Implementation of low-kurtosis pseudo-random excitations to compensate for the effects of nonlinearity on damping estimation by the half-power method

摘要

Pseudo-random excitation with low crest factor is less likely to force a structure under test into nonlinear behavior, which should be avoided, or at least minimized, in the practice of experimental modal analysis. However, simply cutting high peaks and removing them from the excitation time history is not an option because such clipping of the signal introduces frequency distortions of the amplitude spectrum. A better approach is to manipulate phases of the harmonics before generating the time history instead of clipping it afterwards. To do so a new parameter, kurtosis, is used in this paper to characterize the high peak behavior of pseudo-random excitations. An analytical solution is obtained for how the phases should be selected in order to reduce kurtosis and make modal testing excitations smoother with less extreme peaks. This solution was implemented for evaluation of the damping ratio of a SDOF system by the half-power method in the presence of an additional cubic term in the equation of motion. The system response obtained by numerical integration was treated as modal analysis data and the result is that the kurtosis-optimized excitation has compensated for the effect of nonlinearity and allowed to identify the damping ratio with good precision whereas an ordinary Gaussian excitation with randomized phases caused an error of 75 percent. Comparison with the numerical crest factor minimization by time-frequency-domain swapping has been made and experimental results from a modal testing rig with a realistic turbine blade are also presented in the paper.