On-line Fault Detection and Diagnosis of Sequencing Batch Reactor Using MKICA

On-line Fault Detection and Diagnosis of Sequencing Batch Reactor Using MKICA Zhang Ya-chao1, Wang Pu2, Gao Xue-jin*3, Ma Rong4 College of Electronic and Control Engineering, Beijing University of Technology, Beijing 100124, China Engineering Research Center of Digital Community, Ministry of Education, Beijing 100124, China Beijing Laboratory for Urban Mass Transit, Beijing 100124, China zhangyachao66@126.com; 2wangpu@bjut.edu.cn; *3gaoxuejin@bjut.edu.cn; 4marong0506@126.com

1

Abstract Considering the data of Sequencing Batch Reactor (SBR) having the characteristics of non-Gaussian distribution and highly nonlinearity, this research applies Multi-way Kernel Independent Component Analysis (MKICA) to the on-line process monitoring of SBR. Meanwhile, a novel contribution analysis scheme named bar plot is developed for MKICA to diagnose faults. Above all, the three-dimensional data of SBR is expanded into two-dimensional by a new data expanding method; then, Kernel Principal Component Analysis (KPCA) is utilized to map the two-dimensional data into a high dimensional feature space, and make use of Independent Component Analysis (ICA) to extract Independent Components (ICs) in feature space; finally, if MKICA detects a fault occurs during on-line monitoring stage, the bar plot is used to identify the variables causing the fault. The method is successfully applied to an 80L lab-scale SBR. The experimental results demonstrate that, compared with traditional MICA, the proposed method exhibit better performance in fault detection and diagnose.

Keywords Sequencing Batch Reactor (SBR); Multi-way Kernel Independent Component Analysis (MKICA); Process Monitoring; Bar Plot

Introduction As a flexible and low-cost process, Sequencing Batch Reactors (SBRs) are commonly used for biological wastewater treatment. The SBR process is normally operated on a series of predefined phases: fill, react, settle, draw, and idle (Marsili-Libelli et al. 2008). Most of the advantages of the SBR process may be attributed to its single-tank designs and the flexibility that enable it to meet many different treatment objectives (Yoo et al. 2006). With increasingly stringent regulations for effluent quality, the on-line monitoring of SBR processes becomes very important for enhancement of process performance by detecting disturbances leading to abnormal process operation at an early stage. In recent years, several techniques using multivariate statistical analysis have been developed for on-line monitoring of the SBR process. However, the SBR process is highly non-linear and non-Gaussian from the nonlinear biological reaction kinetics (Kim et al. 2008). So, there is a big challenge for real-time on-line monitoring of the SBR process.

In all multivariate statistical analysis methods, Multi-way Principal Component Analysis (MPCA) is considered as the most famous one, which was evolved from Principal Component Analysis (PCA) in order to monitor batch process by Nomikos et al. (1994, 1995). Kim et al. (2008) and Yoo et al. (2004) pointed out that MPCA has a fundamental shortcoming as it assumes a Gaussian distribution of the variables. So, they applied Multi-way Independent Component Analysis (MICA) to the on-line monitoring of SBR, which show a better fault detection ability than MPCA. What's more, Yoo et al. (2006) thought that the real SBR process is highly nonlinear. In their research, a multi-way kernel principal component analysis (MKPCA) was used to tackle the nonlinear problem and obtain better batch monitoring performance of the pilot-scale SBR. In fact, the SBR data not only has non-Gaussian distribution characteristics but also has highly nonlinear characteristics. Considering that KICA combines the advantages of KPCA and ICA, this article conducts in-depth research on KICA, and applies it to the on-line fault detection of the SBR process.

After a fault is detected, fault diagnose is needed. Among the methods based on MSPM, fault diagnosis methods mainly include two types: one is contribution plot method, another is fault reconstruction method. The main idea 94

International Journal of Engineering Practical Research, Vol. 4 No. 1-April 2015 2326-5914/15/01 094-09 Š 2015 DEStech Publications, Inc. doi: 10.12783/ijepr.2015.0401.19

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of contribution plot method is when monitoring statistics detecting a fault, these variables which have the largest contribution to the statistics are considered to be the fault variables (Dunia et al. 1998 ； Fan et al. 2014).

Contribution plot method does not require prior knowledge, and is easy to be used for online fault diagnosis. So this method has been widely applied to the PCA, PLS, ICA and other methods. Nevertheless, it is difficult to calculate contribution plots for KPCA and KICA due to their kernel mapping. The fault reconstruction method defines the reconstruction of fault detection index along the direction of variables as the variables’ contribution, and these variables with largest reconstructed contribution values are considered to be fault sources. Zhang et al.

(2014) pointed out that KICA method is not available for the fault isolation. In their research, a method based on fault direction information is developed for KICA to realize fault diagnosis, where the historical fault information is used to build the model. However, in the actual process of SBR, it is difficult to collect all kinds of historical fault data. So this method can not be effectively applied to the actual. In this paper, a novel contribution analysis scheme named bar plot is developed for MKICA to diagnose faults. The proposed method can be easily applied to kernel methods and it doesn’t need historical fault data.

This paper is structured in three additional sections. The first section is the methodology including the processing of SBR’s three-dimensional data, basic theory of KICA, and the design thought of bar plot. Afterwards, the proposed method is applied to an 80L lab-scale SBR, and detailed analysis of the results is carried out, which demonstrates the effectiveness of the proposed method. Some conclusions are to be submitted at the end.

Methodology Processing of SBR’s Three-dimensional Data As a typical batch process, the data of SBR are three-dimensional array X ( I × J × K ) , where I is the number of batches, J is the number of variables and K is the number of times each batch is sampled. Since the multivariate statistical analysis methods can only model for two-dimensional data, SBR’s three-dimensional data have to be transformed into two-dimensional first of all. The original method is unfolding along batch (Nomikos et al. 1995), which unfolds the three-dimensional array to a matrix , and then normalizes the matrix according to Equation (1).

This method has the shortcoming that future values of the current batch must be estimated to allow online monitoring. xi , kj =

xkj =

xi , kj − xkj

(1)

skj

1 I skj ∑ xi= , kj I i =1

1 I 2 ∑ ( xi , kj − xkj ) I − 1 i =1

To avoid the drawback of unfolding along batch, Lee et al. (2004) proposed a new unfolding method, which first unfolds the array X ( I × J × K ) to a matrix X ( I × KJ ) , and normalizes the matrix according to Equation (1), then unfolds the normalized matrix to X ( KI × J ) along variable. This method is also adopted in our research.

Kernel Independent Component Analysis (KICA) At present, kernel technique has been extensively applied to nonlinear industrial processes. Lee et al. (2007) proposed KICA algorithm, which is a new method of combining KPCA with ICA for nonlinear process monitoring.

The basic idea of KICA is nonlinearly mapping the observational data into feature space, where the data have better linear structure, and then ICA is utilized to extract ICs in feature space. Considering the SBR’s data having the characteristics of non-Gaussian distribution and highly nonlinearity, this research applies MKICA to the on-line process monitoring of SBR. 1) Developing the Normal Operating Condition (NOC) KICA Model The data matrix X ( KI × J ) processed at last step is described as follows: x = [ x1 , x2 ,..., xn ,..., xN ]T

(2)

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xn ∈ ℜ J , 1 ≤ n ≤ N

, N = KI

Then, x is transferred to the high-dimensional feature space through nonlinear mapping ϕ : ℜ J → F , where

ϕ ( xn ) ∈ F . The covariance matrix in feature space will be CF =

1 N T ∑ ϕ ( xn )ϕ ( xn ) N n =1

Let Q = [ϕ ( x1 ),..., ϕ ( xN )] , then C F can be expressed by C F =

(3)

1 QQT . Defining an N × N gram kernel matrix G N

by

Gn, m = 〈ϕ ( xn ), ϕ ( xm )〉 = g ( xn , xm )

(4)

Where, G = QQT . The mean centered kernel matrix G can be easily obtained from G = G − 1N ⋅ G − G ⋅1N + 1N ⋅ G ⋅1N

1 . . .

1  .

Where, 1N = N . 1 .

. . .

(5)

. 1 .  .  ∈ ℜN ×N .  . . . 1

Also, the variance scaling of kernel matrix can be done by the following equation G scl =

G trace(G ) N

(6)

Then, we apply eigenvalue decomposition to G scl = G scl ⋅ α λα

(7)

And, d positive eigenvalues are selected by the following equation

λn ≥ 0.0001 sum(λn )

(8)

By this time, we assume Λ =diag (λ1 , λ2 ,..., λd ) , H = [α1 , α 2 ,..., α d ] . So, the whitened matrix can be obtained by the following equation = Z

N Λ −1 ⋅ H T G scl T ∈ ℜd × N

(9)

ICA is utilized to extract independent component matrix S from Z (Lee et al. 2004), then p primary ICs are chosen to construct primary component space S p , therewith the residual space can be defined E =Z − B p ⋅ S p

(10)

Where, B p is the saved separated matrix when using ICA to calculate S p . Next, we can calculate I 2 and SPE statistics as follows = I 2 (n) S p (n)T ⋅ S p (n)

(11)

SPE = (n) E (n)T ⋅ E (n)

(12)

In the end, the control limits of I 2 and SPE statistics are computed by Kernel Density Estimation.

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2) On-line Fault Detecting Strategy of KICA When we acquire the test data xk ∈ ℜ J at k sample time, the following work is to standardize it according to

the mean and variance at k sample time calculated from equation (1). On the basis of [ g k ]n = [ g ( xk , xn ) ] , we can

acquire kernel vector g k ∈ ℜ N . The mean centered kernel matrix g kscl can be obtained by follows g k = g k − 1k ⋅ G − g k ⋅1N + 1k ⋅ G ⋅1N g kscl = 1k = Where,

g k trace(G ) N

(13) (14)

1 [1,1,...,1] ∈ ℜ N . So, the whitened vector can be achieved N = zk

N Λ −1 H T [ g kscl ( x1 , xk ),..., g kscl ( xN , xk )]T

(15)

ICs will be extracted according to equation (16), thereupon residual vector can be defined as equation (17). = sk B pT ⋅ zk

(16)

ek = zk − B p ⋅ sk

(17)

Now, we can calculate I 2 k and SPEk statistics as follows 2 I= sk T ⋅ sk T k

(18)

SPE= ek T ⋅ ek k

(19)

Finally, to monitor the I 2 k and SPEk statistics whether they surpass their control limits respectively.

Fault Diagnose for MKICA Once a fault is detected by the monitoring method MKICA described above, the following meaningful work is done to judge which variables are causing this fault. Currently, contribution plot method can’t be applied to KICA for fault diagnosis; fault reconstruction method needs a number of historical fault data which limits its application.

In this brief, a novel contribution analysis scheme named bar plot is researched which can be easily applied to kernel methods and doesn’t need historical fault data.

The centroid matrix C ∈ ℜ K × J of X ( KI × J ) which is obtained in section “Processing of SBR’s three-dimensional data” can be calculated by the following equation Ck , j =

1 I ∑ X ki , j I i =1

(20)

Assuming the test data xk at k sample time is abnormal data, and it has been detected by MKICA. Then, we account for how to seek out the faulty source with bar plot method. Above all, we take out the row vector B ( B ∈ ℜ J ) at k sample time from C and let j = 1 . Repeating the following 1) ~ 5) steps until j > J .

1) let B = B ; 2) the value of j th variable in B is replaced by the value of j th variable in xk ; 3) the replaced new data B is monitored by MKICA again, and we can obtain the new I 2 ( j ) and SPE ( j ) statistics; 4) let the new obtained I 2 ( j ) and SPE ( j ) subtract their control limits at k sample time respectively, and the results can be expressed as DI ( j ) and DSPE ( j ) ; 2

5) let j= j + 1 .

When we have achieved J variables’ DI and DSPE ( DI ∈ ℜ J , DSPE ∈ ℜ J ) from above steps, we will judge whether 2

2

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Zhang Ya-chao, Wang Pu, Gao Xue-jin, Ma Rong

the DI ( j ) and DSPE ( j ) statistics are greater than zero respectively. If the results are greater than zero, the j th 2

variable will be regarded as a fault variable; else, it will be regarded as a normal variable.

Summary of Modeling and Monitoring Procedure Following are the detailed procedure of off-line and on-line monitoring method using the MKICA model to monitor the SBR process.

1) Develop the Normal Operating Condition (NOC) Model 1. Acquire an operating data set during normal SBR operation.

2. Unfold X ( I × J × K ) to X ( I × KJ ) and normalize the matrix according to Equation (1), then unfold the normalized matrix to X ( KI × J ) along variable.

3. Obtain the centroid matrix C according to Equation (20).

4. Calculate the gram kernel matrix G according to Equation (4). Then, center and normalize G according to Equation (5) and (6).

5. Apply eigenvalue decomposition to G scl according to Equation (7). Select d positive eigenvalues according to Equation (8).

6. ICA is utilized to extract independent component matrix S from Z which is obtained by Equation (9), then p primary ICs are chosen to construct primary component space S p .

7. Calculate the I 2 and SPE statistics according to Equation (11) and (12) respectively.

8. Carry out the Kernel Density Estimation method to compute the control limits of I 2 and SPE statistics.

2) On-line Monitoring 1. For new batch data up to time k , xk (1× J ) , normalize it and achieve the kernel vector g k .

2. Obtain sk and ek according to Equation (13) ~ (17).

3. Calculate I 2 k and SPEk statistics and judge them whether surpass their control limits. If either of them surpasses the control limit, execute step 4; else, execute step 9.

4. Take out the row vector B ( B ∈ ℜ J ) at k sample time from C and let j = 1 .

5. Let B = B ; replace the value of j th variable in B by the value of j th variable in xk ; monitor the replaced new data B by MKICA again, then we can obtain the new I 2 ( j ) and SPE ( j ) statistics.

6. Let the new obtained I 2 ( j ) and SPE ( j ) subtract their control limits at k sample time respectively, and the results can be expressed as DI 2 ( j ) and DSPE ( j ) .

7. Let j= j + 1 ; if j ≤ J , goto step 5.

8. Judge whether the J values in DI and DSPE are greater than zero respectively. If DI ( j ) or DSPE ( j ) is greater 2

2

than zero, the j th variable will be regarded as a fault variable; else, it will be regarded as a normal variable.

9. Let k= k + 1 ; if k ≤ K , goto step 1; else finish.

Results and Discussion Lab-scale Plant SBR The SBR data used in this paper come from a pilot-scale SBR system. A fill-and-draw SBR with an 80-liter working volume is operated in a 6 h cycle mode and each cycle consists of fill/anaerobic (60 min), aerobic (150 min), anoxic (60min), re-aerobic (30 min) and settling/draw (60min) phases. Temperature (T), PH, oxidation reduction potential

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(ORP), the first derivative of ORP (dORP/dt), dissolved oxygen (DO), six electrodes for conductivity, weight (W) in TABLE 1 are connected to the individual sensors to check the status of the SBR. A set of on-line measurements is obtained every 3 minutes (120 times points per cycle). The experiment lasted for 20 days, and 80 batches of data are collected. Thereinto, two batches fault data are included. Fault 1 is a single fault. Aeration system should have stopped since the process entered the third stage (anoxic) from the second stage (aerobic). But in fact, the aeration system was broken that caused DO rise abnormally. This fault was happened from 211 min (sample number 71) to 290 min (sample number 90). Fault 2 is a multiple fault, in which we artificially increased a sensor fault on the basis of fault 1. The value of PH sensor no longer changes since 131 min (sample number 44) until the end of the reaction, namely the value remains at 130 min.

TABLE 1 REAL-TIME MEASURED VARIABLES OF A SBR

No. 1 2 3 4 5 6 7

Variables Temperature(T) pH oxidation reduction potential(ORP) the first derivative of ORP (dORP/dt) dissolved oxygen (DO) six electrodes for conductivity weight (W)

Considering biological reactions in the settling and drawing phases were assumed as negligible, only the first 100 sampling time instants were used. 30 batches of normal data are selected to build model, and the two fault batches described above are utilized to simulate monitoring on-line. Traditional MICA and our proposed method are experimented respectively.

Analysis of The Results 30 batches of normal operating condition data X (30 × 7 × 100) are used to build MICA and MKICA monitoring model, and Kernel Density Estimation method is utilized to compute the control limits with 99% confidence limits, then two faulty batches data are monitored respectively.

Figure 1 shows the on-line monitoring results of the I 2 and SPE charts of MICA and MKICA for the fault 1 batch.

The fault happened from sample number 71 to 90, although there’s a false alarm point at about sample number 69 in the I 2 chart of MICA and MKICA, in general, both methods’ I 2 charts show very good fault detection performance. Nevertheless, the SPE chart of MICA occurs a number of leakage alarms between sample number 75 and 87. The fault detection performance is much less than the SPE chart of MKICA. Figure 2 shows the on-line monitoring results of the I 2 and SPE charts of MICA and MKICA for the fault 2 batch. Fault 2 is a multiple fault, which is caused by two variables. Thereinto, the first happened is the PH sensor fault started from the sample number 44. This PH sensor fault is a simulation of the value no longer change, so the fault magnitude is lesser at the initial stage, and it is not readily to detect the fault. Both I 2 and SPE charts of MKICA start to detect the occurrence of failure at sample number 48, then they give an alarm until the process has ended. Whereas, the I 2 chart of MICA detects the occurrence of failure at sample number 49. What’s worse is that some leak alarms occur at sample number 50, 55 and 97. In addition, the SPE chart of MICA detects the occurrence of failure starting at sample number 48, but leaks a point at sample number 49. In summary, due to MKICA considers the nonlinear problem of the process variables, no matter at the timeliness of fault detection aspects or at the occurrence of false alarm and alarm failure aspects, MKICA shows better performance than MICA. Once a fault is detected, the next meaningful thing is fault diagnose. The traditional contribution plot considers the variable having the biggest contribution to be faulty source. While, our proposed bar plot method considers all variables greater than zero as fault variables. Figure 3 is the contribution plots of MICA for fault 1 at sample number 75. Figure 3(a) indicates that variable 5 (DO) is the fault variable, which is right. But, Figure 3(b) indicates that variable 7 (W) is the fault variable, which is false. Figure 4 is the new bar plots of MKICA for fault 1 at sample number 75. Both Figure 4(a) and Figure 4(b) indicate that variable 5 (DO) is the fault variable, which is right.

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Figure 5 and Figure 6 are fault diagnosis charts of MICA and MKICA for fault 2 at sample number 80. Fault 2 is a multiple fault at this sample number. From Figure 6(a) and Figure 6(b), we can see clearly that the values of variable 2 (PH) and variable 5 (DO) are greater than zero, so they are fault variables. Our proposed method can completely and accurately identify the two faulty sources. While, because the traditional contribution plot always

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considers the variable having the biggest contribution to be faulty source. Figure 5(a) and Figure 5(b) can only identify variable 2 (PH) as the fault variable, but neglect another fault variable, namely variable 5 (DO). To sum up, the proposed bar plot not only can realize fault diagnosis for MKICA, but also can achieve more accurate results than conventional contribution method used for MICA. Conclusions This paper analyzes the characteristics of the SBR process, and summarizes the current application of multivariate statistical methods for SBR’s fault detection. On this basis, we deeply research MKICA method and successfully apply it to our pilot-scale SBR system. The experimental results illustrate that, in contrast to the fault detection methods based on MICA, the MKICA method takes the non-linear and non-Gaussian characteristics of SBR data into account at the same time. So, no matter at the timeliness of fault detection aspects or at the occurrence of false alarm and alarm failure aspects, MKICA shows better performance than MICA. Conventional contribution method is difficult to apply to KICA for fault diagnosis. Although, fault reconstruction method can realize the fault diagnosis, it needs prior history fault information which limits it application. Based on the above consideration, in this brief, a novel contribution analysis scheme named bar plot is researched which can be easily applied to kernel methods and doesn’t need historical fault data.

ACKNOWLEDGMENT

This work was supported by China's national natural science fund project (No.61174109 and No.61364009). The authors also appreciate the contributions and comments made by ZHAO Chun-hui.

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