water

Article
Development of a Deep Learning-Based Prediction Model for
Water Consumption at the Household Level
Jongsung Kim 1 , Haneul Lee 1 , Myungjin Lee 1 , Heechan Han 2 , Donghyun Kim 3 and Hung Soo Kim 3, *

1 Institute of Water Resources System, Inha University, Incheon 22201, Korea; kjjs0308@naver.com (J.K.);
haneul6802@naver.com (H.L.); lmj3544@naver.com (M.L.)
2 Blackland Research and Extension Center, Texas A&M AgriLife, Temple, TX 76502, USA;
heechan.han@ag.tamu.edu
3 Department of Civil Engineering, Inha University, Incheon 22201, Korea; yesdktpdi@naver.com
* Correspondence: sookim@inha.ac.kr; Tel.: +82-10-3441-1038

Abstract: The importance of efficient water resource supply has been acknowledged, and it is essential
to predict short-term water consumption in the future. Recently, it has become possible to obtain data
on water consumption at the household level through smart water meters. The pattern of these data is
nonlinear due to various factors related to human activities, such as holidays and weather. However,
it is difficult to accurately predict household water consumption with a nonlinear pattern with the
autoregressive integrated moving average (ARIMA) model, a traditional time series prediction model.
Thus, this study used a deep learning-based long short-term memory (LSTM) approach to develop
a water consumption prediction model for each customer. The proposed model considers several
variables to learn nonlinear water consumption patterns. We developed an ARIMA model and an
LSTM model in the training dataset for customers with four different water-use types (detached
houses, apartment, restaurant, and elementary school). The performances of the two models were
evaluated using a test dataset that was not used for model learning. The LSTM model outperformed
the ARIMA model in all households (correlation coefficient: mean 89% and root mean square error:
mean 5.60 m3 ). Therefore, it is expected that the proposed model can predict customer-specific water
Citation: Kim, J.; Lee, H.; Lee, M.;
consumption at the household level depending on the type of use.
Han, H.; Kim, D.; Kim, H.S.
Development of a Deep
Keywords: ARIMA model; household-level; LSTM model; water consumption prediction
Learning-Based Prediction Model for
Water Consumption at the
Household Level. Water 2022, 14,
1512. https://doi.org/10.3390/
w14091512 1. Introduction

Received: 6 April 2022

Water is one of humanity’s most essential resources, and water supply facilities are
Accepted: 6 May 2022
necessary for ensuring an efficient supply of limited water resources. The water supply
Published: 9 May 2022
penetration rate is over 80% in developed countries and less than 50% in developing coun-
tries, depending on the level of development [1]. In Korea, the water supply penetration
Publisher’s Note: MDPI stays neutral
rate was 99.3% in 2019, with the aging water supply network accounting for more than
with regard to jurisdictional claims in
32% [2]. This has caused various water problems, such as water quality deterioration and
published maps and institutional affil-
leakage, and further aggravated water stress.
iations.
Therefore, the focus used to be on establishing water supply facilities, but in recent
years, the importance of efficient water resource supply has been acknowledged. Many
studies have been conducted on short-term future water consumption prediction, which is
Copyright: © 2022 by the authors.
vital for efficient water management [3–6]. For example, Alvisi et al. [7] emphasized that
Licensee MDPI, Basel, Switzerland. water supply should be operated based on future water demand to supply water efficiently.
This article is an open access article They predicted future water consumption patterns using an autoregressive (AR) model,
distributed under the terms and which is a linear time series model that predicts water consumption for adequate water
conditions of the Creative Commons supply. Atsalakis et al. [8] stated that a large-scale water supply management system is
Attribution (CC BY) license (https:// necessary to predict water demand accurately. Therefore, they developed an adaptive neuro-
creativecommons.org/licenses/by/ fuzzy inference system (ANFIS) by applying the neuro-fuzzy concept to a linear time-series
4.0/). model and compared the predictive performance to that of the AR model. Paulo et al. [9]

Water 2022, 14, 1512. https://doi.org/10.3390/w14091512 https://www.mdpi.com/journal/water

Water 2022, 14, 1512 2 of 17

noted that accurate short-term water demand prediction is essential for water managers
to make efficient decisions. They proposed the harmony search optimization algorithm
based on the autoregressive integrated moving average (ARIMA) model to improve water
demand prediction performance. Salah et al. [10] proposed a method for removing noise
from water consumption data and used the noise-removed water consumption data and
an AR model to predict monthly water demand. Furthermore, Haiyan et al. [11] predicted
annual water demand for adequate water supply in Beijing, experiencing a water shortage
as a result of rapid urban growth. The uncertain autoregressive (UAR) model, which can
consider uncertainty in the AR model, was evaluated by comparing its water demand
prediction performance to that of the traditional AR model. Traditional time series analysis
models, such as AR and ARIMA models, have a limitation in that they cannot predict
nonlinear patterns as they are based on linear patterns of past data.
With the recent development of computing technology, machine learning and deep
learning are often used to predict nonlinear data in the hydrology field [12–14]. The
machine learning and deep learning models, such as random forest (RF) and long short-
term memory (LSTM), which can reflect the nonlinear time series characteristics of water
consumption, are being used for predicting water consumption [15–18]. For example,
Bougadis et al. [19] highlighted that it is necessary to predict future water demand and
expand water supply infrastructures to build an optimal water distribution facility based on
accurate water consumption prediction. They evaluated the artificial neural network (ANN)
and ARIMA models for predicting potential water demand and discovered that the ANN-
based prediction model outperformed the ARIMA model. Furthermore, Manuel et al. [20]
stated that it is crucial to predict the water consumption of consumers to provide an
efficient water supply, and they used ANN, RF, and support vector regression (SVR)
algorithms to predict the water consumption of cities in southeastern Spain. SVR had the
best predictive performance among the three machine learning algorithms. Mohammed
et al. [21] stated that governments must plan water distribution to plan for sustainable
development. Moreover, they used an ANN model to predict future water demand and
used various optimization techniques, such as Levenberg–Marquardt (LM) and genetic
algorithms (GA), to develop an optimal model. Li et al. [22] predicted daily water demand
in Hefei, China, by applying various data-driven models, such as LSTM, SVR, and RF
models. The SVR model had a mean absolute percentage error (MAPE) value of 7.66%,
the RF model had a MAPE value of 2.64%, and the LSTM model demonstrated the best
performance with a MAPE value of 1.36%. External factors must be considered to improve
water consumption prediction as water consumption is influenced by nonlinear patterns
such as holidays, weekdays, weather features, and human activities [23–26]. However,
most previous studies have limitations in that they only used past water consumption data
without considering external factors.
Bakker et al. [27] stated that predicting water consumption with only a single predic-
tor can produce accurate results, but prediction errors can occur significantly depending
on weather conditions. They used a multiple regression model that considers various
meteorological variables to predict water consumption in urban areas. They discovered
that prediction errors can be reduced by up to 11% when multiple meteorological vari-
ables are considered. Austin et al. [28] used a multiple regression model that considers
demographics and weather conditions to predict water consumption in Seattle, Wash-
ington. Adam et al. [29] used ANN and multiple linear regression (MLR) models that
consider historical water consumption data, humidity, and daily variables to predict daily
water consumption in Torun, Poland. They discovered that the MAPE for the MLR model
was 2.56%, while that for the ANN model was 2.28%, indicating that the ANN model
performed better. Previous studies have revealed that it is essential to consider external
factors such as weather conditions and previous water consumption data for accurate water
demand prediction.
Smart technology has recently been introduced in the water supply field as a result of
the advancement in information and communication technology and the fourth industrial
Water 2022, 14, 1512 3 of 17

revolution, and internet of things (IoT) devices such as smart water meters are being used
for efficient water management [30–33]. Since data for individual users are collected, water
leaks and errors can be easily assessed, and various services can be provided by analyzing
water consumption patterns for each user. In the United Kingdom, Asset Management
Plan 6 was launched to solve a serious leak problem, and the smart water meter project
was promoted for efficient water management [34]. Maria et al. [35] used household water
consumption data measured by a smart water meter to predict future water consumption
in the United Kingdom. In addition, the effect of weather conditions on household water
consumption was analyzed. Xenochristou et al. [36] predicted water consumption for one
to seven days based on household water consumption data collected at 30-min intervals in
the southwestern part of the United Kingdom. The characteristics of 600 households were
identified and divided into five groups, and a gradient boosting machine (GBM) model
was used to predict the water consumption of each group.
The smart water grid (SWG) project has been promoted in Incheon Metropolitan City,
South Korea, and smart water meters have been installed in urban areas to manage water
to solve the water shortage problem [37]. Choi and Kim [38] used a multiple regression
model, a multilayer perceptron model, and an LSTM model to predict future water con-
sumption based on hourly household and commercial water consumption data collected
through smart water meters. They discovered that the LSTM model has better predictive
performance than the other models. Various studies on smart water meters are being
expanded to establish an efficient water supply plan and provide various water-related
services. However, in South Korea, there are still insufficient studies on smart water meters
to predict consumer-level water consumption.
Therefore, this study aimed to develop a model for predicting consumer-level water
consumption using data from a smart water meter installed in Yeongjong Island, Incheon,
South Korea. In this study we used an LSTM-based model, to predict water consumption
prediction at the household level, that is suitable for time series analysis among deep
learning models and can consider external factors. We evaluated its predictive performance
by comparing it to the ARIMA model, which is a traditional stochastic model.

2. Materials and Methods

2.1. Study Area
The Republic of Korea is a peninsula located at 33◦ –38◦ North and 124◦ –131◦ East,
with mountainous terrain covering more than half of the region. Korea’s rainfall character-
istics are influenced by its monsoon climate, rainfall is concentrated in the summer (June–
October), and regional variations are based on the topographical characteristics. The study
area is Yeongjong Island, which is the sixth-largest island in Korea (total area: 125.7 km2 )
and a representative area with a water shortage problem. It is located in Jung-gu, Incheon.
The SWG project was promoted in Yeongjongdo Island in 2017 to improve efficient wa-
ter management, and smart water meters were installed in about 500 households. Figure 1
shows the study area and the location of the installed smart water meters. According
to the water-use type, the smart water meters were separated into residential, commer-
cial, and public categories. The residential category was further divided into detached
houses and large apartments. This research used a case study to develop a model for
predicting consumer-level water consumption, and one representative household for each
water-use type was selected and analyzed. In Figure 1, the red circle represents the en-
tire location of the installed smart water meter, the blue marker represents the selected
smart water meter, and the orange marker represents a meteorological station that collects
weather information.
 Water 2022, 14, x FOR PEER REVIEW 4 of 18

Water 2022, 14, 1512

the installed smart water meter, the blue marker represents the selected smart water me-
4 of 17
ter, and the orange marker represents a meteorological station that collects weather infor-
mation.

Figure1.1.The
Figure Thelocation
locationof
ofthe
thestudy
studyarea
areaand
andsmart
smartwater
watermeter.
meter.

2.2.
2.2.Data
DataDescription
Description
AAsmart
smartwater
watermeter
metercan
cantransmit
transmitand
andreceive
receivereal-time
real-timewater
water consumption
consumption and water
and wa-
quality data, which can be used to confirm water consumption fees, leakage,
ter quality data, which can be used to confirm water consumption fees, leakage, and ad- and additional
details
ditionalfordetails
each customer.
for each customer.
AA smartwater
smart watermeter
meterhas
hasbeen
beeninstalled
installedininthis
thisstudy
studyarea
areasince
sinceJanuary
January2017
2017asaspart
part
of
of the SWG project,
the SWG project,andandconsumer
consumerwater
water consumption
consumption data
data havehave
since since
beenbeen collected.
collected. This
This
study study
usedused a representative
a representative household
household for water-use
for each each water-use
type astypethe as the sensor,
target target sen-
and
sor,
water consumption data were collected from January 2017 to December 2019. Table 12019.
and water consumption data were collected from January 2017 to December sum-
Table
marizes1 summarizes the water consumption
the water consumption data for thedata forsensor
target the target
based sensor based ontype.
on water-use water-use
Rows
type. Rows 1 and 2 contain descriptions of the type of use, while rows 3–5
1 and 2 contain descriptions of the type of use, while rows 3–5 contain water consumptioncontain water
consumption
statistics. statistics.
Table 1. Water consumption data for each water-use type.
Table 1. Water consumption data for each water-use type.
Description Type A Type B Type C Type D
Description Type A Type B Type C Type D
Use type Residential Residential Commercial Public
Use type Residential Residential Commercial Public
Detached house Apartment
Detail information Detached house Apartment Restaurant Elementary
Elementary school
(1 household)
Detail information (366 households) Restaurant
(1 household) (366 households) school
water consumption range (m3 ) 0.5–2.8 23.8–214.8 0.78–23.7 0–55.9
water consumption
Mean (m3 ) 1.38 0.5–2.8
153.9 23.8–214.810.96 0.78–23.7 0–55.9
24.79
range (m3)
Standard deviation (m3 ) Mean 0.42
(m3) 1.3830.13 153.9 2.48 10.96 9.9524.79
Standard
Type A represents 0.42 use (detached
residential 30.13 2.48 consumption9.95
house), and water is low as
deviation (m3)
the number of users is lower than that for other types. Type B represents residential use
(apartment), with the largest number of users and the highest water consumption. Type C
represents commercial use (restaurant), and it has the second-lowest water consumption
level. Type D represents public use (elementary school) and has the second-highest water
consumption level.
 Type A represents residential use (detached house), and water consumption is low
as the number of users is lower than that for other types. Type B represents residential use
(apartment), with the largest number of users and the highest water consumption. Type
Water 2022, 14, 1512 C represents commercial use (restaurant), and it has the second-lowest water consump- 5 of 17
tion level. Type D represents public use (elementary school) and has the second-highest
water consumption level.
Figure 2 shows the weekly water consumption pattern for each water-use type. Types
Figure 2 shows the weekly water consumption pattern for each water-use type. Types
A, B, and C had similar patterns, and their water consumption was high on weekends and
A, B, and C had similar patterns, and their water consumption was high on weekends
low on weekdays. However, the water consumption pattern of Type D was low on week-
and low on weekdays. However, the water consumption pattern of Type D was low on
ends and high on weekdays.
weekends and high on weekdays.

Figure 2. Water consumption pattern according to the days of the week.

Figure 2. Water consumption pattern according to the days of the week.
The reasons for these patterns are as follows: In Types A and B, individuals do
not have much time to stay at home as they work on weekdays. In Type C, business
The reasons for these patterns are as follows: In Types A and B, individuals do not
is better on weekends than on weekdays depending on the floating population; thus,
have much time to stay at home as they work on weekdays. In Type C, business is better
water consumption is higher on weekends. In Type D, water consumption is high during
on weekends than on weekdays depending on the floating population; thus, water con-
weekdays as students spend more time at school on weekdays than on weekends. In
sumption is higher on weekends. In Type D, water consumption is high during weekdays
addition, the difference in water consumption between the days of the week is small in
as students spend more time at school on weekdays than on weekends. In addition, the
Type C as restaurants are open all days of the week. However, the difference in water
difference in water consumption between the days of the week is small in Type C as res-
consumption between the days of the week is significant in Type D as schools do not open
taurants are open all days of the week. However, the difference in water consumption
on weekends. In this manner, information on weekdays and weekends is an essential
between the days of the week is significant in Type D as schools do not open on weekends.
variable for understanding the water consumption pattern by water-use type.
In this manner, information
Additionally, on weekdays
weather information wasand
usedweekends
to identifyis an essential
nonlinear variable
patterns forfor un-
water
derstanding the water consumption pattern by water-use type.
consumption based on water-use type. Weather data, such as rainfall, relative humidity, and
Additionally,
temperature, were weather
collectedinformation was used
at a meteorological to identify
station near thenonlinear patterns
study area (orangeformarker
water
consumption based on water-use type. Weather data, such as rainfall, relative
in Figure 1). This station is managed by the Korea Meteorological Administration (KMA), humidity,
and
and temperature,
meteorologicalwere
datacollected at a meteorological
were obtained station
as daily data from near the
January 2017study area (orange
to December 2019.
marker in Figure 1). This station is managed by the Korea Meteorological
Figure 3 shows the monthly time series for each weather condition. Rainfall, relative Administration
(KMA),
humidity,and
andmeteorological
temperature alldata were
have obtainedvalues
maximum as dailyin data
summer from(June
January 2017 to De-
to September in
cember 2019.minimum
Korea) and Figure 3 shows
values the monthly
in winter time series
(December to for each weather
February condition. Rainfall,
in Korea).
relative humidity, and temperature all have maximum values in summer (June to Sep-
tember in Korea)for
2.3. Methodology and minimum
Water values Prediction
Consumption in winter (December to February in Korea).
In this study, the traditional ARIMA model and the LSTM model were used to predict
water consumption by consumers, and the performance of the two models was compared.
Figure 4 shows the flow chart for this study, including (1) model training and (2) model
evaluation. The water consumption data of the selected four types mentioned in Section 2.2
were collected from January 2017 to December 2019. The data were divided into a training
dataset (January 2017 to December 2018) for model training and a test dataset (January
2019 to December 2019) for model evaluation. The ARIMA and LSTM models were trained
using optimal parameters in the model training phase. The ARIMA model was trained
Water 2022, 14, 1512 6 of 17

using past data and the periodicity of the data. However, the LSTM model was trained by
considering both the periodicity of the data and external variables such as weather and
weekend information. In the model evaluation phase, the prediction results of the two
Water 2022, 14, x FOR PEER REVIEWmodels were evaluated for observed data, and the best-performing model was chosen 6 of as
18
the final model. The root mean square error (RMSE) and correlation coefficient (CC) were
used as the evaluation metrics in this case.

Water 2022, 14, x FOR PEER REVIEW 7 of 18

Figure3.3.Monthly
Figure Monthlypatterns
patternsofofthree meteorological
three data
meteorological (rainfall,
data relative
(rainfall, humidity,
relative and temperature).
humidity, and tempera-
ture).

2.3. Methodology for Water Consumption Prediction

In this study, the traditional ARIMA model and the LSTM model were used to pre-
dict water consumption by consumers, and the performance of the two models was com-
pared. Figure 4 shows the flow chart for this study, including (1) model training and (2)
model evaluation. The water consumption data of the selected four types mentioned in
Section 2.2 were collected from January 2017 to December 2019. The data were divided
into a training dataset (January 2017 to December 2018) for model training and a test da-
taset (January 2019 to December 2019) for model evaluation. The ARIMA and LSTM mod-
els were trained using optimal parameters in the model training phase. The ARIMA
model was trained using past data and the periodicity of the data. However, the LSTM
model was trained by considering both the periodicity of the data and external variables
such as weather and weekend information. In the model evaluation phase, the prediction
results of the two models were evaluated for observed data, and the best-performing
model was chosen as the final model. The root mean square error (RMSE) and correlation
coefficient (CC) were used as the evaluation metrics in this case.
study.
Figure 4. Flow chart for this study.

2.3.1. ARIMA Model

2.3.1. ARIMA Model
The
The AR model predicts
AR model predicts output
output variables
variables viavia linear
linear dependence
dependence on on the
the stochastic
stochastic term
term
of
of its previous values. This model assumes time series data as stationary,it and
its previous values. This model assumes time series data as stationary, and is expressed
it is ex-
as Equation
pressed (1), where
as Equation p is
(1), the lag
where time
p is the of
lagthe ARofmodel,
time the AR is the AR
∅model, ∅ coefficient, yt−i is the
is the AR coefficient,
previous
𝑦 values before t − i hours and ε is the error term [39–41].
is the previous values before 𝑡 − 𝑖 t hours and 𝜀 is the error term [39–41].
p
yt = 𝑦2 + · · ⋯
𝑦 ∅1 y∅t−𝑦1 + ∅2∅yt− · + ∅∅p y𝑦t− p + ε𝜀t = ∑ ∅∅ i y𝑦t−i + ε𝜀t (1)
(1)
i =1

The moving average (MA) model predicts output variables using the error term (𝜀 )
of its previous values. This model assumes time series data as stationary, similar to the
AR model, and it is expressed as Equation (2). Here, q is the lag time of the MA model, 𝜇
Water 2022, 14, 1512 7 of 17

The moving average (MA) model predicts output variables using the error term (ε t ) of
its previous values. This model assumes time series data as stationary, similar to the AR
model, and it is expressed as Equation (2). Here, q is the lag time of the MA model, µ is the
mean of the series, and θ is the MA coefficient [42–44].
q
y t = µ + ε t + θ 1 ε t −1 + θ 2 ε t −2 + · · · + θ q ε t − q = µ + ∑ θ i ε t − i + ε t (2)
i =1

The autoregressive moving-average (ARMA) model, which combines the AR and MA

models to predict a more accurate output variable, is expressed as Equation (3). The model
is usually referred to as the ARMA (p, q) model, where p is the lag time of the AR part and
q is the lag time of the MA part [45–47].

yt = ∅1 yt−1 + ∅2 yt−2 + · · · + ∅ p yt− p + ε t + θ1 ε t−1 + θ2 ε t−2 + · · · + θq ε t−q (3)

Box et al. [48] proposed an ARIMA model that can be used with nonstationary time
series data. The nonstationary time series is converted into a stationary time series using
the differencing. Here, the differencing is to make the average change in the time series
constant through the difference in continuous observations. The model is usually referred
to as the ARIMA (p, d, q) model and is expressed as Equation (4), where B is the backward
shift operator, ∆ is the differences, and d is the parameter of the differences.

∅ p (B) ∆ d y t = δ + θ q (B) ε t (4)

2.3.2. LSTM Model

Various machine learning models are applied to predict non-linear data. The LSTM
model is an effective advanced neural network model when the input data is sequential
data. Thus, the LSTM model was used to predict water consumption in this study.
Hochreiter and Schmidhuber invented the LSTM, a type of artificial recurrent neural
network (RNN) architecture used in the field of deep learning [49]. The LSTM model was
developed to address the vanishing gradient problem when training traditional RNNs, and
it is widely used in studies related to time series prediction [50–52].
An LSTM unit is composed of a cell state (Ct ), an input gate (it ), an output gate (ot ),
and a forget gate ( f t ), as shown in Figure 5. Each state exchanges information with one
another. The cell state transfers past information (Ct−1 ) and updated information (Ct ) to the
next cell through a forget gate, an input gate, and an output gate to update the information.
The forget gate receives the new input data (xt ) and previous hidden state data (ht−1 ) and
determines what information to convey to the cell state. The input gate determines what
information to update among the new information and generates a new information value
(Cet ) through an activation function (tanh). The output gate determines the information to
be the output. Equations (5)–(10) can be used to depict this process. Here, σ is the activation
function; W f , Wi , WC , and Wo are the weights of each gate; and b f , bi , bC , are bo are the
biases of each gate.  
f t = σ W f ·[ht−1 , xt ] + b f , (5)

it = σ (Wi ·[ht−1 , xt ] + bi ), (6)

et = tanh(WC ·[ht−1 , xt ] + bC ,
C (7)
Ct = f t ·Ct−1 + it ·C
et , (8)
ot = σ (Wo ·[ht−1 , xt ] + bo ), (9)
ht = ot ·tanh(Ct ). (10)
 𝐶 tanh 𝑊 ∙ ℎ ,𝑥 𝑏 , (7)

𝐶 𝑓 ∙𝐶 𝑖 ∙𝐶 , (8)

𝑜 𝜎 𝑊 ∙ ℎ ,𝑥 𝑏 , (9)
Water 2022, 14, 1512 8 of 17
ℎ 𝑜 ∙ tanh 𝐶 . (10)

Figure
Figure 5.
5. Conceptual
Conceptual diagram
diagram of
of the
the LSTM.
LSTM.

2.4. Evaluation
2.4. Evaluation Metrics
Metrics
The RMSE
The RMSE andandCC CCwere
wereusedusedto to
evaluate thethe
evaluate performance
performanceof each model
of each in thisinstudy.
model this
The RMSE
study. is usedistoused
The RMSE indicate representative
to indicate errors in
representative predicted
errors and observed
in predicted values. val-
and observed The
lower the RMSE, the better the performance, and it can be expressed as Equation
ues. The lower the RMSE, the better the performance, and it can be expressed as Equation (11),
where
(11), n is the
where number
n is of data,ofyidata,
the number is the𝑦observed value, and
is the observed ŷi is the
value, andpredicted
𝑦 is thevalue.
predicted
value. r
1 n
RMSE =
n ∑i=i (yi − ŷi )2 . (11)

The CC measures the linear correlation between two datasets (predicted value and
observed value). It is a ratio between the covariance of two datasets, and it is essentially
a normalized measurement of the covariance, with the result always ranging between
−1 and 1. A CC closer to −1 indicates a negative correlation, and a CC closer to +1
indicates a positive correlation. It is expressed as Equation (12), where y is the mean of the
observed value and ŷ is the mean of the predicted value.

∑(yi − y) ŷi − ŷ


CC = q . (12)
2 2
∑ (yi − y) ∑ (ŷi − ŷ)

3. Results
3.1. Application of the ARIMA Model
An autocorrelation function (ACF) analysis was conducted before training the ARIMA
model (Figure 6). The autocorrelation decreased as the lag time increased, but it increased
again when the lag time was seven or eight days. This result indicates that the dataset had
a seven-day or eight-day cycle.
The ARIMA model consists of three parameters: an AR model parameter (p), an MA
model parameter (q), and a differential parameter (d). In this study, the sensitivity of the
parameters was analyzed to build the best ARIMA model for each type. The p and q
parameters were considered from zero to eight with reference to the ACF results, and the
d parameter was considered from zero to one. A total of 162 (8( p) × 8(q) × 2(d)) ARIMA
models were developed according to parameter combination, and the ARIMA model with
the lowest RMSE was selected. Table 2 summarizes the parameters of the optimal ARIMA
model for each type. For Types A and D, the p and q parameters were set at seven, while
the d parameter d was set at zero. For Types B and C, the p and q parameters were set at
eight, while the d parameter d was set at zero.
 3. Results
3.1. Application of the ARIMA Model
An autocorrelation function (ACF) analysis was conducted before training the
ARIMA model (Figure 6). The autocorrelation decreased as the lag time increased, but it
Water 2022, 14, 1512 9 of 17
increased again when the lag time was seven or eight days. This result indicates that the
dataset had a seven-day or eight-day cycle.

Figure 6. ACF results for each type.

Figure 6. ACF results for each type.
Table 2. Parameters of the optimal ARIMA model for each type.
The ARIMA model consists of three parameters: an AR model parameter (p), an MA
Type
model parameter (q), and a Parameter p parameterParameter
differential d study, the Parameter
(d). In this sensitivityq of the
parameters A was analyzed to build
7 the best ARIMA model
0 for each type. The 7p and q pa-
rameters were
B considered from zero
8 to eight with reference
0 to the ACF results,
8 and the d
parameter was considered from zero to one. A total of 162 (8 𝑝 8 𝑞 2 𝑑 ) ARIMA
C 8 0 8
models were developed according to parameter combination, and the ARIMA model with
D 7 0
the lowest RMSE was selected. Table 2 summarizes the parameters of the optimal 7 ARIMA
model for each type. For Types A and D, the p and q parameters were set at seven, while
Table 3 summarizes the performance of the optimal ARIMA model for each type. The
CC and RMSE were used to evaluate the performance of the model in the training dataset.
The average correlation between the four water-use types was calculated as 93%, and the
average RMSE was calculated as 4.43 m3 .
Table 3. Performance of the optimal ARIMA model (training dataset).

Type Correlation RMSE

A 93.91% 0.13
B 87.31% 14.02
C 95.18% 0.73
D 96.02% 2.87

Figure 7 shows the prediction results of the ARIMA model in the training dataset as a
time series. The solid blue lines represent the time series of the observed water consumption.
At the same time, the red dashed lines represent the time series of the predicted water
consumption by the ARIMA model. The solid blue lines and the red dashed lines exhibit
almost similar results. Type D had the best performance in terms of performance by type,
while Type B had the worst performance. This is due to Type D (school) having a relatively
constant pattern, while Type B (apartment) has a complex pattern (see Figure 7).
 Figure 7 shows the prediction results of the ARIMA model in the training dataset as
a time series. The solid blue lines represent the time series of the observed water consump-
tion. At the same time, the red dashed lines represent the time series of the predicted water
consumption by the ARIMA model. The solid blue lines and the red dashed lines exhibit
almost similar results. Type D had the best performance in terms of performance by type,
Water 2022, 14, 1512 10 of 17
while Type B had the worst performance. This is due to Type D (school) having a rela-
tively constant pattern, while Type B (apartment) has a complex pattern (see Figure 7).

Figure 7.
Figure Time series
7. Time series of
of the
the predicted
predicted and
and observed
observed values
values by
by the
the ARIMA
ARIMA model (training dataset).

Overall, the performance of the ARIMA model in the training dataset was excellent,
indicating that it can make similar predictions for the observed water consumption.

3.2. Application of the LSTM Model

In contrast to the ARIMA model, the LSTM model can consider various explanatory
variables to predict the target variable (water consumption). Water consumption data from
the previous 1–7 days, weather conditions (air temperature, rainfall, and relative humidity),
weekend information, and weekday information were used as explanatory variables by
considering Refs. [27–29]. Table 4 shows the description of the target and explanatory
variables used to train the LSTM model.
Table 4. Description of the target and explanatory variables.

Variable Abbreviation Description

Target variable Wt Water consumption corresponding to t day
Wt−1 Water consumption before t − 1 day
Wt−2 Water consumption before t − 2 day
Wt−3 Water consumption before t − 3 day
Wt−4 Water consumption before t − 4 day
Wt−5 Water consumption before t − 5 day
Explanatory variable
Wt−6 Water consumption before t − 6 day
Wt−7 Water consumption before t − 7 day
T Daily air temperature
R Daily rainfall
Rh Daily relative humidity
W.d Weekday and weekend

A sensitivity analysis was also performed on the LSTM model to derive the optimal
parameters. The parameters of the LSTM model mainly deal with “units,” which refers
to the number of chains, “batch size”, which refers to the number of data extracted for
Water 2022, 14, 1512 11 of 17

learning, and “epoch”, which refers to repetitive learning [12]. Here, the epoch and batch
size are determined to repeat until they maximize learning performance according to
the number of data, and units are determined to accommodate the information to the
maximum according to the number of explanatory variables. In this study, the parameters
were considered 6, 12, 24, and 36 for the units; 12, 36, 72, and 144 for the batch size; and
20, 30, 50, and 100 for the epoch; and grid search was performed for this list. In addition,
activation function was considered as “Tanh”, and “dropout layer” was considered as 45%
to minimize overfitting problem. On the other hand, the other parameters such as learning
rate, momentum were set to their default values. The LSTM models were developed using
64 parameter combinations for each type, and the LSTM model with the best performance
was selected. Table 5 shows the parameter combinations for the top four models. The batch
size and epoch in the top four models are 12 and 100, respectively.
Table 5. Parameter combinations for the top four models.

Model Units Batch Size Epoch

Model 1 6 12 100
Model 2 12 12 100
Model 3 24 12 100
Water 2022, 14, x FOR PEER REVIEW Model 4 36 12 100 12 of 18

Figure 8 shows the loss graph for each type using the top four models. Here, the red
line and points represent model 1, the blue line and points represent model 2, the yellow
line and points
line and points represent
represent model
model 3, and the
3, and the green
green line
line and
and points
points represent
represent model
model 4.
4. The
The
x-axis represents the epoch, and the y-axis represents the loss per epoch. When
x-axis represents the epoch, and the y-axis represents the loss per epoch. When the LSTM the LSTM
models
models were trained, the
were trained, the RMSE
RMSE was was used
used as the loss
as the loss metric,
metric, and
and the
the target
target variable
variable was
was
normalized. Thus, the
normalized. Thus, theloss
lossunit
unitinin Figure
Figure 8 differs
8 differs fromfrom
the the original
original consumption
consumption data data
unit.
unit.
In addition, we used 20% of the batch size as a validation to prevent overfitting, andand
In addition, we used 20% of the batch size as a validation to prevent overfitting, the
the
lossloss presented
presented in Figure
in Figure 8 is validation
8 is the the validation
loss.loss.

Figure 8. Loss graph for each type using the top four models.

Figure 8 shows that as the epoch increased, the loss graph for all types decreased and
converged, and the loss trend did not increase again, indicating that the overfitting prob-
lem did not occur. Thus, the loss was the smallest when Type A was model 3, Type B was
model 3, Type C was model 2, and Type D was model 4. The optimal LSTM model for
each type was determined through this result. Table 6 shows the performance of the opti-
Water 2022, 14, 1512 12 of 17

Figure 8 shows that as the epoch increased, the loss graph for all types decreased and
converged, and the loss trend did not increase again, indicating that the overfitting problem
did not occur. Thus, the loss was the smallest when Type A was model 3, Type B was model
3, Type C was model 2, and Type D was model 4. The optimal LSTM model for each type
was determined through this result. Table 6 shows the performance of the optimal LSTM
model in the training dataset, and Figure 9 shows the time series of the LSTM model’s
prediction results. The average correlation for the four types was 89%, and the average
RMSE was calculated to be 5.6 m3 . It can also be seen that Type D has the highest correlation
and Type B has the lowest correlation. All the LSTM models had a correlation of 80% or
higher in the training dataset. Thus, the LSTM models were well-trained well for observing
water consumption data.
Table 6. Performance of the optimal LSTM model (training dataset).

Type Correlation RMSE

Water 2022, 14, x FOR PEER REVIEW 13 of 18
A 90.29% 0.17
B 80.96% 17.07
C 92.00% 0.93
lower. Therefore, the two models had to be evaluated in a test dataset that was not used
D
for model learning. 93.71% 4.24

Figure 9.
Figure Time series
9. Time series of
of the
the predicted
predicted and
and observed
observed values
values of
of the
the LSTM model (training dataset).

When the performance

3.3. Performance of the
Evaluation of Each ARIMA model (see Table 3) was compared to that of
Model
the LSTM model, it was discovered that the performance of the LSTM model was slightly
The two models were evaluated in the test dataset (1 January 2019 to 31 December
lower. Therefore, the two models had to be evaluated in a test dataset that was not used for
2019). Figure 10 shows the time series of the predicted result by each model. The solid
model learning.
blue line represents the observed water consumption time series, the red dashed line rep-
resents the predicted
3.3. Performance time series
Evaluation of EachofModel
the LSTM model, and the solid green line represents
the predicted time series of the ARIMA model. The red dashed line tends to be similar to
The two models were evaluated in the test dataset (1 January 2019 to 31 December
the solid blue line, but the solid green line tends to be more underestimated than the solid
2019). Figure 10 shows the time series of the predicted result by each model. The solid
blue line. In addition, the red dashed line appears to be more similar to the solid blue line
than the green line. Table 7 summarizes the performance evaluation of each model in the
test dataset. The ARIMA model had an average correlation of 62% and an average RMSE
of 8.91 m3. The correlation decreased by about 31%, and the RMSE increased by 4.48 m3 in
comparison to the results in the training dataset. Compared to that in the training dataset,
 Water 2022, 14, 1512 13 of 17

blue line represents the observed water consumption time series, the red dashed line
represents the predicted time series of the LSTM model, and the solid green line represents
the predicted time series of the ARIMA model. The red dashed line tends to be similar to
the solid blue line, but the solid green line tends to be more underestimated than the solid
blue line. In addition, the red dashed line appears to be more similar to the solid blue line
than the green line. Table 7 summarizes the performance evaluation of each model in the
test dataset. The ARIMA model had an average correlation of 62% and an average RMSE
of 8.91 m3 . The correlation decreased by about 31%, and the RMSE increased by 4.48 m3 in
comparison to the results in the training dataset. Compared to that in the training dataset,
the performance of the ARIMA model in the test dataset decreased due to overfitting.
Water 2022, 14, x FOR PEER REVIEW However, the LSTM model had an average correlation of 89% and an average RMSE 14 of of 18
5.60 m3 . These results were similar to the performance in the training dataset. The LSTM
model had a better correlation than the ARIMA model by an average of 27%.

Figure 10.10.
Figure Time series
Time seriesofofthe
thepredicted andobserved
predicted and observed values
values in the
in the testtest dataset
dataset for each
for each model.
model.

Taylor diagrams are mathematical diagrams designed to graphically indicate the

RMSE, CC and Standard deviation (SD) [53]. Figure 11 shows a Taylor diagram for each
region. Green dotted line indicates RMSE, blue dotted line indicates SD, black dotted line
indicates CC, and the green square point is SD of observation. In general, the smaller the
RMSE and SD, and the closer CC is to one, the better the model performance. Here, the
points that are closer to the green square point in this diagram mean better model perfor-
mance, and the red and blue points represent the performance of ARIMA and LSTM in
the diagram. As a result, blue points are closer to the green square point than red points.
Water 2022, 14, 1512 14 of 17

Table 7. Performance evaluation of each model (test dataset).

ARIMA LSTM
Type Correlation RMSE Correlation RMSE
A 65.81% 0.36 92.70% 0.19
B 55.42% 26.37 82.96% 17.58
C 56.42% 2.21 89.15% 1.24
D 69.79% 6.71 91.29% 4.75

Taylor diagrams are mathematical diagrams designed to graphically indicate the

RMSE, CC and Standard deviation (SD) [53]. Figure 11 shows a Taylor diagram for each
region. Green dotted line indicates RMSE, blue dotted line indicates SD, black dotted line
indicates CC, and the green square point is SD of observation. In general, the smaller
the RMSE and SD, and the closer CC is to one, the better the model performance. Here,
the points that are closer to the green square point in this diagram mean better model
performance, and the red and blue points represent the performance of ARIMA and LSTM
in the diagram. As a result, blue points are closer to the green square point than red
Water 2022, 14, x FOR PEER REVIEW 15 of 18
points. Therefore, the LSTM model outperforms the ARIMA model in predicting water
consumption at the household level as it can be trained with various patterns.

Figure 11. Taylor

Figure 11. Taylor diagram for each
each type.
type.

4. Conclusions and Discussion

This study developed a model to predict water consumption for four different water-
use types (A: detached house, B: apartment, C: restaurant, and D: elementary school) us-
ing smart water meter data. The ARIMA model, which is a traditional time series predic-
tion model, and the deep learning-based LSTM model were used as the prediction models.
The LSTM model considered both previous water consumption data and external factors
Water 2022, 14, 1512 15 of 17

4. Conclusions and Discussion

This study developed a model to predict water consumption for four different water-
use types (A: detached house, B: apartment, C: restaurant, and D: elementary school) using
smart water meter data. The ARIMA model, which is a traditional time series prediction
model, and the deep learning-based LSTM model were used as the prediction models. The
LSTM model considered both previous water consumption data and external factors such
as weather and information on weekends and weekdays as explanatory variables. Types
A, B, and C demonstrated a pattern of using much water on weekends, whereas Type D
demonstrated a pattern of using much water on weekdays.
The analysis revealed that the ARIMA model outperformed the LSTM model by a
slight difference in the training dataset, but both models demonstrated excellent perfor-
mance. However, in the test dataset, the ARIMA model’s correlation decreased by about
31% on average, while the LSTM model demonstrated excellent performance (CC: 89%
and RMSE: 5.60 m3 ), similar to the results in the training dataset. These results indicate
that the ARIMA model has an overfitting problem and does not accurately learn the non-
linear characteristics of each water-use type. However, the proposed model was trained
very well for each water-use type by employing a deep learning model to learn nonlinear
characteristics and consider external factors. In addition, the proposed model can maintain
performance even when new data is added. Therefore, this data can inform customers
about the predicted water consumption fee or manage water efficiently.
Since the proposed model was designed to predict water consumption one day later, it
cannot predict water consumption after one week or one month. This model also considers
external factors such as weather and weekend information. Still, it has limitations in that
it does not consider national holidays in Korea, such as Chuseok, and human activities.
Therefore, the model will be improved in future research by designing it to consider various
human activities and national holidays and predict water consumption over long periods,
such as a week or a month. The target area will then be expanded using this model for
all consumers at the household level in a single city. Therefore, it is believed that future
studies will further improve the usability of the model.

Author Contributions: Conceptualization, J.K. and H.L.; Data curation, H.L. and D.K.; Formal
analysis, J.K.; Methodology, J.K., M.L. and D.K.; Supervision, M.L., H.H. and H.S.K.; Writing—
original draft, J.K. and H.L.; Writing—review and editing, H.H. and H.S.K. All authors have read and
agreed to the published version of the manuscript.
Funding: INHA UNIVERSITY Research Grant.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Acknowledgments: This work was supported by INHA UNIVERSITY Research Grant.
Conflicts of Interest: The authors declare no conflict of interest.

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