Predicting the Maximum Displacements of Structures during an Earthquake based on Chaos Theory

The maximum displacements are an important index for the structural health monitoring (SHM) after an earthquake. However, the measurement of displacements is not easy compared to that of accelerations, and nonlinear structural identification is problematic. This study estimates displacements using input and output accelerations with a small database without assuming any physical models. A nonlinear-dynamics prediction algorithm based on chaos theory is proposed combining Takens’s embedding theorem and nearest-neighbor method. Using 12 ground motions in simulation and three motions in experimental cases, the maximum displacements are predicted with 8 % to 25 % mean absolute errors (MAEs). A practical method is developed for robustly and accurately evaluating displacements. • Displacements of structures are predicted by a data-driven method based on chaos theory. • Takens's embedding theorem and nearest-neighbor method are combined to apply to nonlinear responses. • The method was validated using nonlinear simulation and a full-scale multi-story reinforced concrete (RC) building experiment.