Stochastic analysis of Poisson impact series using discrete form, spectrum analysis and time correlation

Abstract

A stochastic model based on Poisson impact series is developed from a random pulse train model. Using the discrete form of the expectation function, first- and second-order time correlation functions are generated. Then, the force and power spectral density functions are generated by the Fourier transform of the first- and second-order correlation functions, respectively. Experimental force and power spectra are compared with those from the developed model and an existing model using single, multiple and ensemble averaged impact samples. Overlapping and consistent matching occur in most of the regions in these comparisons. The effects of noise and pulse shape deviation are discussed. It is shown theoretically and experimentally that the signal-to-noise ratio increases with the impaction rate. Using ensemble averages of a 100 samples, the impact magnitude and its arrival time is validated to be Gaussian and Uniformly distributed. The signal-to-error ratio increases with the number of ensemble averages. The established model is utilised to carry out modal tests of a space truss. Comparing modal parameters, such as mode shapes, natural frequencies, and damping ratios, consistent matching is observed with those obtained from the random noise test.