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Presentation reliability and diagnosis in industrial systems

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Presentation reliability and diagnosis in industrial systems

  1. 1. Programa de Atualização Profissional Reliability and fault diagnosis in industrial systems methodology summary by Gláucio Bastos, M.B.A., Ch.E.
  2. 2. Programa de Atualização Profissional abstract  target: presentation of the advantages and efficiency of Bayesian networks (BN) in the formulation of reliability models for the cases of systems with unknown structure, with common cause failures and redundancy
  3. 3. Programa de Atualização Profissional need  different sources of quantitative and qualitative data are incorporated into the Bayesian models, considered prior probabilities or a priori information  the evaluation of the reliability parameters of the Bayesian hierarchical model method obtains a higher representation using the Weibull distribution and probability density function (PDF) of occurrence of failures of the generic exponential distribution because it allows the modeling of different regions of lifetime curve of a large number of components  if the probabilities a priori are not known, may be defined by statistical sampling techniques or directed learning methods
  4. 4. Programa de Atualização Profissional need  continuous decision-making variables, which in the Bayesian concept of fault diagnosis are the posterior probabilities of failures are of great interest for monitoring the degradation of 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)
  5. 5. Programa de Atualização Profissional need  fault tolerant control ensures high availability and security for current industry systems  modern automation relates to autonomous system, the requirements of control performance and overall system reliability  fault detection and isolation (FDI) techniques involve detection in sensor readings of discrepancies or ‘residuals' in relation to a standard, indicating the occurrence of a failure, including its type and its location in the system
  6. 6. Programa de Atualização Profissional 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 the process being monitored and residues detected according to the specifications of the physical model, each of these parts - the 1st continuous and the other discrete - constituting hybrid BN because some of the random variables are continuous and the other discretes where continuous nodes contain a priori probabilities of failure of components that are used by the inference process in the discrete part to determine the posterior probabilities of failures  this method can be applied in large scale for all types of failure distribution (herein was used the Weibull) of the system components
  7. 7. Programa de Atualização Profissional 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 residuals r = {rj; 1 ≤ j ≤ p}, components Ci , as well with Bayesian reliability model of such components  the arc connecting node Ci to node rj indicates that rj is sensitive to component Ci fail and it is associated with its reliability Ri  to a residual rj there is 02 states: {D(Detected),ND(NotDetected)} and there is also 02 states {F(Faulty), S(Safe)} to a component Ci
  8. 8. Programa de Atualização Profissional Bayesian model for fault diagnosis
  9. 9. Programa de Atualização Profissional 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 fault signature (FSM) matrix: a standard for residuals  when a residual rj is not sensitive to failure of a component Ci, there is no arc between 02 nodes  after residuals detection, the posterior probabilities of failure p(Ci|r1, . . . , rp) can be inferred in the discrete part of the BN
  10. 10. Programa de Atualização Profissional Bayesian model for fault diagnosis * aplication *  the method is simulated in the system below, formed by T1 and T2 tanks, V1 and V2 valves, L1 (De1) and L2 (De2) sensors, pump (P), proportional-integral (PI) controller and controller 'bang-bang‘ K (On-Off)
  11. 11. Programa de Atualização Profissional Bayesian model for fault diagnosis * aplication *  from the parameters of the failure rates, the Weibull type PDFs of both component reliability and system are shown in the following figure with their average and HDIs of 95%, and the decay of its quantile to 90% with the time of operation, especially the 1st quantile - most critical - showing that after operating for 20,000 hrs. the overall system reliability falls to 0.006256
  12. 12. Programa de Atualização Profissional Bayesian model for fault diagnosis * aplication *
  13. 13. Programa de Atualização Profissional Bayesian model for fault diagnosis * 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 identical for all components  it is observed that the flaws in V2 and T2 can not be isolated because both exhibit identical patterns  the simulation scenario presents after operating for 20,000 hrs. the following standard for residuals: [r1, r2, r3, r4, r5] = [0, 0, 0, 0, 1], that matches the pattern of failure for the V2 and T2 components
  14. 14. Programa de Atualização Profissional Bayesian model for fault diagnosis * aplication *  the figure below shows the result of analysis for isolation of faulty components, where the a priori probabilities are determined in the continuous part of the BN and posteriors in the 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
  15. 15. Programa de Atualização Profissional Bayesian model for fault diagnosis * 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 faulty component between V2 and T2, they are statistically identical for each one  comparing the posterior probabilities defined from the standard residuals, the highest probability of failure (0.74) for component V2 relative to that one for the other component T2 (0.51) indicates the malfunction of V2 as the most likely cause of failure of the overall system under this scenario simulation
  16. 16. Programa de Atualização Profissional diagnosis with dynamic BN  temporal dependencies between components to reliability calculations can be modeled by dynamic BN (DBN) with 02 partitions of time, called 2-temporal BN (2-TBN), where the same model describes the BN to the next partition of the sample with 02 networks interconnected by arcs  DBN model has Markovian properties and is therefore only applicable to Markov processes (MC)  besides MC other stochastic models like Input-Output Hidden Markov Model (IOHMM) and, in general, Conditional Markov Process (CMP) - conditional probability distribution (CPD) in BN - can be represented by interconnections of a DBN
  17. 17. Programa de Atualização Profissional diagnosis with dynamic BN  therefore various types of degradation in dynamic systems can be modeled by DBNs, which represent this way more complex types of faults considering the influence of time, as well as exogenous variables (abrupt changes in operation) and environmental conditions (eg. humidity, temperature )  as the DBN is a graphical description of a system evolving in time, allows monitoring and updating of the system over time and also predict the subsequent behavior of the system, hence its application in the field of decision and fault diagnosis in supervisory activities
  18. 18. Programa de Atualização Profissional diagnosis with dynamic BN  in the case of a type 2-TBN, for any variable their transition probabilities are completely determined by the values ​​of the variable 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 of faults this is not guaranteed for the lifetime of a component with PDF Weibull but this can be bypassed considering there stationarity for a given time sequence i, which is feasible in diagnosis in real time, where the sampling period is extremely small to display the dynamics of residuals
  19. 19. Programa de Atualização Profissional diagnosis with dynamic BN * aplication *  for the diagnosis of 02 tanks system whose static form was presented in the previous example, is applied the concept of IOHMM modeled by a DBN, as shown below  it is a distribution over the states of the external observable exogenous variable of input U(i) t−1 that influences the behavior of the hidden (unobservable) X(i) t−1 variables which result is observed through the outputs Y(i) t−1 which are modes of component failure,  therefore applies the formalism of Hidden Markov Model (with unobservable state) of Input-Output – IOHMM
  20. 20. Programa de Atualização Profissional diagnosis with dynamic BN * aplication *  the inputs U(i) t−1 are not considered in DBN out of being the model hybrid, result of inference in continuous part and represent the reliabilities of the components assumed constant throughout the sequence of partitions T of time investigated  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)
  21. 21. Programa de Atualização Profissional diagnosis with dynamic BN * 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
  22. 22. Programa de Atualização Profissional diagnosis with dynamic BN * aplication *  the DBN model in compact form is shown below:  the simulated scenario displays an active residue r5 for only a time partition (02) and then suffers new activation after the time partition 05, which persists until the end of the sequence
  23. 23. Programa de Atualização Profissional diagnosis with dynamic BN * aplication *  as can be seen in the following figure, there is no diagnostic action for partition 02, featuring the DBN robustness against false alarms  when residual remains after the partition 05, the simulation shows posterior probabilities of component V2 slightly larger than those of the component T2

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