A bi-Gamma Distribution Model for a Broadband Non-Gaussian Random Stress Rainflow Range Based on a Neural Network

Abstract

A bi-Gamma distribution model is proposed to determine the probability density function (PDF) of broadband non-Gaussian random stress rainflow ranges during vibration fatigue. A series of stress Power Spectral Densities (PSD) are provided, and the corresponding Gaussian random stress time histories are generated using the inverse Fourier transform and time-domain randomization methods. These Gaussian random stress time histories are then transformed into non-Gaussian random stress time histories. The probability density values of the stress ranges are obtained using the rainflow counting method, and then the bi-Gamma distribution PDF model is fitted to these values to determine the model’s parameters. The PSD parameters and the kurtosis, along with their corresponding model parameters, constitute the neural network input–output dataset. The neural network model established after training can directly provide the parameter values of the bi-Gamma model based on the input PSD parameters and kurtosis, thereby obtaining the PDF of the stress rainflow ranges. The predictive capability of the neural network model is verified and the effects of non-Gaussian random stress with different kurtosis on the structural fatigue life are compared for the same stress PSD. And all life predicted results were within the second scatter band.