presentation reliability and diagnosis in industrial systems

Programa de Atualização Profissional

Reliability and fault diagnosis in industrial

systems

methodology summary

by Gláucio Bastos, M.B.A., Ch.E.


abstract

target: presentation of the advantages andefficiency of Bayesian networks (BN) in theformulation of reliability models for the cases ofsystems with unknown structure, with commoncause failures and redundancy


need

different sources of quantitative and qualitative data areincorporated into the Bayesian models, considered priorprobabilities or a priori information

the evaluation of the reliability parameters of the Bayesianhierarchical model method obtains a higher representationusing the Weibull distribution and probability densityfunction (PDF) of occurrence of failures of the genericexponential distribution because it allows the modeling ofdifferent regions of lifetime curve of a large number ofcomponents

if the probabilities a priori are not known, may be defined bystatistical sampling techniques or directed learning methods


need

continuous decision-making variables, which in the Bayesianconcept of fault diagnosis are the posterior probabilities offailures are of great interest for monitoring the degradationof components

these variables can be used for tasks such as: more intelligent supervision preventive maintenance programs cost analysis of failures using nodes utilities risk-based reconfiguration of defective systems

controlling its overall or partial reliability (prognosis)


need

fault tolerant control ensures high availability and securityfor current industry systems

modern automation relates to autonomous system, therequirements of control performance and overall systemreliability

fault detection and isolation (FDI) techniques involve detectionin sensor readings of discrepancies or ‘residuals' in relationto a standard, indicating the occurrence of a failure,including its type and its location in the system


Bayesian model for fault diagnosis for its structural and causal characteristics, the FDI is performed

with advantage by BN in system Bayesian model-based FDI the diagnosis is made by the

association between the reliability of the components in theprocess being monitored and residues detected according to thespecifications of the physical model, each of these parts - the 1stcontinuous and the other discrete - constituting hybrid BNbecause some of the random variables are continuous and theother discretes where continuous nodes contain a prioriprobabilities of failure of components that are used by theinference process in the discrete part to determine the posteriorprobabilities of failures

this method can be applied in large scale for all types of failuredistribution (herein was used the Weibull) of the systemcomponents


Bayesian model for fault diagnosis the system is composed by n equipments or components

C = {Ci; 1 ≤ i ≤ n} with failure distribution Weibull type Bayesian decision model presented in the following figure

contains random variables associated with residualsr = {rj; 1 ≤ j ≤ p}, components Ci , as well with Bayesianreliability model of such components

the arc connecting node Ci to node rj indicates that rj issensitive to component Ci fail and it is associated with itsreliability Ri

to a residual rj there is 02 states:{D(Detected),ND(NotDetected)} and there is also 02states {F(Faulty), S(Safe)} to a component Ci


Bayesian model for fault diagnosis


Bayesian model for fault diagnosis continuous part of the BN allows you to define a priori

probabilities of component failures then when a residual is detected at instant t, the component

Ci has a priori probabilities: P(Ci = Faulty) = Fi(t) =

1 − Ri(t), where Fi is the cumulative distribution function(CDF)

the discrete part has a structure that depends on the faultsignature (FSM) matrix: a standard for residuals

when a residual rj is not sensitive to failure of a componentCi, there is no arc between 02 nodes

after residuals detection, the posterior probabilities offailure p(Ci|r1, . . . , rp) can be inferred in the discrete partof the BN



* aplication *

the method is simulated in the system below, formed by T1and T2 tanks, V1 and V2 valves, L1 (De1) and L2 (De2)sensors, pump (P), proportional-integral (PI) controller andcontroller 'bang-bang‘ K (On-Off)



* aplication *

from the parameters of the failure rates, the Weibull typePDFs of both component reliability and system are shown inthe following figure with their average and HDIs of 95%, andthe decay of its quantile to 90% with the time of operation,especially the 1st quantile - most critical - showing that afteroperating for 20,000 hrs. the overall system reliability fallsto 0.006256



* aplication *



* aplication * FSM of monitored system is as follows

which was modified by a priori probabilities of false alarms(0.05) and non-detection (0.02), considered to be identicalfor all components

it is observed that the flaws in V2 and T2 can not be isolatedbecause both exhibit identical patterns

the simulation scenario presents after operating for 20,000hrs. the following standard for residuals: [r1, r2, r3, r4, r5] =

[0, 0, 0, 0, 1], that matches the pattern of failure for theV2 and T2 components



* aplication *

the figure below shows the result of analysis for isolation offaulty components, where the a priori probabilities aredetermined in the continuous part of the BN and posteriors inthe discrete part

0

0.2

0.4

0.6

0.8

1

L1 L2 P K V1 V2 T1 T2 PI

Prior

Posterior

Classic

Probababilities of failures for the simulated scenario



* aplication * the figure boasts the explicit advantage of application of

hybrid BN in FDI: although the probabilities of failure calculated by the

conventional method does not allow to isolate the faultycomponent between V2 and T2, they are statisticallyidentical for each one

comparing the posterior probabilities defined from thestandard residuals, the highest probability of failure (0.74)for component V2 relative to that one for the othercomponent T2 (0.51) indicates the malfunction of V2 as themost likely cause of failure of the overall system under thisscenario simulation


diagnosis with dynamic BN

temporal dependencies between components to reliabilitycalculations can be modeled by dynamic BN (DBN) with 02partitions of time, called 2-temporal BN (2-TBN), where thesame model describes the BN to the next partition of thesample with 02 networks interconnected by arcs

DBN model has Markovian properties and is therefore onlyapplicable to Markov processes (MC)

besides MC other stochastic models like Input-Output HiddenMarkov Model (IOHMM) and, in general, Conditional MarkovProcess (CMP) - conditional probability distribution (CPD) inBN - can be represented by interconnections of a DBN



therefore various types of degradation in dynamic systemscan be modeled by DBNs, which represent this way morecomplex types of faults considering the influence of time, aswell as exogenous variables (abrupt changes in operation)and environmental conditions (eg. humidity, temperature )

as the DBN is a graphical description of a system evolving intime, allows monitoring and updating of the system overtime and also predict the subsequent behavior of thesystem, hence its application in the field of decision andfault diagnosis in supervisory activities



in the case of a type 2-TBN, for any variable their transitionprobabilities are completely determined by the values of thevariable in the current time phase and in the previous one -what is the 1st. order Markov property

for systems with 1st order stationary exponential PDF offaults this is not guaranteed for the lifetime of a componentwith PDF Weibull but this can be bypassed considering therestationarity for a given time sequence i, which is feasible indiagnosis in real time, where the sampling period isextremely small to display the dynamics of residuals



* aplication *

for the diagnosis of 02 tanks system whose static form waspresented in the previous example, is applied the concept ofIOHMM modeled by a DBN, as shown below

it is a distribution over the states of the external observableexogenous variable of input U(i)

t−1 that influences the behavior ofthe hidden (unobservable) X(i)

t−1 variables which result is observedthrough the outputs Y(i)

t−1 which are modes of component failure, therefore applies the formalism of

Hidden Markov Model (withunobservable state) of

Input-Output – IOHMM



* aplication *

the inputs U(i)t−1 are not considered in DBN out of being the

model hybrid, result of inference in continuous part andrepresent the reliabilities of the components assumedconstant throughout the sequence of partitions T of timeinvestigated

the states of components X(i)t−1 are determined by CPD

p(X(i)t−1|U

(i)t−1)

the states Y(i)t−1 resulting from evaluation of residuals rj are

associated to CPD p(Y(i)t−1|X

(i)t−1)



* aplication *

the current states X(i)t re calculated using the following

conditional probabilities:

p(X(i)t = Faulty | X(i)

t−1 = Faulty) = 1,

p(X(i)t = Faulty | X(i)

t−1 = Safe) = 1 − R(i)C(T),

p(X(i)t = Safe | X(i)

t−1 = Faulty) = 0 ,

p(X(i)t = Safe | X(i)

t−1 = Safe) = R(i)C(T),

where R(i)C are components reliabilities estimated

during the sequence T



* aplication *

the DBN model in compact form is shown below:

the simulated scenario displays an active residue r5 for only a timepartition (02) and then suffers new activation after the timepartition 05, which persists until the end of the sequence



* aplication *

as can be seen in the following figure, there is no diagnostic action forpartition 02, featuring the DBN robustness against false alarms

when residual remains after the partition 05, the simulation showsposterior probabilities of component V2 slightly larger than those of thecomponent T2

presentation reliability and diagnosis in industrial systems

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