Improved multi-scale kernel principal component analysis and its application for fault detection

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1 chemical engineering research and design 9 ( ) Contents lists available at SciVerse ScienceDirect Chemical Engineering Research and Design j ourna l ho me page: Improved multi-scale kernel principal component analysis and its application for fault detection Yingwei Zhang, Shuai Li, Zhiyong Hu Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang, Liaoning 114, PR China a b s t r a c t In this paper the multiscale kernel principal component analysis (MSKPCA) based on sliding median filter (SFM) is proposed for fault detection in nonlinear system with outliers. The MSKPCA based on SFM (SFM-MSKPCA) algorithm is first proposed and applied to process monitoring. The advantages of SFM-MSKPCA are: (1) the dynamical multiscale monitoring method is proposed which combining the Kronecker production, the wavelet decomposition technique, the sliding median filter technique and KPCA. The Kronecker production is first used to build the dynamical model; (2) there are more disturbances and noises in dynamical processes compared to static processes. The sliding median filter technique is used to remove the disturbances and noises; (3) SFM-MSKPCA gives nonlinear dynamic interpretation compared to MSPCA; (4) by decomposing the original data into multiple scales, SFM-MSKPCA analyze the dynamical data at different scales, reconstruct scales contained important information by IDWT, eliminate the effects of the noises in the original data compared to kernel principal component analysis (KPCA). To demonstrate the feasibility of the SFM-MSKPCA method, its process monitoring abilities are tested by simulation examples, and compared with the monitoring abilities of the KPCA and MSPCA method on the quantitative basis. The fault detection results and the comparison show the superiority of SFM-MSKPCA in fault detection. 211 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Sliding median filter (SFM); Multiscale kernel principal component analysis (MSKPCA); MSPCA; Fault detection; Design; Control 1. Introduction In most chemical plants, on-line monitoring and fault diagnosis of the process operating performance are gaining importance for plant safety and product quality in a process (Qin et al., 21; MacGregor and Kourti, 1995; Kourti et al., 1995; Zhang et al., 21a,b,c; AUndey et al., 23). Multivariate statistical methods has been extensively researched over the last decade for extracting process information from massive data and interpreting them have been developed in various fields (Martin and Morris, 22; Dzykowski et al., 23), such as principal component analysis (PCA) (Qin, 23; Wang et al., 25; Chiang et al., 21), partial least squares (PLS)(Kruger et al., 21; Zhang et al., 26) and more recently independent component analysis (ICA) (Ge and Song, 27; Lee et al., 24a,b,c, 26; Kano et al., 23) have been widely applied in industry for process monitoring. Among them, PCA is the most popular one, which combined with T 2 and Q monitoring charts together with contribution plots have been developed and widely used in the many chemical/biological processes. PCA determines the most accurate lower dimensional representation of the data, in terms of capturing the data directions that have the most variance. The resulting lower dimensional model has been used for detecting out-of-control status and for diagnosing faults leading to the abnormal process operation. Typically, the Hotelling s T 2 statistic and Q statistic are used to describe the pattern variations in the principle component subspace and residual subspaces, respectively. The conventional PCA monitoring is static linear transformation in nature, while most of industrial processes have nonlinear characteristics and process data have dynamical properties. The conventional PCA may lead to false-alarm when applying to process monitoring. Many process monitoring methods have been developed (Westerhuis et al., 1998; Qin Corresponding author. addresses: zhangyi@che.utexas.edu, zhangyingwei@ise.neu.edu.cn (Y. Zhang). Received 15 June 211; Received in revised form 1 November 211; Accepted 22 November /$ see front matter 211 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:1.116/j.cherd

2 1272 chemical engineering research and design 9 ( ) et al., 21; Kramer, 1991; Tan and Mavrovouniotis, 1995; Dong and McAvoy, 1996; Hiden et al., 1999; Shao et al., 1999; Schökopf et al., 1998; Lee et al., 24a,b,c; Thornhill et al., 22). For handling nonlinear processes, a nonlinear PCA based on an auto-associative neural network with a five-layer structure is proposed (Kramer, 1991). Alternative nonlinear PCA methods based on input-training neural networks have been also developed (Tan and Mavrovouniotis, 1995). Dong and McAvoy (1996) proposed a nonlinear PCA based on principal curves and neural networks and applied it to nonlinear process monitoring. Hiden et al. (1999) suggested non-linear principal components analysis using genetic programming. Shao et al. (1999) proposed a nonlinear PCA based upon an input-training neural network. Schökopf et al. (1998) proposed a kernel PCA which used kernel functions to complete nonlinear transformation. Lee et al. (24a,b,c) used this method for nonlinear process monitoring and showed better performance in most industrial applications. Although these nonlinear methods have been successful in many practical situations, their applications are usually restricted to analyzing the events only at a single static scale corresponding to the sampling frequency. However, data from almost all practical processes are inherently dynamical multiscale due to events occurring at different locations and with different localization in time and frequency. With the help of Kronecker production and wavelet analysis, the data can be represented at several different dynamical scales. To consider this multi-scale nature in process monitoring, there has been significant interest in combining the conventional PCA with wavelet transforms (Bakshi, 1998; Misra et al., 22; Rosen and Lennox, 21; Zhang and Ma, 211). Those PCA-based process monitoring methods employ wavelet analysis to transform time-domain signals into the time-frequency domain. Especially, Bakshi (1998) proposed the multiscale PCA methodology, which determines separate PCA models at each wavelet scale. The scales where significant events occur are recombined to obtain a PCA model for all scales together. Multiscale PCA is useful for modeling data containing contributions that change over time and frequency. Although the most noise in the process data can be filtered out by using wavelet transform technology, the outliers in the nonlinear process cannot be removed well. The sliding median filter is a simple sliding-window spatial filter that replaces the center value with the average (mean) of all the pixel values in the window. Image processing researchers commonly assert that median filtering is better than linear filtering for removing outliers in the presence of edges. The sliding median filter technology has been proved much effective in impulse outlier removal which widely used in image processing (Lago et al., 1995; Doymaz et al., 21). In this study, we propose an SMF-MSKPCA algorithm that could be effectively used for the on-line process monitoring. By incorporating the wavelet decomposition technique, sliding median filter technique, KPCA and Kronecker production into MSPCA, it is possible to develop an efficient on-line SFM-MSKPCA algorithm. To show the feasibility of the proposed SFM-MSKPCA algorithm, the monitoring performances of the proposed method are compared with those of the KPCA method. The rest of this paper is organized as follows. The preliminary materials including wavelet transform, sliding median filter technique and KPCA are introduced in Section 2. A detail description of the proposed SFM-MSKPCA based process performance monitoring scheme is then given in Section 3. The simulation examples are given in Section 4. Finally, conclusions are drawn in the last section. 2. Preliminary materials 2.1. Wavelet transform Multi-scale process monitoring algorithm usually uses wavelet transform to decompose the original process measurements into their multi-scale components according to time and frequency characteristics. For the multivariate modeling and monitoring, this provides many advantages over traditional single-scale methods because it enables to separate deterministic and stochastic features from the original process measurements and to offer more meaningful physical interpretation of process phenomena in terms of their time-frequency bands. A wavelet transform (WT) involves the decomposition of a signal function or vector. In a WT treatment, all basis functions a,b () can be derived from a mother wavelet () through the following dilation and translation processes: ( ) a,b () = a 1/2 b a, b Randa /= (1) a where a and b are, respectively, the scale and position parameters. Then a family of discrete wavelets is represented as m,s = 2 m/2 (2 m/2 t s) where m and s are the integers. For most practical applications, the wavelet coefficients are discredited dynamically (i.e. in integer powers of two) by a factor of 2 m for translation and by a factor of 2 m s for dilation. Mallet (1989) developed an efficient way to implement the DWT iteratively using the scaling (lowpass) filter H and the wavelet (high-pass) filter G as follows: a m = Ha m 1, d m = Ga m 1 where a m is the approximation coefficient vector at scale m representing the lower frequency information contained in the upper level approximation coefficient vector a m 1 while d m is the detail coefficient vector representing the higher frequency content. Once the wavelet type and the decomposition level m are specified, the original signal f can be efficiently decomposed into its multi-scale components An algorithm for KPCA KPCA is an extension of PCA and it can always be solved as an eigenvalues problem of its kernel matrix. Nonlinear Iterative Partial Least Squares (NIPALS) algorithm is used for the computation of PCA. Use NIPALS can get the same result as the eigenvalue method proposed by Schökopf et al. (1998). NIPALS gets the PC one by one. This algorithm is list in Table 1. Radial basis function is selected to building the kernel matrix in this paper. The ith row jth ( column element of kernel matrix ) xi x j 2 is computed by K i,j = exp c. In this function, the Euclidean distance of two input vectors are taken as the parameter of exponential (2-norm). Both T 2 statistic and statistic can be used for monitoring the process.

3 chemical engineering research and design 9 ( ) Table 1 NIPALS for KPCA. For comprehension For computation 1 Scale K Scale K 2 Initialize t i Initialize t i 3 p i = T i t i/ T i t i t i = K i t i / t T K i i N t i t i = i p i Loop until t i converges Loop until t i converges 4 i+1 = (I t i t T i /tt i t i) i K i+1 = (I t i t T i /tt i t i)k i (I t i t T i /tt i t i) Go to Step 3 Go to Step 3 Set X R m N be the sample matrix. For a new test sample x new R m, compute the kernel vector k new = (x new ) T (X) R N Let A R N N be the coefficient matrix, which is computed by A = t R N (2) t T (K/N)t A is calculated in the modeling period. It can be used to compute scores of the new test sample t new = k new A R N (3) Note that in modeling period, t i denotes ith column of the whole block scores matrix. But here, t new is a row vector, means the scores on every axis of one test point. The T 2 statistic can be calculated by T 2 new = t new 1 t T new (4) To compute statistic, there is a need for estimating the (x new ). This can be done as ˆ (x new ) = t new P T = t new A T (X) T (5) where P = (X)A. The statistic is defined as = (xnew ) T ˆ (x new ) 2 = (x new ) T (x new ) 2 ˆ (x new ) (x new )+ ˆ (x new ) ˆ (x new ) T = k(x new, x new ) 2t new P T (x new ) + t new P T Pt T new = 1 2t new A T k T new + t new A T KAt T new The T 2 statistic follows an F-distribution and the confidence limit, T 2ˇ, is given by Zhang et al. (21c) The sliding median filter The basic principle of sliding median filter is that each point value in the digital image or real value discrete signal is replaced by mid-value around the adjacent domain in each point value. The sliding median filter (SFM) is used to deal with signals that contaminated with outliers. In this nonlinear signal processing technique, the median of a window containing an odd number of observations is found by sliding it over the entire one dimensional signal (Mallet, 1989). Let the window size of the filter is s = 2l + 1, the number of the observations is N, namely, the observe values are x(1), (6) x(2),..., x(n). When the window is sliding over the observation sequence, the output of the SFM med(x(k)) is: med(x(k)) = x(1 + l), w = 2l + 1 (7) where x(l) represents the lth bigger value in the 2l + 1 observe values, The SFM is actually to compose the order again in term of the size of the 2l + 1 observe values in the window, and then get the middle value of ranked data as the output. Based on above definition, the relation one-dimensional sliding median filter between the input x(k) and output y(k) in the window of the SFM is as follows: y(k) = med(x(k 1),..., x(k),..., x(k + 1)) (8) In order to avoid to dealing with the boundary, one can extend both sides of the input signal. Suppose the length of the signal is N, then the signal after extending is: x(1) 1 l k x(k) = x(k) 1 k N x(n) l + 1 k N + 1 Applying SFM to the signal after extending, one can find the output: y(k) = med(x(k l),..., x(k),..., x(k + l) ) (1) 3. SFM-MSKPCA algorithm Dynamical multiscale PCA is proposed in this section which combined the Kronecker production and wavelet decomposition technique, sliding median filter technique and KPCA. The proposed methodology [ for ] SFM-MSKPCA is illustrated T [ ] in Fig. 1. Let =... 1, T k 1 1 =... 1,..., k 1 T k 1 = 1... and }{{} k 1 k 1 1 [. 1 ] k =... k 1 = , 1 1 k k then the dynamical model matrix is built as follows: (X [(1 : N, 1 : M)] kn ) T T k M (11) where is the Kronecker product. From Eq. (11), we have (X [(1 : N, 1 : M)] kn ) T T k M = [ (X [(1 : N, 1 : M)] kn ) T T, (X [(1 : N, 1 : M)] kn ) T T 1,..., (X [(1 : N, 1 : M)] kn ) T T k M 1 ] (9)

4 1274 chemical engineering research and design 9 ( ) Fig. 1 The flow of fault detection based on SFM-MSKPCA model. where X [(1 : N, 1 : M)] kn = [X [(1 : N, 1 : M)], X [(1 : N, 1 : M)] 1,..., X [(1 : N, 1 : M)] kn 1 ] Thus, the dynamical matrix (X [(1 : N, 1 : M)] kn ) T T k M is monitored in this paper. The SFM-MSKPCA algorithm can be summarized in the following steps: 1) Modeling procedure 2) Modeling procedure (1) Select N historical samples which represent normal operation. (2) Use sliding median filter on N historical samples. (3) The original data are normalized using the mean and standard deviation. ) T (4) Build the dynamical matrix X [(1 : N, 1 : M)] kn T k. M Compute the wavelet decomposition for each variable for by applying a wavelet transform with decomposition level L, and generate L coefficient matrices, X D1 (N/2 M), X D2 (N/2 2 M),..., X DL (N/2 L M) and one approximate coefficient matrix X AL (N/2 L M). (5) Apply KPCA to each of the L + 1 matrices and determine control limits of the monitored indices, T 2 and, at each scale. (6) Select wavelet coefficients larger than the appropriate threshold and reconstruct the approximated data matrix X T. (7) Apply KPCA to the reconstructed data matrix X T and calculate overall control limits, T 2 and. 3) On-line monitoring (1) Scale the current batch data with the mean and standard deviation obtained at step 1. (2) Compute the new model matrix and the wavelet coefficients, project these coefficients onto their respective scale model and calculate the monitoring indices, T 2 and Q, against the limits at each scale. (3) Reconstruct the approximate measurements from the scores at the scales where one of the current monitoring indices violates the limits. (4) Project the reconstructed measurements onto the unified KPCA model and calculate the overall monitoring indices, T 2 and. 4. The simulation result We also applied our SFM-MSKPCA method to a numerical application study and TE process in order to confirm its feasibility in a more realistic situation. Again, the KPCA method is also applied, and the monitoring performances of two methods are compared with each other Simple example Consider the following system with three variables but only one factor: x 1 = t 2 + e 1 x 2 = t 2 3t + e 2 x 3 = t 3 + 3t 2 + e 3 where e 1, e 2 and e 3 are the independent noise variables N(,.1), and t [.1, 2]. Normal data comprising 1 samples are generated according to these equations. These data are scaled to zero mean and unit variance. Two set of test data comprising 2 samples are also generated. For this system, these process variables are X = [x 1, x 2, x 3 ]. The following two disturbances are applied separately during generation of the two test data sets: Disturbance 1: A slope fault is introduced, x 1 is linearly increased from sample 11 to 2 by adding.1(k 1), where k is the sample number. Disturbance 2: A step fault is introduced, x 2 by.1 is introduced starting from samples 81 to 2. To demonstrate the superiority of the proposed method in dealing with the non-linear process, PCA and KPCA model are built respectively to monitor the disturbance 1. Radial basis kernel k(x, y) = exp( ( x y 2 /c)) is selected, and c =.65. The

5 chemical engineering research and design 9 ( ) T Fig. 2 On-line monitoring charts based on PCA for fault 1. 99% control limits is calculated in each simulation. In PCA approach, the number of PCs is 2. In KPCA approach, the number of nonlinear PCs is 23. The T 2 and charts for PCA monitoring of the process with slope fault are shown in Fig. 2. fail to correctly diagnose fault, T 2 exceed its control limit at sample 125. Fig. 3 represents the monitoring charts obtained by applying KPCA. Monitoring results has been improved. The charts detect fault from about sample 161, T 2 charts detect fault from about sample 125. From T 2 charts, KPCA shows the superiority compared to PCA. To demonstrate the effectiveness of SMF-MSKPCA approach over the KPCA approach, two sets of experiments are conducted. The number of nonlinear PCs is 24. When the over-filtering occurs, the fault may be removed or the noise is smoothed. In the SMF-MSKPCA approach, the sliding window size is 2 for avoiding over-filtering, which is determined according to Mallet (1989). If the sliding window size is too long, the filter will filter out the fault point. For test data of disturbance 1, outliers are added in x 3 at about sample k = 4, 5, 63. The monitoring results of KPCA method are show in Fig. 4, and T 2 exceed the 95% confidence limit at around time k = 4, 5, 63. The false alarms occur in Fig. 4. There is no false alarm in Fig. 5. For disturbance 2, comparing the monitoring results of KPCA and SFM-MSKPCA approach, all of them can detect fault at about sample 81. But Fig. 4 On-line monitoring charts based on KPCA for fault 1 with outliers. Fig. 5 On-line monitoring charts based on SFM-MSKPCA for fault 1 with outliers. the conventional KPCA approach gives many false alarms as shown in Fig. 6. In Fig. 7, both and T 2 accurately detect faults occur in sample 81 without false alarms. SFM-MSKPCA can contain important information by using IDWT, and then reduce noise and outliers. T T Fig. 3 On-line monitoring charts based on KPCA for fault T Fig. 6 On-line monitoring charts based on KPCA for fault 2.

6 1276 chemical engineering research and design 9 ( ) Table 2 Monitored variables in the Tennessee Eastman process. No. Process measurements Fig. 7 On-line monitoring charts based on SFM-MSKPCA for fault Tennessee Eastman process In this sub-section, the proposed method is applied to the Tennessee Eastman process and is compared with KPCA monitoring results. The control structure is shown schematically in Fig. 8. There are five major unit operations in the process: a reactor, a condenser, a recycle compressor, a separator, and a stripper. The four reactants A, C, D and E and the inert B are fed to the reactor where the products G and H are formed and a byproduct F is also produced. The process has 22 continuous process measurements, 12 manipulated variables, and 19 composition measurements sampled less frequently. The details on the process description are well explained in (Lee et al., 24a,b,c). A total of 33 variables are used for monitoring in this study. Those variables are listed in Table 1. All composition measurements are excluded since they are hard to measure on-line in practice. A sampling interval of 3 min is used to collect the simulated data for the training and testing sets. A set of monitoring variables is listed in Table 2. Both the training and testing data sets for each fault are composed 1 A feed (stream 1) 2 D feed (stream 2) 3 E feed (stream 3) 4 Total feed (stream 4) 5 Recycle flow (stream 8) 6 Reactor feed rate (stream 6) 7 Reactor pressure 8 Reactor level 9 Reactor temperature 1 Purge rate (stream 9) 11 Product separator temperature 12 Product separator level 13 Product separator pressure 14 Product separator underflow (stream 1) 15 Stripper level 16 Stripper pressure 17 Stripper underflow (stream 11) 18 Stripper temperature 19 Stripper steam flow 2 Compressor work 21 Reactor cooling water outlet temperature 22 Separator cooling water outlet temperature No. Manipulated variables 23 D feed flow valve (stream 2) 24 E feed flow valve (stream 3) 25 A feed flow valve (stream 1) 26 Total feed flow valve (stream 4) 27 Compressor recycle valve 28 Purge valve (stream 9) 29 Separator pot liquid flow valve (stream 1) 3 Stripper liquid product flow valve (stream 11) 31 Stripper steam valve 32 Reactor cooling water flow 33 Condenser cooling water flow XC 1 Feed A XC 2 LI Feed D XC Feed E XA XD XE Analyzer 3 6 LC SC Condenser TI 13 PI Reactor Cooling Reactor TI 8 Condenser 7 Cooling TC TI 12 LI Compressor JI PI 5 Stripper LI LC TI TC Separator XC 9 PHL Purge PI 1 XC TI Steam Analyzer Analyzer XB XE Feed A/B/C 4 11 LC Product Fig. 8 Process layout of the Tennessee Eastman process.

7 chemical engineering research and design 9 ( ) Table 3 Process faults for the Tennessee Eastman process. No. Description Type 1 A/C feed ratio, B composition Step constant (stream 4) 2 B composition, A/C ratio constant Step (stream 4) 3 D feed temperature (stream 2) Step 4 Reactor cooling water inlet Step temperature 5 Condenser cooling water inlet Step temperature 6 A feed loss (stream 1) Step 7 C header pressure loss reduced Step availability (stream 4) 8 A, B, C feed composition (stream 4) Random variation 9 D feed temperature (stream 2) Random variation 1 C feed temperature (stream 4) Random variation 11 Reactor cooling water inlet temperature 12 Condenser cooling water inlet temperature Random variation Random variation 13 Reaction kinetics Slow drift 14 Reactor cooling water valve Sticking 15 Condenser cooling water valve Sticking 16 Unknown 17 Unknown 18 Unknown 19 Unknown 2 Unknown 21 The valve for stream 4 is fixed at the steady state position Constant position T Fig. 9 On-line monitoring charts based on KPCA for fault 5. of 96 observations. All faults in the test data set are introduced from sample 16. The data can be downloaded from Process faults are listed in Table 3. Process dataset is used to compare the performance of KPCA and MSKPCA. The number of nonlinear PCs is 31. When the over-filtering occurs, the fault may be removed or the noise is smoothed. In the SMF-MSKPCA approach, the sliding window size is 2 for avoiding over-filtering, which is determined according to Mallet (1989). If the sliding window size is too long, the filter will filter out the fault point. In the implementation of the SMF-MSKPCA model, Haar wavelet is used and the decomposition level is set to three, which is determined similarly as described earlier. The fault case IDV(5) is associated with condenser cooling water inlet temperature. For this fault, KPCA method performs poorly and its T 2 statistic give false fault before the sampling instant 161, as shown in Fig. 9. SFM-MSKPCA has a better detection performance than KPCA. In Fig. 1, and T 2 statistic gives an alarm at about the sampling instant 161. Comparing with the conventional KPCA approach, SFM-MSKPCA can effectively extract the nonlinear characteristics of nonlinear process and reduce noises and outliers Multi-scale process fault detection in electro-fused magnesia system The electro-fused magnesia furnace (EMF) is one of the main equipments used to produce electro-fused magnesia belongs to a kind of mine hot electric arc furnace. With the development of technology of melting, EMF has already gotten extensive application in the industry (Dong et al., 28; Zhang et al., 21a,b,c). EMF refining technology can enhance the Fig. 1 On-line monitoring charts based on SFM-MSKPCA for fault 5. (1) Transformer, (2) short circuit network, (3) electrode holder, (4) electrode, (5) furnace shell, (6) trolley, (7) electric arc, and (8) burden. quality and increase the production variety. The whole equipment of the EMF has transformer, short net, electrode holder, electrode, furnace, etc. Operating board besides the furnace controls electrode up and down. The furnace shell is round, slightly tapered, facilitate melting in processing. There are rings on the furnace wall and trolley under the furnace. When melting process has completed, move the trolley to cool. The EMF smelting process is shown in Fig. 11. In the melting process, voltage flicker is the types of power quality problems, which is introduced to the power system as a result of the furnace s very large power input ratings. The EMF in this paper takes the light-burned magnesia as the raw material. It makes use of the heat generated both by the burden resistance when the current through the burden and the arc between the electrodes and the burden to melt the burden, and then obtain the fused magnesia crystals with higher purity. The characteristic of the fused magnesium furnace is that it requires a large electrical power. The capacity of a three-phase furnace transformer is up to several thousand or tens of thousands volt-amperes. The required values of the power fluctuate drastically and dramatically when the furnace is working, and the effect of the electrode regulator just adjusts the power though adjusting the location of the electrodes. The target process is a full-scale melting process. The melting process has complicated process dynamics and strong nonlinearity, as well as strong random disturbance.

8 1278 chemical engineering research and design 9 ( ) Fig. 11 Diagram of electro-fused magnesium furnace. Total 12 process observations are collected from the operation database where the on-line measurement data for 3 process variables are accumulated with the data acquisition interval of 1 min. The three process variables are classified into X. Among 8 observations, first 4 observations are used for the model construction and one validation data sets are used for the model validation. The test data set had 4 observations. The number of nonlinear PCs is 27. When the over-filtering occurs, the fault may be removed or the noise is smoothed. In the SMF-MSKPCA approach, the sliding window size is 2 for avoiding over-filtering, which is determined according to Mallet (1989). If the sliding window size is too long, the filter will filter out the fault point. In the implementation of the SFM-MSKPCA model, Haar wavelet is used and the decomposition level is set to three, which is determined similarly as described earlier. The standard KPCA model also is used in the melting process for comparison. The monitoring results obtained by applying the standard KPCA and SFM-MSKPCA to the data set are shown in Figs. 12 and 13. From Fig. 12, the statistics exceed their limit at about sample 82. Fig. 12 also shows the fault occurs at around sample 116. It can be seen from Fig. 13 that there are no sudden variations till about time 126. The target process has strong random disturbance. This sudden fluctuation causes a change in the feed rate that thereby significantly changes the residence time of the feed in the reactor and affects the quality of electro-fused magnesia in the furnace. So, the accurate detection and identification of fault current time is very important. The result of the SFM-MSKPCA model shows that the and T 2 exceed the 95% confidence limit, starting at sample 126 and ending at sample 167. Compare the SFM-MSKPCA with the conventional KPCA approach. SFM-MSKPCA is suited for analyzing process data with outliers and this is clearly evident from Fig. 13. SFM-MSKPCA approach can eliminate the influence of outliers and noises T Fig. 12 Monitoring abilities of the standard KPCA method for EMF.

9 chemical engineering research and design 9 ( ) Fig. 13 Monitoring abilities of the SFM-MSKPCA method for EMF. 5. Conclusion In this paper, in order to improve the fault detection ability of conventional PCA, a new approach based on sliding median filter, wavelet analysis and kernel PCA are proposed for monitoring multi-scale and nonlinear process with outliers and noises. SFM-MSKPCA is proposed by preprocessing the real process data before using KPCA. SFM-MSKPCA can eliminate the influence of outliers and noises which caused by time-varying, uncertainty and unsteady behaviors and at last this can ensure the reliability of the result. The SFM- MSKPCA approach is applied to numerical example, TE and EMF process data sets for process fault diagnosis. It shows that SFM-MSKPCA can detect abnormal events more accurate than the conventional KPCA approach and reduce false alarm. References AUndey, C., Ertunc, S., Cinar, A., 23. Online batch/fed-batch process performance monitoring, quality prediction, and variable-contribution analysis for diagnosis. Industrial and Engineering Chemistry Research 42 (2), Bakshi, B.R., Multiscale PCA with application to multivariate statistical process monitoring. AIChE Journal 44, Chiang, L.H., Russell, F.L., Braatz, R.D., 21. Fault Detection and Diagnosis in Industrial Systems. Springer, London. Dong, B., Zhang, L., Wu, Y., Chai, T.Y., 28. Fuzzy control research on electrodes of electrical-fused magnesia furnace. IEEE Proceedings of Chinese Control and Decision Conference, Dong, D., McAvoy, T.J., Non-linear principal component analysis-based on principal curves and neural networks. Computers and Chemical Engineering 2, Doymaz, F., Bakhtazad, A., Romagnoli, J.A., Palazoglu, A., 21. Wavelet-based robust filtering of process data. Computers and Chemical Engineering 25, Dzykowski, M., Walczak, B., Massart, D.L., 23. Projection methods in chemistry. Chemometrics and Intelligent Laboratory Systems 65, Ge, Z., Song, Z., 27. Process monitoring based on independent component analysis principal component analysis (ICA PCA) and similarity factors. Industrial and Engineering Chemistry Research 46 (7), Hiden, H.G., Willis, M.J., Tham, M.T., Tham, G.A., Non-linear principal components analysis using genetic programming. Computers and Chemical Engineering 23 (3), Kano, M., Tanaka, S., Hasebe, S., Hashimoto, I., Ohno, H., 23. Monitoring independent components for fault detection. AIChE Journal 49, Kourti, T., Nomikos, P., MacGregor, J.F., Analysis, monitoring, and fault diagnosis of batch processes using multi-block and multi-way PLS. Journal of Process Control 5, Kramer, M.A., Nonlinear principal component analysis using auto-associative neural networks. AIChE Journal 37 (2), Kruger, U., Chen, Q., Sandoz, D.J., McFarlane, R.C., 21. Extended PLS approach for enhanced condition monitoring of industrial processes. AIChE Journal 47 (9), Lago, C.L., Juliano, V.F., Kascheres, C., Applying moving median digital filter to mass spectrometry and potentiometric titration. Analytica Chimica Acta 31, Lee, G., Han, C.H., Yoon, E.S., 24a. Multiple-fault diagnosis of the Tennessee Eastman process based on system decomposition and dynamic PLS. Industrial and Engineering Chemistry Research 43, Lee, J.M., Qin, S.J., Lee, I.B., 26. Fault detection and diagnosis based on modified independent component analysis. AIChE Journal 52 (1), Lee, J.M., Yoo, C.K., Choi, S.W., Vanrolleghem, P.A., Lee, I.B., 24b. Nonlinear process monitoring using kernel principal component analysis. Chemical Engineering Science 59, Lee, J.M., Yoo, C.K., Lee, I.B., 24c. Statistical process monitoring with independent component analysis. Journal of Process Control 14, MacGregor J., J.F., Kourti, T., Statistical process control of multivariate processes. Control Engineering Practice 3, Misra, M., Yue, H.H., Qin, S.J., Ling, C., 22. A fast combined fault diagnosis approach based on LWSVM. Computers and Chemical Engineering 26, Mallet, S.G., A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 11 (7), Martin, E.B., Morris, A.J., 22. Enhanced bio-manufacturing through advanced multivariate statistical technologies. Journal of Biotechnology 99 (3), Qin, S.J., 23. Statistical process monitoring: basics and beyond. Journal of Chemometrics 17, Qin, S.J., Valle, S., Piovoso, M.J., 21. On unifying multi-block analysis with application to decentralized process monitoring. Journal of Chemometrics 15 (9), Rosen, C., Lennox, J.A., 21. Multivariate and multiscale monitoring of wastewater treatment operation. Water Research 14, Schökopf, B., Smola, A.J., M.Juller, K., Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 1 (22), Shao, V., Jia, F., Martin, E.B., Morris, A.J., Wavelets and non-linear principal component analysis for process monitoring. Control Engineering Practice 7, Tan, S.F., Mavrovouniotis, M.L., Reducing data dimensionality through optimizing neural network inputs. American Institute of Chemical Engineers Journal 41 (6), Thornhill, N.F., Shah, S.L., Huang, B., Vishnubhotla, A., 22. Spectral principal component analysis of dynamic process data. Control Engineering Practice 1, Wang, X., Kruger, U., Irwin, G.W., 25. Process monitoring approach using fast moving window PCA. Industrial and Engineering Chemistry Research 44 (15), Westerhuis, J.A., Kourti, T., MacGregor, J.F., Analysis of multi-block and hierarchical PCA and PLS models. Journal of Chemometrics 12 (5), Zhang, Y.W., Teng, Y.D., Zhang, Y., 21a. Complex process quality prediction using modified kernel partial least squares. Chemical Engineering Science 65,

10 128 chemical engineering research and design 9 ( ) Zhang, J., Zhao, S.J., Xu, Y.M., 26. Performance monitoring of processes with multiple operating modes through multiple PLS models. Journal of Process Control 16 (7), Zhang, Y.W., Ma, C., 211. Fault diagnosis of nonlinear processes using multiscale PCA and multiscale KPLS. Chemical Engineering Science 66, Zhang, Y.W., Fan, Y.P., Zhang, P.C., 21b. Combining kernel partial least-squares modeling and iterative learning control for the batch-to-batch optimization of constrained nonlinear processes. Industrial and Engineering Chemistry Research 9 (16), Zhang, Y.W., Zhou, H., Qin, S.J., Chai, T.Y., 21c. Decentralized fault diagnosis of large-scale processes using multiblock kernel partial least squares. IEEE Transactions on Industrial Informatics 1, 3 12.