PROCESS FAULT DETECTION AND ROOT CAUSE DIAGNOSIS USING A HYBRID TECHNIQUE. Md. Tanjin Amin, Syed Imtiaz* and Faisal Khan

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1 PROCESS FAULT DETECTION AND ROOT CAUSE DIAGNOSIS USING A HYBRID TECHNIQUE Md. Tanjin Amin, Syed Imtiaz* and Faisal Khan Centre for Risk, Integrity and Safety Engineering (C-RISE) Faculty of Engineering & Applied Science (*Corresponding author: simitaz@mun.ca) ABSTRACT Multivariate statistical process monitoring (MSPM) fault detection and diagnosis (FDD) tools can detect the fault early,and provide the diagnostic information by generating the multivariate contribution plots. Instead of diagnosing the root cause, these tools often point towards a group of variables as the probable causes. A Bayesian network (BN) is widely used to complete the diagnosis. Current practice is to provide a hard evidence in the faulty state of the variable which has the highest contribution in the contribution plot if it is a child node in the BN, and root cause is identified among other variables. This hard evidence based technique ignores the evidence node while searching for the root cause of process abnormality. However, MSPM tools may diagnose the root cause accurately, even if it is an intermediate node in the BN. As a result, conventional hybrid methodologies will provide false diagnosis. This issue can be overcome by updating the BN with multiple likelihood evidence. In this paper, principal component analysis (PCA) has been selected as the MSPM tool and a hybrid method comprised of PCA-BN with multiple likelihood evidence is proposed. This methodology has been successfully applied to the Tennessee Eastman (TE) chemical process. KEYWORDS: Principal component analysis, bayesian network, likelihood evidence, root cause diagnosis 1 INTRODUCTION The necessity of FDD tools is well established in the process industries to maintain the product quality demand, safe operation, and rigorous environmental regulations[1, 2]. FDD is becoming more complex with the advancement of automated control systems. A classification of FDD tools can be found in [3]. Although data driven MSPM tools are widely used in the process industries for fault detection due to their capability of handling numerous variables and ease of application, they are not reliable in root cause diagnosis[4]. On the other hand, knowledge based tools can efficiently diagnose the root cause of process abnormality and lack in robust detection capacity[5].many hybrid methods have been proposed utilizing the individual strength of data based and knowledge based FDD tools[6-9]. PCA became popular in the process industries after the work of Kresta et. al.[10]. PCA can reduce the monitoring cost by projecting the high dimensional process variables in lower dimensional feature space[11]. Like other MSPM tools, PCA is only suitable for fault detection. It can provide some diagnostic information by generating the multivariate contribution plots[7]. The variable which has the highest contribution in the contribution plot is diagnosed as the root cause. This diagnosis result is often misleading mainly due to the smearing effect[12]. Another reason is that symptoms often show more contribution than the root cause variable. These make the task of root cause diagnosis more difficult. A BN is an emerging knowledge based tool in the field of FDD. It can represent the complex cause-effect relationships among the process variables in graphical view[8]. Process measurements are always noisy which result in uncertainty. Classical knowledge based tools (e.g. fault trees, sign digraphs, expert systems etc.) are vulnerable to uncertainty. A BN can handle uncertainty in terms of conditional probabilities. Another advantage is that it can be constructed utilizing the expert knowledge in absence of historical process data[6].however, it needs evidence to propagate the belief throughout the entire network to provide certain conclusion[13]. 469

2 Mallick and Imtiaz [7] proposed a hybrid FDD framework using the early detection capacity of PCA and robust diagnostic capacity of a BN. They considered that the symptoms show more contribution than the root cause in the multivariate contribution plot. Hard evidence (P(fault)=100%) was given in the faulty state of the variable diagnosed by PCA. However, PCA can diagnose the root cause accurately depending on the fault type and magnitude. In such cases, the proposed framework in [7] will fail to diagnose the root cause. The main aim of this work is to improve the diagnostic capacity of this hybrid framework. To do so, multiple likelihood evidence have been used to update the BN. The proposed PCA-BN with multiple likelihood evidence based methodology has been applied to the TE chemical process. Two case studies are presented in this paper. It is found that the proposed hybrid framework successfully diagnoses the root causein both cases. 2 METHODOLOGY 2.1 Principal Component Analysis (PCA) PCA is mainly a dimensionality reduction technique for multivariate data analysis.it is widely used in the process industries to detect the fault. It can reduce the dimension keeping the key information of original data[11]. PCA determines a set of new variables which are known as the principal components (PCs) by performing singular value decomposition (SVD) on the covariance (or correlation) matrix of original data matrix. PCs are linear combinations of original variables and uncorrelated to each other. Usually, first few PCs can explain the information of original data. Geometrically, PCs are obtained by rotating the axes of original coordinate system to a new set of axes to the directions to capture the maximum variability of original data[10]. Consider a data matrix, where n is the number of samples or observations and m is the number of variables. The covariance matrix, R, is given by: (1) SVD of R is performed in such a way so that R=U U T where is a diagonal matrix, which contains the eigenvalues of R 1 2 m). U are the eigen vectors. Columns of U are called the PCs. Cumulative percent variance (CPV) approach is the easiest way to determine the required number of PCs[14]. The algebraic equation of CPV can be expressed as: (2) Where, k is the required number of PCs. Transformation matrix, P contains m number of rows and k number of columns. Score, T of the transformation matrix can be calculated as: Score matrix represents the original data matrix, X in reduced dimension. The residual matrix, E, can be calculated as: 2 Typically, fault detection in PCA is done by monitoring the or squared prediction error (SPE) statistics based control chart. T 2 measures how far a sample lies from the centre of the feature space and SPE measures the Euclidean distance between PC feature space and the residual space. T 2 value and contribution of the i th monitored sample can be obtained from Equation 5 and 6 respectively: (3) (4) 470

3 (5) (6) The threshold value of T 2 is computed as: (7) Where, is the probability obtained from F distribution with degrees of freedom with 1- level of confidence. 2.2 Bayesian Network (BN) A BN is a probabilistic framework, which represents the subjective knowledge in graphical form[6, 9]. It is a directed acyclic graph (DAG). A BN is comprised of four structural components: nodes, acyclic arcs, prior and conditional probabilities. Nodes and arcs are the qualitative part of a BN. Prior and conditional probabilities enable a BN to perform quantitative analysis. A node represents a random variable, while an arc indicates the nature of dependency between the variables. An arc is generated from a parent node (cause) and directed to a child node (effect). Prior is the initial information about a node. The nodes which have no parent nodes are called the root nodes. On the other hand, the nodes which have no child node are called the leaf nodes. An intermediate node serves as both a child and a parent node in a BN[9]. Conditional probability determines the degree of influence between the variables connected by an arc. Two types of conditional probability exist in a BN: likelihood probability and posterior probability. Likelihood probability reflects the probability of a child node given a prior belief of its parent node, and posterior probability is developed based on an evidence in a child node. In this work,prior knowledge, and process flow diagram (PFD) have been used to determine the network structure. If there is any recycling variable in the process, duplicate dummy node is created to avoid the cyclic network. Conditional probability tables (CPTs) have been estimated from PCA residuals using maximum likelihood estimation (MLE) technique proposed by Gharahbagheri et. al. [6]. Message passing from one node to another node in a BN is called inference. (shown in Equation 8) is the governing equation of a BN. (8) Where, P( ) is the prior belief, P(X) is the probability of an observation or evidence, P(X/ ) is the likelihood probability, and P( /X) is the posterior probability. For a certain evidence of X, the updating equation can be written as: (9) -backward (FB) algorithm is used for BN inference in this work[13]. According to this algorithm, the message goes fro Detail of this algorithm can be found in [7]. 471

4 2.3 Hard and Uncertain Evidence Evidence is the new information about an event. A BN needs evidence to diagnose the root cause. This evidence can be certain or probabilistic. When any state of a node is updated with 100% certainty, it is called a hard evidence. If there is any uncertainty in the observation (e.g. P(fault)=60%), this can be considered as an uncertain evidence.hard evidence is currently used in the BN based hybrid methods[6-9]. However, multivariate contributions are uncertain in nature. Hence, it update the BN with uncertain or probabilistic evidence. In this paper, we have used likelihood evidence which is a kind of uncertain evidence. It updates the BN using the likelihood ratio of the observed uncertain evidence. Detail on different types of uncertain evidence is available in[15]. 2.4 PCA-BN with Multiple Likelihood Evidence based FDD Methodology Figure 1 shows the proposed FDD methodology. PCA is the fault detection and primary diagnosis tool. It also serves as observed information provider to the BN which completes the root cause diagnosis using the evidence received from PCA. In this paper, we have used PCA- T 2 contribution plot for generating evidence, since it consistently provides significant information compared to PCA-SPE about a fault to the BN which can be utilized to identify the root cause accurately. Figure 1: Proposed FDD Algorithm 472

5 The off-line phase of the methodology consists of five steps: (1) Historical process data in fault free condition are collected. These data are auto-standardized (median cantered and unit variance). (2) Number of PCs is calculated using Equation 2. (3) Threshold of T 2 control chart is calculated using Equation 7. (4) Prior knowledge and PFDs are integrated to determine the qualitative part of the BN. (5) Prior and CPTs are estimated from PCA residuals and provided to the BN to construct its quantitative part. The on-line phase consists of three steps: (1) On-line samples have been auto-standardized using same median and standard deviation obtained in off-line phase and T 2 value is computed using Equations 5 and 6. To minimize the false alarms, fault is detected when three consecutive samples exceed the threshold. (2) Average contribution of the first ten samples from detection point is used to generate the contribution plot. In a contribution plot, all the variables can have less than 50% contribution. If these evidence are used to update the BN, it will show increased tendency towards the normal operating state. To avoid this, the contributions are re-scaled on a scale of 0-80%. The root cause variable diagnosed by PCA at the first stage is assigned as P(fault)=0.80. Other variables are re-scaled compared to (3) The variables which have more than 10% re-scaled contribution are selected to update the BN. Percentage change in the faulty state is calculate for all the variables. Root cause is diagnosed considering the cause-effect relationship. If the variable with the highest percentage increase in the faulty state is a child node, root cause is diagnosed among its parent nodes. 3 INDUSTRIAL APPLICATION Proposed methodology has been applied to the Simulink model of a real industrial process, the TE chemical process described in [16].The TE chemical process shown in Figure 2 produces two products from four reactants by irreversible and exothermic reactions. It has five major units: thereactor, the product condenser, a vapour-liquid separator,a recycle compressor, and a product stripper. Three gaseous reactants (A, D, and E feed) are fed into the reactor, where liquid products are formed through a catalysed chemical reaction. The products as well as the unreacted feeds leave the reactor. The product stream enters the condenser as vapour, and becomes condensed. Then product stream passes through the vapour-liquid separator, where the condensed and non-condensed products are separated. A centrifugal compressor recycles the non-condensed product back to the reactor, and the condensed product moves into the stripper to be stripped. The final product stream exits from the base of the stripper, and is pumped to the downstream for further refinement. 473

6 Figure 2: Schematic Diagram of the TE Chemical Process There are 22 continuous process variables, 19 variables related to the composition measurement and 12 manipulated variables in the TE chemical process. These 22 continuous process variables are monitored in this study, and their description is listed in Table 1. There are 15 known and 5 unknown faults in the TE chemical process. Description of these faults can be found in[9, 16]. In this paper, two fault scenarios: IDV 1 (step change in A/C feed ratio, B composition constant) and IDV 14 (reactor cooling water valve stiction) are presented as the case studies to demonstrate the suitability of the proposed PCA-BN with multiple likelihood evidence based methodology. In both cases, the faults start after 1000 samples of normal operation, and keep continuing for the 500 test samples fault free samples are generated, and these samples are auto-standardized to zero median and unit variance. 18 PCs can capture more than 85% of total variation, and are selected to calculate the threshold of PCA-T 2. The threshold is computed as with a 95% level of confidence. Prior knowledge and PFDs are used to construct the qualitative part of the BN. The TE chemical process has a recycle variable, XMEAS (5). A duplicate dummy node of XMEAS (5) is created to avoid the cyclic structure. Prior and CPTs are calculated from PCA residuals. Figure 3 shows the constructed BN. Table 1:Description of the Monitored Variables in the TE Chemical Process Variable No Description XMEAS (1) A Feed (Stream 1) XMEAS (2) D Feed (Stream 2) XMEAS (3) E Feed (Stream 3) XMEAS (4) A and C Feed (Stream 4) XMEAS (5) Recycle Flow (Stream 8) XMEAS (6) Reactor Feed Rate (Stream 6) XMEAS (7) Reactor Pressure XMEAS (8) Reactor Level XMEAS (9) Reactor Temperature 474

7 XMEAS (10) Purge Rate (Stream 9) XMEAS (11) Product Separator Temperature XMEAS (12) Product Separator Level XMEAS (13) Product Separator Pressure XMEAS (14) Product Separator Underflow (Stream 10) XMEAS (15) Stripper Level XMEAS (16) Stripper Pressure XMEAS (17) Stripper Underflow (Stream 11) XMEAS (18) Stripper Temperature XMEAS (19) Stripper Steam Flow XMEAS (20) Compressor Work XMEAS (21) Reactor Cooling Water Outlet Temperature XMEAS (22) Separator Cooling Water Outlet Temperature Figure 3: Bayesian Network of the TE Chemical Process 3.1 IDV 1 (step change in A/C feed ratio, B composition constant) After 1000 samples of fault free operation, a step change occurs in the A/C feed ratio which affects the stripper pressure. This fault is detected by the T 2 control chart at 1232 nd sample (Figure 4). The reason of delayed detection is the smaller fault magnitude (0.15% average reduction for the 500 test samples from the normal operating condition samples). Then,the T 2 contribution plot is generated from the average contribution from1232 nd to 1241 st samples. XMEAS (16) has the highest contribution (33.71%) to the fault, and its contribution is assigned as 80% in the re-scaled contribution plot. The contribution of other variables is determined relative to the original contribution of XMEAS (16) (Figure 5). 475

8 Figure 4: T 2 Control Chart for IDV1 T 2 Contribution Plot T 2 Contribution Original Re-scaled Variable No. Figure 5: T 2 Contribution Plot for IDV1 The next step is to identify the root cause of the fault. It can be seen from Figure 5 that XMEAS (7), XMEAS (11), XMEAS (12), XMEAS (13), XMEAS (16), XMEAS (18) and XMEAS (22) have more than 10% re-scaled contribution. These probabilistic contributions can be treated as the likelihood evidence, and these likelihood evidence are used to update the BN. Figure 6(a) shows the updated BN for IDV 1. In the updated BN, XMEAS (16) has the highest increase (94.07%) in the faulty state (Figure 6(b)). However, it is a child node. It has three parent nodes: XMEAS (4), XMEAS (15) and XMEAS (19). XMEAS (19) has an increased probability to be in the normal state. Although both XMEAS (4)and XMEAS (15) have increased proclivity in the faulty state, XMEAS (4) has more increase in the probability to be a faulty state than XMEAS (15) and can be accurately diagnosed as the root cause. 476

9 (a) 100% Change in Probability 60% 20% -20% -60% -100% R Variable No. (b) Figure 6: Root Cause Diagnosis for IDV 1 (a) Updated BN with Multiple Likelihood Evidence (b) Percentage Change in Probability 3.2 IDV 14 (reactor cooling water valve stiction) In this fault scenario, reactor cooling water valve gets stuck from 1001 samples. As a result, reactor temperature gets affected. This fault is detected at 1323 rd sample by the T 2 control chart (Figure 7). The reason of delayed detection lies on the fact that temperature takes longer time to get affected. The T 2 contribution plot is generated from the average contribution of 1323 rd nd samples (Figure 8). XMEAS (9) has the highest contribution in the T 2 contribution plot. It implies that PCA- 477

10 T 2 can diagnose this fault. However, XMEAS (9) is a child node. According to [7], hard evidence will be given in the not_ok state of XMEAS (9) which will lead to false diagnosis. Figure 7: T 2 Control Chart for IDV14 T 2 Contribution T 2 Contribution Plot Original Re-scaled Variable No. Figure 8: T 2 Contribution Plot for IDV 14 XMEAS (6), XMEAS (8), XMEAS (9), XMEAS (11), XMEAS (14) and XMEAS (21) have more than 10% re-scaled contribution. Likelihood evidence of these six variables are used to update the BN. Figure 9(a) shows the updated BN. Figure 9(b) shows the percentage change in probability for all the monitored variables. It should be noted that any negative value in the percentage change plot implies that the variable has increased tendency to be in the normal state. XMEAS (21) has the highest percentage increase in the faulty state. Its only parent node, XMEAS (9) has the second highest increase in the faulty state. Hence, it can be diagnosed as the root cause of the process abnormality. 478

11 (a) 20% Change in Probbaility 0% -20% -40% -60% -80% R Variable No. (b) Figure 9: Root Cause Diagnosis for IDV 14 (a) Updated BN with Multiple Likelihood Evidence (b) Percentage Change in Probability 4 CONCLUSION In this paper, a hybrid methodology is proposed based on PCA-T 2 -BN with multiple likelihoodevidence to improve the diagnostic capacity of PCA and existing PCA-BN framework. Two case studies are presented in a benchmark chemical process. Proposed technique improves the diagnosis of PCA-T 2 in the first case study, and it provides robust performance over the hard evidence based conventional approach in the latter case study.the reason lies on the fact that the proposed hybrid framework enables the BN to get updated with more information about a fault. This methodology does not require any fault signature to detect and diagnose the fault, and provides a comprehensive solution in root cause diagnosis as it can identify the potential source of process abnormality in any node in the BN. Future work may include incorporating the fault propagation 479

12 pathway identification which will provide important information about the affected variables due to a fault. 5 ACKNOWLEDGEMENTS This work was funded by the Natural Sciences and Engineering Research Council (NSERC) under the NSERC Discovery Grant program. REFERENCES [1] Isermann, R., 1982, "Process fault detection based on modeling and estimation methods A survey," Automatica, 20(4), pp DOI: [2] Severson, K., Chaiwatanodom, P., and Braatz, R. D., 2016, "Perspectives on process monitoring of industrial systems," Annual Reviews in Control, 42, pp DOI: [3] Venkatasubramanian, V., Rengaswamy, R., Yin, K., and Kavuri, S. N., 2003, "A review of process fault detection and diagnosis: Part I: Quantitative model-based methods," Computers & chemical engineering, 27(3), pp DOI: [4] Venkatasubramanian, V., Rengaswamy, R., Kavuri, S. N., and Yin, K., 2003, "A review of process fault detection and diagnosis: Part III: Process history based methods," Computers & chemical engineering, 27(3), pp DOI: [5] Venkatasubramanian, V., Rengaswamy, R., and Kavuri, S. N., 2003, "A review of process fault detection and diagnosis: Part II: Qualitative models and search strategies," Computers & Chemical Engineering, 27(3), pp DOI: [6] Gharahbagheri, H., Imtiaz, S., and Khan, F., 2017, "Root cause diagnosis of process fault using KPCA and Bayesian network," Industrial & Engineering Chemistry Research, 56(8), pp DOI: /acs.iecr.6b01916 [7] Mallick, M. R., and Imtiaz, S. A., 2013, "A hybrid method for process fault detection and diagnosis," 10th IFAC International Symposium on Dynamics and Control of Process Systems, Mumbai, pp [8] Wang, Y., Liu, Y., Khan, F., and Imtiaz, S., 2017, "Semiparametric PCA and bayesian network based process fault diagnosis technique," The Canadian Journal of Chemical Engineering. DOI: /cjce [9] Yu, H., Khan, F., and Garaniya, V., 2015, "Modified independent component analysis and bayesian network-based two-stage fault diagnosis of process operations," Industrial & Engineering Chemistry Research, 54(10), pp DOI: /ie503530v [10] Kresta, J. V., MacGregor, J. F., and Marlin, T. E., 1991, "Multivariate statistical monitoring of process operating performance," The Canadian journal of chemical engineering, 69(1), pp DOI: /cjce [11] Chiang, L. H., Russell, E. L., and Braatz, R. D., 2001, Fault Detection and Diagnosis in Industrial Systems, Springer-Verlag London, UK. ISBN:

13 [12] Liu, J., 2012, "Fault diagnosis using contribution plots without smearing effect on non-faulty variables," Journal of Process Control, 22(9), pp DOI: [13] Pearl, J., 1988, Probabilistic reasoning in intelligent systems: networks of plausible inference, Morgan Kaufmann Publishers Inc., San Francisco, USA. ISBN: [14] Jackson, J. E., 1991, A user's guide to principal components, John Wiley & Sons, Toronto, Canada. ISBN: [15] Mrad, A. B., Delcroix, V., Piechowiak, S., Leicester, P., and Abid, M., 2015, "An explication of uncertain evidence in Bayesian networks: likelihood evidence and probabilistic evidence," Applied Intelligence, 43(4), pp DOI: [16] Downs, J. J., and Vogel, E. F., 1993, "A plant-wide industrial process control problem," Computers & chemical engineering, 17(3), pp DOI: 481