Adaptive fault detection under radio frequency energy-harvesting mechanism

This paper focuses on the problem of fault detection and optimal energy allocation in linear time-varying systems through the utilization of radio frequency (RF) energy harvesting technology. To enhance fault detection, an optimal energy-scheduling scheme is developed, effectively utilizing the harvested RF energy. An adaptive Kalman filter incorporating a penalty function is implemented to account for unsuccessful information transmissions at the remote terminal, facilitating the computation of weighted covariances for system state and fault parameter estimation errors. The energy allocation optimization under constrained energy resources is formulated as a weighted covariance minimization problem through a Markov decision process (MDP).The Bellman equation is applied to determine the optimal energy allocation strategy through iterative computation. The optimality and threshold structure of the proposed strategy are rigorously established in Theorems 1 and 2, with its effectiveness being validated through comprehensive numerical simulations.