2.4.3 Back propagation neural network (BPNN)
BPNN is a kind of multi-layer feedforward neural network used for nonlinear functions, which trains the weights and thresholds for many times. When the actual output does not match the observed, it enters the error backpropagation stage: it updates the weights between the hidden layer and the input layer, as well as the thresholds of the hidden layer based on the error of the output values (Maier and Dandy, 2000) . In this paper, the sigmoid (x ) function serves as the activation function for input-hidden layer and hidden-output layer (see Figure 5 (c)), and the formula is as followed: