Adaptive Seasonal Auto-Regressive Integrated Moving Average Model

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1		Chong Han	--	1777	2023-02-03 09:23:09	\|
2	update references and layout	Rita Xu	Meta information modification	1777	2023-02-03 09:49:11	\|

This entry is adapted from the peer-reviewed paper 10.3390/electronics11182934

Harvesting energy from solar radiation has emerged as an effective approach to prolong the lifetime of outdoor energy harvesting sensor networks. The harvested energy must be carefully managed to ensure that sufficient energy is available when solar energy is scarce. For the prediction problem of solar energy power harvesting, an adaptive seasonal auto-regressive integrated moving average model (ASARIMA) for solar energy harvesting prediction.

sensor networks energy harvesting solar powered ARIMA

1. Introduction

A wireless sensor network (WSN) is a type of distributed network composed of sensor nodes deployed in a monitoring area in self-organizing and multi-hop ways. Internal nodes transmit information wirelessly by collecting and processing object information in a detection area ^[1]. Sensors can be placed in any position and can offer wireless communication and other advantages; thus, they are extensively used in military defense, environmental monitoring, and biological/medical or other fields. In general, sensor networks can be regarded as the infrastructure of the Internet of Things (IoT) ^[2]. However, for traditional sensor networks, nodes use limited battery power, which restricts the development of WSNs. Once the power of the nodes is exhausted, if the nodes’ batteries are not replaced or replenished in time, the lifetime of the whole network will be shortened. Therefore, energy limitation is an urgent problem to be solved in the sensor network application field in which the system is expected to run persistently for a long time ^[3]^[4].

In order to solve the problem of the limited battery power supply of nodes, one potential technology is environmental energy harvesting, which is a promising technology for the long-term operation of traditional WSNs. In other words, harvested energy could be collected by the energy harvesting module of a WSN node ^[5]^[6]. This extended sensor network is also a kind of WSN with an energy harvesting device equipped to harvest energy from ambient sources to replenish the battery of the sensor node, which, in essence, is a so-called energy harvesting sensor network (EH-WSN). As a type of clean energy, solar energy has been studied and utilized extensively in recent years. Thus, solar energy collection technology can be used in WSNs to convert the harvested solar energy into electric energy, store it in the energy buffer of the sensor node, and provide energy under the control of an energy management module ^[7]. However, solar nodes are not a reliable and stable source of energy because the energy harvested from them varies significantly over time given their diurnal variation cycles, different weather conditions, monthly trends, and seasonal patterns. Energy prediction is an important part of energy management in solar WSNs that allows a system to make key decisions about utilizing the available energy.

In terms of predicting the time series, the main idea of the auto-regressive integrated moving average (ARIMA) ^[8] is to observe whether the time-series data have a trend; if so, differential castration is performed to obtain a stationary sequence. Sequence modeling is then used to describe the random process and make some predictions for the future. Considering the lag in prediction, the autocorrelation and nonstationarity of the time series, and the periodicity of the data, this research adopts a seasonal ARIMA (SARIMA) time-series prediction model and conducts training in accordance with the appropriate historical data and Akaike information criterion (AIC) ^[9] to select the optimal model for effective prediction. However, the existing SARIMA model only simply selects historical data as the training set and lacks the analysis of weather similarity, thus leading to low prediction accuracy when a weather interleaving phenomenon occurs.

2. ASARIMA

Existing solar power prediction algorithms are divided into two categories. One category forms predictions through artificial intelligence methods, such as knowledge-base neural network (KBNN) or deep learning ^[10]^[11]^[12], after importing numerous data and parameters for training. Ding et al. ^[10] proposed a similar day selection algorithm, which screens out solar data that possess the same weather type and are closest to the predicted time point from historical records and inputs them into a backpropagation (BP) neural network. Liu et al. ^[11] used the multilayer perceptron (MLP) method to predict solar energy harvesting power. In addition, they proposed a knowledge-based neural network (KBNN) to predict solar energy by using the prior prediction equation as the neural network knowledge and utilizing the learning ability of an ANN, thereby establishing a multistream prediction model. The prediction model structure proposed by Asrari et al. ^[12] utilizes a combination of gradient descent optimization and metaheuristic optimization methods to consider the prediction accuracy and computational burden of the constructed model. Gradient descent optimization technology provides the initial parameters of a feedforward ANN. Then, it searches for the optimal set of parameters for the neural network through the initial individual found by the specific shuffled frog leaping algorithm (SFLA) and, finally, uses the parameter set for solar power prediction. In general, these deep learning methods have high accuracy, but the prediction cost is large, and the sensor processor and memory capacity are limited; thus, the neural network prediction method is not suitable in the sensor network scene. The other category is to study the traditional time-series collection power after the trend of change prediction. This kind of method has attracted the attention of scholars who study sensor networks given the relatively small historical data and low algorithm complexity.

The exponentially weighted moving average (EWMA) algorithm, proposed by Kansal et al., is an extensively used solar energy prediction scheme ^[7]. This algorithm relies on the assumption that the amount of energy available at a given time of day is similar to that observed at the same time the previous day. The amount of energy available over the past few days has remained a weighted average, with the contribution of an exponential decline in old data. However, frequent changes in weather conditions can lead to significant prediction errors in the EWMA.

In response to this problem, Piornoel et al. proposed a new approach, that is, the weather-conditioned moving average (WCMA) ^[13]. Similar to the EWMA, the WCMA considers not only the reference day of solar power but also the day and the reference days of the weather. The WCMA considers the time slot from a few days ago as the average energy availability when verifying the prediction for a given time slot and thus avoids the effects experienced with the EWMA; moreover, it compares the conditions on a given day with those of a few days before the change in weighting factor to obtain the average.

Cammarano et al. introduced the concept of typical weather, in which the weather can be divided into different types, namely, sunny day, rainy day, cloudy day, clear to overcast, cloudy, and clear, through similarity matching. The authors established an energy forecast model, called PROfile energy prediction model (Pro-Energy) ^[14], which includes the selection of similar weather and an update to the database; furthermore, the authors verified the model’s accuracy, predicted the relationship among time lengths, and proposed Pro-Energy with variable length time slots ^[15].

Each of the typical algorithms listed above contains a fixed weighting factor, frequently adjusted to a specific set of data to balance current measurements with historical data. Nevertheless, adjusting this factor prior does not necessarily ensure that the previously described scheme efficiently adapts to rapidly changing weather conditions. Dehwah et al. first established the dynamic WCMA (D-WCMA) model by introducing dynamic change factors based on the WCMA and then the universal dynamic WCMA (UD-WCMA) energy prediction model by introducing PROfile in combination with the concept of “typical weather” in Pro-Energy to solve the interference of weighting factors on the model ^[16]. However, dividing typical weather and establishing PROfile are difficult to realize considering the complexity of weather changes. Therefore, the accuracy of the abovementioned model in the test with real data has not been significantly improved. In addition, the UD-WCMA prediction produces several error points when the weather is stable and inevitably has a lag defect.

Artificial intelligence methods use advanced artificial intelligence technologies, such as artificial neural networks and deep learning neural networks, to build solar forecasting models. Ding et al. ^[10] proposed a similar day selection algorithm, which screens out the solar data with the same weather type and closest to the predicted time point from the historical records and inputs it into the BP neural network. Liu et al. ^[11] used the multilayer perceptron (MLP) method to predict solar energy harvesting power. In addition, they also proposed a KBNN to predict the solar energy, using the previous prediction equation as knowledge to join the neural network and using the learning ability of the artificial neural network, thereby establishing a multi-stream prediction model. The model structure proposed by Asrari et al. ^[12] designed a combination of gradient descent optimization and meta-heuristic optimization methods to consider the prediction accuracy and computational burden. The gradient descent optimization technology provides the initial parameters of the feedforward artificial neural network (ANN). It then searches for the optimal parameter set of the neural network through the initial individual found by the specific SFLA algorithm and, ultimately, uses the parameter set for the solar power prediction. Long et al. ^[17] proposed a combined interval prediction model based on upper and lower bound estimations and chose an extreme learning machine (ELM) as the basic prediction engine. Auto-encoding technology was also used to initialize the input weight matrix of the ELM to achieve efficient feature learning. As mentioned above, these kinds of methods have high accuracy, but the prediction cost is large and not suitable for sensor networks.

When a time series or a time series after difference is stationary, researchers can adopt the ARIMA algorithm for prediction. The ARIMA and SARIMA algorithms have various applications. For example, these schemes can be applied to demographic statistics, prediction of the number of future users of a certain product ^[18], path problems in sports ^[19], hemorrhagic fever with renal syndrome incidence ^[20], emergency department visitors ^[21], monthly numbers of dengue cases ^[22], and ecological environment monitoring, such as predicting the monthly flow of river water ^[23].

The solar power harvested by the predicted object is similar to the abovementioned population, water flow, and death toll in the time series formed in time-dominated statistics. Thus, researchers consider applying the ARIMA model to predict solar power harvesting. The stationarity of the time series is tested based on real solar radiation datasets from ORNL RSR (Oak Ridge National Laboratory rotating shadowband radiometer) ^[24], and the results show that the time series formed by solar power harvesting has favorable stationarity. Therefore, time-series prediction can be used. Furthermore, researchers analyze the SARIMA model based on the characteristics of periodically existing data and propose the ASARIMA model in this research. The results confirm that the proposed prediction model may be suitable for various weather conditions when given sufficient historical data to establish the optimal model for predicting solar power.

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Lingsheng Li

Chong Han

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1. Introduction

2. ASARIMA

References