Simulation of Random Processes in the Fatigue Problem under Variable Loading

The method is proposed to generate random processes with stable integral characteristics of cumulative distributions, which at the same time are random in nature. The algorithm consists of the two steps. The first one is generation of the random extrema sequence using the objective Markovian matrix, completed with in-service loading data. The extrema and their sequence are shown to be of importance for the metal fatigue assessment. Therefore, random testing with extrema control is more advantageous as compared to testing with the generation of spectral densities. The next step is the random process generation with its first continuous derivative. The concatenation procedure was proposed to create the continuous function reconstruction with the pointwise specification (local maxima and minima sequence). The regression analysis of two random variables was used to evaluate the frequency component. Spectral analysis of such a continuous process results in the spectral density function, which finds its application in some methods of random fatigue estimation. The major trait of the proposed method is the coincidence of the rain-flow cycle counting characteristics of the initial and resulting processes.