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 the nonlinear and dynamic behavior of RC members for the estim ation of structural integrity. A mathematical technique to solve the multi- objective optimization problem is applied for the learning of the feedforwa rd neural network, which is formulated so as to minimize the Euclidean norm of the error vector defined as the difference between the outputs and the target values for all the learning data sets. The change of the outputs is approximated in the first-order with respect to the amount of weight modifi cation of the network. The governing equation for weight modification to ma ke the error vector null is constituted with the consideration of the appro ximated outputs for all the learning data sets. The solution is neatly dete rmined by means of the Moore-Penrose generalized inverse after summarizatio n of the governing equation into the linear simultaneous equations with a r ectangular matrix of coefficients. The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in three typ es of problems to learn the truth table for exclusive or, the stress-strain relationship described by the Ramberg-Osgood model and the nonlinear and d ynamic behavior of RC members observed under an earthquake.