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 simulatethe nonlinear and dynamic behavior of RC members for the estimation of structural integrity. Amathematical technique to solve the multi-objective optimization problem is applied for the learning of thefeedforward neural network, which is formulated so as to minimize the Euclidean norm of the errorvector 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 weightmodification of the network. The governing equation for weight modification to make the error vectornull is constituted with the consideration of the approximated outputs for all the learning data sets. Thesolution is neatly determined by means of the Moore-Penrose generalized inverse after summarization ofthe governing equation into the linear simultaneous equations with a rectangular matrix of coefficients.The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified inthree types of problems to learn the truth table for exclusive or, the stress-strain relationship described bythe Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under anearthquake.