To select parameters is important in the research area of support vector machine. Based on particle swarm optimization, this paper proposes automatic parameters selection for least squares support vector machine (LSSVM). The effect of this proposed method is demonstrated by function regression problem. Besides, an equipment fault classification further illustrates that LSSVM based on particle swarm optimization has better classification ability than LSSVM based genetic algorithm under the same condition.

Incipient fault signatures in rolling bearings are often compromised by intense background noise and stochastic impulses. Conventional resonance demodulation frequently relies on rigid frequency partitioning, which tends to disrupt the physical continuity of resonance bands and results in the incomplete capture of essential diagnostic information. Furthermore, the robustness of prevailing optimal demodulation frequency band (ODFB) selection indicators remains limited under heavy noise interference. This study develops the WLERgram framework, which utilizes regularized Fourier series to capture the global morphology of the vibration spectrum. By anchoring filter boundaries at natural energy troughs, the method mitigates spectral truncation based on inherent signal characteristics. The framework integrates an Adaptive Morphological Consensus (AMC) strategy, employing multi-scale operators to extract rotation-correlated components and enhance resistance to incoherent interference. By incorporating a Weighted Logarithmic Energy Ratio (WLER) metric, the method utilizes a nonlinear operator to implement differential mapping between coherent fault harmonics and stochastic noise, enabling autonomous optimization of the demodulation band. Validations using synthetic simulations and experimental benchmarks (CWRU and UORED) suggest that WLERgram offers reliable feature extraction performance and diagnostic robustness under harsh noise environments.

The vibration model of the Jeffcott crack rotor is established. RungeKutta method based on matlab language is used to solve the Jeffcott cracked rotor response procedures. The experimental results show that the method can judge accurately the different crack depth rotor fault from the characteristics of vibration signal and axis trajectory.

To improve the effectiveness of Multiscale Range Entropy (MRE) in extracting features from rolling bearing faults, this paper proposes a novel bearing fault diagnosis method that combines the Northern Goshawk Optimization (NGO) algorithm, MRE, and a Deep Extreme Learning Machine (DELM). First, the raw vibration signal is decomposed using Variational Mode Decomposition (VMD) to obtain its Intrinsic Mode Functions (IMFs). Second, the NGO algorithm is employed to optimize the MRE parameters, using the minimum crest factor as the objective function. Then, using these optimized parameters, MRE is applied to extract fault features. The resulting feature set undergoes dimensionality reduction to create the final sample set. Finally, an NGO-optimized DELM is used for fault classification. The experimental results demonstrate that this method effectively extracts the characteristic signals of rolling bearing faults through robust parameter optimization, thereby improving the accuracy of fault diagnosis.