Compound fault diagnosis of rolling bearings using adaptive spiral flying sparrow search algorithm-variational mode decomposition-sample entropy (ASFSSA-VMD-SampEn) with a hybrid particle swarm optimization-convolutional neural network (HPSO-CNN).

As a key component of rotating machinery, rolling bearing fault characteristic signals are susceptible to multi-source coupling interference, leading to weak fault features easily submerged and difficult to extract. Aiming at the large decomposition error and low computational efficiency of Variational Mode Decomposition (VMD) in extracting fault features under single and compound bearing fault modes, as well as the limitations brought by empirical parameter selection, this paper proposes a novel bearing fault diagnosis method. The overall VMD framework is optimized by the Adaptive Spiral Flying Sparrow Search Algorithm (ASFSSA), which is further combined with the Hybrid Particle Swarm Optimization (HPSO)-improved Convolutional Neural Network (CNN). First, the ASFSSA adaptively optimizes VMD's core parameters, including the mode quantity K and penalty factor α, which addresses the issue that traditional VMD parameters rely on empirical assignment and achieve precise decomposition of fault signals. Second, sample entropy (SampEn) is adopted only as the fitness function to quantify the complexity and stationarity of each decomposed intrinsic mode function and provide objective quantitative criteria for parameter optimization. To eliminate circular SampEn self-verification flaws in optimization and evaluation, six external quantitative metrics are added to fully evaluate fault signal decomposition performance. Finally, HPSO optimizes CNN hyperparameters, including learning rate, hidden nodes, and L2 coefficient, to boost the model's fault classification accuracy. Simulations and experiments prove that the method outperforms traditional algorithms for accurate, reliable bearing fault diagnosis.