(Georgia Institute of Technology, 2008-04-01)
Lee, Young Ki
This research develops a fault diagnosis method for complex systems in the presence of uncertainties and possibility of multiple solutions. Fault diagnosis is a challenging problem because data used in diagnosis contain random errors and often systematic errors as well. Furthermore, fault diagnosis is basically an inverse problem so that it inherits unfavorable characteristics of inverse problems: The existence and uniqueness of an inverse solution are not guaranteed and the solution may be unstable. The weighted least squares method and its variations are traditionally used for solving inverse problems. However, the existing algorithms often fail to identify multiple solutions if they are present. In addition, the existing algorithms are not capable of selecting variables systematically so that they generally use the full model in which may contain unnecessary variables as well as necessary variables. Ignoring this model uncertainty often gives rise to, so called, the smearing effect in solutions, because of which unnecessary variables are overestimated and necessary variables are underestimated. The proposed method solves the inverse problem using Bayesian inference. An engineering system can be parameterized using state variables. The probability of each state variable is inferred from observations made on the system. A bias in an observation is treated as a variable, and the probability of the bias variable is inferred as well. To take the uncertainty of model structure into account, multiple Bayesian models are created with various combinations of the state variables and the bias variables. The results from all models are averaged according to how likely each model is. Gibbs sampling is used for approximating updated probabilities. The method is demonstrated for two applications: the status matching of a turbojet engine and the fault diagnosis of an industrial gas turbine. In the status matching application only physical faults in the components of a turbojet engine are considered whereas in the fault diagnosis application sensor biases are considered as well as physical faults. The proposed method is tested in various faulty conditions using simulated measurements. Results show that the proposed method identifies physical faults and sensor biases simultaneously. It is also demonstrated that multiple solutions can be identified. Overall, there is a clear improvement in ability to identify correct solutions over the full model that contains all state and bias variables.