Yanbin Li

This paper addresses the challenge of extracting weak early fault signals from rolling bearings under variable speed conditions, where strong background noise often obscures diagnostic features. We propose a novel fault diagnosis method that integrates variational mode decomposition (VMD) and maximum second-order cyclo-stationarity blind deconvolution (CYCBD). The proposed approach begins by converting non-stationary vibration signals into angular-domain stationary signals using computed order tracking (COT). Subsequently, the parameters of the VMD algorithm are optimized via the sine–cosine and Cauchy mutation sparrow search algorithm (SCSSA) to select the optimal modal components. A key contribution is the introduction of a composite index (CI), combining harmonic significance and the envelope spectrum crest factor, which serves as the fitness function for the SCSSA to optimize the critical parameters of CYCBD for enhanced feature enhancement. Finally, fault characteristics are extracted by analyzing the deconvolved signal with an order envelope spectrum. Both simulation and experimental results demonstrate the superior capability of the proposed VMD-CYCBD method in effectively identifying weak fault features submerged in strong noise under variable speed conditions.

To address the issue of low accuracy in the dynamic modal decomposition (DMD) method used for operational modal analysis (OMA) under noise conditions of aerospace structures, an enhanced identification approach is proposed in this paper, which integrates subspace orthogonal projection with DMD to better determine the modal properties of linear mechanical systems with noisy observations. Subspace orthogonal projection applied to the Hankelized matrix is utilized for denoising observation signals. Compact singular value decomposition (SVD) is employed on the projection matrix in order to acquire the optimal realization of system matrix. Subsequently, DMD is introduced to reduce the dimensionality of the system matrix and extract the dominant modal features. The effectiveness and practicality of the proposed method are confirmed through numerical and experimental examples. The proposed method demonstrates marginally improved identification accuracy in modal frequency and enhanced performance in damping ratios when compared to representative OMA methods under different white noise conditions.

The geometric nonlinearity due to static and thermal load can significantly alter the vibration response of structures. This study presents a semi-analytical approach to illustrate the nonlinear vibration of clamped-clamped beams under static and thermal loads. The von Karman strain and Hamilton’s principle are employed to derive the nonlinear static equilibrium equation and nonlinear governing equation. The vibration equation’s coefficient is variable. The transfer-matrix method and local homogenization are used to solve the equation. The proposed method’s accuracy is validated by commercial software and literature. The numerical results indicate that uniform stress caused by thermal load only reduces the structural mode frequencies. The geometric nonlinearity of the structural static deformation affects both the mode frequencies and mode shapes. And the mode shapes cannot be approximated by harmonic functions. When the static deformation is significant, the structure’s local RMS response is substantially affected. The combined loads have a more significant impact on the acceleration response than the superposition of individual load effects.

A collision with clearance causes obvious nonlinearity in structures, and dynamic response analysis plays an important role in predicting the mechanical performance of the structure. The general form of the nonlinear dynamic equation of a structure and the clearance modeling method are introduced, and the clearance-caused nonlinear term is expressed by nonlinear impact forces. Different clearance collision models of local nonlinear structures are presented. The relationships between different impact forces and clearances are analyzed by two rigid sphere models. The solution methods of the nonlinear dynamic equation are compared by a vibro-impact response, such as the Newmark-β method combined with the Newton–Raphson method, generalized α method and precise integration method. The single degree of freedom model is adopted to compare the efficiency of the different numerical integration algorithms. Taking the beam structure model as a case study, the accurate nonlinear collision model with clearance is established by using the impact force model with high accuracy, and the accuracy of the model is verified by comparing the reference model with the numerical model.

Out-of-plane compression experiments with the strain rate from 0.0001/s to 1000/s are performed on a three-dimensional (3D) fine weave-pierced Carbon/Carbon (C/C) composite using a universal testing machine, a high-speed testing machine, and a split Hopkinson pressure bar (SHPB). The compressive failure mechanism of the composite is analyzed by a multi-scale analysis method, which ranges from micro-scale defect propagation, through meso-scale microstructure failure, to macro-scale material failure. In order to predict the out-of-plane compressive properties of 3D fine weave-pierced C/C composite at different strain rates, a strain-rate-dependent compressive constitutive model is proposed. The results show that the out-of-plane compressive behavior of the 3D fine weave-pierced C/C composite is sensitive to strain rate. With increasing the strain rate, the initial compressive modulus, the maximum stress, and the strain at the maximum stress increase. The difference in mechanical behavior between quasi-static and high strain rate compression is owing to the strain rate effect on the defect propagation of the 3D fine weave-pierced C/C composite. The proposed constitutive model matches well with the experimental data.

An innovative yield criterion based on von Mises stress is proposed to represent the strain rate-dependent behavior under dynamic load. Considering the strain rate in the constitutive model, the distortional strain energy density is derived and the yield criterion is established. A plot of yield strength for a range of strain rate reveals that despite the differences in material properties and test methods, the yield strength rise can be represented by a unified criterion. The overall yield behavior of the material under dynamic load can be explained by introducing the strain rate into the constitutive model and threshold distortional strain energy density. This criterion is in a simple form that may be widely applied.

The transient response analysis is important for the design and evaluation of uncertain engineering systems under impact excitations. In this paper, statistical energy analysis (SEA) is developed to evaluate the high-frequency transient energy response of two-subsystem models considering interval uncertainties. Affine arithmetic (AA) and a subinterval technique are introduced into SEA to improve the computational accuracy. Numerical simulations on a coupled-plate and a plate-cavity system considering interval uncertainties are performed. The analysis precision of the proposed approach is validated by Monte Carlo (MC) method. The results show that the analysis precision of the proposed method decreases with the increasing uncertainty level of parameters. The computational accuracy of the proposed method can be significantly improved by employing AA and subinterval technique.

A stochastic dynamic load identification algorithm is proposed for an uncertain dynamic system with correlated random system parameters. The stochastic Green's function is adopted to establish the relationship between the Gaussian excitation and the response. The Green's function is approximated by the second-order perturbation method, and orthogonal polynomial chaos bases are adopted to replace the corresponding bases in the Tayler series. The stochastic system responses and the stochastic forces are then represented by the polynomial chaos expansion (PCE) and the Karhunen–Loève expansion (KLE), respectively. A unified probabilistic framework for the stochastic dynamic problem is formulated based on the PCE. The stochastic load identification problem of an uncertain dynamic system is then transformed into a stochastic load identification problem of an equivalent deterministic system with the orthogonality of the PCE. Numerical simulations and experimental studies with a cantilever beam under a concentrate stochastic force are conducted to estimate the statistical characteristics of the stochastic load from the stochastic structural response samples. Results show that the proposed method has good accuracy in the identification of force's statistics when the level of uncertainty in the system parameters is not small. Large errors in the identified statistics may occur when the correlation in the random system parameters is neglected. Different correlation lengths for the random system parameters are investigated to show the effectiveness and accuracy of the proposed method.