1. Introduction
It is increasingly common for energy organizations to gather and study energy consumption
for business management. Coordinating the tasks to forecast usage by consumers requires
reliability and precision. During the last four decades, numerous efforts have been
directed at developing smart sensors attached to electricity meters, and making data
on energy consumption available in practice. The promise is that computer-assisted
analysis of such large amounts of data will enhance screening dimensions, reduce the
problem of observer dependency, and reinforce diagnostic certainty in residential
energy usage.
In particular, the demand for electricity in Vietnam in 2021 was forecast by Electricity
Company of Vietnam [1] based on a basic plan and an intensive plan. The basic plan consists of commercial
electricity demand at 235.2 billion kWh, corresponding to electricity production capable
of providing 267.9 billion kWh. The intensive plan covers 236.97 billion kWh in electricity
consumption while the production capability is expected to be 269.9 billion kWh.
Note that energy usage in high-rise buildings with more than 10 floors has received
considerable attention based on very high rates at about 40% of total energy consumption
in the world, according to one United Nations Environment Program report [2].
The consumption rate for high-rise buildings in Vietnam is 35% to 40% of total energy
consumption in the country. According to an Emporis report [3], there are 1443 high-rise buildings of which 1384 are occupied, 46 are under construction,
and 11 are in the planning stages. We note that not all the buildings have smart meters
to measure power consumption once a day. There are buildings where the data are collected
manually each month. At present, the data allow analyzing and making predictions for
future power consumption. The analysis, conceptually, appears to be generally well
regarded for optimizing power generation and balancing the distribution grid, but
in reality is proving difficult to fully adopt. This difficulty comes down to a combination
of necessity in maintaining a smart meter system, and a lack of data analysis. Taken
together, we put forward the argument that building-energy consumption is an interdisciplinary
topic that would greatly benefit from data mining and potential machine learning research.
In this article, we look at an application-driven case study. Informally, we show
how data mining techniques can be extended to handle building energy-consumption data,
which may be regarded as an estimate of future power consumption associated with building
patterns.
Our main contributions are to define energy consumption patterns in the apartments
of a residential building; to prove that the patterns are tractable for weighted clustering;
to apply a k-Means and agglomerative clustering algorithm to solve grouping problems
with apartment-dependent energy consumption constraints; to implement gradient boosting
for predicting energy consumption for each group of apartments and then grouping them
to make forecasts available for the whole building; to provide a comprehensive experimental
evaluation of our method; and to show how the performance of our method compares very
favorably with an approach that uses gradient boosting.
Our experimental evaluation shows that the method enjoys substantial predominance
over traditional methods for implementing clustering analysis. The proposed method
is fit to deal far better with five clusters for our particular selected dataset.
In the next section, we present the data mining method, having reviewed relevant concepts
from the literature.
2. Related Work
We first review methods aimed at electricity-consumption forecasting for residential
buildings in (I). Then, we discuss works focusing on gradient boosting and clustering
analysis in (II).
$\textbf{(I)}$ It is clear that accurate energy consumption prediction is more important
to better avoid energy waste and to ameliorate the quality and effectiveness of energy
systems. Specifically, machine learning methods can be implemented to discover data
patterns and to predict how an electricity network works. An important note is that
every consumer is different, and they all behave in a dissimilar manner. Hence, Paulo
et al. [4] presented a comparison report on how machine learning methods are applied to building-energy
consumption.
Four methods, Linear Regression, the Decision Forest, the Boosted Decision Tree, and
the Artificial Neural Network (ANN), were addressed in experiments with the same real
dataset collected over a period of 150 days in two houses in Iceland.
González-Briones et al. [5] demonstrated variations in the prediction of energy consumption by using k-Nearest
Neighbors, Linear Regression, Random Forest, Support Vector Regression, and the Decision
Tree. Thus, the dataset used for experiments was taken from a shoe store located in
Salamanca, Spain, showing the daily electricity consumption of a dwelling with two
people living in it. Klemenjak et al. [6] conducted an analysis of more than a dozen datasets to offer recommendations for
electricity-consumption data collection, storage, and provision. Based upon the recommendations,
datasets with increased usability and comparability can be created.
Zhang [7] dealt with anomalous consumption detection based on data mining techniques. The proposed
method focuses on each formula to evaluate anomalies in each different time scale,
without using any machine learning algorithms. The dataset was per-household basics,
which can be expanded, but it is necessary to change formulas to assess consumption-based
anomalies.
These papers addressed forecasting of residential electricity consumption. Although
different databases were used for the studies, there are cases where a lack of data
can be observed. The time-series forecast is based principally on the provided data,
and a lack of data could lead to wrong predictions. We address this problem in our
case study with a database in which data were lost for some intervals. In particular,
our solution will include applicable data mining techniques for the case.
$\textbf{(II)}$ Vantuch et al. [8] showed that forecasting accuracy decreases with an increase in the time scale due
to the impossibility of using all variables. The authors processed Support Vector
Regression, Random Forest Regression, eXtreme Gradient Boosting (XGBoost), and the
Flexible Neural Tree on a dataset obtained from Murcia University buildings in Spain
spanning nearly one year. The objective was to predict power consumption for those
buildings in the subsequent few hours. The data were collected at a 15-minute sampling
rate. The best forecast results were achieved by using XGBoost.
To establish a model for energy consumption in a residential house, Ashouri et al.
[9] created a database from 76 buildings in Japan from 2002 to 2004 consisting of eight
types of electrical equipment. It can be seen that the relation between climate conditions,
building characteristics, building services, and operations were analyzed using clustering
analysis and ANN models. Then, recommendations on the use of energy for the inhabitants
of a building can be generated from the ANN. Xu and Chen [10] conducted a case study to find anomalies in data from residential buildings. The
solution outlined in the paper is a combination of the Recurrent Neural Network (RNN)
and quantile regression. However, this is a short paper missing details on the experimental
results.
Clustering-based analysis was addressed by Ullah et al. [11] in order to categorize consumers’ electricity usage into different levels. This work
used a deep auto-encoder to transfer low-dimensional energy consumption data into
high-level representations. Then, an adaptive self-organizing map-clustering algorithm
with statistical analysis determined the levels of electricity consumption.
In principle, XGBoost, the ANN, and the RNN were implemented in the above-mentioned
methods to resolve forecasting. However, due to the discontinuities in the time-series
data, the accuracy of prediction can drop. To allow the deep learning method to work
with insufficient data we propose applying both feature engineering and XGBoost involving
proper clustering. In the following, our method (with details) is described.
3. The Method
We follow the paradigm of Bayesian time-series analysis introduced by Barber et al.
[12]. This involves the construction of a probability model for apartment energy consumption.
For convenience, the following notations are used in describing the model:
$i$ - apartment, $i~ =1\colon n$
$x_{i}$ - energy condition of apartment $i$
$t=1\colon T$ - a time-series
$c_{j}$ - clusters, $j~ =1\colon k$
$e_{t}\left(x_{i}\right)$ - energy consumption of an apartment $i$
$e_{t}~ =~ mean_{j=1\colon n}e_{t}\left(x_{i}\right)$ - averaged consumption of apartments
The functional elements of our method are described in two main parts: covering gradient
boosting in (I) and clustering analysis in (II).
$\textbf{(I)}$ To express the learning process in our method, we use Bayes’ Rule [12] that traces out conditional probability for class $c$ and sample $s$:
A common way of writing a probabilistic model of a time series for energy consumption,
$e_{1\colon T}~ =e_{1},e_{2},\ldots e_{T},$ expresses the statement of a joint distribution
$p\left(e_{1\colon T}\right)$.
In practice, however, identifying all independent entries of $p\left(e_{1\colon T}\right)$
is impracticable without making some statistical independence assumptions. So, for
a time series of more than a few steps, it is necessary to introduce simplifications
for traceability. Thus, we replace $c$ with $e_{T}$ and $s$ with $e_{1\colon T-1}$
in (1); reordering, we have
Furthermore, we can break down $p\left(e_{1\colon T-1}\right)$ as follows:
By continuing the exercise, the joint distribution can be seen as follows:
The above factorization is consistent, based on the causal nature of time (where each
factor expresses a generative model of a variable conditioned on its past) by plugging
in conditional independence to release the variables in each factor-conditioning set.
Note that by imposing $p\left(e_{t}|e_{1\colon t-1}\right)=p(c|e_{t-m\colon t-1})$,
we can derive the $m$th-order Markov model, which is of fundamental importance in
many time-series models [13]. In an$~ m$th\hbox{-}order Markov model, the joint distribution factorizes as
The auto-regressive (AR) model is a Markov model of continuous scalar observations
[14]. For an $m$th-order AR model, we assume a statement of $e_{t}$ is a noisy linear
combination of the previous $m$ observations:
where $a_{1\colon m}$ represents coefficients, and $\varepsilon _{t}$ is independent
noise that is assumed to be zero-mean Gaussian with variance $r$. In this step, a
generative form for the prediction model with Gaussian noise is represented by
where energy consumption value $e_{t}$ is a function of $m$ previous moments:
From (7) it is possible to show that
Using a gradient boosting method, the learning objective of Gradient Tree Boosting
[15,16] is minimization of the error between predicted value $e_{t}$ and actual value $\hat{e}_{t}$.
This minimization is formulated by the following equation:
where $l$ is the loss function that calculates the prediction error, and $\lambda
$ is a function that regularizes the learning task to control overfitting.
$\textbf{(II)}$ Now, we get a closer look at the data level of the apartments; observation
of the energy consumption in a building, $e_{t}$, is calculated by averaging the consumption
of the apartments:
where $x$ denotes apartment conditions for energy consumption, while $e$ is the consumption
value observed at time $t.$ Fig. 1(a) shows the relationship between $x,e$, and$~ t$.
To improve smoothness, we apply clustering to the apartment conditions for energy
consumption $x$ by introducing cluster $c$ for each apartment, as seen in Fig. 1(b). It is well known that k-Means [17] is a method for clustering a dataset, $X=x_{1},x_{2},\ldots x_{N}$, of $N$ unlabeled
data points into $K~ $clusters, where $K$ is specified by the user. In our study of
energy consumption based on (9), the objective of the k-Means algorithm is to minimize the following cost function:
where $C_{i}$ denotes a cluster, and $\mu _{i}$ is the center of cluster $C_{i}$.
The minimization of $V_{t-m\colon t-1}$ in (12) allows us to assign cluster $c$ for each apartment $x_{j}$ using consumption conditions
during the past $\left(t-m\colon t-1\right)\colon $
where the $c_{i}$ is the cluster assigned for apartment $x_{j}$, and $\mu _{i}$ is
the relevant cluster center.
Given the energy consumption for each apartment from (13), implementation of (11) permits us to obtain the average energy consumption for the whole building in the
past:
It should be apparent that general prediction formula (7) can be rewritten for each cluster as follows:
Similarly, the prediction condition based on $m$ previous moments (9) has its specific form applied for a cluster:
Finally, the prediction of energy consumption for the building is achieved by getting
a weighted average of the above prediction for clusters:
where $w\left(c_{i}\right)$ is the weight of cluster $c_{i}$. The weight is proportional
to the number of elements $\left(\textit{numel}\right)$ assigned to the cluster:
While we have shown that the method is based on gradient boosting and clustering,
it is also possible to use some metrics for performance estimation.
By using $e_{i}$ and $\hat{e}_{i}$ to denote prediction value and actual value, respectively,
the Mean Squared Error, Mean Absolute Error, Root Mean Squared Error, and Mean Absolute
Percentage Error are defined by Eqs. (19) to (22):
Fig. 1. Relationships in energy consumption models. a Energy consumption $e$ by time $t$ depends on the consumption conditions of apartment $x$. b-Energy consumption $e$ by time $t$ depends on the consumption conditions of cluster $c$ of apartment $x$.}
4. Experimental Results
Keys to effective time-series prediction are data analysis and the selection of a
suitable learning method. We conducted experiments in three steps: data analysis,
gradient boosting, and data clustering.
4.1 Data Analysis
The proposed method was evaluated on an electricity-consumption dataset collected
from apartment units in buildings in Hanoi, Vietnam. The data were gathered by smart
sensors that allowed recording energy consumption in wattage for apartments in buildings.
The data cover more than 500 apartments and offices from three buildings over two
years (from September 2014 to December 2016) providing three basic features: $ID$
(indicating apartment units), $pkw$ (for wattage), and of course, the index field
of date and time.
Note that there may be apartments and offices in the same building. Despite having
a huge number of data points, the data are not consecutive and were split into intervals
that can cover a few months. This leads to the difficulty of discovering a data trend
as it intuitively should be, and exploring data seasonality, which is often a significant
factor in power consumption. Since gradient boosting (8-12) is a decision tree-based
algorithm, we designed additional features extracted from the original date-time feature
in order to help the algorithm find patterns in the data.
The extracted features are day of the week, the quarter, the month, the year, the
day of the year, the day of the month, and the week of the year, which are commonly
used to handle time-series problems. By checking the data distribution by apartment,
we found that the distribution was uneven. Hence, the total amount of electricity
consumption cannot be gathered from the recorded wattage.
However, we chose averaging the wattage for further analysis and prediction. Fig. 2 demonstrates the energy consumption distribution of the building based on days of
the week and hours of the day in the form of a heat map, where the colors show the
levels of consumption.
It is clear that the levels of energy consumption for work days are mostly the same,
whereas they decrease slightly for weekends. During the day, a high level of energy
consumption is observed for the hours from 7 am to 10 am and from 1 pm to 4 pm in
the afternoon. The consumption distribution completely fits Electricity of Vietnam’s
consumption pricing list [18], which is split into sections for days and hours.
4.2 Gradient Boosting
To implement gradient boosting for time-series apartment energy consumption based
on Eqs. (8) to (12) for this case study, we employed the Extreme Gradient Boosting (XGBoost) package
developed by Chen et al. [19]. This is an open-source software library providing a regularizing gradient boosting
framework.
The package often performs more efficiently than other algorithms, such as ARIMA [20] or PROPHET [20], when there is a lack of data because it does not need to discover cycle patterns.
The issue is found in our data, and that is why XGBoost was our choice for the time-series
solution.
In order to demonstrate the proposed method, we started with the original XGBoost
to get the initial performance. By applying the metrics in Eqs. (19) to (22), the results are as follows:
$\textbf{XGBoost}$
MSE: 0.007421028512366852
MAE: 0.05360403479255469
RMSE: 0.0861453917070835
MAPE: 20.385228594547005
Fig. 3 shows the actual energy consumption in blue, while the prediction is in red. Note
that the model seems to be confused with huge swings of data, and consequently, it
becomes too conservative and has not learned anything.
Fig. 2. Energy consumption distribution of the building based on days of the week and hours of the day.
Fig. 3. Prediction by the original XGBoost showing huge swings of data in our case study. Blue presents actual values, and red indicates the predicted values.
4.3 Data Clustering
Acknowledging the fact that the dataset contains different $IDs$ indicating different
apartments and offices that are associated with different energy consumption conditions,
applying data clustering with formulas (12) to (18) for these $IDs$ could improve prediction performance.
We created an additional 170 features, including the $pkw$ average for each hour in
a day, each day in a week, and the total mean and standard deviation. The aim is to
learn differentiations that may exist in consumption conditions between apartments
or between apartments and offices. Therefore, we applied clustering techniques to
categorize the dataset into groups by using original features and newly extracted
features.
In the following, two cluster algorithms have been used: k-Means clustering and agglomerative
clustering. What is important is that the task of gradient boosting prediction is
conducted separately for each group of apartments based on Eqs. (12) to (16), and is then summarized with Eqs. (17) and (18). Consider XGBoost with support for clustering the dataset by k-Means. We can see
performance improvement through results reported with $k=18$:
$\textbf{k-Means Clustering & XGBoost}$
MSE: 0.001961885122344051
MAE: 0.030668140386704996
RMSE: 0.04429317241228101
MAPE: 11.192344669596173
With k-Means, the predictions in Fig. 4 (in red) show short distances from the actual values in blue. Compared with Fig. 3, there is a noticeable improvement in the predictions.
As can be seen, the performance metrics for predictions using agglomerative clustering
and XGBoost are ameliorated, compared to using only XGBoost:
$\textbf{Agglomerative Clustering & XGBoost}$
MSE: 0.002539348382033498
MAE: 0.031479287301019958
RMSE: 0.05039194759119257
MAPE: 13.59158428571727
In the experiment results shown in Fig. 5, XGBoost was implemented with the assistance of agglomerative clustering ($k~ =~
22$). Prior to clustering, the predictions (in red) closely follow the blue actual
values. Although more computationally expensive, it provides a smooth curve, making
it a preferable candidate for evaluating the usefulness of the predictions.
Table 1 presents an MAE report from the experiments that were conducted to evaluate the sensitivity
of parameter $k$ for clustering data by using the k-Means and agglomerative clustering
methods. The first case with $k=1$ is implementation of XGBoost without any clustering,
where the scores are printed in bold.
The second case is when we applied clustering with two clusters, $k~ =~ 2$, which
changes the MAE value from 0.0536 to 0.0433 for k-Means clustering; from 0.0536 to
0.0426 for agglomerative clustering. Prior to the value of parameter $k,$ MAE changed
for both clustering methods. The experiments were applied to 29 values of $k$. Fig. 6 shows the model of $k$ variations for the k-Means clustering. We note a sharp drop
in MAE results when $k$ runs from 1 to 5. Then the speed is observed to slow down
before starting to fluctuate when $k$ reaches 15.
The event can be interpreted as either overfitting or the amount of data points of
a single cluster is too small. No other significant drops were detected for the remaining
14 blocks of $k$.
Fig. 7 shows an accentuated drop in performance metrics from MSE, MAE, and RMSE for agglomerative
clustering in the clustering data based on the five blocks with $k~ =~ 2\colon 5$
before learning the time-series. Fig. 7 also shows no other remarkable drops for the remaining 24 blocks of $k.$
Table 2 displays the performance of the implemented methods for comparison. The results from
XGBoost are presented in the second row with MSE of 0.007. A combination of agglomerative
clustering with $k=22$ and XGBoost reduces the error metric of MSE to 0.002. In the
last row, application of k-Means ($k=18$) with XGBoost achieved an MSE of 0.001.
For other metrics covering MAE, RMSE, and MAPE, a distinct enhancement was observed
for both clustering methods.
We note the lowest errors were delivered by the combination of k-Means and XGBoost,
where the best scores are underlined.
We suspect better performance could be achieved by sampling more of the data points
to fill lost time intervals. However, our overall focus is more on the differentiation
of consumption conditions, so we do not believe this would be useful for our primary
goals in the time-series analysis.
Fig. 4. XGBoost with support from k-Means clustering when $k=18$. Actual energy consumption is displayed in blue, whereas predictions are in red.
Fig. 5. XGBoost with the support of agglomerative clustering when $k~ =~ 22$. Actual energy consumption is displayed in blue, whereas predictions are in red.
Fig. 6. Performance of XGBoost and k-Means clustering by changing the $k~ $parameter: MSE-yellow, MAE-red, RMSE-blue.
Fig. 7. Performance of XGBoost and Agglomerative clustering by changing the $k$ parameter: MSE-yellow, MAE-red, RMSE-blue.
Table 1. PERFORMANCE FROM MAE (20) WITH $\boldsymbol{k}=1,2,\ldots 29$ FOR K-MEANS CLUSTERING AND AGGLOMERATIVE CLUSTERING.
|
k
|
1
|
2
|
3
|
4
|
5
|
|
k-Means
|
0.0536
|
0.0433
|
0.0341
|
0.0291
|
0.0284
|
|
Agglo.
|
0.0536
|
0.0426
|
0.0342
|
0.0301
|
0.0298
|
|
k
|
6
|
7
|
8
|
9
|
10
|
|
k-Means
|
0.0283
|
0.0284
|
0.0274
|
0.0286
|
0.0270
|
|
Agglo.
|
0.0313
|
0.0314
|
0.0308
|
0.0297
|
0.0287
|
|
k
|
11
|
12
|
13
|
14
|
15
|
|
k-Means
|
0.0256
|
0.0273
|
0.0271
|
0.0295
|
0.0299
|
|
Agglo.
|
0.0293
|
0.0292
|
0.0289
|
0.0284
|
0.0283
|
|
k
|
16
|
17
|
18
|
19
|
20
|
|
k-Means
|
0.0268
|
0.0264
|
0.0307
|
0.0321
|
0.0302
|
|
Agglo.
|
0.0276
|
0.0293
|
0.0306
|
0.0311
|
0.0307
|
|
k
|
21
|
22
|
23
|
24
|
25
|
|
k-Means
|
0.0276
|
0.0324
|
0.0314
|
0.0327
|
0.0307
|
|
Agglo.
|
0.0307
|
0.0315
|
0.0310
|
0.0320
|
0.0325
|
|
k
|
26
|
27
|
28
|
29
|
|
|
k-Means
|
0.0329
|
0.0335
|
0.0333
|
0.0356
|
|
|
Agglo.
|
0.0332
|
0.0334
|
0.0343
|
0.0356
|
|
Table 2. PERFORMANCE BY MSE, MAE, RMSE & MAPE.
|
Methods
|
MSE
|
MAE
|
RMSE
|
MAPE
|
|
XGBoost
|
0.007
|
0.054
|
0.086
|
20.38
|
|
XGBoost & Agglo-merative (k=22)
|
0.002
|
0.032
|
0.050
|
13.59
|
|
XGBoost & k-Means (k=18)
|
0.001
|
0.031
|
0.044
|
11.19
|
5. Conclusion
We presented a method of time-series analysis that is well-suited to energy-consumption
applications. It relies on data mining techniques from raw data to represent specific
data patterns as flow variations in time. These variations are recognized by clustering
data, which allows grouping data points into clusters with similar features. Since
earlier work on energy consumption focused on simple customer-consumption data, this
work has focused on testing our concepts on a more complex dataset with a large number
of units, including apartments and offices.
Our results show the method is proficient at extracting features suitable for input
to time-series prediction by gradient boosting, and it delivers good performance.
Overall, our results are encouraging and represent a significant step toward validating
the implementation of k-Means and agglomerative clustering over an initial dataset.
Even if performance was high, further improvements to energy consumption analysis
are under investigation. These include fulfillment of lost data. Moreover, application
of the method to other problems can be envisaged. It is obvious, for example, that
the method is well-suited to financial time-series forecasting, where distinctions
between data groups are significant.
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Author
Nam Anh Dao received his B.S. in Applied Mathematics and a Ph.D. in Physics\textendash{}Mathematics
from the University of Moldova in 1987 and 1992, respectively. He was involved in
various international software projects. He is currently teaching at Electric Power
University. His research interests include Intellectual Intelligence, Image Processing
and Pattern Recognition, Machine Vision, and Data Science. Main works cover pattern
recognition and image analysis, medical imaging, and machine learning with emphasis
on computer vision. He has also served, or is currently serving, as a reviewer for
many important Journals and Conferences in Image Processing and Pattern Recognition.
Hải Minh Nguyen is a sophomore undergraduate in Computer Science at Hanoi University
of Science and Technology (HUST), Viet Nam. He was involved in power consumption prediction
project. His research interests include Machine Learning and Quantitative Optimization.
Tung Nguyen Khanh received his B.S. in Computer Information Systems from Vietnam National
University-University of Engineering and Technology (VNU-UET) in 2016. Currently,
he is a researcher at the university. Before starting his graduate studies, he worked
at Electricity Company of Vietnam (EVN) as a research engineer. He was involved in
various projects, including building an IoT Secured SmartGateway for electric cabinets
and developing an online Network Security Scanner. His research interests include
electrical data mining and cybersecurity for electrical operation networks.