基于改进PCA的自适应统计过程监控毕业论文外文翻译.docx

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1、外文资料Adaptive Statistic Process Monitoring with a Modified PCALiu Yiqi, Huang Daoping, Li YanCollege of Automation Science and EngineeringSouth China University of TechnologyGuang Zhou, Chinae-mail: liuyiqi769AbstractIn this paper, we propose a modified adaptive PCA method for process monitoring. The

2、 basic idea of our approach is to use the modified PCA to adaptively extract the essential feature components that drive a process and combine them with process monitoring techniques. The Combined Index chart, which puts SPE statistic and T2 statistic together, is presented as online monitoring char

3、t and then contribution plot of this statistical quality is also considered for fault identification. The proposed monitoring method was applied to fault detection and identification in a wastewater treatment plant (WWTP). The simulation results clearly show the power and advantages of the modified

4、PCA monitoring in comparison to classical PCA monitoring Keywords： component; Modified PCA; Classical PCA;Combined Index; wastewater treatmentI. INTRODUCTIONModern industrial processes are large scale interconnected systems. Thus, efficiency of any data-driven monitoring scheme depends upon its abil

5、ity to compress a huge amount of process data and extract the meaningful information within. One of the most common multivariate statistical process control (MSPC) methods used for this purpose is principal component analysis (PCA). Lots of papers have illustrated the advantage of PCA in process mon

6、itoring1,2, dimension reduction 3,4, fault identification5, control and data reconstruction6.Despite its tremendous success, monitoring based on classical PCA is quite complicated and time invariant. Most real industrial processes often suffer from time varying behavior, such as equipment aging and

7、sensor drifting. However, false alarms often result, which significantly compromise the reliability of the monitoring system, when a time invariant PCA model is used to monitor processes with the aforementioned normal changes. Therefore, it is necessary to develop a method that adapts the underlying

8、 PCA model in a continuous and automatic manner in compliance with present process conditions. In fact, there are a few approaches that have already been developed. Wold7 presented the use of exponentially weighted moving average (EWMA) filters in conjunction with PCA and PLS. Li et al.8 used algori

9、thms utilizing rank-one modification and Lauczos tridiagonalization for recursive PCA and considered other essential issues including recursive update of the mean, the number of principal components, and the confidence limits. Another approach is to accommodate the operating condition changes using

10、moving window technique. The fast MWPCA proposed by Wang et al.9 enables online application of a generic moving window-based recursive PCA with a larger window size. To overcome the difficulty of incipient fault detection, a N-Step-Ahead predictor is also proposed. Recently, Liu et al.10 have also p

11、resented the so-called moving window kernel PCA for adaptive monitoring of nonlinear processes. The adaptation mechanism is based on the incremental method. The data covariance matrix is normalized after projecting it to the feature space and an approximate eigen decomposition can be computed with t

12、he help of up and down dating procedure.However, the Moving window PCA shows high sensitivity on fault detection but performs bad tracking process changes. On the contrary, exponentially weighted PCA is good at tracking process changes but bad at the other field. Thus, in this work, we combine the M

13、oving window PCA and Exponentially weighted PCA, and resulting in a modified PCA, which not only shows high sensitivity on fault detection, but also performs better tracking process changes. Furthermore, the occurrence of a fault usually leads to changes in either SPE or T2 or both. The faulty SPE a

14、nd T2 can exceed the control limits if a fault is large enough. Fault detection and identification should be formulated in terms of both indices. These will make index more convenient than two indices. At the same time, the Combined Index (CI) is extended to an adaptive way, the false alarms are hen

15、ce reduced in a flexible way. The paper is organized as follows. Section 2 provides a theoretical background to PCA monitoring. Section 3 describes a modified adaptive PCA algorithm and extends its adaptive characteristics to the confidence limit of the combined index. A wastewater treatment process

16、 case study is presented in Section 4, which is followed by a conclusion in Section 5.II. THE THEORY REVIEW OF CLASSICAL PCA MONITORINGPCA can handle high dimensional, noisy, and correlated data by projecting the data onto a lower dimensional subspace which contains most of the variance of the origi

17、nal data. PCA decomposes the data matrix XRnm (where n is the number of samples and m is the number of variables) as the sum of the outer product of vectors ti and pi plus the residual matrix E. (1)where ti is a score vector which contains information about relationship between samples, and pi is a

18、loading vector which contains information about relationship between variables. The portion of the measurement space corresponding to the lowest m-k singular values can be monitored by using the squared prediction error (SPE), also called the Q statistic11. The SPE is defined as the sum of squares o

19、f each row (sample) of E; for example, for the kth sample vector in X, x(k)Rm: (2)where e(k) is the kth sample vector of E, lk is the matrix of the first lk loading vectors retained in the PCA model, and l is the identity matrix. The upper confidence limit for the SPE can be computed from its approx

20、imate distribution. (3)where c is the standard normal deviate corresponding to the upper 1- percentile, j is the eigenvalues associated with the jth loading vector,i=j=lk+1mji for i=1,2,3 and h0=1-213322 .A measure of the variation with in the PCA model is given by Hotellings T2 statistic. T2 at sam

21、ple k is the sum of the normalized squared scores, and is defined as(4)Where -1 is the diagonal matrix of the inverse of the eigenvalues associated with the retained principal components. The upper confidence limit for T2 is obtained using the F distribution (5) where n is the number of samples in t

22、he data and lk is the number of principal components.III. A MODEFIED PCA MONITORINGThe modified PCA is presented combining the characteristics of both MWPCA and EWPCA. Its algorithm scheme is similar with EWPCA, while moving window technique and adaptive Combined Index confidence limit are incorpora

23、ted in order to make the algorithm adaptively and reduce the false alarms when using classical PCA.A. Fault Detection Using a Combined IndexFrom the practical experience, the SPE and T2 indices behave in a complementary manner. Therefore, it is possible to combine two indices into one to simplify th

24、e fault detection task. In this section, such an index is presented, which incorporates the SPE and T2 in a balanced way. The confidence limit is also established.In reality, one index is more convenient than two indices. Yue and Qin12 propose a combined index for fault detection that combines the S

25、PE and T2 as follows (6) (7)Notice that is symmetric and positive definite. The confidence limit of combined index is calculated using approximate multinomial distribution. The distribution of can be approximated using g(h)2 (8)where the confidence g is given by (9)and the degree of freedom for the

26、2 distribution is (10)j is the jth eigenvalue of the matrix S with a multitude vj, where S=cov(x). If all the eigenvalues are distinctive, vj=1. After g and h are calculated, the confidence limit of can obtained for a given confidence level. For a confidence level r, a fault is detected by if (11)B.

27、 Recursive Determinations of PCs Cumulative Percent VarianceThe CPV is a measure of the percent variance captured by the first lk PCs: (12)Since only the first lk eigenvalues are calculated in the block-wise RPCA, we use the following formula: (13)The number of PCs is chosen when CPV reaches a prede

28、termined limit, say 95%.C. The Scheme of the Modified PCAThe modified PCA is presented combining the characteristics of both MWPCA and EWPCA. Its algorithm scheme is similar with EWPCA, while the data for mean, variance and correlation matrix structure is updating when the window is moving. Addition

29、ally, a combined index is used and updated real time. The modified algorithm is outlined below. 1) Initialize PCA model parameter based on training data. Initialize parameters as follows: （14） （15）where Rt=0 is the correlation matrix, 0 is the initial weighting factor, n0 is the initial sample size.

30、2) Obtain the next testing sample x. Scale it using current scaling parameters.3) Evaluate the combined monitoring index for the testing sample using the current PCA model. Check the combined statistic with control limit. If not exceeded, update the moving window by deleting the oldest data measurem

31、ent and concatenating new sample x to the moving window, and turn to step 4, else turn to step 2.4) Update the correlation matrix: (16)Update the PCA model based on the new correlation matrix R. Other parameters are updated as follows: (17) (18) (19) (20)IV. APPLICATION TO A WASTEWATER PROCESSA. Pro

32、cess DescriptionThis is a particularly interesting case study for the proposed methodology. The biological wastewater treatment plant investigated in this work is Activated Sludge, which is a common example of a wastewater treatment process. It is designed for the removal of organic matter and nutri

33、ents. In this process the influent rate and composition are variables, the population of microorganisms varies overtime (both in quality and number of species), There is really need to monitor the whole process, especially the output variables, which would result in a significant influence on citize

34、ns life. As shown in Fig 1, the proposed wastewater plant process (UCI 1999) comprises of four elements: Pretreatment, Primary Settlers, Aeration Tankers and Secondary Settlers. Also, the parameters needed to be measured are presented.Fig1. Wastewater plant processB. Results and DiscussionsIn this s

35、ection, we apply the proposed PCA to a wastewater process and compare it with the classical PCA in the contribution plot and sensors validity index. The modified PCA algorithm proposed here was tested for its ability to detect abrupt changes in WWTP from UCI database. The data covered a period of on

36、e year and a half. 200 samples were utilized for training classical PCA model and the modified adaptive PCA model; the remaining 200 samples were used for test the performance of models. We selected 19 variables, listed in Table 1, from among the many variables used in the WWTP. These variables were

37、 chosen because they are typically monitored and important variables in WWTP systems.TABLE I. THE PARAMETERS SELECTED FORMONITORINGTwo types of conditions were tested using proposed method, normal condition and abrupt disturbances. As Fig. 2 displays in normal condition, there are many false alarms

38、T2 statistic of classical PCA not just in training stage but also in testing stage.However, as can be noted in Fig. 3, the modified PCA offers a good performance after going into the testing stage and updating the model real time. Apart from the normal condition, we add an abrupt change in the varia

39、ble 14, i.e. pH of effluent, which is important wastewater treatment in WWTP. It can be seen from Fig. 4 that both SPE statistic and when using SPE statistic and T2 statistic can detect the fault, although T2 statistic is not so good. Nonetheless, there are still many false alarms occurring before r

40、eal fault happens. Unlike classical PCA and their statistics, not only the fault is detected, but also few false alarms happen. In addition, the contribution plot method is applied herein, which calculates the contribution to the Combined Index from each sensor (Figure 6). It is obvious that the fou

41、rteenth sensor makes the most contribution and thus can be treated as a faulty sensor.Fig 2. Classical PCA monitoring with SPE and T2 when no faultFig 3. Modified adaptive PCA monitoring with CI and no faultFig 4. Classical PCA monitoring with SPE and T2 when fault occurredFig 5. Modified adaptive P

42、CA monitoring with CI when fault occurredFig 6. Contribution plot using CIV. CONCLUSIONS Due to parameter changes in the most of the real industrial processes, it is necessary to develop an adaptive monitoring scheme to deal with it. In this paper, we have proposed such an algorithm based on mixture

43、 of EWPCA and MWPCA. Furthermore, an adaptive Combined Index confidence limit is integrated into the algorithm. These significantly reduce the false alarms compared to classical PCA. The monitoring system is applied to a wastewater treatment plant from UCI database, and results are demonstrated with

44、 frequently occurring process scenarios. In the current work, the reconstruction of a measurement vector when excluding outliers is not taken into account. In future work, the modified algorithm proposed here could be integrated with reconstruction techniques and used for pretreatment in the soft se

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