commit c95a535beb32438aacac66c74dc0b891f07bcd99
parent 8b541d32182547c2d64cf781720c78d1d72b9e5b
Author: Ivan Gankevich <i.gankevich@spbu.ru>
Date: Tue, 6 Apr 2021 14:16:53 +0300
Wind direction distribution.
Diffstat:
5 files changed, 182 insertions(+), 118 deletions(-)
diff --git a/Makefile b/Makefile
@@ -18,8 +18,9 @@ build/main.pdf: build/inkscape/anemometer.eps
build/main.pdf: build/daily-stats.eps
build/main.pdf: build/daily-rmse.eps
build/main.pdf: build/gnuplot/velocity-dist.eps
-build/main.pdf: build/gnuplot/direction-dist-max.png
-build/main.pdf: build/gnuplot/direction-dist-min.png
+build/main.pdf: build/gnuplot/velocity-xy-dist-max.eps
+build/main.pdf: build/gnuplot/velocity-xy-dist-min.eps
+build/main.pdf: build/gnuplot/direction-dist.eps
#build/main.pdf: build/gnuplot/anemometer.eps
#build/main.pdf: build/gnuplot/anemometer.svg
build/main.pdf:
@@ -56,13 +57,15 @@ build/daily-stats.svg: gnuplot/daily-stats.gnuplot build/daily-stats
build/daily-rmse.svg: gnuplot/daily-rmse.gnuplot build/daily-rmse
gnuplot -d $<
-build/gnuplot/direction-dist-min.svg: gnuplot/direction-dist.gnuplot build/direction/1616497200-hist-xy
- gnuplot -d -c gnuplot/direction-dist.gnuplot \
- build/direction/1616497200-hist-xy build/gnuplot/direction-dist-min.svg 0.024544
+build/gnuplot/velocity-xy-dist-min.svg: gnuplot/velocity-xy-dist.gnuplot build/direction/1616497200-hist-xy
+ gnuplot -d -c gnuplot/velocity-xy-dist.gnuplot \
+ build/direction/1616497200-hist-xy build/gnuplot/velocity-xy-dist-min.svg \
+ 0.024544 4.495469
-build/gnuplot/direction-dist-max.svg: gnuplot/direction-dist.gnuplot build/direction/1616792400-hist-xy
- gnuplot -d -c gnuplot/direction-dist.gnuplot \
- build/direction/1616792400-hist-xy build/gnuplot/direction-dist-max.svg 0.154791
+build/gnuplot/velocity-xy-dist-max.svg: gnuplot/velocity-xy-dist.gnuplot build/direction/1616792400-hist-xy
+ gnuplot -d -c gnuplot/velocity-xy-dist.gnuplot \
+ build/direction/1616792400-hist-xy build/gnuplot/velocity-xy-dist-max.svg \
+ 0.154791 0.801432
#build/main.zip: build/gnuplot/*.eps main.tex
build/main.zip: main.tex
diff --git a/R/minmax.R b/R/minmax.R
@@ -33,6 +33,14 @@ with(list(tmp = data[data$z_rmse == max(data$z_rmse), ]),
direction_rmse_min = data[data$direction_rmse == min(data$direction_rmse), ]
direction_rmse_max = data[data$direction_rmse == max(data$direction_rmse), ]
direction_rmse_mean = mean(data$direction_rmse)
-printf("Min. direction RMSE = %f (%s), mean direction = %f\n", direction_rmse_min["direction_rmse"], direction_rmse_min["timestamp"], direction_rmse_min["direction"])
-printf("Max. direction RMSE = %f (%s), mean direction = %f\n", direction_rmse_max["direction_rmse"], direction_rmse_max["timestamp"], direction_rmse_max["direction"])
+printf("Min. direction RMSE = %f (%s), mean direction = %f, mean speed = %f\n",
+ direction_rmse_min["direction_rmse"],
+ direction_rmse_min["timestamp"],
+ direction_rmse_min["direction"],
+ direction_rmse_min["speed"])
+printf("Max. direction RMSE = %f (%s), mean direction = %f, mean speed = %f\n",
+ direction_rmse_max["direction_rmse"],
+ direction_rmse_max["timestamp"],
+ direction_rmse_max["direction"],
+ direction_rmse_max["speed"])
printf("Mean direction RMSE = %f\n", direction_rmse_mean)
diff --git a/gnuplot/direction-dist.gnuplot b/gnuplot/direction-dist.gnuplot
@@ -1,105 +1,36 @@
-load 'gnuplot/blues.pal'
-set palette defined (0 '#4040c0', 1 '#c0c0c0', 2 '#c04040')
-#set palette defined (0 '#c0c0c0', 1 '#c04040')
-set terminal svg size 450/2,450/2 font 'Free Serif, 10' enhanced round dynamic
-#set terminal png size 450/2,450/2 font 'Free Serif, 10' enhanced
+set terminal svg size 450,450/2 font 'Free Serif, 10' enhanced round dynamic
set xtics nomirror out offset 0,0.25
set ytics nomirror out offset 0.5,0
-#set border 2+8
-unset border
-unset xtics
-unset ytics
-#set key top center outside Left reverse
+set border 1+2 back
unset key
-
-#set xlabel 'υ_x'
-#set ylabel 'υ_y'
-set cbrange [0:*]
-set lmargin 2
-set tmargin 2.5
-set bmargin 1.5
-set rmargin 6
-set size square
-#set lmargin at screen 0.05
-#set rmargin at screen 0.85
-#set bmargin at screen 0.1
-#set tmargin at screen 0.9
-
-positive(x) = x<=25 ? NaN : x
-negative(x) = x>0 ? NaN : x
+set output 'build/gnuplot/direction-dist.svg'
+set xlabel 'θ' offset 0,1.0
+set xrange [-180:180]
+set xtics -180,90
+set yrange [0:4]
+set rmargin 1.5
+set tmargin 1
+set title offset 0,-1
+set multiplot layout 1,2
+positive(x) = x<0 ? (1/0) : x
+negative(x) = x>0 ? (1/0) : x
round(x) = floor(x+0.5)
-length(x,y) = sqrt(x**2 + y**2)
-angle(x,y) = atan2(y,x)
-circle(x,y,z) = length(x,y)>1 ? NaN : z
-#circle(x,y,z) = z
-max(x,y) = x>y ? x : y
-
-filename = ARG1
-filename_tmp = sprintf('%s.tmp', filename)
-filename_cnt = sprintf('%s.cnt', filename)
-filename_out = ARG2
-rmse = ARG3
-
-# Min. direction RMSE = 0.024544 (1616497200), mean direction = -2.399689
-# Max. direction RMSE = 0.154791 (1616792400), mean direction = -2.440686
+rad2deg(rad) = (rad * 180) / pi
+# Min. direction RMSE = 0.024544 (1616497200), mean direction = -2.399689, mean speed = 4.495469
+# Max. direction RMSE = 0.154791 (1616792400), mean direction = -2.440686, mean speed = 0.801432
# Mean direction RMSE = 0.056350
-## interpolation {{{
-## http://www.gnuplotting.org/circular-heat-map/
-#set table filename_tmp
-#set dgrid3d 100,100
-set xrange [-1:1]
-set yrange [-1:1]
-#splot filename using 1:2:3
-#unset table
-## }}}
-#
-## contours {{{
-#set table filename_cnt
-#set contour base
-#set cntrparam levels 5
-#set cntrparam order 8 bspline
-##set cntrlabel onecolor format '%8.3g' font ',7' start 25 interval -1
-#unset surface
-#set dgrid3d 100,100
-#splot filename using 1:2:3 with lines
-#unset table
-## }}}
-set output filename_out
-set multiplot
-
-# polar grid {{{
-# now plot the polar grid only
-# https://stackoverflow.com/questions/18792461/gnuplot-2d-polar-plot-with-heatmap-from-3d-dataset-possible
-r = 3
-unset contour
-set border polar lw 1 lc rgb '#404040' back
-set surface
-set angles degree
-set style line 11 lc rgb '#404040' lw 0.5 dashtype 2
-set grid polar ls 11 nortics back
-set polar
-set rrange[0:r]
-unset raxis
-set rtics format '' scale 0
-unset parametric
-set for [i=0:330:30] label at first (r+0.40)*cos(i), first (r+0.40)*sin(i) center sprintf('%d', i)
-plot NaN w l
-unset polar
-unset grid
-unset border
-# }}}
-#plot filename_tmp using 1:2:(circle($1,$2,$3)) with image
-set border lw 1 1+2+4+8
-unset border
-set colorbox user origin 0.900,0.1 size 0.03,0.8
-set cbtics offset -0.5,0
-s = 0.5
-set xrange [-1*s:1*s]
-set yrange [-1*s:1*s]
-set title offset 0,0.5 sprintf('RMSE = %.0f%%', round(rmse*100))
-#plot filename using 1:2:(positive($3)) with points pt 7 ps 0.25 linecolor palette z
-plot filename using 1:2:(positive($3)) with image
-#plot filename_cnt using (circle($1,$2,$1)):2 with lines lc '#404040'
+set lmargin 5
+set title sprintf('RMSE = %.0f%%, mean speed = %.1fm/s',round(0.154791*100), 0.801432)
+plot \
+'build/direction/vonmises/1616792400' index 0 using (rad2deg($1)):2 every 5 with points pt 6 lc '#404040' title 'Observed PDF of υ_x',\
+'' index 0 using (positive(rad2deg($1))):3 with lines lw 2 lc '#c04040' title 'Estimated PDF of positive υ_x',\
+'' index 0 using (negative(rad2deg($1))):3 with lines lw 2 lc '#4040c0' title 'Estimated PDF of negative υ_x'
+set lmargin 5
+set title sprintf('RMSE = %.0f%%, mean speed = %.1fm/s',round(0.024544*100), 4.495469)
+plot \
+'build/direction/vonmises/1616497200' index 0 using (rad2deg($1)):2 every 5 with points pt 6 lc '#404040' title 'Observed PDF of υ_x',\
+'' index 0 using (positive(rad2deg($1))):3 with lines lw 2 lc '#c04040' title 'Estimated PDF of positive υ_x',\
+'' index 0 using (negative(rad2deg($1))):3 with lines lw 2 lc '#4040c0' title 'Estimated PDF of negative υ_x'
diff --git a/gnuplot/velocity-xy-dist.gnuplot b/gnuplot/velocity-xy-dist.gnuplot
@@ -0,0 +1,109 @@
+load 'gnuplot/blues.pal'
+set palette defined (0 '#4040c0', 1 '#c0c0c0', 2 '#c04040')
+#set palette defined (0 '#c0c0c0', 1 '#c04040')
+f = 0.90
+set terminal svg size 450/2*f,450/2*f font 'Free Serif, 10' enhanced round dynamic
+#set terminal eps size 450/2/72,450/2/72 font 'Free Serif, 10' enhanced round
+#set terminal png size 450/2,450/2 font 'Free Serif, 10' enhanced
+set xtics nomirror out offset 0,0.25
+set ytics nomirror out offset 0.5,0
+#set border 2+8
+unset border
+unset xtics
+unset ytics
+#set key top center outside Left reverse
+unset key
+
+#set xlabel 'υ_x'
+#set ylabel 'υ_y'
+set cbrange [0:*]
+set lmargin 2
+set tmargin 2.5
+set bmargin 1.5
+set rmargin 6
+set size square
+#set lmargin at screen 0.05
+#set rmargin at screen 0.85
+#set bmargin at screen 0.1
+#set tmargin at screen 0.9
+
+positive(x) = x<0 ? NaN : x
+negative(x) = x>0 ? NaN : x
+round(x) = floor(x+0.5)
+length(x,y) = sqrt(x**2 + y**2)
+angle(x,y) = atan2(y,x)
+s = 0.5
+circle(x,y,z) = length(x,y)>s ? NaN : z
+#circle(x,y,z) = z
+max(x,y) = x>y ? x : y
+
+filename = ARG1
+filename_tmp = sprintf('%s.tmp', filename)
+filename_cnt = sprintf('%s.cnt', filename)
+filename_out = ARG2
+rmse = ARG3 + 0
+speed = ARG4 + 0
+
+# Min. direction RMSE = 0.024544 (1616497200), mean direction = -2.399689
+# Max. direction RMSE = 0.154791 (1616792400), mean direction = -2.440686
+# Mean direction RMSE = 0.056350
+
+## interpolation {{{
+## http://www.gnuplotting.org/circular-heat-map/
+#set table filename_tmp
+#set dgrid3d 100,100
+set xrange [-1:1]
+set yrange [-1:1]
+#splot filename using 1:2:3
+#unset table
+## }}}
+#
+## contours {{{
+#set table filename_cnt
+#set contour base
+#set cntrparam levels 5
+#set cntrparam order 8 bspline
+##set cntrlabel onecolor format '%8.3g' font ',7' start 25 interval -1
+#unset surface
+#set dgrid3d 100,100
+#splot filename using 1:2:3 with lines
+#unset table
+## }}}
+set output filename_out
+set multiplot
+
+set border lw 1 1+2+4+8
+unset border
+set colorbox user origin 0.900,0.1 size 0.03,0.8
+set cbtics offset -0.5,0
+set xrange [-1*s:1*s]
+set yrange [-1*s:1*s]
+set title offset 0,0.5
+set title sprintf('RMSE = %.0f%%, mean speed = %.1fm/s', round(rmse*100), speed)
+#plot filename using 1:2:(positive($3)) with points pt 7 ps 0.25 linecolor palette z
+plot filename using ($1+0.005):2:(circle($1,$2,$3)) with image
+#plot filename_cnt using (circle($1,$2,$1)):2 with lines lc '#404040'
+
+# polar grid {{{
+# now plot the polar grid only
+# https://stackoverflow.com/questions/18792461/gnuplot-2d-polar-plot-with-heatmap-from-3d-dataset-possible
+r = 3
+unset contour
+set border polar lw 4 lc rgb '#404040' back
+set surface
+set angles degree
+set style line 11 lc rgb '#404040' lw 0.5 dashtype 2
+set grid polar ls 11 nortics back
+set polar
+set rrange[0:r]
+unset raxis
+set rtics format '' scale 0
+unset parametric
+set for [i=0:330:30] label at first (r+0.40)*cos(i), first (r+0.40)*sin(i) center sprintf('%d', i)
+plot NaN w l
+unset polar
+unset grid
+unset border
+# }}}
+#plot filename_tmp using 1:2:(circle($1,$2,$3)) with image
+
diff --git a/main.tex b/main.tex
@@ -326,10 +326,10 @@ and \(y\) axes the distribution for incident flow is taller than the
distribution for turbulent flow. Distributions for each axis are presented in
figure~\ref{fig-velocity-distributions}.
-RMSE of the approximation has negative correlation with wind speed: the larger
-the wind speed, the smaller the error and vice versa. Larger error for low wind
-speeds is caused by larger skewness and kurtosis (see the first row of
-figure~\ref{fig-velocity-distributions}). RMSE is reduced
+RMSE of wind speed distribution approximation has positive correlation with
+wind speed: the larger the wind speed, the larger the error and vice versa.
+Larger error for low wind speeds is caused by larger skewness and kurtosis (see
+the first row of 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
@@ -350,17 +350,30 @@ and high wind speeds. TODO
\cite{carta2008}
+RMSE of wind direction distribution approximation has negative correlation with
+wind speed: the larger the wind speed, the smaller the error and vice versa.
+Larger error for low wind
+
\begin{figure}
\centering
- \includegraphics{build/gnuplot/direction-dist-max.png}~\phantom{x}~
- \includegraphics{build/gnuplot/direction-dist-min.png}
+ \begin{minipage}{0.49\textwidth}
+ \centering
+ \includegraphics{build/gnuplot/velocity-xy-dist-max.eps}
+ \end{minipage}
+ \begin{minipage}{0.49\textwidth}
+ \centering
+ \includegraphics{build/gnuplot/velocity-xy-dist-min.eps}
+ \end{minipage}
+ \vskip\baselineskip
+ \includegraphics{build/gnuplot/direction-dist.eps}
\caption{Bivariate \(x\) and \(y\) velocity distribution
- in polar coordinates. Data interval with the largest error (top left), data
- interval with the smallest error (top right).
+ in polar coordinates (first row), wind direction distributions fitted into
+ von Mises distribution (second row). Data interval with the largest error (left column), data
+ interval with the smallest error (right column).
Red line shows estimated
- probability density of positive wind speed projections, blue line shows estimated
- probability density of negative wind speed projections and circles denote observed
- probability density of wind speed projections.
+ probability density of positive direction angles, blue line shows estimated
+ probability density of negative direction angles and circles denote observed
+ probability density of direction angles.
\label{fig-direction-distributions}}
\end{figure}
