Application of fuzzy causal networks to waste water treatment plants

Chemical Engineering Science 54 (1999) 2731}2738

Application of fuzzy causal networks to waste water treatment plants

Y.C. Huang, X.Z. Wang*

Department of Chemical Engineering, The University of Leeds, Leeds LS2 9JT, UK

Abstract

A graphical model, the extended fuzzy causal network is introduced and applied to a case study of waste water treatment plants.The structure of the network is developed using parameter sensitivity studies and the relationships between connected parameters areobtained using a learning approach adapted from fuzzy neural networks. The graphical model is shown to be able to translate thecomplex inter-relationships between process parameters into an easily understood form. Comparisons of the approach with neuraland fuzzy neural networks are also made. ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Fuzzy causal networks; Fuzzy signed directed graphs (fuzzy-SDG); Wastewater treatment plants

1. Introduction

Improved performance in operation and control ofprocess plants depends on better understanding of theinter-relationships of process variables. Computer simu-lation is mainly based on principal models and has beenwidely used as a tool to capture the inter-relationships ofprocess variables. If principal models are not available,neural networks (NNs) can be employed to learn empiri-cal models from databases. However, both computersimulation and NNs can only predict the behavior ofa process at speci"ed values of inputs and parameters.They are not able to give the qualitative and causalrelationships of process parameters. Such a causal pic-ture, as indicated by Stephanopoulos (1984), is veryimportant in decision support systems. In this respectexpert systems (ESs) have advantages because the causalrelationship between the condition and the fact is veryclear in such a rule as &&If condition with certainty x thenfact with certainty f (x)''. In addition, the how explanationcapability of an ES can give a picture on how a con-clusion is reached. However, ESs are still not satisfactorysince the overall causal relationships of all process para-meters are buried in the rule base which is still far morecomplex in structure to decision makers. A more direct

*Corresponding author. Tel.: #44 113 233 2427; fax:#44 113 2332405; e-mail: [email protected].

description of the causal relationships between processparameters is the graphical approach.

In recent years, there has been a growing interest ingraphical models. A graphical model usually consists ofnodes representing variables, and arcs that indicate de-pendence between variables (or, no arcs indicating inde-pendence). Graphical models are potentially powerfulbecause they translate a complex problem into an easilyunderstood form. In this paper, an extended fuzzy causalnetwork is introduced and its learning approach de-veloped by reference to a case study of wastewater treat-ment plant.

2. Graphical models

Bayesian graphs are probably the most widely studiedgraphical model. They have gained widely spread use inknowledge-based systems and more recently receivedgreat interest as a data mining and knowledge discoverytool (Buntine, 1996; Heckerman, 1996; Wang et al.,1997a). Though the conditional probabilities are di$cultto obtain, Bayesian graphs including decision trees arestill considered by many researchers as one of the poten-tially most successful data mining tools. The attraction ofBayesian graph is also re#ected in the emergence of manycommercial products such as Hugin (HUGIN), Netica(NETICA) and Microsoft MSBN(MSBN). In parallelwith the development of Bayesian graphs, belief graphs

0009-2509/99/$} see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 4 2 1 - 7

(Almond, 1995) and possibilistic graphs (Sanguesa et al.,1997) have also shown great potential. These graphicalmodels are all able to deal with problems with uncertain-ties.

An alternative way of dealing with uncertainty is fuzzymathematics. Fuzzy theory is di!erent from probabilitiesbecause the former deals with uncertainty in concepts ofde"nitions rather than the frequency of occurrence ofa phenomenon. Fuzzy theory has proved to be verysuccessful in dealing with engineering problems becauseit provides a language for bridging the qualitative deci-sion making and numerical values.

The approach presented in this contribution is anextension of our previous fuzzy signed directed graphmodel (fuzzy-SDG) (Wang et al., 1995, 1996, 1997b). Theapproach combines fuzzy concepts with the graphtheory-based SDG. In the following, we will "rst brie#yintroduce the development of SDG, and then the ex-tended fuzzy-SDG as well as its learning approaches. Wewill then discuss the application of the extended fuzzy-SDG to a database of a wastewater treatment plant.

2.1. Signed directed graph (SDG)

In the past few years there has been a signi"cantprogress in the study of SDG in process industries. Iri etal. (1979) "rst introduced the graph theory-based SDG tofailure diagnosis of chemical processes. Oyeleye andKramer (1988) extended the SDG model to include cer-tain non-physical feedforward paths which explain in-verse and compensatory responses. Yu and Lee (1991)introduced fuzzy membership functions into thebranches so that qualitative and quantitative reasoningcan be combined. Gujima et al. (1993) improved theaccuracy in diagnosis by introducing more values in thenodes and Mohindra and Clark (1993) developed a dis-tributed fault diagnosis system. Based on theseextensions, Wilcox and Himmelblau (1994) developeda possible cause}e!ect graph model, which is able toinclude relatively unconstrained concept families, desig-nate certain statements as exogenous with respect to theimplicit model of the process, and provided a more accu-rate representation of uncertainty about the processstate. Ouassir and Melin (1997) used a SDG model asa tool for rules generation from data. Using SDG, Namet al. (1996) built a knowledge-based fault diagnosticsystem for aromatic process and polypropylene process.Vedam and Venkatasubramanian (1997) developeda SDG-based algorithm for multiple fault diagnosis. Ap-plication of the SDG models to dynamic systems wasalso explored (Umeda et al., 1980). In addition to faultdiagnosis, SDG models have also been applied to hazardand operability study (HAZOP) for continuous andbatch processes (Vaidhyanathan and Venkatasub-ramanian, 1995; Srinivasan and Venkatasubramanian,1996), fault tree and event tree analysis (Kuo et al., 1997).

The developments can be broadly summarized as fol-lows:

z the major application area has been fault diagnosis;z improvement of the method to deal with multiple

faults;z improvement of the approach to deal with dynamic

systems;z application of the approach to safety and operability

analysis;z development of approaches to help in the construction

of a SDG;z application of fuzzy concepts to convert numerical

data to qualitative expression so that the SDG can beused on-line;

However, the following observations are made to theabove models:

z the expressive capability is very limited since they arecrisp graphs } a node or a branch can only take threevalues, i.e. !, 0 and #. It will give ambiguous solu-tions in complicated fault diagnosis. This is more seri-ous for process supervision and qualitative simulation.The application of fuzzy concepts by Han et al. (1994)and Shih and Lee (1995) only makes the input nodes tobe able to convert numerical data to qualitative expres-sion but the graph as a whole is still a crisp one.

z the development of the SDG has been applicationdriven. For example, the algorithms have been de-veloped speci"cally for fault diagnosis and can not beapplied directly to qualitative simulation.

z most SDG models are not able to deal with the uncer-tainty in data and in reasoning simultaneously.

The previous e!orts have been to develop a method forfault diagnosis, rather than a general purpose graphicallanguage for modeling domain problems. In comparison,Bayesian and belief graphs are considered as more uni-versal.

2.2. Fuzzy signed directed graph ( fuzzy-SDG)

The fuzzy-SDG approach was developed by theauthors (Wang et al., 1995, 1996, 1997b) which takes crispSDG as a speci"c instance but has far more features toovercome many of the limitations of a crisp SDG. Theadvantages are that this approach generates fewer am-biguous solutions, can give a more precise description ofthe variables than (!, 0#) and produces a causal ex-planation. In particular, it allows reasoning in both ar-row to and arrow from directions so that it can be usedfor di!erent reasoning tasks, such as single and multiplefault diagnosis, operational supervision and simulationof operations. The present work is an extension of the

2732 Y.C. Huang, X.Z. Wang/Chemical Engineering Science 54 (1999) 2731}2738

fuzzy-SDG and will discuss its application to an indus-trial-scale process.

3. The extended fuzzy causal network and its learningapproaches

3.1. Network architecture

A fuzzy causal network (or fuzzy-SDG) consists of a setof variables and a set of directed links between variables.If there is a link from node A to B we say that B is a childof A, and A is a parent of B. A set of possible states ofa variable are represented by fuzzy values. Combinationof the following three connections: serial connections (Fig.1a), divergent connections (Fig. 1b) and converging con-nections (Fig. 1c) can form any complicated causal fuzzynetworks such as Fig. 1d. Therefore, we just need toconcentrate on the reasoning algorithms for the threebasic connections.

3.2. The nodes

The de"nition of a node is the same as described in ourprevious work (Wang et al., 1995). Since in the design ofprocess control systems, almost all process variables aregiven the ranges of normal, high and low or normal,medium high, high, medium low and low, it should not bea very di$cult step to determine the fuzzy membershipboundary values. Traditionally, fuzzy membership func-tions have been determined empirically. In recent years,there has been a signi"cant progress in determiningmembership functions automatically (e.g., Millemannand Lengelle, 1995). However, it is important to use mostappropriate approach to determine the fuzzy member-ship functions according to the domain problem.

Fig. 1. Basic connections in a fuzzy causal network. (a) Serial connec-tion; (b) diverging connection; (c) converging connection; (d) a causalfuzzy network is a combination of "gures (a), (b) and (c).

3.3. The branch construction and learning

In our previous work, we used an e!ect strength ofa branch to represent links of any two nodes, which isde"ned as the sensitivity that can be estimated theoret-ically using partial derivatives (Wang et al., 1995), orempirically using a learning approach (Wang et al., 1996).Such a weighted branch can overcome many di$cultiesencountered in a crisp SDG as already discussed byWang et al. (1995). However, the original fuzzy-SDGmodel is still very limited in describing a non-linearrelationship between two nodes. A more accurate de-scription requires a more complex relationship.

Two adjacent layers of a fuzzy-SDG is shown in Fig.2a, which depicts the cause}e!ect relationships betweenvariables [X

1, X

2, X

3] and [Z

1, Z

2, Z

3], indicating that

Z1

is dependent on X1

and X3

but independent on X2.

Fig. 2b shows the detail for training this substructure.The substructure involving X

1, X

3and Z

1can be trained

independently. The node X1

is converted into two typesof nodes: X

1[¸, M, H] and l. The "rst type of nodes

takes only discrete values such as H (high), M (medium)and ¸ (low). The second type of nodes takes continuousvalues l between 0 and 1 representing the fuzzy member-ship values when the "rst node takes the value of H, M or¸. The outside of the dashed box of Fig. 2b representsfuzzy processing of the original data. The arrangement isdi!erent from that of the fuzzy neural network previouslystudied (Wang et al., 1997c), that requires three nodes torepresent a variable if the variable takes three fuzzyvalues. However, the present method always uses twonodes, therefore, the size of the network does not increasewith increased values in the fuzzy space.

Inside the box of Fig. 2b is a single layer percetron withno hidden layers. But it also allows to have one hiddenlayer. Details of the #exible internal structure will bediscussed later when the wastewater case study is pre-sented.

Fig. 3 compares a fuzzy-SDG with a fuzzy neuralnetwork. Suppose all the variables in Fig. 3, X1}X3,Z1}Z11 and>1}>3 represent variables in a process. Thenon-linearity between the input variables [X1, X2, X3]and the output variables [>1,>2, >3] are expected to behigh due to their distances. A neural network (or a fuzzyneural network) with only one hidden layer as shown inFig. 3b can usually be able to deal with the high non-linearity between [X1, X2, X3] and [>1, >2, >3]. Theexceptionally good performance of an one-hiddenlayered NN is supported by a proved theorem (Lorentz,1976) that states that any continuous function of N vari-ables can be computed using only linear summations andnon-linear but continuously increasing functions of onlyone variable. It e!ectively states that a three-layeredBPNN with N(2N#1) nodes using continuously in-creasing non-linearity can compute any continuous func-tions of N variables.

Y.C. Huang, X.Z. Wang/Chemical Engineering Science 54 (1999) 2731}2738 2733

Fig. 2. Learning of a convergent fuzzy-SDG.

Fig. 3. Comparison of a fuzzy-SDG and a neural network. (a) A fuzzy-SDG diagram; (b) a neural network.

If we have the knowledge of the cause}e!ect relation-ships between [X1, X2, X3] and [>1,>2,>3] via a num-ber of intermediate variables, e.g. Z1}Z11, we can makeuse of the knowledge to develop a cause}e!ect diagramlike Fig. 3a. The procedure for training the three basic

structures, i.e. serial, divergent and convergent connec-tions (Fig. 1) has been discussed above using the "rstlayer of Fig. 3a as an example. For the case of a conver-gent connection, for instance, the nodes X1, X3 and Z1in Fig. 3a, a single layer percetron (Fig. 2b) can normallygive good performance. It is because the non-linearitybetween any directly connected layers is normally nothigh. If we view the fuzzy-SDG network in the horizontaldirection, it is a di!erent way of linear summation ofa number of small non-linear (e.g. sigmoidal) functions.This is in consistent with the theorem (Lorentz, 1976)supporting NNs as discussed in the last paragraph.Therefore, it is expected that such a fuzzy-SDG candescribe the high non-linearity between [X1, X2, X3]and [>1, >2, >3].

There is no doubt that the relationship between twonodes of connected layers becomes more complex com-pared with the original fuzzy-SDG because the weight isreplaced by a complicated relationship. However, as in-dicated by Wang et al. (1995), the relative magnitudes ofe!ect strengths are not signi"cant, because they dependon the determination of the maximum and minimumboundary values of variables in normalization. In factduring reasoning we are mainly concerned with thevalues of individual nodes and the propagation of rea-soning in the whole network, not the weights of a branch.


Similar observations can be found in the Bayesian net-works in which the branches only mean a link betweentwo nodes. The reasoning in a Bayesian network is basedon the conditional probability calculation, which alsorequires a complex conditional probability table.

4. Application to a waste water treatment plant

4.1. The waste water treatment plant

The waste water treatment plant shown in Fig. 4belongs to a type of plants known as activated sludgeplants. Water in#ow from urban settlements enters theplant and three consecutive treatments are applied. Inthe "rst phase (pre-treatment) sands, stones, and otherinorganic waste are eliminated. Then in the primarytreatment the water is left for some time in the primarysettlers where, by sedimentation, organic materials isseparated. In the last phase, secondary treatment, abalance is attempted to obtain among several di!erentbacterial populations and the organic matter in thewater.

A database comprising 527 data cases representing 527days of operation of a wastewater treatment plant wascollected by Poch and made publicly available by Bejarand Cortes of the University of Catalonia, Spain. Thedata can be found at the Machine Learning DatabasesRepository of the University of California (Merz andMurphy, 1996). There are 38 measured variables whichare given in Table 1. The database has been used forstudies in classi"cation (Sanchez et al., 1997) and pos-sibilistic causal networks construction (Sanguesa andCortes, 1997; Sanguesa et al., 1997). There are somemissing values in the database. Backpropagation neuralnetworks are developed for each section of the plant topredict some missing values. For each section, there areabout 400 data cases that can be used to develop thefuzzy-SDG models.

Fig. 4. The structure of the waste water treatment plant.

4.2. Network construction

From the above discussions it is clear that fuzzy net-work learning involves two aspects: network structureconstruction and fuzzy membership development. If do-main experts are available, network structure can beeasily built using their knowledge. However, for manyengineering problems, such as the wastewater treatmentplant, even domain experts may have great di$culty ingiving a clear picture of the causal relationships of pro-cess variables. Parameter sensitivity study is carried outto "nd the network structure. Three-layered neural net-works are developed for the three processing stages of theplant shown in Fig. 4. The trained NNs are used to testthe sensitivity of an output to an input. Using the "rstlayer as an example, consider the in#uence of SS-E (Sus-pended Solid, input to the primary unit) on the outputvariables, including PH-P, BOD-P, SS-P, SSV-P, SED-Pand COND-P. The result is shown in Fig. 5, which showsthat PH-P, BOD-P, SS-P, SED-P are strongly in#uencedby SS-E, while SSV-P and COND-P are not so sensitiveto SS-E change. Fig. 6 shows the sensitivity of PH-P tochanges of PH-E, SS-E and Q-E in the inputs. It is clearthat PH-E and SS-E a!ect PH-P very signi"cantlythough in di!erent ways, while Q-E's e!ect can be ne-glected.

Most early work on applications of fuzzy systems hasbeen carried out using priori de"ned membership func-tions, such as triangular waveforms. In recent years,automatic estimation of fuzzy membership functions hasattracted attention (e.g., Millemann and Lenglelle, 1995)and most approaches are based on the minimization ofthe fuzziness of output variables. However, the mostsuitable choice of an approach for determining fuzzymembership functions is dependent on the domain prob-lem. In this case study, since there is a large database andwell developed knowledge about the variable values, wehave combined the probability distribution of variablevalues and domain knowledge to determine the fuzzymembership functions. The approach has proved to bevery e!ective. Fig. 7 shows the probability distribution ofthe values of the variable BOD-P, which is a Gaussian-like function. For this variable, we use a Gaussian func-tion as the fuzzy membership function of the mediumvalue and simple right triangles for the low and highvalues.

The causal network created for the wastewater treat-ment plant is shown in Fig. 8. Compared with neuralnetworks, the causal network is more intuitive to engin-eers and supervisors. Neural networks are fully connec-ted and can give predictions for any speci"c inputs.However, it is impossible to qualitatively know theweighted contribution of inputs to the predictions. Incontrast, the causal network is no longer a blackboxbecause it is a partially connected graph. Engineers cantrace forward and backward the network to analyze


Table 1The attributes of the database

1 Q-E (Input #ow to plant) 20 SSV-D (Input VSSto secondary settler)2 ZN-E (Input Zinc to plant) 21 SED-D (Input sediments to secondary settler)3 PH-E (Input pH to plant) 22 COND-D (Input conductivity to secondary settler)4 BOD-E (Input BOD to plant) 23 PH-S (Output pH)5 COD-E (Input COD to plant) 24 BOD-S (Output BOD)6 SS-E (Input SS to plant) 25 COD-S (Output COD)7 SSV-E (Input VSS to plant) 26 SS-S (Output suspended solids)8 SED-E (Input sediments to plant) 27 SSV-S (Output VSS)9 COND-E (Input conductivity to plant) 28 SED-S (Output sediments)

10 PH-P (Input pH to primary settler) 29 COND-S (Output conductivity)11 BOD-P (Input BOD to primary settler) 30 RD-BOD-P (Performance input BOD in primary settler)12 SS-P (Input SS to primary settler) 31 RD-SS-P (Performance input SS to primary settler)13 SSV-P (Input VSS to primary settler) 32 RD-SED-P (Performance input sediments to primary settler)14 SED-P (Input sediments to primary settler) 33 RD-BOD-S (Performance input BOD to secondary settler)15 COND-P (Input conductivity to primary settler) 34 RD-COD-S (Performance input COD to secondary settler)16 PH-D (Input pH to secondary settler) 35 RD-BOD-G (Global performance input BOD)17 BOD-D (Input BOD to secondary settler) 36 RD-COD-G (Global performance input COD)18 COD-D (Input COD to secondary settler) 37 RD-SS-G (Global performance input SS)19 SS-D (Input SS to secondary settler) 38 RD-SED-G (Global performance input sediments)

a. BOD } biological oxygen demand; COD } chemical oxygen demand; SS } suspended solids; VSS } volatile suspended solids.

Fig. 5. The impact sensitivity of suspended solid (SS-E) on the outputvariables. The X-axis is SS-E, >-axis is the normalized values of PH-P,BOD-P, SS-P, SSV-P, SED-P, and COND-P. 1: PH-P; 2: BOD-P; 3:SS-P; 4: SSV-P; 5: SED-P; 6: COND-P.

problems. For example, the output suspended solids,SS-S is observed as (High, 0.10), tracing back the causalgraph and the nodes, SS-D (High, 0.68), SS-P (High,0.28), RD-SSP (Medium, 1.00), SS-E (High, 0.88) andSSV-E (M, 0.87). So the main reason causing SS-S (High,0.10) is due to SS-E (High, 0.88).

4.3. Learning of the fuzzy-SDG

Because the nodes in adjacent layers of the networkshown in Fig. 8 are only partially connected, the networkcan be divided into a number of sub-nets for training. Forexample, In the "rst two layers of Fig. 8, the output nodei.e. PH-P only has relationships with two input nodes,PH-E and SS-E. Therefore, three nodes form a sub-netthat can be trained independently. The sub-net can betrained as a single layer percetron without hidden nodesor with hidden nodes if a single layer percetron is not

Fig. 6. The sensitivity of PH-P to changes PH-E, SS-E and Q-E. X-axisis the normalized values of PH-E, SS-E and Q-E,>-axis is the PH-P. 1:PH-E; 2: SS-E; 3: Q-E.

Fig. 7. Fuzzy membership function determination using the probabilitydistribution of variable values.


Fig. 8. The fuzzy-SDG for the waste water treatment plant M } medium; L } low; H } high.

Fig. 9. Comparisons of fuzzy-SDG without hidden neurons (Fuzzy-SDG-0), fuzzy-SDG with two hidden neurons (Fuzzy-SDG-2) and backpropaga-tion neural networks (BP). S } sigmoidal function.

su$cient to deal with the non-linearity. As alreadypointed out, a single layer percetron can generally handleif the distance between the input and output nodes areclose in the process. The training approach is adaptedfrom the standard Delta error propagation algorithmused for BPNN.

Fig. 9 compares the prediction of PH-P using a causalfuzzy network with no hidden neurons (Fuzzy-SDG-0),with two hidden neurons (Fuzzy-SDG-2) and a fullyconnected neural network with ten hidden neurons (BPprediction). The fully connected neural network has toinclude all the inputs and outputs in the "rst two layers of


Fig. 8. Fig. 9 only shows comparison for part of thedatabase (data cases 123}208). As far as prediction accu-racy is concerned, three approaches give equivalent pre-dictions. The average relative errors for the whole datacases using Fuzzy-SDG-0, Fuzzy-SDG-2 and BP predic-tion are 11.6, 12.3 and 11.6%, respectively.

This e!ectively proves the discussion earlier with refer-ence to Fig. 3 that the highly non-linear relationshipbetween [X1, X2, X3] and [>1, >2, >3] can be e!ec-tively handled by a fuzzy-SDG diagram like Fig. 3a, inwhich, any two layers are only partially connected andapproximated by single layer percetrons without hiddenneurons.

5. Concluding remarks

Because neural networks and fuzzy neural networksare fully connected networks with hidden neurons, likecomputer simulation, they can only give predictions ofoutputs at given values of inputs and parameters. Theyare not e!ective in describing the cause}e!ect relation-ships between parameters. The extended fuzzy causalnetworks introduced can e!ectively describe such causalrelationships between process parameters and also betrained using databases. In addition, the fuzzy conceptsand algorithms provide a method for bridging the quali-tative and quantitative descriptions and dealing withuncertainties in data. With a fuzzy causal network, oper-ators are able to trace and analyze the propagation ofdisturbances and abnormal operations, and develop ef-fective operational strategies.

References

Almond, R.G. (1995). Graphical belief modeling. London: Chapman& Hall.

Buntine, W. (1996). Graphical models for discovering knowledge. InU.M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, & R. Uthurusamy(Eds.), Advances in knowledge discovery and data mining (pp. 59}82).Cambridge, MA: AAAI Press/MIT Press.

Gujima, F., Shibata, B., Tsuge, Y., Shiozaki, J., Matsuyama, H.,& O'shima, E. (1993). Improvements of the accuracy of fault diag-nosis systems, using signed directed graphs. Int. Chem. Engng, 33,671}679.

Han, C.C., Shih, R.F., & Lee, L.S. (1994). Quantifying signed directed-graphs with the fuzzy set for fault diagnosis resolution improve-ment. Ind. Engng Chem. Res., 33, 1943}1954.

Heckerman, D., Bayesian networks for knowledge discovery. In U.M.Fayyad, G. Piatetsky-Shapiro, P. Smyth, & R. Uthurusamy (Eds.),Advances in knowledge discovery and data mining (pp. 273}306).Cambridge, MA: AAAI Press/MIT Press.

HUGIN, Hugin Expert A/S, Niels Jernes Vej 10, DK-9220 Analoborg,Denmark. http://www.hugin.com/products.html.

Iri, M., Aoki, E., O'Shima, E., & Matsuyama, H. (1979). An algorithmfor diagnosis of system failures in the chemical process. Comput.Chem. Engng, 3, 489}493.

Kuo, D.H., Hsu, D.S., Chang, C.T., & Chen, D.H. (1997). Prototype forintegrated hazard analysis. A.I.Ch.E. J., 43, 1494}1510.

Lorentz, G.G. (1976). The 13th problem of Hilbert. In F.E. Browder(Ed.), Mathematical developments from Hilbert problems. AmericaMathematical Society, Providence, RI.

Merz, C., & Murphy, P.M. (1996). UCI repository of machine learningdatabases. http://www.ics.uci.edu/&mlearn/MLRepository.html.Irvine CA, ;niversity of California, Department of Information andComputer Science.

Millemann, S., Lengelle, R. (1995). Fuzzy membership function estima-tion using multilayer percetrons. Proc. E;FI¹'95 } 3rd EuropeanCongress on Intell. ¹ech. Soft Computing, (Vol. 1, pp. 534}537).

Miller, R.M., Itoyama, K., Uda, A., Takada, H., & Bhat, N. (1997).Modeling and control of a chemical waste water treatment plant.Comput. Chem. Engng, 21, s947}s952.

Mohindra, S., & Clark, P.A. (1993). A distributed fault diagnosismethod based on graph models: steady-state analysis. Comput.Chem. Engng, 17, 193}209.

MSBN, DTAS-MSBN, Building 9, 1 Microsoft Way, Redmond, WA98053, USA.

Nam, D.S., Han, C., Jeong, C.W., & Yoon, E.S. (1996). Automaticconstruction of extended symptom-fault associations from thesigned digraph. Comput. Chem. Engng, 20, s605}s610.

NETICA, Nosys Software Corporation, 2315 Dunbar St.,Vancouver,BC, Canada, V6R 3N1. http://www.norsys.com/netica.html.

Ouassir, M., & Melin, C. (1997). Causal graphs and rule generation:application to fault diagnosis of dynamic processes. Proceedings ofthe ¹enth International Conference, Atlanta, Georgia, ;SA, 10}13June (pp. 367}373).

Oyeleye, O.O., & Kramer, M.A. (1988). Qualitative simulation of chem-ical process systems: steady-state analysis. A.I.Ch.E. J., 34,1441}1454.

Sanchez, M., Cortes, U., Bejar, J., DeGracia, J., Lafuente, J., & Poch, M.(1997). Concept formation in WWTP by means of classi"cationtechniques: A compared study. Appl. Intelligence, 7, 147}165.

Sanguesa, R., & Cortes, U. (1997). Learning causal networks from data:a survey and a new algorithm for recovering possibilistic causalnetworks. AI Commun., 10, 31}36.

Sanguesa, R., Cortes, U., & Bejar, J. (1997). Causal dependency dis-covery with POSSCAUSE: an application to waste water treatmentplants. Proceedings of the 1st international conference on the practicalapplication of knowledge discovery and data mining (PADD97). Lon-don, UK, (pp. 199}214).

Shih, R.F., & Lee, L.S. (1995). Use of fuzzy cause}e!ect digraph forresolution fault diagnosis for process plants. Ind. Engng Chem. Res.,34, 1688}1717.

Srinivasan, R., & Venkatasubramanian, V. (1996). Petri net-digraphmodels for automating HAZOP analysis of batch process plants.Comput. Chem. Engng, 20, s719}s725.

Stephanopoulos, G. (1984). Chemical process control: theory and prac-tice. Englewood Cli!s, NJ: Prentice-Hall.

Umeda, T., Kuriyama, T., O'shima, E., & Matsuyama, H. (1980).A graphical approach to cause and e!ect analysis of chemicalprocessing systems. Chem. Engng Sci., 35, 2379}2388.

Vaidhyanathan, R., & Venkatasubramanian, V. (1995). Digraph-basedmodels for automated HAZOP analysis. Reliability Engng SystemSafety, 50, 33}49.

Vedam, H., & Venkatasubramanian, V. (1997). Signed digraph basedmultiple fault diagnosis. Comput. Chem. Engng, 21, s655}s660.

Wang, X.Z., Chen, B.H., & McGreavy, C. (1997a). Data mining forfailure diagnosis of process units by learning probabilistic networks.¹rans. I.Chem.E., 75B, 210}216.

Wang, X.Z., Chen, B.H., Yang, S.H., & McGreavy, C. (1997b). Fuzzyrule generation from data for process operational decision support.Comput. Chem. Engng, 21, s661}s666.

Wang, X.Z., Lu, M.L., & McGreavy, C. (1997c). Learning dynamic faultmodels based on a fuzzy set covering method. Comput. Chem.Engng, 21, 621}630.

Wang, X.Z., Yang, S.A., Veloso, E., Lu, M.L., & McGreavy, C. (1995).Qualitative process modeling-a fuzzy signed directed graph method.Comput. Chem. Engng, 19, s735}s740.

Wang, X.Z., Yang, S.A., Yang, S.H., & McGreavy, C. (1996). Theapplication of fuzzy qualitative simulation in safety and operabilityassessment of process plants. Comput. Chem. Engng, 20, s671}s676.

Wilcox, N.A., & Himmelblau, D.M. (1994). The possible cause}e!ectgraph (PCEG) model for fault diagnosis. Comput. Chem. Engng, 18,103}127.

Yu, C.C., & Lee, C. (1991). Fault diagnosis based on qualitative/quant-itative process knowledge. A.I.Ch.E. J. 37, 617}628.


Documents

Application of fuzzy causal networks to waste water treatment plants