- 學位論文
應用類神經網路從事鋼筋混凝土基腳之最佳化設計
Optimal Design of Reinforced Concrete Isolated Footings Using Neural Networks
摘要
本論文首先以MATLAB之遺傳演算法，從事鋼筋混凝土獨立基腳之最佳化設計，目標函數為鋼筋混凝土獨立基腳之鋼筋與混凝土最低總造價，建立限制式時，以國內所發行之「混凝土工程設計規範與解說」為依據 ，考慮彎矩、單向梁寬及雙向穿孔剪力之強度需求、土壤允許應力與鋼筋伸展長度。最佳化設計結果可得到最低總造價，基腳長度、寬度與厚度、長向鋼筋根數及短向鋼筋根數，總共設計144組獨立基腳。此144組最佳化設計資料經由類神經網路亂數挑選後，將其分為三組:訓練資料、驗證資料及測試資料，訓練資料用於訓練類神經網路，驗證資料則用來監控訓練過程避免網路過度配適，測試資料則代入訓練後之類神經網路，得到目標值與網路輸出值的散佈圖及其相關係數。本論文使用的網路為二層前饋式倒傳遞網路及徑向基網路，輸入項目包含混凝土抗壓強度、鋼筋降伏強度、靜載重、活載重、土壤之容許承載力及基腳底部距離地表之深度，輸出項目為基腳長度、寬度與厚度、長向鋼筋根數、短向鋼筋根數與總造價。數值結果顯示前饋式倒傳遞網路隱藏層之神經元數目，使用9個即可得到效能佳之網路，其中測試資料輸出項目之網路輸出值與目標值之相關係數皆接近1。徑向基網路有newrb與newrbe兩種設計函數，使用newrb設計函數時，雖然測試資料輸出項目之相關係數r也皆接近1，但整體而言網路效能比倒傳遞網路稍差，如果使用newrbe設計函數時由於過度配適所以網路效能較newrb低。
並列摘要
This paper first applies genetic algorithms of the MATLAB software to design reinforced concrete isolated footings. The objective function is to minimize the cost of steel and concrete in the footing. According to the local code for the concrete design, the constraints are built, considering wide-beam and punching shears, bending moment, allowable soil pressure and the development length of reinforcement. The optimal design results consists of the minimum cost, the length, width and thickness of the footing, and the number of steel in the long and short directions. There are totally 144 kinds of isolated footings, the results of which are grouped into three sets: training, validation and testing data. The training data is used to train the neural network, validation data is to monitor the training process to avoid overfitting, and testing data is then substituted into the trained network to obtain the scatter plots of the targets and network output. Two kinds of neural networks are adopted in this paper: feedforward backpropagation networks and radial basis networks. The inputs contain the compressive strength of concrete, yielding strength of steel, dead load, live load, allowable soil pressure and the distance from the bottom of footing to the ground surface. The outputs contain the length, width and thickness of the footing, and the number of the steel in the long and short directions and the minimum cost. Numerical results show that for the testing data the correlation coefficients between the network outputs and targets are close to 1. There are two kinds of design functions for the radial basis network: newrb and newrbe. The results of the newrb show that for the testing data, the correlation coefficients between the network outputs and targets are also close to 1 but a little bit inferior to backpropagation networks, while the function newrbe shows worse performance due to overfitting.