Journal of Sensors

Volume 2018, Article ID 7853695, 16 pages

https://doi.org/10.1155/2018/7853695

## A Robust Data Interpolation Based on a Back Propagation Artificial Neural Network Operator for Incomplete Acquisition in Wireless Sensor Networks

^{1}State Key Laboratory of Marine Resource Utilization in South China Sea, College of Information Science & Technology, Hainan University, Haikou 570228, China^{2}College of Network, Haikou University of Economics, Haikou 571127, China

Correspondence should be addressed to Yong Bai; nc.ude.uniah@iab

Received 13 July 2018; Revised 7 October 2018; Accepted 16 October 2018; Published 20 December 2018

Guest Editor: Aniello Falco

Copyright © 2018 Mingshan Xie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The data space collected by a wireless sensor network (WSN) is the basis of data mining and data visualization. In the process of monitoring physical quantities with large time and space correlations, incomplete acquisition strategy with data interpolation can be adopted to reduce the deployment cost. To improve the performance of data interpolation in such a scenario, we proposed a robust data interpolation based on a back propagation artificial neural network operator. In this paper, a neural network learning operator is proposed based on the strong fault tolerance of artificial neural networks. The learning operator is trained by using the historical data of the data acquisition nodes of WSN and is transferred to estimate the value of physical quantities at the locations where sensors are not deployed. The experimental results show that our proposed method yields smaller interpolation error than the traditional inverse-distance-weighted interpolation (IDWI) method.

#### 1. Introduction

The purpose of a wireless sensor network (WSN) is to obtain the data field or data space of the physical world as accurate and complete as possible through acquisition technology. It is an important part of forecasting, simulation, and prediction to obtain the spatial-temporal distribution information of the monitored object accurately. However, in some scenarios, WSN can take an incomplete acquisition strategy, due to the development cost of the sensing device and the deployment environment factor, energy limitation, equipment aging, and other factors, or because it is not necessary to collect the data in each corner of the monitoring area. The incomplete acquisition strategy is divided into three cases: (a) spatial incomplete acquisition strategy—the actual collected area is smaller than the interested area or the actual acquisition location set is part of the entire acquisition locations in the monitoring area; (b) temporal incomplete acquisition strategy—the actual collection time period is less than the time period in which all devices work. The sleeping schedule is a temporal incomplete acquisition strategy. (c) Incomplete acquisition of attributes—the actual physical quantities collected are less than the interested physical quantities.

Because the constraints of interpolation are relatively small, it is more appropriate to use the interpolation algorithm to complete or refine the entire data space in the case of spatial incomplete acquisition. The interpolation completion algorithm takes advantage of the strong correlation between the data in the data space. At present, data interpolation is the main method to complement the data space of the entire region. In [1], Ding and Song used the linear interpolation theory to evaluate the working status of each node and the whole network coverage case. In [2], Alvear et al. applied interpolation techniques for creating detailed pollution maps.

However, WSN is often affected by many unfavorable factors. For example, it is usually arranged in a harsh environment, the node failure rate is relatively high, it is very difficult to physically replace the failure sensor, and the wireless communication network is susceptible to interference, attenuation, multipath, blind zone, and other unfavorable factors. Data is prone to errors, security is not guaranteed, etc. Therefore, WSN data interpolation technology must be highly fault tolerant to ensure high credibility and robustness of the completed data space [3].

Data interpolation is used to predict and estimate the information at an unknown location by means of using known information. Transfer learning opens up a new path for data interpolation. The goal of transfer learning is to extract useful knowledge from one or more source domain tasks and apply them to new target tasks. It is essentially the transfer and reuse of knowledge. Transfer learning has gradually received the attention of scholars. In [4], the authors are motivated by the idea of transfer learning. They proposed a novel domain correction and adaptive extreme learning machine (DC-AELM) framework with transferring capability to realize the knowledge transfer for interference suppression. To improve the radar emitter signal recognition, Yang et al. use transfer learning to obtain the robust feature against signal noise rate (SNR) variation in [5]. In [6], the authors discuss the relationship between transfer learning and other related machine learning techniques such as domain adaptation, multitask learning, and sample selection bias, as well as covariate shift.

Artificial neural networks have strong robustness. One of the requirements to ensure the accuracy of transfer learning is the robustness of the learning algorithm. Many scholars have combined the neural artificial network with transfer learning. In [7] Pan et al. propose a cascade convolutional neural network (CCNN) framework based on transfer learning for aircraft detection. It achieves high accuracy and efficient detection with relatively few samples. In [8], Park et al. showed that the transfer learning of the ImageNet pretrained deep convolutional neural networks (DCNN) can be extremely useful when there are only a small number of Doppler radar-based spectrogram data.

The research aim of data interpolation of WSN is to complete the data space of the entire monitoring area by using the limited data of the acquisition node to estimate the data at the locations where sensors are deployed. However, data errors of WSN due to various reasons have great impact on the accuracy of data interpolation. Due to the strong robustness of an artificial neural network, an artificial neural network learning operator is generated by using historical measurement data of limited data acquisition nodes in this paper. At the same time, this paper applies the learning property of the artificial neural network to the inverse-distance-weighted interpolation method, which is conducive to improving precision and accuracy of data interpolation. On the basis of analyzing the demand of network models, this paper proposes a robust data interpolation based on a back propagation artificial neural network operator for incomplete acquisition in wireless sensor networks. The detailed steps of the algorithm are discussed in detail, and the algorithm is analyzed based on the MATLAB tool and the measured data provided by the Intel Berkeley Research laboratory [9]. The experimental results are good evaluations of the fault-tolerant performance and lower error of our proposed method.

The main contributions of this paper are as follows: (1) Aiming at the data loss and disturbance error, we propose a fault-tolerant complementary algorithm based on the robustness of the artificial neural network(2) We combine the artificial neural network with the inverse-distance-weighted interpolation algorithm to obtain a novel back propagation artificial neural network operator(3) We use the inverse tangent function to reconcile the relationships among multiple prediction values

The rest of the paper is organized as follows. In Section 2, we summarize the related work. Section 3 introduces the interpolation model in the condition of data error. Section 4 presents how to construct the learning operator set of data acquisition nodes. Section 5 elaborates how to generate the interpolation by the method based on the back propagation artificial neural network operator. We will show the experimental results of our proposed methods compared with the inverse-distance-weighted interpolation in Section 6. The conclusions are given in Section 7.

#### 2. Related Works

##### 2.1. The Inverse-Distance-Weighted Interpolation Method

The inverse-distance-weighted interpolation (IDWI) method is also called “inverse-distance-weighted averaging” or the “Shepard Method.” The interpolation scheme is explicitly expressed as follows:

Given locations whose the plane coordinates are and the values are , where , the interpolation function is where is the horizontal distance between and , where . is a constant greater than 0, called the weighted power exponent.

It can easily be seen that the interpolation of the location is the weighted mean of .

The application of inverse-distance-weighted interpolation is more extensive. Because of its simple computation and having less constraints, the interpolation precision is higher. In [10], Kang and Wang use the Shepard family of interpolants to interpolate the density value of any given computational point within a certain circular influence domain of the point. In [11], Hammoudeh et al. use a Shepard interpolation method to build a continuous map for a new WSN service called the map generation service.

From (1), we can see that the IDWI algorithm is sensitive to the accuracy of the data. However, WSN is usually deployed in a harsh environment, and the probability of data being collected is high. The error tolerance of the interpolation algorithm is required. This paper improves the robustness of interpolation algorithm on the basis of the inverse-distance interpolation algorithm.

##### 2.2. Artificial Neural Network

An artificial neural network (ANN) is an information processing paradigm that is inspired from biological nervous systems, such as how the brain processes information. ANNs, like people, have the ability to learn by example. An ANN is configured for a specific application, such as pattern recognition, function approximation, or data classification, through a learning process. Learning in biological systems involves adjustments to the synoptic connections that exist among neurons. This is true for ANNs as well. They are made up of simple processing units which are linked by weighted connections to form structures that are able to learn relationships between sets of variables. This heuristic method can be useful for nonlinear processes that have unknown functional forms. The feed forward neural networks or the multilayer perceptron (MLP) among different networks is most commonly used in engineering. MLP networks are normally arranged in three layers of neurons; the input layer and output layer represent the input and output variables, respectively, of the model; laid between them is one or more hidden layers that hold the network’s ability to learn nonlinear relationships [12].

The natural redundancy of neural networks and the form of the activation function (usually a sigmoid) of neuron responses make them somewhat fault tolerant, particularly with respect to perturbation patterns. Most of the published work on this topic demonstrated this robustness by injecting limited (Gaussian) noise on a software model [13]. Velazco et al. proved the robustness of ANN with respect to bit errors in [13]. Venkitaraman et al. proved that neural network architecture exhibits robustness to the input perturbation: the output feature of the neural network exhibits the Lipschitz continuity in terms of the input perturbation in [14]. Artificial neural networks have strong robustness. The robustness of the algorithm is a requirement to ensure the accuracy of artificial neural network operator transferring. We can see from the literatures [7, 8] that operator transferring can combine well with an artificial neural network. The learning operator in this paper also adopts an artificial neural network algorithm.

#### 3. Problem Formulations

##### 3.1. Data Acquisition Nodes

To assess the entire environmental condition, WSN collects data by deploying a certain number of sensors in the location of the monitoring area; thus, the physical quantity of the monitoring area is discretized and the monitoring physical quantity is digitized.

*Definition 1. **Interested locations*: in the whole monitoring area, they are the central locations of the segment of the monitoring area that we are interested in.

Sensors can be deployed at each interested location to capture data. The data at all interested locations reflects the information status of the entire monitoring area.

We assumed that is the set of the interested locations, which is a matrix of 1 × *n*.
where is the *i*th interested location in the monitoring area. is the coordinates of the interested location in the monitoring area. Due to the difficulty and limitation of deployment, not all the interested locations can deploy sensors. This paper studies the spatial incomplete collection strategy. We select a subset of as the data acquisition node. represents the potential of a set, that is, the number of elements of . .

*Definition 2. **Data acquisition nodes*: they are the interested locations where the sensors are actually deployed.

The sensors are deployed in these interested locations, so that these locations become data acquisition nodes. The all-data acquisition nodes in the monitoring area act as the sensing layer of the WSN, and the information is transmitted to the server through the devices of the transport layer.

In our research, when the sensors are not deployed at the interested location, we use zero as a placeholder to replace the data acquisition node. When the interested location becomes the data acquisition node, we use 1 as a placeholder to replace the data acquisition node. Suppose that is the set of data acquisition nodes.
where represents the *i*th interested location where the sensors are deployed. indicates the potential of the set . It reflects the total number of elements in the set of data acquisition nodes. This paper investigates the case where multiple types of sensors are deployed at a data acquisition node. The data that the data acquisition node can correctly collect at time is defined as , which is dimensional data that is perceived by the *i*th data acquisition location in . The physical quantity of temperature, humidity, etc. can be measured at the same time. The data is defined as

If , then WSN implements incomplete coverage; if , then WSN implements complete coverage. The data of the interested location where the sensors are not deployed can be assessed by the data of the data acquisition node. The interested location where the sensors are not deployed is indicated as non-data acquisition location.

##### 3.2. Data Acquisition Error

Because the wireless communication network is susceptible to interference, attenuation, multipath, blind zone, and other unfavorable factors, the data error rate is high. Nodes and links in wireless sensor networks are inherently erroneous and unpredictable. The error data which greatly deviated from the ideal truth value is divided into two types: data loss and data disturbance.

*(1) Data Loss*. These reasons, such as nodes cannot work, links cannot be linked, or data cannot be transmitted, cause the data of the corresponding data acquisition nodes to not reach the sink node.

*(2) Data Disturbance*. Due to the failure, the local function of the WSN is in an incorrect (or ambiguous) system state. This state may cause a deviation between the data measured by the sensors of the corresponding data acquisition node and the true value, or the signal is disturbed during the transmission, and the data received at the sink node is deviant from the true value. The data that corresponds to the data acquisition node is not the desired result. The collected data oscillate in the data area near the true value. In this paper, we assumed that the data disturbance obeys the Gauss distribution.

The main idea of our method is based on the fundamental assumption that the sensing data of WSN are regarded as a vector indexed by the interested locations and recovered from a subset sensing data. As demonstrated in Figure 1, the data acquisition consists of two stages: the data-sensing stage and the data-recovering stage. At the data-sensing stage, instead of deploying sensors and sensing data at all interested locations, a subset of interested locations which are the shaded ones in the second subfigure is selected to sense physical quantity and deliver the sensing data to the sink node at each data collection round. Some locations are drawn by the fork in the second subfigure because their data is lost or disturbed. The fork represented the data errors. When the hardware and software of the network node failures or the communication links of the network are broken, the set of sensors which encounter data errors is only the subset of . At the data-recovering stage, the sink node receives these incomplete sensing data over some data collection rounds shown in the third subfigure in which the shaded entries represent the valid sensing data and the white entries are unknown. And then we could use them to recover the complete data by our method.