其特征向量所對(duì)應(yīng)的特征值為 ，為了提取主元特征，將投影到上可得到式（7）。 , （7)式（7）稱(chēng)為KPCA的第k個(gè)主元。3多向核主元分析故障診斷模型對(duì)于間歇過(guò)程其數(shù)據(jù)集比連續(xù)過(guò)程數(shù)據(jù)集多一維“批量”元素,每批數(shù)據(jù)都可以看作一個(gè)二維數(shù)據(jù)陣，多批數(shù)據(jù)則構(gòu)成了三維數(shù)據(jù)陣，其中I為批次數(shù)目,J為變量數(shù)目,K為采樣點(diǎn)數(shù)。將數(shù)據(jù)按批次方向展開(kāi)為，X的每一行均表示一個(gè)批次數(shù)據(jù)，如圖1示。 圖1 MKPCA建模三維數(shù)據(jù)矩陣展開(kāi)后,數(shù)據(jù)處理和分析過(guò)程等同于KPCA方法6。建模步驟如下： （1） 對(duì)于數(shù)據(jù)集按批次方向展開(kāi)成二維數(shù)據(jù)陣，并對(duì)其按式(8）

6、進(jìn)行標(biāo)準(zhǔn)化。 (8）式中：x(j)的樣本均值,S（j）-x(j）的樣本標(biāo)準(zhǔn)差。(2) 計(jì)算核矩陣K,記其元素為，其中： (9）(3) 在特征空間中,根據(jù)式（10）和（11）對(duì)核矩陣進(jìn)行標(biāo)定得到。 (10) （11)其中：。(4) 對(duì)核矩陣進(jìn)行特征值分解,并且使得滿(mǎn)足式（12）。 (12）(5) 對(duì)于每一個(gè)正常批次的數(shù)據(jù)x，根據(jù)式(7)提取其非線性主元。（6) 按式(13)和（14)構(gòu)建監(jiān)控統(tǒng)計(jì)量和SPE. （13) （14)（7） 按式（15）和（16）確定統(tǒng)計(jì)量的置信限. (15)其中：n為樣本個(gè)數(shù)，m為主元個(gè)數(shù)，是檢驗(yàn)水平為、自由度為m，n-1時(shí)的F分布臨界值. （16）其中:為建模所用數(shù)

7、據(jù)的協(xié)方差矩陣的特征值，是當(dāng)檢驗(yàn)水平為時(shí)的正態(tài)分布臨界值，M是全部主元個(gè)數(shù)，m為主元模型中的主元個(gè)數(shù).In this:is used in modeling of the data covariance matrix eigenvalue, is when the test level is normal distribution critical values, M is the total number of principal components, m as the number of principal components in the PCA model。運(yùn)用多向核主元法對(duì)間歇過(guò)

8、程進(jìn)行故障檢測(cè)的步驟如下：Using multiway kernel principal component method for fault detection of batch process，its steps are as follows：當(dāng)對(duì)批次進(jìn)行在線監(jiān)測(cè)時(shí)，僅可知自批次開(kāi)始時(shí)刻到監(jiān)測(cè)時(shí)刻的采樣數(shù)據(jù)。然而，監(jiān)測(cè)過(guò)程的測(cè)試數(shù)據(jù)應(yīng)為完整的批次數(shù)據(jù)。因此，需要對(duì)自監(jiān)測(cè)時(shí)刻至批次結(jié)束時(shí)刻的數(shù)據(jù)進(jìn)行估計(jì)。針對(duì)此問(wèn)題已經(jīng)提出了多種方法,本文采用各變量的均值來(lái)代替其估計(jì)值。When the on-line monitoring of batch， Only known, the sampling

9、 data since batch monitoring time to Monitoring time. However, test data of Monitor process shall be the complete batch data。 Therefore， need to be estimate data since monitored the moment to the end of batch moment。 The data since monitored the moment to the end of batch moment need to be estimated

10、。 To solve this problem， a variety of methods have been proposed， in this paper, using the mean of each variable to replace the estimates.(1) 在第k個(gè)采樣時(shí)刻，新的反應(yīng)批次數(shù)據(jù)為,展開(kāi)處理采集到的數(shù)據(jù),得到展開(kāi)后的數(shù)據(jù)矩陣,對(duì)此矩陣依據(jù)式(8)進(jìn)行標(biāo)準(zhǔn)化。(1） In the first k sampling time, The new reaction batch data is, processing sampled data get the unf

11、olded data matrix ， to standardize the matrix based on this type (8） .（2） 估計(jì)新批次未反應(yīng)完時(shí)刻的數(shù)據(jù)，補(bǔ)足第一步標(biāo)準(zhǔn)化后的數(shù)據(jù)矩陣，得到，作為完整的新批次數(shù)據(jù).(2） Estimation of the new batch did not react time data, supplying the first step of the standardized data matrix, getting as a new integrity batch data.(3） 根據(jù)式(9)計(jì)算測(cè)試數(shù)據(jù)相應(yīng)的核向量。(3） Ac

12、cording to equation (9) calculation the test data corresponding kernel vector （4） 根據(jù)式(17）對(duì)核向量作標(biāo)準(zhǔn)化處理得到.(4) To standardize kernel vector according to the type (17) getting (17）其中：K和在訓(xùn)練時(shí)得到,.Among them： K and obtained during training， （5） 根據(jù)式(18）提取非線性主元。（5) According to equation （18） extract nonlinear p

13、rincipal component. (18)(6) 按式(13）和(14）分別計(jì)算測(cè)試數(shù)據(jù)的和SPE統(tǒng)計(jì)量,并判斷是否超出了各自的置信限。如果出現(xiàn)超出其置信限的情況，則說(shuō)明過(guò)程中出現(xiàn)了故障。(6） According to formula （13） and （14） respectively to calculate the test data of theand SPE statistics， and determine whether it beyond the respective confidence limits. If there is a condition that bey

14、ond its confidence limits, then it appeared failure in the process。4 實(shí)驗(yàn)研究實(shí)驗(yàn)采用微型啤酒生產(chǎn)裝置，測(cè)試數(shù)據(jù)來(lái)自發(fā)酵過(guò)程監(jiān)控?cái)?shù)據(jù)。根據(jù)生產(chǎn)運(yùn)行中各變量的活躍程度和對(duì)生產(chǎn)狀態(tài)的影響，選擇溫度、壓力、液位、糖度、PH值和酒精度6個(gè)過(guò)程監(jiān)測(cè)變量，這些變量反應(yīng)了酵母菌菌體生長(zhǎng)和發(fā)酵產(chǎn)物的合成狀況.過(guò)程周期15天，每1小時(shí)采樣1次，每批次采樣360次。實(shí)驗(yàn)選取12個(gè)正常批次的數(shù)據(jù)建模。由于每一批次數(shù)據(jù)（為采樣次數(shù))的反應(yīng)時(shí)間不同，因此，在將轉(zhuǎn)換成之后,對(duì)多于2160列的直接截取到2160列，對(duì)不足2160列的批次補(bǔ)零，然后將矩陣排列

15、成形式,進(jìn)行標(biāo)準(zhǔn)化處理，核函數(shù)采用徑向基核函數(shù)，按93%的累計(jì)貢獻(xiàn)率提取主成分.其中，MPCA算法的主元數(shù)目為2；而MKPCA算法的主元數(shù)目為4。可以看出，MKPCA算法所選的主元數(shù)目高于MPCA算法所選的主元數(shù)目，這是由于前者從高維特征空間中提取主元,而后者從輸入空間中提取主元.4。The experimental studyThis experiment used device for miniature beer production， testing data from the fermentation process control data. According to the ac

16、tive degree of each variable in the production function and the influence on the production status， choosing the temperature, pressure， liquid level, sugar degree， PH value and alcohol degree, six process monitoring variables， these variables has been synthesized by the reaction of yeast cell growth

17、 and the fermentation products. 15 days as a process cycle， sampling 1 times every 1 hours, each batches samples 360 times. The experiment selected 12 normal batches of data modeling。 Because each batch of data (is the number of sampling） of different reaction time, Therefore, after convertingto , d

18、irecting interception of more than 2160 to 2160, to less than 2160 batches of zero padding, then the matrix is arranged in the form of , standard treatment, kernel function using rbf kernel function， According to 93 of the contribution rate to extract principal component。 Among them, principal compo

19、nent number of the MPCA algorithm is 2； The principal component number of MKPCA algorithm is 4. It is shown that principal component number selected in MKPCA algorithm is higher than that selected in MPCA algorithm。 This is due to the former from high dimensional feature space to extract the princip

20、al component， and the latter from the input space to extract the principal component.個(gè)人收集整理，勿做商業(yè)用途文檔為個(gè)人收集整理，來(lái)源于網(wǎng)絡(luò) Figure 4 PCA statistics monitoring chart Figure 4 PCA SPE statistics monitoring chart Figure 4 MPCA statistics monitoring chart Figure 5 MPCA SPE statistics monitoring chart Figure 4 MKP

21、CA statistics monitoring chart Figure 4 MKPCA SPE statistics monitoring chart對(duì)啤酒發(fā)酵過(guò)程進(jìn)行在線監(jiān)測(cè)，在317-360采樣時(shí)刻引入壓力傳感器故障，對(duì)測(cè)試數(shù)據(jù)分別采用PCA算法、MPCA算法和MKPCA算法進(jìn)行在線監(jiān)測(cè).PCA的和SPE監(jiān)測(cè)結(jié)果如圖2,3所示。MPCA的和SPE監(jiān)測(cè)結(jié)果如圖4，5所示。MKPCA的和SPE監(jiān)測(cè)結(jié)果如圖6，7所示。The online monitoring of the beer fermentation process, The pressure sensor fault was in

22、troduced in 317-360 sampling time， PCA algorithm， MPCA algorithm and MKPCA algorithm were used for the online monitoring of beer fermentation process. The monitoring results of statistics and SPE statistics about PCA were shown in Figure 2, 3. The monitoring results of statistics and SPE statistics

23、about MPCA were shown in Figure 4, 5. The monitoring results of statistics and SPE statistics about MKPCA were shown in Figure 6， 7.個(gè)人收集整理，勿做商業(yè)用途個(gè)人收集整理,勿做商業(yè)用途實(shí)驗(yàn)結(jié)果分析：圖1中PCA的統(tǒng)計(jì)量在故障時(shí)刻不能檢測(cè)出壓力傳感器故障的存在,并且在第12和34采樣時(shí)刻還存在著故障誤報(bào)現(xiàn)象，圖2中PCA的SPE統(tǒng)計(jì)量在317360采樣時(shí)刻能夠及時(shí)的檢測(cè)出故障。由于統(tǒng)計(jì)量沒(méi)有檢測(cè)出過(guò)程故障而SPE統(tǒng)計(jì)量檢測(cè)出了過(guò)程故障，所以PCA算法不能實(shí)現(xiàn)對(duì)啤酒發(fā)

24、酵過(guò)程的監(jiān)測(cè)；從圖3、4中可以看出，當(dāng)采用MPCA算法在線監(jiān)測(cè)時(shí)，圖3的統(tǒng)計(jì)量在317351采樣時(shí)刻并沒(méi)有檢測(cè)出過(guò)程故障,而在352-360采樣時(shí)刻檢測(cè)出了過(guò)程故障，所以MPCA算法的統(tǒng)計(jì)量應(yīng)用在啤酒發(fā)酵過(guò)程時(shí)存在檢測(cè)滯后的現(xiàn)象，即不能及時(shí)檢測(cè)出故障。圖4的SPE統(tǒng)計(jì)量在317360采樣時(shí)刻能夠及時(shí)的檢測(cè)出了過(guò)程故障。同理，MPCA算法也不能及時(shí)準(zhǔn)確的實(shí)現(xiàn)對(duì)啤酒發(fā)酵過(guò)程的在線監(jiān)測(cè);從圖5、6中可以看出，通過(guò)引入核函數(shù)并結(jié)合MPCA算法復(fù)合而成的MKPCA算法的統(tǒng)計(jì)量和SPE統(tǒng)計(jì)量都能及時(shí)準(zhǔn)確的檢測(cè)出過(guò)程故障，而且不存在誤報(bào)現(xiàn)象。因此采用MKPCA算法用于啤酒發(fā)酵過(guò)程的在線監(jiān)測(cè)較PCA算法和MP

25、CA算法可靠。Analysis of experimental results: The pressure sensor fault can not be detected in the fault time from the statistics of PCA in figure 1,and there are fault misreporting phenomenon in the 12 and 34 sampling time. The pressure sensor fault can be detected in the 317360 sampling time from the S

26、PE statistics of PCA in figure 2 in time. Because the pressure sensor fault cant be detected from the statistics and the pressure sensor fault can be detected from the SPE statistics。 So PCA algorithm can't be used for the online monitoring of beer fermentation process。 As can be seen from the f

27、igure 3， 4, When using MPCA algorithm online monitoring, Figure 3,the statistics in 317351 the sampling time didnt detect process faults , however， the process faults were monitored in 352-360 sampling times， therefore， the application of the statistics of MPCA algorithm for the online monitoring of

28、 beer fermentation process exist the phenomenon of hysteresis. That can't detect the fault in time. Figure 4， SPE statistics in 317-360 sampling time can detected the process fault timely。 In the same way, MPCA algorithm can't timely and accurately realize the online monitoring of the beer f

29、ermentation process; In the figure 5and 6, by introducing kernel function and combining the MPCA algorithm of composite MKPCA T statistic and SPE statistics of the algorithm can accurately and timely detect process faults, and there is no false positives。 Above all, Using MKPCA algorithm is better t

30、han PCA algorithm and MPCA algorithm文檔為個(gè)人收集整理,來(lái)源于網(wǎng)絡(luò)文檔為個(gè)人收集整理,來(lái)源于網(wǎng)絡(luò)通過(guò)實(shí)驗(yàn)結(jié)果可知，引入非線性核函數(shù)能夠充分提取過(guò)程中存在的非線性信息，有效計(jì)算出高維特征空間中的主元。與PCA和MPCA算法相比,MKPCA算法表現(xiàn)出更好的監(jiān)測(cè)性能，更適于對(duì)非線性間歇過(guò)程進(jìn)行在線監(jiān)測(cè)。Through the experimental results we can know that by introducing the nonlinear kernel function can fully extract the nonlinear inform

31、ation which existed in the process, principal component in the high dimensional feature space can be calculated effectively. Compared with PCA and MPCA algorithm， MKPCA algorithm shows better monitoring performance， more suitable for online monitoring of nonlinear batch process。5 結(jié)論本文針對(duì)間歇發(fā)酵過(guò)程緩慢時(shí)變和非線

32、性等特點(diǎn)，利用核理論方法對(duì)MPCA算法進(jìn)行了改進(jìn),提出了適用的多向核主元分析故障診斷算法。通過(guò)引入非線性核函數(shù)，能夠充分提取過(guò)程中存在的非線性信息,有效計(jì)算出高維特征空間中的主元，并將研究結(jié)果應(yīng)用于啤酒發(fā)酵過(guò)程監(jiān)測(cè)。通過(guò)與PCA算法、MPCA算法進(jìn)行對(duì)比實(shí)驗(yàn)表明所提出的模型可以有效處理間歇過(guò)程批次間存在的非線性屬性，獲取過(guò)程變量間的非線性關(guān)系，提高了故障診斷的及時(shí)性和準(zhǔn)確性.5 ConclusionThis article based on the intermittent fermentation process slow time-varying， nonlinear and other

33、characteristics， using of kernel theory method improved the MPCA algorithm， it puts forward the suitable multiway kernel principal component analysis algorithm for fault diagnosis。 By introducing nonlinear kernel function， to fully extract the nonlinear information which exist in the process. Effect

34、ively calculate the principal component in the high dimensional feature space， and the research results can be applied to beer fermentation process monitoring. Through with the PCA algorithm and the MPCA algorithm comparative experiments ,it show that the existence of the nonlinear property where am

35、ong batch process batch can be effectively treated by the programs model what have been proposed， obtaining the nonlinear relationship among the process variables, Improving the timeliness and accuracy of fault diagnosis。文檔為個(gè)人收集整理,來(lái)源于網(wǎng)絡(luò)個(gè)人收集整理，勿做商業(yè)用途參考文獻(xiàn)1 C. Zhang， Y。 Li, Study on the faultdetection method in batch process based on statistical pattern analysis, Yi Qi Yi Biao Xue Bao/Chinese Journal of