7/28/2019 06221481

1/6

Fault Isolability Analysis Based on Steady State Fault

Signatures

Ketan P. DetrojaDepartment of Electrical Engineering

Indian Institute of Technology Hyderabad

Yeddumailaram, India.Ketan@iith.ac.in

Ravindra D. GudiDepartment of Chemical Engineering

Indian Institute of Technology Bombay

Mumbai, Indiaravigudi@iitb.ac.in

Abstract Once a fault has occurred, it is highly desirable to

quickly detect and reliably isolate the fault. Reliable fault

isolation is a key to ensure correct remedial action; therefore

fault isolation module must determine the current fault scenario

unambiguously and uniquely. However, it may be difficult to

differentiate between all possible fault situations due to various

practical and physical limitations. The task of a fault isolation

module is to generate a set of candidate faults, which might have

occurred such that misclassification is minimized while no

candidate fault scenarios are missed. Fault isolation schemes

essentially rely on fault signatures, either during transient or at

steady state. Our main focus is on methods relying on steady state

fault signatures, such as clustering based algorithms. These fault

isolation schemes may sometimes misclassify if another historical

event match the current fault scenario. It is therefore necessary

to i) analyze the process, ii) analyze how different faults manifest

themselves and iii) determine which faults can exhibit similar

steady state fault signatures. Specifically, it may be very

important and useful to determine which faults can be uniquely

isolated from given process input-output data. In this paper we

propose a simple fault isolability analysis based on steady state

process model. A steady state process model can be obtainedeither based on first principles model or based on process input-

output data. The proposed fault isolability analysis has been

validated by obtaining simple steady state process model of the

benchmark quadruple tank process for normal and fault

operation. Fault isolability predictions, obtained using the

proposed fault isolability analysis, are found to be accurate.

Keywords-Fault isolability, steady state fault signature, fault

diagnosis

I. INTRODUCTIONAny deviation from normal/ acceptable behavior of a plant

is considered a fault situation. A plant operation can deviatefrom normal/acceptable region due to numerous reasons, suchas sensor biases, actuator biases, process disturbances, etc.Further, these faults can manifest themselves with differentintensities. Thus, Fault diagnosis essentially involves threetasks, namely fault detection, fault isolation and faultidentification[1-3]. The task of fault detection, determining ifsomething is wrong with the plant, is a relatively simple task ascompared to fault isolation, determining what exactly is wrongwith the plant. In order to perform fault isolation, any faultdiagnostic framework should be able hypothesis all possiblefault scenarios and then determine the current plant operation

status uniquely and unambiguously. It should however benoted that if there is no observable difference between faultsignatures of more than one fault, it may be difficult to isolatethem irrespective of the algorithm used. Various fault isolationschemes look at fault signatures from different perspective, i.e.steady state fault signatures or transient fault signatures. While

diagnostic schemes based on each of them may have theiradvantages and disadvantages, both are prevalent and havegenerated considerable interest in academia and industry alike.

The aim of this work is two folds: i) Generate a pool offaults that are likely to result in similar fault signatures and ii)Assist fault diagnosis schemes and/or operators in makinginformed decision on possible root cause(s). This is the firststep towards hybrid fault diagnostic framework that looks atsome a priori knowledge of how different faults manifestthemselves and historical data based approached for faultdiagnosis. Our main focus is on methods that look at steadystate fault signatures for fault isolation, e.g. Principlecomponents analysis (PCA), Fisher discriminant analysis

(FDA), clustering based algorithms, etc. While these [4, 5]methods have been quite successful in both academia as well asindustrial practices, it is important to note that faults havingnon-unique signatures are always difficult to discriminate in anunambiguous way. This will happen primarily because some

processes may exhibit similar system response under influenceof different fault cases and there is no observable difference

between these fault signatures. Even for an ideal FDI method,it may not be possible to always uniquely isolate such faultsignatures. Therefore, it is important to find out which faultscan be uniquely isolated. Although some work has been doneto predict fault isolability [6, 7], such detailed analysis may not

be required to determine fault isolability when historical databased diagnostic schemes are employed. In this paper we

propose a simple process analysis method based on steady statemodel is proposed. Although, developing detailed first

principles based model may be difficult for large-scale systemsit is relatively easy to obtain steady state gains for variousinput-output pairing, i.e. steady state model of the process. Thissimple yet elegant approach can be very useful when steadystate process model of the plant is available. Such faultisolability analysis could be a prerequisite task before whichfault diagnosis steps are carried out so as to highlight

potentially similar fault scenarios. Fault isolability analysis willgroup a set of faults that have similar fault signatures. Theoperators would therefore know that the set of faults presented

978-1-4577-1829-8/12/$26.00 2012 IEEE

7/28/2019 06221481

2/6

7/28/2019 06221481

3/6

III. FAULT ISOLABILITY ANALYSIS FORQUADRUPLE TANKPROCESS

The Quadruple tank process is a multivariable laboratoryprocess with an adjustable zero [8]. This process consists offour interconnected water tanks, two pumps and associatedvalves. A schematic diagram of the process is shown in Fig. 1.

The inputs are the currents supplied to the control valves so

as to manipulate the flow output of the fixed speed pumps andthe outputs are the water level measurements of the two bottomtanks. The flow outlet of the control valve is split before it goes

to the individual tanks and 1

and 2

are the fraction of the

total flow going to the bottom tanks. The nonlinear modelderived based on the first principles is given in (7).

dh1

dt=

a1

A1

2gh1

+

a3

A1

2gh3

+

1

A1

f1

dh2

dt=

a2

A2

2gh2

+

a4

A2

2gh4

+

2

A2

f2

dh3

dt=

a3

A3

2gh3

+

1 2( )

A3

f2

dh4

dt=

a4

A4

2gh4

+

1 1

( )A

4

f1

(7)

For tanki,Ai is the cross-section of the tank, ai is the cross-section of the outlet hole and hi is the water level. The currentapplied to the valve i, determines the total flow fi. Theacceleration of gravity is denoted byg.

The proposed fault isolability analysis is validatedanalytically as well as using experimental data. The analytical

validation is based on the first principles based model of thequadruple tank process, while experiments were carried out onthe quadruple tank process system available at Indian Instituteof Technology Bombay.

As discussed earlier, fault isolability analysis can be carriedout to check which fault scenarios would result in differentsignatures. From the first principles model given in , the steadystate model can be derived as

(8)

where,

Ti

=

Ai

ai

2hi

SS

gand

hi

SS

is steady state heightfori

thtank during normal operation.

The first principles model given in (8) is valid even when asensor is biased, however the output equation will now be

y1

= h1

+ fsensor

1

y2

= h2

+ fsensor

2(9)

where,fsensor

1

andfsensor

2

are sensor bias magnitudes forbias in Y1 and Y2 respectively and only one of them is non-zeroat a time (single fault hypothesis).

Thus, the steady state model given in (8) will be changed tothe following under sensor bias condition.

(10)

The first principles model for actuator bias condition can bewritten as follows:

dh1

dt=

a1

A1

2gh1

+

a3

A1

2gh3

+

1

A1

f1

+ factuator

1( )

dh2

dt=

a2

A2

2gh2

+

a4

A2

2gh4

+

2

A2

f2

+factuator

2( )

dh3

dt

=

a3

A 3

2gh3

+

1 2

( )

A 3

f2

+factuator

2( )

dh4

dt=

a4

A4

2gh4

+

1 1

( )A

4

f1

+ factuator

1( )

(11)

where,factuator

1

andfactuator

2

are sensor bias magnitudes forbias in U1 and U2 respectively and only one of them is non-zeroat a time (single fault hypothesis).

Actuator bias affects the plant in a different way throughsteady state process gain matrix. The steady state model foractuator bias is given by

(12)

7/28/2019 06221481

4/6

It is clear from (10) and (12) that sensor and actuator biasescan be easily discriminated in the original larger dimensionalspace. Statistical method used for the data compression andmodel building can be used to generate a lower dimensionalsubspace where these fault signatures can be discriminated.

We next consider disturbances in the process that can affectthe steady state plant in many different ways. We will nowcheck if leak in tank 1 can be isolated from sensor and actuator

biases. If we assume that the amount of leakage is equivalent to

discharge from an orifice having cross sectional area ofl1, the

first principles model given in (8) will become:

dh1

dt=

a1

+ l1

( )A

1

2gh1

+

a3

A1

2gh3

+

1

A1

f1

dh2

dt=

a2

A2

2gh2

+

a4

A2

2gh4

+

2

A2

f2

dh3

dt=

a3

A 3

2gh3

+

1 2

( )A 3

f2

dh4

dt=

a4

A4

2gh4

+

1 1

( )A

4

f1

(13)

The steady state model for leak in tank 1 can then bewritten as given below:

(14)

where, Tl

=

A1

al

2h1

SS

g.

It is clear from (10) & (14) that leak in tank 1 is equivalent

to a bias of 1T12

A1T

1+T

l( )

U1

ss+ 1

2( )T

1

2

A1T

1+T

l( )

U2

ssmagnitude in

sensor 1. For small magnitude leak in one of the lower tanks,the effect of this fault on steady state plant is similar to that ofsensor bias in one of the sensors. Thus, leak in the tank and

bias in sensor generate similar fault signatures and it will bedifficult to isolate these faults for the quadruple tank process. Itshould however be noted that both these faults have similarsteady state fault signatures and it may be necessary to isolatethese faults using some model based techniques that analyzetransients.

IV. EXPERIMENTALVALIDATION OF FAULT ISOLABILITYANALYSIS

In the previous section, it was analytically shown thatsensor and actuator biases could be easily discriminated for thequadruple tank process. It was also found that somedisturbances, e.g. leak in tank 1 and bias in sensor 1, couldresult in similar fault signature. It has been shown that sensorand actuator biases for the quadruple tank process could bediscriminated by CA based FDI scheme proposed in [9]. Wewill therefore focus on the case when there is a bias in sensor 1and leak in tank 1.

As stated earlier, experimental setup is available atAutomation laboratory, in the Department of ChemicalEngineering of IIT Bombay. The system has a multivariableadjustable zero and we selected the operating conditions suchthat the system exhibited non-minimum phase behavior. The

presence of right half plane multivariable zero andconsequently inverse response makes it a difficult system tocontrol. The experimental studies on the quadruple tank

process setup were conducted under closed-loop. Levels intank-1 and tank-2 were controlled by manipulating the control

valves, i.e. the process becomes a 2x2 system. The operatingrange for levels in the bottom tanks is 0-55 cm and for totalflow from the control valve is 20-250 cm

3/s. The setup has a

provision to introduce leak of different magnitudes in all thetanks. The levels in tank-1 and tank-2 were controlled bymanipulating flow rates f2 and f1 respectively. Single loop PIcontrollers were implemented for both the loops with

K1,Ti1( ) = 8.2,0.0368( ) , K2,Ti2( ) = 0.5,0.0284( ) . The

experiments were carried out for normal operating condition aswell as biases in each of the sensors and actuators and also forleak in tank 1. Various sensor and actuator bias situations werecreated by a computer program. For instance, for generating asensor bias during online plant operation, a constant value wasadded to the measured value that reaches to the computerthrough data acquisition module. The setup has a provision tointroduce leak of different magnitudes in all the tanks.Interfacing of the data acquisition module (Advantech ADAM-5000) with the computer and online controller implementationwas done using MATLAB

.

To validate the fault isolability predictions obtained usingthe proposed method, we carried out the followingexperimental case study. We first introduced a leak equivalentto an orifice of cross sectional area 0.05 cm

2in tank 1. The

plant data corresponding to this leak fault was collected. Nextwe calculated equivalent bias magnitude for a leak of crosssectional area 0.05 cm

2. The calculations can be carried out

from (14) and we found that leak of cross sectional area 0.05cm

2is equivalent to a bias of -3.16652 cm in sensor 1. Thus,

we introduced a bias of -3.16652 cm in sensor 1 and collecteddata for sensor bias. The system responses are compared forleak in tank 1 and bias in sensor 1. As can be seen from Fig. 2and Fig. 3, the quadruple tank process exhibits similar systemresponse under both the fault situations. Further, it is clear that(see Fig. 4) although during transients input-output signaturesare different; steady state fault signatures for these faults areidentical. Hence, leak in tank 1 and bias in sensor 1 cannot beisolated uniquely if their magnitudes are such that they result in

7/28/2019 06221481

5/6

similar system response. However, it must be noted that ifdifferent magnitudes of these faults are chosen, it may result indistinct system response and appear as distinct clusters. Whenviewed from fault line perspective [5], leak in tank 1 and biasin sensor 1 will be on the same fault line. Hence, out analyticalcalculations and experimental results, both corroborate the factthat leak in tank 1 and bias in sensor 1 are difficult to isolate ifwe rely on historical data based methods.

500 1500 2500 3500 4500 5500120

140

160

180

200

220

Time

u1

500 1500 2500 3500 4500 5500160

170

180

190

200

210

Time

u2

Bias in Sensor 1Leak in Tank 1

Figure 2: Validation of the proposed fault isolability analysis

500 1500 2500 3500 4500 550023

24

25

26

27

28

29

Time

y1

500 1500 2500 3500 4500 5500171819202122

232425

y2

Bias in Sensor 1Leak in Tank 1

Figure 3: Validation of the proposed fault isolability analysis

500 1500 2500 3500 4500 5500-5-4-3-2-10123

Time

Dee

ny

500 1500 2500 3500 4500 5500-10

-505

1015202530

Time

Dee

nu

Difference in y1Difference in y2

Difference in u1Difference in u2

Figure 4: Difference in inputs (u) and outputs (y) for leak in Tank 1 andbias in Sensor 1.

Thus, whether any disturbance or fault will generate adistinct signature from sensor and actuator biases depends onthe process and also the kind of disturbance introduced.Further, care must be taken when fault isolation is performedand the proposed fault isolability analysis can provide suchinformation a priori.

V. CONCLUSIONS AND FUTURE WORKWe have proposed a simple yet elegant approach to fault

isolability study based on steady state process model. It hasbeen shown that even for a nonlinear and highly interactingsystem, the proposed fault isolability analysis can correctly

predict if a fault will have distinct signature. In case of thequadruple tank process, fault in one of the lower tanks issimilar to corresponding sensor bias. This was validatedanalytically as well as using experimental data.

Here we have proposed a steady state model based faultisolability analysis method and validated it on the benchmarkquadruple tank process. However, further work is needed toextend the presented work to large-scale systems where first

principles based models are difficult to obtain. The main task

there is to obtain steady state process model from historicaldata. Extension of the proposed methodology to multiple faultscenarios could also be a future area of research.

REFERENCES

[1] V. Venkatasubramanian, R. Rengaswamy, K. Yin, and S.

N. Kavuri, "A review of process fault detection and

diagnosis Part I : Quantitative model based methods,"Computers & Chemical Engineering, vol. 27, pp. 293-

311, 2003.

7/28/2019 06221481

6/6

[2] V. Venkatasubramanian, R. Rengaswamy, K. Yin, and S.

N. Kavuri, "A review of process fault detection and

diagnosis Part II : Qualitative models and searchstrategies," Computers & Chemical Engineering, vol. 27,

pp. 313-326, 2003.

[3] V. Venkatasubramanian, R. Rengaswamy, K. Yin, and S.

N. Kavuri, "A review of process fault detection and

diagnosis Part III : Process history based methods,"

Computers & Chemical Engineering, vol. 27, pp. 327-346, 2003.

[4] L. H. Chiang, E. L. Russell, and R. D. Braatz, Fault

detection and diagnosis in industrial systems. London:

Springer-Verlag, 2001.

[5] K. P. Detroja, R. D. Gudi, and S. C. Patwardhan, "A

Possibilistic Clustering Approach to Novel FaultDetection and Isolation," Journal of Process Control, vol.

16, pp. 1055-1073, 2006.

[6] J. Stoustrup and N. Niemann, "Fault isolability condition

for linear systems with additive faults," in American

Control Conference, Minnesota, USA, 2006, pp. 2345-

2350.

[7] K. Mattias and N. Mattias, "Fault isolability prediction of

diagnostic models," in International workshop on

Principles of Diagnosis, California, USA, 2005, pp. 163-

168.

[8] K. H. Johansson, "A quadruple-tank process: amultivariable laboratory process with an adjustable zero,"

IEEE transactions on Control Systems Technology, vol. 8,

pp. 456-465, 2000.

[9] K. P. Detroja, R. D. Gudi, S. C. Patwardhan, and K. Roy,

"Fault Detection and Isolation using Correspondence

Analysis," Industrial and Engineering Chemistry

Research, vol. 45, pp. 223-235, 2006.