Whole learning algorithm of the neural network for modeling nonlinear and dynamic behavior of RC members

A new sort of learning algorithm named whole learning algorithm is proposed to simulate<br />the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A<br />mathematical technique to solve the multi-objective optimization problem is applied for the learning of the<br />feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error<br />vector defined as the difference between the outputs and the target values for all the learning data sets.<br />The change of the outputs is approximated in the first-order with respect to the amount of weight<br />modification of the network. The governing equation for weight modification to make the error vector<br />null is constituted with the consideration of the approximated outputs for all the learning data sets. The<br />solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of<br />the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients.<br />The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in<br />three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by<br />the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an<br />earthquake.