Time-shift-multiscale-weighted-fuzzy-diversity-entropy-based feature extraction for gearbox under strong noise environment

Abstract Effectively extracting vibration signal features of the gearbox under different fault types and severities in noisy environments remains a key challenge for gearbox fault diagnosis. Diversity entropy (DE) has certain advantages in capturing the nonlinear dynamic characteristics of signals. DE can identify potential nonlinear features by considering the diversity and complexity of the signals. However, DE only considers the cosine similarity between orbits, neglecting variations in signal amplitude and differences in the system’s state structure and spatial distribution leads to its inability to effectively distinguish valid information from noise in the signals. To address this issue, this paper proposes a time shift multiscale weighted fuzzy DE (TSMWFDE), this method introduces a weighted adaptive similarity based on cosine similarity and Tanimoto similarity, which simultaneously considers the system’s amplitude variations. It applies fuzzy processing to the weighted adaptive similarity, reducing errors caused by differences in state or spatial distribution. To some extent, it compensates for the shortcomings of DE and can better extract signal features of different fault types and severities of the gearbox in noisy environments. Based on this, a novel gearbox fault diagnosis scheme, TSMWFDE-Newton–Raphson-based optimizer-Support vector machine, is proposed for gearbox fault diagnosis. The paper also designs experiments under different noise conditions, fault types, and fault severities, and compares the proposed approach with other existing methods. The results show that, compared to other denoising algorithm-based and entropy-based fault diagnosis methods, the results show that, compared to other denoising algorithm-based and entropy-based fault diagnosis methods, the proposed approach achieves the best signal feature extraction capability and fault recognition accuracy—exceeding 98% accuracy at SNR = 3 dB noise levels in identifying different fault types and severities, demonstrating the ability to detect gearbox faults under noisy environments.