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.2017 Mar 9;17(3):551.
doi: 10.3390/s17030551.

An Elimination Method of Temperature-Induced Linear Birefringence in a Stray Current Sensor

Affiliations

An Elimination Method of Temperature-Induced Linear Birefringence in a Stray Current Sensor

Shaoyi Xu et al. Sensors (Basel)..

Abstract

In this work, an elimination method of the temperature-induced linear birefringence (TILB) in a stray current sensor is proposed using the cylindrical spiral fiber (CSF), which produces a large amount of circular birefringence to eliminate the TILB based on geometric rotation effect. First, the differential equations that indicate the polarization evolution of the CSF element are derived, and the output error model is built based on the Jones matrix calculus. Then, an accurate search method is proposed to obtain the key parameters of the CSF, including the length of the cylindrical silica rod and the number of the curve spirals. The optimized results are 302 mm and 11, respectively. Moreover, an effective factor is proposed to analyze the elimination of the TILB, which should be greater than 7.42 to achieve the output error requirement that is not greater than 0.5%. Finally, temperature experiments are conducted to verify the feasibility of the elimination method. The results indicate that the output error caused by the TILB can be controlled less than 0.43% based on this elimination method within the range from -20 °C to 40 °C.

Keywords: geometric rotation effect; stray current sensor; temperature-induced linear birefringence.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Schematic diagram of stray current formation mechanism: 1. Overhead lines; 2. Train; 3. Running rail; 4. Cable for returning the primary stray current; 5. Track bed; 6. Stray current control mat; 7. Soil; 8. Buried pipe; 9. Corrosion part of buried pipe.
Figure 2
Figure 2
Configuration of the stray current sensor and its sensor head: (a) Configuration of stray current sensor: SF represents the CSF; M represents the mirror; MS1, MS2, MS3, and MS4 represent four multilayer solenoids in series; (b) Configuration of the sensor head: 1. Multilayer solenoid; 2. Cylindrical silica rod; 3. CSF; 4. Mirror; 5. Heat-insulated cotton; 6. Plastic bend.
Figure 3
Figure 3
Polarization evolution of the CSF element.
Figure 4
Figure 4
The initial condition of the differential equation of the CSF in each section: (1) for the forward propagating light,Eab(0),Ecd(0),Eef(0), andEgh(0) are the initial conditions in sections AB, CD, EF, and GH; (2) for the back propagating light,Aab(2π),Acd(2π),Aef(2π), andAgh(2π) are the initial conditions in sections AB, CD, EF, and GH.
Figure 5
Figure 5
The simulation results to evaluate the effect of theLen &num on the output error U: (a)Len = 600 mm andnum = 64; (b)Len = 300 mm andnum = 1.
Figure 6
Figure 6
The flowchart on the optimization ofLen andnum in this work.
Figure 7
Figure 7
The MEFR versus the unknown parameters.
Figure 8
Figure 8
The birefringence and effective factor versus the unknown parameters.
Figure 9
Figure 9
The output error distribution of our sensor using this CSF when the Cur is changed within the range from 10.0 A to 30.0 A and theT is changed within the range from −20 °C to 40 °C.
Figure 10
Figure 10
The results of the temperature experiments for different input currents: (a) the input current is about 15.0 A; (b) the input current is about 20.0 A; (c) the input current is about 25.0 A; (d) the input current is about 30.0 A.
Figure 10
Figure 10
The results of the temperature experiments for different input currents: (a) the input current is about 15.0 A; (b) the input current is about 20.0 A; (c) the input current is about 25.0 A; (d) the input current is about 30.0 A.
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