Comparison between free space propagation and guided propagation

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Fault Detection and localization methods

In previous sections we have seen the variety of the existing cable types, as well as the faults that may occur and affect the cable performance. Thus, several methods emerged to inspect the presence of a damage in the cable, and a vast majority focused on the hard faults that may exist, because they are generally at the origin of the incidents that occur, such as fires and data breaks, and are also easier to detect and locate [23] as we will be seeing in the next chapter. However, the importance of soft faults should not be under-estimated, as a soft fault might develop into a hard one [24] [25] and might also cause the appearance of electrical arcing while the damaged cable is in use, thus threatening the safety of the system. We begin by exposing the most common methods used today for the detection and location of cable faults, and their major limitations.

Visual inspection

It is a classic and common way to inspct the presence of anomalies in the tested cables, such as the case in the domain of aircraft [26, 27]. Visual inspection means inspecting the cable’s health using ‘raw’ human senses; it entails accessing the cables and then carefully checking the insulation for holes and cracks, often no larger than the head of a pin. However, whole sections of wiring might never get inspected: chafed insulation can be hidden under clamps or around corners, or within multiwire bundles, which makes accessing the inspected wires very difficult. Also, the quality of the inspection is often subjective, and depends on the ‘eye quality’ of the inspector.

Radiographic inspections

X-Rays and other radiographic techniques have been successfully used to find problems in electrical wiring [16]. The advantage of these techniques is that they allow inspection through the insulation, thus allowing the technicians to see the conductors inside the insulation. However, this method presents the same inconvenience as the visual inspection method: it requires a human intervention, as well as an X-ray generator and detector that have to be placed near the cable under test. Thus, this imaging technique cannot be applied to cables that are not easily accessible.

Low frequency and DC methods

These methods require having a ‘healthy’ cable with the same characteristics as the tested cable. Among the most common methods are the ‘three-wire’ fault location method and the loop method.

Capacitive and inductive methods

Other methods to determine the position of a hard fault are capacitive and inductive methods [32]. Capacitance measurement tend to locate an open circuit while induction measurement is used to locate a short circuit. These methods are also used for single cable configurations and cannot be applied to more complex network configurations, including one or several junctions and discontinuities, such as a single junction network, equivalently pointed to as a Y -network. An example will help us illustrate the principle of these methods: let us consider a symmetrical two-wire line, as shown in Fig. 1.18. D denotes the distance between the two conductors, d the diameter of the conductors,  » the permittivity of the dielectric separating the conductors, and μ the magnetic permeability of the insulator between the two conductors. For a symmetrical two-wire line, the capacitance and inductance per unit length are given.

Radio Frequency (RF) radiation

RF shield testing is a method for locating damage to shields used in coax or STP wires [16]. A radio frequency source is applied to a shielded wire. Any place along the wire where the grounded shield is not complete will radiate, and that radiation can be picked up and its source located with a radio receiver. But in domains such as the aircraft, the majority of the wiring is not shielded, and therefore cannot be tested using this technique, because the wire radiates along its entire length, giving no information other than the routing of the wire.

High frequency techniques

High frequency techniques are defined as the techniques that use frequencies with wavelengths shorter than two times the length of the cable being tested. They include impedance spectroscopy and reflectometry methods.

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Impedance spectroscopy

This method consists of analyzing the insulation characteristics of the cable at various frequencies [16] [33] [34]. It can be accomplished using a network analyzer to inject a sine wave into one end of the cable and monitor the impedance of the cable with respect to the airframe or

Table of contents :

Introduction
Chapter 1 
1 State of the art 
1.1 Introduction
1.2 Electrical cables
1.2.1 Introduction
1.2.2 Coaxial cables
1.2.3 Twisted pair
1.2.4 Power cables
1.3 Wire faults
1.4 Fault Detection and localization methods
1.4.1 Visual inspection
1.4.2 Radiographic inspections
1.4.3 Low frequency and DC methods
1.4.3.1 Three-wire fault location method
1.4.3.2 Loop methods
1.4.4 Capacitive and inductive methods
1.4.5 Medium frequency techniques
1.4.5.1 Tone injection
1.4.5.2 Radio Frequency (RF) radiation
1.4.6 High frequency techniques
1.4.6.1 Impedance spectroscopy
1.4.6.2 Reflectometry methods
1.5 Conclusion
Chapter 2 
2 Guided Wave Propagation: Concepts and Tools 
2.1 Introduction
2.2 Guided Propagation Modeling
2.2.1 Two conductor transmission line
2.2.2 Multiport modeling: Scattering parameter matrix
2.2.2.1 S-parameter matrix of a parallel load
2.2.2.2 S-parameter matrix of a two-conductor transmission line
2.2.2.3 S-parameter matrix of an n-branch junction
2.2.2.4 Simulation of complex networks using the S-parameter matrices
2.2.3 Graph representation of networks
2.2.4 Space-time (or ZT) diagram
2.3 Difference system
2.3.1 Comparison between free space propagation and guided propagation
2.3.2 Example of the difference system in the case of guided propagation
2.3.3 Difference system in the case of a hard fault
2.3.4 Difference system in the case of a soft fault
2.3.5 Discussion on the definition of a hard and a soft fault
2.4 Conclusion
Chapter 3 
3 Fault Detection 
3.1 Introduction
3.2 Time Reversal (TR)
3.2.1 Literature overview
3.2.2 Example of TR in acoustics
3.2.3 Matched Pulse (MP)
3.3 MP echo
3.3.1 Example of a MP echo
3.3.2 Localization using the MP echo
3.4 Mathematical analysis
3.4.1 Modeling of the impulse response of the difference system
3.4.2 Detection gain
3.4.2.1 Definition
3.4.2.2 Calculus of the input energies
3.4.2.3 Calculus of the instantaneous powers
3.4.2.4 Calculus of the detection gain
3.4.3 Signal to Noise Ratio (SNR)
3.4.3.1 Standard TDR case
3.4.3.2 MP case
3.4.3.3 SNR gain
3.4.4 Detection probability
3.4.4.1 True Positive probability (TP)
3.4.4.2 False Positive probability (FP)
3.5 Parametric study
3.5.1 Simulation Model
3.5.2 Single-Y network simulation
3.5.2.1 Detection gain
3.5.2.2 ROC Curves
3.5.2.3 Detection probabilities
3.5.3 Double-Y network simulation
3.5.3.1 Detection gain
3.5.3.2 ROC Curves
3.5.3.3 Detection probabilities
3.5.4 Conclusion
3.6 Experimental validation
3.6.1 Introduction
3.6.2 Experimental setup
3.6.3 Fault characterization
3.6.3.1 Variation in the cable cross section
3.6.3.2 Broken shield
3.6.3.3 Conclusion
3.6.4 Studied networks configurations
3.6.5 Results
3.6.5.1 Detection gain
3.6.5.2 ROC Curves
3.6.5.3 Detection probabilities
3.7 Conclusion
Chapter 4 
4 Fault location 
4.1 Introduction
4.2 Existing fault location methods
4.2.1 Reflectometry methods
4.2.1.1 Standard Reflectometry
4.2.1.2 Distributed reflectometry
4.2.1.3 Iterative methods
4.3 The DORT method
4.3.1 Introduction
4.3.2 Principle of the method : an example in acoustics
4.3.2.1 Time Reversal Operator (TRO)
4.3.2.2 Description of the DORT method
4.3.2.3 DORT in three and one dimensional cases
4.3.3 Application of the DORT to fault location: examples in guided propagation
4.3.3.1 Paths designation
4.3.3.2 Single transmission line
4.3.3.3 Single junction network
4.3.3.4 Double junction network
4.4 Fault location criterion using the DORT method
4.4.1 The local maximum
4.4.2 The contrast
4.4.2.1 Definition of the plateau
4.4.2.2 Calculus of the delimiting intervals
4.4.2.3 Calculus of the contrast
4.4.3 Influence of the number of testing ports on the DORT performance
4.5 Statistical study: database definition
4.5.1 Studied model and influencing parameters
4.5.2 Database generation
4.6 Statistical study: results analysis
4.6.1 Estimator of the fault location probability
4.6.2 Influence of the relative position of the fault
4.6.3 Influence of the sources configuration and number
4.6.3.1 Conditional location probabilities
4.7 Experimental study
4.7.1 Experimental setup
4.7.2 Single-junction network
4.7.3 Double junction network
4.7.4 Conclusion
4.8 Multiple fault location using the differential DORT method
4.8.1 Location of two faults using the differential DORT
4.9 Conclusion
Conclusion
Glossary
Publications
Bibliography

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