CN102168956A - Pendulum bob-constant section beam fiber bragg grating dip angle sensor and calibration method - Google Patents

Abstract

A pendulum-constant cross-section beam fiber optic grating inclination sensor, in which one end of the constant cross-section beam is fixed and the other end is connected to a pendulum; two fiber gratings are respectively fixed on two opposite sides of the constant cross-section beam. The calibration method is: change the inclination angle of the simply supported beam according to the step length Δθ, and record the sensor center wavelength value λ ⁱ at each inclination angle point θ _i ; take the inclination angle θ as the abscissa, and the difference Δλ of the measured sensor center wavelength change at the corresponding corner as the ordinate Coordinates set the Cartesian coordinate system; get the discrete distribution map of Δλ data points, using a polynomial

Perform linear fitting on discrete data points, and calculate β ₁ and λ according to the principle of least squares method and the necessary conditions for multivariate extremum and the obtained θ _i and λ ⁱ data, and obtain the fitted

The invention has high measurement precision, strong anti-electromagnetic interference ability and good stability, is suitable for industrialized production, and is especially suitable for monitoring deformation of civil engineering structures.

Description

Pendulum-constant cross-section beam fiber grating inclination sensor and its calibration method

technical field

The invention discloses an optical fiber grating inclination sensor and a calibration method, in particular to a pendulum-equal-section beam optical fiber grating inclination sensor and a calibration method, belonging to the technical field of pressure sensors.

technical background

Through the review of domestic and foreign materials, it is found that so far, there are few researches on fiber grating inclination sensors, and they are still in the exploratory stage.

In 2000, Ferdinand and others developed the first fiber Bragg grating inclination sensor by using fiber gratings. Two fiber Bragg gratings are symmetrically stretched between the fixed end and the rotating end. When the structure rotates, the wavelengths of the two gratings are in opposite directions. The direction changes, but the influence of temperature is consistent. Thus, temperature self-compensation is realized.

In 2003, Guan et al. used a bracket, a pendulum, and a grating. The pendulum is suspended on the bracket and can swing freely. The fiber grating is connected to the pendulum and the bracket in a way that can prevent the swing of the pendulum. One side is connected to the pendulum, and the other The side is connected to the bracket, and the grating is in a stretched state, so that the corresponding strain occurs on the symmetrically arranged grating, and the change of the wavelength reflected from the grating is measured to calculate the tilt angle.

In 2004, Zhao et al. attached two fiber gratings symmetrically to an equal-strength beam with a pendulum, and calculated the tilt angle by measuring the strain of the beam.

In 2005, Dong et al. attached three fiber gratings to three strain beams arranged at 120°. The strain beams were connected to the disk above the pendulum through steel strings. This method not only measures the size of the angle at the same time, but also measures the angle direction, but with lower accuracy.

In 2006, Toshimitsu et al used a fiber grating connected to a pendulum to make an inclination sensor whose temperature has a great influence.

The existing fiber grating inclination sensor is difficult to be applied to bridge structural deformation monitoring due to the shortcomings of low measurement accuracy, short life, and large volume. Therefore, a new type of pendulum-equal cross-section fiber fiber grating inclination sensor is produced and its calibration method is designed. It is of great significance for the deformation monitoring of civil engineering structures.

Contents of the invention

The object of the present invention is to provide a pendulum-constant cross-section beam fiber grating inclination sensor and a calibration method, so that it can be conveniently applied to the deformation monitoring of civil engineering structures.

A pendulum-equal-section beam fiber optic grating inclination sensor of the present invention comprises: a positioning seat, a pendulum, an equal-section beam, an optical fiber grating, and a connecting sleeve, one end of the connecting sleeve is fixedly connected to the positioning seat, and the other end is connected to the positioning seat. One end of the pendulum is hinged through the first hinge shaft; the cross-section of the constant-section beam is rectangular and is inserted into the connecting sleeve, one end of which is fixedly connected to the positioning seat, and the other end is fixed through the second hinge. The shaft is connected to the pendulum; the first hinge axis and the second hinge axis are perpendicular to each other; the fiber grating has two pieces, which are fixedly installed on the two opposite sides of the equal-section beam, and the equal-section beam The two opposite sides refer to the sides corresponding to the longer side in the cross-sectional rectangle of the constant-section beam.

In the present invention, the pendulum is made of pure copper.

In the present invention, the constant-section beam is made of QBe ₂ beryllium bronze.

In the present invention, the optical fiber grating is written in the germanium-doped photosensitive optical fiber by using a phase mask method.

In the present invention, the sleeve is made of stainless steel.

In the present invention, the constant-section beam is riveted to the positioning seat.

A further improvement of the present invention is that a casing is provided outside the positioning seat, the pendulum, the constant-section beam, the fiber grating, and the connecting sleeve, and the positioning seat is fixedly installed at one end of the casing.

A method for calibrating a pendulum-equal-section beam fiber grating inclination sensor of the present invention comprises the following steps:

The first step: Prepare an I-shaped simply supported beam, a fiber grating sensor network analyzer, a dial gauge, and a level; one end of the simply supported beam is hinged on the hinge shaft, and the other end is supported by a jack support;

Step 2: Adjust the axis of the I-shaped simply supported beam to the level with a level ruler, and then paste the pendulum-equal-section beam FBG inclination sensor on the surface of the beam, so that the pendulum-equal-section beam FBG inclination sensor The axis is perpendicular to the axis of the beam; at this time, the FBG in the pendulum-equal-section beam FBG inclination sensing is in a strain-free state; the pendulum-equal-section beam FBG inclination sensing and the FBG sensor network analyzer electrical connection;

然后，按设定步长进行正行程、反行程的测量，在每个倾角点θ_i静置2分钟，待光纤光栅传感网络分析仪读数稳定后，记录摆锤-等截面梁光纤光栅倾角传感器中的两根光纤光栅在相应倾角处的中心波长值

i＝1.2…m；最后，记录反行程结束时，θ＝0°的摆锤-等截面梁光纤光栅倾角传感器中光纤光栅的中心波长值

Step 3: Adjust the shape of the jack piston so that the simply supported beam rotates around its hinge axis, gradually change the inclination angle of the simply supported beam according to the step length Δθ=0.2°, and measure the simply supported beam in real time with a dial indicator The inclination angle θ _i ; after reaching the measurement upper limit, let it stand for 5 minutes, and then steadily drop to the measurement lower limit, and the inclination angle increases counterclockwise to be the forward stroke, and the forward stroke and the reverse stroke are reversed once for one cycle; first, record θ = At 0°, the central wavelength value of the fiber grating in the pendulum-constant cross-section beam fiber grating inclination sensor

Then, measure the forward stroke and reverse stroke according to the set step length, and stand still at each inclination point _θi for 2 minutes. After the reading of the fiber grating sensor network analyzer is stable, record the inclination angle of the pendulum-equal cross-section beam fiber grating The central wavelength values of the two fiber gratings in the sensor at the corresponding inclination angles

i=1.2...m; Finally, record the central wavelength value of the fiber grating in the pendulum-equal cross-section beam fiber grating inclination sensor with θ=0° at the end of the reverse stroke

或与

之差，即或

其中

根据第三步所得的θ_i、

数据，得到中心波长变化之差Δλ数据点的离散分布图，根据离散分布图中Δλ数据点的分布形状，采用一次多项式对离散的数据点进行线性拟合，确定一次多项式为式中Φ(θ_j)是以倾角θ_j为自变量的函数，其中θ_j为实际工程中所需测量的倾角，

为实际工程中所测量的光纤光栅倾角传感器中光纤光栅中心波长值变化

与之差；Step 4: Set up a Cartesian rectangular coordinate system with the inclination θ as the abscissa and the difference of the center wavelength change Δλ as the ordinate, where Δλ is the change of the center wavelength value of the FBG measured in real time by the FBG inclination sensor at the corresponding corner.

or with

difference, that is or

in

According to the θ _i obtained in the third step,

According to the distribution shape of the Δλ data points in the discrete distribution graph, the discrete data points are linearly fitted by a first-order polynomial, and the first-order polynomial is determined as where Φ(θ _j ) is a function of the inclination angle θ _j as an independent variable, where θ _j is the inclination angle to be measured in actual engineering,

It is the change of the central wavelength value of the fiber grating in the fiber grating inclination sensor measured in the actual project

and Difference;

Φ为一次多项式集合；取j＝i，得到：令

即

将第三步所得的θ_i、

数据代入I中，当Φ(θ_i)满足

时，由求多元极值的必要条件可得：

即得到含有2个未知数β₁、λ的两个方程，解方程组，得β₁、λ，从而得到拟合的

实现摆锤-等截面梁光纤光栅倾角传感器的标定，即

Step 5: According to the principle of the least square method, there is

Φ is a polynomial set of degree one; take j=i, get: make

Right now

The θ _i obtained in the third step,

Data is substituted into I, when Φ(θ _i ) satisfies

, it can be obtained from the necessary conditions for multivariate extremum:

That is to get two equations containing 2 unknowns β ₁ , λ, and solve the equations to get β ₁ , λ, so as to get the fitted

Realize the calibration of the pendulum-constant cross-section beam fiber grating inclination sensor, namely

The working principle and advantages of this method are briefly described as follows:

When in use, the present invention is fixedly installed on the measured structure, so that the axis of the casing in the present invention is perpendicular to the horizontal plane where the measured structure is located, and when the measured structure is inclined, the sensor of the present invention also produces a corresponding inclination. , under the action of gravity, the pendulum will rotate around the hinge axis to maintain its vertical position. Since one end of the pendulum is fixedly connected to one end of the constant-section beam, the constant-section beam will prevent the pendulum from rotating. At this time, the moment generated by the pendulum due to its center of gravity and its axis offset relative to the hinge axis will act on one end of the constant-section beam, forcing the constant-section beam to bend and deform around the fixed connection point between it and the positioning seat, and paste it on The two fiber gratings on the opposite sides of the constant-section beam will deform together with the surface of the constant-section beam, so that the grating on one side will be elongated, while the grating on the other side will be shortened, causing the central wavelength of the grating to shift. By detecting the fiber grating The change of the inclination angle can be measured by the change of the center wavelength. This new type of fiber grating inclination sensor has a good linear relationship.

The pendulum-constant cross-section beam fiber grating inclination sensor has many advantages compared with other sensors for measuring deformation. The first is that its measurement accuracy has been greatly improved. All instruments for measuring deformation need a reference point, and the pendulum-equal-section beam fiber grating inclination sensor uses the direction of gravity as the reference point, regardless of the position of the sensor. The direction of gravity is always fixed, while other instruments for measuring deformation use a certain position as a reference point. This reference point cannot always be the same as the direction of gravity, which will bring certain problems to long-term monitoring. error. In addition, the fiber grating inclination sensor calculates the measured angle by measuring the change of the central wavelength of the grating, and the fiber grating has the advantages of resistance to electromagnetic interference and low signal attenuation, so the fiber grating inclination sensor can be used in harsh environments. Using the pendulum-constant cross-section beam fiber grating inclination sensor to measure bridge deflection does not require a static reference point, is not affected by sunlight, rain, fog, etc., and reduces the dependence on environmental conditions, especially suitable for measuring flyover bridges and river bridges The deflection is relatively convenient, and the installation is relatively convenient, which greatly improves the work efficiency. In addition, because the pendulum of the present invention is made of pure copper with high density, the size of the sensor is small enough and has a high sensitivity coefficient; Beryllium bronze with high strength, high elastic limit, good impact toughness and fatigue strength, strong oxidation resistance and corrosion resistance is used as the material of the elastic element of the equal cross-section beam, which greatly improves the sensitivity coefficient of the present invention, namely The accuracy of the measured data; and the present invention designs a dual optical fiber grating differential structure, and one optical fiber grating is glued to the upper and lower surfaces of the equal-section beam to realize temperature self-compensation. Based on the excellent characteristics of fiber gratings and the designed differential structure of dual fiber gratings, in summary, the present invention has the following advantages:

1. The measurement accuracy has been greatly improved compared with the previous fiber grating inclination sensor.

2. Small size, easy to use outdoors for deformation monitoring of bridge structures.

3. The structure is simple, the installation is relatively convenient, and the work efficiency is high.

4. Its use is not limited by the measured environmental conditions.

5. The elastic element structure with equal cross-section is used, which is simple in structure and easy to process.

6. The temperature self-compensation of the sensor is realized, so that it can adapt to the complex and changeable external test environment and be directly applied to the actual project.

To sum up, the present invention has high measurement accuracy, strong anti-electromagnetic interference capability, good stability, is suitable for industrial production, and is suitable for deformation monitoring of various engineering structures, especially for monitoring deformation of civil engineering structures.

Description of drawings

Accompanying drawing 1 is the structure diagram of the present invention.

Accompanying drawing 2 is the left side view of accompanying drawing 1.

Accompanying drawing 3 is a schematic diagram of the fiber grating structure in the present invention.

Accompanying drawing 4 is the discrete distribution diagram of the experimental data obtained in Example 1 of the present invention.

In the figure: 1-optical fiber grating, 2-beam of equal section, 3, 8-hinge shaft, 4-pendulum, 5-sleeve, 6-locating seat, 7-connecting sleeve.

Detailed ways

The specific implementation manner of the present invention will be described in detail below in conjunction with the accompanying drawings and embodiments.

Example 1

A pendulum-equal section beam fiber optic grating inclination sensor, comprising: a positioning seat 6, a pendulum 4, an equal section beam 2, an optical fiber grating 1, and a connecting sleeve 7, one end of the connecting sleeve 7 is fixedly connected to the positioning seat 6 On, the other end is hinged with one end of the pendulum 4 through the first hinge shaft 3; the cross-section of the equal-section beam 2 is rectangular and is inserted into the connecting sleeve 7, and one end thereof is fixedly connected to the positioning On the seat 6, the other end is connected to the pendulum 4 through the second hinge shaft 8; the first hinge shaft 3 and the second hinge shaft 8 are perpendicular to each other; the fiber grating 1 has two pieces, which are respectively fixedly installed on the Referring to the two opposite sides of the constant-section beam 2 , the two opposite sides of the constant-section beam 2 refer to the sides corresponding to the longer side in the cross-sectional rectangle of the constant-section beam 2 .

In this embodiment, the pendulum 4 is made of pure copper with a mass of 164g.

In this embodiment, the constant-section beam 2 is made of QBe ₂ beryllium bronze.

In this embodiment, the fiber grating 1 is composed of a core 9 containing 10 grating regions, and is covered with a cladding 12. It is written in a germanium-doped photosensitive optical fiber by a phase mask method. The Bragg wavelength is 1550nm, and the reflectivity Greater than 90%.

In this embodiment, the casing 5 is made of low-carbon stainless steel with strong corrosion resistance.

In this embodiment, the constant-section beam 2 and the positioning seat 6 are riveted by rivets 11 .

Example 2

A pendulum-equal-section beam fiber optic grating inclination sensor is that a sleeve 5 is arranged outside the positioning seat 6, the pendulum 4, the equal-section beam 2, the fiber grating 1, and the connecting sleeve 7 described in embodiment 1. The positioning seat 6 is fixedly installed on one end of the sleeve 5 .

The calibration method of the pendulum-equal cross-section beam fiber grating inclination sensor prepared in embodiment 1 or embodiment 2 of the present invention is as follows:

The first step: Prepare an I-shaped simply supported beam, a fiber grating sensor network analyzer, a dial gauge, and a level; one end of the simply supported beam is hinged on the hinge shaft, and the other end is supported by a jack support;

Step 2: Adjust the axis of the I-shaped simply supported beam to the level with a level ruler, and then paste the pendulum-equal-section beam FBG inclination sensor on the surface of the beam, so that the pendulum-equal-section beam FBG inclination sensor The axis is perpendicular to the axis of the beam; at this time, the FBG in the pendulum-equal-section beam FBG inclination sensing is in a strain-free state; the pendulum-equal-section beam FBG inclination sensing and the FBG sensor network analyzer electrical connection;

然后，按设定步长进行正行程、反行程的测量，在每个倾角点θ_i静置2分钟，待光纤光栅传感网络分析仪读数稳定后，记录摆锤-等截面梁光纤光栅倾角传感器中的两根光纤光栅在相应倾角处的中心波长值

i＝1.2…m；最后，记录反行程结束时，θ＝0的摆锤-等截面梁光纤光栅倾角传感器中光纤光栅的中心波长值

测量过程中应平稳地升压和降压，不应中断，避免出现超调和回调现象。本实施例进行了4个的行程循环测量，所测得数据见表1、表2、表3、表4：The third step: adjust the shape of the jack piston to make the simply supported beam rotate around its hinge axis, gradually change the inclination angle of the simply supported beam according to the step length Δθ=0.2°, and measure the simply supported beam in real time with a dial gauge The inclination angle θ _i of the beam; after reaching the upper limit of the measurement, let it stand for 5 minutes, then steadily drop to the lower limit of the measurement, and the inclination angle increases counterclockwise as the forward stroke, and the forward stroke and the reverse stroke are reversed once as one cycle; first, record θ = 0, the center wavelength value of the fiber grating in the pendulum-constant cross-section beam fiber grating inclination sensor

Then, measure the forward stroke and reverse stroke according to the set step length, and stand still at each inclination point _θi for 2 minutes. After the reading of the fiber grating sensor network analyzer is stable, record the inclination angle of the pendulum-equal cross-section beam fiber grating The central wavelength values of the two fiber gratings in the sensor at the corresponding inclination angles

i=1.2...m; Finally, record the central wavelength value of the fiber grating in the pendulum-equal cross-section beam fiber grating inclination sensor with θ=0 at the end of the reverse stroke

During the measurement process, the pressure should be raised and lowered smoothly without interruption, so as to avoid overshoot and callback. The present embodiment has carried out 4 stroke cycle measurements, and the measured data are shown in Table 1, Table 2, Table 3, and Table 4:

Table 1 Measurement data of fiber grating inclination sensor cycle experiment 1

Table 2 Measuring data of fiber grating inclination sensor cycle experiment 2

Table 3 Measuring data of fiber grating inclination sensor cycle experiment three

Table 4 Measuring data of FBG inclination sensor cycle experiment 4

或与之差，即或

其中

根据第三步所得的θ_i、

数据，得到中心波长变化之差Δλ数据点的离散分布图，根据离散分布图中Δλ数据点的分布形状，采用一次多项式对离散的数据点进行线性拟合，确定一次多项式为

式中Φ(θ_j)是以倾角θ_j为自变量的函数，其中θ_j为实际工程中所需测量的倾角，

为实际工程中所测量的光纤光栅倾角传感器中光纤光栅中心波长值变化

与

之差；Step 4: Set up a Cartesian rectangular coordinate system with the inclination θ as the abscissa and the difference of the center wavelength change Δλ as the ordinate, where Δλ is the change of the center wavelength value of the FBG measured in real time by the FBG inclination sensor at the corresponding corner.

or with difference, that is or

in

According to the θ _i obtained in the third step,

According to the distribution shape of the Δλ data points in the discrete distribution graph, the discrete data points are linearly fitted by a first-order polynomial, and the first-order polynomial is determined as

where Φ(θ _j ) is a function of the inclination angle θ _j as an independent variable, where θ _j is the inclination angle to be measured in actual engineering,

It is the change of the central wavelength value of the fiber grating in the fiber grating inclination sensor measured in the actual project

and

Difference;

令即

将第三步所得的θ_i、

数据代入I中，当Φ(θ_i)满足

时，由求多元极值的必要条件可得：

即得到含有2个未知数β₁、λ的两个方程，解方程组，得β₁、λ，从而得到拟合的实现摆锤-等截面梁光纤光栅倾角传感器的标定，即

Step 5: According to the principle of the least square method, there is Φ is a polynomial set of degree one; take j=i, get:

make Right now

The θ _i obtained in the third step,

Data is substituted into I, when Φ(θ _i ) satisfies

, it can be obtained from the necessary conditions for multivariate extremum:

That is to get two equations containing 2 unknowns β ₁ , λ, and solve the equations to get β ₁ , λ, so as to get the fitted Realize the calibration of the pendulum-constant cross-section beam fiber grating inclination sensor, namely

The performance indicators of the pendulum-equal cross-section beam fiber grating inclination sensor obtained in this embodiment are as follows:

Range Resolution Sensitivity hysteresis repeatability Linearity total accuracy 3.2° 0.45% 27pm/deg 2.15% 2.65% 0.46% 3.44%

Claims (8)

1. pendulum-uniform beam fiber grating obliquity sensor, comprise: positioning seat, pendulum, uniform beam, fiber grating, adapter sleeve, described adapter sleeve one end is fixedly connected on the described positioning seat, and an end of the other end and described pendulum is hinged by first hinge; The xsect of described uniform beam is rectangle and is inserted in the described adapter sleeve that the one end is fixedly connected on the described positioning seat, and the other end is connected with described pendulum by second hinge; Described first hinge is vertical mutually with second hinge; Described fiber grating has 2, is fixedly mounted on two relative sides of described uniform beam respectively, two sides that described uniform beam is relative be meant with described uniform beam xsect rectangle in long corresponding side, limit.

2. a kind of pendulum according to claim 1-uniform beam fiber grating obliquity sensor, it is characterized in that: described pendulum is made by fine copper.

3. a kind of pendulum according to claim 1-uniform beam fiber grating obliquity sensor, it is characterized in that: described uniform beam is by QBe ₂Beryllium-bronze is made.

4. a kind of pendulum according to claim 1-uniform beam fiber grating obliquity sensor is characterized in that: described fiber grating adopts the phase mask method to write in mixing the germanium light-sensitive optical fibre.

5. a kind of pendulum according to claim 1-uniform beam fiber grating obliquity sensor, it is characterized in that: described sleeve pipe is by the stainless steel manufacturing.

6. a kind of pendulum according to claim 1-uniform beam fiber grating obliquity sensor is characterized in that: rivet between described uniform beam and the described positioning seat.

7. a kind of pendulum according to claim 1-uniform beam fiber grating obliquity sensor, it is characterized in that: be provided with a sleeve pipe outside described positioning seat, pendulum, uniform beam, fiber grating, adapter sleeve, described positioning seat is fixedly mounted on an end of described sleeve pipe.

8. the scaling method of pendulum-uniform beam fiber grating obliquity sensor comprises the steps:

The first step: prepare an I shape free beam, an optical fiber grating sensing network analyser, a clock gauge, a surveyor's staff; The one end hinge of described free beam is contained on the hinge, and the other end is supported by a lifting jack;

Second step: with surveyor's staff I shape free beam axis is adjusted to level, then, pendulum-uniform beam fiber grating obliquity sensor is sticked on the beam surface, make the pendulum-axis of uniform beam fiber grating inclination angle sensing and the axis normal of beam; At this moment, the fiber grating in pendulum-uniform beam fiber grating inclination angle sensing is in no strain regime; Pendulum-uniform beam fiber grating inclination angle sensing is electrically connected with the optical fiber grating sensing network analyser;

The 3rd step: adjust the shape journey of jack piston, described free beam is rotated around its hinge, ° progressively change the inclination angle of free beam, measure the inclination angle [theta] of described free beam simultaneously with clock gauge in real time by step delta θ=0.2 _iLeft standstill 5 minutes after reaching the measurement upper limit, steadily drop to measurement lower limit again, increasing counterclockwise with the inclination angle is positive stroke, positive stroke and revesal, and past once is 1 circulation instead; At first, during record θ=0 °, the centre wavelength value of fiber grating in pendulum-uniform beam fiber grating obliquity sensor

Then, carry out the measurement of positive stroke, revesal by setting step-length, at each inclination angle point θ _iLeft standstill 2 minutes, treat optical fiber grating sensing network analyser stable reading after, the two piece fiber gratings of record in pendulum-uniform beam fiber grating obliquity sensor are in the centre wavelength value of corresponding tilting position I=1.2 ... m; At last, when the record revesal finishes, the centre wavelength value of fiber grating in the pendulum-uniform beam fiber grating obliquity sensor of θ=0 °

The 4th step: the difference Δ λ that with the inclination angle [theta] is horizontal ordinate, center wavelength variation is that ordinate is provided with Descartes's rectangular coordinate system, wherein, Δ λ be fiber grating centre wavelength value that the fiber grating obliquity sensor is measured in real time in corresponding corner change with Or with

Poor, promptly

Or

Wherein

θ according to the 3rd step gained _i,

Data obtain the Discrete Distribution figure of the difference Δ λ data point of center wavelength variation, according to Δ λ distribution of data points shape among the Discrete Distribution figure, adopt an order polynomial that discrete data point is carried out linear fit, determine that an order polynomial is

Φ (θ in the formula _j) be with inclination angle [theta] _jBe the function of independent variable, wherein θ _jBe the inclination angle of required measurement in the actual engineering,

For fiber grating centre wavelength value in the fiber grating obliquity sensor measured in the actual engineering changes With

Poor;

The 5th step:, have according to principle of least square method:

Φ is a polynomial expression set; Get j=i, obtain: Order: That is: θ with the 3rd step gained _i,

Among the data substitution I, as Φ (θ _i) satisfy

The time, can get by the necessary condition of asking Multivariate Extreme Value:

Promptly obtain containing 2 unknown number β ₁, λ two equations, the group of solving an equation, β ₁, λ, thereby obtain match

Realize the demarcation of pendulum-uniform beam fiber grating obliquity sensor, promptly

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