TITLE OF THE INVENTION
WATER DEMAND PREDICTION SYSTEM AND METHOD
BACKGROUND OF THE INVENTION
1. Field of the Invention
[0001]
The present invention relates to a water demand
prediction system and method for predicting water demand
for each reference period in a predetermined water
distribution area in which water is distributed from
water distribution equipment through a distribution pipe
network.
2. Description of the Related Art
[0002]
Conventionally, control for distributing water to
consumers including general households is applied to
water supply facilities. The water demand not only varies
in response to the day-of-week and the time for each day
and for each predetermined time but also varies from
external factors such as the weather and air temperature.
Thus, prior arts that attempt to predict the water demand
accurately are available.
[0003]
JP-2012-099049-A discloses a water distribution
3
amount plan prediction system that acquires performance
values of the water demand for a day-of-week which is
same as the day-of-week of a prediction date and which is
selected from within a predetermined period in the past,
averages the performance values by time and performs
water demand prediction using water demand pattern values
for 24 hours a day calculated by the averaging.
[0004]
The water distribution amount plan prediction
system acquires the latest water demand performance value
and corrects, in the case where the displacement between
the water demand pattern value that is a prediction value
and the performance value departs from an acceptable
range, the pattern value such that the displacement
between the pattern value and the performance value
decreases. To this end, the water distribution amount
plan prediction system adds or subtracts a fixed amount
to or from the pattern value to improve the accuracy in
water demand prediction.
SUMMARY OF THE INVENTION
[0006]
The water distribution amount plan prediction
system described above can improve the predicting
accuracy of the water demand in such a case that the
4
water demand increases or decreases uniformly. However,
in such a case that the water demand shifts in time so as
to be advanced or postponed, for example, by change of
the washing time in accordance with the weather,
correction of the pattern value conversely deteriorates
the water demand prediction accuracy. Therefore, it is an
object of the present invention to provide a system that
can predict the water demand accurately even in such a
case that the change of the water demand is not uniform.
[0007]
In order to achieve the object described above,
according to the present invention, there is provided a
method of predicting water demand for every reference
period in a predetermined water distribution area in
which water distribution is performed from water
distribution facilities through a water distribution pipe
network. According to the method, water demand by the
predetermined water distribution area, weather
information of the water distribution area and day-ofweek information is acquired, and weather information of
the predetermined period, day-of-week information and
water demand in a predetermined range before the
reference period are set as related conditions related to
water demand in the reference period, and then a
similarity between the related conditions in reference
5
periods in a predetermined period in a past and the
related conditions in a reference period in which the
water demand is to be predicted is calculated and water
demand in the reference period in which the water demand
is to be predicted is predicted, for example, by
preferentially using a water demand performance value in
the reference period having a condition that the
similarity is high.
[0008]
With the present invention, even in such a case
that the change of the water demand is not uniform, the
water demand can be predicted accurately.
The above and other objects, features and
advantages of the present invention will become apparent
from the following description and the appended claims,
taken in conjunction with the accompanying drawings in
which like parts or elements denoted by like reference
characters.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009]
FIG. 1 is an exemplary block diagram of a water
supply system including a computer system as a water
demand prediction system;
FIG. 2 is a view of an exemplary water demand data
6
management table;
FIG. 3 is a view of an exemplary day-of-week and
weather data management table;
FIG. 4 is a view of an exemplary setting screen
image of water demand prediction conditions;
FIG. 5 is a view of an exemplary prediction
condition management table;
FIG. 6 is an explanatory view of a kernel ridge
regression model;
FIG. 7 is a graph illustrating a relationship
between most recent water demand data in a prediction
date and a learning date;
FIG. 8 is a graph illustrating another relationship
between most recent water demand data in a prediction
date and a learning date;
FIG. 9 is a graph illustrating a further
relationship between most recent water demand data in a
prediction date and a learning date;
FIG. 10 is a view of an example of a water demand
prediction data management table;
FIG. 11 is a view of an exemplary prediction result
display data management table;
FIG. 12 is a view of an exemplary prediction result
display screen image; and
FIG. 13 is a view of an exemplary model parameter
7
management table.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0010]
In the following, an embodiment of the present
invention is described in detail with reference to the
drawings. It is to be noted that the present invention
shall not be restricted by the embodiment described
below.
[0011]
FIG. 1 depicts a block diagram of a water supply
system 102. The water supply system 102 includes water
distribution facilities 100, a monitoring controlling
system (SCADA) 103 for the water distribution facilities
100, a computer system 101 for predicting the water
demand, and a network 111 that connects the monitoring
controlling system 103 and the computer system 101 to
each other.
[0012]
The water distribution facilities 100 include a
water purification plant 104, a pump 105, a reservoir
106, a water distribution network 109 and measuring
instruments 107 and 108. The monitoring controlling
system 103 monitors and controls the pump 105 and
measuring instruments 107 and 108.
8
[0013]
Water purified by the water purification plant 104
is pumped to the reservoir 106 by the pump 105, stored
once in the reservoir 106 and then is distributed to
consumers 110 via the water distribution network 109. The
pump 105, water level gauge 107 and flow meter 108
measure the operation state, namely, ON/OFF state, of the
pump 105, the water level in the reservoir 106 and the
water distribution amount, namely, the demanded water
amount, to the consumers 110, respectively, in a cycle of
one minute, and transmit them to the monitoring
controlling system 103.
[0014]
The monitoring controlling system 103 acquires a
water demand measurement value in a unit of one minute in
a target water distribution area in which water is
distributed from the water distribution facilities 100
via the water distribution network 109. Then, the
monitoring controlling system 103 calculates the sum
total of the water demand measurement values for one hour
to totalize a one-hour unit demanded amount for every one
hour and transmits the sum total to the computer system
101 through the network 111.
[0015]
A climate information providing system (climate
9
information source) 112 exists outside the water supply
system 102 and delivers performance values of weather
information of an area including the target water
distribution area and prediction values of weather
information in the near future such as next day, two days
after and so forth to the computer system 101 through the
network 111 every time the latest values are obtained.
[0016]
The computer system 101 acquires water demand data
from the monitoring controlling system 103 and acquires
weather information data including prediction data from
the climate information providing system 112 through the
network 111. Then, the computer system 101 performs
predicting calculation of the demand for a period from
predetermined time such as, for example, 0 o'clock up to
24 hours ahead every day, namely, after every reference
period. Then, the computer system 101 transmits
prediction results to the monitoring controlling system
103 through the network 111.
[0017]
The monitoring controlling system 103 acquires the
water demand prediction results and drafts a water
operation plan for every one hour from the predetermined
time up to 24 hours ahead in accordance with the water
demand prediction results. The water operation plan
10
includes a water purification plan for the water
purification plant 104, an operation plan for the pump
105, a water reservation plan for the reservoir 106 and
so forth. Then, the monitoring controlling system 103
performs operation control of the water purification
equipment of the water purification plant 104 and the
pump 105 on the basis of the water operation plan. Daily
water demand prediction and water operation plan drafting
based on the daily water demand prediction are performed
in such a manner as described above, and operation
control of the water supply system is performed on the
basis of the water operation plan such that an
appropriate amount of water is supplied to the customers.
[0018]
The computer system 101 includes general computer
hardware elements such as a controller including a
central processing unit (CPU), a storage device including
a random access memory (RAM), a hard disk, a flash memory
and so forth, an inputting unit 121 including a keyboard,
a mouse and so forth, and a display unit 122 including a
display, a printer and so forth.
[0019]
In the storage device, a data acquisition unit 123,
a prediction condition setting unit 124, a water demand
prediction unit 125, a prediction result display unit 126
11
and a model parameter determination unit 127 are set as
function modules implemented by execution of a program by
the controller. Each function module may be paraphrased
as a means, a unit or the like.
[0020]
In the storage device, a water demand data
management table 131, a day-of-week and weather data
management table 132, a prediction condition management
table 133, a model parameter management table 134, a
water demand prediction data management table 135 and a
prediction result display data management table 136 are
stored. The tables are used by the controller when the
controller executes any of the modules.
[0021]
The data acquisition unit 123 acquires water demand
performance data transmitted from the monitoring
controlling system 103 and weather information data
transmitted from the climate information providing system
112 and registers the acquired data into a predetermined
table.
[0022]
The prediction condition setting unit 124 sets,
into a predetermined table, conditions that are inputted
by a manager of the computer system 101 using the
inputting unit 121 and that are to be used in prediction
12
calculation. The conditions include prediction start
time, related conditions related to the water demand such
as the weather, a day-of-week, water demand for a
predetermined most recent period, and the number of most
recent days in the past, namely, of learning days.
[0023]
The water demand prediction unit 125 performs
prediction of the water demand on the prediction day on
the basis of a kernel ridge regression model using the
related condition data in the prediction day and each day
within the predetermined period in the past. Then, the
water demand prediction unit 125 delivers a result of the
prediction to the monitoring controlling system 103.
[0024]
The prediction result display unit 126 creates a
display screen image of the water demand prediction
result and displays the display screen image on the
display unit 122.
[0025]
The model parameter determination unit 127
determines model parameters of a kernel ridge regression
model to be used for prediction calculation of the water
demand.
[0026]
The water demand data management table 131 is a
13
data group for managing water demand measurement values
for every one hour.
[0027]
The day-of-week and weather data management table
132 is a data group for managing day-of-week information
and weather information, which includes weather
prediction information, for every day.
[0028]
The prediction condition management table 133 is a
data group for managing conditions for prediction
calculation such as prediction start time, related
information related to the water demand such as the
weather, day-of-week, water demand for a predetermined
most recent period and so forth, and the number of most
recent days in the past, namely, of learning days, to be
used for prediction calculation.
[0029]
The model parameter management table 134 is a data
group for managing model parameters of a kernel ridge
regression model to be used for prediction calculation of
the water demand.
[0030]
The water demand prediction data management table
135 is a data group for managing water demand prediction
values for every one hour.
14
[0031]
The prediction result display data management table
136 is a data group for managing display information of
prediction results in regard to a water demand prediction
value for every one hour after prediction start time,
measurement values, namely, performance values, a water
demand integration error and a reservoir water level
conversion value of the integrated error.
[0032]
The computer system 101 executes processes (1) to
(5) given below to implement prediction of the water
demand by referring to the water demand in a day in the
past having conditions close to the conditions related to
the water demand at present to achieve water demand
prediction of high accuracy conforming to a variation of
the water demand.
[0033]
Process (1): acquisition of water demand and
weather information
Process (2): setting of prediction conditions
Process (3): prediction of water demand
Process (4): displaying of a water demand
prediction result
Process (5): determination of model parameters
In the following, the processes (1) to (5) are
15
descried with reference to FIGS. 2 to 13. Regarding the
acquisition process (1) of water demand and weather
information, every time the monitoring controlling system
103 aggregates water demand in a unit of one hour in a
target delivery area, the monitoring controlling system
103 transmits the latest water demand measurement value
and measurement time of the latest water demand
measurement value to the computer system 101 through the
network 111.
[0034]
The data acquisition unit 123 of the computer
system 101 successively acquires the water demand
measured value, namely, the performance value, and
measurement time of the water demand measured value
transmitted thereto and registers them into the water
demand data management table 131. FIG. 2 depicts an
example of the water demand data management table 131
registered by the data acquisition unit 123.
[0035]
The climate information providing system 112
delivers performance values of weather information of the
area including the target water distribution area and
prediction values of weather information of the next day
once a day to the computer system 101 through the network
111.
16
[0036]
The data acquisition unit 123 acquires the weather
information delivered as described above and classifies
the weather information into information on the highest
temperature, presence or absence of sunny, presence or
absence of rain and presence or absence of snow. Then,
the data acquisition unit 123 registers the acquired
information into the day-of-week and weather data
management table 132 together with the date, the day-ofweek, namely, Monday to Sunday or public holiday,
distinction between performance and forecast to update
the day-of-week and weather data management table 132.
FIG. 3 depicts an example of the day-of-week and weather
data management table 132 registered by the data
acquisition unit 123.
[0037]
The setting process (2) of prediction conditions is
described. Generally, the daily water demand in a time
series for 24 hours changes by an influence of the
weather and the highest temperature of the day, the dayof-week, the most recent water demand in a time series
and so forth. However, there is a tendency that, between
days in which conditions related to the water demand are
similar to each other, there is a similar water demand.
[0038]
17
Therefore, the computer system 101 predicts water
demand in a prediction day using water demand performance
data, which may be data of a plurality of days, in the
past having related conditions similar to those of the
prediction day. The setting process (2) of prediction
conditions is setting in advance of preconditions,
namely, prediction conditions, necessary for the water
demand prediction calculation described hereinabove such
as prediction start time, related conditions related to
the water demand, the number of most recent days in the
past for reference in prediction calculation and so
forth.
[0039]
A manager of the computer system 101 would operate
the inputting unit 121 to input prediction start time,
related conditions related to the water demand selected
from among the weather, highest temperature, day-of-week
and most recent water demand and the number of most
recent days in the past to be referred to in prediction
calculation. Then, the prediction condition setting unit
124 of the computer system 101 registers the set
prediction conditions into the prediction condition
management table 133.
[0040]
FIG. 4 depicts an example of a display screen image
18
for prediction condition setting displayed on the display
unit 122 by the prediction condition setting unit 124.
The display screen image is configured such that the
manager can select a related condition or conditions that
are appropriate to the target water distribution area
from among related conditions related to the water
demand, representative ones of which are the weather and
highest temperature of the day, day-of-week, most recent
water demand in time series and so forth.
[0041]
In the case where the most recent water demand in
time series is selected, the manager would either use
most recent water demand for several hours in prediction
calculation or input also a period for them. For example,
in the case where the prediction start time is 0 o'clock
and the period of the most recent water demand is eight
hours, water demand prediction is performed for 0 to 24
o'clock of the next data using water demand time series
data from 16 to 0 or 24 o'clock.
[0042]
In the case where the most recent water demand in
time series is selected, the manager would select whether
the water demand is used as "water demand time series
data alone" for prediction calculation, whether the water
demand is used as the "water demand time series data +
19
difference data" or whether the water demand is used as
the "water demand time series data + total amount data."
[0043]
By using not only most recent water demand time
series data but also difference data or total amount data
of the recent water demand time series data as related
conditions related to the water demand in prediction
calculation as hereinafter described, prediction
calculations of different features become possible. The
predication calculations may be a prediction in which a
waveform is similar to that of the performance value
trend, a prediction in which the integration error with a
performance value is small, or the like prediction.
[0044]
In the case where the day-of-week information is
selected, the manager would select whether the day-ofweek information is used as "by weekday and holiday (two
categories)" information in prediction calculation,
whether the day-of-week information is used as "by each
day-of-week and holiday (eight categories)" information,
or whether, 'although the day-of-week is used as "by each
day-of-week and holiday (eight categories)" information,
it is used as "changing a predetermined day-of-week among
three or more consecutive holidays" information.'
[0045]
20
'Although the day-of-week is used as "by each dayof-week and holiday (eight categories)" information, it
is used as "changing a predetermined day-of-week among
three or more consecutive holidays" information'
signifies that the day before consecutive three or more
days is changed to Friday and the first day of the
consecutive holidays is changed to Saturday and then the
last day is changed to Sunday. This is because, depending
upon a water distribution area, such day-of-week change
as just described sometimes results in improvement of the
prediction accuracy of the water demand. For example, in
the case of three consecutive holidays of "Friday that is
a public holiday, Saturday, and Sunday," although the day
before is Thursday, since the day before is a weekday
before the holiday, it sometimes indicates a pattern
similar to that of the water demand in Friday. On the
other hand, for example, in the case of three consecutive
holidays of "Saturday, Sunday, and Monday that is a
public holiday," although Monday, which is a public
holiday, of the last day of the three consecutive
holidays, since this is a public holiday before a
weekday, it sometimes indicates a pattern of water demand
similar to that of Sunday. Therefore, such changes of a
week day sometimes lead to improvement in prediction
accuracy.
21
[0046]
FIG. 5 depicts an example of the prediction
condition management table 133 registered by the
prediction condition setting unit 124. Setting contents
of the prediction condition management table 133 in FIG.
5 correspond to setting contents at the time of setting
of prediction as depicted in FIG. 4.
[0047]
The setting process of prediction conditions is
performed in such a manner as described above by the
prediction condition setting unit 124.
[0048]
Now, the prediction process (3) of water demand is
described. The computer system 101 performs water demand
prediction on the day of prediction preferentially
utilizing water demand performance values in at least one
day in a most recent predetermined period in the past
having related condition data similar to those on the day
of the prediction. In the water demand prediction, the
computer system 101 uses related condition data related
to the water demand on the day of prediction including
data of the weather, highest temperature, day-of-week and
most recent water demand time series, related condition
data related to the water demand in each day in the most
recent predetermined period in the past and water demand
22
performance data corresponding to the prediction target
time zone of each of the days.
[0049]
For example, a similarity between the related
condition data on the day of prediction and the related
condition data on the days in the most recent
predetermined period in the past is calculated. Then,
prediction calculation is performed using such a model
formula that prioritizes the water demand performance
value in the prediction target time zone in the day in
the past having a related condition data that has high
similarity. For example, the prediction calculation is
performed by weighted averaging water demand performance
values in response to the similarities in the days in the
past. As such a model of prediction calculation based on
similarities as described above, for example, a kernel
ridge regression model is utilized by the computer system
101.
[0050]
The kernel ridge regression model is described with
reference to FIG. 6. It is considered that, when
performance data as learning data indicated by round
marks on an XY plane are given, a value Ynew of a Y
coordinate corresponding to an input of a value Xnew of
an X coordinate is predicted. At this time, it can be
23
estimated that the value Ynew takes a value proximate to
a Y coordinate of the performance data in the proximity
of the value Xnew, and performance data remote from the
value Xnew need not be taken into consideration very
much. Therefore, when N pieces of performance data as
learning data are given, the value Ynew of Y
corresponding to the input Xnew can be represented by the
following expression 1:
[0051]
[Expression 1]
Ynew(Xnew)
= ∑ (function representative of closeness between X(i) and Xnew)
𝑁
𝑖=1
× (Y(i))
...... (expression 1)
The kernel ridge regression model is based on the way of
thinking described above. In particular, the kernel ridge
regression model is a model where a function
representative of closeness of the input data and the
performance data in the expression 1 is represented by a
Gaussian kernel function and a multiplier for the
function is represented not by the Y coordinate value of
the performance data but by a parameter and is formulated
in the following manner.
[0052]
24
Where
Yt: water demand at time t with the time step being
a unit of one hour,
Z1: binary variable representative of presence or
absence of sunny on the prediction date where 1: present
and 0: absent,
Z2: binary variable representative of presence or
absence of rain on the prediction date,
Z3: binary variable representative of presence or
absence of snow on the prediction date,
Z4: highest temperature in the prediction date, and
Wi: binary variable representative of a day-of-week
of the prediction date where one variable only of W1 is
used when days are categorized into a weekday and a
holiday and eight variables of W1 to W8 corresponding to
Monday to Sunday and a public holiday are used when days
are categorized into Monday to Sunday and a public
holiday, and where input data (vectors) composed of
related condition data, namely, of the weather, highest
temperature, day-of-week and most recent water demand
time series, for the water demand is represented by
[0053]
[Expression 2]
Xt = (Yt, Yt-1, ..., Yt-m+1, Z1, Z2, Z3, Z4, Wi),
the water demand Yt+n at time t+n (n = 1, ..., 24) is
25
predicted using
Yt + n(Xt) = ∑ 𝛼𝑖 × 𝑘(𝑋𝑡, 𝑋𝑡(𝑖))
𝑁
𝑖=1
...... (expression 2)
where N: number of days of learning data
αi = regression parameter (i = 1, ..., N)
(Xt(i), Yt+n(i)): ith day model learning
data for most recent N days in the past, namely, input
and output pair data on the day in the past corresponding
to time same as that of the input and output data on the
prediction day. Here, k(Xt, Xt(i)) is a Gaussian kernel
function representative of closeness between the input
data Xt of the prediction day and the learning input data
Xt(i) on the ith day in the past, and is defined by
[0054]
[Expression 3]
k(Xt, Xt(i)) = exp(-β × ||Xt - Xt(i)||^2)
...... (expression 3)
where ||Xt - Xt(i)||: distance between input data,
namely, vectors, Xt and Xt(i), namely, L2 norm, a square
root of the residual sum of squares of the components of
the vectors, is defined by
β: hyper parameter, β > 0
The Gaussian kernel function assumes continuous values
from 0 to 1, and has a value nearer to 1 as the distance
between the input data Xt on the prediction day and
26
learning input data Xt(i) on the ith day in the past
decreases and has a value nearer to 0 as the distance
increases. Therefore, data of a day in the past having
input data similar, namely shorter in distance, to input
data of the prediction day, has a greater influence on
the prediction value. The input data are related
condition data related to the water demand such as data
of the weather, highest temperature, day-of-week, and
most recent water demand time series. Thus, prediction is
performed which preferentially utilizes data in a day in
the past having input data similar, namely, nearer in
distance, to the input data of the prediction day.
[0055]
In the foregoing description, the input data
vectors corresponding the prediction day and a day in the
past, which is a learning date, are configured from the
weather, the highest temperature, a day-of-week and a
most recent water demand time series. Here, however,
paying attention only to the water demand time series, a
case in which water demand data corresponding to the
prediction day and water demand data corresponding to two
learning days 1 and 2 are available as depicted in an
example of FIG. 7 is assumed.
[0056]
At this time, it is assumed that the other
27
conditions of the weather, highest temperature and dayof-week are same among the days. Further, it is assumed
that learning day 1 data that is the most recent water
demand is always higher by a predetermined amount than
the prediction day data and learning day 2 data
fluctuates upwardly and downwardly by the predetermined
amount from the prediction day data. At this time,
generally it is predicted that, if the other conditions
are same, then also in the water demand data after the
prediction start time in the prediction day and the
learning days 1 and 2, the relationships described above
tend to continue for some period. Since the distance,
namely, the similarity, between the two input data
vectors is calculated by the L2 norm, namely, by the
square sum of errors of the components as described
hereinabove, the distances between the prediction day
data and the two learning day 1, 2 data become about the
same. Thus, the prediction result becomes likely to
reflect the water demand performances in the prediction
time zone of the learning day data 1 and 2 to a similar
extent on the water demand prediction on the prediction
day. It is to be noted that FIG. 7 is an image view and
the prediction result may not necessarily become such as
depicted in FIG. 7.
[0057]
28
Here, if the difference value of a most recent
water demand time series at each time from that at
preceding time is added as a component of the input data
vector, then the difference values of the most recent
water demand time series between the prediction day data
and the learning day 1 data have values similar to each
other. Therefore, it is likely to occur that the
distance, namely, the similarity, to the prediction day
data becomes smaller from the learning day 1 data than
from the learning day 2 data and the prediction result
reflects the water demand performance of the learning day
1 data in the prediction time zone significantly on the
water demand prediction on the prediction day, namely,
the prediction result has a waveform similar to that of
the performance value but indicates an increase by a
predetermined amount from the performance value of the
prediction day as depicted in FIG. 8. However, it is to
be noted that, in this case, since the prediction value
is normally higher than the performance value, the
integration error of the water demand prediction
increases. Since the prediction error of the water demand
appears as an error between the performance and the
prediction of the reservoir water level, there is the
possibility that increase in the integration error may
lead to deviation of the reservoir water level from the
29
upper or lower limit water level. Therefore, for the
water operation, a prediction result that the prediction
value varies upwardly and downwardly around the
performance value such that the integration error does
not become great is sometimes more desirable than a
prediction result of the water demand that normally
exceeds the performance.
[0058]
If the total value of a most recent water demand
time series is added as a component of the input data
vector, then since the total values of the recent water
demand time series of the prediction day data and the
learning day 2 data have values similar to each other, it
is likely to occur that the distance, namely, the
similarity, to the prediction day data becomes smaller
from the learning day 1 data than from the learning day 2
data and the prediction result reflects the water demand
performance of the learning day 2 data in the prediction
time zone significantly on the water demand prediction on
the prediction day, namely, the prediction result
indicates a variation upwardly or downwardly by a
predetermined amount from the performance value of the
prediction day as depicted in FIG. 9. In this case, since
the performance value and the water demand total value
are likely to become close to each other, reduction of
30
the integration error of the water demand prediction can
be anticipated.
[0059]
Therefore, by newly adding the difference value or
the total value of a recent water demand time series to
the input data vector corresponding to the prediction day
and a day in the past, namely, a learning day, it becomes
possible to select a prediction result similar in
waveform to a water demand performance, a prediction
result that the integration error is small or the like
prediction result. The addition of the difference value
or the total value to the input data vector corresponds
to difference data addition or total amount addition at
the time of selecting the recent water demand selected as
a related condition data related to the water demand
which is described hereinabove in connection with the
setting process (2) of prediction conditions. Thus, it is
sufficient if the manager of the computer system 101
changes over the selection described above in accordance
with an object of the water demand prediction.
[0060]
Here, the regression parameter αi (i = 1, ..., N)
is determined such that, every time prediction
calculation is performed, an evaluation function R
including the square sum of errors with respect to
31
prediction results obtained when learning data of all
days in the past are inputted to the expression 2 and a
normalization term for overfit prevention to learning
data is minimized as given by an expression 4 given
below.
[0061]
[Expression 4]
R = ∑ (𝑌𝑡 + 𝑛(𝑋𝑡(𝑖)) − 𝑌𝑡 + 𝑛(𝑖))^
𝑁
𝑖=1 2 + (normalization term)
...... (expression 4)
The evaluation function R is a function of the
regression parameter αi, and the regression parameter αi
that minimizes the evaluation function R can be
calculated analytically although the expression for the
calculation is omitted. Therefore, every time the
prediction calculation is performed, the regression
parameter αi can be calculated using the input data Xt of
the prediction day obtained till time t and the
input/output data Xt(i) and Yt+n(i) in a day in the past,
namely, in the learning data day. Consequently, the water
demand prediction value Yt+n at the prediction target
time t+n can be calculated from the expression 2. By
repeating the calculation described above with n changed
to n = 1, ..., 24 and the calculation also of the
parameter αi, the water demand prediction value in the
prediction target time zone, namely, for 24 hours from
32
time t+1 to time t+24, can be calculated.
[0062]
The normalization term includes a parameter λ not
depicted that prescribes a degree of prevention of
overfit with respect to learning data. β included in the
kernel function and λ included in the normalization term
are hyper parameters, namely, parameters for controlling
the behavior of the algorithm, and are determined in
advance by a Brute force method or the like such that,
using data for a predetermined period in the past, the
square sum of errors between the prediction value and the
performance value of the water demand calculated using
the calculation described above is minimized.
[0063]
Therefore, it is possible to perform prediction
calculation of the water demand on the predication day
preferentially utilizing the water demand performance
values in a day or days within a most recent
predetermined period having the related condition data
similar to those of the prediction date on the basis of a
kernel ridge regression model. In the prediction
calculation, related condition data related to the water
demand on the prediction day including data of the
weather, highest temperature, day-of-week and most recent
water demand time series, related condition data related
33
to the water demand in each day in the most recent
predetermined period in the past and water demand
performance data corresponding to the prediction target
time zone of each of the days are used.
[0064]
The prediction process (3) of water demand is
performed basically once a day at a point of time at
which the latest water demand measurement value till the
prediction star time is acquired. However, as hereinafter
described, in the case where the manager of the computer
system 101 decides that the water demand prediction error
has increased, the prediction process, namely, reprediction, of the water demand can be performed by an
instruction from the manager.
[0065]
The water demand prediction unit 125 of the
computer system 101 acquires prediction start time,
related condition data related to the water demand
including data of the weather, highest temperature, dayof-week and most recent water demand time series, and the
number of most recent days, namely, the number of days of
learning data, which are necessitated in water demand
prediction, from the prediction condition management
table 133.
[0066]
34
Then, the water demand prediction unit 125 acquires
data from the water demand data management table 131 and
the day-of-week and weather data management table 132.
The data include data of the most recent water demand
performance values, weather, highest temperature and days
of week till the prediction start time in the prediction
day and the predetermined days in the past, namely, in
the learning days. The data further include water demand
performance value data in the prediction time zone in the
predetermined days in the past, namely, in the learning
days.
[0067]
At this time, the water demand prediction unit 125
performs category change of day-of-week information and
information addition in accordance with the setting
contents performed by the process (2) described above.
Here, the category change is change by weekday and
holiday, by day-of-week and holiday and by day-of-week
and holiday + change of a predetermined day-of-week among
three or more consecutive holidays. The information
addition is addition of water demand time series data
related information to the input data vector, namely,
addition of water demand time series data alone, water
demand time series data + difference data or water demand
time series data + total amount data. Then, the water
35
demand prediction unit 125 acquires the hyper parameters
β and λ of the kernel ridge regression model described
hereinabove from the model parameter management table
134.
[0068]
The water demand prediction unit 125 performs
calculation of the water demand prediction value in the
prediction time zone of the prediction day using
prediction calculation based on the kernel ridge
regression model described above using the acquired data.
The water demand prediction unit 125 registers a result
of the prediction into the water demand prediction data
management table 135 and delivers the result of the
prediction to the monitoring controlling system 103
through the network 111. As a result, the monitoring
controlling system 103 can formulate an operation plan of
the pump 105 and a planned water level of the reservoir
106 based on the water demand prediction result delivered
thereto. FIG. 10 depicts an example of the water demand
prediction data management table 135 registered by the
water demand prediction unit 125.
[0069]
The prediction process of water demand is performed
by the water demand prediction unit 125 in such a manner
as described above.
36
[0070]
Now, the displaying process (4) of a water demand
prediction result is described. This process (4) is
executed every time the latest water demand prediction
result by the process (3) described above is obtained and
every time the latest water demand measurement value,
namely, a performance value, by the process (1) described
above is obtained. The prediction result display unit 126
of the computer system 101 acquires the latest prediction
result from the water demand prediction data management
table 135, and acquires the latest water demand
performance value from the water demand data management
table 131. Then, the prediction result display unit 126
calculates the sum total of prediction errors, each of
which is equal to a “prediction value - performance
value,” from the prediction start time, which is one
o'clock, to each point of time to calculate the
integrated error of the water demand.
[0071]
Then, the prediction result display unit 126
divides the calculated integration error by the sectional
area of the reservoir 106 to calculate a water level
conversion value of the reservoir 106. Then, the
prediction result display unit 126 registers the acquired
and calculated prediction day of the water demand,
37
performance value, integration error and reservoir water
level conversion value of the water demand integration
error into the prediction result display data management
table 136. Further, the prediction result display unit
126 creates a prediction result display screen image for
displaying the data in the form of a graph and causes the
display unit 122 to display the prediction result display
screen image.
[0072]
FIG. 11 depicts an example of the prediction result
display data management table 136 registered by the
prediction result display unit 126. Further, FIG. 12
depicts an example of a prediction result display screen
image created by the prediction result display unit 126.
[0073]
The display process of a water demand prediction
result is performed in such a manner as described above
by the prediction result display unit 126.
[0074]
The manager of the computer system 101 can browse
the prediction result display screen image and make a
decision about whether or not the water demand prediction
error is increasing. Then, in the case where it is
decided that the water demand prediction error is
increasing, the computer system 101 can perform re-
38
prediction of the water demand using the latest data. In
the case where re-prediction is to be performed, the
manager would operate the inputting unit 121 to input new
prediction start time that is time at present and give
instruction to perform re-prediction from the prediction
start time.
[0075]
Then, the water demand prediction unit 125 performs
prediction calculation of the water demand from the new
prediction start time to 24 hours ahead using the latest
water demand performance value, weather data and so
forth, registers a result of the prediction into the
water demand prediction data management table 135 and
delivers the result of the prediction to the monitoring
controlling system 103 as in the process (3). This makes
it possible to perform re-prediction calculation of the
water demand using the latest data even in the case where
the prediction error increases.
[0076]
Now, the determination process (5) of a model
parameter is described. It is sufficient if the process
(5) is performed periodically such as, for example, once
a year or once every six months. The model parameter
determination unit 127 sets initial values, here,
sufficiently high values, for the parameters β and λ of
39
the kernel ridge regression model described above and
sets each day within a predetermined period in the past,
for example, within three months, most recent from now to
a prediction day. Then, the model parameter determination
unit 127 calls the water demand prediction unit 125 and
executes the prediction process (3) of water demand in
the prediction time zone of each prediction day. At this
time, conditions registered in the prediction condition
management table 133 are selectively used for the
prediction.
[0077]
Then, the model parameter determination unit 127
acquires the water demand performance values of the
prediction days from the water demand data management
table 131 and calculates the square sum of the prediction
errors between the prediction values and the performance
values in all prediction time zones and all prediction
days.
[0078]
The model parameter determination unit 127 repeats
the prediction process while successively decreasing the
values of the parameters β and λ by predetermined values.
Then, the model parameter determination unit 127
registers the values of the parameters β and λ that
minimize the square sum of the calculated prediction
40
errors, as optimum parameter values into the model
parameter management table 134. FIG. 13 depicts an
example of the model parameter management table 134.
[0079]
The determination process of a model parameter is
performed in such a manner as described above by the
model parameter determination unit 127.
[0080]
In the embodiment described above, if correction of
a model parameter is continued to advance learning of a
kernel ridge regression model, then the computer system
101 can predict the water demand on the basis only of
related conditions at a point of time at which the water
demand is to be predicted.
[0081]
As described above, according to the embodiment of
the present invention, prediction calculation of the
water demand on a predication day is performed
preferentially utilizing the water demand performance
values in a day or days within a most recent
predetermined period having the related condition data
similar to those of the prediction date. In the
prediction calculation, related condition data related to
the water demand on the day of measurement including data
of the weather, highest temperature, day-of-week and most
41
recent water demand time series, related condition data
related to the water demand in each day in the most
recent predetermined period in the past and water demand
performance data corresponding to the prediction target
time zone of each of the days are used. As a result,
since prediction is performed with reference to the water
demand in a day in the past that indicates a close change
of the water demand, water demand prediction of high
accuracy adapted to a change of the water demand is made
possible.
While a preferred embodiment of the present
invention has been described using specific terms, such
description is for illustrative purposes only, and it is
to be understood that changes and variations may be made
without departing from the spirit or scope of the
following claims.

WHAT IS CLAIMED IS:
1. A water demand prediction system that predicts
water demand for every reference period in a
predetermined water distribution area in which water
distribution is performed from water distribution
facilities through a water distribution pipe network, the
water demand prediction system comprising:
a memory; and
a controller, wherein
execution of the controller on a basis of a
prediction program for water demand includes
acquiring performance values of the water
demand in the predetermined water distribution area, the
performance values being measured continuously by the
water distribution facilities, from a monitoring
controlling system of the water distribution facilities
and recording the acquired performance values together
with information on a weather and information on a dayof-week into the memory,
setting related conditions to be utilized in
prediction of the water demand, the related conditions
including the information on the weather, the information
on the day-of-week and the performance values of the
water demand for a predetermined period preceding to the
43
reference period,
obtaining the related conditions for each
reference period in regard to the performance values of
the water demand for a predetermined period in a past,
the performance values being recorded in the memory, and
calculating a similarity between the related conditions
and related conditions for a reference period in which
the water demand is to be predicted,
performing prediction calculation of the
water demand by referring to the similarities on a basis
of at least one of the performance values of the water
demand among the performance values of the water demand
in a plurality of the reference periods in the
predetermined period in the past, and
transmitting a result of the prediction
calculation to the monitoring controlling system.
2. The water demand prediction system according to
claim 1, wherein
the performing prediction calculation of the water
demand includes preferentially utilizing, in the
prediction calculation of the water demand, a performance
value of the water demand in a reference period in which
the similarity is higher among the reference periods in
the predetermined period in the past.
3. The water demand prediction system according to
44
claim 2, wherein
the performing prediction calculation of the water
demand includes performing prediction of the water demand
on a basis of the similarity using a kernel ridge
regression model in which the related conditions in the
reference period within which the water demand is to be
predicted are used as input data, and in which the
related conditions and the water demand performance
values in the reference periods in the predetermined
period in the past are used as learning data.
4. The water demand prediction system according to
claim 1, wherein
the setting related conditions to be utilized in
prediction of the water demand includes setting
difference values of the water demand for individual
points of time for a predetermined period before the
reference period as one of the related conditions.
5. The water demand prediction system according to
claim 1, wherein
the setting related conditions to be utilized in
prediction of the water demand includes adding a total
value of the water demands for a predetermined period
before the reference period to the related conditions.
6. The water demand prediction system according to
claim 1, wherein
45
the setting related conditions to be utilized in
prediction of the water demand includes, as the
information on the day-of-week, at least one of those
including: setting a day before three or more consecutive
holidays to Friday; regarding a first day of three or
more consecutive holidays as Saturday; and setting a last
day of three or more consecutive holidays to Sunday.
7. The water demand prediction system according to
claim 1, wherein
the controller displays at least one of those
including: the predicted water demand and a performance
value of the water demand; an integration error between
the predicted water demand and a performance value of the
water demand after predetermined time; and a water level
conversion value of a reservoir of the water distribution
facilities from the integration error.
8. The water demand prediction system according to
claim 1, wherein
the water demand prediction system is configured so
as to allow a manager of the water demand prediction
system to input a predetermined period before the
reference period and the predetermined period in the past
through an inputting apparatus.
9. The water demand prediction system according to
claim 1, wherein
46
the water demand prediction system is configured so
as to allow a manager of the water demand prediction
system to input information on a day-of-week as one of
the related conditions to the water demand prediction
system through an inputting apparatus, and the
information on a day-of-week has a plurality of forms
such that the manager is allowed to select a
predetermined form from among the plurality of forms.
10. The water demand prediction system according
to claim 1, wherein
the water demand prediction system is configured so
as to allow a manager of the water demand prediction
system to input a form of a performance value of the
water demand as one of the related conditions through an
inputting apparatus, and the performance value of the
water demand has a plurality of forms such that the
manager is permitted to select a predetermined form from
among the plurality of forms.
11. A method, for a computer, of predicting water
demand for every reference period in a predetermined
water distribution area in which water distribution is
performed from water distribution facilities through a
water distribution pipe network, the method comprising:
acquiring water demand by the predetermined water
distribution area, weather information of the water
47
distribution area and day-of-week information;
setting weather information of the predetermined
period, day-of-week information and water demand in a
predetermined range before the reference period as
related conditions related to water demand in the
reference period; and
calculating a similarity between the related
conditions in reference periods in a predetermined period
in a past and the related conditions in a reference
period in which the water demand is to be predicted, and
predicting water demand in the reference period in which
the water demand is to be predicted preferentially using
a water demand performance value in the reference period
having a condition that the similarity is high.