Fatigue assessment of non-stationary random loading in the frequency domain by a quasi-stationary Gaussian approximation

The power spectral density (PSD) is a fundamental technique of random vibration fatigue providing an effective statistical characterization that can be processed by linear systems theory and load spectrum estimators. This lays the basis for a statistical-based fatigue assessment. While the PSD assembles a full stochastic characterization of stationary Gaussian loading, for loading subjected to changing operational, environmental, and excitational conditions, it provides no means of a fluctuating spectral density. Therefore, the PSD neither qualifies to characterize varying loads, nor reproduces comparable stress amplitudes to a referencing non-stationary excitation following a statistical-based stress analysis. Consequently, this paper employs the non-stationarity matrix to characterize the varying evolution of realistic loading and proposes a system of equations that decomposes this characterization into stationary Gaussian portions. The fundamental idea is to approximate realistic loading by abstracting a series of stationary segments, whose assembly in return embodies a full statistical characterization. The resulting quasi-stationary load definition better reflects the fatigue damage potential of realistic, nonstationary loading and allows to implement load spectrum estimators, ensuing computationally efficient and statistically robust structural lifetime predictions. Further, quasi-stationary load definitions are utilized to advance the concept of damage-equivalent statistical load definitions to be independent of a specific Miner exponent.