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.

Combined with the long-term observation data of three-dimensional ultrasonic anemometer at the deck of a long-span suspension bridge in the coastal area of Guangdong Province，the average wind characteristics of the wind field at the bridge site are statistically analyzed. Taking the wind speed exceeding 8 m/s as the standard of strong wind，the fluctuating wind characteristics of the bridge site are analyzed based on strong wind samples. The results show that the coastal areas of Guangdong are mainly affected by the southeast monsoon in spring and summer and the northwest strong wind in autumn and winter. The downwind turbulence intensity is obviously greater than the transverse wind and vertical turbulence intensity，and the ratio of each component is roughly I_u∶ I_v∶I_w=1∶0.86∶0.60. There is a significant positive correlation between gust factor and turbulence intensity，and the empirical formula recommended by Cao and Choi can better reflect the relationship between the two，and the empirical formula recommended by Cao is more suitable for coastal areas. Turbulence integral scale has a negative correlation with turbulence intensity. With the increase of turbulence intensity，turbulence integral scale first decreases rapidly and then tends to be stable. Based on the measured data，the empirical formula of turbulence integral scale and turbulence intensity is given，and the correlation between the two is significant. In the measured data，the downwind power spectral density is in good agreement with Kaimal spectrum，the transverse wind power spectral density is in good agreement with Von Karman spectrum，and the vertical power spectral density is in good agreement with Panofsky spectrum at high frequency band.

Existing bridges undergo time-varying load effects and resistance degradation during service. The complex loads and diverse failure modes make the existing bridges face greater risks in service. Therefore，it is urgent to make time-dependent reliability assessment for the service bridges. The classical time-varying reliability analysis method is more complex and difficult as the number of random variables increases. In this paper，probability density evolution theory is introduced to solve the above problem，which is more advantageous for solving the reliability of complex structures with multiple random variables. The dynamic reliability of the existing bridge in serviceability limit state and ultimate limit state is analyzed by considering the bridge resistance degradation and load effect increase，as well as the time-varying factors such as shrinkage and creep effect of concrete bridges. The accuracy and computational efficiency for this method are compared with the Monte Carlo method，and the effectiveness of the proposed method is verified.

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.

Based on the basic principle of variational method and limit equilibrium method，the stability of soil slope under earthquake action is analyzed accurately. Combining the limit equilibrium method of slope stability analysis and the pseudo-static method，the auxiliary functional under constraint conditions is constructed by introducing Lagrange multiplier into the equilibrium equation of sliding soil. The first order ordinary differential equations with the basic unknowns of potential sliding surface，normal stress of sliding surface，force of sliding body，safety factor and Lagrange multiplier are obtained by using Euler equation. The coupled nonlinear differential equations are solved numerically by using the shooting method，and an accurate solution for slope stability analysis under seismic action is obtained. The effectiveness of the model and method is verified by numerical examples.

Based on the Biot’s poroelastic model and the Euler-Bernoulli beam equations，the dynamic response of extended helical pile foundations with multiple helixes is studied. The equivalent stiffness model is used to simulate the helixes on the helical pile. With the utilization of the integral transform，the variable separation methods，and the impedance matrix transfer method，the analytical solution to the dynamic response of helical piles with multiple helixes is derived. Through the comparisons with the simplified analytical solutions and the experimental results，the correctness of the proposed model is justified. Finally，with the presentation of a comprehensive parametric study，some dominant impact factors on the dynamic responses are revealed，and the optimal design scheme is suggested accordingly. The main conclusion of this study can be concluded as：An increase of the extension ratio of helix will increase the complex impedance and resonance frequency at the pile top of the helical pile. An increase of the ratio of helix spacing to width will increase the complex impedance of the pile top，but the effect on the resonance frequency is not significant. An increase of the vertical static load at the top of the pile will significantly reduce the complex impedance and resonance frequency at the pile top. The helix inclination has an optimal range in the effect of complex impedance of the pile top.

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.

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.

The parameters design and vibration control of the system of Spar-floating offshore wind turbine （S-FOWT） coupled tuned mass damper-inerter （TMDI） under the joint wind-wave loads are studied in this paper. The theoretical model of 15-DOF Spar-FOWT with high fidelity is established based on multi-body dynamics modeling method and compared with FAST from both cases of damped free vibration and forced vibration. The damping efficiency of the FOWT-TMDI system under wind and wave loads is analyzed. In order to obtain the global optimal system parameters，the surrogate model method is used to optimize the time-varying and fully-coupled system. An example analysis shows that the model of 15-DOF Spar-FOWT has high fidelity which accurately secures the global dynamical characteristics of the wind turbine system. Meanwhile，the TMDI optimized by the proposed method has the expected control effect and the desired objective of “reduction in mass and stroke” is achieved. Compared with TMD，in addition，the TMDI has anticipative efficiency of the vibration reduction while reducing 75% of the mass and reducing about 80% of the damper stroke.

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.