tire {Splinets}

Data on tire responses to a rough road profile

Description

These are simulated data of tire responses to a rough road at the high-transient event. The simulations have been made based on the fit of the so-called Slepian model to a non-Gaussian rough road profile. Further details can be found in the reference. The responses provided are measured at the wheel and thus describing the tire response. There are 100 functional measurments, kept column-wise in the matrix. Additionally, the time instants of the measurements are given as the first column in the matrix. Since the package uses the so-called "lazy load", the matrix is directly available without an explicit load of the data. This means that data(tire) does not need to be invoked. The data were saved using compress='xz' option, which requires 3.5 or higher version of R. The data are uploaded as a dataframe, thus as.matrix(tire) is needed if the matrix form is required.

Usage

data(tire)

Format

numerical 4095 x 101 dataframe: tire

References

Podg\mbox{\'o}rski, K, Rychlik, I. and Wallin, J. (2015) Slepian noise approach for gaussian and Laplace moving average processes. Extremes, 18(4):665–695, <doi:10.1007/s10687-015-0227-z>.

See Also

truck for a related dataset;

Examples

#-----------------------------------------------------#
#----------- Plotting the trucktire data -------------#
#-----------------------------------------------------#

#Activating data:
 data(tire)
 data(truck)
 
 matplot(tire[,1],tire[,2:11],type='l',lty=1) #ploting the first 10 tire responses
 
 matplot(truck[,1],truck[,2:11],type='l',lty=1) #ploting the first 10 truck responses
 
 #Projecting truck data into splinet bases
 knots1=seq(0,50, by=2)
 Subtruck= truck[2048:3080,] # selecting the truck data that in the interval[0,50]
 TruckProj=project(as.matrix(Subtruck),knots1)
 
 MeanTruck=matrix(colMeans(TruckProj$coeff),ncol=dim(TruckProj$coeff)[2])
 MeanTruckSp=lincomb(TruckProj$basis,MeanTruck)
 
 plot(MeanTruckSp) #the mean spline of the projections
 
 plot(TruckProj$sp,sID=1:10) #the first ten projections of the functional data
 
 Sigma=cov(TruckProj$coeff)
 Spect=eigen(Sigma,symmetric = TRUE)
 
 plot(Spect$values, type ='l',col='blue', lwd=4 ) #the eigenvalues
 
 EigenTruckSp=lincomb(TruckProj$basis,t(Spect$vec))
 plot(EigenTruckSp,sID=1:5) #the first five largest eigenfunctions