樁基礎設計成本分析之粒子群演算法

Cost Analysis of Pile Foundation Design with Particle Swarm Optimization Method

陳柏維(Po-Wei Chen)

指導教授 ： 張德文

淡江大學/工學院/土木工程學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00916

摘要

本研究利用粒子群演算法(Particle Swarm Optimization, PSO)進行樁基礎最佳化設計法，其目標函數需符合國內樁基礎規範計算及成本低價化。在初始時，族群中的每個粒子可於空間中隨機產生一個隨機值，先以迭代方式搜尋目標函數最佳解。於每次迭代中，藉由跟蹤個體最佳值與群體最佳值，不斷更新速度與空間中所處位置以求最適值。其目標函數為總造價之最小值，包含土方開挖費用、樁帽費用、基樁費用及夯實回填費用等共四項。本分析系統所探討樁基礎設計變數有基樁間距、樁徑、樁長、樁帽有效深度、樁數等；束制條件為基樁間距檢核、樁頂位移量檢核、彎矩檢核、單樁承載力檢核、單樁拉拔力檢核、樁帽抗剪強度檢核、負摩擦力檢核、單樁沉陷量檢核及土地限制等。以上所述相關內容，經參數影響分析並探討其敏感度，最後透過利用國內外設計實際案例以驗証本研究採用最佳化方式之可行性。
本研究結果分述如下：(1)對於低維度的問題，權重因子選取範圍介於0.4~0.6之間，粒子數為20~40之間；至於高維度的問題，權重因子選取範圍介於0.6~0.9之間，粒子數為40~60之間選取。至於學習因子其對結果影響甚微，故一般均取值為2，(2)本研究發現以慣性權重式粒子群演算法的收斂速度比壓縮因子式粒子演算法較快；(3)經案例分析顯示，樁徑尺寸與樁數數目將主控整體總造價的變化。大致而言，程式執行運算時間約於15~30分鐘完成，相較於傳統上規劃設計更具效率性；(4)本研究因未考慮工期因素及小尺寸基樁施作時，仍存有發生斷樁之危機與疑慮。

關鍵字

粒子群演算法 ； 樁基礎 ； 最佳化

並列摘要

This study adopted Particle Swarm Optimization (PSO) in designing and evaluating all the cost from pile foundations. Its objection function included the limitation of standards and minimum cost of pile foundation. Initially, a particle would random to generate a position in given group, and then search the best fit solution in iteration method. In each iteration process, particles would renew its velocity and acceleration to estimate their next positions by tracing the individual and group best value. The cost of piles would involve excavation expense, pile cap and pile construction expense, land backfill expense. The parameters of optimization system included pile spacing, the diameter of pile, pile length, pile cap thickness, number of piles. The subjection function would involve the spacing width, pile displacement, bending moment, shear force, bearing capacity, pull-out force, negative frictional force and settlement. Based on the above procedure, the preliminary study is prior to discuss parametric relationship and sensitivity about parameters. Finally, this study would validate with the practical engineering cases to show its reliability and accuracy.
The conclusions were drawn as follows: (1). For the low dimension problem, weight factors would lie in 0.4 to 0.6 and numbers of particle are set up about 20 to40. On the other hand, for the high dimension problem, weight factors would lie in 0.6 to 0.9 and numbers of particle are set up about 40 to60.The learning factors would not almost affect solutions and could be set to 2 (2) The speed law of Particle Swarm Optimization uses inertia weight types better than compression ones. (3) Case studies would show pile diameters and numbers of piles would govern the results of cost minimization. Generally, the program would complete total analyses effectively about 15 to 30 minute, which was prior to traditional methods. (4) The study might design failure due to construction period and small dimension piles.

並列關鍵字

Particle Swarm Optimization ； Pile Foundation ； Optimization

參考文獻

26. 陳柏村(2006)，「質群演算法於組合型時間成本最佳化問題之研究」，淡江大學土木工程學系碩士班碩士論文。

34. 環台水泥製品股份有限公司(2007)，「預力基樁產品規格」。

23. 鄧永亟(2004)，「利用PSO演算法探討高速銑削最佳化」，大同大學機械工程研究所碩士論文。

6. 鐘明劍(2006)，「樁基礎最佳化設計之研究」，中央大學土木工程學系碩士論文。

24. 葉思緯(2004)，「應用粒子群最佳化演算法於多目標存貨分類之研究」，元智大學工業工程與管理研究所碩士論文。