Active Fault Detection Based on Tensor Train Decomposition

Abstract

The paper deals with active fault detection of stochastic systems based on tensor train representation of the Bellman function. The faulty and faulty-free behavior of the system is represented using multiple models. The active fault detection problem is treated as an optimal design problem similar to optimal stochastic control. The original problem is reformulated as a perfect state information problem by introducing an information state that contains statistics computed by a state estimator. The Bellman function is computed using the value iteration algorithm over a rectilinear grid set up in the information state space. Within the value iteration algorithm, the Bellman function is represented using the tensor train decomposition, and considerable attention is devoted to designing a rectilinear grid that respects the constraints placed on the elements of the information state.