PSD-to-Rainflow Vibration Fatigue Screener

Concept

A drop-in fatigue post-processor for durability and CAE teams. The user supplies a power spectral density (PSD) of a stationary random loading environment — measured by accelerometers on a physical article or produced directly by frequency-domain finite element analysis of a component. The module applies the closed-form expression derived in the source work (via Monte Carlo simulation and digital time-history generation) that maps any input PSD to the probability density function of rainflow counted ranges, together with the companion closed form for the distribution of ordinary ranges. It then combines that range distribution with the material's strain-life/S-N curve to output expected fatigue damage and crack-initiation life, with the range PDF providing natural confidence bands. The single wedge: collapse the usual "measure PSD → synthesize a representative time history → rainflow count it → assess damage" pipeline into one direct spectral calculation, so random-vibration fatigue screening becomes a routine post-processing step on frequency-domain FE results. Scope is deliberately limited to stationary, ergodic random processes — the regime the closed-form link was derived and validated for — with non-stationary histories routed to conventional time-domain rainflow counting instead.

Why now

The source thesis demonstrates, using a Monte Carlo approach and digital simulation techniques, a closed-form expression defining the probability density function of rainflow counted ranges for any given power spectral density of a stationary and ergodic random process, plus a closed-form expression for the distribution of ordinary ranges. It explicitly motivates this search by the increased use of finite element analysis offering frequency-domain information about components — meaning the PSD inputs the method consumes are already standard outputs of CAE and test instrumentation. The same work establishes confidence in the rainflow method for better fatigue life predictions and shows that range-pair, Wetzel's and rainflow counting give identical counts whenever a service history starts and ends at an extreme peak, so the spectral route is anchored to the same counting method trusted in time-domain analysis. Together these results make a direct PSD-to-damage calculation a defensible product rather than a heuristic.