Research on multi-response kurtosis control of linear structures under multiple correlated non-stationary excitations using a novel high-order moment estimation method

Abstract

The kurtosis of stress responses can significantly accelerate the fatigue damage process of structures, making it a key parameter in the assessment of structural fatigue damage under non-stationary and non-Gaussian random excitation. However, a kurtosis transfer model for linear systems under multiple excitations has not yet been established, presenting challenges for the control of response kurtosis. To address this issue, this paper first derives the theoretical formula for evaluating the second and fourth order mixed moments of random signals and establishes a method for evaluating the mixed moments of response components based on amplitude and phase. A transfer formula for kurtosis from multiple non-stationary excitations to multiple responses is then derived. Finally, based on the kurtosis transfer formula, an active control method for multiple response kurtoses is proposed. Simulations show that the proposed kurtosis transfer model can adapt to variations in multiple parameters of non-stationary excitation forces and evaluate response kurtosis with high accuracy. The evaluation of response kurtoses in experiments is significantly influenced by resonance peaks, but using the averaged frequency response function still allows for accurate evaluation of response kurtosis with acceptable precision. Both simulations and experiments demonstrate that the proposed kurtosis control algorithm can achieve kurtosis control in various situations, with the control speed and accuracy being influenced by the power value in the algorithm.