To solve the problem that the early weak fault diagnosis effect based on feature mode decomposition （FMD） is susceptible to the filter length L，frequency band segment K and mode decomposition number n，a diagnostic method is proposed in which a genetic algorithm is used to optimize the preset parameters of FMD，and the kurtosis，envelope entropy and modified adaptive envelope spectrum characteristic energy ratio as the comprehensive objective function. The method uses genetic algorithm to compare the comprehensive objective function values of each component signal decomposed by FMD under different preset parameters，and selects L，K and n corresponding to the maximum value as the preset parameters of FMD. The bearing fault type is determined by the envelope spectrum characteristics of the signal processed by FMD. The open bearing fault data of Western Reserve University and University of Cincinnati show that this method has good anti-noise ability and effective early fault diagnosis ability.

In order to study the suppression mechanism of vortex-induced vibration （VIV） by adding aerodynamic countermeasures such as guide vanes near maintenance rails and spoilers on handrails，the displacement and pressure measurement on a large-scale sectional model was conducted in wind tunnel tests. Based on the spatial-temporal distribution and statistical characteristics of surface pressure，an aerodynamic wave hypothesis is proposed and further verified using the spectral proper orthogonal decomposition （SPOD） method. Moreover，the complex spatial-temporal pressure field is quantified and deconstructed with the spatial-temporal energy spectrum of the aerodynamic force，revealing the mechanism of vertical VIVs as well as its suppression by aerodynamic countermeasures in a streamlined box girder. The results reveal that there are three lock-in ranges of vertical VIVs for the original girder while the largest VIV response appears in the 3rd order lock-in range. The addition of guide vanes near maintenance rails reduces the maximum amplitude of model displacement by 53.1% whereas the installation of spoilers on handrails eliminates VIVs. The complicated pressure field on the girders surface can be expressed as a linear superposition of aerodynamic forces related to multiple spatial-temporal distribution modes induced by different excitation sources. The pressure on the original girder is dominated by the 1st order SPOD mode where the component at the fundamental frequency of bridge girder is the main ingredient. Meanwhile，the spatial-temporal distribution mode of aerodynamic force on the upper surface contribute more to the VIVs. The predominant aerodynamic forces mode distributing harmonic on the upper surface travels downstream，with the contribution value presenting a wave-like distribution，collectively referring to as the “aerodynamic wave effect”. The aerodynamic wave intensity acting on the upper surface is much greater than that of the lower surface. The propagation of the aerodynamic wave could be characterized by the monotonously decreasing phase lag between the distributed aerodynamic forces and the vortex-excited forces （VEFs）. The wavelength of the aerodynamic wave on the original girder is approximately consistent with the wavelength of the contribution value，which corresponds to the distance between the windward and leeward crash barriers. With the addition of guide vanes near maintenance rails，the predominant mode of aerodynamic wave on the upper surface is similar with that on the original girder while the wave intensity decreases，resulting in a reduction of VIV response. The spatial-temporal energy spectrum of aerodynamic force on the upper surface turns into a broadband distribution after the installation of spoilers on handrails，and the frequency lock-in phenomenon disappeared. Thus，VIVs were eliminated. This study provides a new perspective for the analysis of pressure field on girder surface and constructing mathematical models of the vortex-excited force on bridge girders，which could deeply reveal the mechanism of VIV.

Environmental vibration energy is a kind of renewable and clean energy with abundant reserves and wide distribution. Through energy harvesting technology，the mechanical energy in the environment is converted into electrical energy to power low-power electronic devices and wireless sensor networks，which is an effective solution to break the limitations of traditional power supply methods. In this paper，the bursting oscillation and energy capture efficiency of a mechanical nonlinear multistable piezoelectric cantilever beam device are studied under low frequency excitation. By analyzing the potential energy of the system，it can be seen that the system has multi-stable characteristics with the change of system parameters. According to the fast and slow dynamic analysis method，the external excitation term is regarded as a slow variable and control parameter to adjust the dynamic behavior of the fast subsystem，and the time history diagram，phase diagram and transition phase diagram of the system are obtained. The motion state and energy capture performance of the system under low frequency excitation are analyzed by numerical method. The results show that the system exists bursting oscillation under low frequency excitation，and the system has good energy capture characteristics when the system is bistable. In addition，the time-delay feedback control can control the clustering phenomenon and ensure the stable operation of the system.

The principle of the hydraulic drifter is introduced，and the process of drilling into rocks by the drifter is established as a physical model of rock with three-degree-of-freedom dry friction. The concept of rate of penetration （ROP） is introduced. The stick and non-stick modes are studied，explaining the differences between these two types of motion. The periodic trajectories of the nonlinear piecewise smooth dynamical system mathematical model are segmented. By using the pseudo-arclength continuation method and Floquet theory，the angular frequency and amplitude of the hydraulic force are taken as control parameters to obtain stable periodic trajectories and the point of maximum ROP. Bifurcations such as period-doubling bifurcation，saddle-node bifurcation，and torus bifurcation are discovered. The data acquisition system for drilling rocks with a hydraulic drifter is introduced，and the displacement and velocity of the piston obtained from the model and experiments are compared. The results indicate that to make the drifter work on the period-1 trajectory，the range of angular frequency should be ω<6.814，and the range of amplitude should be 0.03<a<3.051. There is a strong correlation between the experiments and the model，and compared with the experiment，the piston in the model undergoes deceleration before colliding with the drill tool，adding an impact deceleration stroke.

According to certain selection criteria，this paper selects 8 mainshock-aftershock events and 560 mainshock-aftershock sequences from NGA-West2 ground motion database，uses ASK14 ground motion prediction equation to carry out residual analysis on the mainshock-aftershock sequences，obtains the intra event residual of mainshock-aftershock sequences at each station，and standardizes them. According to the geostatistical semivariogram method，the exponential semivariogram model and the manual fitting method are used to calculate the spatial autocorrelation of the spectral acceleration period of the mainshock-aftershock sequence. Since the Pearson linear correlation coefficient can better measure the linear relationship between the fixed-distance variables，the Pearson linear correlation coefficient is used to calculate the cross-correlation of the normalized intra-event residuals between different spectral acceleration periods of the mainshock-aftershock sequence without considering the spatial cross-correlation. According to Markov’s hypothesis，the spatial information is introduced into the calculation of the cross-correlation，and then the expression of the change of the spatial cross-correlation with the spatial distance （h） is obtained. The results show that the mainshock is significantly different from aftershocks in terms of spatial autocorrelation and cross-correlation characteristics，and aftershocks generally have higher spatial correlation in the long-period stage. Neglecting the spatial correlation between the mainshock and aftershocks or using the characteristics of the mainshock to replace the characteristics of the aftershocks will adversely affect the research on earthquake hazard analysis，damage assessment，and the synthesis of main and aftershock sequences.

To investigate the effect of waviness on the slippage and vibration characteristics of the full ceramic bearing，displacement excitation and thermal deformation are coupled to propose the dynamic waviness model. The Hertz contact theory and time-varying displacement excitation are combined to obtain the calculation method of time-varying contact stiffness coefficient，and the stiffness coefficient is analyzed in detail. The effects of time-varying contact stiffness coefficient and time-varying displacement excitation are also taken into account to model the slipping dynamic of the full ceramic bearing. The effects of rotational speed and waviness on the slippage and nonlinear vibration characteristics of the full ceramic bearing are analyzed. The results show that an increase in rotational speed，waviness amplitude and wave number all lead to an enlarged contact stiffness coefficient between the ball and the raceway. The contact stiffness coefficient is more sensitive to changes in wave number. The increase in rotational speed can exacerbate slippage. Both the increase in waviness amplitude and wave number can have the effect of inhibiting slippage. However，the waviness amplitude and wave number can be too large resulting in abnormal vibration of the inner ring. The maximum fundamental frequency deviation between simulation and test is 2.75 Hz，the maximum error is 0.37%. This research can be used for the optimal design of the full ceramic bearing structures as well as for health monitoring.

The Bagley-Torvik（B-T） equation is a differential equation of motion with fractional （3/2）-order derivative terms that is applied to describe the motion of a rigid plate in Newtonian，viscous fluid. In this paper，we develop non-stationary analytic solutions of the B-T equation whose inhomogeneous term is a stochastic process. The B-T equation is transformed into a half-order state-space equation in matrix form and eigen-analysis is performed to obtain complex eigenvalues and eigenvectors. Subsequently，the generalized coordinate transformation is introduced to decouple the equation into a system of independent 1/2-order differential equations which are solved by Laplace transform to obtain the solution in generalized coordinates； The generalized coordinate solution is converted into a natural coordinate solution to obtain the impulse or step response function. When the inhomogeneous term of the equation is a stochastic process，the Laplace transform can be used to derive the time-varying frequency response function from which the analytical solution of the non-stationary stochastic response can be obtained by relying on the relationship between the excitation and the response power spectral density. The correctness of the method is verified by numerical cases using the Spanos-Solomos fully non-statoionary stochastic excitation as an example.

Reconstructing the sound field environment inside the aircraft cabin during actual flight in a laboratory environment can provide a means for analyzing the acoustic environment inside the aircraft cabin，subjective evaluation，and noise reduction design. Based on the principle of sound pressure matching，this paper adopts a regularization method based on the L-curve method to solve the problem of inverse transformation of ill conditioned matrices. The effectiveness of the method in solving ill conditioned problems and improving reconstruction accuracy is demonstrated through simulation examples. Independently designed and built an aircraft cabin sound field reconstruction system. Conduct flight tests on transport aircraft，measure the noise at the pilot’s ear position under typical flight conditions，and use it as the target sound field. By using the sound pressure matching method，the full flight profile sound field reconstruction was achieved through the aircraft cabin sound field reconstruction system. Through sound field reconstruction experiments and subjective evaluation experiments，it shows that the reconstruction error in each frequency band of the one-third octave band is within 3 dB （A），and the subjective auditory fidelity and restoration are relatively high，providing support for subsequent analysis and subjective evaluation of the aircraft cabin acoustic environment.

The riser bundle system is an important equipment to explore oil and gas in ocean engineering. Under ocean flows，upstream and downstream risers in tandem will experience vortex-induced vibrations and wake-induced vibrations，respectively，which seriously threatens the structural fatigue life. To predict the vibration responses of a downstream flexible riser，this paper develops a semi-empirical frequency-domain prediction method for wake-induced vibrations based on the classical vortex-induced vibration prediction method of a single flexible riser. Considering the wake shielding effect on the downstream riser due to the existence of the upstream riser，the reductive wake velocity becomes the flow velocity to excite the vibrations of the downstream riser. Then，the upstream-to-downstream diameter ratio is utilized to determine whether the frequency capture occurs. The added mass coefficient of the downstream riser will be adjusted when the frequency capture occurs，otherwise it is 1 constantly. Subsequently，the prediction is based on the resonance condition. The excitation coefficients from a series of forced oscillation tests of a rigid cylinder are approximate to be the wake-induced force coefficients. According to the balance between the modal structural damping force and the modal hydrodynamic force amplitudes，the modal amplitude can be non-iteratively solved. Afterwards，the wake-induced vibration displacements can be calculated based on the mode superposition method. By comparing prediction results with the experimental results，the proposed method can basically correctly predict the dominant frequency，displacement，strain and fatigue damage of the wake-induced vibration for the downstream flexible riser. Therefore，the present method is conducive to the multiple-riser system design in practical engineering.

During real-time hybrid simulation（RTHS） of nonlinear specimens，the interaction between the specimen and the loading system can lead to variations in the specimen’s behavior，consequently affecting the time delay in the servo system. Online estimation of the system’s time delay enables the application of an adaptive time-delay compensation method for controlling time-varying systems. Nevertheless，during the initial stages of parameter identification，the estimated values frequently exhibit notable fluctuations，which can have a detrimental impact on the effectiveness of control. To this end，a two-stage adaptive time-delay compensation method driven by the inverse model for RTHS is proposed. Firstly，the inverse model controller of the system is used to perform coarse compensation to eliminate the test error caused by the main time delay. Then，the adaptive delay compensation method based on recursive least squares is used to compensate the remaining delay to further control the accuracy. By using the two-story shear frame as the prototype and the self-centering viscous dampers as the specimens，a time-delay compensation RTHS is carried out simultaneously on the two experimental substructures. Numerical simulations and experimental results show that the control accuracy of the proposed method is higher than that of the single-stage time-delay compensation method，and it can be applied to RTHS involving multiple experimental substructures.