小波神經網路於土木工程之應用

Abstract

工程行為的預測充滿著極度的困難，而一般常用的傳統預測方法的準確度通常無法令人滿意或是計算的過程顯得繁雜而無效率。因此這個研究主要在於應用一個新穎的預測方法，不僅是探討其於工程行為模擬的適用性也一併實際應用於近似求解結構工程的問題。這個預測模式是由相似於類神經網路（Artificial Neural Network）架構所改良發展出來的，小波轉換（Wavelet Transform）被用於取代類神經網路中神經元（neuron）的激發函數（activation function）而建構出小波神經網路（Wavelet Neural Network）中的小波元（wavelon）。同時小波神經網路的訓練是採用類似於類神經網路常用的BP（back-propagation）學習演算法，根據工程問題所在的輸入與輸出數據代入網路中，訓練之後的網路能用於準確地模擬工程的行為。兩個運用小波神經網路的案例在此被提出：1.高性能混凝土的壓力強度預測，2.五層樓鋼構架震動台試驗地震反應之系統識別。模擬的結果驗證了小波神經網路預測結構行為的準確性。這個研究的成果同時也可提供工程師解決近似（approximation）問題一個有價值的參考。

Forecasting engineering behavior under unforeseen circumstances is extremely difficult, accounting for why conventional forecasting methods are often inaccurate and inefficient in terms of computational time. Therefore, this study presents a novel stochastic methodology capable of approximating not only engineering behaviors but also structural engineering problems. Approximate models are developed based on the architecture similar to the Artificial Neural Network (ANN). Wavelet Transform is then used as the activation function for the “wavelon” in the Wavelet Neural Network (WNN) instead of “neuron” in the ANN. Next, the forward networks and back-propagation based learning algorithm are adopted to converge the WNNs during training. Additionally, the WNN are used to simulate the engineering behavior within a desired accuracy while depending only on input and output data of a certain engineering problem. Also presented herein are two case studies involving the use of WNNs to predict high-performance concrete (HPC) strength and identify the structural vibration during an earthquake. Simulation results indicate that the proposed model accurately estimates structural behavior to minimize the discrepancy between simulation results and real world problems. Results in this study provide a valuable reference for engineers attempting to solve approximate problems.