Kurtosis-guided Duffing for weak signal detection

Detecting weak signals embedded in strong noise remains a critical challenge across numerous engineering fields, including mechanical fault diagnosis, underwater acoustics, and biomedical monitoring. The Duffing oscillator is a well-established nonlinear tool capable of amplifying weak periodic signals through bifurcation dynamics. However, its performance is often compromised by noise-induced pseudo-periodic responses that closely resemble genuine signal-driven behavior. To address this limitation, we propose a Kurtosis-guided Duffing (KG-Duffing) framework that adaptively modulates the excitation strength using a sliding-window kurtosis measure. The proposed method enhances the system’s sensitivity to structured signal components while suppressing activation during noise-dominated intervals, thereby reducing false alarms. Comparative experiments demonstrate that KG-Duffing achieves superior robustness under both Gaussian and non-Gaussian noise conditions. Validation on synthetic signals, noise-only scenarios, and real-world bearing vibration data confirms that KG-Duffing effectively suppresses pseudo-periodic oscillations, lowers false alarm rates, and improves detection accuracy compared to the classical Duffing oscillator and several benchmark techniques. These results highlight KG-Duffing as a robust and adaptive nonlinear framework for weak signal detection in highly noisy environments.