<p>Entropy-based feature extraction methods have emerged as a focal point in fault diagnosis, leveraging their inherent advantages, which include independence from prior knowledge, elimination of the need for preprocessing, and straightforward implementation. However, multiscale entropy encounters challenges in capturing early fault characteristics, as it predominantly emphasizes low-frequency fault information, potentially overlooking valuable high-frequency data. To address this limitation, a novel hierarchical fractional-order Boltzmann–Shannon interaction entropy is proposed to extract fault information across both high and low frequencies and enhance the noise-resistant performance of the algorithm. By hierarchically decomposing vibration signals and subsequently computing the fractional-order Boltzmann–Shannon interaction entropy of the resultant sub-signals at each level, a comprehensive multidimensional fault characteristic vector is constructed. Furthermore, to mitigate the sensitivity to parameter selection within the kernel extreme learning machine (KELM) model, this study incorporates the Newton–Raphson-based optimizer (NRBO) to optimize the regularization coefficients and kernel function parameters, thereby establishing an optimal NRBO–KELM model for gear fault diagnosis. Validation with the WT-planetary gearbox datasets and HUST gearbox fault datasets demonstrates that the proposed method achieves 100% diagnostic accuracy across 100 experimental samples, significantly outperforming existing methods. This result highlights the method’s potential and effectiveness in handling diverse gearbox configurations and fault scenarios.</p>