2.3 A Comprehensive Diagnosis Scheme

Instead of just providing nominal values, the state estimation scheme can be used for diagnosis by reconstructing the entire set of states of the process if the process parameters have been estimated precisely. The reconstructed results are then compared and the set of most consistent states is chosen as the best estimate. This set can then be used to generate residuals based on the actual observations to detect whether a fault occurred.

To identify faults, the set of system equations are modified so that the three basic types of faults listed below can be explicitly identified as parameters and terms of the equations:

• Instrument faults; which refers to sensor faults.
• Actuator faults.
• Component faults; which refers to the different parts or sub-systems in the process where the fault can occur.

By explicitly incorporating these faults into the parameters of system equations as part of the observer system, diagnosis algorithms can be designed to detect and isolate faults. A unifying representation, in discrete form, is given by

(1)

where represents a disturbance term due to noise, and represents the effects introduced by the fault term. Entries of can be used to model actuator and component faults and entries of can be used to model sensor faults [6].

State estimation requires parameter estimation to determine precise models of the process under scrutiny. Like state estimation schemes, diagnosis schemes can be based on parameter estimation techniques. The advantage of these schemes is the close relation between estimated values and physical coefficients. Given that nominal values can be derived from state estimation schemes or from design documents, comprehensive diagnosis can proceed by performing one or several of the following techniques (Fig. 3):

• Quantitative parameter estimation is derived from numerical models of the process. Typically filtering methods may be applied to estimate system parameters based on a vector of residuals. These parameters represent aggregate behavior of process components, and, therefore, a fault may cause a number of parameter deviations. This process is computationally intensive, and may be subject to the convergence problems that occur in numerical estimation. To improve performance, other techniques can be used to narrow down the parameter search space.
• Performance of diagnosis algorithms can be enhanced by incorporating sophisticated sensitivity analysis schemes. The degree to which different faults affect measurements can be exploited by the parameter estimation procedure to rank possible causes by the sensitivity of the observables to the hypothesized causes.
• Failure mode mappings can further enhance the fault identification and isolation process. They represent a discrete event systems approach that requires knowledge about how process components may fail, and what effects these failures have on system parameters.
• Dependency analysis techniques rely on a topological functional model of the process and capture a weighted dependency between parameters and measured variables. These weights could be a function of various parameters, such as proximity to the observed fault. Sometimes the weights may capture process delay times, and in such cases the dependency graph represents a dynamic model of system behavior. Observed deviations can be traced back to parameter values which can be ordered in terms of when their effects become active.

Note that the techniques described above are not mutually exclusive. Any of these methods can be effectively developed into a diagnosis system. However, developing a diagnosis framework that integrates two or more of these approaches is likely to produce more efficient and robust systems. It remains a challenge to see how best to develop such systems.

  
Figure 3: Complementary diagnosis schemes.