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Ind. Eng. Chem. Res. 1997, 36, 2672-2678
Fault Diagnosis Based on Weighted Symptom Tree and Pattern Matching Young Seok Oh, Kyung Joo Mo, and En Sup Yoon* Department of Chemical Engineering, Seoul National University, Kwanak-Gu, Shilim-Dong San 56-1, Seoul 151-742, Korea
Jong Han Yoon LG Engineering Co., Ltd., C.P.O. Box 6762, Seoul 121-721, Korea
This paper presents a fault detection and diagnosis methodology based on the weighted symptom tree (WST) and pattern matching between the coming fault propagation trend and the simulated one. In the first step, backward reasoning is used to find the possible cause candidates for the faults. The weighted symptom tree is used to generate these candidates. The weights are determined by dynamic simulations. By using a weighted symptom tree, the suggested methodology can generate the cause candidates and rank them according to their likelihoods of occurrence. In the next step, the fault propagation trends identified from the partial or complete sequence of measurements are compared to the standard fault propagation trends, which have been generated using dynamic simulation and stored a priori. A pattern matching algorithm based on a number of triangular episodes is used to match those trends effectively. The proposed methodology was illustrated using the Tennessee Eastman challenge process and showed enhanced diagnostic resolution. Introduction Every industrial process possesses the potential of deviating outside its normal and intended range of behavior. Unless detected early and contained, process deviations may lead to a serious impact on process economy, safety, product quality, and pollution level (Nam et al., 1996). Therefore, a fault detection and diagnosis system, which can monitor the status of the processes, detect a fault before the fault proceeds to a failure, diagnose the causes of the disturbances, and provide operators with accurate information and advice, is being actively studied. A variety of approaches to fault diagnosis have been explored by many researchers, and a number of competing technologies such as rule-based expert system, estimation methodology, signed directed graph, qualitative simulation, and neural network are now in use (Becraft et al., 1991). No single method, however, has been proven universally superior to other methods. Methodologies for fault diagnosis can be categorized into various groups based on different criteria of classification: qualitative or quantitative methods depending on the rigorousness of the process knowledge employed (Kramer and Palowitch, 1987; Yu and Lee, 1991); experience-oriented or logic-oriented methods depending on whether data-based techniques are used or causal relations of a process are used (O’Shima and Matsuyama, 1994); model-based or knowledge-based methods depending on whether estimation techniques by models are used or AI-based techniques are used (Zhang et al., 1996). In particular, the reasoning direction classifies the diagnosis methods into a forward reasoning or backward reasoning method. Most diagnosis is an induction process in nature like medical diagnosis. If a fault takes place, the symptom patterns are generated. Diagnosis
task is the opposite search process to a causal origin using the generated symptom pattern, that is, a backward reasoning process. However, logically, the diagnostic induction process is incomplete. In other words, the results of the diagnosis may include uncertainties. Forward reasoning is to infer symptoms from the cause of fault. Therefore, if sufficient information of the cause of fault and proper process models are available, forward reasoning methods can estimate symptoms that a fault generates. The methodologies have good performance even when a process shows complicated behavior. However, direct application of forward reasoning methods is impossible because, in general, the diagnosis starts inference only after symptoms are detected. In this paper, forward and backward reasoning methods are incorporated to enhance the resolution of diagnosis. Firstly, after symptoms are detected, backward reasoning is used to find a list of possible fault candidates for the observed symptoms. A weighted symptom tree has been proposed and utilized in this backward reasoning step. Secondly, forward reasoning is used to verify each candidate in the list of candidates. Fault propagation trends identified from observations are compared with standard fault propagation trends stored a priori to validate or invalidate the fault candidates. Triangular episodes (Cheung and Stephanopoulos, 1990) are generated and used to represent the fault propagation trends in this step. The Tennessee Eastman challenge process example illustrates the design and performance of the proposed methodology. Procedures for the construction of a diagnosis system are presented together with the Tennessee Eastman challenge process example. The illustration shows effectiveness and high resolution of the proposed methodology. Weighted Symptom Tree
* To whom correspondence should be addressed. Tel.: +82-2-873-2605. Fax: +82-2-884-0530. E-mail: esyoon@ pslab.snu.ac.kr. S0888-5885(97)00009-2 CCC: $14.00
Symptom Tree. The symptom tree (Yoon and Han, 1987), a real time variation of fault tree, is a fault-tree© 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2673 Table 1. Tabular Form of the Weighted Symptom Tree S1 S2 S3 S4
Figure 1. Symptom tree.
F1
F2
F3
F4
w11
w12 w22
w13 w23 w33
w14 w24
w41
w42
F5
F6
F7
F8
w35
w36
w37 w47
w48
w44
abnormal range. Conventional methods use variables that are strictly positive, zero, or negative (+, 0, or -) and therefore, these are unstable near or at threshold values. By introducing trapezoidal function, the membership value has an intermediate region that changes continuously from -1 to 1. Moreover, the membership values in this work adopt asymmetric trapezoidal function; this function has upper and lower boundaries with different absolute values and is more practical in real operation conditions. Figure 3 shows an example of a membership function. The membership value for a normalized variable is represented and calculated using the following equation (1). Parameters in eq 1 were determined from either dynamic simulation or the knowledge of the experienced.
Figure 2. Weighted symptom tree.
mi ) (ri - ria)/(rimax - ria)
for ria < ri < rimax
like representation of causal relationships. The top node is a symptom that represents a deviation of process variables from its normal and intended range of behavior, and the bottom node is the basic event that represents a cluster of physical faults that have a direct effect on the above symptom. The symptom tree is used to hypothesize fault candidates more efficiently; that is, it reduces the search space to find the real cause of a fault. If more than one symptom exists, intersection of the symptom tree for each symptom provides a list of fault candidates. For example, if a system, which is represented as a symptom tree in Figure 1, has symptoms S1, S2, and S4, the following manipulation gives {F2, F4} as a list of candidates.
mi ) (ri - rib)/(rib - rimin)
for rimin < ri < rib
mi ) 0
for rib < ri < ria
mi ) 1
for rimax e ri
mi ) -1
for ri e rimin
{F1, F2, F3, F4} ∩ {F2, F3, F4} ∩ {F1, F2, F4, F7, F8} ) {F2, F4} A symptom tree is simple to construct and to apply. However, it employs only qualitative terms or does not contain any form of quantitative information so that it cannot rank the suggested candidates. Therefore, it is impossible to determine which is the most probable cause among the proposed ones. Weighted Symptom Tree. After the limitations of the symptom tree were recognized, a weighted symptom tree was developed and constructed by attaching weight to the edge between the symptom and the cause as shown in Figure 2. Weight wij represents the statistical information between the ith symptom Si and the jth fault Fj. The weighted symptom tree can be represented in tabular form, in which the cells in the first column are symptoms and the cells in the first row are faults. The values in cells indicate the weights between the corresponding symptoms in the symptom column and the corresponding faults in the fault row. The blank cells indicate irrelevance between the symptoms and the faults. The weighted symptom tree in Figure 2 can be converted into tabular form as shown in Table 1. In this work, each process variable is represented by a membership value, which is based on the trapezoidal function of fuzzy set theory. The membership value of a variable means how much a variable belongs to an
(1)
The weights in the weighted symptom tree are calculated using averaged membership values obtained from various fault simulation results. For example, let the calculation of wij, a weight between Fj and Si, be considered. For a fault Fj, l0 different simulation runs with different fault size or intensity are carried out for a given period of time t0, and membership values of a process variable pi are calculated at each sampling time (let sampling time be 1 in this section). Then we obtain membership values at each sampling time from zero to t0 for each simulation run l (l ) 1,2,3, ..., l0) as follows:
m1ij(1), m1ij(2), m1ij(3), ..., m1ij(t), ..., m1ij(t0)
for l ) 1
m2ij(1), m2ij(2), m2ij(3), ..., m2ij(t), ..., m2ij(t0)
for l ) 2
l
l
l
l
l
mlij(1), mlij(2), mlij(3), ..., mlij(t), ..., mlij(t0) l
l
l
l
l
l for l ) l l
l l l l l (1), mij,0 (2), mij,0 (3), ..., mij,0 (t), ..., mij,0 (t0) mij,0 for l ) l0
Taking an average of membership values over time and over simulation runs gives the averaged membership value, m j ij:
m j ij )
1
l0
1
t0
∑ ∑mlij(t) l l)1 t t)1 0
(2)
0
One fault can cause deviations of many process variables, and symptom is defined as the deviation of a variable from its normal operation value. That is, one
2674 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997
triangular episodes, a formal framework that can describe generic trends of process variables. The triangular-episode-based description of a trend has been proven efficient in unambiguous inferences during various engineering activities, e.g., diagnosis, scheduling, and others. Let x be a reasonable function or a process variable. QS(x,t), the qualitative state of x at time t, is defined as the triplet of qualitative values as follows:
QS(x,t) ) 〈[x(t)], [∂x(t)], [∂∂x(t)]〉 Figure 3. Membership value of a normalized process variable.
(6)
where [x] is the sign of x or zero. The trend of a variable x is represented qualitatively by the continuous sequence of qualitative states over a given period of time. For any (ti, tj) ⊂ [a,b] such that QS(x, t) is constant ∀t ∈ (ti, tj), an episode of x over (ti, tj) is the pair 〈t-extent, QS(x, ti, tj)〉 defined as follows: (1) Temporal extent of the episode
t-extent ) (ti, tj) (2) Qualitative state of x over (ti, tj)
QS(x, ti, tj) ) QS(x, t) ∀t ∈ (ti, tj) Figure 4. Example of weight calculation.
fault can cause many symptoms to occur. To represent the relative intensity of effect of a fault to symptoms, weight is defined. Weight wij is the relative effect of fault Fj to symptom Si among all symptoms and given by
wij )
m j ij
∑i mj ij
(3) Pattern Matching of Trends
In the case of a process with changing operation mode, the weight for each operation mode is prepared by eq 4, and Figure 4 illustrates the calculation of weight for Fj:
∑k (dkfkmij,k)
wij,k ) (dkfkmij,k)/
(4)
In eq 4, subscript k denotes the kth operation mode. dk is the ratio of time operated in the kth operation mode to the whole operation time, and fk is the probability of occurrence of Fj under the kth operation mode. The selection of candidates for the cause of the fault and ranking procedure are carried out as follows: (1) Calculate mi for all measured variables or symptoms. (2) Check if there exists a symptom with mi equal to 1 or -1. If any, proceed to step 3. If not, return to step 1 and continue at the next sampling time. (3) Find out all symptoms with non-zero mi. (4) For these symptoms, calculate the likelihood Lj using eq 5.
Lj )
∑i (miwij)
Without regard to the numerical values of a trend, there are only seven basic patterns for a scalar function, and these patterns correspond exactly to the seven basic types of triangular episodes in Figure 5. Every trend, which is considered to be twice-differentiable, can be represented as a contiguous sequence of the triangular episodes like an example in Figure 6. In this work, this methodology is adopted and utilized as the basis for pattern matching of fault propagation trends.
(5)
(5) According to Lj, rank the candidates. (6) Store the ranked candidates in a list of candidates in descending order.
For the faults included in the weighted symptom tree, the standard fault propagation trends are prepared for the next step of diagnosis. Under the assumption that a fault occurred, dynamic simulation is carried out. The effect of the assumed fault is propagated into process variables as time proceeds, and these fault propagation trends of each process variable are represented by triangular episodes. The episodes are stored a priori and used as the standard fault propagation trends in pattern matching. On the basis of the characteristics of process dynamics, the time period for standard trends and a sampling time are determined. The trends or triangular episodes of process variables are identified from the measurements and are compared to the standard trends. A pattern-matching algorithm based on the number of matching episodes is used to match those trends. The candidate with the largest number of matching episodes in a list of fault candidates proposed in the first step is selected as the final cause of fault. A more precise pattern-matching algorithm can be used if the trend is significantly different for the same fault at a different magnitude. In the proposed methodology, however, the pattern matching is used in the second step and applied to the search spacescandidate setswith only a small number of candidates. Therefore, the proposed algorithm is satisfactory to this kind of pattern matching.
Pattern Matching of Fault Propagation Trends
Illustration in Tennessee Eastman Challenge Process
Triangular Episodes. Cheung and Stephanopoulos (1990) represented trends of process variables using
Tennessee Eastman Challenge Process. To demonstrate the diagnosis using the proposed methodology,
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2675
Figure 5. Triangular componentssgeometrical basis of episodes.
Figure 6. Triangular representation of a trend.
we consider the Tennessee Eastman challenge process (Downs and Vogel, 1993), which we will hereafter abbreviate as the “TE process”. Many previous works on the TE process were performed, and most of the research was about control strategies (Ricker, 1995) and optimization (Ricker and Lee, 1995a). The TE process produces two liquid products and two liquid byproducts from four gaseous reactants. The reactions are given below, all of which are irreversible and exothermic.
A(g) + C(g) + D(g) f G(l)
product 1
A(g) + C(g) + E(g) f H(l)
product 2
A(g) + E(g) f F(l)
byproduct
3D(g) f 2F(l)
byproduct
The process has five unit operations: a two-phase reactor, a product condenser, a flash separator, a recycle compressor, and a product stripper. Figure 7 shows a diagram for the process. Diagnosis Description The TE process has 41 measurements, and 23 of them were used to diagnose faults in this study. Measurements were reconciled by the extended Kalman filter to reduce noise levels, and these reconciled data were used to identify patterns of measured data. Thirteen different disturbances were selected and listed in Table 2 and were reported to have similar effects on streams and units so that the discrimination between each other is difficult. For these disturbances, simulation runs were carried out several times previously to construct a weighted symptom tree, and the mathematical models of Ricker and Lee (1995b) were used for the dynamic simulation. The standard fault propagation trends were
constructed together with the weighted symptom tree. The membership value for each process variable was calculated using eq 1, and ria and rib were set to a half of rimax and rimin, respectively, in this illustration. The variables in the TE process change so significantly with time that time periods with fixed length were employed and different weights for different time periods were prepared and utilized. The length of time period was set to 0.5 h in this illustration. Table 3 shows the constructed weighted symptom tree of TE process, especially the weights between the fault, loss of feed A (IDV1-), and all possible symptoms. Each fault in Table 2 was simulated to occur at time zero, and fault diagnosis was carried out for 2 h after it occurred. At any time when a variable hits the upper or lower bound or membership value of the variable reaches +1 or -1 the diagnosis starts. The diagnosis in the case of loss of feed A is described in detail below. Loss of Feed A (IDV1-) In this situation, the pipe for stream 1 is blocked, and therefore, feed A in stream 1 is not supplied. The changes of variables in this case are represented in Figure 8 using their membership values. The loss of feed A causes the decrease of component A in the reactor feed stream. The levels of separator and stripper decreased in their early stages but returned to the original values by control actions or increased a little. The pressures of reactor, separator, and stripper showed similar trends. After 0.4 h, composition of component D in the purge stream hit the upper bound, and the level of stripper and composition of component A in the purge stream hit lower bound continually. This triggered the diagnosis. Figure 8 shows that many variables have nonzero membership values, and by using these values and weights in the weighted symptom tree of Table 3, the likelihood of each fault was calculated according to eq 5. The calculated likelihoods are arranged in Table 4, and the candidates were ranked according to these likelihoods. For example, in the time period from 0 to 0.5 h in Table 4, the fault IDV5 with likelihood equal to 0.480 was ranked first, IDV1- (0.458) second, IDV8+ (0.292) third, and so on. In this illustration, we confine the set of fault candidate, which will be used in the next step, to include the first two faults among the ranked candidates. Therefore, IDV5 and IDV1- were selected and stored in a set of fault candidates in this time period. From 0.6 h, IDV1- and IDV6 were selected and
2676 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997
Figure 7. Flowsheet of Tennessee Eastman challenge process. Table 2. Selected Faults for TE Challenge Process no.
fault
designation
1 2 3 4 5 6 7
A feed loss (stream 1) A feed (stream 1), control valve stuck high D feed (stream 2), control valve stuck low D feed (stream 2), control valve stuck high E feed (stream 3), control valve stuck low E feed (stream 3), control valve stuck high C header pressure losssreduced availability (stream 4) C header (stream 4), control valve stuck high Reaction kinetics. No. 1 reaction rate slow drift A/C feed ratio low (stream 4), B composition constant B composition high (stream 4), A/C feed ratio constant Purge gas (stream 9), control valve stuck low Purge gas (stream 9), control valve stuck high
IDV1IDV1+ IDV2IDV2+ IDV3IDV3+ IDV4-
8 9 10 11 12 13
IDV4+ IDV5 IDV6 IDV7 IDV8IDV8+
stored in a set of fault candidates. The negative likelihoods in Table 4 can be obtained in the case where mi and wij in eq 5 have different signs, which means that observed symptoms show trends opposite to the behavior expected from the jth fault; therefore, the jth fault cannot be the cause of the symptoms. The result of the first step of the diagnosis shows that the true fault, IDV1-, is ranked first except the case in the time period from 0 to 0.5 h. In the second step, the standard fault propagation trends for the first and second candidates proposed in the previous step were referred. Standard triangular episodes were obtained every 0.1 h and compared with those of reconciled measurements. Table 5 shows the triangular episodes of three process variables for 2 h: reactor pressure, reactor liquid level, and separator pressure. The letters from A to G in Table 5 correspond to the seven different episodes in Figure 5. From 0 to 0.5 h, IDV1- and IDV5 are the two components of the fault candidate set, for which episodes were obtained and compared. From 0.6 to 2.0 h, IDV1- and IDV6 are the two candidates, for which episodes were obtained and shown in Table 5. This is why there are some blank cells in columns *5 and *6 in Table 5. For the other process variables, the episodes were obtained, and the
Table 3. Weights between the Symptoms and the Faults in TE Challenge Process IDV1- at time (h) 0.5 reactor pressure reactor liquid level separator pressure separator liquid level stripper bottoms level stripper pressure reactor feed flowrate A in reactor feed B in reactor feed C in reactor feed D in reactor feed E in reactor feed F in reactor feed A in purge B in purge C in purge D in purge E in purge F in purge G in purge H in purge G in product H in product
1
1.5
2
0.0066
0.0406 0.008 -0.0674
-0.0153
-0.0509 -0.0896
-0.0261 -0.0866
-0.0481
-0.0936 -0.1097
-0.0866 -0.0866
0.0191
0.035 0.0479 0.051
0.0771 0.0848 0.0866
-0.0674 -0.0674 -0.0382 0.0674 0.0674 0.0674
-0.0129
-0.1209
-0.0866
-0.0674
0.7782 0.0001
0.0948 0.1209 0.0948
0.0866 0.0866 0.0866
0.0674 0.0674 0.0674
0.1066 -0.0197
-0.0156 0.0275 -0.0479
-0.0131 -0.0631 0.0346 -0.0022
-0.0665 -0.0674 0.0528 -0.0523
number of episodes with matching type was calculated for each candidates and summarized in Table 6. The candidate with the higher number of matching episodes is the final fault candidate. Table 6 indicates that IDV1- is the final fault candidate in the whole time range, and this means that the right cause was located in this case. For the time from 0 to 0.5 h, the second-step diagnosis selected IDV1- as the final fault candidate even though it was selected as the second most probable fault in the first-step diagnosis. This means that the second-step diagnosis is able to compensate for the results of first step and therefore enhances the diagnosis resolution. Summary of Diagnosis Results We carried out diagnoses for 13 different faults in Table 2 and for four time periods; that is, 52 cases of
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2677
Figure 8. Trends of measured variables in case of loss of feed A. Table 4. Ranking of Fault Candidates for Fault IDV1(WST) 0.5 h Lj IDV1- 0.458 IDV1+ -0.058 IDV2- -0.077 IDV2+ 0.065 IDV3- 0.024 IDV3+ 0.086 IDV4- 0.154 IDV4+ -0.022 IDV5 0.480 IDV6 0.234 IDV7 0.148 IDV8- 0.112 IDV8+ 0.292
1h
1.5 h
Table 5. Episode Comparison of Fault Candidates for Fault IDV1-a
2h
rank
Lj
rank
Lj
rank
Lj
rank
2
0.782 -0.828 -0.163 0.146 -0.176 0.208 0.290 -0.272 0.144 0.507 0.250 -0.145 0.221
1
0.952 -0.910 -0.300 0.339 -0.364 0.259 0.366 -0.345 0.023 0.594 0.292 -0.153 0.119
1
0.934 -0.942 -0.330 0.446 -0.330 0.368 0.385 -0.333 -0.059 0.677 0.325 -0.206 0.152
1
1
2
2
2
diagnoses. The first-step diagnosis using a weighted symptom tree gives the results that the true cause of fault was selected as the first-ranked candidate in 48 cases. This means that 92.3% of all trials give the right answers. In the second-step diagnosis, for each candidate ranked first and second in the first step, fault propagation trends were obtained from fault simulation runs and compared with the trends of measured data. The results show that the true cause was determined as the final cause of fault in 51 cases. This means that 98% of trials give the right answer. The first-step diagnosis reasons very fast because it uses simple cause-effect relations in which symptoms are directly related to faults. However, it is fragile to measurement noise. This implies that it might have poor precision, not poor accuracy. Therefore, the purpose of the first-step diagnosis is to narrow the whole search space into a small space with two or three candidates, rather than to find the final and one candidate. The second-step diagnosis selects the final candidate in the narrowed space using the pattern matching of fault propagation trends, which is more precise and robust than the weighted symptom tree method.
time reactor pressure reactor liquid level separator pressure (h) *F *1- *5 *6 *F *1- *5 *6 *F *1- *5 *6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
F F G F G A G G G G G G G G A G G A G A
F F G F G G G A C C G G A C G A G A A E
A C A E A A E A C C E C A E E A E A A E
G F A C F A A E E A E E A F A E F A E G
F A G G F F A E E A F A G F A A F G A E
F A F D F G A E E A G A E F A A F G A E
F D G F G A G G G G G G A G A G G A G A
F B B D G G G A C C G G A E C A G A A E
A A A A A A A A C C E C A E C A E A A E
a *F: episodes of reconciled output variable. *1-: episodes of fault candidate IDV1-. *5: episodes of fault candidate IDV5. *6: episodes of fault candidate IDV6.
Conclusion This paper has presented a fault detection and diagnosis methodology based on the weighted symptom tree and pattern matching between the coming fault propagation trend and the simulated one. Membership values for each variable were calculated and used for preparing weights in the weighted symptom tree. The methodology was illustrated using the Tennessee Eastman challenge process example and gave the right answers for 98% of all trials. The proposed fault diagnosis methodology has many advantages over the conventional fault diagnosis methodologies: it can perform credible diagnosis when the operating conditions change dynamically or are in a range far away from the normal one, estimate the
2678 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 6. Ranking of Fault Candidates for Fault IDV1(Pattern Matching)a 0.5 h
1h
1.5 h
2h
episum rank episum rank episum rank episum rank IDV1IDV5 IDV6 a
71 47 55
1
126 84 101
1
179 113 142
1
240 150 195
1
Episum ) number of matching episodes.
changes of process hereafter, and diagnose the continual faults. Moreover, it has higher diagnostic resolution by combining the forward and backward reasoning methods, higher robustness to measurement noises and model uncertainties thanks to the use of membership values and pattern matching of fault propagation trends, and higher flexibility for the maintenance and expansion thanks to the use of weights in the weighted symptom tree. Acknowledgment This work was supported by the Korea Science and Engineering Foundation (KOSEF) through the Automation Research Center at POSTECH and by YuKong, Ltd. Nomenclature dk ) ratio of time operated in kth operation mode to the whole operation time fk ) relative likelihood of occurrence of Fj under kth operation mode Fj ) jth fault l0 ) total number of simulation runs mi ) membership value of ith variable mij,k ) membership value between ith symptom and jth fault at kth operation mode mijl(t) ) membership value between ith symptom and jth fault in lth simulation run at time t m j ij ) membership value averaged over time and different fault sizes pi ) ith process variable Lj ) likelihood of occurrence of jth fault ri ) residual of ith process variable ria ) bound value for ri from which membership value begins to increase from 0 to 1 rib ) bound value for ri from which membership value begins to decrease from 0 to -1
rimax ) upper bound value for ri rimin ) lower bound value for ri Si ) ith symptom t0 ) whole time period wij ) weight between Si and Fj wij,k ) weight between Si and Fj at kth operation mode
Literature Cited Becraft, W. R.; Guo, P. L.; Lee, P. L.; Newell, R. B. Fault diagnosis strategies for chemical plants:A review of competing technologies. Proc. 4th Int. Symp. Process Systems Eng.(PSE’91) 1991, II, 12.1-12.15. Cheung, J. T. Y.; Stephanopoulos, G. Representation of process trends-Part I. A formal representation framework. Comp. Chem. Eng. 1990, 14, 495-510. Downs, J. J.; Vogel, E. F. A plant-wide industrial process control. Comput. Chem. Eng. 1993, 17, 245-355. Kramer, M. A.; Palowitch, B. L. A rule-based approach to fault diagnosis using the signed directed graph. AIChE J. 1987, 33(7), 1067-1078. Nam, D. S.; Han, C. H.; Jeong, C. H.; Yoon, E. S. Automatic construction of extended symptom-fault association from the signed digraph. Comput. Chem. Eng. 1996, 20, S605-S610. O’Shima, E.; Matsuyama, H. Practical problems in application of failure diagnostic systems. Proc. 5th Int. Symp. Process Syst. Eng. (PSE’94) 1994, II, 925-930. Ricker, N. L. Optimal steady-state operation of the Tennessee Eastman challenge process. Comput. Chem. Eng. 1995, 19, 949959. Ricker, N. L.; Lee, J. H. Nonlinear model predictive control of the Tennessee Eastman challenge process. Comput. Chem. Eng. 1995a, 19, 961-981. Ricker, N. L.; Lee, J. H. Nonlinear modeling and state estimation for the Tennessee Eastman challenge process. Comput. Chem. Eng. 1995b, 19, 983-1005. Yoon, E. S.; Han, J. H. Process failure detection and diagnosis using the tree model. IFAC Workshop on Fault Detection and Safety on Chemical Plants 1987, 126-129. Yu, C.; Lee, C. Fault diagnosis based on qualitative/quantitative process knowledge. AIChE J. 1991, 37(4), 617-628. Zhang, J.; Martin, E. B.; Morris, A. J. Fault detection and diagnosis using multivariate statistical techniques. Trans. IChemE. 1996, 74, 89-96.
Received for review January 2, 1997 Revised manuscript received April 17, 1997 Accepted April 18, 1997X IE970009I
X Abstract published in Advance ACS Abstracts, June 1, 1997.
