Fault Diagnosis

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


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.


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


matrix defined in (6.6)


fault vector


admissible set of actuator/process faults

g, h

functions defining the state-space model in (6.1)


rate constant [(mol/m−3)1−n  s−1]


matrix gains of the observers


vector of measurement noise


number of compounds involved in the reaction


number of considered actuator/process faults


scalar residual


residual vector


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


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


time [s]


temperature [K]


fault time [s]


time set


control input variable


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


set of admissible inputs vectors


vector of state variables


set of admissible state vectors


vector of measured output variables


set of admissible output vectors


Euclidean norm

Greek Symbols


positive gain setting the parameter estimate update rate


magnitude of the fault


vector of system uncertainties


parameter US


vector of unknown parameters characterizing the fault magnitude


normalization factor of residuals


time constant setting the fault evolution rate


regressor matrix of the fault model

Subscripts and Superscripts




energy balance








mass balance












variables referred to the observers SM1 and SM2


fault affecting the cooling system


fault affecting the heat transfer coefficient


initial conditions

nominal value




estimation error


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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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