When the gear system starts or stops in non-stationary working conditions, a sharp change of the speed can cause it to exhibit complex vibration characteristics which has a significant impact on the performance and lifespan of the gear. Considering the influence of time-varying meshing stiffness, backlash and gear meshing error, a dynamics model of spur gear system was established. The influence of external load and angular acceleration on the vibration characteristics of the start-stop process was studied. At the same time, the time-frequency analysis of the non-stationary vibration signal of the gear system was carried out by using the short-time Fourier transform. The results show that increasing the load and angular acceleration during the start and stop processes will exacerbate the degree of vibration and impact of the gear pair, and both will make the unstable motion process in the early start period end earlier, and the unstable motion process in the late stop period appear later, but the impact components in the late start period (the early stop period) will increase (decrease). In the frequency domain, increasing the external load will enhance the energy of the harmonic component of the gear system’s meshing frequency, but it has no effect on the fundamental energy of the meshing frequency. However, increasing the angular acceleration will enhance the energy of both the fundamental and harmonic components of the meshing frequency.

Gear’s Circular plot is a result presentation method which needs to be combine with time synchronous averaging (TSA), which can clearly display gear meshing vibration waveform extracted by TSA. Aiming at the problem of parameter setting of gear’s Circular plot and lack of the quantitative index, F_i index for waveform edge recognition and Y_i index based on Hu-moments were proposed. Firstly, TSA algorithm was used to extract the gear meshing vibration signal, and the upper and lower edges of the vibration signal waveform were determined by calculating the minimum F_i index. Secondly,Circular plot of gears were drawn by the upper and lower edge parameters. Then, the Circular plot of the gear was divided into four parts, and Y_i index of the Circular plot was obtained by calculating Hu-moments of the picture after segmentation. Finally,based on the Y_i and F_i indices extracted from the gear Circular plot, a K-nearest neighbors (KNN) classifier was utilized to classify the gear vibration signals. The results show that there is a significant difference between the Y_i and F_i indices of the vibration signals of normal gears and those of abnormal gears. By combining with the KNN classifier，it is possible to distinguish between normal and abnormal gear signals，which proves the effectiveness of this method.

To overcome the difficulty in early fault diagnosis with weak fault characteristics of rolling bearings that are easily drowned out by noise in the complex operation environment, an early fault diagnosis method was proposed by integrating the improved artificial gorilla troops optimizer (IGTO) algorithm, the optimized resonance-based sparse signal decomposition (RSSD), multi-parameter and sparse maximum harmonics-to-noise-ratio deconvolution (SMHD) method. Firstly, taking the squared envelope spectrum correlated kurtosis (SE-SCK) negative value of the low resonance component as the objective function, IGTO was used to simultaneously optimize the quality factor Q, weight coefficient λ and Lagrange multiplier μ of RSSD, for the achievement of the optimal matching of wavelet basis function and dissipation function. Secondly, the obtained optimal low resonance component was inputed into SMHD for filtering processing. Finally, the fault features were extracted by the perform envelope spectrum analysis. The algorithm comparison experiments show that the proposed IGTO algorithm has significantly improved optimization performance. The results of simulation and XJTU-SY bearing full life cycle fault signal test show that the proposed method is more useful in extracting early weak fault characteristics of bearings.

During the gear meshing process, the driving speed plays a crucial role in evaluating mesh stiffness, a factor that many scholars often overlook along with the accompanying centrifugal effects. Based on Euler beam theory,a original computational algorithm was proposed to calculate the dynamic mesh stiffness of spur gears considering driven-speed effects by introducing centrifugal effects into the velocity field. Using the driving speed as a control parameter, the dynamic mesh stiffness in relation to driving speed was investigated, and the nonlinear relation between centrifugal effects and dynamic mesh stiffness was demonstrated. The results indicate that, under the influence of a centrifugal field, both the natural frequency and the dynamic mesh stiffness of the gears increase with rising driving speed. Additionally, materials with a high elastic modulus tend to suppress the impact of driving speed on dynamic mesh stiffness, while higher density has the opposite effect. The research results provide reference for further analysis of gear vibration and noise under centrifugal effects.

In response to the problem of the gearbox fault diagnosis and analysis based on multi-sensor data under dataset imbalanced conditions, a gearbox fault diagnosis method based on a kurtosis index data fusion and a generative adversarial neural networks (GAN) was proposed. This method weighted the fusion of multiple sensor data based on signal kurtosis,highlighting the fault sensitive components of the gearbox in the fused signal. Then, a wavelet packet transform was used to extract the energy coefficients of each frequency band of the signal as signal features. Finally, the classification and recognition of signal features were implemented based on a back propagation (BP) neural network. Due to the fact that in actual working conditions, fault signals were more difficult to obtain than normal signals, GAN was used to expand the fault data section of the dataset, and the expanded dataset was used to train BP neural network. Through test analysis, it is shown that the fault accuracy of the described method is as high as 98%, which verifies the correctness of the proposed method and provides new ideas and methods for multi-sensor data fusion and fault diagnosis problems.

In response to challenges such as large sampling data, extended diagnosis time, and subjective fault feature selection in traditional bearing fault diagnosis, based on compressed sensing (CS) and deep multi-kernel extreme learning machine (D-MKELM) theory, a CS-DMKELM intelligent diagnosis model for rolling bearings was proposed. Firstly, sparse signals were obtained through threshold processing of transformed domain signals. A Gaussian random matrix was employed as the measurement matrix to compress the processed data. Secongly, the compressed data was used as the input signal for the D-MKELM. Particle swarm optimization (PSO) algorithm was applied to optimize critical parameters, enabling intelligent fault diagnosis. Results demonstrate that the proposed method, using only a small amount of bearing diagnostic data,automatically extracts feature information of bearings from a limited number of measurement signals through the D-MKELM.The proposed method enables rapid fault diagnosis of bearings. With a diagnostic time of 0.55 s, a final recognition accuracy of 99.29% was achieved. The proposed method reduces the diagnostic time and exhibits the high diagnostic accuracy,providing a new approach for handling massive bearing data in the fault diagnosis.

In order to solve the problem of difficult to accurately extract early faults of solar wheels under the strong noise background, an improved grey wolf algorithm (newGWO) was proposed to optimize and improve the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and the maximum correlated kurtosis deconvolution (MCKD) for early fault feature extraction of solar wheels.NewGWO was used to optimize the selection of parameters of the white noise amplitude weight and noise addition times that affected the decomposition effect.The fault vibration signal was decomposed by newGWO-ICEEMDAN, and the minimum envelope entropy was selected as the fitness function to obtain several related modal components.Then, the envelope spectrum peak factor was selected as the best modal component index. MCKD signals optimized by newGWO were enhanced for the selected optimal intrinsic mode function（IMF）components. Finally, an envelope demodulation analysis was performed on the obtained signals to extract the solar wheel fault characteristic frequency and multiple frequency components. Simulation signals and experiments show that this method can make the early fault impact characteristics more obvious, and realize the early fault characteristic frequency extraction of solar wheels.

Aiming at the problem of structural vibration modeling and characteristic analysis of rectangular sheets under arbitrary boundary conditions, an improved Fourier series method was proposed.Based on the Rayleigh-Ritz method, the allowable function of vibration displacement of thin plates was expressed as a linear combination of double Fourier cosine series function and auxiliary series function, which effectively avoided the possible discontinuities or singularities of the traditional Fourier series at the boundary. Firstly, the variational equation of the sheet vibration model was established by using the Hamilton energy variational principle, and the energy expressions in the equation were calculated and the displacement tolerance function was brought in. Secondly, the variational solution of the unknown Fourier coefficient was carried out to obtain the matrix equation of the model. The matrix equation was solved by numerical calculation method to obtain the free vibration frequency and eigenvector of the thin plate. Finally, the classical boundary conditions and elastic boundary conditions were used as examples to calculate and analyze. The calculation efficiency and accuracy of the proposed method were verified by comparison with the results of finite element simulation and existing literature. Additionally, the influence of the aspect ratio and constrained the spring stiffness coefficient on the vibration characteristics of the thin plate was discussed.

To address the problem that it is difficult to label variable working condition gearbox fault samples and the significant data distribution discrepancies in practical engineering, which result in reduced accuracy of fault diagnosis models,a semi-supervised gearbox fault diagnosis method based on masked contrastive learning is proposed. Firstly, a random mask was used to hide part of the information in the unlabeled dataset, generating two different masked instances for each unlabeled sample. Secondly, a dynamic convolutional neural network was employed to dynamically weight and aggregate the masked instances, enabling discriminative feature modeling of different masked instances. Then, a contrastive learning framework was constructed with the optimization goal of maximizing the similarity between features of different masked instances. By enhancing the consistency of feature representations of masked instance pairs, the model's dependency on labels was reduced. Finally, during the fine-tuning phase, a domain-conditioned feature correction strategy was introduced to generate target domain feature corrections. By aligning source domain features and target domain corrected features according to the metric of minimizing domain feature distribution discrepancies, the method explicitly reduces the domain distribution differences caused by varying working conditions. Validation on a variable working condition gearbox fault dataset demonstrates the effectiveness of the proposed method.

Based on Reddy’s layerwise theory (RLWT) and O(1) homogenization method, a three-scale layerwise multiscale analysis method (LMAM) for composite honeycomb sandwich structures was established. The macroscopic model of composite laminates was discretized by RLWT, and the microscopic unit cell model composed of fibers and matrix was established by three-dimensional finite element method. In the numerical example, the numerical simulation of the cubic block with inclusions was carried out, and the simulation results were compared with those of the direct numerical simulation (DNS)method, which verified the correctness of the LMAM. LMAM is also used to calculate and analyze the macroscopic,mesoscopic and microscopic stress distribution of composite honeycomb sandwich structures.