基于MOPSO算法的斜拉橋索力優化分析

張玉平 劉雪松 李傳習

摘 要： 針對斜拉橋設計和監控計算中合理成橋狀態和施工狀態索力的確定問題，提出了一種基于MOPSO算法的斜拉橋索力優化方法。該方法在PSO算法的基礎上通過增加外部儲備集和優化更新策略來適應多目標、多約束的索力優化，較單目標優化方法僅有單一解的局限性，MOPSO算法考慮因素更全面，得到的Pareto最優解集可供決策者根據經驗進一步篩選。采用Python編程語言，聯合有限元軟件編寫基于該方法的優化程序，選取主塔、主梁的彎曲應變能之和，主塔成橋后在恒載作用下的縱橋向位移平方和作為目標函數，以施工過程及成橋后結構處于安全狀態和索力總體分布均勻作為約束條件。工程算例優化結果表明，該方法能夠快速搜尋到Pareto最優解集，并從中篩選出最優解，其結構應力處于安全范圍，主塔線形合理，索力總體分布均勻。該方法可應用于斜拉橋成橋和施工階段索力的確定及梁拱組合體系橋梁吊桿索力的確定。

關鍵詞： 斜拉橋;索力優化;粒子群優化算法;多目標優化;有限元

中圖分類號：U448.27? ? 文獻標志碼：A? ?文章編號：2096-6717（2020）02-0107-08

Optimization of cable tension of cable-stayed bridges based on multi-objective particle swarm optimization algorithm

Zhang Yuping， Liu Xuesong， Li Chuanxi

（School of Civil Engineering， Changsha University of Science & Technology， Changsha 410114， P.R.China）

Abstract：? To solve the problem of determining reasonable completion state and construction state in cable-stayed bridge design and monitoring calculation， a cable force optimization method based on MOPSO algorithm is proposed.This method adapts to multi-objective and multi-constraint cable force optimization by adding external reserve set and optimizing update strategy based on PSO algorithm.Compared with the single objective optimization method which has the limitation of single solution， MOPSO algorithm considers more comprehensive factors.The Pareto optimal solution set obtained by MOPSO algorithm can be further screened by decision makers based on experience.Python programming language and finite element software are used to compile the optimization program based on this method.The sum of the bending strain energy of the main tower and the main beam， and the sum of squares of longitudinal displacement under dead load is taken as the objective function after the completion of the bridge.The constraints are that the structure is in a safe state during the construction process and after the completion of the bridge and the overall distribution of cable forces is uniform.The optimization results of engineering examples show that the proposed method can quickly find the Pareto optimal solution set and select the optimal solution.The stress of the structure is in the safe range， the main tower is reasonable in alignment， and the overall distribution of cable forces is uniform.The method can be applied to determine the cable force in completion and construction of cable-stayed bridge and the suspender force of girder and arch combination bridge.

Keywords： cable-stayed bridge; optimization of cable tensions; particle swarm optimization algorithm; multi-objective optimization; finite element

現代斜拉橋多為密索體系，屬于高次超靜定結構，可以通過人為調整斜拉索各次張拉控制力，在一定范圍內調整主梁、主塔等結構的變形和受力狀態，因此，斜拉橋的設計自由度較大。如何通過優化索力來確定合理成橋狀態與合理施工狀態是斜拉橋設計和監控計算中需要解決的一個關鍵問題。……