In view of complex noise background in engineering practices, this paper presents a rescaled method to detect failure features of bearing structure in the Poisson white noise background. To realize the scale transformation of the fault signal with Poisson white noise, a general scale transformation (GST) method is introduced based on the second-order underdamped nonlinear system. The signal features are successfully extracted through the proposed rescaled method in the simulated and experimental cases. We focus on the influence of Poisson white noise parameters and damping coefficient on the response of nonlinear system. The impulse arrival rate and noise intensity have opposite effects on the realization of stochastic resonance (SR) and the extraction of bearing fault features. Poisson white noise with smaller impulse arrival rate or larger noise intensity is easier to induce SR to extract bearing fault features. The optimal matching between the nonlinear system and the input signal is formed by the optimization algorithm, which greatly improves the extraction efficiency of fault features. Compared with the normalized scale transformation (NST) method, the GST has significant advantages in recognizing the bearing structure failure. The differences and connections between Poisson white noise and Gaussian white noise are discussed in the rescaled system excited by the experiment signal. This paper might provide several practical values for recognizing bearing fault mode in the Poisson white noise.

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