In Situ Calibration Algorithms for Environmental Sensor Networks 

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Overview of fault diagnosis for sensor networks through existing reviews

In the last decade, while sensor networks gained in popularity, the question of their de2870 pendability became a major subject. In particular, multiple contributions were made on fault diagnosis as reported in various surveys [98, 106, 114, 185]. In these publications, the research works are classified by the way the diagnosis is performed. First, the place where the decision is computed, e.g. if it is a centralised, decentralised or hybrid approach, is considered. Then, the general mathematical approach used for the diagnosis (testing, comparisons, majority voting, statistics, probabilities, machine learning algorithms, fuzzy logic, Faults are generally characterised by « hard » or « soft » and as « permanent », « transient » or « temporary »[98, 106, 185]. Only Muhammed et al. [114] used a taxonomy similar to the one of  Ni et al. [115] that inspired the one used in this manuscript. In particular, these authors report It could be for instance an actual correlation between the true values at two very distant points that could be exploited in a specific situation.

State-of-the-art of fault diagnosis applied to sensor networks

that the existing diagnosis algorithms are often targeting multiple faults. For those addressing the drift fault22, stuck-at or out-of-range faults are also detected by the same algorithm in the In the following surveys [98, 114, 185], the diagnosis approaches reported concern mainly static sensor networks. Mahapatro et al. [98] listed eight algorithms that could be applied to static and mobile sensor networks.23 Zhang et al. [185] reported two references explicitly dealing with mobile sensor networks [1, 28]. They also stated that approaches designed for static networks behave poorly when applied to mobile ones. This indicates that algorithms exploiting specificities related to networks with mobile nodes in the diagnosis approach have not been deeply investigated so far. In addition, other subjects such as energy consumption, communication range needed, communication failures, or the amount of required neighbour nodes are taken into account in the surveys on fault diagnosis for sensor networks [98, 106, 114, 185]. Zhang et al. [185] underline it is challenging to design a diagnosis approach having satisfying performances or properties regarding all the features of interest for such an algorithm, e.g. for instance diagnosing faults  well with low energy consumption, few communications between nodes and so on.

Existing methods of diagnosis compatible with the concept of rendez-vous addressing any fault

The methods used to carry out the diagnosis of any fault in sensor networks are diverse in terms of concepts and tools on which they are based on. According to the surveys cited [98, 106, 114, 185], different main ideas come out like the use of comparisons between instruments, the use of statistics and probabilities, as well as the use of machine learning models (regressors, classifiers…). As the goal in this chapter is to propose a diagnosis algorithm for sensor networks based on rendez-vous between the nodes, we focus here on approaches compatible with this idea, e.g. it consists at least in comparison of values measured by different instruments.

Related works

Chen et al. [29] introduced a faulty sensor detection algorithm consisting of four steps of evaluation. First, each instrument compares its measured value at the instant of the diagnosis with the measured values of its neighbours. If the difference between two instruments is higher than a first threshold, the deviation of the difference since the last comparison is computed. If it is higher than a second threshold, the test between the two instruments is marked as positive. In a second step, each instrument determines if it is likely good or faulty depending on the number of positive tests and its number of neighbours. This information is shared between the it is actually good and share this result. Then, for the remaining undetermined instruments, their statuses are decided if all their neighbours are non-faulty and if all the initial tests gave the same results. If ambiguities remains, they are removed based on the likely statuses of the instruments. Xu et al. [179] proposed an extension of this work dealing with the particular case of tree-like networks to reduce the number of communications. To avoid intermittent faults, they also proposed to compute the initial test result based on multiple comparisons of values between two instruments, instead of a unique comparison. In the same way, Saha et al. [128] developed a similar algorithm but with comparisons for multiple quantities (measurand and remaining energy). Ssu et al. [142] proposed an approach to diagnosis faults between sources and sinks. The main idea is to send a request through two paths and to compare the results obtained at the sin node. If the results are different, then at least one faulty path exists. The algorithm tries to identify it with the help of a third path and a majority voting procedure, but the faulty paths cannot always be identified. Such a method is particularly relevant to diagnose communication or hardware-related faults.
Lee et al. [83] presented a distributed algorithm to isolate faulty nodes. Initially, the nodes are all assumed as faulty. A comparison is made between the measured values of neighbour nodes and if the result is higher than a threshold, then the test is positive. If less than a predefined number of positive tests has been obtained, or if the test with a non-faulty node is negative, then the diagnosed instrument is non-faulty. The algorithm works either based on single comparisons between neighbours or with comparisons repeated multiple times. Mahapatro et al. [97, 99] introduced a clustering-based diagnosis algorithm. The clustering part is used for the definition of the neighbours around cluster heads, the cluster heads being the instruments with the highest residual energy levels. They also compare the measured values between instruments of a cluster and a majority voting strategy is used to determine the state of the nodes.
Chanak et al. [28] developed a comparison-based scheme using a reference mobile sink node moving between the static nodes of the network. When it is close to a node, several diagnoses are performed to detect hardware and software faults. This also enables a low consumption of energy for the transmission of the measurement results as it is no longer necessary to communication with a distant gateway. The core of this contribution lies in the determination of an optimal path to meet with each node. Luo et al. [92] proposed an approach using the concept of average consensus. Each instrument estimates first its status regarding the average consensus measured value build with the values of its neighbours. Each instrument also estimates the statuses of its neighbours. Then, the decisions of all the instruments are merged to make the final decision.
In reaction to contributions computing the average value of the neighbours of an instrument by weighting their values with the inverse of the distance between them, Xiao et al. [178] argued that the distance does not control alone the relationship between the values of two instruments, notably if a closer one is actually faulty. Thus, they propose to take into account an indicator of trustworthiness computed for each node of the network. This confidence value is used in voting procedures that are used to determine the status of instruments.  Ji et al. [69] also developed their algorithm around a weighted average of the values measured by an instrument. The weights are representing a confidence level associated to each instrument. The difference between the measured value of an instrument and the average is compared to threshold. If it is greater than the threshold, the confidence level of the instrument is decreased and once it reaches zero, the instrument is reported as faulty. This idea of trust between instruments has been extensively studied and extended, as did for instance Jiang et al. [70]. Their robust trust model is based on direct comparisons but also on third parties and recommendations, with concerns about the security of the communications between the instruments. Their trust framework is also adapted for mobile sensor networks. Wang et al. [164] exploited Petri nets to introduce a trust-based formal model aimed at detecting faults in sensor networks.

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Table of contents :

Abstract
Résumé
List of publications
List of Figures
List of Tables
List of Acronyms and Abbreviations
List of Notations
General Introduction 
1 Context of the thesis
2 Contributions
3 Organisation of the manuscript
1 Low-cost Measuring Instruments for Air Quality Monitoring: Description, Performances and Challenges 
Introduction
1 Measurement of ambient quantities with low-cost instruments
1.1 Definition of a measuring instrument
1.2 Measuring chain of an instrument
1.3 Low-cost instruments
2 Threats to data quality for measuring instruments
2.1 Introduction
2.2 Faults
2.3 Discussion
3 Calibration of measuring instruments
3.1 Definition
3.2 Analysis
3.3 In situ calibration
3.4 Discussion
4 Sensor networks
4.1 Definition
4.2 Characteristics of interest in this work
5 Problem statement
5.1 Motivations
5.2 Objectives of the thesis
2 In Situ Calibration Algorithms for Environmental Sensor Networks 
Introduction
1 Scope of the taxonomy
2 Taxonomy for the classification of the algorithms
2.1 Use of reference instruments
2.2 Mobility of the instruments
2.3 Calibration relationships
2.4 Instrument grouping strategies
3 Comparison to other taxonomies
4 Review of the literature based on this classification
4.1 Overview
4.2 Mobile and static nodes
4.3 Calibration relationships
4.4 Pairwise strategies
4.5 Blind macro calibration
4.6 Group strategies
4.7 Comment regarding other surveys
5 Conclusion
3 Framework for the Simulation of Sensor Networks Aimed at Evaluating In Situ Calibration Algorithms 
1 Challenges for the comparison of in situ calibration algorithms
2 Description of the framework
2.1 Simulation-based strategy
2.2 Functional decomposition
3 Comparison of in situ calibration strategies for blind static sensor networks
3.1 Frame of the study
3.2 Application of the framework
3.3 Results
3.4 Conclusions
4 Evaluation of measurements after correction
4.1 Problem statement
4.2 Evaluation with an error model
4.3 Means of visualisation
4.4 Conclusion
5 Sensitivity of the calibration algorithms to the specificities of the case study
5.1 Using a more realistic model of the true values
5.2 Density of the sensor network
5.3 Instrument modelling
5.4 Parameters of calibration strategies
5.5 Summary of the results
6 Discussion and conclusion
4 Diagnosis of Drift Faults in Sensor Networks 
1 Motivations
2 State-of-the-art of fault diagnosis applied to sensor networks
2.1 Overview of fault diagnosis for sensor networks through existing reviews .
2.2 Existing methods of diagnosis compatible with the concept of rendez-vous addressing any fault
2.3 Positioning of the contribution
3 Definition of concepts for a drift diagnosis algorithm based on rendez-vous
3.1 Validity of measurement results
3.2 Compatibility of measurement results
3.3 Rendez-vous
4 Algorithm for the diagnosis of calibration issues in a sensor network
4.1 General idea
4.2 Procedure for the diagnosis of all the instruments in a sensor network
4.3 Improvements and extensions of the presented algorithm
4.4 Conclusion
5 Application of the algorithm to a first case study
5.1 Definition of the case study
5.2 Configuration of the diagnosis algorithm
5.3 Definition of the true status of an instrument
5.4 Metrics for the evaluation of performances of the diagnosis algorithm
5.5 Results
5.6 Explanations of false results
5.7 On the parameters of the diagnosis algorithm
5.8 Conclusion
6 On the assumption regarding the top-class instruments being always predicted as non-faulty
6.1 Theoretical discussion Case study with the instrument of class cmax 260 drifting
6.3 Conclusion
7 Means to reduce false results
7.1 Keep the predicted status of instruments unchanged once they are predicted as faulty
7.2 Alternate definition for rates used to decide of the status of the instruments
7.3 Adjustment of the maximal tolerated values for the different rates used to determine the statuses of the instruments
7.4 Conclusion
8 Adjustment of the minimal size required for a set of valid rendez-vous to allow a prediction between the statuses faulty and non-faulty
Algorithm determining an upper boundary for |v|min
8.2 Application to the case study
8.3 Conclusion
9 Sensitivity of the algorithm to changes in the case study
9.1 Influence of the values of drift
9.2 Influence of the true values
9.3 Influence of the model used for the true values
9.4 Influence of the density of instruments
9.5 Influence of other faults
9.6 Conclusion
10 Combination with a simple calibration approach
Conclusion and perspectives 
1 Conclusion
2 Perspectives
A Diagnosis Algorithm for Drift Faults in Sensor Networks: Extensions 
1 Formulation reducing the number of iterations of the algorithm
2 Diagnosis with the prediction as non-faulty based on the highest sufficient class
3 From a centralised to a decentralised computation
4 Multiple measurands
4.1 General idea
4.2 Diagnosis of drift faults in a sub-network with instruments having influence quantities
4.3 Conclusion
5 Diagnosis algorithm for drift faults in sensor networks with an event-based formulation
6 Real-time diagnosis algorithm of drift faults in sensor networks
6.1 Choice of an event-based approach
6.2 General idea
6.3 Initialisation of the algorithm
6.4 Allowed changes of status
6.5 Conclusion
C Sensitivity of the Diagnosis Algorithm: Case Study with Values Related Over Time for the Parameters of the True Values’ Model 
1 Introduction
2 Model used
3 Results
4 Conclusion

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