CN106940173A - The matrix strain correction method of wide range fiber grating sensor - Google Patents

Abstract

The present invention discloses a kind of matrix strain correction method of wide range fiber grating sensor, it is characterised in that：Strained by wide range fiber grating Sensor monitoring matrix；Structure is：Bare optical fibers and bare optical gratings sensor is placed in inside inner layer steel pipe, inner layer steel pipe is placed in inside two sections of outer layer fine steel tubes, it is ensured that inside and outside two layers of steel pipe relative can be slided；Reserving gaps at outer layer pipe transition joint；It is r to choose inner layer steel pipe radius_m, outer layer pipe radius is r_i, bare optical fibers and bare optical gratings sensor is placed in inside inner layer steel pipe；It is L that outer layer pipe two ends, which exceed inner layer steel pipe length,₁, i.e., it is L that fiber grating, which pastes length,₁, the distance between glue-line is L₂, i.e. fiber grating gauge length is L₂.The big strain variation of wide range fiber grating sensor real-time perception structure, (FBG) demodulator demodulation reflection wavelength data, obtains structural strain according to matrix strain correction equation, obtains the stress performance parameter of structural elements.

Description

The matrix strain correction method of wide range fiber grating sensor

Technical field

The present invention relates to the matrix strain correction method of wide range fiber grating sensor, belonging to wide range fiber grating should Become transfer theory field.

Background technology

Greatly across special engineering structures such as prestressed structure, high-rise building and ocean platforms in environmental attack and load effect Long term under, produce big strain variation, once allowing strain value more than structure, easily occur brittle break, produce huge Loss.Carry out big strain monitoring to special engineered, structural damage is recognized in time, have important for reduction special engineering structure disaster Meaning.Fiber-optic grating sensor is widely used in monitoring structural health conditions neck with good characteristics such as its sensitivity height, electromagnetism interferences Domain, traditional fiber grating sensor monitoring range is only 3000 μ ε, it is impossible to meets the requirement of the big strain monitoring of unique construction, is based on The big strain monitoring method of fiber grating is the direction for being worth exploring.In terms of scholar has carried out all much strain monitoring new methods Attempt, including：Prestressing force measuring method, the composite construction for pasting fiber grating after 5000 μ ε again are stretched to prestress wire With the fiber grating desensitization method for packing for becoming trapezium structure etc., but these methods are accurate in strain monitored over time and strain monitoring Had the obvious disadvantage that in terms of degree.This patent belongs to wide range fiber grating strain transfer theory field, is related to wide range light Fine grating-matrix strain error modification method, had both realized the big strain measurement of unique construction, big strain measurement had been solved again Accuracy problem.

The content of the invention

The present invention relates to the matrix strain correction method of wide range fiber grating sensor, first, sealed using double-layer pipe Preparation technology is filled, wide range fiber grating sensor is devised, establishes the strain of the big strain of matrix-fiber grating small strain Pass through mechanism.Secondly, wide range fiber grating strain update equation is given, the big strain monitoring of unique construction is realized with repairing Just.

The technical solution adopted by the present invention is：

A kind of matrix strain correction method of wide range fiber grating sensor, it is characterised in that：Pass through wide range optical fiber Grating sensor monitoring matrix strain；

Structure is：Bare optical fibers and bare optical gratings sensor is placed in inside inner layer steel pipe, inner layer steel pipe is placed in two sections of thin steel of outer layer Inside pipe, it is ensured that inside and outside two layers of steel pipe relative can be slided；Reserving gaps at outer layer pipe transition joint；

It is r to choose inner layer steel pipe radius_m, outer layer pipe radius is r_i, bare optical fibers and bare optical gratings sensor is placed in inner layer steel pipe Portion；

It is L that outer layer pipe two ends, which exceed inner layer steel pipe length,₁, i.e., it is L that fiber grating, which pastes length,₁The distance between, glue-line For L₂, i.e. fiber grating gauge length is L₂。

Wide range fiber grating sensor and fiber Bragg grating (FBG) demodulator composition strain perceive acquisition system, and (FBG) demodulator demodulation is anti- Ejected wave is long, and perceiving bare optical fibers and bare optical gratings by wavelength change situation strains.

Consider the influence of bearing clamping length, fiber grating gauge length and intermediate gelatine layer, obtain optic fiber grating wavelength Matrix strain Equation：

(1) bare optical fibers and bare optical gratings, which are strained, is：

In formula, ε_{It is naked}Strained for bare optical fibers and bare optical gratings, K_εFor bare optical fibers and bare optical gratings ga(u)ge factor, Δ λ_BWavelength change；

(2) to cementing section of optical fiber infinitesimal body Model force analysis, mechanical balance equation is set up：

In formula, r_fFor fiber grating radius, τ_f(x,r_f) it is fiber outer surface, glue-line inner surface shearing stress, σ_fCut for optical fiber Face direct stress；

(3) to glue-line infinitesimal body Model force analysis, mechanical balance equation is set up：

2πr_j·τ_j(x,r_j)·dx-2πr_f·τ_f(x,r_f)·dx+π(r_j ²-r_f ²)·dσ_j=0

In formula, r_jFor glue-line micro unit radius, τ_j(x,r_j) it is glue-line outer surface shearing stress, σ_jFor glue-line section direct stress；

(4) because the rate of change of fibre strain is consistent with glue-line strain variation rate, the springform of fiber grating and glued layer Amount difference is larger, is simplified glue-line shear strain variation relation formula：

In formula, E_fFor optical fiber elastic modelling quantity, ε_fFor fibre strain；

(5) A and B points are glue-line boundary point, M and N points are cementing section of optical fiber boundary point, and displacement coordination equation is as follows：

Wherein,

In formula, u_AFor glue-line A point displacements, u_MFor cementing section of optical fiber M point displacement, G_jFor glue-line modulus of shearing, r_iFor outer layer steel Bore, u_iFor correspondence matrix displacement, u at A points_fFor cementing section of deformation of optical fiber, L₁Length, L are pasted for optical fiber₂For optical fiber gauge length Length, L_aFor bearing clamping length；

(6) Second Order Nonhomogeneous Linear Differential of cementing section of fibre strain and matrix strain is set up in derivation：

In formula, ε_iStrained for matrix；

(7) according to equivalent section method, the strain of free segment optical fiber is equal to the mean strain of cementing section of optical fiber, therefore, naked light Fiber grating strain is equal to the mean strain of cementing section of optical fiber：

In formula, ε_f2(x) strained for bare optical fibers and bare optical gratings,For the mean strain of cementing section of optical fiber；

(8) the matrix strain correction equation of wide range fiber grating sensor：

(FBG) demodulator demodulation wide range fiber grating sensor wavelength data Δ λ_B, pass through wide range fiber grating sensor Matrix strain correction equation, corrects the big strain of matrix, solves the problems, such as the accurate measurement of wide range fiber grating sensor.

It is an advantage of the invention that：Based on wide range fiber grating Sensor monitoring and correct matrix strain.Wide range optical fiber The big strain variation of grating sensor real-time perception structure, (FBG) demodulator demodulation reflection wavelength data, according to matrix strain correction equation Structural strain is obtained, the stress performance parameter of structural elements is obtained.

Brief description of the drawings

Fig. 1 is fiber-optic grating sensor schematic diagram.

Fig. 2 is Fig. 1 partial enlarged drawing.

Fig. 3 is cementing section of optical fiber micro unit force diagram.

Fig. 4 is glue-line micro unit force diagram.

Embodiment

The example of the present apparatus is described in detail with reference to accompanying drawing as follows：

As shown in figure 1, bare optical fibers and bare optical gratings sensor 3 is placed in inside inner layer steel pipe, inner layer steel pipe is placed in two sections of outer layers Inside steel pipe 1,1mm gap is reserved at outer layer pipe transition joint, it is ensured that inside and outside two layers of steel pipe relative can be slided.Outer layer steel It is L that pipe two ends, which exceed inner layer steel pipe length,₁, i.e., it is L that fiber grating, which pastes length,₁, the distance between glue-line 2 L₂, i.e. fiber grating Gauge length scope is L₂, the clamp distance that bearing 4 is bonded by epoxy glue between two sections of outer layer pipes, bearing is La.

In Fig. 2, Fig. 3, Fig. 4, model hypothesis as shown in the figure are carried out, it is considered to which bearing clamping length, fiber grating paste length The influence of the parameter to fiber grating strain transport such as degree and gauge length, sets up the big strain of matrix-fiber grating small strain Force-transmission mechanism.(FBG) demodulator demodulates reflection wavelength data, and structural strain is obtained according to matrix strain correction equation (29), obtains structure Component strain parameter.

Fig. 1 is wide range fiber grating sensor pictorial diagram, and the encapsulation scheme of wide range fiber grating sensor is as follows：Adopt Double-layer pipe encapsulation technology is used, it is r to choose inner layer steel pipe radius_m(being slightly larger than bare optical fibers and bare optical gratings radius), bare optical fibers and bare optical gratings are passed Sensor is placed in inside inner layer steel pipe.It is r to choose outer layer pipe radius_i, inner layer steel pipe is placed in inside two sections of outer layer pipes, it is ensured that Inside and outside two layers of steel pipe relative can be slided.1mm gap is reserved at outer layer pipe transition joint, outer layer pipe two ends exceed internal layer Length of steel pipe is L₁, i.e., it is L that fiber grating, which pastes length,₁, the distance between glue-line is L₂, i.e. fiber grating gauge length is L₂。 Inner layer steel pipe plays fixed fiber grating, two sections of outer layer pipes of connection and support.Outer layer pipe produces relative displacement and passed through End glue-line passes to fiber grating, plays matrix-fiber grating strain transmission.Bearing clamps two sections of outer layer pipes respectively, Clamp distance between bearing is L_a.Bare optical fibers and bare optical gratings sensor, double-layer pipe and two clamping bearings have collectively constituted wide range Fiber Bragg grating strain sensor, by adjusting bearing clamp distance and fiber grating gauge length, improves wide range optical fiber light The strain of gate sensor can survey scope.

Wide range fiber grating sensor establishes matrix and greatly should by carrying out desensitization processing to bare optical fibers and bare optical gratings sensor The force-transmission mechanism of change-fiber grating small strain, because matrix strain and fiber grating strain are inconsistent, it is necessary to carry out wide range light Fiber grating strain transmission analysis, continues amendment wide range fiber grating sensor and surveys strain, the analysis uses hypothesis below：

(1) fiber grating is linear elastic materials.

(2) fiber grating axial stress is that, by the shear stress transmission on contact surface, detrusion occurs for glue-line.(3) bearing Respectively with sensor, support holder firmly, optical fiber is bonded closely, without Relative sliding with glue-line.

Fiber Bragg grating (FBG) demodulator demodulates wavelength change, and bare optical fibers and bare optical gratings strain is：

In formula, ε_{It is naked}Strained for bare optical fibers and bare optical gratings, K_εFor bare optical fibers and bare optical gratings ga(u)ge factor, Δ λ_BFor wavelength change.

Fig. 1 is wide range fiber grating Fundamentals of Sensors figure, A and B points are glue-line boundary point, M and N points are cementing section of optical fiber Boundary point, using N points as the origin of coordinates.Fig. 3 is cementing section of optical fiber micro unit force diagram, and it is research object to take cementing section of optical fiber, right Its force analysis：

In formula, σ_fFor fiber cross-sections direct stress, τ_f(x,r_f) it is fiber outer surface (glue-line inner surface) shearing stress, r_fFor light Fine grating radius.

Fig. 4 is glue-line micro unit force diagram, to its force analysis：

2πr_j·τ_j(x,r_j)·dx-2πr_f·τ_f(x,r_f)·dx+π(r_j ²-r_f ²)·dσ_j=0

(4)

In formula, τ_j(x,r_j) it is glue-line outer surface shearing stress, r_jFor glue-line micro unit radius, σ_jFor glue-line section direct stress.

Wushu (3) is substituted into (5)：

In formula, E_fFor optical fiber elastic modelling quantity, E_jFor glue-line elastic modelling quantity.

Optical fiber has identical strain variation rate with glue-line：

In formula, ε_fFor fibre strain, ε_jStrained for glue-line.

Fiber grating differs larger with the elastic modelling quantity of glue-line, therefore is believed that：

Wushu (8) (9) substitutes into (7)

Detrusion occurs for glue-line, obtains：

In formula, u is glue-line axial displacement, G_jFor glue-line modulus of shearing, γ is glue-line shearing strain.(11) formula is integrated：

In formula, u_AFor glue-line A point displacements, u_MFor cementing section of optical fiber M point displacement, r_iFor outer layer pipe internal diameter.

A point displacements and M point displacement coordination equations are as follows：

In formula, u_iFor correspondence matrix displacement, u at A points_fFor cementing section of deformation of optical fiber, L₁Length, L are pasted for optical fiber₂For light Fine gauge length, L_aFor bearing clamping length.

Wherein：

In formula, μ is Poisson's ratio.By formula (19) to x derivations, show that cementing section of fibre strain strains the differential equation with matrix：

General solution of differential equation is：

In formula, ε_f(x) it is cementing section of fibre strain, ε_iStrained for matrix, C₁And C₂For integral constant, cementing section of optical fiber side Boundary's point is free end face, and due to symmetry, therefore boundary condition is：

ε_f(L₁)=ε_f(-L₁)=0 (22)

Determine integral constant：

Cementing section of fibre strain transport is distributed as：

In formula, α (x) is cementing section of fibre strain transport.Average strain transfer rate is represented by the cementing length model of optical fiber The average value of internal strain is enclosed, cementing section of optical fiber average strain transfer rate is：

In formula,For cementing section of optical fiber average strain transfer rate,For cementing section of optical fiber mean strain.Cementing section of light Fine non-homogeneous strain is equivalent to the mean strain along cementing section of fiber span, according to equivalent section method, free segment optical fiber should Become the mean strain for being equal to cementing section of optical fiber, bare optical fibers and bare optical gratings strain is equal to the mean strain of cementing section of optical fiber：

In formula, ε_f2(x) strained for bare optical fibers and bare optical gratings, wide range fiber grating strain transducer transport is：

In formula, α is wide range fiber grating strain transducer transport.Obtained by formula (28) and formula (1), wide range The matrix strain correction equation of fiber-optic grating sensor is：

Formula (29) is the matrix strain correction equation of wide range fiber grating sensor, solves answering for big strain structure Become measurement and amendment problem.

Claims (3)

1. a kind of matrix strain correction method of wide range fiber grating sensor, it is characterised in that：Pass through wide range optical fiber light Gate sensor monitoring matrix strain；

Structure is：Bare optical fibers and bare optical gratings sensor is placed in inside inner layer steel pipe, inner layer steel pipe is placed in two sections of outer layer fine steel tubes Portion, it is ensured that inside and outside two layers of steel pipe relative can be slided；Reserving gaps at outer layer pipe transition joint；

It is r to choose inner layer steel pipe radius_m, outer layer pipe radius is r_i, bare optical fibers and bare optical gratings sensor is placed in inside inner layer steel pipe；

It is L that outer layer pipe two ends, which exceed inner layer steel pipe length,₁, i.e., it is L that fiber grating, which pastes length,₁, the distance between glue-line is L₂, i.e. fiber grating gauge length is L₂。

2. the matrix strain correction method of wide range fiber grating according to claim 1, it is characterised in that：Wide range light Fiber grating sensor and fiber Bragg grating (FBG) demodulator composition strain perceive acquisition system, and (FBG) demodulator demodulation reflection wavelength passes through wavelength Situation of change perceives bare optical fibers and bare optical gratings strain.

3. the matrix strain correction method of wide range fiber grating according to claim 1, it is characterised in that：Consider bearing The influence of clamping length, fiber grating gauge length and intermediate gelatine layer, obtains the matrix strain Equation of optic fiber grating wavelength：

(1) bare optical fibers and bare optical gratings, which are strained, is：

In formula, ε_{It is naked}Strained for bare optical fibers and bare optical gratings, K_εFor bare optical fibers and bare optical gratings ga(u)ge factor, Δ λ_BWavelength change；

(2) to cementing section of optical fiber infinitesimal body Model force analysis, mechanical balance equation is set up：

$2{\mathrm{\πr}}_f\×{\mathrm{\τ}}_f(x,r_f)dx+\mathrm{\π}\×r_f^2{\mathrm{d\σ}}_f=0$

In formula, r_fFor fiber grating radius, τ_f(x,r_f) it is fiber outer surface shearing stress, σ_fFor fiber cross-sections direct stress；

(3) to glue-line infinitesimal body Model force analysis, mechanical balance equation is set up：

2πr_j·τ_j(x,r_j)·dx-2πr_f·τ_f(x,r_f)·dx+π(r_j ²-r_f ²)·dσ_j=0

In formula, r_jFor glue-line micro unit radius, τ_j(x,r_j) it is glue-line outer surface shearing stress, σ_jFor glue-line section direct stress；

(4) because the rate of change of fibre strain is consistent with glue-line strain variation rate, the elastic modelling quantity phase of fiber grating and glued layer Difference is larger, is simplified glue-line shear strain variation relation formula：

${\mathrm{\τ}}_j(x,r_j)=-\frac{r_f^2}{2r_j}\·\frac{{\mathrm{d\σ}}_f}{dx}=-\frac{r_f^2}{2r_j}\·E_f\·\frac{{\mathrm{d\ϵ}}_f}{dx}$

In formula, E_fFor optical fiber elastic modelling quantity, ε_fFor fibre strain；

(5) A and B points are glue-line boundary point, M and N points are cementing section of optical fiber boundary point, and displacement coordination equation is as follows：

$u_A-u_M=-\frac{E_f}{2G_j}\·r_f^2\·ln\left(\frac{r_i}{r_f}\right)\·\frac{{\mathrm{d\ϵ}}_f}{dx}=-\frac{1}{k^2}\·\frac{{\mathrm{d\ϵ}}_f}{dx}$

Wherein,

$u_A=u_i\·\frac{L_a}{L_2+2L_1}$

$u_M=u_f+\frac{u_f}{L_1}\·\frac{L_2}{2}$

In formula, u_AFor glue-line A point displacements, u_MFor cementing section of optical fiber M point displacement, G_jFor glue-line modulus of shearing, r_iFor in outer layer pipe Footpath, u_iFor correspondence matrix displacement, u at A points_fFor cementing section of deformation of optical fiber, L₁Length, L are pasted for optical fiber₂For optical fiber gauge length, L_aFor bearing clamping length；

(6) Second Order Nonhomogeneous Linear Differential of cementing section of fibre strain and matrix strain is set up in derivation：

$\frac{{\mathrm{d\ϵ}}_f^2}{{\mathrm{dx}}^2}-\frac{(L_2+2L_1)\·k^2}{2L_1}\·{\mathrm{\ϵ}}_f=-\frac{L_a\·k^2}{L_2+2L_1}\·{\mathrm{\ϵ}}_i$

In formula, ε_iStrained for matrix；

(7) according to equivalent section method, the strain of free segment optical fiber is equal to the mean strain of cementing section of optical fiber, therefore, bare fibre light Grid strain is equal to the mean strain of cementing section of optical fiber：

$E_f\·{\mathrm{\ϵ}}_{f2}\left(x\right)\·\mathrm{\π}\·r_f^2=E_f\·\stackrel{\‾}{{\mathrm{\ϵ}}_f}\left(x\right)\·\mathrm{\π}\·r_f^2$

${\mathrm{\ϵ}}_{f2}\left(x\right)=\stackrel{\‾}{{\mathrm{\ϵ}}_f}\left(x\right)$

In formula, ε_f2(x) strained for bare optical fibers and bare optical gratings,For the mean strain of cementing section of optical fiber；

(8) the matrix strain correction equation of wide range fiber grating sensor：

${\mathrm{\ϵ}}_i=\frac{{(L_2+2L_1)}^2\·{\mathrm{\Δ\λ}}_B}{2L_1\·L_a\·\{1-\frac{\sinh (\sqrt{\frac{L_2+2L_1}{2L_1}}\·k\·L_1)}{\sqrt{\frac{L_2+2L_1}{2L_1}}\·k\·L_1\·\cosh (\sqrt{\frac{L_2+2L_1}{2L_1}}\·k\·L_1)}\}\·K_{\mathrm{\ϵ}}}$

(FBG) demodulator demodulation wide range fiber grating sensor wavelength data Δ λ_B, pass through the matrix of wide range fiber grating sensor Strain correction equation, corrects the big strain of matrix, solves the problems, such as the accurate measurement of wide range fiber grating sensor.