Virkler25 {HMMRel} | R Documentation |
Fatigue crack growth in materials: Virkler dataset (tests 1 to 25)
Description
The data consist of an aluminum alloy specimen that was tested to investigate fatigue crack propagation. Starting from an initial crack of length 9 mm for a particular item in test, the number of cycles for the size of the crack to reach a predetermined value was recorded successively. That is, it is registered the number of cycles every time an increment of size 0.2 mm in length occurs. The experiment finishes once a critical size of the crack is reached, meaning the failure of the item. The data were first published in Virkler et al. (1979) where there were 68 specimens tested to grow the initial crack of 9 mm to the final crack of 50 mm. The first 25 tests are included.
Format
A data frame with 26 variables:
- CrackLength
Length of the crack in the material.
- CycleCount1
Cycle count for the first test.
- CycleCount2
Cycle count for the second test.
- CycleCount3
Cycle count for the third test.
- CycleCount4
Cycle count for the fourth test.
- CycleCount5
Cycle count for the fifth test.
- CycleCount6
Cycle count for the sixth test.
- CycleCount7
Cycle count for the seventh test.
- CycleCount8
Cycle count for the eighth test.
- CycleCount9
Cycle count for the ninth test.
- CycleCount10
Cycle count for the tenth test.
- CycleCount11
Cycle count for the eleventh test.
- CycleCount12
Cycle count for the twelfth test.
- CycleCount13
Cycle count for the thirteenth test.
- CycleCount14
Cycle count for the fourteenth test.
- CycleCount15
Cycle count for the fifteenth test.
- CycleCount16
Cycle count for the sixteenth test.
- CycleCount17
Cycle count for the seventeenth test.
- CycleCount18
Cycle count for the eighteenth test.
- CycleCount19
Cycle count for the nineteenth test.
- CycleCount20
Cycle count for the twentieth test.
- CycleCount21
Cycle count for the twenty-first test.
- CycleCount22
Cycle count for the twenty-second test.
- CycleCount23
Cycle count for the twenty-third test.
- CycleCount24
Cycle count for the twenty-fourth test.
- CycleCount25
Cycle count for the twenty-fifth test.
References
Virkler, D. A., Hillberry, B. M., and Goel, P. K. (1979). The statistical nature of fatigue crack propagation. Journal of Engineering Materials and Technology, 101 , 148–153 .
Examples
data(Virkler25)
i<-1 ## choose specimen number 1
ti<-Virkler25[,(i+1)]/10000 ## cycles at which the cracksize increases 0.2 units.
yt<-Virkler25[,1] ##
### the system is observed every 2000 cycles (0.2 unit times)
### observations:
t.obs<-seq(0,max(ti),by=0.2)
yi<-approx(x=ti,y=yt,xout=t.obs,method='linear',rule=2)$y
yi<-diff(yi)
#discretize the observations:
yi<-kmeans(yi,4)$cluster ## consider an alphabet of 4 signals
Nx<-2; # consider 2 hidden states
Ny<-4
alpha0<-c(1,0)
estim<-fit.hmmR(Y=yi,P0=NA,M0=NA,alpha0=alpha0,max.iter=50,epsilon=1e-9,Nx=Nx,Ny=Ny)
estim$P
estim$M