“…In this section, a simulated vibration signal of a faulty rolling bearing is constructed to evaluate the efficiency of the proposed method. Considering a rolling bearing running with constant speed and assuming its inner race, outer race, or rollers have local damage, the excited vibration signal can be modeled as a series of periodic transient impulse features [ 38 , 39 ], and the vibration acceleration signal x ( t ) measured from the rolling bearing can be modeled as Equations (18) – (20): where s(t ) is an ideal impulsive vibration signal with no noise; n ( t ) is white Gaussian noise; M is the number of the fault impulses induced by the local damage; A m is the amplitude of the m th fault impulse; a m is the amplitude modulation coefficient, where 0 < a m < 1; f r is the rotating frequency of the bearing; ζ is the structural damping coefficient; T p is the time period between two consecutive fault impulses, and T p = 1/ f c , in which f c represents the FCF of inner race, outer race, or balls; τ i ( i = 1, 2, …, M ) represents the effect of random slippage of the balls and can be assumed to be a zero mean, uniformly distributed random sequence with a standard deviation of 0.01 T p ~0.02 T p ; ω r is the excited resonance frequency; and u ( t ) represents the unit step function.…”