Rain-flow fatigue damage due to nonlinear combination of vector Gaussian loads

The problem of estimating the mean rain-flow fatigue damage in randomly vibrating structures is considered. The excitations are assumed to be through a vector of mutually correlated, stationary Gaussian loadings. The load effect leading to fatigue damage is considered to be a nonlinear function of the vector of excitation loads and is thus non-Gaussian. Its probabilistic characteristics are, however, unknown. The fatigue damage is assumed to follow a linear damage accumulation rule. Though exact expressions for the mean fatigue damage are difficult to determine, approximations and bounds for the mean rain-flow fatigue damage can be developed. Computing these quantities requires the mean level crossing statistics for the associated non-Gaussian response to be estimated. For the special case when the load effect can be expressed as quadratic combinations of Gaussian processes, analytical expressions are developed for computing the level crossing statistics. These, in turn, are used to determine approximations and the bounds for the mean fatigue damage. The applicability of the proposed method is demonstrated through a numerical example. With respect to this example, a comparative study on the quality of the bounds and the approximations is carried out viz–viz the predictions from existing techniques available in the literature.