In the context of the rapidly evolving field of building ventilation, fan noise control stands out as a pivotal technology to enhance the quality of life. This study aimed to elucidate the inherent randomness, distinct characteristics, and potential low-dimensional noise structure essential for developing effective noise control methods. In this study, a stochastic dynamics model for the noise of centrifugal fans with various volute tongue structures is constructed using the Langevin regression method and experimental measurements. An empirical noise model capturing the peak characteristics of noise discrete tonal is developed through parametric mode expansion and an empirical mean-field model of turbulent wakes, facilitating accurate noise predictions. The research findings demonstrate the effectiveness of the Langevin equation employing the cubic Stuart-Landau equation and multiplicative noise to predict fan noise across different volute tongue structures. While stochastic dynamics models unavoidably lose the characteristic discrete noise peaks, predictions of the total A-weighted sound pressure level remain within a 2.2% error margin. The stochastic dynamics models applied to centrifugal fan aerodynamic noise and turbulent wakes exhibit striking resemblances, suggesting a fundamental connection between turbulence and noise generation. The extended empirical noise model maintains discrete pitch noise peaks by introducing shift modes, indicating that stronger Langevin deformations correspond to larger translational amplitudes of the shift modes. The advancement of stochastic dynamics and empirical noise models lays a foundational framework for the formulation of effective noise control strategies.