  Dynamic analysis of structures subjected to earthquake excitation is a
time-consuming process, particularly in the case of extremely small time step
required, or in the presence of high geometric and material nonlinearity.
Performing parametric studies in such cases is even more tedious. The
advancement of computer graphics hardware in recent years enables efficient
training of artificial neural networks that are well-known to be capable of
learning highly nonlinear mappings. In this study, artificial neural networks
are developed with adaptive training algorithms, which enables automatic nodes
generation and layers addition. The hyperbolic tangent function is selected as
the activation function. Stochastic Gradient Descent and Back Propagation
algorithms are adopted to train the networks. The neural networks initiate with
a small number of hidden layers and nodes. During training, the performance of
the network is continuously tracked, and new nodes or layers are added to the
hidden layers if the neural network reaches its capacity. At the end of the
training process, the network with appropriate architecture is automatically
formed. The performance of the networks has been validated for inelastic shear
frames, as well as rocking structures, of which both are first built in finite
element program for dynamic analysis to generate training data. Results have
shown the developed networks can successfully predict the time-history response
of the shear frame and the rock structure subjected to real ground motion
records. The efficiency of the proposed neural networks is also examined, which
shows the computational time can be reduced by 43% by the neural networks
method than FE models. This indicates the trained networks can be utilized to
generate rocking spectrums of structures more efficiently which demands a large
number of time-history analyses.
