類神經網路在鋼結構設計上之應用

Abstract

基於數學演算法中之L-BFGS演算法與線搜尋演算法 (Line Search Algorithm),本研究係發展一新的類神經網路學習演算法來改良向後推導 學習法(Error Backpr- opagation Learning Algorithm,BP)並應用於鋼 結構設計領域中,BP演算法係基於最陡下降演算法(The Steep- est Descent Method),然其演算法中常數項的學習因子 (或學習速率)( Learning Ratio)常讓該神經網路在學習過程中呈現出非系統化的收斂情 況。而且最佳的學習因子常數系隨學習問題的不同而有很大的差異, 所以 依試誤(Trail-and -error)方式所選定的學習因子讓BP演算法的學習收斂 不盡理想。本研究引進L-BFGS最佳化演算理論來增進BP梯度演算步驟 , 並結合了線搜尋演算法( Line Search),使得在搜尋誤差的最小值過程中, 改變了每次搜尋距離即學習速率。本研究將所發展之L-BFGS類神經網路學 習演算法應用於軸載重鋼結構柱設計領域中。由測試結果證實本研究所發 展的學習演算法具有較BP演算法較佳的收斂特性, 且由試誤法求取學習因 子的問題在新的演算法中已由線搜尋法所取代。 Based on mathematical optimization L-BFGS algorithm and line search algorithm,a new artif- ical neural network learning algorithm has been developed to improved the learning capability of Error Backpropagation learning algorithm(BP) and the new algorithm has been applied to the domain of steel column design problem.BP learning algo- rithm, based on the steepest descent method , is widely used for training multilayer neural netw- orks. The algorithm , however , has a non-system converge rate for a constant learning ratio. The optimum value of learning ratio is dependent on the problem. As a result, the BP algorithm has a slow learning rate for the problem of arbitrary trail-and-error of the learning ratio . In this project,the L-BFGS optimization algorithm is used to improved the calculation of gradient direction of BP learning algorithm.Instead of constant lea- rning ratio , the step length in the line search in the new algorithm is adapted during the learn- ing process. The new learning algorithm has been applied to the problem of steel column design . The new algorithm has better converge rate than the BP algorithm. The problem of arbitrary trail -and-error of the learning ratio encountered in the BP algorithm is removed in the new algorithm.