A stochastic approach for generating individual jumping loads considering different jumping force patterns

Abstract

This study establishes a stochastic model for generating individual jumping force signals based on a database of individual jumping force records. A total of 1296 vertical jumping loads at a jumping frequency of 1.5–3.5 Hz were experimentally measured with high quality. To generate a jumping ground reaction forces (GRFs) curve, the proportions of different force patterns were first obtained based on the database and subsequently used to assign the numbers of individual jumping pulses for different force patterns. Then, a half-sine square function, three Gauss superposition functions, and two Gauss superposition functions were respectively used to generate ‘single-peaked’, ‘double-peaked’, and ‘merging’ shape jumping forces. To reflect the near-periodic nature of the jumping forces, the function parameters and coefficients were randomly generated from their normal distributions, and these parameters and coefficients were assigned to each jumping force. Finally, the generated individual jumping pulses were randomly arranged and connected to form a jumping GRF signal. A comparison of the jumping load–time history curves and Fourier amplitude spectra between the measured and generated results verified the reliability of the model. Compared with the conventional half-sine model, the stochastic approach for generating jumping loads in this study can better reflect the temporal characteristics of the real jumping GRF signals, and the model is convenient to be applied in the vibration serviceability assessment of civil engineering structures, such as stadium stands. • A stochastic model to generate individual jumping loads was established based on a database of 1296 vertical jumping force records. • Different jumping force shapes can be described by the model. • Comparison of jumping load time-history curves and the Fourier amplitude spectra between measured and generated results verified the model's reliability. • The coefficient of correction for the jumping impact factor parabolically varies with the increase of the jumping frequency from 1.5 to 3.5 Hz.