Purpose: This paper proposes an intelligent fault diagnosis method, which aims to obtain the outstanding fault diagnosis results of the gearbox.Design/methodology/approach: An intelligent fault diagnosis method based on energy entropy-weighted complementary ensemble empirical mode decomposition (EWCEEMD) and support vector machine (SVM) optimized by whale optimization algorithm (WOA) is proposed. The raw signal is first denoised by the wavelet noise reduction method. Then, complementary ensemble empirical mode decomposition (CEEMD) is used to generate several intrinsic mode functions (IMFs). Next, energy entropy is used as an indicator to measure the sensibility of the IMF and converted into a weight coefficient by function. After that, IMFs are linearly weighted to form the reconstruction signal, and several features are extracted from the new signal. Finally, the support vector machine optimized by the whale optimization algorithm (WOA-SVM) model is used for gearbox fault classification using feature vectors.Findings: The fault features extracted by this method have a better clustering effect and clear boundaries under each fault mode than the unimproved method. At the same time, the accuracy of fault diagnosis is greatly improved.Originality/value: In most studies of fault diagnosis, the sensitivity of IMF has not been appreciated. In this paper, energy entropy is chosen to quantify sensitivity. In addition, high classification accuracy can be achieved by applying WOA-SVM as the final classification model, improving the efficiency of fault diagnosis as well.

Purpose: This paper proposes an improved fatigue life analysis method for optimal design of electric multiple units (EMU) gear, which aims at defects of traditional Miner fatigue cumulative damage theory.Design/methodology/approach: A fatigue life analysis method by modifying S–N curve and considering material difference is presented, which improves the fatigue life of EMU gear based on shape modification optimization. A corrected method for stress amplitude, average stress and S–N curve is proposed, which considers low stress cycle, material difference and other factors. The fatigue life prediction of EMU gear is carried out by corrected S–N curve and transient dynamic analysis. Moreover, the gear modification technology combined with intelligent optimization method is adopted to investigate the approach of fatigue life analysis and improvement.Findings: The results show that it is more corresponded to engineering practice by using the improved fatigue life analysis method than the traditional method. The function of stress and modification amount established by response surface method meets the requirement of precision. The fatigue life of EMU gear based on the intelligent algorithm for seeking the optimal modification amount is significantly improved compared with that before the modification.Originality/value: The traditional fatigue life analysis method does not consider the influence of working condition and material. The life prediction results by using the method proposed in this paper are more accurate and ensure the safety of the people in the EMU. At the same time, the combination of intelligent algorithm and gear modification can improve the fatigue life of gear on the basis of accurate prediction, which is of great significance to the portability of EMU maintenance.

The paper analyzes the correlation features between stress strength, multiple failure mechanisms, and multiple components. It investigates the effects of different correlation features on reliability and proposes a method for structural reliability analysis that considers the joint effects of multiple correlation features. To portray the stress–strength correlation structure, the Copula function is utilized and the influence of the correlation degree parameter on reliability is clarified. The text describes the introduction of time-varying characteristics of structural strength and correlation parameters. A time-varying Copula is then constructed to calculate the structural reliability under the stress–strength correlation characteristics. Additionally, a time-varying hybrid Copula is constructed to characterize the intricate and correlation features of multiple failure mechanisms and components. The article proposes the variational adaptive sparrow search algorithm (VASSA) to obtain optimal parameters for the time-varying hybrid Copula. The effectiveness and accuracy of the proposed method are verified through actual cases. The results indicate that multiple correlation features significantly influence structural reliability. Incorporating multiple correlation features into the solution of structural reliability yields safer results that align with engineering practice.

Purpose: This paper aims to establish the relationship between crosswind speed and pantograph-catenary lateral deviation, as well as quantify the influence of crosswind speed and rod size uncertainty on pantograph-catenary contact reliability.Design/methodology/approach: The closed vector method is used to establish the pantograph-catenary kinematics formula. A new prediction model is proposed by using the bird swarm algorithm to optimize the grey model. The lateral deviation of the pantograph and catenary is predicted via the new model. Then the relationship between the effective length of the rod and operating mileage is inferred by combining the effective length theory with the Gamma process, as well as the pantograph-catenary contact reliability model is established according to reliability theory.Findings: The results obtained show the impacts of uncertainty design parameters of pantograph rods on pantograph-catenary contact reliability index, and the results at crosswind speed of 0 ms⁻¹ and 5 ms⁻¹ are 5.0630 and 4.1442, respectively. The reliability decreases with the increasing crosswind speed, and can be greater than the reliability calculated for rod size degradation due to long-term use.Originality/value: Most preceding works on pantograph-catenary contact reliability were based on principles of dynamics, without considering the pantograph-catenary relative motion. This research reveals the law of pantograph-catenary relative motion for uncertainty design parameters and crosswind, and quantifies the reliability from the angle of kinematics.

Compound faults present a considerable challenge in fault diagnosis for gear transmission systems, as existing studies predominantly focus on individual failure modes. To address this limitation, the present study proposes a novel dynamic response analysis model that simultaneously considers tooth profile wear and root crack faults. A numerical model for tooth profile wear is developed based on the Archard wear law, which allows for the calculation of wear progression over multiple operating cycles. The potential energy method is then employed to derive a time‐varying mesh stiffness model, capturing the interactive effects of tooth wear and root cracks on system stiffness and dynamic behavior. A six‐degree‐of‐freedom dynamic model of the gear transmission system is constructed using the lumped mass method, with time‐varying mesh stiffness as an input. The dynamic response is solved using the fourth‐order Runge–Kutta method to simulate the system under various levels of cracks and wear. Experimental validation confirms the model’s effectiveness in representing the complex dynamics of compound faults, demonstrating its superiority over traditional models that focus on single failure modes. This model provides an innovative theoretical framework and dynamic support for fault diagnosis in gear transmission systems subject to multiple failure modes.