Series Transformation
General
The series transformation option of hymosincludes:
- algebraic transformation of series,
- transformation of non-equidistant series into equidistant series,
- creation of accumulative series, and
- error spreading.
These transformation options are dealt with in the next Sections.
Algebraic Transformations
The following algebraic transformations are available to create a series Y by some function of series Xp , p=1,2,...
1. |
linear equation |
Yi,new = C 1*Yi,old+C2*X2,j+C3*X3,k+C4*X4,l+C5*X5,m+C6 |
|---|---|---|
2. |
multiplication |
Yi = X1,j * X2,k |
3. |
division |
Yi = X1,j /X2,k |
4. |
involution |
Yi = X1,j X2,k |
5. |
natural logarithm |
Yi = ln(Xj ) |
6. |
common logarithm |
Yi = 10 log(Xj )) |
7. |
exponential |
Yi = exp(Xj ) |
8. |
power of 10 |
Yi = 10^Xj^ |
9. |
power |
Yi = XjCl |
10. |
power of constant |
Yi = C 1{}Xj |
11. |
polynomial |
Yi = C0 + C1 X1,j + C2 X1,j 2 + C3 X1,j 3 + C4 X1,j 4 |
12. |
conditional |
Yi = max (X1,j , X2,k , X3,l , X4,m , C) |
13. |
conditional |
Yi = min (X1,j , X2,k , X3,l , X4,m , C) |
14. |
conditional |
Yi = mean (X1,j , X2,k , X3,l , X4,m ) |
15. |
drift |
Yi = X1 + C1 dt +C0 |
16. |
conditional |
if Xi < C1 then Yi = C0 else Yi = Xi |
17. |
conditional |
if Xi > C1 then Yi = C0 else Yi = Xi |
18. |
conditional |
if Xi < C1 then Yi = C0 else Yi = Xi |
19. |
conditional |
if Xi = missing then Yi = C0 else Yi = Xi |
20. |
conditional |
if X1 = missing then Y = X2 else Y = X1 |
where:
Xp = equidistant time series p
Cp = coefficients
In the application of the above transformations different start dates can be applied for each of the series, i.e. i may differ from j, k, etc. This can be achieved by entering a value for the time shift per series.
Series Codes
The series to use in the Transformation function can be selected by highlighting the series in the series list box and pressing the '>>' button. To remove a series from the selected series spreadsheet, select the series in the spreadsheet and press the '<<' button.
Save Relation
A relation made with the algebraic function can be saved to the database. This is very useful when a relation has to used many times on the same series. To save a relation in the database, make a relation by selecting a resulting series ID and entering series ID's in the spreadsheet. When all the coefficients are entered, a name must be given for the relation, in the relation textbox, and the relation can be saved to the database by pressing the <Save Relation> button.
Delete Relation
A relation can be removed from the database by pressing the <Delete Relation> button. The relation, selected from the relations list box, will be removed from the HYMOS database.
Examples
The database contains a time series with some gaps. You want to fill the gaps with values from a second series, therefore you can use option 20. Select the series with gaps and the series without gaps and press <Execute>. When HYMOS detects missing values, the values from the second series are used to fill up the gaps.
Non-equidistant to equidistant series
Non-equidistant time series can be transformed into equidistant time series. The function computes the equidistant values in 2 steps. First it aggregates the non-equidistant time steps to equidistant time steps, when calculating the function makes a difference between accumulated parameters and instantaneous parameters. Generally, the non-equidistant series may not fill all equidistant time steps. You can select one of the following options to fill in the gaps:
zero: the series values at intermediate time steps will be filled with zero's
missing: the series values at intermediate time steps will be filled with missing values
linear interpolation: the series values at intermediate time steps will be a linear interpolation between surrounding non-equidistant series observations
equal to last: the series values at intermediate time steps will be equal to the last observation, (i.e. block-type filling-in).
A special option is "Average over time step". This option uses a weighted average over the values in the next time step. In the previous example, the value for 01-01-2000 05:30 is 0.0033, this is the weighted average for all time steps between 05:00 and 05:30 ((15*-0.015 + 2*0.019 + 5*0.017 + 6*0.026 + 2*0.022)/30 = 0.0033). For filling the gaps the value of the next time step is used.
Example:
The underneath table shows the differences between the 4 options for filling in the gaps.
Original Series |
|
Equidistant |
|
|
|
|
|
|
|
|
Zero |
Missing |
Linear |
Equal Last |
Average |
01-01-2000 00:15 |
-0.049 |
01-01-2000 |
-0.049 |
-0.049 |
-0.049 |
-0.049 |
-0.0495 |
01-01-2000 00:30 |
-0.05 |
01-01-2000 00:30 |
-0.05 |
-0.05 |
-0.05 |
-0.05 |
-0.0500 |
01-01-2000 00:45 |
-0.05 |
01-01-2000 01:00 |
0 |
|
-0.045 |
-0.05 |
-0.0405 |
01-01-2000 01:45 |
-0.04 |
01-01-2000 01:30 |
-0.04 |
-0.04 |
-0.04 |
-0.04 |
-0.0405 |
01-01-2000 02:00 |
-0.041 |
01-01-2000 02:00 |
-0.041 |
-0.041 |
-0.041 |
-0.041 |
0.0033 |
01-01-2000 05:45 |
-0.015 |
01-01-2000 02:30 |
0 |
|
-0.03346 |
-0.041 |
0.0033 |
01-01-2000 05:47 |
0.019 |
01-01-2000 03:00 |
0 |
|
-0.02593 |
-0.041 |
0.0033 |
01-01-2000 05:52 |
0.017 |
01-01-2000 03:30 |
0 |
|
-0.01839 |
-0.041 |
0.0033 |
01-01-2000 05:58 |
0.026 |
01-01-2000 04:00 |
0 |
|
-0.01086 |
-0.041 |
0.0033 |
01-01-2000 06:00 |
0.022 |
01-01-2000 04:30 |
0 |
|
-0.00332 |
-0.041 |
0.0033 |
01-01-2000 06:15 |
0 |
01-01-2000 05:00 |
0 |
|
0.004214 |
-0.041 |
0.0033 |
01-01-2000 09:15 |
-0.01 |
01-01-2000 05:30 |
0.01175 |
0.01175 |
0.01175 |
0.01175 |
0.0033 |
01-01-2000 09:30 |
-0.013 |
01-01-2000 06:00 |
0.011 |
0.011 |
0.011 |
0.011 |
0.0000 |
01-01-2000 09:45 |
-0.013 |
01-01-2000 06:30 |
0 |
|
0.0075 |
0.011 |
-0.0115 |
01-01-2000 10:00 |
-0.014 |
01-01-2000 07:00 |
0 |
|
0.004 |
0.011 |
-0.0115 |
01-01-2000 10:15 |
-0.008 |
01-01-2000 07:30 |
0 |
|
0.0005 |
0.011 |
-0.0115 |
01-01-2000 10:30 |
-0.009 |
01-01-2000 08:00 |
0 |
|
-0.003 |
0.011 |
-0.0115 |
01-01-2000 10:45 |
-0.022 |
01-01-2000 08:30 |
0 |
|
-0.0065 |
0.011 |
-0.0115 |
|
|
01-01-2000 09:00 |
-0.01 |
-0.01 |
-0.01 |
-0.01 |
-0.0115 |
|
|
01-01-2000 09:30 |
-0.013 |
-0.013 |
-0.013 |
-0.013 |
-0.0135 |
|
|
01-01-2000 10:00 |
-0.011 |
-0.011 |
-0.011 |
-0.011 |
-0.0085 |
|
|
01-01-2000 10:30 |
-0.0155 |
-0.0155 |
-0.0155 |
-0.0155 |
-0.0220 |
For this option the end time of the processing period is important. When for example the end time of your period is 1-1-1999 and your new time step is 1 hour then HYMOS will use all values up to 1-1-1999. For computing the last value for the new series HYMOS requires all values from 31-12-1998 23:00:01 to 1-1-1999 00:00:00 (last value included). Because the processing period does not include the value of 1-1-1999 00:00:00, HYMOS will only compute new equidistant values until 31-12-1998 22:00:00..
Series Codes
The series to transform from non-equidistant to equidistant can be selected or de-selected by clicking the checkbox of the series in the series list box. Only one series may be selected in one execution.
Accumulative Series
Under the accumulative series option a series Y is created which is a continuous summation of a basic series X as follows:
Series Codes
The series to accumulate can be selected or de-selected by clicking the checkbox of the series in the series list box. Only one series may be selected in one execution.
Error Spreading
Errors may have an accumulative character, when the phenomenon causing the error has to do e.g. with siltation, weed growth, etc. hymosoffers the possibility to correct for this type of error by applying a continuously growing adjustment from the time the error is thought to have commenced till the error was detected and quantified. Let the error be DX observed at time t=i+k and assumed to have commenced k intervals before, then the applied correction reads:
X corr,j = X meas,j - ((j-i)/k)DX for j=i,i+1,....,i+k
Input for this option are:
- series code,
- start and end date of the series correction
- error DX (mind the sign of the correction!)
Series Codes
The series for Error spreading can be selected or de-selected by clicking the checkbox of the series in the series list box. Only one series may be selected in one execution.
