The determination of the number of active modes is always an obstacle to the identification of dynamic systems. To tackle this issue, a new blind modal estimation method is proposed through which the number of active modes does not need to be presupposed, even in underdetermined blind source separation cases. Firstly, the spatial time–frequency distribution matrices are constituted from the smoothed pseudo Wigner–Ville distribution of acceleration signals. The auto-source time–frequency points that contain modal information about only one mode are selected and then the density peaks clustering algorithm is introduced to identify the mode shape vectors. Finally, one can reconstruct the time–frequency distributions of modal coordinates and estimate the natural frequencies and damping ratios. The method is verified by a numerical study and a vibration experiment. The anti-noise study demonstrates that the method performs well.

A key issue in the control, health monitoring, and condition assessment of civil structures is the estimation of structural modal parameters based on measured structural responses. However, field measurements of structural responses from civil structures under strong wind or earthquake excitations usually exhibit non-stationary feature and therefore cannot be adequately deal with by traditional modal identification methods. In this study, a novel procedure is integrated for modal parameter identification of civil structures from non-stationary structural responses on the basis of the variational mode decomposition (VMD) technique. First, the VMD algorithm is applied to decompose measured vibration signals into individual mode components. Then, the random decrement technique (RDT) is employed to obtain free vibration response of each mono component. Next, normalized Hilbert transform (NHT) is used to estimate modal natural frequency and damping ratio. The performance of the developed approach is evaluated using simulated non-stationary responses of a frame structure, and the identified results are validated. The effects of crucial factors such as levels of noise involved in structural response and data length on the modal parameter estimations are examined through detailed parametric study. Furthermore, the approach is applied to modal identification based on field measured non-stationary responses of a high-rise building during Typhoon Nida. The case study illustrates that the integrated method is an efficient tool for estimating the modal parameters of civil structures from non-stationary structural responses.

The seismic response characteristics of a lead-rubber-bearing(LRB) base-isolated structure under rare and very rare earthquakes were investigated. The acceleration, ductility coefficient, and shear strain of the LRB increase significantly under very rare earthquakes in comparison to rare earthquakes; in particular, the shear strain of the LRB may exceed the ultimate shear strain and cause damage to the base-isolated structure. The criterion selected for the optimum tuned inerter damper (TID) of the TID–LRB hybrid control system is the minimization of the mean value of the maximum shear strain of the LRB. For each inertance mass ratio of the TID, there exists an optimum tuning frequency ratio and damping ratio of the TID to minimize the shear strain of the LRB, and the effectiveness is increased with a higher inertance mass ratio. By equipping the TID with appropriate parameters, the safety of the LRB during rare and very rare earthquakes can be ensured. Finally, the pounding response of the base-isolated structure collision with the moat wall under very rare earthquakes was analyzed. It was observed that under very rare earthquakes, the ductility coefficients of the superstructure by equipping with the suitable TID were improved, and the shear strain of the LRB was reduced. In addition, equipping the TID can reduce the required width of the isolation joint to avoid collision between the isolation layer and the moat wall, and with an increase in the inertance mass ratio, the required width of the isolation joint is smaller.

A two-stage damage identification method for beam structures based on support vector machine and swarm intelligence optimization algorithms is proposed. First, the frequencies and mode shapes of the beam structure are obtained using the smooth orthogonal decomposition method, and the normalized modal curvature is calculated as the input of a pre-trained support vector machine to determine the damage location. Then, the stiffness loss at the damaged location of the structure is calculated using swarm intelligence algorithms. The fitness function is the sum of the residual squares of the frequencies of the damaged structure identified by the smooth orthogonal decomposition method and the frequencies calculated for each iteration of the intelligent optimization algorithm. Numerical examples of a damaged simply supported beam structure are used to verify the damage identification performance of the two-stage method. The accuracy of the support vector machine model under different damage degrees and noise levels is studied using the Monte-Carlo method, and an uncertainty of the damage degree prediction value is studied by comparing the particle swarm optimization algorithm, moth-fire algorithm, and mayfly algorithm.

The smooth orthogonal decomposition (SOD) is an output-only modal analysis method, which has simple structure and gives good results for undamped or lightly damped vibration systems. In the present study, the SOD method is extended to incorporate various measurements that contain the displacement, the velocity, the acceleration, and even the jerk (derivation of the acceleration). Several generalized eigenvalue problems (EVPs) are put forward considering different measurement combinations, and it is proved that all these EVPs can reduce to the eigenvalue problems of the undamped vibration system. These different methods are called extended smooth orthogonal decomposition (ESOD) methods in this paper. For the damped vibration system, the frequencies obtained by different ESOD methods are different from each other. Thus, a cost function is defined and a search algorithm is proposed to find the optimal frequency and damping ratio that can explain these differences. Although the search algorithm is derived for the single-degree-of-freedom (SDOF) vibration systems, it is effective for the multi-degrees-of-freedom (MDOF) vibration system after assuming that the smooth orthogonal coordinates (SOCs) computed by the ESOD methods are approximate to the modal coordinate responses. In order to verify the ESOD methods and the search algorithm, simulations are carried out and the results indicate that all ESOD methods reach correct results for undamped vibration systems and the search algorithm can give accurate frequency and damping ratio for damped systems. In addition, the effects of measurement noises are considered and the results show that the proposed method has anti-noise property to some extent.

A novel damage identification method that utilizes the smooth orthogonal decomposition (SOD) combined with the improved beetle antennae search algorithm (BAS) presented by previous scholars is proposed. Firstly, the damage index which can track the curvature changing of mode shape identified by the SOD method is generated by an adaptive polynomial fit method. The locations of structure damages are determined according to the damage index. Thus, the number of possible damaged elements needed to be taken into account can be reduced when calculating the degree of damage. Then, the reduction in the stiffness at the damage location of the structure is calculated by the improved BAS in which the fitness function is constructed by calculated frequencies of the damaged structure in each iteration and the modal frequencies obtained by SOD. The BAS algorithm is improved through a fusion strategy of simulated annealing theory. Thus, the improved BAS algorithm is efficient and adaptive. The effect of this combined application in damage identification has been verified by numerical examples of a simply supported beam with single damage and a cantilever beam with double damage. The numerical results show that this combined algorithm exhibits high reliability in damage identification of beam‐like structures.