A probabilistic study of the robustness of an adaptive neural estimation method for hysteretic internal forces in nonlinear MDOF systems

Abstract The Volterra/Wiener neural network (VWNN) has been shown to be an effective tool for on-line estimation of non-linear restoring forces and responses. However, the power of the VWNN for on-line identification has not been fully harnessed due to the high sensitivity of its parameters. This study adopts a probabilistic approach in examining the effects of the VWNN's parameters on the robustness and stability of its estimation capabilities. Large ensembles of simulations were conducted in which random (earthquake-like) ground motions were used to excite representative non-linear structures, and on-line estimation of their acceleration responses was performed. The nonlinearity in the system was introduced via hysteretic restoring forces, and a variety of cases were tested, including softening and hardening. The results showed that each design parameter within the VWNN was linked to a certain type of performance sensitivity. The adaptive gain that controls the change in the weights of the VWNN was also directly linked to the stability of the estimates, as small increases in the gain led to the estimates diverging. Within the neural network, the weight within the transfer function was found to directly correlate with accuracy. The optimum set of parameters for a given excitation often produced unstable solutions for other excitations, but by understanding the relationships between the parameters and their sensitivities, a set of parameters could be carefully chosen to consistently produce accurate and stable on-line estimates for all simulations. The knowledge gained from the relationships between VWNN parameters also allowed for informed decisions on parameter sets for simulations involving different classes of nonlinearities. Offering users a starting point provides a necessary and helpful feature so often missing from other non-linear identification schemes that deal with non-parametric identification of complex nonlinear systems.

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