I am calculating pressure derivatives using algorithms from this PDF:
I have been able to implement the "two-points" and "three-consecutive-points" methods relatively easily using dplyr's lag/lead functions to offset the original columns forward and back one row.
The issue with those two methods is that there can be a ton of noise in the high resolution data we use. This is why there is the third method, "three-smoothed-points" which is significantly more difficult to implement. There is a user-defined "window width",W, that is typically between 0 and 0.5. The algorithm chooses point_L and point_R as being the first ones such that ln(deltaP/deltaP_L) > W and ln(deltaP/deltaP_R) > W. Here is what I have so far:
#If necessary install DPLYR
#install.packages("dplyr")
library(dplyr)
#Create initial Data Frame
elapsedTime <- c(0.09583, 0.10833, 0.12083, 0.13333, 0.14583, 0.1680,
0.18383, 0.25583)
deltaP <- c(71.95, 80.68, 88.39, 97.12, 104.24, 108.34, 110.67, 122.29)
df <- data.frame(elapsedTime,deltaP)
#Shift the elapsedTime and deltaP columns forward and back one row
df$lagTime <- lag(df$elapsedTime,1)
df$leadTime <- lead(df$elapsedTime,1)
df$lagP <- lag(df$deltaP,1)
df$leadP <- lead(df$deltaP,1)
#Calculate the 2 and 3 point derivatives using nearest neighbors
df$TwoPtDer <- (df$leadP - df$lagP) / log(df$leadTime/df$lagTime)
df$ThreeConsDer <- ((df$deltaP-df$lagP)/(log(df$elapsedTime/df$lagTime)))*
((log(df$leadTime/df$elapsedTime))/(log(df$leadTime/df$lagTime))) +
((df$leadP-df$deltaP)/(log(df$leadTime/df$elapsedTime)))*
((log(df$elapsedTime/df$lagTime))/(log(df$leadTime/df$lagTime)))
#Calculate the window value for the current 1 row shift
df$lnDeltaT_left <- abs(log(df$elapsedTime/df$lagTime))
df$lnDeltaT_right <- abs(log(df$elapsedTime/df$leadTime))
If you look at the picture linked above, you will see that based on a W of 0.1, only row 2 matches this criteria for both the left and right point. Just FYI, this data set is an extension of the data used in example 2.5 in the referenced PDF.
So, my ultimate question is this: How can I choose the correct point_L and point_R such that they meet the above criteria? My initial thoughts are some kind of while loop, but being an inexperienced programmer, I am having trouble writing a loop that gets anywhere close to what I am shooting for.
Thank you for any suggestions you may have!
