Distributed Faulty Sensor Node Detection in Wireless Sensor Networks based on Copula Theory Farid Lalem Lab-STICC UMR CNRS 6285 Université de Bretagne Occidentale, Brest, France 20, Avenue Victor Le Gorgeu, 29238 Brest, France Farid.Lalem@univ- brest.fr Ahcène Bounceur Lab-STICC UMR CNRS 6285 Université de Bretagne Occidentale 20, Avenue Victor Le Gorgeu, 29238 Brest, France Ahcene.Bounceur@univ- brest.fr Reinhardt Euler Lab-STICC UMR CNRS 6285 Université de Bretagne Occidentale 20, Avenue Victor Le Gorgeu, 29238 Brest, France Reinhardt.Euler@univ- brest.fr Mohammad Hammoudeh Faculty of Science & Engineering Manchester Metropolitan University Manchester, UK M.Hammoudeh@mmu.ac.uk Rahim Kacimi IRIT-UPS University of Toulouse 118 route de Narbonne, Université de Toulouse, France kacimi@irit.fr Sanaa Kawther Ghalem Industrial computing and networking Laboratory-RIIR University of Oran 1, Ahmed Benbella 31000, Oran, Algeria ghalemsanaa@gmail.com ABSTRACT Wireless Sensor Networks (WSNs) are arising from the pro- liferation of Micro-Electro-Mechanical Systems (MEMS) tech- nology as an important new area in wireless technology. They are composed of tiny devices which monitor physi- cal or environmental conditions such as temperature, pres- sure, motion or pollutants, etc. Moreover, the accuracy of individual sensor node readings is decisive in WSN ap- plications. Hence, detecting nodes with faulty sensors can strictly influence the network performance and extend the network lifetime. In this paper, we propose a new approach for faulty sensor node detection in WSNs based on Copula theory. The obtained experimental results on real datasets collected from real sensor networks show the effectiveness of our approach. 1 . Keywords Wireless Sensor Networks; Copulas; Faulty sensors; Failure nodes. 1. INTRODUCTION A Wireless Sensor Network (WSN) consists of low cost wireless nodes, working on batteries, that perform a collab- orative effort in order to perceive physical or environmental 1 This work is part of the research project PERSEPTEUR supported by the French Agence Nationale de la Recherche ANR. c  2017 ACM. ISBN . DOI: conditions, such as temperature, humidity, light, sound, vi- bration, pressure, motion, pollutants, etc. [1]. This feature of sensor networks provides a wide range of applications that include military surveillance, habitat mon- itoring, seismic detection, security and health applications, etc. Also, sensor nodes are prone to faults, often unreliable and suffer from inaccuracy and incompleteness because of their intrinsic natures or the harsh environments in which they are used [9]. Furthermore, faulty sensor nodes may generate faulty data, which could affect the analysis of the data, prevent from tak- ing correct decisions and, beyond, lead to a waste of limited resources and reduce the network lifetime [12]. In order to ensure the network performance and extend the network lifetime, the WSN should be able to detect the faulty sensor nodes, to take actions to avoid the spreading of erroneous data over the network, and to maintain the WSN resources at a high level [8]. For this purpose, the aim of the work presented here is to develop an approach for faulty sensor node detection in WSNs, by using Copula theory which is a powerful tool to model and analyze multivariate distributions. In the following, we propose a new fully distributed ap- proach for faulty sensor node detection using Copula theory. Based on historical measurements of data, we assign to each sensor node a local polygon arising from the application of Copula theory. Faulty sensor nodes are then detected by calculating the probability that a sensed value falls outside this polygon during a period of time T . If the calculated probability is less than a predefined threshold, the sensor node is considered good, otherwise the sensor node is de- clared faulty and an alert will be sent to the sink. The remainder of the paper is organized as follows. In the next section, we present an overview of related work. Section 3 describes basic concepts of Copula theory. In Sec- tion 4, the proposed approach to detect faulty sensor nodes is shown. Simulation results and a performance evaluation