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Fault Diagnosis

  • Fabrizio Caccavale
  • Mario Iamarino
  • Francesco Pierri
  • Vincenzo Tufano
Part of the Advances in Industrial Control book series (AIC)

Abstract

This chapter is focused on model-based fault diagnosis for chemical batch reactors. First, the basic principles of model-based fault diagnosis are briefly overviewed. Then, a general approach to fault diagnosis for chemical batch reactors, based on nonlinear adaptive observers, is presented. The proposed approach combines both the physical redundancy and analytical redundancy concepts to design an effective diagnosis scheme. Namely, redundant temperature sensors are considered both in the jacket and in the reactor vessel; then, sensor measurements are processed so as to recognize the faulty sensor and output a healthy measure. The healthy measure is used to feed a bank of observers, in such a way to perform detection, isolation, and identification of process and actuator faults. The main properties of the diagnosis algorithms (convergence, isolability, and detectability) are rigorously analyzed. Finally, a case study, based to the phenol–formaldehyde reaction introduced in Chap.  2, is developed.

Keywords

Fault Diagnosis Fault Tree Sensor Fault Actuator Fault Fault Isolation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Principal Symbols

Ad(y)

matrix defined in (6.6)

f

fault vector

\(\mathcal{F}_{\mathrm{a}}\)

admissible set of actuator/process faults

g, h

functions defining the state-space model in (6.1)

kc

rate constant [(mol/m−3)1−n  s−1]

L

matrix gains of the observers

n

vector of measurement noise

NC

number of compounds involved in the reaction

NF

number of considered actuator/process faults

r

scalar residual

r

residual vector

Sj,i

temperature sensors in the cooling jacket (i=1,2)

Sr,i

temperature sensors in the reactor (i=1,2)

t

time [s]

T

temperature [K]

tf

fault time [s]

\(\mathcal{T}\)

time set

u

control input variable

U

overall heat transfer coefficient [J m−2 K−1 s−1]

\(\mathcal{U}\)

set of admissible inputs vectors

x

vector of state variables

\(\mathcal{X}\)

set of admissible state vectors

y

vector of measured output variables

\(\mathcal{Y}\)

set of admissible output vectors

‖⋅‖

Euclidean norm

Greek Symbols

γ

positive gain setting the parameter estimate update rate

δ

magnitude of the fault

η

vector of system uncertainties

θ

parameter US

θf

vector of unknown parameters characterizing the fault magnitude

μ

normalization factor of residuals

τ

time constant setting the fault evolution rate

ϕ

regressor matrix of the fault model

Subscripts and Superscripts

a

actuator

E

energy balance

f

fault

j

jacket

m

measured

M

mass balance

max 

maximum

min 

minimum

p

process

r

reactor

s

sensor

SM

variables referred to the observers SM1 and SM2

u

fault affecting the cooling system

U

fault affecting the heat transfer coefficient

0

initial conditions

nominal value

\(\;\widehat{~}\)

estimate

\(\;\widetilde{~}\)

estimation error

References

  1. 1.
    E. Alcorta Garcia and P.M. Frank. Deterministic nonlinear observer-based approaches to fault diagnosis: a survey. Control Engineering Practice, 5(5):663–670, 1997. CrossRefGoogle Scholar
  2. 2.
    K.J. Aström and B. Wittenmark. Adaptive Control, 2nd Edition. Addison-Wesley, Reading, 1995. MATHGoogle Scholar
  3. 3.
    M. Basseville and I.V. Nikiforov. Detection of Abrupt Changes—Theory and Application. Information and System Sciences Series. Prentice Hall, New York, 1993. Google Scholar
  4. 4.
    F. Caccavale, M. Iamarino, F. Pierri, and V. Tufano. An adaptive controller-observer scheme for temperature control of non-chain reactions in batch reactors. International Journal of Adaptive Control and Signal Processing, 22:627–651, 2008. MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    F. Caccavale, F. Pierri, M. Iamarino, and V. Tufano. An integrated approach to fault diagnosis for a class of chemical batch processes. Journal of Process Control, 19:827–841, 2009. CrossRefGoogle Scholar
  6. 6.
    C.C. Chang and C.C. Yu. On-line fault diagnosis using the signed directed graph. Industrial and Engineering Chemistry Research, 29(7):1290–1299, 1990. CrossRefGoogle Scholar
  7. 7.
    C.T. Chang and J.W. Chen. Implementation issues concerning the EKF-based fault diagnosis techniques. Chemical Engineering Science, 50(18):2861–2882, 1995. CrossRefGoogle Scholar
  8. 8.
    J. Chen and R.J. Patton. Robust Model-Based Fault Diagnosis for Dynamic Systems. Kluwer Academic, Dordrecht, 1999. MATHCrossRefGoogle Scholar
  9. 9.
    Y. Chetouani, N. Mouhab, J.M. Cosmao, and L. Estel. Application of extended Kalman filtering to chemical reactor fault detection. Chemical Engineering Communications, 189(9):1222–1241, 2002. CrossRefGoogle Scholar
  10. 10.
    S.K. Dash, R. Rengaswamy, and V. Venkatasubramanian. Fault diagnosis in a nonlinear CSTR using observers. In Proceedings of the 2001 Annual AIChE Meeting, Reno, NV, p. 282i, 2001. Google Scholar
  11. 11.
    R. Dorr, F. Kratz, J. Ragot, F. Loisy, and J.L. Germain. Detection, isolation, and identification of sensor faults in nuclear power plants. IEEE Transactions on Control Systems Technology, 5(1):42–52, 1997. CrossRefGoogle Scholar
  12. 12.
    R. Dunia and S. Joe Qin. Joint diagnosis of process and sensor faults using principal component analysis. Control Engineering Practice, 6:457–469, 1998. CrossRefGoogle Scholar
  13. 13.
    P.M. Frank. Analytical and qualitative model-based fault diagnosis—a survey and some new results. European Journal of Control, 2:6–28, 1996. MATHGoogle Scholar
  14. 14.
    P.M. Frank and X. Ding. Survey of robust residual generation and evaluation methods in observer-based fault detection systems. Journal of Process Control, 7:403–424, 1997. CrossRefGoogle Scholar
  15. 15.
    J.B. Fussell. Fault tree analysis—state of the art. IEEE Transactions on Reliability, 23(1):51–53, 1974. CrossRefGoogle Scholar
  16. 16.
    J. Gertler. Analytical redundancy methods in fault detection and diagnosis. In Proceedings of IFAC SAFEPROCESS Symposium, pages 9–21, 1991. Google Scholar
  17. 17.
    J.J. Gertler. Fault Detection and Diagnosis in Engineering Systems. Marcel Dekker, New York, 1998. Google Scholar
  18. 18.
    J. Gertler and D. Singer. A new structural framework for parity equation based failure detection and isolation. Automatica, 26:381–388, 1990. MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    D.M. Himmelblau. Fault Detection and Diagnosis in Chemical and Petrochemical Processes. Elsevier Press, Amsterdam, 1978. Google Scholar
  20. 20.
    J.C. Hoskins and D.M. Himmelblau. Artificial neural networks models of knowledge representation in chemical engineering. Computers and Chemical Engineering, 12:881–890, 1988. CrossRefGoogle Scholar
  21. 21.
    Y. Huang, G.V. Reklaitis, and V. Venkatasubramanian. A heuristic extended Kalman filter based estimator for fault identification in a fluid catalytic cracking unit. Industrial & Engineering Chemistry Research, 42:3361–3371, 2003. CrossRefGoogle Scholar
  22. 22.
    P.A. Ioannou and J. Sun. Robust Adaptive Control. Prentice Hall, Upper Saddle River, 1996. MATHGoogle Scholar
  23. 23.
    R. Isermann. Process faults detection based on modelling and estimation methods—a survey. Automatica, 20(4):387–404, 1984. MATHCrossRefGoogle Scholar
  24. 24.
    P. Kaborè, S. Othman, T.F. McKenna, and H. Hammouri. Observer-based fault diagnosis for a class of nonlinear systems—application to a free radical copolymerization reaction. International Journal of Control, 73:787–803, 2000. MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    M. Karpenko, N. Sepehri, and D. Scuse. Diagnosis of process valve actuator faults using a multilayer neural network. Control Engineering Practice, 11:1289–1299, 2003. CrossRefGoogle Scholar
  26. 26.
    P. Kesavan and J.H. Lee. A set based approach to detection of faults in multivariable systems. Computers and Chemical Engineering, 25:925–940, 2001. CrossRefGoogle Scholar
  27. 27.
    H.K. Khalil. Nonlinear Systems, 2nd Edition. Prentice Hall, Upper Saddle River, 1996. Google Scholar
  28. 28.
    R. Li and J.H. Olson. Fault detection and diagnosis in a closed-loop nonlinear distillation process: application of extended Kalman filter. Industrial Engineering Chemical Research, 30(5):898–908, 1991. CrossRefGoogle Scholar
  29. 29.
    J.F. MacGregor, J. Christiana, K. Costas, and M. Koutoudi. Process monitoring and diagnosis by multiblock PLS methods. AIChE Journal, 40(5):826–838, 1994. CrossRefGoogle Scholar
  30. 30.
    R.S.H. Mah and A.C. Tamhane. Detection of gross errors in process data. AIChE Journal, 28:828, 1982. CrossRefGoogle Scholar
  31. 31.
    A. Marciniak, C.D. Bocaniala, R. Louro, J. Sa da Costa, and J. Korbicz. Pattern recognition approach to fault diagnosis in the DAMADICS benchmark flow control valve. In Proceedings of the 5th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes, pages 957–962. 2003. Google Scholar
  32. 32.
    N. Mehranbod, M. Soroush, M. Piovoso, and B.A. Ogunnaike. A probabilistic model for sensor fault detection and identification. AIChE Journal, 49(7):1787, 2003. CrossRefGoogle Scholar
  33. 33.
    N. Mehranbod, M. Soroush, and C. Panjapornpon. A method of sensor fault detection and identification. Journal of Process Control, 15:321–339, 2005. CrossRefGoogle Scholar
  34. 34.
    K. Patan and T. Parisini. Identification of neural dynamic models for fault detection and isolation: the case of a real sugar evaporation process. Journal of Process Control, 15:67–79, 2005. CrossRefGoogle Scholar
  35. 35.
    R.J. Patton, P.M. Frank, and R.N. Clark. Issues in Fault Diagnosis for Dynamic Systems. Springer, London, 2000. Google Scholar
  36. 36.
    R.J. Patton, F.J. Uppal, and C.J. Lopez-Toribio. Soft computing approaches to fault diagnosis for dynamic systems: a survey. In Preprints of the 4th IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, Budapest, pages 298–311, 2001. Google Scholar
  37. 37.
    F. Pierri and G. Paviglianiti. Observer-based actuator fault detection for chemical batch reactors: a comparison between nonlinear adaptive and \(\mathcal{H}_{\infty}\)-based approaches. In Proceedings of the Mediterranean Control Conference, pages 1–6, 2007. Google Scholar
  38. 38.
    F. Pierri, G. Paviglianiti, F. Caccavale, and M. Mattei. Observer-based sensor fault detection and isolationfor chemical batch reactors. Engineering Applications of Artificial Intelligence, 21:1204–1216, 2008. CrossRefGoogle Scholar
  39. 39.
    M.M. Polycarpou and A.J. Helmicki. Automated fault detection and accommodation: a learning systems approach. IEEE Transactions on Systems, Man, and Cybernetics, 25:1447–1458, 1995. CrossRefGoogle Scholar
  40. 40.
    C. Rojas-Guzman and M.A. Kramer. Comparison of belief networks and rule-based expert systems for fault diagnosis of chemical processes. Engineering Application of Artificial Intelligence, 6:191, 1993. CrossRefGoogle Scholar
  41. 41.
    D. Ruiz, J. Canton, J.M. Nougues, A. Espuña, and L. Puigjaner. On-line fault diagnosis system support for reactive scheduling in multipurpose batch chemical plants. Computers and Chemical Engineering, 25:829–837, 2001. CrossRefGoogle Scholar
  42. 42.
    D. Ruiz, J.M. Nougues, and L. Puigjaner. Fault diagnosis support system for complex chemical plants. Computers and Chemical Engineering, 25:151–160, 2001. CrossRefGoogle Scholar
  43. 43.
    N.J. Scenna. Some aspects of fault diagnosis in batch processes. Reliability Engineering and System Safety, 70(1):95–110, 2000. CrossRefGoogle Scholar
  44. 44.
    O.A.Z. Sotomayor and D. Odloak. Observer-based fault diagnosis in chemical plants. Chemical Engineering Journal, 112:93–108, 2005. CrossRefGoogle Scholar
  45. 45.
    R. Tarantino, F. Szigeti, and E. Colina-Morles. Generalized Luenberger observer-based fault detection filter design: An industrial application. Control Engineering Practice, 8:665–671, 2000. CrossRefGoogle Scholar
  46. 46.
    H. Vedam and V. Venkatasubramanian. Signed digraph based multiple fault diagnosis. Computers and Chemical Engineering, 21:655–660, 1997. Google Scholar
  47. 47.
    H. Vedam and V. Venkatasubramanian. PCA-SDG based process monitoring and fault diagnosis. Control Engineering Practice, 7:903–917, 1999. CrossRefGoogle Scholar
  48. 48.
    V. Venkatasubramanian, R. Vaidyanathan, and Y. Yamamoto. Process fault detection and diagnosis using neural networks—I steady state process. Computers and Chemical Engineering, 14:699–712, 1990. CrossRefGoogle Scholar
  49. 49.
    V. Venkatasubramanian, R. Rengaswamy, and S.N. Kavuri. A review of process fault detection and diagnosis part II: Qualitative models and search strategies quantitative model-based methods. Computers and Chemical Engineering, 27:313–326, 2003. CrossRefGoogle Scholar
  50. 50.
    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 and Chemical Engineering, 27:293–311, 2003. CrossRefGoogle Scholar
  51. 51.
    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 and Chemical Engineering, 27:327–346, 2003. CrossRefGoogle Scholar
  52. 52.
    A.S. Willsky. A survey of design methods for failure detection in dynamic systems. Automatica, 12:601–611, 1976. MathSciNetMATHCrossRefGoogle Scholar
  53. 53.
    M. Witczak, J. Patton, and J. Korbicz. Fault detection with observers and genetic programming: application to the DAMADICS benchmark problem. In Proceedings of the 5th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes, pages 1203–1208, 2003. Google Scholar
  54. 54.
    S. Yoon and J.F. MacGregor. Fault diagnosis with multivariate statistical models part I: using steady state fault signature. Journal of Process Control, 11:387–400, 2001. CrossRefGoogle Scholar
  55. 55.
    D.L. Yu, J.B. Gomm, and D. Williams. Sensor fault diagnosis in a chemical process via RBF neural networks. Control Engineering Practice, 7:49–55, 1999. CrossRefGoogle Scholar
  56. 56.
    X. Zhang, M.M. Polycarpou, and T. Parisini. A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems. IEEE Transactions on Automatic Control, 47:576–593, 2002. MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Fabrizio Caccavale
    • 1
  • Mario Iamarino
    • 2
  • Francesco Pierri
    • 3
  • Vincenzo Tufano
    • 4
  1. 1.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  2. 2.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  3. 3.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  4. 4.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly

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