A calibration and testing method for a two-dimensional fiber optic grating oblique measurement device

Abstract

This invention belongs to the field of fiber optic sensing technology, specifically relating to a calibration and testing method for a two-dimensional fiber Bragg grating inclinometer. Based on a constructed calibration and testing system for the fiber Bragg grating inclinometer, this invention measures the wavelength drift of multiple fiber Bragg gratings adhered to the surface of an elastic cylindrical cantilever under different tilt and azimuth angles. It analyzes the parameters of the fitting curves between wavelength drift and tilt and azimuth angles, corrects the parameters based on the difference between the actual and theoretical states, and obtains the corrected fitting parameters, thus completing the calibration. Compared with existing methods that rely solely on theoretical deduction to obtain inclinometer results, the calibrated two-dimensional inclinometer provides more accurate measurement results.

Description

Technical Field

[0001] This invention belongs to the field of fiber optic sensing technology, specifically relating to a calibration and testing method for a two-dimensional oblique measurement device of a fiber optic grating. Background Technology

[0002] Inclined measuring devices are instruments used to measure tilt angles and azimuth angles, and are widely used in engineering fields, including oil drilling equipment, geological observation, flight control, and robotics. Traditional electromagnetic inclined measuring devices suffer from electrical signals that are highly susceptible to electromagnetic interference and cannot be transmitted over long distances. These drawbacks make inclined measurement work time-consuming, labor-intensive, and inefficient.

[0003] Fiber Bragg grating (FBG) sensing offers advantages such as resistance to electromagnetic interference and long-distance signal transmission, leading to rapid development inclinometer technology based on FBG sensing. Chinese patent application CN113970318A discloses a FBG-based inclinometer sensor and tilt monitoring device, which uses a cross-beam structure to fix a dual fiber Bragg grating (FBG) sensor and utilizes the strain difference under gravity to achieve two-dimensional tilt measurement. Chinese patent application CN 114777734A proposes an in-situ fiber optic inclinometer and inclinometer method based on a vertical cantilever beam and dual FBGs, achieving two-dimensional tilt measurement through the tension / compression difference of FBGs attached to both sides of the cantilever beam. The existing technical solution described above involves attaching multiple FBGs to a cantilever beam. In use, the cantilever beam with FBGs is embedded or fixed to the object being tested. As the object tilts and bends, the cantilever beam generates surface strain. The FBGs measure the strain through wavelength drift, and the obtained strain is then used to deduce the tilt of the cantilever beam using theoretical mechanics and materials mechanics, thus obtaining the tilt amount of the object being tested. The drawback of this method is that it does not perform calibration tests on the cantilever beam with FBGs; it only deduces the tilt amount based on theory, resulting in a relatively large error. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the technical problem to be solved by this invention is to provide a calibration and testing method for a two-dimensional fiber optic grating inclinometer, which calibrates theoretical parameters through calibration and testing, thereby making the measurement results of the inclinometer more accurate.

[0005] The structure of the two-dimensional inclinometer device for calibrating and testing a fiber Bragg grating includes a fixed block, an elastic cylindrical cantilever, a mass block, and multiple fiber Bragg gratings (FBGs). The elastic cylindrical cantilever and the mass block are assembled into a cantilever beam, with the elastic cylindrical cantilever and the mass block having the same radius. Multiple fiber Bragg gratings (FBG1-FBGn) are pasted on the surface of the elastic cylindrical cantilever at fixed angular intervals. The core idea of ​​this invention is to build an inclination angle-azimuth angle testing system for this two-dimensional inclinometer device. Under different inclination angles and azimuth angles of the elastic cylindrical cantilever, the wavelength drift of the multiple FBGs pasted on the surface of the elastic cylindrical cantilever is tested. The parameters of the wavelength drift versus the fitting curves of the inclination angle and azimuth angle are analyzed. Based on the difference between the actual state and the theoretical state, corrections are made to obtain the corrected fitting parameters, thus completing the calibration. Specifically, the following steps are included:

[0006] Step S1: Customize cylinders made of different rubber materials, and make stainless steel fixing blocks and mass blocks;

[0007] Step S2: Measure the stress-strain curves of the different rubber material cylinders customized in Step S1, analyze the stress-strain relationship, and select the cylinder with a linear relationship between strain and stress to prepare the elastic cylindrical cantilever.

[0008] Step S3: Attach multiple FBGs to the surface of the elastic cylindrical cantilever selected in step S2, and assemble the stainless steel fixing block and mass block completed in step S1 with the elastic cylindrical cantilever to form a probe.

[0009] Step S4: Record the initial wavelength of all fiber Bragg gratings pasted in step S3;

[0010] Step S5: Assemble the tilt angle-azimuth angle testing system and configure the data acquisition system. The tilt angle-azimuth angle testing system includes the probe prepared in step S3 and a two-dimensional rotating platform. The two-dimensional rotating platform includes an X-axis rotary stepper motor, a Y-axis rotary stepper motor, a control circuit, and a computer. The X-axis rotary stepper motor is used to adjust the tilt angle from 0° to 90°; the Y-axis rotary stepper motor is used to adjust the azimuth angle from 0° to 360°. The probe is fixed on a tripod, and the tripod is mounted on the rotation axis of the Y-axis rotary stepper motor. The data acquisition system consists of a spectrometer, a demodulator, a computer, and data acquisition software.

[0011] Step S6: Keeping the azimuth angle of the elastic cylindrical cantilever constant, increase the tilt angle θ from 0° to 90° in 10° increments. Use the data acquisition system to record the wavelength shift results of all fiber Bragg gratings as the tilt angle changes, and fit the test data. The fitting curve formula is as follows:

[0012] i = 1, 2 … n

[0013]

[0014] or

[0015]

[0016]

[0017]

[0018] in This refers to the Bragg wavelength shift of the fiber grating after eliminating the temperature effect through differential operations. λi is the Bragg wavelength, Pe is the photoelastic coefficient, α is the initial phase, and ε is the phase coefficient. 0i The tensile strain ε is caused by gravity. maxi The bending strain caused by gravity, θ 0i It is the initial phase shift caused by the ratio of tensile strain to bending strain;

[0019] All fiber Bragg gratings A are obtained by fitting the above formula. i and B i ·sin(α i +α) parameter value, A i = λ i (1-p e )ε 0i The tensile strain caused by gravity is constant for a fixed elastic cylindrical cantilever; however, there are slight differences in the fitted value of A based on the test data. This is due to differences in the bonding points, adhesive thickness, width and length when multiple fiber Bragg gratings are bonded to the elastic cylindrical cantilever.

[0020] Step S7: Keeping the tilt angle of the elastic cylindrical cantilever constant, increase the azimuth angle α from 0° to 360° in 30° increments, and record the Bragg wavelength shift of the fiber grating; at θ = 30°, the ΔΛ of each FBG can be written as a sine function of α:

[0021] i = 1, 2 … n

[0022] The first term in the above equation can be viewed as the constant 'DC' term of the ΔΛ(α) function, while the second term is the variable 'AC' term with an amplitude of B. i / 2, Based on the above formula, fit the test data to obtain the fitted curve and corresponding parameter B. i B iThe bending strain originating from the elastic cylindrical cantilever should theoretically be constant. However, due to differences in the bonding of multiple fiber Bragg gratings, such as variations in bonding points and adhesive strength, the B-value fitted based on test data... i The values ​​differ to some extent;

[0023] Step S8: Based on the difference between the actual bonding point and the design point of the fiber Bragg grating revealed in step S7, the angle is corrected by replacing the design angle with the actual bonding angle, and finally the corrected fitting parameter value is obtained. The standard deviation of the parameter is reduced, and the calibration is completed.

[0024] Preferably, in step S1, two types of rubber material cylinders are customized. The first type is a natural crushed stone cylinder (NR) with sulfur carbon black, a hardness of 70, and diameters of 30 mm, 25 mm, and 20 mm, respectively. The second type is a polyurethane cylinder (PUR) with diameters of 30 mm, 25 mm, and 20 mm, respectively.

[0025] Preferably, in step S3, eight fiber Bragg gratings are pasted along the surface of an elastic cylindrical cantilever at fixed 45° intervals. When pasting each fiber Bragg grating, a prestress is applied by suspending a 400g weight to achieve a wavelength shift of 2.0 nanometers in the fiber Bragg grating. Then, adhesive is poured into both sides of the fiber Bragg grating.

[0026] By adopting the above technical solution, the beneficial effect of the present invention is that the calibration and testing method proposed in this invention can reveal the difference between the actual parameters and design parameters of the fiber optic grating two-dimensional inclinometer device and make corresponding corrections. Compared with the existing method of obtaining the inclinometer results by theoretical back-calculation alone, the measurement results of the calibrated two-dimensional inclinometer device are more accurate. Attached Figure Description

[0027] Figure 1 This is a probe for a two-dimensional fiber optic oblique measurement device, in which eight FBGs are attached to the ECC along eight busbars.

[0028] Figure 2 ECC stress-strain curves: (a) NR with a diameter of 25 mm; (b) NR with a diameter of 20 mm.

[0029] Figure 3 This is a tilt angle-azimuth angle calibration test system.

[0030] Figure 4 The graph shows the relationship between the wavelength drift and tilt angle of the eight FBGs.

[0031] Figure 5 The graph shows the relationship between wavelength drift and azimuth for eight FBGs.

[0032] Figure 6 The axis angles for the eight FBG actual (blue hollow circles) adhesive points and the design (green solid circles) adhesive points.

[0033] Figure 7 The wavelength variations of eight FBGs are shown at seven azimuth angles (α = 0, 30°, 60°, 90°, 120°, 150° and 180°). Detailed Implementation

[0034] The technical solution of the present invention will now be described more clearly and completely with reference to the accompanying drawings.

[0035] I. Probe Preparation

[0036] like Figure 1 The fiber Bragg grating two-dimensional inclinometer probe shown includes an elastic cylindrical cantilever (ECC) with a fiber Bragg grating (FBG) attached to its surface, a fixing block, and a mass block. The ECC is made of rubber, while the fixing block and mass block are made of 304 stainless steel. The ECC and mass block have the same radius of 15 mm and lengths of 60 mm and 25 mm, respectively.

[0037] ECC is the most important component of a fiber optic grating two-dimensional inclinometer. Besides the aforementioned geometric parameters, the elastic modulus is a crucial physical parameter that must be kept constant during angle measurement to ensure accuracy. To find a suitable rubber cylinder, two types were customized: natural crushed stone cylinders (NR; sulfur carbon black; hardness 70; diameters 30 mm, 25 mm, and 20 mm) and polyurethane cylinders (PUR; diameters 30 mm, 25 mm, and 20 mm). The stress-strain curves of both rubber cylinders were measured using a universal testing machine (Instron 5967). It was found that the relationship between strain and stress was non-linear for the PUR cylinder; while for the NR cylinder, the relationship was more linear. Figure 2 As shown, its strain is proportional to the stress and can be described by Young's modulus E = σ / ε, where σ = F / (πd 2 / 4)) is stress, ε = δl / l0 is strain; therefore, NR cylinders are chosen to prepare ECC.

[0038] Eight FBGs (FBG1-FBG8) were attached along the eight busbars of the ECC at fixed angular intervals (45°). Prestress was applied to each FBG by suspending a 400g weight to achieve a wavelength shift of 2.0 nm, and then adhesive was poured onto both sides of the FBG.

[0039] The initial wavelengths of eight FBGs were recorded as 1536.800nm ​​(FBG1), 1539.840nm (FBG2), 1542.560nm (FBG3), 1545.120nm (FBG4), 1549.280nm (FBG5), 1551.860nm (FBG6), 1554.200nm (FBG7), and 1557.200nm (FBG8), and their reflectivity was greater than 80%.

[0040] II. Test System Setup

[0041] like Figure 3 The tilt-azimuth testing system shown includes a fiber Bragg grating two-dimensional inclinometer probe and a two-dimensional rotating platform. The rotating platform comprises an X-axis rotary stepper motor, a Y-axis rotary stepper motor, a control circuit, and a computer. The X-axis rotary stepper motor adjusts the tilt angle (θ) from 0 to 90°; the Y-axis rotary stepper motor adjusts the azimuth angle (α) from 0 to 360°. The fiber Bragg grating two-dimensional inclinometer probe is fixed on a tripod, which is then mounted on the rotation axis of the Y-axis rotary stepper motor. The X-axis rotary stepper motor, Y-axis rotary stepper motor, control circuit, and computer are connected.

[0042] like Figure 3 As shown, the data acquisition system includes a spectrometer (Yokogawa, AQ63708, 600-1700 nm), a demodulator (WHUT, OP-FBG2000, resolution: 1 pm, sampling rate: 2000 Hz), a computer, and data acquisition software. The spectrometer and demodulator are connected to the computer, and the data acquisition software is installed and configured.

[0043] All tests were conducted at room temperature (25°C).

[0044] III. Calibration and Testing of the Fiber Bragg Grating Two-Dimensional Incline Measurement Device

[0045] 1. Tilt angle test

[0046] Keeping the azimuth angle of the elastic cylindrical cantilever ECC constant, the tilt angle θ is increased from 0° to 90° in 10° increments. The wavelength drift results of eight FBGs as a function of the tilt angle are recorded using a data acquisition system. The test data are then fitted, and the fitting curve formula is as follows:

[0047] i = 1, 2 … 8

[0048]

[0049] or

[0050]

[0051]

[0052]

[0053] in This refers to the Bragg wavelength drift of the FBG after eliminating the temperature effect through differential operations. λi is the Bragg wavelength, Pe is the photoelastic coefficient, α is the initial phase, and ε is the phase coefficient. 0i The tensile strain ε is caused by gravity. maxi The bending strain caused by gravity, θ 0i It is the initial phase shift caused by the ratio of tensile strain to bending strain;

[0054] Figure 4 The test results of wavelength drift of eight FBGs as a function of tilt angle θ are shown, where θ varies from 0° to 90°. Detailed parameters are shown in Table 1.

[0055] Table 1 Inclination Angle θ i and fitting parameters

[0056] Curve FBG# <![CDATA[A i ]]> <![CDATA[B i ·sin(a i +a)]]> <![CDATA[R 2 ]]> Solid red FBG2 202.268 1024.111 0.9994 Solid green FBG3 223.833 901.062 0.9930 Solid black FBG1 208.978 824.866 0.9945 Dash green FBG7 221.855 -455.944 0.9971 Dash black FBG5 244.142 -647.153 0.9947 Dash red FBG6 239.889 -750.513 0.9974

[0057] The above fitting yielded eight fiber Bragg gratings A. i Parameter value, A i = λ i (1-p e )ε 0i The tensile strain caused by gravity is constant for a fixed ECC; however, the fitted value of A derived from the test data shows a slight difference (mean: A). av = 223.494, Standard deviation: σ A = 16.488), this is because of the differences that exist when the eight FBGs are pasted on the ECC, such as differences in the pasting points, adhesive thickness, width and length;

[0058] 2. Azimuth test

[0059] Keeping the ECC tilt angle constant at 30°, the azimuth angle α is increased from 0° to 360° in increments of 30°, and the Bragg wavelength drift of the eight FBGs is recorded. At θ = 30°, the ΔΛ of each FBG can be written as a sine function of α:

[0060] i = 1, 2 … 8

[0061] The first term in the above equation can be viewed as the constant 'DC' term of the ΔΛ(α) function, while the second term is the variable 'AC' term with an amplitude of B. i / 2, Figure 5 The "AC" portion of ΔΛ(α) corresponding to the eight FBGs (FBG1, FBG2, ..., FBG8) is shown. The curves are plotted based on the "AC" portion of the fitting formula described above. Detailed test parameters are listed in Table 2.

[0062] Table 2 Azimuth angle α i and fitting parameters

[0063] FBG# <![CDATA[α i (Input)]]> Max. order <![CDATA[B i ]]> <![CDATA[α i (Item.)]]> Max. angle <![CDATA[R 2 ]]> FBG1 45 2 867.8 39.416 50.584 0.9994 FBG2 90 1 800.4 83.217 6.783 0.9991 FBG3 135 8 884.4 132.576 317.424 0.9991 FBG4 180 7 969.6 181.153 268.847 0.9993 FBG5 225 6 1023.2 224.024 225.976 0.9988 FBG6 270 5 795.6 269.013 180.987 0.9995 FBG7 315 4 730.2 315.106 134.894 0.9991 FBG8 360 3 564.4 357.777 92.223 0.9987

[0064] like Figure 5 and Figure 6 As shown, there are certain differences between the actual pasting points and the design points of the eight FBGs. When the azimuth angle α = 6.783°, FBG2 reaches its peak value, while FBG6 reaches its trough value; when the azimuth angle changes to α = 92.223°, FBG8 reaches its peak value, while FBG4 reaches its trough value; when the azimuth angle is α = 180.987°, FBG6 reaches its peak value, while FBG2 reaches its trough value; when the azimuth angle changes to α = 268.847°, FBG4 reaches its peak value, while FBG8 reaches its trough value. On the other hand, B i The bending strain derived from ECC should theoretically be constant; however, the B strain fitted based on test data... i The values ​​vary (average: B) av =829.45; Standard deviation: σ B = 143), which is also due to differences in the eight FBGs when pasted on the ECC, such as differences in the pasting points and adhesive strength.

[0065] 3. Angle Correction

[0066] according to Figure 6 The difference between the actual bonding points and the design points of the eight FBGs shown is used to correct the angle, and the actual bonding angle is used to replace the design angle. Figure 7 The “AC” portion of ΔΛ, calculated based on the actual fitting angles of the eight FBGs, is shown, with the azimuth angles ranging from [0, 180°] in 30° increments. The curve is plotted based on the “AC” portion of the fitting formula, with detailed parameters listed in Table 3. The final result is B. av = 829.564 and σ B = 27.6.

[0067] Table 3 Azimuth angle α and corrected fitting parameters

[0068] α (Input) α (Mea.) Error B <![CDATA[R 2 ]]> 0 -0.094 0.094 822.142 0.9858 30 29.995 0.005 860.612 0.9801 60 57.541 2.459 865.328 0.9728 90 86.814 3.186 834.148 0.9702 120 118.847 1.153 802.566 0.9756 150 151.545 1.545 810.796 0.9854 180 182.042 2.042 842.124 0.9872 210 210.501 0.501 864.014 0.9814 240 238.732 1.268 852.532 0.9664 270 267.921 2.079 818.760 0.9553 300 299.558 0.442 789.536 0.9602 330 331.922 1.922 792.206 0.9752

Claims

1. A calibration and testing method for a two-dimensional fiber optic grating oblique measurement device, characterized in that, The method comprises the following steps: Step S1, customizing cylindrical bodies of different rubber materials, and making a stainless steel fixing block and a mass; Step S2, measuring the stress-strain curve of the cylindrical body of different rubber materials customized in step S1, analyzing the stress-strain relationship, and selecting the cylindrical body with linear relationship between strain and stress to prepare an elastic cylindrical cantilever; Step S3, pasting a plurality of fiber Bragg gratings to the surface of the elastic cylindrical cantilever selected in step S2, and assembling the stainless steel fixing block and the mass completed in step S1 and the elastic cylindrical cantilever into a probe; Step S4, recording the initial wavelength of all the fiber Bragg gratings pasted in step S3; Step S5, assembling a tilt angle-azimuth angle test system and a data acquisition system, the tilt angle-azimuth angle test system comprising the probe prepared in step S3 and a two-dimensional rotating platform, the two-dimensional rotating platform comprising an X-axis rotating stepper motor, a Y-axis rotating stepper motor, a control circuit and a computer, the X-axis rotating stepper motor being used for adjusting the tilt angle from 0° to 90°, the Y-axis rotating stepper motor being used for adjusting the azimuth angle from 0° to 360°, the probe being fixed on a triangular support, and the triangular support being mounted on the rotating shaft of the Y-axis rotating stepper motor, and the data acquisition system comprising a spectrometer, a demodulator, a computer and data acquisition software; Step S6, keeping the azimuth angle of the elastic cylindrical cantilever unchanged, increasing the tilt angle θ from 0° to 90° at a step of 10°, recording the wavelength drift of all the fiber Bragg gratings with the change of the tilt angle by using the data acquisition system, and fitting the test data, the fitting curve formula being as follows: i = 1, 2 … n; ； Or ； ； ； wherein is the fiber Bragg wavelength shift after eliminating the temperature effect by differential operation, λi is the Bragg wavelength, Pe is the photoelastic coefficient, α is the initial phase, ε 0i is the tensile strain caused by gravity, ε maxi is the bending strain caused by gravity, θ 0i is the initial phase shift caused by the ratio of tensile strain and bending strain; The A parameters of all FBGs are obtained by fitting the above equations i and B i • the sin(a i + a) parameter values, A i = l i (1 - p e ) e 0i from the tensile strain caused by gravity, which is constant for a fixed elastic cylindrical cantilever; however, the fitted values of A based on the test data have slight differences due to the differences in the multiple FBGs pasted on the elastic cylindrical cantilever, the differences in the pasting points, the thickness, width and length of the adhesive; Step S7, keeping the tilt angle of the elastic cylindrical cantilever unchanged, increasing the azimuth angle α from 0° to 360° at a step of 30°, and recording the Bragg wavelength drift of the fiber grating; when θ = 30°, the ΔΛ of each fiber Bragg grating can be written as a sine function of α: i = 1, 2 … n; The first term of the above formula can be regarded as the constant 'DC' term of the ΔΛ(α) function, while the second term is the variable 'AC' term with amplitude B i / 2, the fitting curve and the corresponding parameter B are obtained according to the above formula i , B i The bending strain of the elastic cylindrical cantilever should be constant in theory, but due to the differences in the pasting of multiple fiber Bragg gratings, the differences in the pasting points and the bonding strength, the B i value fitted based on the test data has certain differences; Step S8, based on the difference between the actual fitting point and the design point of the fiber Bragg grating disclosed in step S7, correcting the angle, replacing the design angle with the actual fitting angle, finally obtaining the corrected fitting parameter value, reducing the standard deviation of the parameter, and completing the calibration.

2. The method of claim 1, wherein, In the step S1, two kinds of rubber material cylindrical bodies are customized, the first kind is natural crushed stone cylindrical body NR, sulfur carbon black, 70 hardness, and the diameters are 30 mm, 25 mm and 20 mm respectively; the second kind is polyurethane cylindrical body PUR, and the diameters are 30 mm, 25 mm and 20 mm respectively.

3. The method of claim 1, wherein the method further comprises: In the step S3, eight fiber Bragg gratings are pasted along the surface of the elastic cylindrical cantilever at a fixed angle interval of 45°, when pasting each fiber Bragg grating, a pre-stress is applied by hanging a 400g weight, so that the fiber Bragg grating reaches a wavelength drift of 2.0 nanometers, and then adhesive is poured on both sides of the fiber Bragg grating.

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