Moving PCA for process fault detection a performance and sensitivity study

Moving PCA FOR PROCESS FAULT DETECTION – A PERFORMANCE AND SENSITIVITY STUDY DOAN XUAN TIEN NATIONAL UNIVERSITY OF SINGAPORE 2005 Moving PCA FOR PROCESS FAULT DETECTION – A PERFORMANCE AND SENSITIVITY STUDY DOAN XUAN TIEN (B.Eng.(Hons.), University of Sydney) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2005 Acknowledgements First of all, I would like to thank my supervisor, A/Prof Lim Khiang Wee for his invaluable guidance, support and encouragement throughout my time here He has given advices not only from an academic point of view but also from practical senses which I have not experienced He has actively searched for better ways to support me and in the end he encourages and helps me planning the first step in my career For all of that and much more, I would like to express my deepest gratitude to him I am also grateful to Dr Liu Jun for his time and efforts in evaluating my progress and managing ICES–related issues With his support, my life in ICES could not get more enjoyable I would also thank the Institute of Chemical and Engineering Sciences (ICES) for granting me the research scholarship and funds needed to pursuit my Master degree It has been a wonderful experience for me in ICES and I look forward to continuing working here I would like to dedicate this to my parents, my sisters and brothers-in-law for their understandings and supports over these years i Contents Fault detection approaches – An overview 1.1 Fault detection – A definition 1.2 Why fault detection is critical 1.3 Current FDI approaches 1.3.1 Model–based FDI approaches 1.3.2 Process history–based FDI approaches 1.4 Principal Component Analysis (PCA) 13 1.4.1 Model development 13 1.4.2 Number of Principal components (PCs) 16 1.4.3 Conventional multivariate statistics 18 1.4.4 Performance criteria 22 1.5 Thesis objectives 23 PCA for monitoring processes with multiple operation modes 26 ii 2.1 Motivation 26 2.2 Moving Principal Component Analysis 33 2.2.1 Alternative scaling approach 33 2.2.2 Practical issues 37 2.2.3 Detection rule 38 2.2.4 MPCA algorithm 40 2.3 Algorithms for conventional PCA, APCA, and EWPCA 42 2.3.1 Conventional PCA 42 2.3.2 APCA 44 2.3.3 EWPCA 45 2.4 A preliminary comparison between algorithms 47 2.5 Simulation studies 48 2.5.1 Tennessee Eastman Process (TEP) 48 2.5.2 Methodology 50 2.5.3 Results 51 2.6 Industrial case study 55 2.6.1 Process description 55 2.6.2 Results 57 2.7 Chapter conclusion 61 iii Evaluation of MPCA Robustness 63 3.1 Introduction 63 3.2 Moving window size 65 3.3 Number of principal components retained a 70 3.4 Confidence limit 77 3.5 Monitoring indices 80 3.5.1 Theory and implementation 80 3.5.2 Comparative results 84 3.6 Conclusion 87 Conclusion 88 A Process time constants 96 A.1 TEP 96 A.2 Industrial case study 96 iv Executive Summary Process monitoring and fault detection is critical for economic, environmental as well as safety reasons According to how a–priori knowledge of process is used, fault detection (and isolation) methods can be classified as process model–based or process history based or somewhere in between Although the choice is often context– dependent, the use of process history based methods has become more popular due to the fact that massive databases of online process measurements are available for analysis This thesis evaluates the Principal Component Analysis approach (PCA), one of many process history–based methods for process monitoring and fault detection using operating data from an oil refinery and simulation data from a well–known research case study Although successful applications of PCA have been extensively reported, it has the major limitation of being less effective with time–varying and/or non–stationary processes or processes with multiple operation modes To address the limitation, this thesis proposes a Moving Principal Component Analysis (MPCA), which is based on the idea that updating scaling parameters (mean and standard deviation) from a moving window is adequate for handling the process variation between different operation modes MPCA performance is compared with other published approaches including conventional PCA, adaptive PCA, and Exponentially Weighted PCA in monitoring Tennessee Eastman Process (TEP) simulation and analyzing an industrial data set It is shown that the proposed MPCA method performs better than the other approaches when performance is measured by missed detection, false alarms, time delay and computational requirement v Sensitivity of MPCA performance is also investigated empirically by varying critical parameters including moving window size, number of principal components retained, and confidence limits The results indicate that MPCA method is not sensitive to those parameters in monitoring TEP process Its performance does not change significantly with varying the size of moving window, number of principal components retained, or confidence limits However, tuning of parameters is necessary for industrial application of MPCA It has also been found that reasonable MPCA performance could be achieved using moving window size of – process time constant, PCs, and 99% – 99.9% confidence limits In addition, several monitoring indices including conventional statistics (T and Q), combined QT and standardized Q index are also implemented in MPCA It is shown that MPCA performance does not depend much on the form of the monitoring index being employed All of the indices perform well although the standardized Q statistic requires more computation time vi List of Figures 1.1 Transformations in a fault detection system 1.2 Classification of FDI methods 2.1 Original operation data from a Singapore petrochemical plant X16 and X08, correspond to two different periods of plant operation The plant is in normal steady state in X16 but appears to experience some disturbance in X08 27 2.2 Conventional PCA (– T statistic) monitoring results: test data X08 is scaled against the mean and standard deviation of the training data X16 and subsequently analyzed by a PCA model derived from X16 28 2.3 Conventional PCA (– Q statistic) monitoring results: test data X08 is scaled against the mean and standard deviation of the training data X16 and subsequently analyzed by a PCA model derived from X16 29 2.4 Monitoring by T statistic for test data: X08 is initially scaled against its mean and standard deviation (ie auto–scaled) and then analyzed by a PCA model derived from X16 35 vii 2.5 Monitoring by Q statistic for test data: X08 is initially scaled against its mean and standard deviation (ie auto–scaled) and then analyzed by a PCA model derived from X16 36 2.6 MPCA implementation 40 2.7 MPCA schematic diagram 41 2.8 Conventional PCA implementation 42 2.9 Schematic diagram for conventional PCA method 43 2.10 Implementation of APCA method 45 2.11 APCA schematic diagram 46 2.12 Tennessee Eastman Process 49 2.13 Performance of four PCA methods in monitoring TEP– T statistic Simulated faults include idv(1) (feed composition), idv(4) (reactor cooling water inlet temperature) and idv(8) (feed composition) at 3000–4000, 7000–8000, 10000–11000, respectively 52 2.14 Performance of four PCA methods in monitoring TEP – Q statistic Simulated faults include idv(1) (feed composition), idv(4) (reactor cooling water inlet temperature) and idv(8) (feed composition) at 3000–4000, 7000–8000, 10000–11000, respectively 53 2.15 Process diagram for the industrial case study 56 2.16 Performance of four PCA methods in industrial case study – T statistic 58 2.17 Performance of four PCA methods in industrial case study – Q statistic 59 viii The implementation of the newly proposed MPCA approach with the Johan’s standardized Q statistic is very similar to MPCA using the original Q index The difference is that the residuals need to be replaced by the scaled ones and the upper control limit g˜χ2h;α for a chosen significant level α must be calculated accordingly In ˜ addition, the moving window is taken as the normal operating condition and hence sj is evaluated (online) based on the moving window The following parameter settings is chosen as a result of empirical analysis Table 3.11: Parameter settings for MPCA using Johan’s standardized Q index 3.5.2 Parameters TEP simulation industrial case study No of PCs 2 Window size (samples) 700 80 Confidence limit 99.99% 99.9% Comparative results The comparative study of MPCA approach using different indices is meant to serve two purposes The first one is to determine whether or not the performance of the proposed MPCA approach strongly depends upon the index it employs The second goal is to identify if possible the index which would yield the best overall performance The results obtained from analyzing TEP simulation and the industrial data set, are tabulated in Tables 3.12 and 3.13 Besides false alarms, missed detection, and maximum detection delay, cpu time in 10−3 s is also shown The additional num- 84 ber gives how much time (per sample) the online processing would require (on a Dell Pentium IV 3.4G, 512Mb RAM PC) and hence is a relative measure of computational requirement for each method Table 3.12: Comparative study of MPCA performance – TEP study Indices missed false max delay cpu time detection alarms (samples) (ms/sample) conventional T 92 2.8 conventional Q 88 2.6 combined QT 90 2.7 standardized Q 84 5.5 As can be seen in Table 3.12for TEP simulation, there is not much difference between MPCA performance using different statistics although T has a few more false alarms than any other indices All three simulated faults are detected; maximum detection delays for every indices are roughly the same; the time to analyze one data sample for each statistic are also similar (except for standardized Q which takes about twice longer) However, as shown in Table 3.13, the difference between those statistics become more significant when applying to the industrial data set In terms of missed detection and false alarms, the combined QT index appears to be the least sensitive with no false alarms and missed detection Conventional T statistic continues to be the most sensitive index producing false alarms Interestingly, the standardized Q, which is modified to improve its sensitivity, does not seem more sensitive than the other indices including the conventional Q statistic 85 Table 3.13: Comparative study of MPCA performance – industrial case study Indices missed false max delay cpu time detection alarms (samples) (ms/sample) conventional T 22 0.23 conventional Q 31 0.24 combined QT 33 0.21 standardized Q 40 0.38 The standardized Q index is also the method which requires the most computational resource Its cpu time per sample is about twice that of any other indices The reason is that in implementing MPCA with the standardized Q index, the residual is scaled against the standard deviation of the residuals from the moving window which needs to be evaluated online This obviously takes more time to carry out and hence is shown up in the standardize Q cpu time per sample Overall, MPCA performance in terms of false alarms and missed detection is considered reasonable in four cases with different monitoring indices The worst false alarm rate is out of 1440 samples, equivalent to 2.1 · 10−3 , which is about one order magnitude smaller compare to other methods [9] Similarly for the missed detection rate (The corresponding rates for MPCA in TEP simulation study are even smaller) These numbers are even slightly better than similar industrial statistics reported in [18] 86 3.6 Conclusion The chapter has studied the sensitivity of the proposed MPCA approach to changes in a number of parameters including the moving window size, the number of PCs retained and the significant level for setting the upper control limit It is found that in TEP simulation, MPCA performance does not change significantly to variations in the above parameters On the contrary, it appears that MPCA is much more sensitive in the industrial case study Any deviation from the base case scenario is likely to degrade MPCA performance The results also indicate that the moving window size seems to be less important than the number of PCs retained and the confidence level In addition, the chapter also implements the proposed MPCA with different monitoring indices including conventional statistics (T and Q), combined QT and standardized Q Comparison between MPCA using different monitoring indices indicates that conventional statistics including T and Q appear to work reasonably well compared to either combined QT or standardized Q index Both false alarm and missed detection rates are very much lower than those from other published methods The two newly proposed statistics including the combined QT and standardized Q need further modifications to improve their performance 87 Chapter Conclusion To address the time–invariant limitation of PCA technique, this thesis proposes a Moving Principal Component Analysis (MPCA) Its performance is compared with that of other published approaches including conventional PCA, adaptive PCA, and Exponentially Weighted PCA in monitoring Tennessee Eastman Process (TEP) simulation and analyzing an industrial operation data set MPCA is based on the idea that updating scaling parameters (mean and standard deviation from a moving window) is adequate for handling the process variation between different operation modes It is shown that the proposed MPCA method is simpler and requires less online computation and storage, yet performs better than the other approaches when performance is measured by missed detection, false alarms, time delay and computational requirement MPCA robustness is investigated empirically by changing critical parameters including moving window size, number of principal components retained, and confidence limits The results indicate that MPCA method is generally more sensitive in an88 alyzing the industrial data set In addition, moving window size seems to be less critical than the other two parameters Moreover, it is also shown that conventional statistics works better than the combined QT and standardized Q indices Future work The proposed MPCA method is developed for monitoring processes at different operating modes Further modification of MPCA is required for monitoring transition between process modes One obvious solution is to integrate MPCA with other scheme such as described in R Srinivasan et al ([1, 32]) In this way, the monitoring system would switch from MPCA to Srinivasan’s scheme when process transition occurs and back to MPCA when the process reaches new operating modes Clearly, further work is required for designing such a switching mechanism In addition, it might be possible for MPCA to deal with process transition by using a different method in updating the moving window Currently, it is updated when the new data is diagnosed as normal/in–control Consequently, it captures normal process dynamics in an operation mode but the dynamics during mode transition is discarded An alternative updating scheme for moving window would be: to update the window as soon as the new data becomes available regardless whether it is faulty or not Consequently, a more robust approach in estimating the scaling parameters from the moving window needs to be employed and a mechanism to differentiate between a fault and a process transition is needed 89 Bibliography [1] Sundarraman A and Srinivasan R Monitoring transitions in chemical plants using enhanced trend analysis Computers and Chemical Engineering, (27):1455–1472, 2003 [2] Westerhuis J A., Gurden S P., and Smilde A K Standardized Q–statistic for improved sensitivity in the monitoring of residuals in MSPC Journal of Chemometrics, (14):335–349, 2000 [3] ACTT The case for change Online newsletter, November 1999 Issue 12 [4] Junghui Chen and Jialin Liu Derivation of function space 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calculation gives rough estimated time constant of the case study τc = 50 minutes (or samples) 96 10.3 MV4 10.2 new steady state 10.1 10 9.9 at τ MV4 9.8 9.7 9.6 9.5 9.4 9.3 initial state 9.2 τ 9.1 3000 3100 3200 3300 3400 3500 3600 sample 3700 3800 3900 4000 Figure A.1: TEP step response 97 20.2 20 initial state process variables 19.8 19.6 at time constant τ 19.4 new steady state 19.2 19 600 650 700 750 800 850 900 samples Figure A.2: Step response for the industrial case study 98 [...]... recognize that fault detection is more appropriate than change detection in describing the cause of performance degradation and that a fault can be either a failure in a physical component, or a change in process performance [37] From a pattern recognition point of view, fault detection is in effect a binary classification: to classify a process data as either normal (conforming) or faulty (nonconforming)... 3.11 Parameter settings for MPCA using Johan’s standardized Q index 84 3.12 Comparative study of MPCA performance – TEP study 85 3.13 Comparative study of MPCA performance – industrial case study 86 xi Chapter 1 Fault detection approaches – An overview 1.1 Fault detection – A definition Generally, fault detection is defined as the “determination of the faults present in a system and. .. of detection [14] It is therefore to ascertain whether or not (and if so, when) a fault has occurred A fault can be thought of as any change in a process that prevents it from operating in a proper pre-specified manner Since performance of a process is usually characterized by a number of variables and parameters, a fault can also be defined to be any departure from an acceptable range of observed process. .. but incorporate additional information on the evolution and magnitude of process variables Quantitative approaches Quantitative process history–based approaches can be further classified as either statistical or non–statistical Artificial neural networks (ANN) are an important class of non–statistical approaches while principal component analysis (PCA) /projection to latent structure (PLS) are two of... triggered at an unmanageable rate of one alarm every 2 − 3 seconds [3] The “alarm flooding” issue and the human error factor have raised the challenge to develop more effective methods for process monitoring and fault detection 3 Figure 1.1: Transformations in a fault detection system 1.3 Current FDI approaches In general, fault detection and isolation (FDI 1 ) tasks can be considered as a series of transformations... vulnerable to noise and lead to frequent false alarms during normal operation Last but not least, storage and computational requirements also plays an important role in evaluating the performance of a fault detection method, especially in an online context Usually, quick real–time fault detection would require algorithms and implementations which are computationally less complex, but might impose a high... be seen as containing the statistical index chosen for monitoring purpose The transformation from the feature space into the 5 decision space is a functional mapping and is very much dependent on the statistical index used Lastly, the class space for fault detection has two values: 0 for normal and 1 for fault A threshold function maps the decision space into the class space Again, a priori process. .. types of faults, the advantages of both monitoring indices can be fully utilized by employing the two measures together [21] 1.4.4 Performance criteria In order to compare various fault detection methods, it is useful to identify a set of desirable criteria based on which performance of a fault detection system can be evaluated A common set of such criteria or standards for any fault detection approach... Consequently, fault detection is at the heart of a process monitoring system, which continuously determines the state of the process in real– time 1.2 Why fault detection is critical Any industrial process is liable to fault or failure In all but the most trivial cases, the existence of a fault may lead to situations with human safety and health, financial, environmental and/ or legal implications The... decomposition can be done, which result in structural hierarchy and functional hierarchy The former contains the connectivity information, while the later represents the means-end relationships between the process and its subsystems Qualitative model–based FDI approaches have a number of advantages as well as disadvantages One of the major advantages is that qualitative models do not require exact, precise information ... Comparative study of MPCA performance – TEP study 85 3.13 Comparative study of MPCA performance – industrial case study 86 xi Chapter Fault detection approaches – An overview 1.1 Fault. .. usually characterized by a number of variables and parameters, a fault can also be defined to be any departure from an acceptable range of observed process variables and/ or parameters The term fault. .. more appropriate than change detection in describing the cause of performance degradation and that a fault can be either a failure in a physical component, or a change in process performance