考慮Kanai-Tajimi濾波器以直接輸出回饋進行隔震層阻尼係數之最佳化設計

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Title:	考慮Kanai-Tajimi濾波器以直接輸出回饋進行隔震層阻尼係數之最佳化設計
Authors:	林宣瑩;Lin, Hsuan-Ying
Contributors:	土木工程學系
Keywords:	Kanai-Tajimi 濾波器;隔震層阻尼係數最佳化設計;直接輸出回饋;迭代更新參數;被動隔震系統;地震力;隨機白噪加速度;Kanai-Tajimi filter;optimal design of damping coefficient of isolation layer;direct output feedback;iterative update parameters;passive isolation system;seismic force;random white noise acceleration
Date:	2023-07-26
Issue Date:	2024-09-19 14:14:56 (UTC+8)
Publisher:	國立中央大學
Abstract:	本文目標為針對基礎隔震結構之隔震層阻尼係數進行最佳化設計，並將Kanai -Tajimi 濾波器納入考量，使地震力更為符合台灣各地區場址之地盤影響。此 Kanai-Tajimi濾波器參數之決定將以台灣耐震設計規範參數為基準，使白噪加速度通過此濾波器所產生之地表加速度能與台灣耐震設計規範所公布之設計反應譜相符；另外，為確保隔震層阻尼係數最佳化設計結果之分析，更貼近受地震外部擾動作用下設計之真實情況，本文亦修正真實地震歷時至符合各場址設計反應譜之地震歷時，以便進行歷時分析比較。針對隔震層阻尼係數進行最佳化設計，將運動方程式中隔震層阻尼係數拆分為初始阻尼係數與待設計之阻尼係數，經由移項配置，使隔震層部分之待設計阻尼力比擬為主動控制力，從而將隔震層阻尼係數之最佳化設計問題轉換為主動控制增益矩陣之最佳化控制問題。由於此主動控制力並不為全狀態回饋，因此需使用直接輸出回饋方法求解最佳增益矩陣。而在求解增益矩陣最佳值之過程中，傳統直接輸出回饋方法須定義控制力權重值，且二次效能目標函數將受控制力權重之影響，因此增益矩陣最佳值並不為最佳隔震層阻尼係數，然而當控制力權重值等於零時，直接輸出回饋中之增益矩陣將不易求解，因此引入參數迭代更新法，僅須選取一組適當之控制力權重值，解得含待設計阻尼係數之增益矩陣，依此對初始阻尼係數進行更新，並持續迭代直至增益矩陣收斂至零，即完成更新，得隔震層阻尼力之最佳設計。本研究最後於Etabs中建立一個多自由度隔震系統之上部結構，從Etabs中取得上部結構參數，透過上述隔震層阻尼係數之最佳化設計方法於Matlab中進行設計，得該隔震層最佳阻尼係數，接著使用 Etabs 建立此最佳化設計之多自由度隔震系統，並輸入通過 Kanai-Tajimi 濾波器之白噪加速度、與設計反應譜相符之地震歷時以及幾筆較著名之真實地震歷時資料，對此結構系統進行歷時分析，確認本研究所提及最佳化隔震層阻尼係數之設計具有良好之隔震效果，並且證實此最佳化設計法所計算之最佳阻尼比為使結構絕對加速度反應最小之最佳值。 ;The objective of this study is to optimize the isolation layer damping coefficient for basic seismic isolation structures and incorporate the Kanai-Tajimi filter to better account for the ground effects at various locations in Taiwan. The determination of parameters for the Kanai -Tajimi filter is based on Taiwan Seismic Design Code, ensuring that the ground acceleration generated by passing white noise through this filter matches the design response spectrum specified in the seismic design code. Additionally, to ensure a more realistic analysis of the optimized design under seismic excitation, real earthquake records are also modified to match the design response spectra on different locations for time history analysis.The study focuses on the optimization of the isolation layer damping coefficient. The damping coefficient is divided into an initial damping coefficient and a controlling damping coefficient. By rearranging the terms in equation of motion, the controlling damping force in the isolation layer can be treated as an active control force, transforming the optimization design problem of the isolation layer damping coefficient into an optimization control problem of the active control gain matrix. Since this active control force is not full-state feedback, the study employs a direct output feedback method to find the optimal gain matrix. Traditionally, direct output feedback methods require defining control force weightings, cause the quadratic performance index be influenced by these weightings. Therefore, the optimal value of the gain matrix is not the optimal damping coefficient of the isolation layer. However, when the control force weighting is zero, the gain matrix in direct output feedback is not easy to be solved. To figure out this problem, this study introduces a parameter iterative updating method that only requires selecting an appropriate control force weighting to obtain the gain matrix that includes the controlling damping coefficient. Following, the initial damping coefficient is updated iteratively until the gain matrix converges to zero, completing the optimization and obtaining the optimal design of the isolation layer damping force. Finally, a multi-degree-of-freedom isolated system is established for the upper structure in Etabs. The floor parameters of the structure are therefore obtained and exported in matlab.Using the optimization method for the isolation layer damping coefficient mentioned above, the study obtains the optimal damping coefficient for the isolation layer. Then, the optimized multi-degree-of-freedom isolated system is created in Etabs and subjected some ground accelerations. These ground accelerations contain the Kanai-Tajimi filter shaped white noise,the design response spectrum matched ground acceleration, and some notable real earthquake records. The time history analysis results confirm that the design of the optimal damping coefficient of the seismic isolation layer mentioned in this research has a good seismic isolation effect, which verify that the optimal damping ratio calculated by this optimization method is the best value to minimize the absolute acceleration response of the structure.
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