Random process simulation for stochastic fatigue analysis

Abstract

A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment, E(R\sp{\rm m}), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is found to be 9 to 13 times faster than the Gaussian technique and to produce comparable values for E(R\sp{\rm m}) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode. A key parameter in the autoregressive model is the correlation coefficient \rho\sb1 between adjacent extrema. A linear regression of \rho\sb1 on Vanmarcke's bandwidth parameter is presented as a practical description of \rho\sb1's dependence on bandwidth for both unimodal and bimodal psd's. The effect of psd shape on the expected fatigue damage rate is also investigated. For bimodal psd's, the contribution of the two frequency components to the damage rate is determined for frequency ratios from 1.5 to 15. The relative contribution of the two modes is measured by a parameter b which is the ratio of the mean squared value of the high frequency component to that of the other component. It is found that both components must be considered for b values from 0.01 to 10. The effect of high frequency truncation of the psd on the expected damage rate is also studied for two unimodal psd's