COMPARISON OF ANALYTICAL COUNTING METHODS FOR GAUSSIAN-PROCESSES

For structural components under random loading, realistic fatigue life predictions require a damage accumulation law together with a cycle counting method. If the classical, linear and memory-less summation rule according to Palmgren/Miner is adopted and the underlying stress process is ergodic substantial simplifications can be reached. From experiments and certain theoretical considerations, so-called rainflow range or local range counting appears most appropriate. Even if the underlying is a Gaussian process, easy analytical solutions are at most available for special types of processes. Therefore, counting usually must be done numerically at observed or artificial stress histories which is extremely time consuming. But a number of approximations exist. Several of them are reviewed and tested against simulations for a variety of bandwidths and shapes of stress spectra. While most of the prediction equations overestimate the moments of the two selected types of ranges, the equation provided by Dirlik is shown to have the best fit with respect to the simulated rainflow ranges. Naboishikov's formula proves to be the most accurate predictor for local ranges whenever the irregularity factor alpha is larger than 0.6.