Rainflow Matrix Beispiel Essay

Algorithms

Fatigue analysis studies how damage accumulates in an object subjected to cyclical changes in stress. The number of cycles necessary to break the object depends on the cycle amplitude. Broadband input excitation contains cycles of diverse amplitude, and the presence of hysteresis in the object has the effect of nesting some cycles within others, either completely or partially. Rainflow counting estimates the number of load change cycles as a function of cycle amplitude.

Initially, turns the load history into a sequence of reversals. Reversals are the local minima and maxima where the load changes sign. The function counts cycles by considering a moving reference point of the sequence, Z, and a moving ordered three-point subset with these characteristics:

  1. The first and second points are collectively called X.

  2. The second and third points are collectively called Y.

  3. In both X and Y, the points are sorted from earlier to later in time, but are not necessarily consecutive in the reversal sequence.

  4. The range of X, denoted by r(X), is the absolute value of the difference between the amplitude of the first point and the amplitude of the second point. The definition of r(Y) is analogous.

The algorithm is as follows:

At the end, the function collects the different cycles and half-cycles and tabulates their ranges, their means, and the points at which they start and end. This information can then be used to produce a histogram of cycles.

Consider the following reversal sequence:

StepZReversalsThree Reversals?Yr(Y)Xr(Y)r(X) < r(Y)?Z in Y?Actions
1AA, B, CYesAB3BC4NoYes
  1. Count AB as ½ cycle.

  2. Discard A.

  3. Set Z to B.

2BB, CNoRead D.
3BB, C, DYesBC4CD8NoYes
  1. Count BC as ½ cycle.

  2. Discard B.

  3. Set Z to C.

4CC, DNoRead E.
5CC, D, EYesCD8DE6YesRead F.
6CC, D, E, FYesDE6EF4YesRead G.
7CC, D, E, F, GYesEF4FG7NoNo
  1. Count EF as 1 cycle.

  2. Discard E and F.

8CC, D, GYesCD8DG9NoYes
  1. Count CD as ½ cycle.

  2. Discard C.

  3. Set Z to D.

9DD, GNoRead H.
10DD, G, HYesDG9GH8YesRead J.
11DD, G, H, JYesGH8HJ7YesRead K.
12DD, G, H, J, KYesHJ7JK4YesRead L.
13DD, G, H, J, K, LYesJK4KL3YesRead M.
14DD, G, H, J, K, L, MYesKL3LM5NoNo
  1. Count KL as 1 cycle.

  2. Discard K and L.

15DD, G, H, J, MYesHJ7JM5YesRead N.
16DD, G, H, J, M, NYesJM5MN1YesRead P.
17DD, G, H, J, M, N, PYesMN1NP4NoNo
  1. Count MN as 1 cycle.

  2. Discard M and N.

18DD, G, H, J, PYesHJ7JP9NoNo
  1. Count HJ as 1 cycle.

  2. Discard H and J.

19DD, G, PYesDG9GP10NoYes
  1. Count DG as ½ cycle.

  2. Discard D.

  3. Set Z to G.

20GG, POut of data

Count GP as ½ cycle.

Now collect the results.

Cycle CountRangeMeanStartEnd
½3–0.5AB
½4–1BC
141EF
½81CD
13–0.5KL
112.5MN
170.5HJ
½90.5DG
½101GP

Compare this to the result of running on the sequence:

q = rainflow([-2 1 -3 5 -1 3 -4 4 -3 1 -2 3 2 6])
q = 0.5000 3.0000 -0.5000 1.0000 2.0000 0.5000 4.0000 -1.0000 2.0000 3.0000 1.0000 4.0000 1.0000 5.0000 6.0000 0.5000 8.0000 1.0000 3.0000 4.0000 1.0000 3.0000 -0.5000 10.0000 11.0000 1.0000 1.0000 2.5000 12.0000 13.0000 1.0000 7.0000 0.5000 8.0000 9.0000 0.5000 9.0000 0.5000 4.0000 7.0000 0.5000 10.0000 1.0000 7.0000 14.0000

References

[1] ASTM Standard E 1049, 1985 (2011). "Standard Practices for Cycle Counting in Fatigue Analysis." West Conshohocken, PA: ASTM International, 2011.

Introduced in R2017b

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