Under the action of strong seismic excitations,structures exhibit time-varying dynamic characteristics due to damage. Variational mode decomposition (VMD) can be used to analyze the instantaneous frequency variation of structural seismic responses and reveal the damage condition of structures during earthquake. When VMD is adopted for decomposing the non-stationary responses,there exists the problem of mode aliasing due to the artificially presetting the number of decomposed modes K and the quadratic penalty factor α. Aiming at solving this problem,an improved variational mode decomposition (IVMD) algorithm is proposed in this study,which,combined with Hilbert transform (HT),can more accurately identify the instantaneous frequencies of time-varying structures under non-stationary seismic excitations. The multiple signal classification (MUSIC) algorithm is used to determine the number of decomposition modes K. The comprehensive objective function is constructed based on the overall orthogonal coefficient and energy ratio coefficient,and the slap swarm algorithm (SSA) is used to optimize and determine the optimal quadratic penalty factor α. Based on the optimized parameters K and α,IVMD-HT is used to identify the instantaneous frequency of time-varying structures from the seismic responses. A simulated signal and the seismic responses of a 4-layer time-varying frame structure show that the accuracy of identified instantaneous frequencies by using the IVMD algorithm is higher than the identified ones by using the VMD algorithm. The feasibility of the proposed method is verified by using shaking table test data of a 12-story reinforced concrete frame structure model.
| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |