Zero Crossings, Peaks, and Other Statistical Measures of Random Responses

Abstract

A survey is made of statistical information that can be calculated for the stationary random response of nonlinear oscillators. The average frequency of zero crossings can be obtained using Rice's method, if the joint distribution of response displacement and response velocity is known. For lightly damped systems, an approximation can be obtained. if the deterministic amplitude-frequency relation for the nonlinear system is known. For lightly damped systems, the probability density distributions for peaks and envelopes can often be calculated. From these distributions follow other statistics, such as the autocorrelation function for the envelope, the expected size of clumps of cycles above a threshold. and the expected fatigue damage due to linear-damage accumulation.