Dynamic Analysis of Nonlinear Frames by Prandtl Neural Networks

Abstract

A new type of activation function, based on the use of the Prandtl–Ishlinskii operator, has been developed and used in the feed forward neural networks in order to improve their capabilities in learning to identify and analyze nonlinear structures subject to dynamic loading. The genetic algorithm has been used in its training. The neural network, which is referred to as the Prandtl neural network here, has been trained and used in the analysis of two shear frames, a single degree of freedom (SDOF) and a 3DOF, both subjected to earthquake excitations. To assess the capabilities of the Prandtl neural network under ideal situations, the data on the response of the frames have been obtained through the integration of their governing nonlinear equations of motion. The training has been based on the white noise while the strong earthquakes of 200% El Centro in 1940 and Gilroy have been used for testing. Results have shown the high precision of the Prandtl neural network in solving highly hysteretic problems. The issue is important for two main applications in structural dynamics and control: (1) analysis of highly nonlinear structures where it is desired to train a neural network to directly learn the behavior of a structure from experimental data; and (2) intelligent active control of structures where neural network emulators are designed to provide as precise predictions about the future response of the structures as possible, in order to be used in the determination of the required control forces.