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Rotating machinery is an important and easily damaged component in large-scale equipment. Under the coupling action of system components, the occurrence rate of compound faults is very high, which seriously endangers equipment safety. The vibration signals of the damaged rotating machine include equipment operation vibration information, periodic impacts, environmental noise, and even accidental impacts. To effectively extract multi-fault features from compound fault signals, a multi-period pulse detection indicator called harmonic spectrum correlation kurtosis (HSCK) is proposed in this paper. Based on this, an adaptive matching extraction strategy for multiple fault features is proposed. By introducing variational mode decomposition, an adaptive plane paving method for signal components is designed, and an enhanced cyclic frequency estimation method is proposed to pre-determine the fault characteristic frequency as a prior parameter of HSCK, so as to obtain the optimal center frequency and bandwidth of multiple resonance bands. The implementation of this strategy can obtain more periodic pulse information with a high signal-to-noise ratio. Simulation results show that the strategy is accurate and effective. The data of wheel-bearing compound fault and bearing multi-element compound fault indicate that the proposed strategy can be used for compound fault diagnosis of rotating machinery.