A novel Lanczos quaternion singular spectrum analysis method and its application to bevel gear fault diagnosis with multi-channel signals

•A novel multi-channel signal processing method named LQSSA is proposed.•Lanczos method is used in the decomposition to reduce calculation time.•Filter factor is obtained by introducing Lagrange multiplier to improve signal purity.•Each LQSSC is derived from multi-channel signals by periodic similarity.•Simulation and experimental signals of bevel gear verify the effectiveness and superiority of LQSSA.