［ Systems・Components ］

Dam Influent Prediction byMachine Learning
Keywords

Nobuaki Takase,Osamu Harakawa

Hydraulic power generation, Optimal power generation plan, Flow rate prediction, Machine learning, Ensemble learning

Abstract

In planning the daily power generation plan in a hydroelectric power plant,
many constraints such as dam inﬂuent rate, dam-designated water level, andmaintenance discharge should be considered. This work is extremely complicated. We developed a predictive approach for the dam inﬂuent rate by using amachine learning. Such a new technique for dam inﬂuent rate prediction is expected to be a method to establish a model for predicting future inﬂuent rates
based on past inﬂuent data and meteorological data. It is used to realize a highly
accurate prediction without considering physical characteristics in a river system. In the developed technique, an approach called “ensemble leaning”, which
is a type of machine learning, is applied. Using multiple simple and coordinative
learners, the developed method realized a superb prediction accuracy even inrainy weather when obtainable data is minimal.

1 Preface
When planning a daily power generation at
a hydropower plant, the dam inﬂuent rate, damdesignated water level, maintenance discharge rate,
and many other restrictive conditions must be taken
into consideration. This work is extremely complicated. If a future inﬂuent rate can be predicted withhigh accuracy, control of dam water level and discharge rate becomes easy, and stable and efﬁcientplant operation can be carried out.
In order to achieve accurate prediction of future
dam inﬂuent rate, however, it is necessary to establish a physical model with which future meteorological data, the shape of river systems, amount ofsnow fall, and other critical information can be accurately grasped. Such a practice is challenging. For
example, although an outstanding physical model
can be established for a single river system, anotherphysical model must be established from the beginning when another river system is added to this project.
Meanwhile, if a machine learning model ismade to learn the relationship among meteorological data, past inﬂuent rate data, and future inﬂuentdata, a highly accurate prediction of the dam inﬂuent rate becomes possible without direct consideration of physical characteristics of river systems.

This paper introduces a high-accuracy dam inﬂuent
rate prediction approach by using a machine learning model.

2 Outline of Hydropower Generation
Business Operations
Fig. 1 shows an outline of business operations
at a dam-type hydropower plant. An example ofpower generating operations for 24 hours to be ofﬁcially notiﬁed to a power company at 9:00 every day
is presented. Essentials for the calculation of power
generation plan are shown below.
( 1) The dam water level is maintained within theupper and lower limits of the speciﬁed water level.
( 2 ) For the protection of ecological systems in rivers, maintenance discharge (minimum dischargerate) is secured.
( 3 ) The higher the dam water level, the higher thepower generating efﬁciency. The dam water level is,therefore, kept as high as possible.
( 4 ) When the dam water level exceeds the speciﬁed level, overﬂow (gate discharge to prevent dam
overﬂow) is inevitably caused.
In order to secure high-efﬁciency plant operation, it is necessary to set up the water level as highas possible to maximize power generation efﬁciency for ( 3 ) while restrictions of ( 1) and ( 2 ) are satisMEIDEN REVIEW Series No.181 2021 No.1

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1/3
09:00

Influent rate:
Present
Influent rate:
An hour before

Past
meteorologicalobservation
data

Rainfall: Present
Rainfall:An hour before

…

1/2
09:00

Past daminfluent rate

1/4
09:00
Time

Reporting period ofpower generation plan

1/3
09:00

Predicted dam
influent rate ofk hours ahead…

☆Present time
1/2
09:00

XGBoostTemperature:
Present
Temperature:
An hour before

Reporting of 24-hour
power generation plan
1/1
09:00

…

Lapseof time ☆Present time
1/1
09:00

Reporting of 24-hour
power generation plan

Meteorologicalprediction
mesh data

1/4
09:00

1×1×kTime
Reporting period ofpower generation plan

Fig. 1ﬁed. At the same time, overﬂow must be preventedfor ( 4 ).
For these reasons, it is necessary to grasp
future inﬂuent rate accurately in order to establish ahigh-efﬁciency power generating plan. The dam
catchment area (area occupied by river systems) is,
however, generally wide, and in addition, mountain
ranges may be snowbound in winter. In many cases,
it is therefore difﬁcult to achieve future inﬂuent rate
predictions.

3 Dam Inﬂuent Rate Prediction ModelFig. 2 shows a dam inﬂuent rate prediction
model. Input data for this prediction model generally
involves actual data of past-to-present inﬂuent rates,
actual meteorological data obtained in the past topresent, predicted meteorological data, and seasonal items. The meteorological data input enteredin the dam inﬂuent rate prediction model is considered to cover the amount of rainfall, temperatures,
atmospheric pressures, and humidity. This model
employs the amount of rainfall and temperatures. Inaddition to actual data of present dam inﬂuent rate
data and actual meteorological data, it is now possible to investigate time-serial trends of each data if
the past several hours of actual data input isacquired.
MEIDEN REVIEW Series No.181 2021 No.1

k1×1×kOutline of Business Operations at a Dam-Type
Hydropower Plant

This diagram shows an example of business operations when adaily power generation plan for 24 hours toward the next day isreported at 09:00 to the power utility company. The lapse of timegoes from upper to lower. In this diagram, an example of an operation plan at a time point of 1/1 09:00 is shown in the upper
diagram and a plan at a time point of 1/2 09:00 is shown in thelower diagram.

46

Amount of rainfall

Temperaturek

Seasonal item
2Fig. 2

Dam Influent Rate Prediction Model

When all data of past inﬂuent rates and meteorological information are entered in the XGBoost prediction model, the predicted
dam inﬂuent rate of time k (＝ 1, … , 48) can be obtained.

For meteorological prediction data, theMesoScale Model (MSM) Grid Point Value (GPV)(1)is used. For GPV, the atmosphere is sectioned byregularly aligned mesh points and forecast meteorological values are obtained at each grid point
based on various observatory data by using asupercomputer. The MSM is a numerical forecast
model that can manage the coverage of Japan
proper and its offshore areas. Since this model cangenerate forecast outputs of prediction 8 times aday at the intervals of 3 hours and 39 hours ahead(51 hours ahead at 0:00 and 12:00), it is suitable formeteorological prediction at a time span of several
hours to one day ahead. This development is forJapanese hydropower generation business operations. Since the purpose of prediction is for theacquisition of dam inﬂuent data for 48 hours ahead,
we adopted the MSM for our numerical prediction
model. It should be noted that the use of the dam
inﬂuent rate prediction model from our R&D activities is not limited to Japan. It is available throughout
the world through proper selection from numericalprediction models.
Factors for causing an increase in dam inﬂuent
rate are rainfall and snow melting. An increase inthe inﬂuent rate due to snow melting can be pre-dicted based on the amount of snowfall in the river
basin and actual temperature data gained in previous several hours. It is, however, difﬁcult to accurately grasp actual snow amounts in river basins.
For our development, we focused on snow melt
occuring shortly after the snow season. As such, wedevised an approach by which seasonal items areinputted in the dam inﬂuent prediction model. Fig. 3shows an outline of seasonal items. The seasonal
items are variables that ﬂuctuate during the periodof one year. By making the prediction model todeﬁnitively learn the snow-melting season and otherperiods, it is possible to predict an increase in dam
inﬂuent rate due to the snow melt.
For the learning of dam inﬂuent rate prediction
model, ensemble methods are used. For this model

Seasonal
item 1…

Seasonal
item 22014

Fig. 3

2015

2016

YearOutline of Seasonal Items

The seasonable items are acceptable if they are of a periodic
function of a one-year cycle. In this case, the seasonal item 1 isexpressed by a cosine wave and the seasonal item 2 isexpressed by a sine wave.

DataFig. 4(a) Split into different conditions(subsampling, etc.)

in particular, a development approach called theeXtreme Gradient Boosting(2) (“XGBoost” hereafter)
is used.

3.1 Ensemble Learning Method
The Ensemble Learning Method is a kind ofmachine learning method. In machine learning, themodel learns the relationship among data groups
based on large amounts of input/output data. Whenthe unknown input data is put into the model, it outputs inference results. In our development, the input
data is the past dam inﬂuent data or meteorological
data while the output data is the future dam inﬂuentdata. A feature of the ensemble learning method isthat a high-accuracy learner can be establishedthrough coordination of multiple weak learners.
Fig. 4 shows an example of a bugging approach forthe ensemble learning method. In order to constructa model where regression lines are given to thedata shown on the left, the following steps are executed:( a ) Split into different conditions( b ) Build Weak learners( c ) Majority/mean of the weak learners
In ( a ), data is split into different samples by making sampling with replacement by the bootstrap
sampling method. In ( b ), learning is performed
with a weak learner (comparatively simple learningmodel) for the respective samples split in ( a ). In
learning model for a weak learner, a decision tree
is generally used. In ( c ), output values of a ﬁnal
model are obtained through the processing ofmajority, mean, and total sum of the respective
outputs from weak learners made under ( b ). Since(b) Making Weak learner(c) Majority/mean ofweak learner

Example of Bugging Approach for the Ensemble Learning Method

Black points are data. This is an example where blue lines of data regression are drawn by two weak learners.

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Weak learner

Data

Total sum of weak learners

Prediction error(Black dot –Blue line)

Prediction error(Black dot –Blue line)

＋…

…

＋…

…
Fig. 5Outline of Boosting Technique

For a prediction error caused by a weak learner, the creation of another weak learner is repeated to decrease prediction errors.

computation cost for weak learner making is generally low, ensemble methods can assure highspeed and high generalization performance.

3.2 XGBoost
In the case of XGBoost, the weak learner ismade to learn with an algorithm called “boosting”
which is different from bugging explained in 3.1
above. Fig. 5 shows an outline of the boosting technique. By boosting, a learning model is establishedby producing a new weak learner where errors generated from former weak learners are minimized. Inaddition to this boosting technique, the XGBoost isequipped with an algorithm where suppression ofover-speed learning and overﬁtting is devised. For
this reason, performance generalization can beobtained even for a region where errors can be easily caused and the volume of data is small. For ourdevelopment, it is preferable to make it possible toaccomplish precise restriction when the dam inﬂuent rate becomes high in the case of heavy rain.
Data of rainy weather, however, is only about 20% of
the overall data volume and such data tends tobecome smaller in the case of heavy rain. It is,therefore, difﬁcult to construct a learning model thatcan make accurate prediction while the amount ofdam inﬂuent is large at the time of heavy rain. If theXGBoost is adopted, we can expect accurate prediction even though the dam inﬂuent rate is highwhen the volume of data tends to be small. For our48

MEIDEN REVIEW Series No.181 2021 No.1

development, the XGBoost was adopted for ensemble learning.

4 Numerical Experiments
In our simulation, the effectiveness of the proposed approach for this research is shown. In thiscase, we made a prediction of dam inﬂuent rate
relating to a dam facility in Japan. With the dam
inﬂuent rate prediction model equipped with theXGBoost, we entered inputs of actual dam inﬂuentdata, amount of rainfall, and actual meteorological
data gathered in the previous 12 hours to the present time. For meteorological forecast mesh data by
the MSM, inputs of mesh data of about 34-hours ofrainfall and values of temperature forecast gatheredclose to the objective dam were entered. The learning period was set at 1 July 2008 to 31 December
2016. The veriﬁcation period was set at 1 January
2017 to 30 November 2017.
Figs. 6 to 8 show a comparison of actual
ﬂowrate values and predicted ﬂowrate values. Fig. 6is for rainless days, Fig. 7 is for snow melting days,and Fig. 8 is for heavy rainy days of 17.5 mm at amoment. Fig. 9 shows actual rainfall values andpredicted rainfall values by MSM measured in thesame period for Fig. 8.
In Fig. 6, the inﬂuent rate on a rainless day
varies from approximately 10 m3/s to 20 m3/s andthe prediction model makes an accurate forecast. In

250200
150
100
Actual flowrate

Predicted flowrate

500Present time

24 hours ahead

Dam influent rate (m3/s)

Dam influent rate (m3/s)

250

200
Actual flowrate

15010050

Predicted flowrate
0
Present time

48 hours ahead

24 hours ahead

Fig. 6Comparison of Actual Flowrate Values andPredicted Flowrate Values: Rainless Days

The result of prediction in rainless days is shown. The solid line
indicates actual values of dam inﬂuent rate and the dotted line
shows prediction output values from the dam inﬂuent prediction
model.

The result of prediction in heavy rainy days is shown. The solidline indicates actual values of dam inﬂuent rate and the dottedline shows prediction output values from the dam inﬂuent prediction model.

17.5

200

Actual flowrate

150100Predicted flowrate

50

24 hours ahead

48 hours ahead

Amount of rainfall (mm)Dam influent rate (m3/s)

Comparison of Actual Flowrate Values andPredicted Flowrate Values: Heavy Rainy Days

Fig. 8250

0Present time

15.0

Actual rainfall

12.5
Predicted rainfall

10.0
7.5
5.0
2.5
0.0
Present time

24 hours ahead

TimeFig. 7

48 hours ahead

TimeTime

Comparison of Actual Flowrate Values andPredicted Flowrate Values: Snow Melting Days

48 hours aheadTimeFig. 9

Actual Rainfall Values and Predicted RainfallValues: Heavy Rainy Day

The result of prediction at the time of snow melting is shown. The
solid line indicates actual values of dam inﬂuent rate and thedotted line shows the prediction output values from the dam inﬂuent prediction model.

Actual and predicted rainfall values at the time of heavy rain areshown. The solid line indicates actual rainfall values and the dotted line shows predicted rainfall values by the MSM.

Fig. 7, the predicted ﬂowrate shows a good consistency even though the actual ﬂowrate changes
around more than 100 m3/s due to snow melting.
Obviously, the seasonal items of the prediction
model shown in Fig. 2 duly identiﬁes the snowmelting season. The occurrence of snow melting isestimated based on meteorological data. In Fig. 8, it
is possible to conﬁrm a sufﬁcient prediction of trends
to increase the ﬂowrate when heavy rainfall resultsin the rise of the inﬂuent level from 10 m3/s to 200
m3/s, though occasional errors can be seen at thetime of the rising. Since the MSM achieves an accurate prediction of future rainfall as shown in Fig. 9, it
is possible to consider that the learning model has
successfully forecast the correct dam inﬂuent rate
based on the given future rainfall data.
Table 1 shows the prediction accuracy throughout the simulation period. The mean absolute error

Table 1Prediction Accuracy throughout the Simulation
PeriodThe result of a day and that of the next day are shown. The mean
absolute error of one-day accumulation means an index to showwhether the total amount of inﬂuent for a single day can bepredicted.
Evaluation index
Mean absolute error for 24 hours of a day
measured at the intervals of an hour

Prediction error
10.7％

Mean absolute error for 24 hours of the next 13.6％
day measured at the intervals of an hour
Mean absolute error of one-day accumulation for a day

7.0％

Mean absolute error of one-day accumulation for the next day

10.1％

of one-day accumulation denotes an index to showwhether the total amount of inﬂuent for a single day
can be predicted. The prediction accuracy is evaluated based on the predicted dam inﬂuent rate, mean
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absolute error of actual values, and 95 percentile※1of actual dam inﬂuent rate, using the formula: (meanabsolute error) / (95 percentile value) × 100%. Basedon Table 1, we conﬁrmed that the 24-hour forecasterror of a day is about 10%, the mean absolute errorof one-day accumulation of a day is 7%, and that ahigh-accuracy prediction is performed throughout
the veriﬁcation period.
The learning time of the prediction model isabout 600 seconds. Compared with deep learningtechnology using a neural network that requires
thousands to tens of thousands of seconds, we candeclare that our prediction model learning byensemble learning approach assures high-speed
performance.

learning is short, this technology can be expected topromote a wider application to other river systems.
Regarding the data of the Mesoscale Model
Grid Point Value (MSM) used for our development,
we use the database(3) collected and distributed by
Research Institute for Sustainable Humanosphere.
・All product and company names mentioned in this paper are
the trademarks and/or service marks of their respective owners.
(Note)※1. 95 percentile value: A dose value corresponding to the upper
5% group when the result of dose computation is placed in theorder from higher to lower values.

《References》

5 Postscript
This paper introduced a high-accuracy dam
inﬂuent rate prediction approach by using a machinelearning model for the purpose of optimal management of hydropower generation plants. Thisapproach can construct a simulation model without
any dependence on singular characteristics of riversystems. Since the learning time for ensemble

50

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( 1 ) Meteorological Business Support Center: MesoScale Model
Grid Point Value, http://www.jmbsc.or.jp/jp/online/file/f-online10200.
html( 2 ) Tianqi Chen, Carlos Guestrin: “XGBoost: A scalable tree boostingsystem”, Proceedings of the 22Nd ACM SIGKDD International
Conference on Knowledge Discovery and Data Mining, pp.785794, ACM, 2016.
( 3 ) Research Institute for Sustainable Humanosphere of Kyoto
University: Sustainable Humanosphere database: http://database.
rish.kyoto-u.ac.jp