Verma Vivek Kumar1
Srikant Satya Sai1
-
(Department of Electronics & Communication Engineering, SRM Institute of Science and
Technology Ghaziabad, India
vermavn@gmail.com, satyas@srmist.edu.in
)
Copyright © The Institute of Electronics and Information Engineers(IEIE)
Keywords
Energy harvested wireless sensor network (EHWSN), Solar energy forecast, Prophet library, Hample filter
1. Introduction
Wireless sensor networks employ a group of sensor nodes to carry out various functions,
with each activity involving sensing, data processing, and communication. Communication
uses the greatest energy of all of these. Wireless sensor networks (WSNs) are used
in various applications, where they are left unattended for long periods, including
flood detection, forest fire detection, and hazardous industrial applications. Batteries
are commonly used to power WSNs but must be replaced regularly. Most of the work was
done in the context of the medium access control (MAC) protocol architecture[1] to control power consumption owing to poor transmission. On the other hand, such
a system fails after a certain period due to limited battery capacity. A network powered
by an ambient energy source, such as solar energy, thermal energy, and RF energy,
has been proposed to overcome this. Compared to other sources of energy, solar energy
is considered the most efficient in terms of energy density (15mw/cm2) and availability[2]. The amount of energy captured by solar-powered nodes varies with variations in solar
energy, weather, and monthly and seasonal swings. To solve this, researchers have
developed a variety of solar prediction methodologies that have been divided into
three categories.[3] as shown in Fig. 1.
This study used the Facebook Prophet library with the Hample filter to forecast global
horizontal irradiance (GHI) over the next 24 hours. The data from the same month of
the previous years were used to test the model ability to forecast in any season.
Fig. 1. Time Series Prediction Techniques.
2. Motivation
Life on Earth is dependent on the quality of the air and water, but the dumping of
dangerous chemicals into the water causes a variety of human health problems, including
mortality. According to the WHO, air pollution is responsible for 80% of deaths caused
by respiratory disorders. WSN can also be used to identify forest fires and handle
disasters, such as earthquakes and floods. As a result, there is an urgent need for
a low-cost, stand-alone wireless networks that can monitor pollution parameters and
operate continuously. Because WSN is battery-powered, sustaining continuous operation
presents a variety of issues.
WSN uses the energy management procedure to reduce power consumption by properly designing
the medium access control (MAC) protocol[1], routing protocol[4], and topology management, but the WSN nodes still die after some time. To achieve
the goal of continuous operation, one must rely on energy harvesting technologies,
such as wind, solar, and thermal. Combining WSN with energy harvesting has resulted
in a new type of WSN known as an energy harvested wireless sensor network (EH-WSN).
Harvested energy is very indeterminate in this scenario due to seasonal volatility
and several other environmental factors; hence good protocol design is necessary
2.1 Solar Data Description
NREL Solar Radiation Research laboratory data was used in this research (Andreas,
A.; Stoffel, T.; (1981). NREL Solar Radiation Research Laboratory (SRRL): Baseline
Measurement System (BMS); Golden, Colorado (Data); NREL Report No. DA-5500-56488.
2021). The location has a latitude of 39.742$^{\circ}$ north, a longitude of 105.18$^{\circ}$
west, an elevation of 1828.8 m AMSL, and a measuring instrument of CMP22. Between
2010 and 2015, The data were utilized for training, while the data for 2016 were used
for testing. Data samples were taken every minute, but the data was averaged for 30
minutes to limit the effects of noise and the number of samples. Night samples were
also removed to limit the amount of data. This is highly useful in a wireless sensor
network with limited memory.
3. Literature Review
3.1 Classical Exponential and Moving Average Method for EHWSN
Various studies on energy harvesting wireless sensor networks have been undertaken
to reduce power consumption, but the performance of WSNs has been disregarded. As
a result, Kansal et al.[5] proposed the EWMA model, in which life was no longer an issue if operating in a proper
ENO (Electrically Neutral Operation) state; it is a way in which energy harvesting
is equal to or greater than energy consumption, which is given as
where $B_{Available}$ is the battery capacity, $P_{Harvested}$ is harvested energy,
$P_{Consumed}$ is consumed energy, and $P_{leak}$ is battery leakage
The energy gathered was calculated using the exponentially weighted moving average
approach. The energy harvested at any given moment was similar to the energy harvested
the day before in the same slots. Excessive weather changes caused the above strategy
to fail. Many scholars presented prediction systems that include weather changes,
such as WCMA[6], Pro-Energy[7], IPro-Energy[8], and UD-WCMA[9]. A statistical time series method, such as ARIMA, which can be seasonal or non-seasonal,
can be used because the preceding models cannot effectively manage data non-stationarity.
3.2 Classical Statistical Time Series Method
Yang et al.[10] proposed three ARIMA models that employed global horizontal irradiance (GHI) as an
input parameter with seasonal components eliminated, and another model that links
GHI with the zenith angle with various cloud situations and achieves greater accuracy
than the other two. Colak et al.[11] used ARIMA(2,2,2) to predict one hour, two hours, and three hours ahead of time,
and reported a~lower mean absolute error than other models. Prema et al.[12] used the multiplicative holt winter method and reported that a two-month period produces
the best results, with a MAPE of less than 9.28 %, but the error increases on cloudy
days. When the seasonality is added to the ARIMA model, the model is called the SARIMA
model, and it produces the best prediction results when used with seasonal data, such
as solar data. Using 37 years of NREL data, Shadab et al.[13] reported that ARIMA (1, 0, 1) (0, 1, 1)12 yielded the smallest mean percentage error
(MPE) and suggested a hybrid model for future research. To validate his finding further,
Shadab et al. examined 34 years of data from the Indian state of Haryana and reported
the following results: MAPE (6.556), MAE (.2659), R2 (.9293), and RMSE (.3529).
3.3 Facebook Prophet Library and Artificial Neural Network (ANN) Method
The Facebook Team[14] just built the Prophet Library for business forecasting and made it public for use
in other domains. This method is an enhanced variant of the Classical Time Series
method that does not require much subject knowledge. To improve business sales forecasting,
which necessitates precise modeling, Ensafi et al.[15] applied Prophet, LSTM, and CNN models. They reported that LSTM outperformed the other
two. Bashir et al.[16] used a combination of Prophet and LSTM for electrical load forecasting. Prophet was
used for linear data, and LSTM was used for non-linear data Bitcoin mining considerable
energy and produces much electronic trash. Hence, predicting waste generation patterns
is important. Jana et al.[17] reported the use of Prophet and a deep learning model to control the generation of
electronic garbage. When solar energy is injected into the grid, proper grid planning
is essential to predict solar energy. Gupta et al.[18] use the Prophet Model in conjunction with the extreme gradient boost (XGB). Ge et
al.[19] employed the empirical mode decomposition (EMD) technique first and, subsequently,
the LSTM method for forecasting. The hybrid combination produced better results than
standard techniques. When the grid was powered by solar energy, intermittency concerns
in economic load dispatch were eliminated. Bhatt et al.[20] used three deep learning algorithms with a sliding window approach to convert input
data into 12 steps lag datasets, with first-order differencing applied to the outputs.
Faisal et al. [21] utilized LSTM and Gated Recurrent Unit (GRU) for solar forecasting in five Bangladeshi
cities and found that the GRU model performed better in terms of MAPE, which in this
case, is 19.28 %. Mohan et al.[22] utilized both the ARIMA and Prophet models to anticipate covid-19 patients. He found
that the latter is significantly more accurate for long-term forecasting. In addition
to using neural networks, Shardga et al.[23] used statistical techniques, such as ARMA, ARIMA, and SARIMA. He found that while
both can make short-term forecasts without measuring weather parameters, neural networks
are more accurate than statistical techniques. Here, the outliers are eliminated using
Hample Filters.
4. Methodology
This section examines the Prophet Library for solar prediction and the Hample filter
for detecting and rectifying data anomalies. The recommended methodology will then
be investigated. Fig. 2 presents a flowchart of the proposed method.
4.1 Prophet Library
The prophet is a Facebook-developed open-source library for time series forecasting
that is ideal for univariate forecasting. For non-linear trends, seasonality, and
the holiday effect, it employs an additive regression model. Before utilizing this
model, the names of two columns were changed to 'ds' and 'y,' where 'ds' stands for
date and 'y' stands for the GHI value, and a future frame that includes the training
and forecasting dates was then built. The following is a representation of the entire
model:
where $y(t)$ represents the trends (which may be saturated or piecewise linear), $w(t)$
represents the periodic changes, $l(t)$represents the effects of holidays, and $e(t)$represents
the error
$y(t)$for saturated growth is represented as
where $M$, $n$ and $m$ are the capacity, growth, and offset parameters, respectively
The growth rate is not constant but changes at the changepoints. The changepoints
occur at time $f_{j\hspace{0pt}\hspace{0pt}\hspace{0pt}}\,,$ where $j=1,....,S$; $S$
is the number of change points.
The rate at time t is given as $n+k(t)^{T}\delta $ where
The correct adjustment at the change point is calculated as:
Piecewise linear growth after adjustment is expressed as:
4.2 Hample Filters nnn
The Hample filter is a great filter for eliminating outliers[24]. The median of the data sequence $l=[l(1),\,\,l(2),....\,\,l(N)]$ is used to determine
it, followed by the median absolute deviation (MAD) from the median. This work on
the threshold $L$and median of half window length for data sequence. The number of
outliers depends on the threshold value, i.e., the outlier will increase or decrease
with increasing or decreasing threshold. Once an outlier is detected, it will be replaced
by the median value of windowed data. The Data Sequence window is represented as
The outlier in Hample is represented as
$
\begin{equation*}
Outlier\left(n\right)=\left\{\begin{array}{l}
1if\left| l\left(n\right)-l'\left(n\right)\right| >L*P\\
0otherwise
\end{array}\right.
\end{equation*}
$
where $l'(n)$ is the median; $L$is the threshold, where $W(n)$ is given as
5. Proposed Methodology
The main objective of this study was to assess the performance of the model and forecast
solar energy for EHWSN using the Prophet Library. The Hample filter removed outliers
in the data before applying the model. The model was evaluated for June to determine
its effectiveness. The same month data from the previous years were used for training
and testing. Fig. 2 shows the proposed methodology.
Fig. 2. Proposed Methodology.
6. Experiment and Result Discussion
A one-minute sampling dataset from the NREL laboratory was gathered for seven years,
from June 1, 2010, to June 30, 2016, to investigate the aforementioned models. The
data was resampled again for a half-hour period to reduce the quantity of samples
taken. For training and cross-validation on June 18, 2017, the data was collected
from June 1, 2010, to June 17, 2017. Outliers were removed using the Hample filter
with a standard deviation of 3 and a window size of 3 before utilizing the forecasting
model. Fig. 3 depicts the raw signal, filtered signal, and outlier. The following metrics were
used to assess the Prophet Model performance.
Fig. 3. Original data and Hample-Filtered data with Outliers.
6.1 MSE
This was evaluated by calculating the squared difference between the predicted and
true values. In the equation given below, $y_{A}$ is the actual value and $y_{P}$
is the predicted value.
6.2 MAE
MAE checks the closeness of the predicted value to the actual value and is expressed
as
6.3 MAPE
MAPE is used to measure the accuracy of the model. MAPE measures accuracy in terms
of percentage. The equation for calculating the MAPE is given below:
6.4 RMSE
The RMSE is calculated by first calculating MSE and then calculating the square root
of the MSE.
$
\begin{equation*}
RMSE=\sqrt{1/n\sum _{i=1}^{n}\left(y_{A}-y_{P}\right)^{2}}
\end{equation*}
$
6.5 Result Analysis
The Prophet Library has a cross-validation feature that may be used to calculate the
forecast inaccuracy. This can be done by choosing cutoff points in the historical
data, running the model up to those cutoff points, and comparing the predicted values
to the measured values. By default, a 3${\times}$prediction horizon is selected for
the initial training period, with cutoffs placed halfway down the horizon. This process
is continued until the final cutoff points and for the desired prediction horizon.
This is performed by choosing the cutoff points, period, and prediction horizon, as
shown in Fig. 4. For this study, a cutoff of five years, a time frame of 24 hours, and a forecast
horizon of 24 hours were used.
This results in 17 forecasts with a cutoff point ranging from 2016/05/31 to 2016/06/16,
with the forecast cutoff point shifting right by 24 hours after that. Therefore, for
the most recent forecast, the MSE, MAE, MAPE, and RMSE values for unfiltered data
were 292.81, 14.56, 19.37, and 17.11, as shown in Fig. 5; the corresponding graph is shown in Fig. 6.
The Hample filter removes outliers in the second procedure, and the filtered data
is then cross-validated again. The MSE, MAE, MAPE, and RMSE values for this filtered
data are 292.55, 14.86, 14.86, and 17.10, respectively, as shown in the table and
figures.
Fig. 4. Cross-validation of the data[14].
Fig. 5. Evaluation metric for 1 to 24 Hour Prediction horizon using Prophet Library.
Fig. 6. (a)-(d) Graphs of MAE, MSE, MAPE, and MSE for the 24 Hour Prediction horizon without a Hample filter.
Fig. 7. Evaluation metric for 1 to 24 Hour horizon using the Prophet Library after Hample Filter.
Fig. 8. (a)-(d) Graphs of MAE, MSE, MAPE, and MSE for the 24 Hour Prediction horizon with a Hample filter.
Fig. 9. Actual and Forecasted solar irradiance for 18/6/2016.
Table 1. Performance comparison for Prophet and Hample filtered-Prophet model.
|
Model
|
VMSE
|
MMAE
|
MMAPE
|
RRMSE
|
|
Prophet Model
|
2292.81
|
114.56
|
119.37
|
117.11
|
|
Hample-Prophet Model
|
292.56
|
14.86
|
14.86
|
17.10
|
Table 2. Performance comparison of RMSE and MAPE with Amandeep et al.[25].
|
Model
|
VRMSE
|
Accuracy
|
|
Ensemble Approach
(Arithmetic Mean)
|
240.84
|
74.54
|
|
Ensemble Approach
(Harmonic Mean)
|
40.62
|
74.54
|
|
Ensemble Approach
(Quadratic mean)
|
58.36
|
72.72
|
|
Ensemble Approach
(Median)
|
42.01
|
78.18
|
|
Prophet
|
17.11
|
80.63
|
|
Hample-Prophet
|
17.11
|
85.14
|
7. Conclusion
This paper presented a Facebook Prophet based on the Hample filter. The forecasting
model was tested, and the Hample filter was implemented on real-time data acquired
from NREL using the Python Framework and MATLAB. The data were resampled for one hour
to minimize the number of sample points, noise, and memory resources in EHWSN. Data
from 2010 to 2015 was used to train the model, and the data from 2016 was utilized
to test it. The Mean Squared Error (MSE), Mean Absolute Error (MAE), Mean Absolute
Percentage Error (MAPE), and Root Mean Squared Error (RMSE) values for the Prophet
model were 292.81, 14.56, 19.37, and 17.11, respectively, while for the Prophet model
based on the Hample Filter, they were 92.56, 14.86, 14.86, and 17.10, respectively.
MAPE was reduced to 18.60 %, while the remaining metrics changed slightly. Prophet
and Hample-Prophet gave the best result regarding the RMSE and accuracy compared to
previous work based on the Ensemble approach. As a result, the proposed model improves
forecast accuracy. This expected result will be applied in the next work on the power
management of energy harvesting wireless sensor networks.
ACKNOWLEDGMENTS
This research was not funded by any agency
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Author
Satya Sai Srikant is presently working as Associate Professor in Department of
Electronics and Communication Engineering, SRM Institute of Science and Technology,
Delhi-NCR Campus, Modinagar, Ghaziabad, since 2009. He has 7 years of experience as
Design Engineer in R&D organization and more than 12 years of experience in Teaching
and Research at SRM Institute of Science and Technology. He qualified his M.Tech degree
from University of Delhi in Microwave Electronics in the year 2002 and obtained PhD
degree from SOA University, Bhubaneswar Odisha, in “Microwave Processing of Beach
Placer Heavy Minerals” in the year 2014.His research area includes Microwave and RF
circuits; Antenna Technologies, Wireless and communication system; Applications of
microwave technology in mineral processing and materials technology in various sectors
of RF and other industries. He has published more than 40 papers in International
conferences and Journals. He has authored one International book “Basic Electronics
Engineering – Including Laboratory Manual” under Springer Publication, and also published
four book chapters. He also published three published patents, in which one of them
was Granted patent also. He is currently guiding six PhD scholars and two scholars
has successfully completed PhD, under his supervision.
Vivek Kumar Verma received his B.Tech. degree in Electronics & Communication engineering
from M.J.P. Rohilkhand University, Bareilly (UP), India, in 2002, and M.Tech. Degree
in Energy Management from DAVV, Indore, India, in 2010. He is currently pursuing his
Ph.D. degree in Electronics & Communication Engineering with SRM Institute of Science
and Technology Ghaziabad, India. His current research interests include machine learning
algorithms, artificial intelligence methods, Embedded Systems & Industrial Automation.