Cycle counting methods for bi-modal stationary Gaussian processes

The cycle counting procedure is a fundamental step in the fatigue analysis of structures. This paper is devoted to cycle counting methods, starting from the spectral properties of the loading process. Cycle counting methods for stationary Gaussian narrow-band and broad-band processes proposed in literature are discussed. Focusing attention on bi-modal processes, which are usual in dynamic response of structures, the cycles histograms obtained by the Peak and Peak-Valley Counting methods are expressed in closed form. From these, a couple of upper and lower bounds for the mean total damage and for the mean fatigue life are obtained. Then, an advanced formulation of the cycle counting is developed, obtaining a new closed form solution of the cycles histogram which better approximate the Rainflow Counting results. The proposed method is finally applied to several different bi-modal processes, comparing the results with other criteria and with solutions based on simulated time-histories.