I have a question about generalizing the FLORIS model across wind speeds/directions and turbine type:
Typically when analyzing wake effects in a wind farm simulations are run across a reasonable observed wind spectrum (i.e. 0 m/s to 30 m/s) and across the entire wind rose (i.e. 0 deg to 360 degrees). Many of the examples provided (i.e. example_0030_demo_energy_ratio.py) show iteration through variable wind speed and wind direction in order to capture varying wake effects under these conditions. However many of the other variables used in the wake simulation depend on wind speed and direction. For example tip speed ratio, turbulence intensity, axial induction factor. These variables are not updated throughout the wind speed/direction simulations?
My question is what are best practices for running FLORIS across a range of wind speed and directions? Should all dependent variables be updated with each run and the example leaves this out to simplify?
Similarly, many of the turbine/wake model variables are difficult to track down/compute across turbine types i.e. pP, pT, mE, ka etc. Do you have any guidelines on these variables? In particular, for the wake constants are the defaults values in the example_input.json file broadly applicable across wind turbine types? Is the expectation that these variables are determined experimentally.
Related
I have a very large dataset (~55,000 datapoints) for chicken crops. Chickens are grown over ~35 day period. The dataset covers 10 sheds of ~20,000 chickens each. In the sheds are weighing platforms and as chickens step on them they send the weight recorded to a server. They are sending continuously from day 0 to the final day.
The variables I have are: House (as a number, House 1 up to House 10), Weight (measured in grams, to 5 decimal points) and Day (measured as a number between two integers, e.g. 12 noon on day 0 might be 0.5 in the day, whereas day 23.3 suggests a third of the way through day 23 (8AM). But as this data is sent continuously the numbers can be very precise).
I want to construct either a Time Series Regression model or an ML model so that if I take a new crop, as data is sent by the sensors, the model can make a prediction for what the end weight will be. Then as that crop cycle finishes it can be added to the training data and repeat.
Currently I'm using this very simple Weight VS Time model, but eventually would include things like temperature, water and food consumption, humidity etc.
I've run regression analyses on the data sets to determine the relationship between time and weight (it's likely quadratic, see image attached) and tried using randomForrest in R to create a model. The test model seemed to work well in regards to the MAPE value being similar to the training value, but that was by taking out one house and using that as the test.
Potentially what I've tried so far is completely the wrong methodology but this is a new area so I'm really not sure of the best approach.
I have my Response variable which is Proportion of Range Exposed to extreme events for terrestrial mammal species in the future. More clearly, it is the Difference of Proportion of Range Exposed (DPRE) from historical period to future green gases emission scenarios (it is a measure of the level of increase/decrease of percentage of range exposed): it means that my response variable goes from -1 to 1 (where +1 implies that the range will experience a +100% increase in the proportion of exposure: from 0% in historical period, to 100% in the future scenario).
As said, I am analyzing these differences for all terrestrial mammals (5311 species, across different scenarios and for two time periods, near future (means of 2021-2040) and far future (means of 2081-2100).
So, my Explicative variables are:
3 Scenarios of green gas emissions (Representative Concentration Pathways: RCP2.6, RCP4.5 and RCP8.5);
Time Periods (Near Future and Far Future): NF and FF;
Species: 5311 individuals.
I am not so expert in statistics , so I'm not sure which of the two suggestions I recieved:
Friedman test with Species as blocks (but in which I should somehow do a nested model, with RCPs as groups, nested within TimePeriods; or a sort of two way Friedman, with RCP and TimePeriod as the two different factors).
Linear Mixed Models with RCP*TimePeriod as fixed effects, and (TimePeriod | Species ) as random effects.
I run t-test, and all distribution result to be not normal, this is why I was suggested to use Friendman instead of ANOVA; I run pairwise Wilcoxon Rank Sum test and in this case I found significative differences from NF and FF for all RCPs.
I have to say I run 3 Wilcoxon, one for every RCP, so maybe a third option would be to create 3 different models, one for every RCP, but this would also go away from the standard analysis of "repated measures" for Friedman test.
Last consideration: I have to run Another model, where the Response variable is the Difference of Proportion of Subrange Exposed. In this case, other Explicative variables are mantained, but in this case analysis is not global but takes in consideration the difference that could be present across 14 IUCN Biomes. So every analysis is made across RCPs, for NF and FF and for all Biomes. Should I create and run 14 (biomes) x 3 (RCPs) x 2 (Time Periods) = 84 models, in this case? OR a sort of double nested (Time Periods and Biomes) model?
If necessary I can provide the large dataframe.
I'm fitting a logarithmic curve to 20+ data sets using the equation
y = intercept + coefficient * ln(x)
Generated in R via
output$curvePlot <- renderPlot ({
x=medianX
y=medianY
Estimate = lad(formula = y~log(x),method = "EM")
logEstimate = lad(formula = y~log(x),method = "EM")
plot(x,predict(Estimate),type='l',col='white')
lines(x,predict(logEstimate),col='red')
points(x,y)
cf <- round(coef(logEstimate),1)
eq <- paste0("y = ", cf[1],
ifelse(sign(cf[2])==1, " + ", " - "), abs(cf[2]), " * ln(x) from 0 to ",xmax)
mtext(eq,3,line=-2,col = "red")
output$summary <- renderPrint(summary(logEstimate))
output$calcCurve <-
renderPrint(round(cf[2]*log(input$calcFeet)+cf[1]))
})
The curve consistently "crosses twice" on the data; fitting too low at low/high points on the X axis, fitting too high at the middle of the X axis.
I don't really understand where to go from here. Am I missing a factor or using the wrong curve?
The dataset is about 60,000 rows long, but I condensed it into medians. Medians were selected due to unavoidable outliers in the data, particularly a thick left tail, caused by our instrumentation.
x,y
2,6.42
4,5.57
6,4.46
8,3.55
10,2.72
12,2.24
14,1.84
16,1.56
18,1.33
20,1.11
22,0.92
24,0.79
26,0.65
28,0.58
30,0.34
32,0.43
34,0.48
36,0.38
38,0.37
40,0.35
42,0.32
44,0.21
46,0.25
48,0.24
50,0.25
52,0.23
Full methodology for context:
Samples of dependent variable, velocity (ft/min), were collected at
various distances from fan nozzle with a NIST-calibrated hot wire
anemometer. We controlled for instrumentation accuracy by subjecting
the anemometer to a weekly test against a known environment, a
pressure tube with a known aperture diameter, ensuring that
calibration was maintained within +/- 1%, the anemometer’s published
accuracy rating.
We controlled for fan alignment with the anemometer down the entire
length of the track using a laser from the center of the fan, which
aimed no more than one inch from the center of the anemometer at any
distance.
While we did not explicitly control for environmental factors, such as
outdoor air temperature, barometric pressure, we believe that these
factors will have minimal influence on the test results. To ensure
that data was collected evenly in a number of environmental
conditions, we built a robot that drove the anemometer down the track
to a different distance every five minutes. This meant that data would
be collected at every independent variable position repeatedly, over
the course of hours, rather than at one position over the course of
hours. As a result, a 24 hour test would measure the air velocity at
each distance over 200 times, allowing changes in temperature as the
room warmed or cooled throughout the day to address any confounding
environmental factors by introducing randomization.
The data was collected via Serial port on the hot wire anemometer,
saving a timestamped CSV that included fields: Date, Time, Distance
from Fan, Measured Temperature, and Measured Velocity. Analysis on the
data was performed in R.
Testing: To gather an initial set of hypotheses, we took the median of
air velocity at each distance. The median was selected, rather than
the mean, as outliers are common in data sets measuring physical
quantities. As air moves around the room, it can cause the airflow to
temporarily curve away from the anemometer. This results in outliers
on the low end that do not reflect the actual variable we were trying
to measure. It’s also the case that, sometimes, the air velocity at a
measured distance appears to “puff,” or surge and fall. This is
perceptible by simply standing in front of the fan, and it happens on
all fans at all distances, to some degree. We believe the most likely
cause of this puffing is due to eddy currents and entrainment of the
surrounding air, temporarily increasing airflow. The median result
absolves us from worrying about how strong or weak a “puff” may feel,
and it helps limit the effects on air speed of the air curving away
from the anemometer, which does not affect actual air velocity, but
only measured air velocity. With our initial dataset of medians, we
used logarithmic regression to calculate a curve to match the data and
generated our initial velocity profiles at set distances. To validate
that the initial data was accurate, we ran 10 monte carlo folding
simulations at 25% of the data set and ensured that the generated
medians were within a reasonable value of each other.
Validation: Fans were run every three months and the monte carlo
folding simulations were observed. If the error rate was <5% from our
previous test, we validated the previous test.
There is no problem with the code itself, you found the best possible fit using a logarithmic curve. I double-checked using Mathematica, and I obtain the same results.
The problem seems to reside in your model. From the data you provided and the description of the origin of the data, the logarithmic function might not the best model for your measurements. The description indicates that the velocity must be a finite value at x=0, and slowly tends towards 0 while going to infinity. However, the negative logarithmic function will be infinite at x=0 and negative after a while.
I am not a physicist, but my intuition would tend towards using the inverse-square law or using the exponential function. I tested both, and the exponential function gives way better results:
I have 700 hourly time series from 2010 to 2014 of gas consumption. One time serie represents the consumption of one companies.
Some have constant consumption, other consume only 4 months of the year and some have a high volatility consumption. As a consequence I would like to cluster them according to the shape of the consuption curve.
I tried the R package "kml", but i do not have good results. I also tried the "kmlShape" package, but it seems that i have too much data, and each time R quit..
I wondered if using Fast fourier transform and then cluster it could be a good idea? My goal is to really distinguish the group that the consumption is constant to those whose consumption is variable.
Then I would like to cluster the variable consummer in function of the peak and when they consumme.
I also tried to calculate the mean et variance of each clients, then cluster it with k-mean but it not very good, i can see 2 cluster, one with 650 clients and on other with 50...
thanks
first exemple`
2nd exemple
Here are three exemple of what I have, I have 700 curves likes that, some are high variables, some pretty constant.
I would like to cluster them according to their shape in order to have one group where the consumption is pretty constant, an other where the consumption is highly variable and try to cluster it according to the time the peak appear
I am doing my master thesis in Electrical engineering about the impact of the humidity and
temperature on power consumption
I have a problem that is related to statistics, numerical methods and mathematics topics
I have real data for one year (year 2000)
Every day has 24 hours records for temperature, humidity, power consumption
So, the total points for one parameter, for example, temperature is 24*366 = 8784 points
I classified the pattern of the power to three patterns:
Daily, seasonally and to cover the whole year
The aim is to find a mathematical model of the following form:
P = f ( T , H , t , date )
Where,
P = power consumption,
T = temperature,
t = time in hours from 1 to 24,
date = the date number in the year from 1 to 366 ( or date number in a month from 1 to 31)
I started drawing in Matlab program a sample day, 1st August showing the effect of time,
humidity and temperature on power consumption::
http://www7.0zz0.com/2010/12/11/23/264638558.jpg
Then, I make the analysis wider to see what changes happened when drawing this day with the next day:
http://www7.0zz0.com/2010/12/11/23/549837601.jpg
After that I make it wider and include the 1st week of august:
http://www7.0zz0.com/2010/12/11/23/447153078.jpg
Then, the whole month, august:
http://www7.0zz0.com/2010/12/12/00/120820248.jpg
Then, starting from January, I plot power and temperature for 1st six months without
humidity (only for scaling):
http://www7.0zz0.com/2010/12/12/00/908911392.jpg
with humidity :
http://www7.0zz0.com/2010/12/12/00/102651717.jpg
Then, the whole year plot without humidity:
( P,T,H have constant values but I separate H only for scaling since H values are too much higher than P and H and that cause shrinking of the plot making small plots for P and T)
http://www7.0zz0.com/2010/12/11/23/290259320.jpg
and finally with humidity:
http://www7.0zz0.com/2010/12/11/23/842530863.jpg
The reason I have plotted these figures is to follow the behaviors of all parameters. How P is changing with respect to Temperature, Humidity, and time in hours and time in day number.
It is clear that these figures represent cyclic behavior but this behavior is not
constant. It is starting to increase and then decrease during the whole year.
For example the behavior of 1st January is almost the same as any other day in the year
but the difference is in shifting up or down, left or right.
Also, Temperature and Humidity are almost sinusoidal. However, Power consumption behavior is not purely sinusoidal as seen in the following figure:
http://www7.0zz0.com/2010/12/12/00/153503144.jpg
I am not expert in statistics and numerical methods, and this matter now does not have relation with electrical engineering concept.
The results I am aiming to get are:
Specify the day number in the year from 1 to 366,
then specify the hour in that day,
temperature and humidity also will be specified.
All of these parameters are to be specified by the user
The result:
The mathematical model should be capable to find the power consumption in that specific hour of that day.
Then, the Power found from the model will be compared to the measured real power from the
data and if the values are very close to each other, then the model will be accurate and
accepted.
I am sorry for this long question. I actually read many papers, many helps but I could not
reach to the correct approach of how to find one unified model by following the curves
behavior from starting till the end of the year and also having more than one independent
variable has disturbed me a lot.
I hope this problem is not difficult for statistics and mathematics experts.
Any help will be highly appreciated,
Thanks in advance
Regards
About this:
"Also, Temperature and Humidity are almost sinusoidal. However, Power consumption behavior is not purely sinusoidal"
Seems in local scale (several days/weeks order) temperature and humidity can be expressed as periodic train of Gaussians:
After such assumption we can model power consumption as superposition of temperature and humidity trains of Gaussians. Consider this opencalc spreadsheet chart:
in which f1 and f2 are train of gaussians (here only 4 peaks, but you may calculate as many as you need for data fitting) and f3 is superposition of these two trains,-
just (f12 + f22)1/2
However i don't know to what degree power consumption follows the addition of train of gaussians. You may invest time to explore this possibility.
Good luck!