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Genetic programming for real-time prediction of offshore windS. B. Charhate a; M. C. Deo a; S. N. Londhe aa Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India

First Published:March2009

To cite this Article Charhate, S. B., Deo, M. C. and Londhe, S. N.(2009)'Genetic programming for real-time prediction of offshorewind',Ships and Offshore Structures,4:1,77 88

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Ships and Offshore Structures

Vol. 4, No. 1, 2009, 7788

Genetic programming for real-time prediction of offshore wind

S.B. Charhate, M.C. Deo and S.N. Londhe

Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India

(Received 31 March 2008; final version received 19 September 2008)

Wind speed and its direction at two offshore locations along the west coast of India are predicted over future time-steps of3 to 24 hrs based on a sequence past wind measurements made by floating buoys. This is done based on a relatively newsoft computing tool using genetic programming. The attention of investigators has recently been drawn to the application ofthis approach that differs from the well-known technique of genetic algorithms in basic coding and application of geneticoperators. Unlike most of the past works dealing with causative modeling or spatial correlations, this study explores theusefulness of genetic programming to carry out temporal regression. It is found that the resulting predictions of windmovements rival those made by an equivalent and more traditional artificial neural network and sometimes appear moreattractive when multiple-error criteria were applied. The success of genetic programming as a modelling tool reported in this

study may inspire similar applications in future in the problem domain of offshore engineering, and more research in thecomputing domain as well.

Keywords: genetic programming; artificial neural networks; wind speed; wind direction; wind prediction

Introduction

The knowledge of magnitude and direction of wind plays

a vital role in the planning, design and operation of coastal

and ocean engineering facilities. Information on wind fur-

ther enables oneto obtainthe same of wind-generatedwaves

and currents. Forecasting of wind speed and direction in

real-time and over future time-steps helps in planning engi-

neering worksin thecoastal andoffshoreregion, scheduling

aircraft operations, predicting output of wind turbines andissuing warnings for fishing, recreational or similar activi-

ties in the ocean.

For a large number of ocean locations of the world data

on wind speed and direction are routinely collected through

floating wave-rider buoys, whichareessentially designed to

obtain measurements of waves, but additionally and simul-

taneouslyprovidesupplementary information likewindand

temperature parameters. If such wind observations, made at

a sampling interval of 1 hr or 3 hr are available on real-time

basis in the form of a time series, then the problem of pre-

diction of wind speed for future time-steps can be tackled

as a uni-variate time series-forecasting issue. Investigators

like More and Deo (2002), Cadenas and Rivera (2007)

had previously shown that the real-time prediction of wind

speed observed by wave buoys canbe satisfactorily done by

the soft computing tool of artificial neural networks (ANN)

and further such predictions could be more advantageous

than the traditional stochastic modeling methods of Auto

Regressive Moving Average (ARMA) or Auto Regressive

Corresponding author. Email: [email protected]

Integrated Moving Average (ARIMA). Zhang (2003) sug-

gested that a combined ANN and ARIMA model would

work marginally better for this purpose than individual

ANN or ARIMA approach. Investigators working in the

field of hydraulic or hydrologic engineering (e.g. Drecourt,

1999; Muttil and Liong, 2004) have found that another soft

approach, namely, genetic programming (GP) worked ei-

ther equally well or some times even better than the ANN.

This has provided motivation to authors to apply the tech-nique of GP to the problem of online wind prediction. A

specialty of this work is that it provides application of GP to

the task of temporal regression as against the earlier studies

dealing with evaluation of causal or spatial relationships

with the help of GP.

Genetic Programming and Past Applications

The GP is similar to genetic algorithms (GA) in concept

but unlike the latter, which has a set of numbers, it provides

its solution in the form of a computer programme or an

equation. Basically in GP a random population of individ-

uals (equations or computer programmes) is created, the

fitness of individuals is evaluated and then the parents are

selected out of these individuals. The parents are then made

to yield offspring by following the process of reproduc-

tion, mutationandcross-over. (See Appendix1 to know how

these operations are carried out.) The creation of offspring

continues (in an iterative manner) util a specified number

ISSN: 1744-5302 print/ 1754-212X online

Copyright C

2009 Taylor & Francis

DOI: 10.1080/17445300802492638http://www.informaworld.com


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78 S.B. Charhate et al.

Figure 1. Coastline of India showing wave buoy locations at stations DS1 and DS7.

of offsprings in a generation are produced and further util

a specified number of generations are created. The best or

the fittest resulting offspring at the end of all this process,

i.e. an equation or a computer programme, is the solution

to the problem. The GP thus transforms one population of

individuals into another in an iterative manner by followingnatural genetic operations like reproduction, mutation and

cross-over. More details of the working of GP can be found

in Koza (1992).

Applications of GP in coastal engineering are rare, un-

like in the field of water resources and hydraulics that

started around 1999. (For example, see Drecourt 1999;

Whigham and Crapper 2001; and Muttil and Liong 2004).

Some of these authors have also presented comparisons

with other models. Drecourt (1999) reported that GP han-

dles peak flows better while ANN takes care of noise ef-

ficiently. Muttil and Liong (2004) found the performance

of GP marginally better than ANN. Most recently Charhate

et al. (2007) made a forecast of coastal currents in a tide-

dominated areaoff the Gulf of Khambhat and found that GP

predictions were more satisfactory than ordinary ANN and

ARIMA schemes. Kalra and Deo (2008) reported the use-

fulness of GP in in-filling gaps in wave-height-time series.

The Database and Model Calibration

The National Institute of Ocean Technology (NIOT) at

Chennai, India has been collecting oceanographic data

since recent past through a series of wave-rider buoys de-

ployed along the coastal and offshore belt of India. These

floating buoys havewind anemometers fitted at the standard

heightof 3 m above sea level through whichwind-speed ob-

servations are routinely collected every 3 hrs. The present

study is based on such observations collected by NIOT and

these pertain to two deep-water locations off Goa (station:

DS1) and off Minicoy (station: DS7), respectively. Figure 1depicts sites of the data collection. Station DS7 is open to

both Arabian as well as Bay of Bengal and large variations

in the wind are expected at this place. The duration of data

collection varied from April 2004 to July 2005 and from

June to September 2006 at site DS1, while at station DS7

data collected belonged to the three-years period of 2004 to

2006.

This study involved time-series forecasting over lead-

time steps of 3, 6, 9, 12 and 24 hrs based on the previous

segment of wind measurements. By trial it was noticed that

a sequence of three preceding observations was sufficient

for the GP model to recognise an unknown hidden pattern

in these and use the same to produce the forecasted value.

Two different types of models were developed to see the

more advantageous of the two. These included prediction

of wind speed alone and of speed and direction together.

In case of station DS1 the measurements of the first 11

months were used to calibrate the GP model while the re-

maining 4 months observations were used for verifying or

testing the developed models. The results obtained using

these models at DS1 were further validated with the obser-

vation for a period of June 2006 to September 2006. For

station DS7 the first 24 months observations were used for


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Ships and Offshore Structures 79

Ws(t)

Ws(t-1)

Ws(t-2)

Ws(t+1)

Bias

Weight

Input layer

Hidden layer

Output layer

Figure 2. The ANN used.

training and the remaining 12 months were used to test the

calibrated model.

While applying GP a typical choice of control param-

eters used is as follows: population size = 2048; No. ofgenerations= 405; mutation frequency = 80%; cross-overfrequency = 52%. The programmes were generated withthe help of Discipulus software (Fancone, 1998), and were

furtherprocessed for application to new data sets using Tur-

boC in the C++ environment. The statistical measures ofcorrelation coefficient (R), root mean square error (RMSE)

and mean absolute error (MAE) were used to compare the

GP predictions with actual observations and were evaluated

by using MATLAB, which also facilitated generation of the

scatter plots between the target output and the one obtained

through GP.

The coefficient of correlation (R) measures the linear

association of two given variables. However, it cannot de-

tect any complex non-linear dependency between them, if

present. It is also very sensitive to deviations at larger ob-

servations. The root mean square error indicates an overall

agreement (without any upper bound)between theobserved

DS13 hr ahead GP prediction

0

5

10

15

20

0 5 10 15 20

Observed wind speed in m/s

Predictedwindspeedinm/s Exact fit

R=0.95

Figure 4. Observed versus GP-predicted wind speed at stationDS1 (lead-time: 3 hr; testing data).

and modeled datasets and is assumed to be good for pre-

dictions that are iteratively arrived at. But it gives only an

overall picture of errors. The mean absolute error also gives

only an overall agreement between the observed and mod-

eled datasets, but it is useful for practical interpretations.

It is not weighted towards high- or low-magnitude events,

but instead evaluates all deviations from the observed val-

ues in an equal manner and regardless of sign. The MAE

is non-negative, has no upper bound and is hence advanta-

geous, but provides no information about under-estimation

or over-estimation. It is comparable to the total sum of ab-

solute residuals. It may thus be seen that a given measure

of error statistics is associated with some advantages and

some drawbacks and hence a combination of multiple-error


0

4

8

12

16

1 101 201 301 401 501 601 701 801 901

Time in hr

Windspeedinm/s

Observation

Prediction

03-04-2005 26-07-2005

Figure 3. Observed versus GP-predicted wind speed at station DS1 (lead-time: 3 hr; testing data).


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0

4

8

12

16

20

1 300 599 898 1197 1496 1795 2094 2393 2692

Time (hr)

Windspeed(m/s)

Observation

Prediction

01-01-2006 26-12-2006

Figure 5. Observed versus GP-predicted wind speed at station DS7 (lead-time: 6 hr; testing data).

measures accompanied by a physical examination of scat-ter and time-series plots, as done in this study, can give a

reasonable idea of performance of the model fit.

The same problem of predicting wind speed and di-

rection was also solved by using a 3-layer feed-forward

artificial neural network (Figure 2), trained using the most

appropriate form of the error-back propagation algorithm.

A similar division of training and testing of data like the

earlier GP was maintained.

It is to be noted that applications of ANN to derive the

direction of wind are too sparse; a few noticeable among

them are, Thiria et al. (1993) who evaluated the wind di-

rection using simulated data as well as employing a spatial

Figure 6. Observed versus GP-predicted wind speed at stationDS7 (lead-time: 6 hr; testing data).

input context, and, Cornford et al. (1999), who estimatedwind vectors from the scatterometer data.

Attempts to forecast the wind speed anddirectionbased

on their current direct measurements did not yield good

results. Hence, a different training scheme was adopted.

According to it, if U = resultant wind-speed vector and= angle made by U with the North direction, then thetwo orthogonal wind components along the NorthSouth

and EastWest directions would be given by u andv, where

u = U cos andv = U sin . From the measured valuesofU and, u andv components were obtained as above

and the same were thereafter separately predicted using

two separate GP models and such predictions were further

combined using U = u2 + v2 and= tan1 vu

Results

The best programme obtained at the end of the GP-

calibration process anddeveloped using the training portion

of thesamplewas tested for theobservationsnot involved in

the training exercise. The resulting predictions of speed and

direction over the time-steps of 3, 6, 9, 12 and 24 hr were

compared against their target values. A similar process was

followed in the case of ANN as well.

Figures 3 and 4 show typical comparisons between the

GP-predicted 3-hr wind speeds with corresponding actual

observationsat DS1during testing in theformof time series

and scatter plots. Figures 5 and 6 depict similar plots for 6-

hr predictions at the other location, i.e. DS7. These figures

pertain to the case when the predictions were not based on

wind-vector resolution. For the latter case (predictions on

the basis of vector resolution), the model forecasted versus

observed speeds are shown in Figures 7 to 10 for site DS1

and in Figures 11 to 14 for station DS7 as examples. These

figures pertain to the cases of higher lead-time varying

from 9 to 24 hr. The time-series plots of observed versus


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0

5

10

15

20

1 101 201 301 401 501 601 701 801 901

Time (hr)

Winds

peed(m/s)

ObservationPrediction

Figure 7. Observed versus GP-predicted wind speed at station DS1 (predictions based on components; lead-time: 12 hr; testing data).

predicted directions for the 24-hr lead-time at DS1 and12-hr lead-time at DS7 are shown in Figures 15 and 16,

respectively.

It may be noticed that the technique of GP carried out

the intended task well and even higher levels of wind speed

were also well-predicted by this method.

The third column in Tables 1 and 2 shows the testing

performance of GP for wind-speed predictions in terms of

the error statistics when the observed total speed was not

broken into components to build the model along with a

similar comparison based on the ANN model. The fourth

and the fifth columns in Tables 1 and 2 show the perfor-

mance of GP and ANN models when the u

v components

Combined uvcomponents

0

5

10

15

20

0 5 10 15 20

Observed wind speed (m/s)

Predicted

windspeed(m/s)

R=0.87

Figure 8. Observed versus GP-predicted wind speed at stationDS1 (predictions based on components; lead-time: 12 hr; testingdata).

were used to build the model and predict the resultant windspeed and direction.

It appears that the trainingofGPand ANN modelsmade

on the basis of splitting the wind vector into two orthogonal

components was useful, although a separate model for wind

speed alone (the third column in Tables 1 and 2) would be

preferable for better performance in case only the wind

speed is desired.

The tables and figures referred above indicate that the

GP is able to recursively recognize an unknown hidden pat-

tern in the preceding sequence of wind measurements and

make a satisfactory forecast of future values accordingly.

An excellent performance of the GP in this problem of

wind-speed prediction based on temporal correlations with

preceding observations is thus noteworthy.

Although it is difficult to specify any cut-off level for a

good model fit, R > 0.80 can be normally regarded as an

indicationof satisfactorymodelperformance. The forecast-

ing at station DS1 can be therefore seen to be satisfactory

even over the longer lead-time of 24 hr as reflected in high

values ofR and low values ofRMSE andMAE. However,

the same at station DS7 was good only up to the lead-time

of 9 hr. This is due to highly open nature of this site that is

exposed to both the Arabian Sea as well as an Indian Ocean.

Tables 1 and 2 also show how an equivalent ANN is

performed in comparison with the GP. These tables alongwith Figures 3 to 16 indicate that the results of GP surely

rival those of the much researched and established tool of

ANN for all the lead-times. Although the relatively small

differences in error statistics between GP and ANN meth-

ods may not necessarily mean statistically significant devi-

ations between them, it may be noted that GP marginally

but consistently yielded more attractive statistics. This was

true at the open location DS7 where wider variations in

the wind speed and direction can be expected. The present

study may prompt additional research to know if GP could


7/13


Table 1. Wind speed and direction forecasting at station DS1.

1 2 3 4 5

Speed prediction without using Speed prediction using u andvcomponents components Wind direction

Mean deviationLead-time Method R RMSE m/s MAEm/s R RMSE m/s MAEm/s R (degrees)

3 hr GP 0.95 1.20 0.91 0.92 1.78 1.23 0.90 15ANN 0.95 1.24 0.94 0.90 1.87 1.28 0.88 17

6 hr GP 0.92 1.48 1.11 0.90 1.59 1.32 0.88 18ANN 0.91 1.55 1.19 0.87 1.69 1.41 0.85 20

9 hr GP 0.91 1.63 1.19 0.89 1.68 1.46 0.86 19ANN 0.90 1.65 1.23 0.86 1.81 1.58 0.83 22

12 hr GP 0.90 1.60 1.21 0.87 1.70 1.52 0.86 21ANN 0.88 1.72 1.29 0.84 1.86 1.61 0.81 24

24 hr GP 0.87 1.80 1.33 0.86 1.84 1.68 0.79 26ANN 0.87 1.91 1.45 0.81 1.97 1.77 0.75 28

Table 2. Wind speed and direction forecasting at station DS7.

1 2 3 4 5

Speed prediction without using Speed prediction using u andvcomponents components Wind direction

Mean deviationLead-time Method R RMSE m/s MAEm/s R RMSE m/s MAEm/s R (degrees)

3 hr GP 0.86 1.30 0.96 0.83 1.52 1.31 0.78 21ANN 0.87 1.39 1.04 0.81 1.58 1.39 0.77 23

6 hr GP 0.81 1.42 1.10 0.78 1.75 1.41 0.72 23ANN 0.82 1.48 1.15 0.77 1.78 1.48 0.70 28

9 hr GP 0.78 1.60 1.23 0.75 1.86 1.72 0.68 26

ANN 0.75 1.66 1.29 0.73 1.93 1.84 0.65 3012 hr GP 0.75 1.62 1.21 0.74 1.95 1.69 0.65 29

ANN 0.72 1.70 1.38 0.71 2.04 1.80 0.63 3224 hr GP 0.69 1.83 1.42 0.67 2.12 1.86 0.62 34

ANN 0.67 1.88 1.48 0.66 2.21 1.93 0.60 38

0

5

10

15

20

1 101 201 301 401 501 601 701 801 901

Time (hr)

Windspeed(m/s)




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0

5

10

15

20

0 5 10 15 20


Predictedwindspeed(m/s)

R=0.86


be really more useful in situations where the input varia-

tions are large and random or if GP can deal with input

noise more efficiently than ANN. It may also inspire more

work to understand if the capability of GP to generate innu-

merable new values and assess their usefulness efficiently

gives it an edge over the ANN.

In general the long-interval predictions were less accu-rate than the corresponding short-interval forecasting for

both techniques. This could be attributed to the highly un-

predictable dependency between the values separated by

longer intervals in general. The direction prediction using

0

5

10

15

20

0 5 10 15 20


Predictedwinds

peed(m/s)

R=0.75

Figure 12. Observed versus GP-predicted wind speed at stationDS7 (predictions based on components; lead-time: 9 hr; testing

data).

both approaches was found to be quite good with mean

errors within 15 to 26 at DS1 and 21 to 34 at DS7.It has been widely reported in many water-related ap-

plications (e.g. Thirumalaiah and Deo, 1998; Hong and

Rao, 2003; More and Deo, 2003) that soft tools like ANN

are generally more beneficial than traditional statistical re-

gressions and hence in this work such a comparison with

regression methods was not studied again.

A forecasting model can be said to work well if it shows

better performance than a persistence model in which thecurrent observation is given as the forecasted value. This

can be verified from Tables 3 and 4, which show, as exam-

ples, error statistics during the testing of GP and persistence

model. The underlying forecasting is made over different

0

5

10

15

20

1 132 263 394 525 656 787 918 1049 1180 1311 1442 1573

Time (hr)

Windspeed(m/s)




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Table 3. Wind speed forecasting at station DS1.

1 2 3

Speed prediction without using components

Lead-time Method R RMSE m/s MAEm/s

3 hr GP 0.95 1.20 0.91Persistence model 0.90 1.39 1.11





Table 4. Wind speed forecasting at station DS7.

1 2 3

Speed prediction without using components

Lead-time Method R RMSE m/s MAEm/s




12 hr GP 0.75 1.62 1.21

Persistence model 0.59 2.10 1.7924 hr GP 0.69 1.83 1.42

Persistence model 0.55 2.31 1.82

0

5

10

15

20

1 117 233 349 465 581 697 813 929 1045 1161 1277 1393 1509

Time (hr)

Windspee

d(m/s)


01-05-2006 16-12-2006



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0

5

10

15

20

0 5 10 15 20


Predictedwindspe

ed(m/s)

R=0.74


lead-times and for stations DS1 and DS7, respectively. A

significant difference in the relative-error statistics, espe-

cially at longer intervals, clearly reveals that the GP (and

hence the ANN performing at a similar level to GP) worked

better than the persistence model in this study.

Implementation of the Developed Models into the

Fields

The studies described so far for the prediction of wind

speed and direction based on GP are currently being

implemented in the field through an integrated platform

or a graphical user interface (GUI). The 3-hr measure-

ments of wind speed and direction collected at a num-

ber of buoy locations in the Arabian Sea (Figure 17) are

sent by telemetry to a server located at NIOT Chennai

in India. Currently such observations are made available

to registered clients of NIOT through a Web-based ser-vice. The GUI under consideration connects the models

developed in this study to this Web server. An intelligent

approach of generation of necessary input files is used

and this involves in-filling missing data by spatial corre-

lation with neighbouring stations through the GP method.

The user has to click on the station (Figure 17) where he

wants to have the predictions. This will generate the screen

having a Load button. Clicking on this Load button

will bring appropriate input files into the picture, which

in turn will be linked to the executable wind-prediction

programme developed in this study. The predictions of

speed and direction will be made after clicking on the but-

ton Show forecasts and will be displayed as shown in

Figure 18.

Conclusions

The preceding sections described the development of mod-

els based on genetic programming to obtain predictions of

wind speed and its direction over lead-time varying from

3 hrs to 24 hrs. The performance of the GP models during

testing was found to be satisfactory as judged by the error

statistics of correlation coefficient, root mean square error

and mean absolute error. The relatively new soft comput-ing tool of GP was able to successfully recognize a hid-

den pattern in the preceding 3-hr wind-speed observations

and make predictions for future time steps accordingly in

0

50

100

150

200

250

300

350

400

1 101 201 301 401 501 601 701 801 901

Time interval (hr)

Winddirection(degrees)

Observed winddirection

Predicted wind

direction

R=0.79

Figure 15. Observed versus GP-predicted wind direction for 24-hr ahead forecast at DS1.


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0

50

100

150

200

250

300

350

400

1 101 201 301 401 501 601 701 801 901 1001 1101 1201 1301 1401 1501 1601

Time interval (hr)

Winddirection(degree)

Observed

wind direction

Predicted wind

direction

R= 0.65

Figure 16. Observed versus GP-predicted wind direction for 12-hr ahead forecast at DS7.

a satisfactory manner. A comparison with corresponding

predictions yielded by artificial neural networks showed

that the GP-based predictions rivaled those of more tradi-

tional and established ANNs. Further for the open ocean

location DS7, where wider variations in the adjacent wind

measurements can be expected, the GP showed possibility

of marginally better performance than the ANN even at the

24-hr ahead prediction.

Figure 17. The Front screen showing the buoy locations.


12/13


Figure 18. The Prediction window.

The preceding section also showed that the training of

GP and ANN models developed on the basis of splitting the

wind vector into two orthogonal components was useful in

predicting both wind speed and its direction simultaneously

over different time intervals, although a separate model forwind speed alone would be preferable for better perfor-

mance in case only wind speed is desired.

The success of the technique of GP noticed in the cur-

rent study dealing with temporal regression may inspire

other applications of GP in coastal and ocean engineering

such as a spatial mapping or a cause-effect modeling.

Figure 19. Programme [(q+ ()1/2)/ 3 p] in the form of a treestructure.

Appendix 1

Examples of genetic operations

Generating population

A programme [(q+ ()1/2

) / 3 p] is given in Figure 19 inthe form of a tree structure. A population of random trees

representing the programmes is initially constructed and

genetic operations are performed on these trees to generate

individuals with the help of two distinct sets: the terminal

set T and the function set F. For Figure 19,

{ +/} F and{, 3, p , q} T.

In order to generate a random tree one has to pick ran-

domly from T F, until all branches end up in terminals.

Cross-over

Two random nodes are selected from inside such pro-

gramme (parents) and thereafter the resultant sub-trees are

swapped, generating two new programmes as in Figure 20.

Mutation

A sub-tree is replaced by another one randomly (Figure 21).


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Child 1

+

* p5 q

2*

/

+

v_

p

q

/

+

v_

q

Child 2

Parent 2

Crossover

Parent 1

q

_

2 p_

v

+

//

q

+

v_

q5

p*+

v

v

Figure 20. Cross-over.

*+

* p5 q

_+

q

//

+

v_

p2

q

Mutation

v

Figure 21. Mutation.

Reproduction

This means an exact duplication of the programmme if it is

found to be acceptable by the fitness criteria.

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Prediction of Offshore Wind (India)

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