# Study of Three-Component FBG Vibration Sensor for Simultaneous Measurement of Vibration, Temperature, and Verticality

Authors: Jiang Shan-chao; Wang Jing; Sui Qing-mei; Ye Qing-lin; Wang Li-jun
Journal: Journal of Sensors
 (2015)

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## Abstract

To achieve simultaneous measurement of measurand vibration, temperature, and verticality, a three-component fiber Brag grating (TVFBG) vibration  sensor is proposed in this paper. Polymer and metal diaphragm sensitization methods are utilized to improve this sensor measurement sensitivity. Project matrix theory is adopted to analyze this sensor. Theoretically,9×9 nonsingular measuring coefficient matrix of this TVFBG sensor made up by three 3×3 measurand coefficient matrixes is established. In order to effectively extract measurand, Hilbert-Huang transform (HHT) is accepted to process this sensor’s center wavelength signals. Calibration experiments are carried out to verify the performance of this TVFBG sensor. Experiment data confirm that this sensor has excellent frequency response and show good linearity at temperature and verticality measurement. Wrist rotation angle measurement experiment is also implemented to further identify this sensor practical value. Through analyzing by HHT, experiment results show that the angle measurement sensitivities of three fiber Brag gratings which are included in this sensor are separately 25.2 pm/°, 38.2 pm/°, and 38.3 pm/°.


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## Body

## 1. Introduction

Simultaneous multiparameter measurement has provided one way which reduces the number of measuring sensors and cuts down detection cost to monitor the health status of engineering structure. Based on the characteristics of fiber Bragg grating (FBG), such as high accuracy, small size, immunity to electromagnetic interference, and multiplexing capacity, FBG sensors have been widely used in aerospace, energy industry, transportation, and geotechnical and civil engineering [1–8]. During the latest decades, there are many works about isochronous multiparameter measurement by FBG sensors have been down. Rao et al. [9] performed the simultaneous measurement of static strain, temperature, and vibration using a multiplexed in-FBG/fibre-F-P sensor. Zhang et al. [10] demonstrated an integrated inline microfiber sensor based on fiber Bragg gratings to simultaneously measure vibration and temperature information for state estimation of cable-stayed bridges.Based on available research results, a three-component FBG vibration (TVFBG) sensor for synchronous measurement of vibration, temperature, and verticality is proposed in this paper. Due to the fact that axial strain sensitive coefficient of bare FBG is only 0.003 nm/MPa [11], many methods have been reported to improve its coefficient, such as polymer sensitization [12, 13], metal diaphragm sensitization [14, 15], and some other mechanical structures [1, 16]. Polymer and metal diaphragm sensitization methods are both used to improve measurement sensitivity of this TVFBG sensor.According to project matrix theory,9×9 nonsingular measuring coefficient matrix made up by three 3×3 measurand coefficient matrixes is established. All these 3×3 matrixes are deduced from this sensor theoretical model. Three fiber Bragg gratings (TFBGs) are included in this TVFBG sensor as the sensitive elements. All center wavelengths of TFBGs contain the information of vibration, temperature, and verticality. So as to effectively extract the measurand vibration, temperature, and verticality, Hilbert-Huang transform (HHT) is used to analyze the dynamic wavelength signals. Calibration experiment is carried out to test this sensor performance and wrist rotation angle measurement experiment further proves its practical value.Generally speaking, in this sensor polymer and metal diaphragm sensitization methods are used to improve its measuring sensitivity. Theoretical calculation model based on project matrix theory is set up and HHT is utilized to extract and reconstruct the measurand. It realizes three-parameter measurement at the same time. Due to calibration and wrist rotation measurement experiment results, this TVFBG sensor possesses great potential in engineering application.


## 2. Structure of the TVFBG Sensor

Basic metal transfer structure and prototype of this TVFBG sensor are shown in Figure1. This TVFBG sensor is composed of three sensing elements and one metal transfer structure. All these three sensing elements are equidistant distributed around the axial direction and the angle interval is 120° in the circumferential distribution. The sensing element which is shown in Figure 1(c) includes two connection terminals, one spring as the elastic element and one fiber Bragg grating as sensitive element.Figure 1
Basic block diagram and prototype of this TVFBG sensor.
(a)
Schematic diagram of metal transfer structure
(b)
Prototype of this TVFBG sensor
(c)
Sensing element component parts
(d)
Components of link robMetal transfer structure shown in Figure1(a) is made up by three link rods, upper fixed and lower free rings. Link rod exhibited in Figure 1(d) is composed of two omnidirectional wheels distributed at both ends and the middle elastic element. Basic geometric parameters of this metal transfer structure are presented in Table 1.Table 1
Basic geometric parameters of metal transfer structure (unit: mm).
Length
Height
Outer radius
Inner radius
The ring
7
110
70
Link rod
155
4
Omnidirectional wheel
5
Elastomer in the middle of link rod
2.5
5
4


## 3. Signal Analysis and Measurand Identification

Due to the advantages unlimited by fixed wavelet and adaptive signal processing, HHT [13, 17] is widely adopted as a powerful tool to deal with nonlinear and nonstationary signals. HHT is utilized to pick out three different signals ΔλiV, ΔλiT, and ΔλiP (i=1,2,3) from the original center wavelengths λFBGi (i=1,2,3). ΔλiV, ΔλiT, and ΔλiP are wavelength changes caused by external vibration, temperature, and verticality angle. Through analyzing by HHT, the original signals could be expressed as(1)λFBG1=λ10+∑i=1nc1i,λFBG2=λ20+∑i=1nc2i,λFBG3=λ30+∑i=1nc3i,where λi0 (i=1,2,3) and cmi (m=1,2,3) stand for residual signals and intrinsic mode functions of the original signals.


### 3.1. Vibration Identification

Because of middle elastic element, the external vibration signal induces axial dynamic strain on these TFBGs and further leads to the center wavelength changes. Relationship between axial strainε and center wavelength shift Δλ could be expressed as(2)Δλλ=1-peε,where pe is the elastic-optic coefficient of optical fiber and its theoretical value equals 0.22. So, the efficiency of dynamic stress F worked on the optical fiber could be expressed as(3)F=Eε=ke·Vt,where E is elasticity modulus of optical fiber, ke is the elastic coefficient of elastomer in the link rob, and V(t) represents the exterior dynamic signal.Through (2) and (3), we could get that(4)Δλ1V=1-peE·λ10·ke1·V1t,Δλ2V=1-peE·λ20·ke2·V2t,Δλ3V=1-peE·λ30·ke3·V3(t)orΔλ1VΔλ2VΔλ3V=V·V1tV2tV3t,where V1t, V2t, and V3(t) are exterior vibration signals and V represents the vibration coefficient matrix.


### 3.2. Temperature Identification

Temperature changes can be obtained by(5)Δλ1T=λ10·α+ξ·T1t,Δλ2T=λ20·α+ξ·T2t,Δλ3T=λ30·(α+ξ)·T3(t)orΔλ1TΔλ2TΔλ3T=T·T1tT2tT3t,where α is thermal expansion coefficient, ξ is thermooptic coefficient of FBG, T1(t), T2(t), and T3(t) are the measured temperature, and T is the coefficient matrix of temperature.


### 3.3. Verticality Identification

While connecting line between upper and lower ring center points is not parallel with geodetic vertical line, the free ring could ceaselessly wiggle until the connecting line parallels the geodetic vertical line based on the function of omnidirectional wheel. The angle between geodetic vertical line and axis of this sensor metal transfer structure is selected as vertical evaluation standard and named as verticality angleα. When this sensor position changes from Figures 2(a) to 2(b), verticality angle α is generated by gravity.Figure 2
(a) The fixed ring parallels the ground plane. (b) Verticality angleα between the fixed ring and the ground plane.
(a)
(b)Adding the Cartesian coordinate system to this sensor and assuming that the link rod with FBG1 is vertical orthogonal withx-axis, verticality calculation model is shown in Figure 3.Figure 3
Verticality calculation model of this sensor.
(a)
Cross section of these three fiber Bragg gratings
(b)
Geometry of verticality reconstruction based on the center wavelength changesSo, the length changesΔLi (i=1,2,3) of three link robs are expressed as (6)ΔL1=r1+cos⁡θ·sinα,ΔL2=r1-cos⁡⁡π3+θ·sinα,ΔL3=r1-cos⁡⁡π3-θ·sinα,where r is radius of the upper fixed ring and θ is the directional angle between radius line ① and x axis in the XY plane.Based on the above analysis, verticality calculation formula is expressed as(7)Δλ1v=λ10·1-pe·r1+cos⁡θ·sinαh,Δλ2v=λ20·1-pe·r1-cos⁡⁡π3+θ·sinαh,Δλ3v=λ30·1-pe·r1-cos⁡⁡π3-θ·sinαhorΔλ1vΔλ2vΔλ3v=V·P1tP2tP3t,where h is height of this sensor and V is the verticality coefficient matrix. Through (7), verticality angle α and directional angle θ are obtained.The measurand identification could be concluded in four steps.(1)
Use HHT to extract different signalsΔλiV, ΔλiT, and ΔλiP (i=1,2,3) from the center wavelengths λFBGi (i=1,2,3).(2)
External dynamic signalsV1(t), V2(t), and V3(t) are obtained by bringing ΔλiV (i=1,2,3) to (4).(3)
Environment temperaturesT1(t), T2(t), and T3(t) are picked out by bringing ΔλiT (i=1,2,3) to (5).(4)
Verticality angleα and directional angle θ are calculated by bringing ΔλiP (i=1,2,3) to (7).Therefore, the relationship between center wavelength changes and measurand could be expressed as(8)ΔλFBG1ΔλFBG2ΔλFBG3⟶HHTΔλ1VΔλ2VΔλ3VΔλ1TΔλ2TΔλ3TΔλ1PΔλ2PΔλ3P=VTPV1tV2tV3tT1tT2tT3tP1tP2tP3t.


## 3.1. Vibration Identification

Because of middle elastic element, the external vibration signal induces axial dynamic strain on these TFBGs and further leads to the center wavelength changes. Relationship between axial strainε and center wavelength shift Δλ could be expressed as(2)Δλλ=1-peε,where pe is the elastic-optic coefficient of optical fiber and its theoretical value equals 0.22. So, the efficiency of dynamic stress F worked on the optical fiber could be expressed as(3)F=Eε=ke·Vt,where E is elasticity modulus of optical fiber, ke is the elastic coefficient of elastomer in the link rob, and V(t) represents the exterior dynamic signal.Through (2) and (3), we could get that(4)Δλ1V=1-peE·λ10·ke1·V1t,Δλ2V=1-peE·λ20·ke2·V2t,Δλ3V=1-peE·λ30·ke3·V3(t)orΔλ1VΔλ2VΔλ3V=V·V1tV2tV3t,where V1t, V2t, and V3(t) are exterior vibration signals and V represents the vibration coefficient matrix.


## 3.2. Temperature Identification

Temperature changes can be obtained by(5)Δλ1T=λ10·α+ξ·T1t,Δλ2T=λ20·α+ξ·T2t,Δλ3T=λ30·(α+ξ)·T3(t)orΔλ1TΔλ2TΔλ3T=T·T1tT2tT3t,where α is thermal expansion coefficient, ξ is thermooptic coefficient of FBG, T1(t), T2(t), and T3(t) are the measured temperature, and T is the coefficient matrix of temperature.


## 3.3. Verticality Identification

While connecting line between upper and lower ring center points is not parallel with geodetic vertical line, the free ring could ceaselessly wiggle until the connecting line parallels the geodetic vertical line based on the function of omnidirectional wheel. The angle between geodetic vertical line and axis of this sensor metal transfer structure is selected as vertical evaluation standard and named as verticality angleα. When this sensor position changes from Figures 2(a) to 2(b), verticality angle α is generated by gravity.Figure 2
(a) The fixed ring parallels the ground plane. (b) Verticality angleα between the fixed ring and the ground plane.
(a)
(b)Adding the Cartesian coordinate system to this sensor and assuming that the link rod with FBG1 is vertical orthogonal withx-axis, verticality calculation model is shown in Figure 3.Figure 3
Verticality calculation model of this sensor.
(a)
Cross section of these three fiber Bragg gratings
(b)
Geometry of verticality reconstruction based on the center wavelength changesSo, the length changesΔLi (i=1,2,3) of three link robs are expressed as (6)ΔL1=r1+cos⁡θ·sinα,ΔL2=r1-cos⁡⁡π3+θ·sinα,ΔL3=r1-cos⁡⁡π3-θ·sinα,where r is radius of the upper fixed ring and θ is the directional angle between radius line ① and x axis in the XY plane.Based on the above analysis, verticality calculation formula is expressed as(7)Δλ1v=λ10·1-pe·r1+cos⁡θ·sinαh,Δλ2v=λ20·1-pe·r1-cos⁡⁡π3+θ·sinαh,Δλ3v=λ30·1-pe·r1-cos⁡⁡π3-θ·sinαhorΔλ1vΔλ2vΔλ3v=V·P1tP2tP3t,where h is height of this sensor and V is the verticality coefficient matrix. Through (7), verticality angle α and directional angle θ are obtained.The measurand identification could be concluded in four steps.(1)
Use HHT to extract different signalsΔλiV, ΔλiT, and ΔλiP (i=1,2,3) from the center wavelengths λFBGi (i=1,2,3).(2)
External dynamic signalsV1(t), V2(t), and V3(t) are obtained by bringing ΔλiV (i=1,2,3) to (4).(3)
Environment temperaturesT1(t), T2(t), and T3(t) are picked out by bringing ΔλiT (i=1,2,3) to (5).(4)
Verticality angleα and directional angle θ are calculated by bringing ΔλiP (i=1,2,3) to (7).Therefore, the relationship between center wavelength changes and measurand could be expressed as(8)ΔλFBG1ΔλFBG2ΔλFBG3⟶HHTΔλ1VΔλ2VΔλ3VΔλ1TΔλ2TΔλ3TΔλ1PΔλ2PΔλ3P=VTPV1tV2tV3tT1tT2tT3tP1tP2tP3t.


## 4. Calibration Experiment

For testing the performance of this TVFBG sensor, frequency response, temperature sensitivity, and verticality measuring experiment are all carried out. The basic instruments in these experiments are ASE broadband flattened light source, optical fiber circulator, and sense 20/20. Sense 20/20 is produced by Bay Spec, Inc., and acts as fiber dynamic demodulation instrument. Some other auxiliary equipment such as INV1601 vibration platform produced by Beijing Dongfang Vibration and Noise Technology Research Institute, thermostatic water tank, and protractor are also used in these experiments. The initial center wavelengths of FBG1, FBG2, and FBG3 are 1540.5533 nm, 1534.4096 nm, and 1530.7497 nm.


### 4.1. Frequency Response Experiment

Figure4 shows diagram and basic instruments of frequency response experiment which is set up to simulate the exterior vibration environment. This sensor is adhered together with vibration platform through epoxy resin. Its status is kept vertical. In order to improve coupling coefficient, a thin layer ethyl α-cyanoacrylate is coated at the surface of simply supported beam. Detection frequency ranges of sense 20/20 are 0–5 KHz and its frequency demodulation precision is 1 Hz. JZ-1 type vibration source included in the INV1601 vibration platform generates a series frequency from 100 Hz to 1 KHz in steps of 100 Hz with precision 0.1 Hz. The output amplitude is kept at 1.3 m/s2 in the whole experiment. Comparative analysis data between detected data by this TVFBG sensor and generated data by JZ-1 are utilized as reference indicator to evaluate this sensor frequency response.Figure 4
Frequency response experiment platform.
(a)
Basic diagram of frequency response experiment
(b)
Instruments in frequency response experiment


### 4.2. Temperature Sensitivity Experiment

Thermostatic water tank is utilized to change this sensor environment temperature. Diagram of temperature sensitivity experiment is shown in Figure5. So as to avoid that the center wavelengths of TFBGs are influenced by exterior strain, this TVFBG sensor is statically placed at the bottom of the tank. SM125 (demodulation ranges 1510–1590 nm, demodulation precision 1 pm) is chosen as fiber interrogator. In this whole process, temperature variation ranges are 20°C–60°C and its step interval is 5°C. Water temperature is also measured by thermal resistance which is selected as contrastive data with this TVFBG sensor. Water temperature is remaining stable for almost one minute at each step. The heating and cooling processes are repeated twice.Figure 5
Diagram of temperature sensitivity experiment platform.


### 4.3. Verticality Measuring Experiment

Protractor which is used in teaching acts as measure verticality angle measuring instrument and its precision is 1°. Instruments used in this experiment are shown in Figure6. Achieving the purpose that data processing is more convenient, the axis of FBG1 is kept vertical orthogonal with zero depicting line at the beginning of this experiment. The manually controlled FBG1 axis rotates counterclockwise to change the verticality angle α. Due to metal transfer structure, center wavelength of FBG2 is increased and these other two wavelengths are both decreased. Limited by the theoretical maximum strain value of FBG which is 7860 με, small ranges verticality measuring experiment is carried out. The manually controlled verticality angle α increases from 0° to 5° with step interval 1°.Figure 6
Instruments in the verticality response experiment.


## 4.1. Frequency Response Experiment

Figure4 shows diagram and basic instruments of frequency response experiment which is set up to simulate the exterior vibration environment. This sensor is adhered together with vibration platform through epoxy resin. Its status is kept vertical. In order to improve coupling coefficient, a thin layer ethyl α-cyanoacrylate is coated at the surface of simply supported beam. Detection frequency ranges of sense 20/20 are 0–5 KHz and its frequency demodulation precision is 1 Hz. JZ-1 type vibration source included in the INV1601 vibration platform generates a series frequency from 100 Hz to 1 KHz in steps of 100 Hz with precision 0.1 Hz. The output amplitude is kept at 1.3 m/s2 in the whole experiment. Comparative analysis data between detected data by this TVFBG sensor and generated data by JZ-1 are utilized as reference indicator to evaluate this sensor frequency response.Figure 4
Frequency response experiment platform.
(a)
Basic diagram of frequency response experiment
(b)
Instruments in frequency response experiment


## 4.2. Temperature Sensitivity Experiment

Thermostatic water tank is utilized to change this sensor environment temperature. Diagram of temperature sensitivity experiment is shown in Figure5. So as to avoid that the center wavelengths of TFBGs are influenced by exterior strain, this TVFBG sensor is statically placed at the bottom of the tank. SM125 (demodulation ranges 1510–1590 nm, demodulation precision 1 pm) is chosen as fiber interrogator. In this whole process, temperature variation ranges are 20°C–60°C and its step interval is 5°C. Water temperature is also measured by thermal resistance which is selected as contrastive data with this TVFBG sensor. Water temperature is remaining stable for almost one minute at each step. The heating and cooling processes are repeated twice.Figure 5
Diagram of temperature sensitivity experiment platform.


## 4.3. Verticality Measuring Experiment

Protractor which is used in teaching acts as measure verticality angle measuring instrument and its precision is 1°. Instruments used in this experiment are shown in Figure6. Achieving the purpose that data processing is more convenient, the axis of FBG1 is kept vertical orthogonal with zero depicting line at the beginning of this experiment. The manually controlled FBG1 axis rotates counterclockwise to change the verticality angle α. Due to metal transfer structure, center wavelength of FBG2 is increased and these other two wavelengths are both decreased. Limited by the theoretical maximum strain value of FBG which is 7860 με, small ranges verticality measuring experiment is carried out. The manually controlled verticality angle α increases from 0° to 5° with step interval 1°.Figure 6
Instruments in the verticality response experiment.


## 5. Data Analysis and Results

Analyzing the experiment data acquired in previous calibration experiment, the basic characteristics of the TVFBG sensor are identified in this section.


### 5.1. Frequency Characteristic Analysis

Limited by length of this paper, Figure7 just displays parts of sectional graphs of the demodulation software interface and the controller signals generated by JZ-1. These sectional graphs just display the frequency signals detected by FBG1.Figure 7
Left: front panel of vibration source controller. Right: demodulation software interface sectional graphs.
(a)
100 Hz
(b)
500 Hz
(c)
1000 HzFast Fourier transform (FFT) is selected to extract frequency information of this TVFBG sensor in the frequency response experiment. The detected frequency data are shown in Table2.Table 2
Detected frequency data by this TVFBG sensor.
Generated frequency/Hz
Detected frequency/Hz
FBG1
FBG2
FBG3
100
100.4028
100.4028
100.4028
200
200.8057
200.8057
200.8057
300
301.2085
301.2085
301.2085
400
401.3062
401.6113
401.3062
500
502.0142
502.0142
502.0142
600
602.417
602.417
602.417
700
702.8198
702.8198
702.8198
800
803.2227
803.2227
803.2227
900
903.6255
903.6255
903.6255
1000
1004.0283
1004.0283
1004.0283Formula of relative measuring error is expressed as(9)δF=FFBGi-FVSFVS·100%,where FFBGi (i=1,2,3) and FVS represent detected frequency and the generated frequency, respectively.Calculating the measuring error between generated and detected frequency through (9), its ranges are from 0.327% to 0.403%. Such data effectively prove that this TVFBG sensor has excellent frequency response.


### 5.2. Temperature Sensitivity Analysis

Data in the first heating process are displayed in Table3 and Figure 8 shows changes of center wavelengths following the temperature variations in the whole temperature sensitivity experiment.Table 3
Experiment data in first heating procedure.
Temperature/°C
Center wavelength of FBG/nm
FBG1
FBG2
FBG3
20
1540.400517
1534.314647
1530.703881
25
1540.553308
1534.40965
1530.749724
30
1540.609982
1534.470089
1530.804002
35
1540.666616
1534.529987
1530.860776
40
1540.724015
1534.593595
1530.918992
45
1540.780719
1534.657476
1530.979152
50
1540.838631
1534.72566
1531.039742
55
1540.897591
1534.797819
1531.100086
60
1540.952174
1534.864976
1531.129372Figure 8
Fitting curves between center wavelengths and temperature.
(a)
(b)
(c)Figure8 exhibits the fact that the relationship between temperature and center wavelengths has excellent linearity and reproducibility. Temperature sensitivities of FBG1 analyzed by least squares method are 0.0114 pm/°C, 0.0113 pm/°C, 0.0113 pm/°C, and 0.0113 pm/°C in the twice heating and cooling processes. Average value of these four sensitivities is selected as temperature sensitivity of FBG1 and its value is 11.3 pm/°C. Similarly, temperature sensitivities of FBG2 and FBG3 are 13.4 pm/°C and 11.2 pm/°C. Temperature sensitivities of TFBGs are all approximated to the bare FBG. Therefore, this sensor realizes precise temperature measurement.


### 5.3. Verticality Measuring Analysis

Table4 gives the center wavelengths of this TVFBG sensor in the verticality measuring experiment.Table 4
Data of verticality measuring experiment.
Angleα/°
Center wavelength of FBG/nm
FBG1
FBG2
FBG3
0
1540.0843
1535.2864
1530.4722
1
1540.0578
1535.336
1530.4356
2
1540.0352
1535.3691
1530.3994
3
1540.0033
1535.4215
1530.3658
4
1539.9825
1535.4581
1530.3223
5
1539.9491
1535.4874
1530.2847Fitting curves between wavelengthλB and verticality angle α are λFBG1=-0.0267α+1540.3 (R2=0.9969),  λFBG2=0.0407α+1535.3 (R2=0.9935), and λFBG3=-0.0375α+1530.5 (R2=0.9988). Due to the fact that the verticality angle α is very small, its sine value equals itself. Relationship between λB and α presents excellent linearity and the verticality measuring sensitivities are 26.7 pm/°, 40.7 pm/°, and 37.5 pm/° severally. All these verticality coefficients are available just under calibration experiment conditions. So, this TVFBG sensor realizes verticality measuring and shows excellent measuring linearity at small verticality angle ranges.


## 5.1. Frequency Characteristic Analysis

Limited by length of this paper, Figure7 just displays parts of sectional graphs of the demodulation software interface and the controller signals generated by JZ-1. These sectional graphs just display the frequency signals detected by FBG1.Figure 7
Left: front panel of vibration source controller. Right: demodulation software interface sectional graphs.
(a)
100 Hz
(b)
500 Hz
(c)
1000 HzFast Fourier transform (FFT) is selected to extract frequency information of this TVFBG sensor in the frequency response experiment. The detected frequency data are shown in Table2.Table 2
Detected frequency data by this TVFBG sensor.
Generated frequency/Hz
Detected frequency/Hz
FBG1
FBG2
FBG3
100
100.4028
100.4028
100.4028
200
200.8057
200.8057
200.8057
300
301.2085
301.2085
301.2085
400
401.3062
401.6113
401.3062
500
502.0142
502.0142
502.0142
600
602.417
602.417
602.417
700
702.8198
702.8198
702.8198
800
803.2227
803.2227
803.2227
900
903.6255
903.6255
903.6255
1000
1004.0283
1004.0283
1004.0283Formula of relative measuring error is expressed as(9)δF=FFBGi-FVSFVS·100%,where FFBGi (i=1,2,3) and FVS represent detected frequency and the generated frequency, respectively.Calculating the measuring error between generated and detected frequency through (9), its ranges are from 0.327% to 0.403%. Such data effectively prove that this TVFBG sensor has excellent frequency response.


## 5.2. Temperature Sensitivity Analysis

Data in the first heating process are displayed in Table3 and Figure 8 shows changes of center wavelengths following the temperature variations in the whole temperature sensitivity experiment.Table 3
Experiment data in first heating procedure.
Temperature/°C
Center wavelength of FBG/nm
FBG1
FBG2
FBG3
20
1540.400517
1534.314647
1530.703881
25
1540.553308
1534.40965
1530.749724
30
1540.609982
1534.470089
1530.804002
35
1540.666616
1534.529987
1530.860776
40
1540.724015
1534.593595
1530.918992
45
1540.780719
1534.657476
1530.979152
50
1540.838631
1534.72566
1531.039742
55
1540.897591
1534.797819
1531.100086
60
1540.952174
1534.864976
1531.129372Figure 8
Fitting curves between center wavelengths and temperature.
(a)
(b)
(c)Figure8 exhibits the fact that the relationship between temperature and center wavelengths has excellent linearity and reproducibility. Temperature sensitivities of FBG1 analyzed by least squares method are 0.0114 pm/°C, 0.0113 pm/°C, 0.0113 pm/°C, and 0.0113 pm/°C in the twice heating and cooling processes. Average value of these four sensitivities is selected as temperature sensitivity of FBG1 and its value is 11.3 pm/°C. Similarly, temperature sensitivities of FBG2 and FBG3 are 13.4 pm/°C and 11.2 pm/°C. Temperature sensitivities of TFBGs are all approximated to the bare FBG. Therefore, this sensor realizes precise temperature measurement.


## 5.3. Verticality Measuring Analysis

Table4 gives the center wavelengths of this TVFBG sensor in the verticality measuring experiment.Table 4
Data of verticality measuring experiment.
Angleα/°
Center wavelength of FBG/nm
FBG1
FBG2
FBG3
0
1540.0843
1535.2864
1530.4722
1
1540.0578
1535.336
1530.4356
2
1540.0352
1535.3691
1530.3994
3
1540.0033
1535.4215
1530.3658
4
1539.9825
1535.4581
1530.3223
5
1539.9491
1535.4874
1530.2847Fitting curves between wavelengthλB and verticality angle α are λFBG1=-0.0267α+1540.3 (R2=0.9969),  λFBG2=0.0407α+1535.3 (R2=0.9935), and λFBG3=-0.0375α+1530.5 (R2=0.9988). Due to the fact that the verticality angle α is very small, its sine value equals itself. Relationship between λB and α presents excellent linearity and the verticality measuring sensitivities are 26.7 pm/°, 40.7 pm/°, and 37.5 pm/° severally. All these verticality coefficients are available just under calibration experiment conditions. So, this TVFBG sensor realizes verticality measuring and shows excellent measuring linearity at small verticality angle ranges.


## 6. Wrist Rotation Angle Measurement Experiment

So as to verify the practical value of this TVEBG sensor, wrist rotation angle measurement experiment is implemented. Wrist rotation angle changes from −10° to 10° with step interval of 5° under the same condition in verticality measuring experiment. Sense 20/20 is chosen as the dynamic fiber interrogator. Wavelength data of FBG1 corresponding to angle 0° are selected as sample data to explain signal processing. The sample data processed by HHT is shown in Figure9.Figure 9
Sample data analyzed by HHT.
(a)
(b)
(c)
(d)
(e)
(f)After HHT analysis, trend signals are chosen as the corresponding verticality angle data. Using the same signal processing methods, the extracted data are shown in Table5.Table 5
Extracted center wavelength data analyzed by HHT.
Wrist rotation angleα/°
Center wavelength of FBG/nm
FBG1
FBG2
FBG3
−10
1540.31
1534.899
1530.858
−5
1540.2125
1535.0854
1530.6487
0
1540.0843
1535.2864
1530.4722
5
1539.9491
1535.4874
1530.2847
10
1539.8126
1535.653
1530.082Least squares method is used to acquire verticality measuring sensitivities and these values corresponding to TFBGs are 25.2 pm/°, 38.2 pm/°, and 38.3 pm/° separately. Hence, this sensor can be used in practical measurement.


## 7. Conclusion

A three-component FBG vibration sensor which could simultaneously measure vibration, temperature, and verticality is realized in this paper. Project matrix theory is chosen as basic theory to establish this sensor theatrical calculation model. HHT is used to analyze this sensor’s wavelength signals and reconstruct measurand. Calibration experiments consisting of frequency response, temperature sensitivity, and verticality measuring experiment are carried out. Calibration experiments data confirm that this sensor could realize frequency, temperature, and verticality measurements with high precision. This TVFBG sensor’s frequency measuring errors at ranges of 100–1000 Hz are all less than 1% and its temperature and verticality measuring sensitivities are 11.3 pm/°C, 13.4 pm/°C, 11.2 pm/°C, 26.7 pm/°, 40.7 pm/°, and 37.5 pm/°. In order to further verify this sensor practical value, wrist rotation angle experiment is also implemented. Wrist rotation experiment results show that this sensor realizes wrist angle measuring and its sensitivities are 25.2 pm/°, 38.2 pm/°, and 38.3 pm/°. All these experiment data prove that this sensor has certain practical value in engineering.



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*Source: 382865-2015-07-27.xml*