A mathematical model of the process is used in model-based fault diagnosis to describe the expected behavior of the process. In most model-based FDD techniques, measured values of process variables are compared to their estimated values. The estimations are based on a process model describing the expected (nominal) operation, past measurements of process variables, and noise/disturbance information. The difference between measured and estimated values are residuals that are subjected to statistical tests to detect significant magnitudes of residuals that indicate presence of faults. Various
FDD methods based on residuals are discussed in Section 8.3.1. Another group of model-based FDD techniques use parameter estimation. They are presented in Section 8.3.2. In this approach, model parameters are estimated for nominal operating conditions. They are estimated repeatedly as new measurement information is collected. Significant deviations in model parameter values are used for FDD. Hidden Markov models provide another FDD framework. Markov processes, hidden Markov models and their use in FDD are discussed in Section 8.3.3.
Model-based FDD has its origins in various engineering areas. Material and energy balance calculations were used for gross error detection and data reconciliation in chemical process operations [235, 359, 519]. FDD applications in aerospace systems were reported  leading to parity relations concepts [101, 187]. Kalman filters were used in aerospace and nuclear power industries for FDD [168, 650]. Diagnostic observers were also proposed for similar applications [105, 161, 163, 458]. FDD by parameter estimation has been used in manufacturing industries [50, 251]. Excellent review papers [44, 162, 457] and books [45, 189, 456, 518] report recent developments in the FFD theory and applications in many areas. The presentation of various model-based FFD techniques in this text is based on these resources and the research of Cinar and co-workers [292, 414].
Input-output relations for systems subject to faults. Consider a process that receives measured inputs u« subject to sensor faults <5um, controlled inputs uc subject to actuator faults due, process faults Sup that are interpreted as additional inputs, and measured outputs y subject to sensor faults Sy (Figure 8.8). Additive faults acting on the process include:
• output sensor faults Sy(t)
In addition, there are additive disturbances acting on the process (these are usually unmeasured input disturbances) (d) and various noises acting on measurements and the process:
• input actuator noise vc(i)
actuator faults ( uc)
controlled inputs measured inputs
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