本研究之目的在探討應用希爾伯特-黃轉換(HHT)和快速傅立葉轉換(FFT)法，偵測鋼結構建築受強地震作用造成損傷之敏感度分析。首先，分別建立皆為四跨之三層、五層及十層樓鋼結構有限元素模型，透過輸入四種不同類型之地震紀錄(日本311、集集921、El Centro與Kobe)，進行非線性動力歷時反應分析，再擷取樓層加速度訊號建立HHT及FFT頻率反應曲線。最後藉由比較各頻譜間之頻寬比(RB)，並結合桿件有效勁度比(RES)的變化，探討由HHT和FFT頻譜計算之RB指標對於偵測鋼結構模型地震損傷之敏感程度。 研究成果顯示：1.本研究建立之鋼結構模型皆出現一樓柱底先達降伏，進入非線性反應階段，造成斷面勁度折減及產生結構損傷。2.由三層、五層及十層樓模型利用HHT頻譜計算之RB指標分析結果得知，當一樓柱桿件之RES剩餘80%時，無論一樓或頂樓的RB即開始出現變化，並有隨RES持續折減而增大之趨勢，其中又以一樓處的RB變化量較為明顯。3.反觀經由FFT頻譜分析計算所得之RB，在RES=60%即結構受損嚴重狀態時，RB仍未產生變化。4.以HHT加速度反應頻譜為基礎之損傷指標RB，具有較採用FFT分析更為良好的偵測結構地震損傷敏感度。This study aims to investigate the relationship between structural damage and sensitivity indices using the Hilbert-Huang transform (HHT) method. Two damage detection indices are proposed: the ratio of bandwidth (RB), and the ratio of effective stiffness (RES). The nonlinear four bays multiple degree of freedom models with various predominant frequencies are constructed using the SAP2000 program. Adjusted PGA earthquake data are used as the excitations. Next, the damage detection indices obtained using the HHT and the fast Fourier transform (FFT) method are evaluated based on the acceleration responses of the structures to earthquakes.Simulation results indicate that, the column of the 1st floor is the first yielding position and the RB value is changed when the RES=85% in the three-story and five-story cases versus the RES=90% in the ten-story cases. Moreover, the RB value of the 1st floor changes more than those from the top floor. In addition, when the structural response is nonlinear (i.e., RES<100%), the RB and the RES curves indicate the incremental change in the HHT spectra. However, the same phenomenon can be found from FFT spectra only when the stiffness reduction is large enough. Therefore, the RB estimated from the smoothed HHT spectra is an effective and sensitive index for detecting structural damage.
