應用基因演算法為基礎之推廣卡氏過濾理論於加裝加勁消能器之結構系統識別

Using GA-Based Extended Kalman Filter to Parameter Identification of Structural Systems with Added-Damping-and-Stiffness Devices

廖偉俊(WAI-CHOUN LIEW)

指導教授 ： 王淑娟

朝陽科技大學/理工學院/營建工程系/碩士(2016年)

摘要

在各種系統識別方法發展下，地震紀錄的取得是必需的。目前台灣地區在各地重要之大樓、學校及橋樑等土木結構物上皆裝有強震儀，可隨時紀錄地震發生時之相關資料，利用其地震紀錄來識別對應之結構系統參數，據此進行結構物安全評估，並根據地震後結構物的破壞情形，進行修補工作。所發展之系統識別方法，及其數學模式架構，可以應用於往後類似建築物之系統識別上，便於快速了解該建築物受震後之結構系統特性。
本研究提出兩種識別方法，首先使用的方法是頻率域之遞迴式改良型基因演算法，該法於非線性系統之識別是採用自動分段方式進行識別，其分段方式為一開始設定分段點數，過後利用程式依據分段點數進行分段，各分段視為等值線性系統。接著，再提出加入Wen’s非線性回復力模式的以基因演算法為基礎之推廣卡氏過濾理論，該法是在每進行一次基因演算世代循環中，搜尋及演化推廣卡氏過濾理論識別時所需之起始值；相對的，也藉由推廣卡氏過濾理論快速識別系統參數，增快基因演算法的收斂率，大幅減少運算時間。另外，在單自由度及多自由度系統中，其回復力模式為Wen’s之非線性模式，使得上述識別方法得以對非線性系統進行識別。首先將該識別法應用於數值模擬系統之動力特性識別，驗証其可行性；也為了更加確定加入Wen’s非線性回復力模式的以基因算法為基礎之推廣卡氏過濾理論之可行性，亦對於含有雜訊的數值模擬地震紀錄及反應再進行識別來探討新式識別法之識別效果。最後再應用上述兩種識別法於加裝圓棒型加勁消能器之三層樓鋼構進行系統識別。
頻率域之遞迴式改良型基因演算法隨著PGA值的增加識別所得之結果有：1）誤差指數會隨之變大、2）識別所得之阻尼比 及頻率 的區間範圍皆會隨之變大、3）各震度對應三個不同振態的阻尼比 之最大值會逐漸變大、及4）各震度對應三個不同振態的頻率 之最小值會逐漸變小。加入Wen’s非線性回復力模式的以基因算法為基礎之推廣卡氏過濾理論識別所得之結果有：1）加裝D20H100加勁消能器之識別結果顯示，對應各震度的第一自由度之勁度 會隨著震度的增加而下降，而第二與第三自由度之勁度 則會在一定區間內變化、2）加裝D20H80加勁消能器之識別結果顯示，對應各震度的第一自由度及第三自由度之勁度 皆會隨著震度的增加而下降，但第二自由度之勁度 則會隨著震度的增加而稍微上升、3）加裝2種不同加勁消能器的識別結果顯示，越高自由度之 值越趨近於1，說明越高自由度受到的地震震度相同時，其行為越趨向線性系統、4）加裝D20H80加勁消能器之識別結果顯示，當震度為El 600時，其第一樓層的 值與震度為El 550之一樓層的 值相比大幅度增加；二樓及三樓則大幅下降。因此，判斷D20H80加勁消能器於El 600時開始破壞。

關鍵字

基因演算法 ； Wen's模式 ； 推廣卡氏過濾理論

並列摘要

Field of system identification has become important discipline due to the increasing need to estimate the behavior of a system with partially known dynamics. In the past few decades, many optimization techniques have been developed for system identification problems. Identification is basically a process of developing or improving a mathematical model of a dynamic system through the use of measured experimental data. However, collecting of strong motion data is essential when performing the system identification analysis. Fortunately, the strong motion data recorded by accelerographs, which were installed under the Taiwan Strong-Motion Instrumented Program (TSMIP) since 1993, has accumulated to a remarkable amount. In addition to updating the structural parameters for better response prediction, system identification techniques made possible to monitor the current state or damage state of the structures.
Two methods were proposed to the parameter identification in this study. One is the frequency-domain recursive hybrid GA and the other is the GA-based extended Kalman filter. For the frequency-domain recursive hybrid GA, time histories of the measurement were divided into a series of time intervals, and then the model of equivalent linear system is employed to identify the modal parameters of the system for each time interval. For the second method, Wen’s model is used as the restoring force of each story shear and the analysis of the extended Kalman filter is performed after the initial values of state variables used in the analysis are acquired by the evolution process of GA for each generation. The process of exploring this algorithm is implemented by using the simulated SDOF system and MDOF system considering the effect of noise contamination. Finally, these identification strategy are also applied to the identification of the three-story steel frame with added-damping-and-stiffness devices.
According to the result of frequency-domain recursive hybrid GA, the conclusions when the PGA value becomes larger can be reached as follows: (1) the error index will become larger. (2) the interval range of the identified modal damping ratios and modal frequencies will become larger. (3) The maximum damping ratio value of three different modes will become larger. (4) The minimum frequency value of three different modes will become smaller. According to the result of GA-based extended Kalman filter, the conclusions are as follows: (1) The stiffness of first DOF will become smaller with the increasing PGA value. (2) The behavior in the higher DOF will tend to be a linear system when subjected to same excitation intensity. (3) The D20H80 model of added-damping-and-stiffness devices experienced extensive damage when subjected to excitation of El 600 earthquake.

並列關鍵字

Genetic algorithm ； Wen’s model ； Extended Kalman filter

參考文獻

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