Energy Fluctuation Scale and Diffusion Models

The energy fluctuation scale, θE, of a narrow‐band Gaussian response is introduced. It is shown that E and associated bandwidth measures (e.g., 1/vOθE) are: (1) Simply related to both the spectral density and correlation functions of the response; (2) less sensitive to high frequency information and precise envelope definition than traditional bandwidth measures; and (3) consistent with diffusion models of various response quantities of interest. These diffusion models are found to simplify the practical analysis of a wide range of reliability problems (e.g., various first‐passage problems, statistics of extrema in narrow‐band responses, etc.). Further, because θE is related to statistics of envelope time averages, it has direct application to the analysis of fatigue damage and crack growth under stochastic loading.