Direct measurement of dynamic loads on engineering structures is challenging due to environmental constraints. Therefore，the indirect identification or reconstruction of dynamic loads，using dynamic response information，has emerged as a highly effective method. Over decades，dynamic load identification has evolved，resulting in a series of valid solutions. This paper begins by reviewing the research history and main achievements of dynamic load identification methods. It provides a systematic exposition of typical frequency domain and time domain methods，as well as dynamic load identification methods which are based on various approaches such as function fitting，regularization strategies，Bayesian frameworks，and data-driven techniques. The advantages and disadvantages ，as well as application scope of each method，are also discussed. Additionally，this paper summarizes common issues in the load identification process，including uncertainties in structural parameters and input conditions. Identifying the position of dynamic loads is also a crucial aspect of the dynamic load identification problem. This paper analyzes the methods currently available for position identification. This paper delves into the engineering applications of dynamic load identification methods and analyzes the limitations of current methods. Considering the current challenges in the field of dynamic load identification and the increasing demands in practical engineering applications，the paper anticipates the technical difficulties that need to be addressed. It also discusses potential future development directions and key areas in dynamic load identification.

Aircraft often operate in complex and variable dynamic load environment，and dynamic load localization is the primary problem that needs to be solved in this field. This paper focuses on the dynamic load localization requirements of common and prone to abnormal vibrations in aircraft structures. Combining deep neural network，a rapid dynamic load localization method for aircraft structures is developed. By using Long Short-Term Memory （LSTM） neural network，the inverse implicit function model which can accurately describe the corresponding relationship between the dynamic load location and vibration response of the structure is constructed. A dynamic load localization method based on the LSTM neural network classification model is proposed. A simplified finite element model of the entire aircraft structure is established to simulate several typical dynamic load conditions that the aircraft may encounter during actual flight. The noise resistance and robustness of the established deep neural network are also studied. The simulation results show that the proposed method can accurately identify the location of dynamic loads under various load conditions，and can still maintain high locating accuracy under the measurement noise level of 10 dB and the parameter perturbation of 2.8%.

Sparse regularization has been proven to be effective in addressing the ill-posed problem in moving force identification （MFI）. However，existing methods often neglect frequency characteristic disparities between static and dynamic components in moving loads，thereby limiting the identification accuracy. Therefore，an MFI method integrating response prior information and weighted dictionary is proposed. A linear relationship between vehicle-induced bridge responses and moving vehicle loads is established in bridge-vehicle system. Once frequency domain analysis is separately performed on bending moment and acceleration responses，the obtained frequency prior information is then employed to construct weighted dictionaries that correspond to both static and dynamic load components. Subsequently，the static and dynamic components of moving loads are individually solved by alternating direction method of multipliers （ADMM）. The effectiveness of proposed method is demonstrated through numerical simulations on a real bridge，and a series of MFI experiments are conducted in laboratory. Results show that the weighted dictionaries considering response prior information significantly improves the accuracy of force identification and enhance its robustness to noise.

The fatigue failure of the structure under vibration conditions has brought hidden dangers to its own service life and the personal safety of the user. At present，there are solutions for the structural vibration fatigue such as adding reinforcement bars and laying a large amount of damping materials，but the efficiency is often low and the additional mass is excessive. In order to solve the above problems，an additional acoustic black hole （ABH） is installed on the structure to reduce the stress amplitude and extend the service life by reducing the structural response. Using a cantilever plate as the reference structure，the steady state dynamics analysis is carried out by the finite element method. The results show that the stress response at the gap of cantilever plate is significantly reduced after the addition of rectangular acoustic black hole （RABH）. Through stress and fatigue experiments，it is verified that additional RABH can reduce the stress response at the dangerous point of the structure and extend the vibration fatigue life of cantilever plate structure.

A novel vibration method，the master-slave distributed vibration test method，was proposed. Aiming at its control requirements，an online waveform replication technique for vibration loads was developed and an integrative prototype system with measuring and controlling functions was constructed. Therein，a signal processing method of frame segmentation and reconstruction was proposed for solve the problem that time waveform replication for long-duration continuous vibration loads. A method for dynamic transfer function estimation based on sample database construction and weighted average was proposed to reduce the influence of nonlinear property on control precision. A spectrum correction method was introduced to improve the frequency domain control accuracy. A test with 1 master vibrator and 2 slave vibrators was performed using the developed online vibration load replication control technique，and the results show that the technique has a high replication precision in both time domain and frequency domain，has a subsecond overall delay time，and has a subpercent overall root-mean-square error. The technique can provide a key technique for supporting online distributed vibration tests.

The problem of load identification denotes identifying loads based on the measurement of structural responses，which is the inverse problem in structural dynamics. A load identification method based on time-delay neural network is proposed in this paper，and numerical examples based on simulation and experiments are provided to show that the method overperforms normal back-propagation neural network in accuracy of identification. Additionally，statistic pooling is introduced on the basis of the method，and it is proved that the method performs well in noisy environment compared with BP neural networks. based on the load identification methods mentioned above，a sensor placement optimization based on particle swarm optimization algorithm is proposed，and the optimal sensor placement is able to reduce the error of identification by 90% compared with the random sensor placements，meanwhile the minimum spacing of installation among sensors is also ensured during the optimization.

Jointed structures are widely used in engineering applications，and local nonlinear characteristics at the connection interface have an important influence on their dynamic modeling and characteristic prediction. Aiming at the problem that local connection parameters of nonlinear structural systems are unknown or difficult to measure，this paper proposes an identification method of local linear connection stiffness based on the FRF transformation from the perspective of inverse dynamic problems. By further combining with the time-domain nonlinear subspace identification method，the local linear and nonlinear connection stiffness of nonlinear structural systems can be finally obtained. The numerical example and experimental setup of the three degrees-of-freedom structural system are designed and further built to validate the proposed method. The results demonstrate that the proposed method can separate and identify the underlying linear FRF and nonlinear parameters of the nonlinear structural system，and subsequently realize the joint identification of the local linear and nonlinear connection stiffness.

The time-varying mesh stiffness is a core parameter of gear systems，and the mesh stiffness identification is of great significance for the dynamic analysis and condition monitoring of gear transmission systems. Since it is difficult to directly measure the mesh stiffness，it is necessary to develop a data-driven time-varying mesh stiffness identification method. To deal with this problem，an alternating state-parameter optimization method is proposed to identify the time-varying mesh stiffness of gear systems. The Fourier series with the fundamental frequency of the mesh frequency is constructed to characterize the mesh stiffness. Furthermore，a Reproducing Kernel Hilbert Space （RKHS）-based de-noise method is further proposed to estimate the system state and parameter. The system state and stiffness parameter are alternately optimized with the joint constrains of dynamic model and data to realize the time-varying mesh stiffness identification of gear transmission systems. The simulation and experimental studies validate the effectiveness of the new mesh stiffness identification method for gear systems.

The study of the influence of potential well parameters on the output of a nonlinear energy harvester system is conducive to the design of the high-performance energy harvester system. Meanwhile，the stochastic resonance phenomenon in the corresponding electromechanical coupling dynamics model of the energy harvester system can be used to enhance the characteristics of weak faults，so as to effectively identify weak faults. This paper proposes a decoupled saddle-point-degradation bistable potential function，and the electromechanical dynamic model is introduced. The bifurcation diagram under different excitation amplitudes is obtained to discuss the effect of the barrier width and the barrier height on the responses （periodic response and chaotic response）. According to the methods of the Poincaré map，the frequency spectrum analysis，and the Lyapunov exponent，the periodic response and the chaotic response are examined at a fixed excitation amplitude，which is consistent with that obtained from the bifurcation diagram. Based on the electromechanical dynamic model perturbed by the random noise，the stochastic-resonance-based method is proposed for fault diagnosis，which achieves the enhancement of the simulated and experimental bearing fault characteristics.

The dynamic method for identifying axial force is grounded in vibration theory，making the vibration equation of a bar member crucial for accurate axial force estimation. Traditionally，the Timoshenko beam is derived from the equilibrium of transverse forces and moments. In this paper，an energy-based approach is applied to derive a new vibration equation for the Timoshenko beam under axial loading. The Ressiner energy equation for a Timoshenko beam，incorporating displacement，stress and axial force，is established using a condensation hypothesis from an energy perspective. The motion equation and stress equilibrium are calculated using the extremum principle，leading to a new free vibration equation for the Timoshenko beam under axial force. Compared to classical textbooks，the proposed dynamics equation includes two additional terms related to axial forces and shear effects. The new equation is validated through numerical simulations and laboratory experiments to identify the axial force in bar members. The results demonstrate that the proposed equation significantly improves the accuracy of axial force identification，confirming its correctness and applicability.

Spinning cylindrical shells are critical components in practical engineering structures. The boundary conditions at the shell ends are diverse and significantly influence the vibration characteristics of the shell. To study these characteristics under various boundary conditions，a dynamic model of the spinning cylindrical shell is established using Lagrange equations and Novozhilov’s shell theory. The mathematical description of the boundary conditions for the cylindrical shell is combined with the discretized displacement functions，which are constructed based on a linear combination of Chebyshev polynomials. These functions satisfy the boundary conditions and are independent of the cylindrical shell's parameters. The vibration characteristics of stationary cylindrical shells are determined by solving the eigenvalue problems，revealing the influence of rotary inertia on the vibration characteristics. The applicability of different shell theories with respect to various geometrical parameters of the shell is discussed. Additionally，circumferential wave-dependent mode functions are identified and used to compute the natural frequencies of shell modes with the zero circumferential waves，as well as the travelling waves of the spinning cylindrical shell under different boundary conditions. The impact of structural parameters on the natural frequencies of the travelling waves is also analyzed.

Floating raft vibration isolation systems in the ships or submarines have the requirement of low weight and small volume. To reduce the weight of floating raft vibration isolation systems and improve its vibration suppression effect，nonlinear energy sink cell （NES cell） is applied to the structural optimization of the floating raft vibration isolation system. NES cells are placed on all the substructures of the floating raft system. The mechanical model of the floating raft system with four degrees of freedom and the vibration damping system with NES cell are established. The modal analysis of the floating raft system is carried out. The approximate analytical expression of steady-state response for nonlinear system is derived by Harmonic balance method （HBM） and verified by Runge-Kutta （RK）. The vibration suppression effect under the different total weight and NES cell number is compared by force transitivity response，and the influence of the NES cell number and total weight of the system for the 1st-order mode is analyzed. The results show that NES cell can effectively improve the vibration suppression efficiency of the floating raft system for all the modes while reducing the total weight of the system and realize the structural optimization of the floating raft system effectively.

This paper considers a quadrotor transportation system with a four-cable-suspended payload. The relative position between quadrotor and payload is introduced and used to derive the tension of cables and describe the transportation system. A cost function inspired by payload and time is built to equipoise rapid UAV positioning and payload swing elimination. Then，the pseudo-spectral method is applied to transform the optimal control problem into a nonlinear programming problem and solve the optimal trajectory. A quadrotor transportation system’s trajectory tracking is facilitated by a PID controller. The optimal trajectory is validated through the presentation of both simulation and experimental results at last.

A rate gyro adaptive weighting method is proposed for the problem that the serious coupling of elastic vibration signals and rigid-body signals in the feedback control loop of flexible launch vehicles will significantly reduce the stability of the attitude control system. The method can be applied to the cases where there are deviations in the shape slope and frequency of elastic vibration. The rate gyro observation signal is converted into a frequency domain expression，and the interpolated discrete Fourier transform method is used to identify the elastic frequency. An adaptive updating algorithm for the rate gyro weighting coefficient matrix is derived based on the frequency domain，which eliminates the elastic vibration signals of each order in a stepwise manner. A simulation calibration is carried out under different cases of deviation. Simulation results indicate that the rate gyro adaptive weighting method can realize significant suppression of elastic vibration signals in the rate gyro measurement signals and reduce the adverse effect of elastic vibration signals on the stability of the attitude control system from the source. Thus the performance of the launch vehicle attitude controller is improved and the difficulty in the controller design is reduced.

In order to solve the problem that it is difficult to fully consider the dynamic characteristics （amplitude-phase frequency characteristics） requirements in the PID parameter design of electromechanical servo system，a PID design method for dynamic characteristics is proposed. The 9-order Transfer Function （TF） model of electromechanical servo system is established based on dynamic equation. The relationship between Routh criterion and TF coefficient is used to supplement the stability constraint of the system and the compatibility constraint of TF coefficient to ensure the stability of the system and the compatibility of TF coefficient in the PID design process. On this basis，based on the idea of parameter identification，the rational fraction orthogonal polynomial method is used to identify the coefficients in the TF model，so that the PID parameters are quickly determined，which improving the design efficiency，and multiple groups of controller parameters that meet the original index can be identified by adjusting the index data. The simulation results show that the designed PID parameters not only meet the requirements of dynamic characteristics，but also take into account the compatibility of system stability and TF coefficient. The design results are in good agreement with the simulation experiments.

At present，the big aviation countries already have mature gust wind tunnel test technology，but which is relatively backward in China，especially the gust wind tunnel tests equipment and technology of full aircraft model are lack. In this paper，a gust generator，a five-degree-of-freedom suspension system and a full elastic aircraft model are developed，and the wind tunnel tests of the whole model are carried out. The test results show that the gust field is stable，and the deviation of the gust velocity between the two ends and the center of the wind tunnel is less than 25%. The support stiffness of the model suspension system is small and the stability is good，which can meet the requirements of the gust wind tunnel test. The simulation results of the non-uniform gust field are close to those of the wind tunnel test，and the error of the moment of the wing root is less than 15%，and the error of wing tip overload is less than 0.2g.

In order to suppress the nonlinear vibration during the motion of a flexible manipulator，a model-free hybrid control strategy of trajectory tracking and vibration suppression based on a novel online observation of disturb forces is proposed. The Lagrange equation and singular perturbation method are employed to model and decouple the dynamics of the manipulator，which are decomposed into a slow subsystem representing rigid motion and a fast subsystem representing flexible vibration. Considering the complexity of modeling and uncertainty of model parameters，PD control method is adopted to realize trajectory tracking，and model-free adaptive control algorithm is proposed to realize nonlinear vibration control of flexible links. To solve the control divergence problem caused by unknown external disturb forces，a modified extended state observer is proposed to online estimate and real-time compensate the disturb force，which can improve the convergence performance of model-free vibration control algorithm effectively. The simulation results show that the proposed method can effectively suppress the vibration of the flexible manipulator in the presence of disturb force，and has good dynamic performance and robustness.

This paper investigates the dynamics and control problems of the long-term deorbiting of an electrodynamic tethered satellite system. The dynamics modeling of the system is carried out based on a dumbbell model assumption. To improve the accuracy of the system model，the orbital dynamics is described using a set of modified equinoctial elements，involving the effects of Lorentz force，atmospheric drag and J₂ perturbation force. Three current control strategies are proposed to regulate the electrodynamic forces for achieving a stable long-term deorbiting process，namely，the constant current input，the directionally variable current input，and the optimal control strategies. In the design of the optimal control strategy，the long-term deorbiting problem is formulated as an inverse problem of dynamics with nonlinear constraints，which is further solved via a nonlinear programming method to obtain the optimal reference trajectories. The deorbiting of the system is then achieved using the modified current control input obtained from a tracking feedback control law. Additionally，an energy-based current switch control strategy is adopted to ensure the stability of system and the efficient utilization of Lorentz force. Case studies of the system with designed physical parameters are conducted to analyze the deorbiting efficiency and to validate the effectiveness of the proposed control strategies.