WIND SPEED PREDICTION by pharmphresh33

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									                                 WIND SPEED PREDICTION
    Sagar Gadsing, Electrical and Computer Engineering, Portland State University
                                E-mail:sagar@pdx.edu
                       ECE 557: Engineering Data Analysis and Modeling, Fall 2004
                                      Instructor: James McNames



Abstract – Wind speed is one of the most                      A. Data Collection
important criteria for windsurfing. This paper
predicts the wind speed, using the regression                 The data was collected from internet (NDBC
model. Four factors affecting the wind speed have             government link). The parameters considered for
been taken into consideration. Various results                predicting the wind speed are: average wind direction
have been explained using graphs and tables. The              measured in degrees clockwise from true North;
wind speed prediction made for next 24 hours was              direction in degrees clockwise from true North of the
satisfactory.                                                 GSP; maximum 5-second peak gust during the
                                                              measurement hour; the minute of the hour that the
Index Terms –                                                 GSP occurred; the predicted wind speed for previous
                                                              day.
      GSP: Maximum 5-second peak gust during the
measurement hour.
                                                              B. Statistics Summary
                    I Introduction
                                                              I had a very large data set. There were many reading
Wind surfing is a very popular sport, especially along        of wind speed along with the corresponding
the coastal areas. Unfortunately, the adventure largely       parameters, out of which I found that most of data was
depends on the natural conditions, such as wind               corrupted and was with repetitive values. There were
speed. In this paper I have tried to predict the wind         abrupt and periodic changes in the input values, which
speed, which will be of help for the surfers. If the wind     made me, feel that the data is corrupted. Every 3rd
speed is predicted and put up on a popular website,           reading was same and uniform through out the
wind surfers can refer to the data and make their plans       collected data. All the entries in these rows were 999’s.
accordingly. If this kind of information is not made          Hence much of the data was discarded.
available, wind surfers may be disappointed after
                                                              C. Prediction of Wind Speed
reaching the coast only to find that it is either too windy
or there is not wind at all.                                  For predicting the wind speed a relationship between
                                                              past parameters and present wind speed was
There are many factors that affect the wind speed. I          established. The following model was used for
have made my best effort to use as many parameters            achieving the goal. The model is given by
as possible. I was not able to use the parameters I
wanted, only because data for those parameters was
                                                                                   ^        n
not available.                                                                     Y = wo + Σ ( wi * xi ) --- (1)
                                                                                                i=1
An effort was made to predict the wind speed using
fuzzy logic, though it was directed towards predicting        Here ‘w’, represents the weights and Yhat is the
the wind conditions for wind turbines [1]. There have         expected value of the output. Xi, represents the input
been hardly any efforts done for predicting wind speed        parameter. The weights were calculated from the true
for windsurfing.                                              values and the pseudo inverse of data matrix.

                  II. Methodology                             The data matrix ‘A’ is given by

This section describes the methodology used to predict                      A = [ 1, x1, x2, …] ---(2)
the wind speed at a given time.
                                                              and the weight, w, is given by,
                                           w = A’ * Yt ---(3)
                                                                                          Fig I shows the predicted values of wind speed against the true
                                                                                          values.
    The inverse of matrix A cannot be calculated, since it is
    not a square matrix. Hence I calculated the pseudo
                                                                                          The plot in fig I shows the variation of true and
    inverse of matrix A, using the MATLAB.
                                                                                          predicted values of the wind speed. The values are
                                                                                          very closely matched, which indicates that the model
    I started with a large data set, applied the test to it, but
                                                                                          has performed well.
    at the end the value of performance coefficient (R2)
    turned out to be very insignificant (merely 11%). Then I
    analyzed the data, and found that there was a lot of
    inconsistency in it. There were many repetitive values,                                                                                                               wind speed for 18th
    which were unexpected. Deleting much of the
    corrupted data, improved my value of R2, and I ended
    up with R2 = 0.9.                                                                                                                               14

                                                                                                                                                    12
    To measure performance of the model I calculated the
    performance coefficient (R2). The value of R2 indicates




                                                                                                                       w i n d s p e e d (m / s )
                                                                                                                                                    10
    how well the data fits.
                                                                                                                                                    8                                                           yt for 18/10
    The performance coefficient is given by                                                                                                                                                                     yh for 18/10
                                                                                                                                                    6
                                      R2 = (1-SSE/SSTO) ---( 4 )                                                                                    4

    The value of SSTO is calculated by                                                                                                              2

                                                                                                                                                    0
                                     SSTO = Σ (yi – ymean)2 ---( 5 )
                                                                                                                                                         1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
    and the value of SSE is calculated by                                                                                                                                    time
                                  ^
                    SSE= Σ ( yi – y )2 ---( 6 )
                                                                                                                                                                                                   th
                                                                                          Fig II shows the predicted values for wind speed on 18 against the
    Code has been written in Matlab to calculate the                                      true values.
    values of R2.
                                                                                          The above graph shows the predicted wind speed on
    I have applied the above model for predicting the wind                                the 18th and the true wind speed plotted against the
    speed 24 hours in advance. For accomplishing this, I                                  time.
    have established a relationship between the present
    inputs and present estimated value with wind speed
    after 24 hours. For example, suppose I want to predict
    the wind speed on the 22nd of Nov at 11am, the input                                                                                                                 wind speed for 19th
    parameters used are recorded at 11 am on 21st Nov.
    Also, I have predicted the wind speed for the 21st of                                                              16
    Nov on the 20th of Nov. This estimated wind speed has
    also been taken into account to predict the wind speed                                                             14
    on the 22nd. Thus the model essentially predicts wind                                                              12
                                                                                          w i n d s p e e d (m / s )




    speed for next 24 hours.
                                                                                                                       10
                                                                                                                                                                                                                 yt for 19/10
                                              III. Results                                                                  8
                                                                                                                                                                                                                 yh for 19/10
                                      wind speed measurement for 17th                                                       6
                                                                                                                            4
                   18
                   16                                                                                                       2
                   14
                                                                                                                            0
wind speed (m/s)




                   12
                   10                                                      yt for 17/10                                                             1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
                   8                                                       yh for 17/10
                                                                                                                                                                            time
                   6
                   4
                   2                                                                                                                                                                                    th
                   0
                                                                                          Fig III shows the predicted values for wind speed on 19                                                            plotted
                        1   4   7 10 13 16 19 22 25 28 31 34 37 40 43 46
                                                                                          against the true values.
                                               time
The fig III shows the predicted wind speed for 19th                                      The above scatter plot shows the relation among all
plotted against the true values of the wind speed. It can                                the input and the output (predicted value of only 17th).
be observed that the difference in the predicted values                                  The X-axis starts with x1 all the extreme left and ends
and the true values goes on increasing.                                                  with y output on the extreme right. Similarly on the Y-
                                                                                         axis, the first value is y which goes up to output x1.
In all of the above graphs the X-axis reads “time”,                                      The scatter plot clearly shows that most of the inputs
which is nothing but the every half hour of the day, i.e.                                are not correlated. However there is some correlation
1 corresponds to 12:00 O’clock, 2 corresponds to                                         between the input variables x4 and the output y. Also a
11:30 and so on.                                                                         significant correlation can be seen between the input
                                                                                         variables x1 and x2.
                                          plot for r^2
                                                                                                            IV Discussion
1.2
                                                                                         This paper predicts the wind speed 24 hours in
 1                                                                                       advance. If this model is used to estimate wind speed
0.8                                                                                      48 hours in advance, using the estimated value after
                                                                                         24 hours, the error goes on accumulating.
0.6                                                                                r^2
                                                                                         Several different models can be built, each one
0.4
                                                                                         specifically designed to predict a value after a specified
0.2                                                                                      duration. Also efforts can be made to increase the
                                                                                         values of R2, which implies a more reliable model for
 0                                                                                       predicting the future values. Using a good set of data
                     17th                    18th                    19th
                                                                                         will definitely help to build a better model. If there
                                             date                                        would have been no corrupted data, the results would
                                                                                         have been essentially unbiased.
                                      2
Fig IV shows the values of R for different days.
                                                                                         More accurate and better results would have been
The above information depicts that, the farther the                                      predicted, provided we get some more related
value of wind speed I try to predict, the more                                           parameters, such as temperature and altitude.
inaccurate result I get. This is because; the error in the
prediction goes on increasing.                                                           More number of samples per hour would have helped
                                                                                         to predict the wind speed after a short duration, which
Also I have used the current estimated values for                                        is also useful for windsurfing.
predicting the future values. The prediction error goes
on adding up and the result becomes unreliable.
                                                                                                            V. Conclusion
           400

           200
  x1




                                                                                         The wind speed can be predicted satisfactorily in
             0
           400
                                                                                         advance. The estimated values become more and
           200
                                                                                         more unreliable as we try to predict the farther outputs.
  x2




                                                                                         Thus this paper shows how present input values and
            0
           10                                                                            the present predicted value can be used to predict a
            5
                                                                                         future value.
      x3




          0                                                                                                 VI. References
       4000

       2000                                                                              [1] “A New Approach for Wind Speed Prediction” by
 x4




            0                                                                            Y.D.Song, Department of Electrical Engineering, North
           20                                                                            Carolina.
           10
      y




            0                                                                            [2] “Real time continuous wind data” from National
                 0   200 400 0   200 400 0      5   10 0   2000 4000 0   10   20         Data Buoy Center.
                     x1          x2            x3           x4           y

Fig V shows a scatter plot, which includes all the inputs and the
output.

								
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