應用小波分析辨識地下水水位模擬之類神經網路架構

Abstract

本研究將倒傳遞類神經網路之隱藏神經元個數的決定，視為一般參數檢定的過程，使用AIC指標（Akaike’s Information Criterion）來決定隱藏神經元個數並優選模式。 此外，因為類神經網路的各個權重 主要是模擬不同生物神經元間的連結強弱，權重為正且越大表示連結越強且增益越大；權重為負且越小表示連結雖強但是為抑制的功用；若權重接近零，表示連結很弱。因此本研究分析在不同隱藏層神經元個數下，各個權重值的大小之變化趨勢，將每一組權重視為一系列的頻譜，找出一適合的門檻值，使用小波分析將之過濾，把過於接近零，也就是連結度越弱的權重予以剔除，進而得出一種更加快速的方式以決定隱藏層神經元個數，以期建立一精確之類神經模式以模擬地下水水位。 結果顯示，以小波分析過濾權重，的確能夠快速地找出合理的隱藏層神經元個數，而且隨著訓練資料筆數的增加，所決定之隱藏神經元個數亦隨之增加，證明了本論文方法論之可行性與可靠度。

Artificial neural network (ANN) is a flexible mathematical structure which is capable of idengifying complex nonlinear relationships between input and output data sets. ANN models have been found useful and efficient, particularly in problems for which the characteristics of the processes are difficult to be described using physical equations. Thus, in this paper, the capability of an artificial neural network to provide a data-driven approximation of groundwater flow model is demonstrated. To identify an ANN model, the number of nodes in every layer must be selected, especially in the hidden layer. In this paper, AIC criterion (Akaike’s Information Criterion) is applied to calibrate the ANN model, and the weights of the network are analyzed as a signal by wavelet analysis in orde to decide the number of nodes in the hidden layer. After an mathematical simulation, the result improve that the new approach deduced in this study can quickly offer a useful reference and application for the decision of the number of nodes in the hidden layer.