commit 0fda1b187f09aed54ecbbb5c3268e88d462da040
parent 39c7a388abf35e1f90074d2151d6c1d695806f57
Author: Ivan Gankevich <i.gankevich@spbu.ru>
Date: Mon, 26 Apr 2021 16:06:53 +0300
Add comparison graph.
Diffstat:
6 files changed, 197 insertions(+), 31 deletions(-)
diff --git a/Makefile b/Makefile
@@ -23,6 +23,7 @@ build/main.pdf: build/gnuplot/velocity-xy-dist-min.eps
build/main.pdf: build/gnuplot/direction-dist.eps
build/main.pdf: build/gnuplot/acf.eps
build/main.pdf: build/gnuplot/hold-peak.eps
+build/main.pdf: build/gnuplot/vtestbed.eps
#build/main.pdf: build/gnuplot/anemometer.eps
#build/main.pdf: build/gnuplot/anemometer.svg
build/main.pdf:
@@ -66,6 +67,7 @@ build/gnuplot/velocity-xy-dist-max.svg: gnuplot/velocity-xy-dist.gnuplot build/g
gnuplot -d -c gnuplot/velocity-xy-dist.gnuplot max
build/gnuplot/direction-dist.svg: build/gnuplot/direction_rmse.gnuplot
+build/gnuplot/vtestbed.svg: gnuplot/vtestbed.gnuplot
#build/main.zip: build/gnuplot/*.eps main.tex
build/main.zip: main.tex
diff --git a/R/distributions.R b/R/distributions.R
@@ -216,13 +216,19 @@ fit_velocity_acf <- function (velocity, plot=TRUE, axis="x", timestamp=0, write=
if (debug) {
plot(acf_x$lag, acf_x$acf, xlab='Lag', ylab=paste('DEBUG ACF', axis))
}
- model <- nls(acf ~ a*exp(-abs(b*lag)**c),
- data=acf_x,
- start=list(a=1,b=1,c=1),
- control=list(warnOnly=TRUE),
- algorithm="port",
- lower=c(0,0,1e-6), upper=c(1000,1000,10))
- c <- summary(model)$coefficients
+ v_mean <- mean(velocity)
+ c <- tryCatch({
+ model <- nls(acf ~ a*exp(-abs(b*lag)**c),
+ data=acf_x,
+ start=list(a=1,b=1,c=1),
+ control=list(warnOnly=TRUE),
+ algorithm="port",
+ lower=c(0,0,1e-6), upper=c(1000,1000,10))
+ c <- summary(model)$coefficients
+ },error=function(cond) {
+ message(cond)
+ c(1,1,1)
+ })
acf_est <- c[[1]]*exp(-abs(c[[2]]*acf_x$lag)**c[[3]])
if (plot) {
plot(acf_x$lag, acf_x$acf, xlab='Lag', ylab=paste('ACF', axis))
diff --git a/R/vtestbed.R b/R/vtestbed.R
@@ -23,7 +23,7 @@ data$direction <- direction(data$wind_velocity_x,data$wind_velocity_y)
#hist(data$direction)
-do_fit_velocity <- function (velocity) {
+do_fit_velocity <- function (velocity, suffix="no-suffix") {
velocity_hist <- normalize_hist(hist(velocity, plot=FALSE, breaks=100))
x = velocity_hist$x;
v = velocity_hist$density;
@@ -32,10 +32,15 @@ do_fit_velocity <- function (velocity) {
plot(x, dist$actual_density, xlab='Wind speed', ylab='PDF')
lines(d, col='green', lwd=2)
lines(dist$x, dist$estimated_density, col='red', lwd=2)
+ path <- file.path('build', 'vtestbed', suffix)
+ make_directory(path)
+ filename <- file.path(path, "velocity")
+ write.table(data.frame(x=dist$x,actual=dist$actual_density,estimated=dist$estimated_density),
+ filename, row.names=FALSE, quote=FALSE)
dist
}
-do_fit_direction <- function (direction) {
+do_fit_direction <- function (direction, suffix="no-suffix") {
hist <- normalize_hist(hist(direction, plot=FALSE, breaks=1000))
x = hist$x;
v = hist$density;
@@ -44,14 +49,24 @@ do_fit_direction <- function (direction) {
plot(x, dist$actual_density, xlab='Direction', ylab='PDF')
lines(d, col='green', lwd=2)
lines(dist$x, dist$estimated_density, col='red', lwd=2)
+ path <- file.path('build', 'vtestbed', suffix)
+ make_directory(path)
+ filename <- file.path(path, "direction")
+ write.table(data.frame(x=dist$x,actual=dist$actual_density,estimated=dist$estimated_density),
+ filename, row.names=FALSE, quote=FALSE)
dist
}
-do_fit_acf <- function (velocity, axis="x") {
+do_fit_acf <- function (velocity, axis="x", suffix="no-suffix") {
v = velocity
model <- fit_velocity_acf(v, axis=axis, plot=FALSE, write=FALSE);
plot(model$lag, model$actual, xlab='Lag', ylab=paste('ACF ', axis, sep=""))
lines(model$lag, model$estimated, col='red', lwd=2)
+ path <- file.path('build', 'vtestbed', suffix)
+ make_directory(path)
+ filename <- file.path(path, sprintf("acf-%s", axis))
+ write.table(data.frame(lag=model$lag,actual=model$actual,estimated=model$estimated),
+ filename, row.names=FALSE, quote=FALSE)
model
}
@@ -62,18 +77,54 @@ banner <- function (str) {
}
banner("Virtual testbed")
-dist_speed <- do_fit_velocity(data$speed)
-dist_direction <- do_fit_direction(data$direction)
-#model_acf_x <- do_fit_acf(data$wind_velocity_x, axis="X")
-model_acf_y <- do_fit_acf(data$wind_velocity_y, axis="Y")
-#model_acf_z <- do_fit_acf(data$wind_velocity_z, axis="Z")
+dist_speed <- do_fit_velocity(data$speed, suffix="vtb")
+dist_direction <- do_fit_direction(data$direction[data$direction<=0], suffix="vtb")
+model_acf_x <- do_fit_acf(data$wind_velocity_x, axis="X", suffix="vtb")
+model_acf_y <- do_fit_acf(data$wind_velocity_y, axis="Y", suffix="vtb")
+model_acf_z <- do_fit_acf(data$wind_velocity_z, axis="Z", suffix="vtb")
banner("Anemometer")
data_real <- select_samples(time_start, time_delta)
-dist_speed_real <- do_fit_velocity(data_real$speed)
-dist_direction_real <- do_fit_direction(data_real$direction)
-model_acf_x <- do_fit_acf(data_real$x[data_real$x<=0], axis="X")
-model_acf_y <- do_fit_acf(data_real$y[data_real$y<=0], axis="Y")
-model_acf_z <- do_fit_acf(data_real$z[data_real$z<=0], axis="Z")
+dist_speed_real <- do_fit_velocity(data_real$speed, suffix="anem")
+dist_direction_real <- do_fit_direction(data_real$direction[data_real$direction<=0], suffix="anem")
+model_acf_x_real <- do_fit_acf(data_real$x[data_real$x<=0], axis="X", suffix="anem")
+model_acf_y_real <- do_fit_acf(data_real$y[data_real$y<=0], axis="Y", suffix="anem")
+model_acf_z_real <- do_fit_acf(data_real$z[data_real$z<=0], axis="Z", suffix="anem")
-#print(data)
+# https://stackoverflow.com/questions/27455948/in-r-whats-the-simplest-way-to-scale-a-vector-to-a-unit-vector
+normalise <- function(x) {
+ x <- as.vector(x)
+ s <- max(abs(x))
+ if (s == 0) {
+ ret <- x
+ } else {
+ ret <- x/s
+ }
+ ret
+}
+
+banner("Comparison")
+plot(dist_speed$x, normalise(dist_speed$actual_density), xlab='Wind speed', ylab='PDF')
+lines(dist_speed$x, normalise(dist_speed$estimated_density), col='red', lwd=2)
+points(dist_speed_real$x, normalise(dist_speed_real$actual_density), col='blue')
+lines(dist_speed_real$x, normalise(dist_speed_real$estimated_density), col='blue', lwd=2)
+
+plot(dist_direction$x, normalise(dist_direction$actual_density), xlab='Wind direction', ylab='PDF')
+lines(dist_direction$x, normalise(dist_direction$estimated_density), col='red', lwd=2)
+points(dist_direction_real$x, normalise(dist_direction_real$actual_density), col='blue')
+lines(dist_direction_real$x, normalise(dist_direction_real$estimated_density), col='blue', lwd=2)
+
+plot(model_acf_x$lag, model_acf_x$actual, col='red', xlab='Lag', ylab="ACF X")
+lines(model_acf_x$lag, model_acf_x$estimated, col='red', lwd=2)
+points(model_acf_x_real$lag, model_acf_x_real$actual, col='blue')
+lines(model_acf_x_real$lag, model_acf_x_real$estimated, col='blue', lwd=2)
+
+plot(model_acf_y$lag, model_acf_y$actual, col='red', xlab='Lag', ylab="ACF Y")
+lines(model_acf_y$lag, model_acf_y$estimated, col='red', lwd=2)
+points(model_acf_y_real$lag, model_acf_y_real$actual, col='blue')
+lines(model_acf_y_real$lag, model_acf_y_real$estimated, col='blue', lwd=2)
+
+plot(model_acf_z$lag, model_acf_z$actual, col='red', xlab='Lag', ylab="ACF Z")
+lines(model_acf_z$lag, model_acf_z$estimated, col='red', lwd=2)
+points(model_acf_z_real$lag, model_acf_z_real$actual, col='blue')
+lines(model_acf_z_real$lag, model_acf_z_real$estimated, col='blue', lwd=2)
diff --git a/gnuplot/vtestbed.gnuplot b/gnuplot/vtestbed.gnuplot
@@ -0,0 +1,66 @@
+set terminal svg size 450,450/2 font 'Free Serif, 10' enhanced round dynamic
+set xtics nomirror out offset 0,0.5
+set ytics nomirror out offset 0.5,0
+set border 1+2 back
+set xlabel offset 0,1.25
+set title offset 0,-1
+set tmargin 1
+set lmargin 6
+set rmargin 1
+unset key
+
+set output 'build/gnuplot/vtestbed.svg'
+
+set multiplot layout 2,3
+
+n = 1
+set xrange [0:40]
+set yrange [0:*]
+set xlabel 'Lag'
+
+set title 'ACF X'
+set xtics 0,10
+plot \
+'build/vtestbed/anem/acf-X' using 1:2 every n with points pt 6 lc '#404040' notitle,\
+'' using 1:3 with lines lw 2 lc '#404040' title 'Real',\
+'build/vtestbed/vtb/acf-X' using 1:2 every n with points pt 6 lc '#c04040' notitle,\
+'' using 1:3 with lines lw 2 lc '#c04040' title 'Simulated'
+
+set title 'ACF Y'
+plot \
+'build/vtestbed/anem/acf-Y' using 1:2 every n with points pt 6 lc '#404040' notitle,\
+'' using 1:3 with lines lw 2 lc '#404040' title 'Real',\
+'build/vtestbed/vtb/acf-Y' using 1:2 every n with points pt 6 lc '#c04040' notitle,\
+'' using 1:3 with lines lw 2 lc '#c04040' title 'Simulated'
+
+set title 'ACF Y'
+plot \
+'build/vtestbed/anem/acf-Z' using 1:2 every n with points pt 6 lc '#404040' notitle,\
+'' using 1:3 with lines lw 2 lc '#404040' title 'Real',\
+'build/vtestbed/vtb/acf-Z' using 1:2 every n with points pt 6 lc '#c04040' notitle,\
+'' using 1:3 with lines lw 2 lc '#c04040' title 'Simulated'
+
+n = 5
+
+set xrange [0:*]
+set xtics 0,2
+set xlabel 'Velocity, m/s'
+set title 'Wind speed'
+plot \
+'build/vtestbed/anem/velocity' using 1:2 every n with points pt 6 lc '#404040' notitle,\
+'' using 1:3 with lines lw 2 lc '#404040' title 'Real',\
+'build/vtestbed/vtb/velocity' using 1:2 every n with points pt 6 lc '#c04040' notitle,\
+'' using 1:3 with lines lw 2 lc '#c04040' title 'Simulated'
+
+n = 20
+
+set xrange [*:0]
+set xtics -4,1
+set key top right Left reverse width -20
+set xlabel 'Direction, degrees'
+set title 'Wind direction'
+plot \
+'build/vtestbed/anem/direction' using 1:2 every n with points pt 6 lc '#404040' notitle,\
+'' using 1:3 with lines lw 2 lc '#404040' title 'Real',\
+'build/vtestbed/vtb/direction' using 1:2 every n with points pt 6 lc '#c04040' notitle,\
+'' using 1:3 with lines lw 2 lc '#c04040' title 'Simulated'
diff --git a/main.bib b/main.bib
@@ -160,3 +160,16 @@
year = {1988},
institution = {Sandia National Labs., Albuquerque, NM (USA)}
}
+
+@InProceedings{ bogdanov2020vtestbed,
+ author = {Bogdanov, Alexander and Degtyarev, Alexander and Gankevich,
+ Ivan and Khramushin, Vasily and Korkhov, Vladimir},
+ title = {Virtual Testbed: Concept and Applications},
+ booktitle = {Computational Science and Its Applications -- ICCSA 2020},
+ year = {2020},
+ publisher = {Springer International Publishing},
+ address = {Cham},
+ pages = {3--17},
+ isbn = {978-3-030-58817-5},
+ doi = {10.1007/978-3-030-58817-5\_1}
+}
diff --git a/main.tex b/main.tex
@@ -23,7 +23,7 @@
\lstset{language=R,literate={<-}{{$\gets$}}1}
-\titlerunning{TODO}
+\titlerunning{Wind simulation using high-frequency velocity component measurements}
\authorrunning{A.\,Gavrikov, I.\,Gankevich}
\institute{Saint Petersburg State University\\
@@ -43,7 +43,8 @@
\and strain gauge
\and anemometer
\and three-dimensional ACF
- \and wind velocity PDF.
+ \and wind velocity PDF
+ \and autoregressive model.
}
\end{abstract}
@@ -369,7 +370,7 @@ sampleToSpeed <- function(x, c1, c2) {
Over a period of one month we collected 3.1M samples and filtered out 12\% of
them as having too large unnatural values. We attributed these values to
measurement errors as they spread uniformly across all the time span and are
-surrounded by the values of regular magnitude. TODO picture of a large error.
+surrounded by the values of regular magnitude.
From the remaning data we choose days with wind speeds above the average as
reported by EMERCOM of Russia\footnote{https://en.mchs.gov.ru/} for Saint
@@ -454,10 +455,6 @@ similar shapes, for \(x\) and \(y\) axes the distribution for incident flow is
taller than the distribution for turbulent flow. The best-fit and worst-fit
distributions for each axis are presented in figure~\ref{fig-velocity-distributions}.
-%RMSE is reduced
-%when~\eqref{eq-velocity-distribution} is used as the distribution for both low
-%and high wind speeds. TODO
-
\begin{figure}
\centering
\includegraphics{build/gnuplot/velocity-dist.eps}
@@ -521,8 +518,6 @@ correspondence between the measurements of the two anemometers
anemometers.\label{fig-hold-peak}}
\end{figure}
-%TODO asymmetry
-
Finally, we computed autocovariance for each axis as
\begin{equation}
K(\tau) = \Expectation\left[ \left(X_t-\bar{X}\right)\left(X_{t-\tau}-\bar{X}\right) \right]
@@ -551,7 +546,40 @@ are presented in figure~\ref{fig-acf}.
\subsection{Wind simulation using measured ACFs}
-TODO Anton
+We simulated three-dimensional wind velocity using autoregressive model
+implemented in Virtual Testbed~\cite{bogdanov2020vtestbed} and using the data
+obtained with three-axis anemometer on March 28, 2021, 01:00-03:00 UTC. We
+approximated four-dimensional autocovariance function using~\eqref{eq-acf} by
+setting the corresponding parameters from one-dimensional autocovariance
+functions estimated from the data obtained with anemometer, all other
+parameters were set close to nought. Non-nought parameters are listed in
+table~\ref{tab-arma-parameters}. We found that velocity and direction
+distributions and ACFs of each axis of simulated wind and real wind are close
+to each other (see~figure~\ref{fig-vtestbed}).
+
+\begin{table}
+ \centering
+ \caption{Input parameters for AR model that were used to simulate wind velocity.
+ \label{tab-arma-parameters}}
+ \begin{tabular}{lllll}
+ \toprule
+ Axis & ACF \(a\) & \phantom{0}ACF \(b\) & \phantom{0}ACF \(c\) & \phantom{0}Mean velocity \\
+ \midrule
+ \(x\) & 1.793 & \phantom{0}0.0214 & \phantom{0}0.2603 & \phantom{0}-2.439 \\
+ \(y\) & 1.423 & \phantom{0}0.01429 & \phantom{0}0.2852 & \phantom{0}-2.158 \\
+ \(z\) & 0.9075 & \phantom{0}0.06322 & \phantom{0}0.3349 & \phantom{0}-1.367 \\
+ \bottomrule
+ \end{tabular}
+\end{table}
+
+\begin{figure}
+ \centering
+ \includegraphics{build/gnuplot/vtestbed.eps}
+ \caption{Comparison of simulated wind velocity and direction distributions
+ and per-axis ACFs
+ between the data from the anemometer and the data from Virtual Testbed
+ (2021, March 28, 01:00--03:00, UTC).\label{fig-vtestbed}}
+\end{figure}
\section{Discussion}
