We present a fault detection method called the gray-box. The term “gray-box” refers to the approach wherein a deterministic model of system, i.e., “white box,” is used to filter the data and generate a residual, while a stochastic model, i.e., “black-box” is used to describe the residual. The residual is described by a three-tier stochastic model. An auto-regressive process, and a time-delay feed-forward neural network describe the linear and nonlinear components of the residual, respectively. The last component, the noise, is characterized by its moments. Faults are detected by monitoring the parameters of the auto-regressive model, the weights of the neural network, and the moments of noise. This method is demonstrated on a simulated system of a gas turbine with time delay feedback actuator.

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