螢火蟲演算法於高層建築抗風阻尼器最佳化設計之應用

FIREFLY ALGORITHM OPTIMIZATION OF TUNED LIQUID COLUMN DAMPERS FOR VIBRATION CONTROL OF WIND-EXCITED BUILDINGS

10.6652/JoCICHE.202309_35(5).0007

劉明怡(Ming-Yi Liu)；鄧宇雯(Yu-Wen Teng)

螢火蟲演算法 ； 調諧液柱阻尼器 ； 最佳化 ； 高層建築 ； 風力 ； firefly algorithm ； tuned liquid column damper ； optimization ； high-rise building ； wind load

中國土木水利工程學刊

35卷5期（2023 / 09 / 01）

501 - 509

繁體中文;英文

本研究以受風力作用且裝設調諧液柱阻尼器（tuned liquid column damper, TLCD）之高層建築為主體，利用螢火蟲演算法搜尋TLCD的最佳化參數，包含理論模式與數值算例兩部分，其中，理論模式分為頻率域分析和最佳化分析兩個階段，數值算例則分為數學函數最佳化分析與TLCD最佳化分析兩種類型。在數學函數最佳化分析方面，茲以碗形sphere function、板形Matyas function，以及谷形Rosenbrock function等三類數學函數為基礎，在不同疊代次數之條件下，利用螢火蟲演算法分別搜尋三者的極值和極值點、決定這些計算值與真值之絕對誤差，並估算計算時間，以評估螢火蟲演算法對於這三類數學函數最佳化分析的適用性；在TLCD最佳化分析方面，接續數學函數最佳化分析之結果，茲以受風力作用且裝設TLCD的主結構之雙自由度系統模型為基礎，給定質量比和主結構阻尼比，在設定主結構無因次位移變異數最小值為目標函數的前提下，利用螢火蟲演算法搜尋TLCD之最佳化參數，包含調諧頻率比最佳值與TLCD阻尼比最佳值，並決定這些計算值和基於微積分的演算法所得真值之相對誤差，以評估螢火蟲演算法對於TLCD最佳化分析的適用性。結果顯示在綜合考量計算精度與計算效率之前提下，選擇疊代次數等於10^3，此時，調諧頻率比最佳值、TLCD阻尼比最佳值和主結構無因次位移變異數最小值三者的相對誤差均介於-2.0%與2.0%之間，滿足工程實務的要求，因此，螢火蟲演算法適用於TLCD最佳化分析。

The objective of this paper is to investigate the firefly algorithm optimization of tuned liquid column dampers (TLCDs) for vibration control of high-rise buildings under wind loads. Theoretical models, including the frequency domain analysis and optimization analysis, are presented for this purpose. Numerical examples, including the mathematical function optimization and TLCD optimization, are also provided to illustrate the theoretical models. In the aspect of the mathematical function optimization, three types of mathematical functions: the bowl-shaped sphere function, plate-shaped Matyas function and valley-shaped Rosenbrock function are provided to evaluate the applicability of the firefly algorithm. For each mathematical function under a variety of iteration numbers, the determination of the extreme value and its extreme points, the calculation of the corresponding absolute error between the computed and true values, and the estimation of the computation time are conducted using the firefly algorithm. In the aspect of the TLCD optimization, based on the results of the mathematical function optimization, a two-degree-of-freedom system consisting of a TLCD attached to a main structure under wind loads is presented to evaluate the applicability of the firefly algorithm. For a given mass ratio and damping ratio of the main structure, the optimal TLCD parameters, including the optimal tuning frequency ratio and TLCD damping ratio, are determined by minimizing the dimensionless variance of displacement of the main structure as the objective function, and the corresponding relative error between the computed value determined by the firefly algorithm and the true value obtained from the calculus-based algorithm is calculated under these conditions. In comprehensive consideration of the computational accuracy and efficiency, the relative error in each of the optimal TLCD parameters and objective function is between -2.0% and 2.0% when the iteration number is selected as 10^3, which satisfies the requirements for engineering applications. Consequently, the firefly algorithm is applicable to the TLCD optimization.

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