Gray-box approach to fault diagnosis of dynamical systems

Model-based fault diagnosis has become an important approach for diagnosis of dynamical systems. By comparing the observed sensor values with those of the predicted values by the model, e.g., the residual, the health of the system can be assessed. However, because of modeling errors, sensor noise, disturbances, etc., direct comparison between observed and predicted values can be difficult. In an effort to address this problem, we present a new method called the gray-box method. It is called a “gray-box” because 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. Instead of setting a threshold on the residual, the residual is modeled by a three-tier stochastic model. The linear and non-linear components of the residual are described by an auto-regressive process, and a time-delay feed-forward neural network, respectively. The last component, the noise, is characterized by its moments. The stochastic model provides a complete description of the residual, and the faults can be detected by monitoring the parameters of the auto-regressive model, the weights of the neural network, and the moments of noise. The method is robust to system modeling errors and is applicable to both linear and non-linear systems