Rainflow Counting

Peak-and-valley simply counts consecutive peaks and valleys without considering their matching; level-crossing counts how many times stress crosses a threshold. Rainflow is superior because it pairs reversals according to the 'rain-flow' rule, matching the physical stress-strain hysteresis cycles in the material. This makes rainflow more accurate for irregular, non-stationary loading.

Imagine rain falling on a roof with peaks and valleys. A drop rolls downhill until it hits a valley or a level equal to its starting height, matching that pair as a cycle. In the algorithm, you scan the stress history left to right, extract half-cycles by matching each reversal with another reversal of opposite sign at a similar level, or until interrupted by a larger reversal. Different variants (three-point, four-point) have been proposed, but the four-point algorithm is standard.

Yes, if your data contains noise. High-frequency oscillations or measurement noise will create spurious peaks and valleys, inflating cycle counts and damage predictions. Apply a low-pass filter or smoothing window before extracting turning points. However, be careful not to lose real, small-amplitude reversals that contribute to fatigue.

Rainflow counting itself is agnostic to the damage model. You can use it to extract cycles and then apply a crack-growth law (e.g., Paris equation) instead of Miner's rule. However, crack propagation is nonlinear and sequence-dependent, so linear cumulative damage assumptions may not hold. For corrosion-fatigue, rainflow with adjusted S-N curves (e.g., using lower fatigue strength) is a practical approach.

Rainflow gives you a histogram of cycle amplitudes and mean stresses. You compare each cycle to the S-N curve (or Goodman diagram) for your material and design stress level to compute damage fraction. Sum damage fractions using Miner's rule; if the sum exceeds 1, failure is expected. Use this to size components, select materials, or reduce design stresses.