Editing Rainflow-counting algorithm (section)

=== Pagoda roof method ===
This method considers the flow of water down of a series of pagoda roofs. Regions where the water will not flow identify the rainflow cycles which are seen as an interruption to the main cycle.

# Reduce the time history to a sequence of (tensile) peaks and (compressive) valleys.
# Imagine that the time history is a template for a rigid sheet ([[pagoda]] roof).
# Turn the sheet clockwise 90° (earliest time to the top).
# Each "tensile peak" is imagined as a source of water that "drips" down the pagoda.
# Count the number of half-cycles by looking for terminations in the flow occurring when either:
#* case ('''a''') It reaches the end of the time history;
#* case ('''b''') It merges with a flow that started at an earlier ''tensile peak''; or
#* case ('''c''') An opposite ''tensile peak'' has greater or equal magnitude.
# Repeat step 5 for ''compressive valleys''.
# Assign a magnitude to each half-cycle equal to the stress difference between its start and termination.
# Pair up half-cycles of identical magnitude (but opposite sense) to count the number of complete cycles. Typically, there are some residual half-cycles.

==== Example ====
[[File:Rainflow analysis for tensile peaks.svg|thumb|right|Figure 3: Rainflow analysis for tensile peaks]]

The stress history in Figure 2 is reduced to tensile peaks in Figure 3 and compressive valleys in Figure 4. From the tensile peaks in Figure 3:
*The first half-cycle starts at tensile peak 1 and terminates opposite a greater tensile stress, peak 3 (case '''c'''); its magnitude is 16 MPa (2 - (-14) = 16).
*The half-cycle starting at peak 9 terminates where it is interrupted by a flow from earlier peak 8 (case '''b'''); its magnitude is 16 MPa (8 - (-8) = 16).
*The half-cycle starting at peak 11 terminates at the end of the time history (case '''a'''); its magnitude is 19 MPa (15 - (-4) = 19).
Similar half-cycles are calculated for compressive stresses (Figure 4) and the half-cycles are then matched.

[[File:Rainflow analysis for compressive valleys.svg|thumb|right|Figure 4: Rainflow analysis for compressive valleys]]

{| class="wikitable"
! Stress (MPa)
! Whole cycles
! Half cycles
|-
|10
|2
|0
|-
|13
|0
|1
|-
|16
|1
|1
|-
|17
|0
|1
|-
|19
|0
|1
|-
|20
|1
|0
|-
|22
|1
|0
|-
|29
|0
|1
|}