混合式遺傳演算法應用於斜張橋及脊背橋鋼索預力最佳化設計與施工規劃之研究

Study on Optimum Design of Post-Tensioning Cable Forces and Feasible Erection Scheme for Cable-Stayed and Extradosed Bridges Using Hybrid Genetic Algorithm

王俊穎(Chun-Ying Wang)

指導教授 ： 宋裕祺

國立臺北科技大學/工程學院/工程科技研究所/博士(2013年)

https://doi.org/10.6841/NTUT.2013.00044

摘要

人工智慧演算法主要從自然界或生物界的生存規律或法則獲得啟發，仿效其原理進而發展成為求解最佳化問題的方式，與傳統最佳化方式多依賴函數導數或梯度不同，人工智慧演算法多採用個體之間的相互競爭或學習的模式進行隨機化搜索，具有算法簡單、易於在電腦程式中操作與實現等多項優點，對於不易以數學函數表示之複雜或非線性問題更顯見其長處，其中遺傳演算法(GA, Genetic Algorithm)從1975年發軔至今已廣泛被應用於多項研究領域，其卓越的全域搜索能力在最佳化問題的求解上普遍得到良好的成效。
然而，GA在實際應用方面仍有些無法完全盡如人意之處，如早熟或局部搜索能力不佳等問題，為此，本文研擬一套混合式的遺傳演算法(HGA, Hybrid Genetic Algorithm)演算程序，將粒子群演算法(Particle Swarm Optimization)之局部模型作為GA演算過程之突變操作的手段，在不影響原遺傳演算法的搜索性能為前提下，使得HGA不僅能保有傳統GA固有之隨機搜索及個體競爭的特性外，同時又能兼具粒子群演算法之個體間訊息交換與資訊共享的長處，冀能提升演算法求解精度，改善易陷入局部極值的缺點，本文依上述方式研擬HGA演算流程及開發相關應用程式，再利用文獻所載之數學函數及桁架最佳化設計對無約束及約束最佳化問題求解及驗証。
斜張橋的整體力學行為與鋼索預力值具有直接的關係，無論是施工階段或服務階段，皆可透過鋼索預力的調整使得到橋梁在成橋狀態下維持其最佳狀態，此外，亦須考量施工過程中如何確保最終主梁閉合時，其線形得以與目標線形最接近之問題。因此，鋼索預力值的求解在工程實務上亦屬最佳化問題的範疇，過去相關的求解方式多依賴數學規劃方法，求解在數個約束條件下符合設計者目標之最佳值，但鮮少以人工智慧演算法應用此類問題上，本文以社子大橋為例，分別以最小應變能及成橋時的線形為目標函數，配合商用分析軟體Midas Civil分析模組，進行鋼索預力值的運算與探討。
最後，本文以脊背橋為研究對象，引入斜張橋鋼索預力最佳化的概念，考量預力混凝土時間相依特性及施工程序，分別利用應變能最小、最經濟鋼索及主梁局部應力為目標函數進行最佳化鋼索預力的研究，演算過程中可有效解決大量迭代的分析流程，達到自動化運算的目的。文中運用程式整合技術克服HGA計算核心和商用軟體Midas Civil施工階段分析模組之間的銜接問題，同時開發一系列視覺化檢核模組，包括施工階段主梁應力呈現、鋼索軸力變化、服務階段預力混凝土撓曲強度與剪力強度計算與檢核模組等，研究成果可供相關設計與橋梁施工規劃之參考。

關鍵字

粒子群演算法 ； 人工智慧 ； 鋼索初始預力 ； 橋梁施工階段分析 ； 預力混凝土橋梁 ； 正裝分析 ； 倒拆分析

並列摘要

This dissertation proposed a hybrid genetic algorithm (HGA) to deal with optimization on post-tensioning cable forces as well as feasible erection scheme of cable-stayed bridge and extradosed bridge. The HGA proposed combined conventional genetic algorithm (GA) and local particle swarm optimization (PSO) model, denoted as PSO-GA. The local PSO model was employed in a new mutation strategy of GA for increasing the probability of skipping from local minimum to global optimum efficiently. The efficiency and accuracy of PSO-GA proposed were investigated through some case studies on minimization of mathematical functions and optimal designs of a 10-bar truss structure with constraints on member stress as well as node displacement. The benefit of PSO-GA proposed on accelerating convergence is able to be assured.
The determination on post-tensioning cable forces of the cable-stayed bridge to have an optimum structural performance is the core of structural analysis and design for engineers. For past few decades, traditional mathematical programming approaches were used to do the optimization problem since the total construction cost or total strain energy of the completed bridge can be expressed in an explicit mathematical form and therefore served as objective function (OF). However, this kind of OF is unable to be obtained any more for plan on erection scheme because determination of post-tensioning force for the cable most newly implemented in every stage of cantilever construction for cable-stayed bridge is depending on different structural systems during erection process. The superiority of PSO-GA on dealing with this kind of complex problem can be shown and therefore becomes the motive of this study. A practical cable-stayed bridge was employed as research target. The comparisons between analytical results obtained from PSO-GA proposed and actual erection data provided by constructor were carried out. It showed the proposed method even have a better result than that adopted in practical construction.
Similar to the case of cable-stayed bridges, this dissertation applied PSO-GA to deal with optimum design of extradosed bridge considering three different OFs. The results showed the structural performance of extradosed bridge can be improved by the post-tensioning forces determined of the cables and the more economical designs can be obtained.
The presented PSO-GA procedure can deal with optimum design of post-tensioning cable forces and feasible erection scheme for cable-stayed and extradosed bridges. The procedure developed were already linked with soft ware of MIDAS-CIVIL, an automatic operation can be easily performed for engineers. The results obtained could benefit engineers an efficient and accurate design.

並列關鍵字

Particle Swarm Optimization ； Artificial Intelligence ； Construction Stage Analysis ； Prestressed Concrete Bridges

參考文獻

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