Structural optimization for performance-based design in earthquake engineering: Applications of neural networks

This work addresses an approach to performance-based design in the context of earthquake engineering. The objective is the optimization of the total structural cost, under constraints related to minimum target reliabilities specified for the different limit states or performance requirements. The problem involves (1) the use of a nonlinear, time-stepping dynamic analysis to investigate the responses of relevance to the performances’ evaluation and (2) the integration of the responses into measures of damage accumulated during the earthquake. The random responses are deterministically obtained for different combinations of the design parameters and the intervening random variables, of which some are associated with the structure and some with the earthquake characteristics. The approach uses a neural network representation of the responses and, for each one, the variability associated with different earthquake records is accommodated by developing two networks: one for the mean response over the records, and another for the corresponding standard deviation. The neural network representation facilitates the estimation of reliability by Monte Carlo simulation, and the reliability achieved in each performance level, for a specific combination of the design parameters, is itself represented with a neural network. This is then used within an optimization algorithm for minimum total cost under reliability constraints. An application example uses a reinforced concrete, multi-storey plane structure with seismic demands corresponding to the city of Mendoza, Argentina.