$H_{i}/H_{\infty}$ Optimization Based Fault Detection for Traction Rectifier in High-Speed Train

The traction rectifier plays an important role in safe operation of high-speed trains. Any occurrence of unexpected faults in the traction rectifier may result in safety deterioration to high-speed trains. In this paper, an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{i}/H_{\infty}$</tex> optimization based method is used to achieve fault detection of the traction rectifier affected by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{2}$</tex>-norm bounded multi-source disturbances. First, the rectifier with potential faults is described as a linear discrete time-varying system model. The residual is generated by applying an observer-based fault detection filter (FDF). Then, an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{i}/H_{\infty}$</tex> optimization criteria is introduced by using the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{-}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> sensitivity indices. Based on this, the design of FDF can be reformulated as an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{i}/H_{\infty}$</tex> optimization problem. A feasible solution of the post-filter and observer gain matrix is given in terms of Riccati recursions. Consequently, the sensitivity of residual to faults and robustness of residual against disturbances can be improved. Finally, a simulation is carried out to demonstrate the effectiveness of the method.