Fault Identification in Chemical Processes Through a Modified Mahalanobis-Taguchi Strategy

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1 Fault Identification in Chemical Processes Through a Modified Mahalanobis-Taguchi Strategy Pedro Saraiva *, Nuno Faísca, Raquel Costa and Alcides Gonçalves GEPSI-PSE Group, Department of Chemical Engineering University of Coimbra, Pólo II, Pinhal de Marrocos, Coimbra, Portugal Abstract On the chemical process industries an appropriate identification of faults has become at present one of the most critical and challenging PSE activities. Recently, Taguchi and Jugulum (2002) described a new data based approach for diagnosis and forecasting using multivariate data, the so-called Mahalanobis-Taguchi System (MTS). MTS is considered to be a non-parametric approach, and has been applied with success in a number of different fields. In the present work, we apply a modified version of MTS (referred as MMTS) to perform fault identification in chemical processes. The performance of our MMTS approach is evaluated by its application to a continuousstirred-tank-reactor (CSTR) simulated by Kano et al. (2002) and comparing the results obtained here with those provided by these authors. The results thus obtained show that indeed MMTS seems to be a quite promising data based approach for on-line fault detection in chemical processes. Keywords: fault detection, process quality, Mahalanobis-Taguchi Strategy 1. Introduction One of the most critical and challenging tasks for the chemical process industries, as well as within the scope of PSE research activities, is related with the proper and timely identification of faults. Many approaches have been developed to address this issue, which may be classified within one of two major paradigms: Process History-Based methods (data based) and Model-Based techniques (Venkatasubramanian et al., 2003a, 2003b, 2003c). Recently, Taguchi and Jugulum (2002) described a new data based approach for diagnosis and forecasting using multivariate data, the so-called Mahalanobis-Taguchi System (MTS). It is composed by four major stages: 1) a group of normal (no faults present) data records must be selected, and its underlying scaled Mahalanobis Distances ( ) are computed, thus leading to a proper definition of a measurement scale for detecting faults; 2) such a measurement scale is validated by confirming that it clearly discriminates between normal and abnormal items by comparing the values of faulty situations with those of normal operation; 3) a subset of the initial variables can be defined in order to provide a simpler, yet sounder, basis for identifying particular * Author to whom correspondence should be adressed: eq1pas@eq.uc.pt

2 types or all the faults; 4) to carry out fault identification, the final MTS scale (only with the useful variables) is used, so that the of each item is compared with a given threshold, and from this comparison one comes up (or not) with the identification of a certain fault. MTS is considered to be a nonparametric approach, not relying in any sort of underlying probability distribution, and has been applied with success in a number of different fields. In particular, the idea of using Mahalanobis Distances () as a continuous measurement of the degree of abnormality for a certain data record seems to be quite promising (Woodall et al., 2003a; Jugulum et al., 2003; Abraham and Variyath, 2003; Hawkins, 2003; Woodall et al., 2003b.) In the present work, we apply a modified version of MTS to perform fault identification in chemical processes. The resulting Modified Mahalanobis-Taguchi Strategy (MMTS) provides a framework for process monitoring which combines the abnormality measurement concept advanced by Taguchi and Multiple Regression Analysis (MRA). In order to evaluate the performance of the MMTS approach for fault diagnosis in chemical processes, we tested its application to a continuous-stirred-tank-reactor (CSTR) simulated by Kano et al. (2002) and compare the results obtained. 2. Methodology Our MMTS approach does comprise the following four main steps: 2.1 Construction of a measurement scale We want to build a scale that makes it possible to measure, by comparison with normal data, the degree of abnormality associated with a given fault. Thus, we need to define what is a normal situation and what are the important variables for building such a measurement scale. Therefore, we begin with a collected set of normal data (X ij, i = 1, 2, k variables; j = 1, 2,, n cases). The ensemble of all the corresponding values constitutes the so-called Mahalanobis space, with values computed as: T 1 j = ZijC Zij i =1,2,,k ; j =1,2,,n (1) where Z ij represents the vector of standardized values ( Zij ( Xij mi ) si transpose and T = ), is its 1 C the inverse of the correlation matrix, C = 1 T ( n 1 ) Z Z, m ij ij i and s i being, respectively, the mean and standard deviation for the i th variable. If equation (1) is divided by k and n is large, the average value of these scaled ( ) will be, approximately, equal to one (Woodall et al., 2003a). Therefore, the construction of the Mahalanobis space is based on: n j= 1 Z ij 1 k T 1 j = ZijC Zij i = 1, 2,, k ; j = 1, 2,, n (2).

3 2.2 Validation of the measurement scale With the objective of testing how good the measurement scale is, a set of values, corresponding to abnormal situations, is now confronted with the scores for normal records. These scores are computed using the correlation matrix as found just from normal data. If the new values are significantly greater than one, we are able to differentiate normal from faulty situations using such a scale. 2.3 Identification of useful variables The goal of this step is to select, from all of the available variables, the ones that provide added value for fault diagnosis. As few as possible variables are kept for achieving reliable fault identifications. Rather then adopting the procedure suggested by Taguchi and Jugulum (2002) for doing so (Woodall et al., 2003a; Abraham and Variyath, 2003; Hawkins, 2003; Woodall et al., 2003b), we will be making use of stepwise MRA as a supporting tool for variable selection, since it is a classical and statistically sound approach. The choice of the particular subset of available variables for performing fault identification can be made for each of the different kinds of abnormal situations that may occur. 2.4 Fault diagnosis After having determined which variables should be monitored in order to identify each kind of fault, it is necessary for each case to construct Mahalanobis spaces and measurement scales that take into account only the relevant subset of variables. A fault is identified every time that the computed value in such a scale is above a given threshold. Taguchi and Jugulum (2002) defined such thresholds by means of quadratic loss functions, whereas here we will base such a choice on the corresponding average run length (ARL) scores obtained for normal data (Kano et al., 2002). This option derives from the fact that ARL is a well defined and accepted criterion for evaluating the performance of Statistical Process Control (SPC) and fault diagnosis procedures, used namely by Kano et al. (2002). 3. Results Our MMTS approach was applied for fault diagnosis in a CSTR (Figure 1) simulated and studied earlier on by Kano et al. (2002), making use of the same monitored variables (Table 1) and data, which cover normal operating conditions as well as eleven different abnormal situations (Table 2). X 5 LC X 4 X 2 X 9 FC X 6 X 1 X 8 FC X 7 TC X 3 Figure 1 Simulated CSTR with feedback control.

4 Table 1 Monitored process variables. X 1 reactor temperature X 2 reactor level X 3 reactor outlet flow rate X 4 coolant flow rate X 5 reactor feed flow rate X 6 MV of level controller X 7 MV of outlet flow controller X 8 MV of temperature controller MV of coolant flow controller X 9 Table 2 Process faults. Case Operation Mode N normal operation F 1 catalyst deactivation - ramp F 2 heat exchanger fouling - ramp F 3 dead coolant flow measurement F 4 bias in reactor temperature measurement F 5 coolant valve stiction F 6 feed flow rate step F 7 feed concentration ramp F 8 feed temperature ramp F 9 coolant feed temperature ramp F 10 upstream pressure in coolant line step downstream pressure in outlet line - step F 11 In order to evaluate the performance of our MMTS approach, we compared its performance with the ones obtained earlier on by Kano et al. (2002) through a Combined Multivariate Statistical Process Control (CMSPC) technique, the one that provided the best results amongst four different methodologies explored by these authors. As suggested by Kano et al. (2002), we will be using ARL values as our fault diagnosis performance criteria for comparative purposes. Table 3 summarizes the evaluation of MMTS performance, as compared with the results obtained by Kano et al. (2002). One can observe that there is little or no difference at all between the ARL scores obtained based upon CMSPC and MMTS without variable selection, as well as that a small subset of variables is able to present similar performances, sometimes making use of just a single monitored variable. Table 3 Average run length (ARL) comparisons. Case CMSPC MMTS without MMTS with variable selection variable selection ARL Number of variables used N F F F F F F F F F F F

5 ARL Number of selected variables Figure 2 Average run length (ARL) for detecting fault F 5 as more and more variables are taken into account ( MMTS Results, CMSPC performance). As an illustrative example, Figure 2 shows for a particular fault how the MMTS performance evolves as the number of supporting variables is increased. The final number of variables used, according to the stepwise MRA methodology comprises three variables, since additional ones do not provide significant our fault diagnosis capability. Therefore, to detect fault F 5 we would suggest monitoring only variables X 1, X 8 and X 9 and use them to support the MMTS approach. The results presented in the last two columns clearly show the effectiveness of our MMTS approach when applied to chemical processes. In fact, after selecting a reduced subset of useful variables, MMTS still leads to ARL values that are similar to the ones obtained by making use of all the variables and exploring the best of the techniques examined by Kano et al. (2002), the only exception being associated with the detection of fault F 10. One way to further test the robustness of our methodology for achieving a proper identification of a subset of variables for performing fault diagnosis, in addition we did combine the original variables together with simulated white noise factors, by considering four new such variables on top of the earlier ones: X~N(0,1), Y~N(2,1), W~N(0,10) and Z~N(20,5). Attending to the fact that such noise variables are independent from the simulated process, and useless from a fault diagnosis perspective, one should expect our stepwise MRA selection procedure to choose, first of all, the original variables that are really helpful for differentiating a certain fault from normal operation. This is exactly what happened to be the case for instance regarding fault F 6. With the four noise factors added, the variables selected for supporting fault diagnosis are exactly the same ones that ore obtained before, under the absence of such four noise factors. 4. Concluding Remarks This article presents what we believe to be the first application of a MTS based approach for monitoring and fault identification in chemical processes. We introduce some adaptations to the original MTS method, thus leading to the so-called MMTS

6 approach. This methodology allows us to select the most convenient subset of variables to monitoring a given chemical process and perform fault diagnosis, leading eventually to a cheaper and efficient fault diagnosis system. The performance of our MMTS approach is quite competitive when compared with the results obtained over the same sets of data based upon a number of different alternative techniques. A simulated CSTR case study was employed in order to support such a comparative analysis, with quite positive conclusions. Such preliminary results point out that indeed MMTS does seem to provide a practical way for performing fault identification in a number of relevant chemical processes. Future work may address a number of pending issues and refinements, namely regarding on how to optimise the definition of thresholds in the measurement space to differentiate normal from faulty process conditions. Acknowledgments The authors acknowledge finantial support provided by FCT research project POCTI/EQU/32647, as well as data and software provided by M. Kano and R. Jugulum. References Abraham, B. and A. M. Variyath, 2003, Technometrics, 45 (1), 22. Hawkins, D.M., 2003, Technometrics. 45 (1), 25. Jugulum, R., G. Taguchi, S. Taguchi and J. O. Wilkins, 2003, Technometrics. 45 (1),16. Kano, M., S. Tanaka, S. Hasebe, I. Hashimoto and H. Ohno, 2002, Proceedings of International Symposium on Design, Operation and Control of Chemical Plants (PSE Asia 2002). Taguchi, G. and R. Jugulum, 2002, The Mahalanobis-Taguchi Strategy. Wiley, New York. Venkatasubramanian, V., R. Rengaswamy, K. Yin and S. N. Kavuri, 2003a, Comp. Chem. Eng. 27, 293. Venkatasubramanian, V., R. Rengaswamy and S. N. Kavuri, 2003b, Comp. Chem. Eng. 27, 313. Venkatasubramanian, V., R. Rengaswamy, S. N. Kavuri and K. Yin, 2003c, Comp. Chem. Eng. 27, 327. Woodall, H. W., R. Koudelik, K. L. Tsui, S. B. Kim, Z. G. Stoumbos and C. P. Carvounis, 2003a, Technometrics. 45 (1), 1. Woodall, H. W., R. Koudelik, K. L. Tsui, S. B. Kim, Z. G. Stoumbos and C. P. Carvounis, 2003b, Technometrics. 45 (1), 29.