## Abstract

During every field test the test engineer is faced with a decision about when sufficient data has been collected to characterize a particular operation. This paper describes some statistical techniques for taking measured data and projecting what the expected time history and resulting fatigue damage would be if test data were collected for much longer times. Sufficient data has been collected when the fatigue damage computed from both the measured and the expected time histories converge.

History

Life

Maximum

Minimum

Original

29,890

1.89

-2.12

10X

26,760

2.25

-2.50

100X

16,170

2.88

-3.25

1000X

10,190

3.25

-3.63

## Rainflow Reconstruction

The objective of rainflow reconstruction is to obtain a time history that will have similar fatigue damage as the original rainflow histogram[5]. In essence, we wish to perform rainflow counting backwards. Starting with the rainflow histogram, reconstruct a time history, cycle by cycle, that has the same rainflow count. The largest overall cycle in the histogram is known. In the To-From format, rainflow counting distinguishes the difference between a Peak-Valley-Peak (PV) cycle and a Valley-Peak-Valley (VP) cycle. VP cycles are stored above the principle diagonal of the histogram and PV cycles below. The row of the histogram is less than the column for any VP cycle. Similarly, the column is less than the row for any PV cycle. The process for inserting VP cycles is illustrated in Fig. 7. The numbers on the left indicate histogram bins, row or column, and are proportional to the magnitude of the resulting loading history. The reconstructed time history is denoted P and V and the cycle to be inserted is denoted as r and c. Figure 7. Inserting a VP cycle An VP cycle ( r < c ) can be inserted into any PV reversal if c <= P and r > V. A VP cycle can not be inserted into a PV cycle of the same magnitude. Figure 8. Insertion of a PV cycle Figure 8 shows the insertion of a PV cycle. An PV cycle ( c < r ) can be inserted into any VP reversal if r < P and c >= V. A PV cycle can not be inserted into a VP cycle of the same magnitude. These two simple rules provide the basis for rainflow reconstruction. The process starts with the largest cycle either PVP or VPV. The next largest cycle is then inserted in an appropriate location in the reconstructed time history. After the first few cycles, there are many possible locations to insert a smaller cycle. All possible insertion locations are determined and one is selected at random.

## Summary

Reliability of a vehicle or structure is influenced by the distribution of loading during the entire service usage. A technique for estimating the long term durability from short term measured loads has been described.

## References

[1] Dressler, K, B. Grunder, M. Hack and V.B. Koettgen, "Extrapolation of rainflow matrices", SAE Paper 960569, 1996
[2] Silverman, B.W. "Density estimation for statistics and data analysis" Chapman and Hall, New York, 1986
[3] Scott, D.W. "Multivariate density estimation" Wiley, New York, 1992
[4] Roth, J.S. "Statistical modeling of rainflow histograms" Materials Engineering-Mechanical Behavior Report No. 182, UILU-ENG 98-4017, University of Illinois, 1998
[5] Khosrovaneh, A.K. and N.E. Dowling, "Fatigue loading history reconstruction based on the rainflow technique", International Journal of Fatigue, Vol. 12, No. 2, 1990, 99-106