第五章 結論與建議
5.2 建議
時變系統之識別上，以移動最小平方差法架構TVARX 模式對於跳耀變 化之時變系統之識別效果不盡理想，未來研究可進一步探討不同權重函數 對識別結果之影響。
在局部動態識別中，須以識別之自由度以及相鄰之自由度之資料進行 識別；而在現地量測時，每個自由度資料並不是相當齊全，未來之研究可 探討如何在不完全自由度之下進行局部動態識別。
參考文獻
Carydis, P. and Mouzakis, H. P. “Small amplitude vibration measurement of buildings undamaged, damaged and repaired after earthquakes Earthq.” 1986;
Spectra 3:123–42
Choi, H. I. and Williams, W. J. “Improved time-frequency representation of multicomponent signals using exponential kerner.” IEEE Transactions on Acoustics. Speech and Signal Processing, 1989; 17(6): 862-871.
Cohen, L. “Time-frequency distributions－A review.” Proceedings of the IEEE, 1989; 77(7): 941-981.
Huang, C. S. “Structural identification from ambient vibration measurement using the multivariate AR model.” Journal of Sound and Vibration. 2001;
241(3): 337-359.
Huang, C. S. and Lin H. L. “Modal identification of structures from ambient vibration, free vibration and seismic response data via a subspace approach.”
Earthquake Engineering and Structural Dynamics. 2001; 30:1857-1878.
Huang, C. S., Hung, S. L., Lin, C. I. and Su, W. C. “A wavelet-based approach to identifying structure modal parameters from seismic response and free vibration data.” Computer-Aided Civil and Infrastructure Engineering. 2005;
20:408-423.
Huang, C. S., Hung, S. L., Wen, C. M. and Tu, T. T. “A neural network approach for structural identification and diagnosis of a building from seismic response data.” Earthquake Engineering and Structural Dynamics. 2003;
32:187-206.
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C. and Shin, H. H. “The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis.” Proceedings of the Royal Society of London 1998;
A454: 903-995.
Jones, D. L. and Baraniuk, R. G. “An adaptive optimal-kernel time-frequency representation.” IEEE Transactions on Signal Processing 1995; 43 (10):
2361-2371.
Kijewski, T. and Kareem, A. “Wavelet transforms for system identification in civil engineering.” Computer-aided Civil and Infrastructure Engineering
2003; 18(5): 339-355.
Lin, C. C. and Wang, C. E. and Wu, H. W. and Wang, J. F. “On-line building damage assessment based on earthquake records.” Institute of Physics Publishing 2005; 14:S137-S153
Liu, G. R. Mesh, Free Methods- Moving beyond the Finite Element Method.
CRC Press, NY. 2003.
Martin, W. and Flandrin, P. “Wigner-Ville spectral analysis of non-stationary processes.” IEEE Transactions on Acoustics, Speech and Signal Processing 1985; ASSP-33: 1461-1470.
Marmarelis, V. Z. “Nonlinear and nonstationary modeling of physiological system: an overview in Advanced Methods of Physiological System Modeling, edited by Marmarelis V. Z..” Biomedical Simulations Resource, 1,pp.1-24,1987.
Niedwiecki, M., Identification of Time-Varying Processes, John Wiley & Sons, Inc. New York, NY, USA 2000
Qian, S., Introduction to Time-frequency and Wavelet Transforms. Prentice-Hall PTR, NJ, 2002.
Tsatsanis, M. K. and Giannakis, G. B. “Time-varying system identification and model validation using wavelets.” IEEE Transactions on Acoustics,Speech and Signal Process, 41, pp. 3512-3523,1993.
Udwadia, F. E. and Jerath, N. “Time variations of structureproperties during strong ground shaking.” J. Eng. Mech. Div.ASCE. 1980;106 111–21.
Watson, G. A. Approximation Theory and Numerical Methods, John Willey &
Sons, NY. 1980
Wu, W. H and Wang, J. F. and Lin, C. C. “Systematic assessment of irregular building–soil interaction using efficient modal analysis Earthq.” Eng. Struct.
Dyn. 2001; 30:573–94
Yang, J. N., Lei, Y., Pan, S. W. and Huang, N. “System identification of linear structures based on Hilbert-Huang spectral analysis, part I ： normal modes.“ Earthquake Engineering structure. 2003; 32(10): 1533-1554.
Zou, R., Cupples, W. A., Yip, K. P., Holstein-Rathlou, N. H. and Chon, K. H.
“Time-varying properties of renal autoregulatory mechanisms.” IEEE Transactions on Bio-medical Engineering. 2002; 49: 1112–1120.
Zou, R., Wang, H. and Chon, K. H. “A robust time-varying identification algorithm using basis function.” Annals of Biomedical Engineering. 2003;
31: 840-853.
黃炯憲、洪士林、蘇威智、陳承俊，「利用小波包識別橋樑動態特性」，中 央氣象局報告，2003。
黃炯憲，「微動量測分析工具探討(二)─時間序列法」，國家地震工程研究中 心報告NCREE-99-018，1999。
蘇威智，「以時間序列模型識別結構之模型參數」，國立交通大學，博士論 文，2008。
劉靖俞，「應用遞迴最小平方差法識別時變系統之瞬時模態參數」，國立交 通大學，碩士論文，2009。
表 4.1：鋼構之材料性質
Dir-2m Dir-3m
Column(1F~5F) H125x125x6.5x9 H125x125x6.5x9 Beam(1F~5F) H150x75x5x7 H100x100x6x8 Girder(1F~5F) H100x50x5x7 H100x50x5x7
表 4.2：六層樓所識別之案例
Test No. Excitation case PGA(ideal) Direction Description Remarks
Case 1 White Noise 50 gal x
Case 2 White Noise 100 gal x
Case 3 El Centro 100 gal x
With no cuts
Strain Gauges were not mounted. DX0
was not ready for service. The disp. of
shaking table (Long Dis) is used instead.
Case 4 White Noise 50 gal x
Case 5 White Noise 100 gal x
Case 6 El Centro 100 gal x
Damage scenario 1 *:
A cut with 3.75cm deep at the medium height of each of the
two south-side columns in 1st floor (with Strain gauges 7
and 8).
Strain Gauges were mounted.
Case 7 White Noise 50 gal x
Case 8 White Noise 100 gal x
Case 9 El Centro 100 gal x
Case 10 El Centro 500 gal x
Damage scenario 2 *:
A cut with 7.5cm deep at the medium
height of each
columns in 1st floor
表 4.3：case1、case2 與 case3 試驗之識別結果變化區間
表 4.4：case4、case5 與 case6 試驗之識別結果變化區間
表 4.5：case7、case8、case9 與 case10 試驗之識別結果變化區間
圖 3.1：三層樓剪力構架示意圖
圖 3.2：平滑變化時變系統之理論模態
0 5 10 15 20 25 30
(m/sec²)/Hz*9.8² (m²/sec)/Hz(m²/sec)/Hz(m²/sec)/Hz
1st mode
2nd mode
3rd mode
圖 3.5：以 921 地震輸入對平滑變化之時變系統識別結果
1st mode
2nd mode
3rd mode
圖 3.6：各組支撐參數(
d
m)於不同節點數下之識別誤差圖 3.7：以 921 地震輸入對平滑變化之時變系統識別之 MAC 圖
圖 3.8：加入 5%噪訊比之輸入及頻譜圖
圖 3.9：加入 5%噪訊比每個自由度之位移輸出反應及其頻譜圖
(m/sec²)/Hz*9.8² (m²/sec)/Hz(m²/sec)/Hz(m²/sec)/Hz
1st mode
2nd mode
3rd mode
圖 3.10：以 921 地震輸入加入噪訊比 5%對平滑變化之時變系統識別結果
1st mode
2nd mode
3rd mode
圖 3.11：各組支撐參數(
d
m)與不同節點數在模型階數( , )I J
為(15,15)之識別 誤差圖 3.12：利用不同階數分析含雜訊反應於不同時間點所得之瞬時頻率 (
l
n=10，d
m=4)圖 3.13：利用不同階數分析含雜訊反應於不同時間點所得之瞬時頻率 (
l
n=20，d
m=4)圖 3.14：利用不同階數分析含雜訊反應於不同時間點所得之瞬時頻率 (
l
n=30，d
m=4)圖 3.16：以 921 地震輸入加入噪訊比 5%之 MAC 圖
(a)
(b)
(c)
圖 3.17：各子結構系統之理論瞬時擬自然振動頻率及阻尼比
(a)
(b)
(c)
圖 3.18：各子結構系統之識別結果
圖 4.1：國家地震工程研究中心之五層樓鋼構架
圖 4.2：國家地震工程研究中心之六層樓鋼構架
圖 4.3：五層樓鋼構架之上視平面圖
圖 4.4：五層樓鋼構架之側視平面圖
3000mm
2000mm Beam
Girder
Column Beam
2000mm 3000mm
5 @ 13 00 mm 5 @ 13 00 mm
DOF
5 1
2
3
4
圖 4.5：10%Kobe 地震輸入反應及其頻譜圖
(m/sec ²)/Hz * 9 .8 ²
圖 4.6：10%Kobe 地震作用下各樓層之位移反應圖
圖 4.7：10%Kobe 地震作用下各樓層之位移頻譜圖
(m ²/sec)/Hz (m ²/sec)/Hz (m ²/sec)/Hz (m ²/sec)/Hz (m ²/sec)/Hz
圖 4.8：60%Kobe 地震輸入反應及其頻譜圖
(m/sec ²)/Hz * 9 .8 ²
圖 4.9：60%Kobe 地震作用下各樓層之位移反應圖
圖 4.10：60%Kobe 地震作用下各樓層之位移頻譜圖
(m ²/sec)/Hz (m ²/sec)/Hz (m ²/sec)/Hz (m ²/sec)/Hz (m ²/sec)/Hz
圖 4.11：10%與 60%Kobe 地震下最底層柱之應變歷時圖
圖 4.12：10% Kobe 地震下各自由度之識別瞬時動態特性
(圖 4.12 續上頁)
圖 4.13：10% Kobe 地震下各模態之 MAC 以及 e 值
(圖 4.13 續上頁)
圖 4.14：60% Kobe 地震下各自由度之識別瞬時動態特性
(圖 4.14 續上頁)
圖 4.15：60% Kobe 地震下各模態之 MAC 以及 e 值
(圖 4.15 續上頁)
(a) (b)
(c) (d)
圖 4.16：五層樓各個自由度之局部動態識別
圖 4.17：六層樓鋼構架之側視圖
圖 4.18：六層樓鋼構架之立體圖
圖 4.19：Damage Scenario 1
圖 4.20：Damage Scenario 2
Reduced section
Reduced
section
圖 4.21：在最底層實驗示意圖
Y X
(a) (North-East Corner) (b) (South-East Corner)
(c) (South-West Corner) (d) (North-West Corner) 圖 4.22：case 9 與 case 10 試驗中最底層柱之應變歷時
圖 4.23：case 3 試驗中輸入歷時及其頻譜
(mm/sec ²) /H z*9 800 ²
圖 4.24：case 3 試驗中各樓層之位移反應
圖 4.25：case 6 試驗中輸入歷時及其頻譜
(mm/sec ²) /H z*9 800 ²
圖 4.26：case 6 試驗中各樓層之位移反應
圖 4.27：case 9 試驗中輸入歷時及其頻譜
(mm/sec ²) /H z*9 800 ²
圖 4.28：case 9 試驗中各樓層之位移反應
圖 4.29：case10 試驗中輸入歷時及其頻譜
(mm/sec ²) /H z*9 800 ²
圖 4.30：case10 試驗中各樓層之位移反應
1st floor
2nd floor
3rd floor
圖 4.31：case 3、case 6、case9 與 case 10 試驗中各樓層之位移頻譜
4th floor
5th floor
6th floor
(圖 4.31 續上頁)
1st mode
2nd mode
3rd mode
圖 4.32：case1、case2 和 case3 試驗識別之結果
4th mode
5th mode
6th mode
(圖 4.32 續上頁)
1st mode
2nd mode
3rd mode
圖 4.33：case1、case2 和 case3 試驗各模態之 MAC 以及 e 值
4th mode
5th mode
6th mode
(圖 4.33 續上頁)
1st mode
2nd mode
3rd mode
圖 4.34：case4、case5 和 case6 試驗識別之結果
4th mode
5th mode
6th mode
(圖 4.34 續上頁)
1st mode
2nd mode
3rd mode
圖 4.35：case4、case5 和 case6 試驗各模態之 MAC 以及 e 值
4th mode
5th mode
6th mode
(圖 4.35 續上頁)
1st mode
2nd mode
3rd mode
圖 4.36：case7、case8 、case9 和 case10 試驗識別之結果
4th mode
5th mode
6th mode
(圖 4.36 續上頁)
1st mode
2nd mode
3rd mode
圖 4.37：case7、case8、case9 和 case10 試驗各模態之 MAC 以及 e 值
4th mode
5th mode
6th mode
(圖 4.37 續上頁)
(a)
(b)
(c)
圖 4.38：六層樓各個自由度之局部動態識別