FBG-Based Sensitivity Structure Based on Flexure Hinge and Its Application for Pipeline Pressure Detection

With the widespread application of pipelines in engineering, more and more accidents occur because of pipeline leakage. Therefore, it is particularly important to continuously monitor the pipeline pressure. In this study, a non-intrusive and high-sensitivity structure based on FBG (Fiber Bragg grating) sensor is proposed. Firstly, the basic sensing theory of FBG and the state of a pipeline wall under inner pressure are analyzed. Then, structural sensitivity is deduced based on the flexure hinge and mechanical lever. Subsequently, finite element simulation for the whole sensitization structure is carried out, and optimal parameters are determined to obtain the maximum sensitivity. Finally, laboratory experiments are conducted to verify the function of the designed sensitivity structure. The experimental results show a good agreement with the simulation results. In the experiment, it can be found that the designed structure has a strain sensitivity of 9.59 pm/με, which is 11.51 times the pipeline surface strain. Besides, the structure is convenient to operate and has a good applied prospect for the engineering practice.


Introduction
It is well known that pipelines are widely used in transporting fluids due to the advantages of good stability and cost-effectiveness [1], which are especially suitable for oil and natural gas transportation. The transport medium is flammable, toxic, explosive, and corrosive; even a small leak will cause serious consequences [2,3]. Owing to the extension of service time of many pipeline infrastructures, especially in the case of long-distance transportation pipelines, it leads to more frequent leakage accidents. Therefore, the timely and accurate detection of pipeline leaks is crucial to avoid extreme safety accidents.
At present, there are two kinds of method for pipeline detection: the intrusive detection method and the non-intrusive detection method. For the intrusive detection method, the sensor is directly contact with the fluid, which will undermine the integrity and the service life of pipeline. Compared with the intrusive detection method, the non-intrusive sensor can be installed directly on the pipeline surface, and the pipeline will not be damaged. This means that the non-intrusive method has the advantages of preserving pipeline integrity and safely operations in a variety of applications. Hence, the non-intrusive method has become an important research direction.
In the field of engineering, there are multiple sensors widely used for pipeline pressure detection, such as resistance sensors [4,5], capacitive sensors [6,7], and FBG (Fiber Bragg grating) sensors, etc. Resistance sensors and capacitive sensors can monitor the pressure fluctuation from the change of resistance or capacitance values. The method has the advantages of high accuracy and strong stability. However, the sensor mentioned above is easily disturbed by the external environment and is generally fabricated into an intrusive model of a pipeline under internal pressure is built, and the stress-strain state is analyzed. Subsequently, the primitive model of the sensitization structure is designed, and the theoretical formula of strain magnification is deduced based on mechanical principles. Then, by the finite element method (FEM), we simulate the strain magnification of the designed structure. Finally, the laboratory experiment is conducted, and the experimental results are compared with the simulation results. The results demonstrate that the sensitization structure is feasible and reliable. Compared with the pipeline wall strain, the designed sensitization structure has a strain sensitivity of 9.59 pm/µε, which is 11.51 times the pipeline surface strain.

Basic Sensing Theory of FBG
FBG sensing technology takes optical fibers and light waves as the medium and carrier, respectively [27]. Optical fibers consist of a core layer, a cladding layer, and a coating layer. Because the refractive index of the cladding layer is smaller than the refractive index of the core layer, the light wave can travel along the core layer.
When the wide band light passes through, there is a selective transmission in which a narrow part of the spectrum is reflected and other wavelengths are transmitted. The reflected part of the spectrum is called the Bragg wavelength λ B . According to the Maxwell's equations and the coupled-mode theory of optical fibers, λ B can be expressed by the following formula [28,29]: where n e is the effective refractive index and Λ is the period length of the optical fiber [30].
In engineering applications, the dependence of optical features of a grating structure on temperature and strain is used, which is reflected in the change in the Bragg wavelength λ B . The relation between the Bragg wavelength change ∆λ B , the relative deformation ε, and the temperature variation ∆T is expressed by the following equation: where ξ is the coefficient of thermal expansion, α f is the thermo-optic coefficient, and P e is the photo elastic coefficient.

Analyses of Pipeline Stress-Strain State
As shown in Figure 1, D is the inside diameter of the pipeline, and δ is the pipeline wall thickness. When D/δ > 20, it can be defined as thin-walled circular tubes. Most of pipelines used in engineering can be classified as thin-walled circular tubes. Thus, applying an internal pressure P on the pipeline, principal stresses in three directions would be generated on the pipeline wall including σ x , σ y , and σ z (σ x is circumferential stress, σ y is axial stress, and σ z is radial stress). The principal stress at each point of the cylinder wall can be calculated according to the thin-walled cylinder theory as follows: Hence, based on the Fourth theory of strength [31], the equivalent stress on cylinder outside wall can be calculated as Equation (6): According to the Generalized Hooke Law, the value of equivalent elastic strai along the cylinder wall can be obtained as follows: where is the elastic modulus of pipeline material (304 stainless steel).

Sensitization Structure Design
The assembly diagram of the designed sensitization structure is shown in Figu In detail, the sensitization structure is composed of a flexure hinge sheet, a pipe-clip bolts. Firstly, two-petal pipe-clips are fastened by #1 bolts, making the inner side o pipe-clip closely attach to the pipeline wall to further make sure the pipeline wall stra transmitting to the pipe-clip as much as possible. Then, the flexure hinge sheet is pl on the upper part of the pipe-clip, and both ends of the flexure hinge sheet are fixed t pipe-clip by #2 bolts. The pipe-clip is set as a bridge to transmit strain from the pip wall to flexure hinge sheet. Then, an FBG is glued on the flexure hinge sheet by an a sive with two ends fixed. More details are shown in Figure 2. Hence, based on the Fourth theory of strength [31], the equivalent stress σ e on the cylinder outside wall can be calculated as Equation (6): According to the Generalized Hooke Law, the value of equivalent elastic strain ε e along the cylinder wall can be obtained as follows: where E is the elastic modulus of pipeline material (304 stainless steel).

Sensitization Structure Design
The assembly diagram of the designed sensitization structure is shown in Figure 2. In detail, the sensitization structure is composed of a flexure hinge sheet, a pipe-clip, and bolts. Firstly, two-petal pipe-clips are fastened by #1 bolts, making the inner side of the pipe-clip closely attach to the pipeline wall to further make sure the pipeline wall strain is transmitting to the pipe-clip as much as possible. Then, the flexure hinge sheet is placed on the upper part of the pipe-clip, and both ends of the flexure hinge sheet are fixed to the pipe-clip by #2 bolts. The pipe-clip is set as a bridge to transmit strain from the pipeline wall to flexure hinge sheet. Then, an FBG is glued on the flexure hinge sheet by an adhesive with two ends fixed. More details are shown in Figure 2.
As the core part of the designed structure, the flexure hinge sheet mainly consists of two levels of leverage (first hinge-lever and second hinge-lever), a circle hinge, a guide arm, and a fixed end, as shown in Figure 3. The distances between the points A and B, B and C, E and F, D and E are denoted by L 1 , L 2 , L 3 , and L 4 , respectively. Besides, b is the width of the narrowest part of the circle hinge. The radius and the thickness of the circle hinge are denoted by r and w, respectively. Moreover, the overall thickness of the flexure hinge sheet is w. The length and width of the whole flexure hinge sheet are W s and L s , respectively. pipe-clip closely attach to the pipeline wall to further make sure the pipeline wall strain is transmitting to the pipe-clip as much as possible. Then, the flexure hinge sheet is placed on the upper part of the pipe-clip, and both ends of the flexure hinge sheet are fixed to the pipe-clip by #2 bolts. The pipe-clip is set as a bridge to transmit strain from the pipeline wall to flexure hinge sheet. Then, an FBG is glued on the flexure hinge sheet by an adhesive with two ends fixed. More details are shown in Figure 2.  As the core part of the designed structure, the flexure hinge sheet mainly consists of two levels of leverage (first hinge-lever and second hinge-lever), a circle hinge, a guide arm, and a fixed end, as shown in Figure 3. The distances between the points A and B, B and C, E and F, D and E are denoted by L1, L2, L3, and L4, respectively. Besides, b is the width of the narrowest part of the circle hinge. The radius and the thickness of the circle hinge are denoted by r and w, respectively. Moreover, the overall thickness of the flexure hinge sheet is w. The length and width of the whole flexure hinge sheet are Ws and Ls, respectively.

Static Analyses of Structures
For the proposed sensitization structure, the principle of strain transmission and amplification is derived in this section. The schematic diagram of working principle of the whole sensitization structure is shown in Figure 4. The relationship between the pipeline inner pressure p and the strain of FBG is obtained by calculating. Firstly, as shown in Figure 5, the pipeline inner pressure p (Pa) causes the strain on the outer wall of pipeline, and then generate a tension Fx (N) at the two ends of the pipe-clip. Because of the influence of friction and other factors, this can result in the strain's incomplete pass to the pipe-clip. Hence, assuming there is a coupling coefficient

Static Analyses of Structures
For the proposed sensitization structure, the principle of strain transmission and amplification is derived in this section. The schematic diagram of working principle of the whole sensitization structure is shown in Figure 4. The relationship between the pipeline inner pressure p and the strain of FBG is obtained by calculating.  As the core part of the designed structure, the flexure hinge sheet mainly consists of two levels of leverage (first hinge-lever and second hinge-lever), a circle hinge, a guide arm, and a fixed end, as shown in Figure 3. The distances between the points A and B, B and C, E and F, D and E are denoted by L1, L2, L3, and L4, respectively. Besides, b is the width of the narrowest part of the circle hinge. The radius and the thickness of the circle hinge are denoted by r and w, respectively. Moreover, the overall thickness of the flexure hinge sheet is w. The length and width of the whole flexure hinge sheet are Ws and Ls, respectively.

Static Analyses of Structures
For the proposed sensitization structure, the principle of strain transmission and amplification is derived in this section. The schematic diagram of working principle of the whole sensitization structure is shown in Figure 4. The relationship between the pipeline inner pressure p and the strain of FBG is obtained by calculating. Firstly, as shown in Figure 5, the pipeline inner pressure p (Pa) causes the strain on the outer wall of pipeline, and then generate a tension Fx (N) at the two ends of the pipe-clip. Because of the influence of friction and other factors, this can result in the strain's incomplete pass to the pipe-clip. Hence, assuming there is a coupling coefficient  Firstly, as shown in Figure 5, the pipeline inner pressure p (Pa) causes the strain on the outer wall of pipeline, and then generate a tension F x (N) at the two ends of the pipeclip. Because of the influence of friction and other factors, this can result in the strain's incomplete pass to the pipe-clip. Hence, assuming there is a coupling coefficient k p between the pipeline inner pressure and the tension F x on the end of the pipe-clip, as shown in Equation (8). Then, the tension F x is transmitted to the ends of the flexure hinge sheet. The tension on the ends of the flexure hinge sheet is defined as F Ax . Clearly, F x and F Ax are a pair of interaction forces. Subsequently, the beam A-C rotation about point A under the tension FAx and generates a displacement at the point of B (∆B). θ is the deflection angle of A-C. Then, the displacement of point D (∆D) is amplified by the first hinge-lever, and the second hinge-lever. ∆B is along the X-axis direction. Since the guide arm has the function of guidance, ∆D is changed to the Y-axis direction by the guide arm. The amplification effect depends on the leverage ratios and the stiffness of the circle hinge.
Then, the relationship between the tension and displacement of the circle hinge is analyzed. As shown in Figure 6, a circle hinge is used as an example to calculate the actual displacement of the circle hinge. Simultaneously, for simplifying processes of the subsequent analysis. Assuming that: (1) The displacement only occurs at the circle hinge, and the rest of the flexure hinge sheet can be considered to be rigid. (2) The circle hinge only produces rotational displacement.  Subsequently, the beam A-C rotation about point A under the tension F Ax and generates a displacement at the point of B (∆B). θ is the deflection angle of A-C. Then, the displacement of point D (∆D) is amplified by the first hinge-lever, and the second hingelever. ∆B is along the X-axis direction. Since the guide arm has the function of guidance, ∆D is changed to the Y-axis direction by the guide arm. The amplification effect depends on the leverage ratios and the stiffness of the circle hinge.
Then, the relationship between the tension and displacement of the circle hinge is analyzed. As shown in Figure 6, a circle hinge is used as an example to calculate the actual displacement of the circle hinge. Simultaneously, for simplifying processes of the subsequent analysis. Assuming that: (1) The displacement only occurs at the circle hinge, and the rest of the flexure hinge sheet can be considered to be rigid. Subsequently, the beam A-C rotation about point A under the tension FAx and generates a displacement at the point of B (∆B). θ is the deflection angle of A-C. Then, the displacement of point D (∆D) is amplified by the first hinge-lever, and the second hinge-lever. ∆B is along the X-axis direction. Since the guide arm has the function of guidance, ∆D is changed to the Y-axis direction by the guide arm. The amplification effect depends on the leverage ratios and the stiffness of the circle hinge.
Then, the relationship between the tension and displacement of the circle hinge is analyzed. As shown in Figure 6, a circle hinge is used as an example to calculate the actual displacement of the circle hinge. Simultaneously, for simplifying processes of the subsequent analysis. Assuming that: (1) The displacement only occurs at the circle hinge, and the rest of the flexure hinge sheet can be considered to be rigid. (2) The circle hinge only produces rotational displacement.  It shows that the width b(x) of the circle hinge varies with the change of x. Then, the width b(x) and the sectional area A(x) of the circle hinge can be calculated by using Equation (10). b The moment of inertia I(x) of the circle hinge is set up based on the theoretic of mechanics of materials as follows: Due to the flexure hinge sheet's axially symmetric structure, it is reasonable to take half of the structure as a subject for analysis. As shown in Figure 7, there exists a bending moment M and a shear force S in the cross-section D. To simplify the calculation, coefficients K 1 and K 2 are introduced. The displacement of point D can be expressed as Equation (14).
where E is the elasticity modulus of the steel, and G is the shear modulus of the steel. U a , U b , and U c are the tensile, shear, and bending energy, respectively.

Analysis of Pipeline Wall Strain
Thin-walled pipeline is established as a model by Ansys workbench. The material of the pipeline is set as 304 stainless steel. The Young's modulus and Poisson's ratio of the stainless steel are set as 0.33 and 200 GPa, respectively. The length, outer diameter, and Finally, substituting Equation (13) into Equation (14), the strain on FBG can be derived.

Analysis of Pipeline Wall Strain
Thin-walled pipeline is established as a model by Ansys workbench. The material of the pipeline is set as 304 stainless steel. The Young's modulus and Poisson's ratio of the stainless steel are set as 0.33 and 200 GPa, respectively. The length, outer diameter, and wall thickness are 500 mm, 89 mm, and 3 mm, respectively. A static pressure of 1.0 MPa is applied to the inside surface of pipeline, and both ends of the pipeline are set as fixed supports. Figure 8

Analysis of Pipeline Wall Strain
Thin-walled pipeline is established as a model by Ansys workbenc the pipeline is set as 304 stainless steel. The Young's modulus and Poi stainless steel are set as 0.33 and 200 GPa, respectively. The length, ou wall thickness are 500 mm, 89 mm, and 3 mm, respectively. A static pres applied to the inside surface of pipeline, and both ends of the pipelin supports. Figure 8 shows the equivalent elastic strain distribution of under a pressure of 1.0 MPa. As shown in Figure 8, the minimum value is 6.68 × 10 −5 appearing outer wall, and the maximum value is 7.44 × 10 −5 appearing on the pip Figure 9 shows the strain curve along with the pipeline's wall thickn equivalent elastic strain gradually decreases along with the wall thic and the equation of pipeline wall strain and wall thickness is obtaine fitting, as shown in Equation (15). The fitting coefficients R 2 is 0.9988 an As shown in Figure 8, the minimum value is 6.68 × 10 −5 appearing on the pipeline's outer wall, and the maximum value is 7.44 × 10 −5 appearing on the pipeline's inner wall. Figure 9 shows the strain curve along with the pipeline's wall thickness variation. The equivalent elastic strain gradually decreases along with the wall thickness increasing, and the equation of pipeline wall strain and wall thickness is obtained by using linear fitting, as shown in Equation (15). The fitting coefficients R 2 is 0.9988 and shows the wall thickness and strain coincide with a linear relation. The theoretical strain value calculated according to the formula Equation (7) is 6.12 × 10 −5 ; the outer wall strain obtained by finite element is 6.68 × 10 −5 . The relative errors of both values are below 8%; this indicates that the result of the simulations consists well with the theoretical strain value. ε e = −2.5340 × 10 −6 × δ d + 74.231 × 10 −6 R 2 = 0.9988 (15) thickness and strain coincide with a linear relation. The theoretical stra according to the formula Equation (7) is 6.12 × 10 −5 ; the outer wall strai element is 6.68 × 10 −5 . The relative errors of both values are below 8% the result of the simulations consists well with the theoretical strain va = −2.5340 × 10 × + 74.231 × 10 (R 2 = 0.9 Figure 9. Strain along with the pipeline wall thickness variation.

Sensitivity Analysis of the Critical Dimensions
The critical dimensions (pipe-clip thickness δp, first hinge-le hinge-lever L3-L4, and circle hinge radius r) are simulated to further zation ability of the proposed structure. Firstly, the sensitization str according to the initial values provided in Table 1. The whole structu cording to Figure 2. Then, a pressure of 1.0 MPa is applied to the inn line, and the correlation between the pipeline's outer wall strain an structure strain is observed and analyzed. The magnification times ar tio of strain on the sensitization structure and pipeline wall. The s pipeline wall, sensitization structure, and magnification times are pres For the pipe-clip, it is more intuitive to observe amplification effe As shown in Figure 10a, the deformation sensitivity is affected by the δp. As the pipe-clip thickness increases, the deformation value gradu

Sensitivity Analysis of the Critical Dimensions
The critical dimensions (pipe-clip thickness δ p , first hinge-lever L 1 -L 2 , second hingelever L 3 -L 4 , and circle hinge radius r) are simulated to further analyze the sensitization ability of the proposed structure. Firstly, the sensitization structure is modeled according to the initial values provided in Table 1. The whole structure is assembled according to Figure 2. Then, a pressure of 1.0 MPa is applied to the inner surface of pipeline, and the correlation between the pipeline's outer wall strain and the sensitization structure strain is observed and analyzed. The magnification times are defined as the ratio of strain on the sensitization structure and pipeline wall. The strain value on the pipeline wall, sensitization structure, and magnification times are presented in Figure 10. when r = 1.0 mm. Based on the above optimization results, the dimensions are determined as follows: δp = 3 mm, L1-L2 = 3-3 mm, L3-L4 = 13-2 mm, r = 1 mm. Moreover, considering the difficulty of processing and assembly, the remaining parameters are determined as shown in Table  2. Finally, the dimension parameters and material properties of the proposed sensitization structure are confirmed. For the pipe-clip, it is more intuitive to observe amplification effect by deformation. As shown in Figure 10a, the deformation sensitivity is affected by the pipe-clip thickness δ p . As the pipe-clip thickness increases, the deformation value gradually decreases, and the deformation on the pipe-clip end is approximately linear with the pipe-clip thickness δ p , it means that the value δ p should be as small as possible. However, a small value of δ p will increase the processing difficulty. Hence, the value of δ p is set to be 3.0 mm, which is consistent with pipeline wall thickness.
The effect of the first hinge-lever L 1 -L 2 is shown in Figure 10b; the strain on the sensitization structure increases from 190 µε to 310 µε with the increment of L 1 when L 1 < 3 mm, and then decreases to 280 µε when L 1 > 3 mm. As we know, the strain on the pipeline wall is stable. Since the strain on the pipeline wall is much less than the strain on the sensitization structure, the magnification times shows an almost similar tendency to the variation of strain on the sensitization structure. Finally, the value for L 1 -L 2 is determined to be 3 mm-3 mm.
For the second hinge-lever L 3 -L 4 , the strain on the sensitization structure increases from 320 µε to 840 µε with the increment of L 3 (the decrease of L 4 ), as shown in Figure 10c. The strain on the pipeline wall is stable at a certain value of 60 µε. The magnification times also increase with the increment of L 3 , and the magnification times increase to 14 when l 3 = 13 (L 4 = 2). Hence, the value of L 3 -L 4 is set as 13 mm-2 mm.
The sensitivity with the variation of r is plotted in Figure 10d. The strain on the sensitization structure increases from 830 µε to 840 µε, with the radius r increasing to 1.0 mm. Then, the strain on FBG gradually decreased to 780 µε when r > 1.0 mm and the strain on the pipeline wall remained static. This indicates that the sensitivity of proposed structure is very significant when r = 1.0 mm, and the magnification times increase to 14.0 when r = 1.0 mm.
Based on the above optimization results, the dimensions are determined as follows: δ p = 3 mm, L 1 -L 2 = 3-3 mm, L 3 -L 4 = 13-2 mm, r = 1 mm. Moreover, considering the difficulty of processing and assembly, the remaining parameters are determined as shown in Table 2. Finally, the dimension parameters and material properties of the proposed sensitization structure are confirmed.

Sensitization Ability of the Structure
According to the dimensions provided in Table 2, the optimized structure is established. Then, a pressure of 1.0 MPa is applied on the inner surface of pipeline, and both ends of the pipeline are set as fixed supports. The friction conditions between the pipeline and pipe-clip are set as frictional. Both ends of the flexure hinge sheet are fixed to the pipe-clip by bolt connections. The equivalent elastic strain values on pipeline wall and sensitization structure are obtained and shown in Figure 11. The sensitization structure exhibits a uniform strain distribution with a value of 8.40 × 10 −4 . Meanwhile, the strain on the pipeline wall is 6.50 × 10 −5 ; the difference in strain values is obvious. Poisson's ratio of the sensitization structure 0.33

Sensitization Ability of the Structure
According to the dimensions provided in Table 2, the optimized structure is established. Then, a pressure of 1.0 MPa is applied on the inner surface of pipeline, and both ends of the pipeline are set as fixed supports. The friction conditions between the pipeline and pipe-clip are set as frictional. Both ends of the flexure hinge sheet are fixed to the pipe-clip by bolt connections. The equivalent elastic strain values on pipeline wall and sensitization structure are obtained and shown in Figure 11. The sensitization structure exhibits a uniform strain distribution with a value of 8.40 × 10 −4 . Meanwhile, the strain on the pipeline wall is 6.50 × 10 −5 ; the difference in strain values is obvious. In order to get a more precise results of magnification times of the sensitization structure, the internal pressure is increased from 0.1 MPa to 1.0 MPa with 0.1 MPa interval. The strain values under different pressure are shown in Figure 12, and the curve between the pressure values and strain results is plotted. For sensitization structure, the slope of the fitting curve is 843.40, while for pipeline wall strain, the slope of the fitting In order to get a more precise results of magnification times of the sensitization structure, the internal pressure is increased from 0.1 MPa to 1.0 MPa with 0.1 MPa interval. The strain values under different pressure are shown in Figure 12, and the curve between the pressure values and strain results is plotted. For sensitization structure, the slope of the fitting curve is 843.40, while for pipeline wall strain, the slope of the fitting curve is 65.80. The fitting coefficient R 2 are 0.9999 and 0.9993, respectively. Hence, it can be found that there is a stable and good linear relationship between the pressure and the strain. Furthermore, the magnification times of this sensitization structure is 12.81 (843.40/65.80 = 12.81).

Experimental System Setup and Results
The experimental system for pipeline internal pressure detection is built up as shown in Figure 13, which includes a stainless-steel pipeline (with a length of 500.0 mm, a wall thickness of 3.0 mm, and an outer diameter of 89.0 mm), a sensitization structure, a pressure pump with pressure gauge (with a maximum pressure of 3.0 MPa), an FBG demodulator (the model is si255, produced by the TONGWEI Technology Co., Ltd., Shenzhen, China), a spectrum software, and several FBGs. The detailed parameters of FBG are listed in Table 3. Both the ends of pipeline are sealed by flanges, and the sensitization structure is mounted in the middle of the pipeline. Then, by using 353 ND glue, two FBG sensors are attached to the surface of sensitization structure and pipeline outer wall, respectively. The FBG on the sensitization structure is marked as #1FBG, which is parallel to the pipeline axis. The FBG on pipeline wall is marked as #2FBG and is perpendicular to the pipeline axis. The laboratory temperature is maintained at about 25.0 degrees. In order to reduce the effect of the temperature, #3FBG, which is being used for temperature compensation, only has one fixed end. The arrangement of #1FBG, #2FBG, and #3FBG is

Experimental System Setup and Results
The experimental system for pipeline internal pressure detection is built up as shown in Figure 13, which includes a stainless-steel pipeline (with a length of 500.0 mm, a wall thickness of 3.0 mm, and an outer diameter of 89.0 mm), a sensitization structure, a pressure pump with pressure gauge (with a maximum pressure of 3.0 MPa), an FBG demodulator (the model is si255, produced by the TONGWEI Technology Co., Ltd., Shenzhen, China), a spectrum software, and several FBGs. The detailed parameters of FBG are listed in Table 3. Both the ends of pipeline are sealed by flanges, and the sensitization structure is mounted in the middle of the pipeline. Then, by using 353 ND glue, two FBG sensors are attached to the surface of sensitization structure and pipeline outer wall, respectively.

Analyses of Experimental Results
To verify the temperature effect on the testing results, the central wavelength variation of #3FBG in five minutes is recorded, as shown in Figure 14. Obviously, the central wavelength of the #3FBG is almost constant, which means that the temperature remains stable (ΔT = 0). Thus, it is reasonable to ignore the temperature effect when testing the function of the proposed structure.  The FBG on the sensitization structure is marked as #1FBG, which is parallel to the pipeline axis. The FBG on pipeline wall is marked as #2FBG and is perpendicular to the pipeline axis. The laboratory temperature is maintained at about 25.0 degrees. In order to reduce the effect of the temperature, #3FBG, which is being used for temperature compensation, only has one fixed end. The arrangement of #1FBG, #2FBG, and #3FBG is shown in Figure 13. Then, pressurizing the pipeline pressure from 0 MPa to 1.0 MPa with a pressure pump, the center wavelength variations of #1FBG and #2FBG with 0.1 MPa intervals are recorded. To verify the accuracy and reliability of the proposed structure, two samples are tested, and two circle processes of increasing pressure and decreasing pressure are conducted for every sample. Then, the average values of each pressurized cycle or depressurized cycle are recorded and shown in Table 4.

Analyses of Experimental Results
To verify the temperature effect on the testing results, the central wavelength variation of #3FBG in five minutes is recorded, as shown in Figure 14. Obviously, the central wavelength of the #3FBG is almost constant, which means that the temperature remains stable (∆T = 0). Thus, it is reasonable to ignore the temperature effect when testing the function of the proposed structure.
To verify the temperature effect on the testing results, the central wavelength tion of #3FBG in five minutes is recorded, as shown in Figure 14. Obviously, the c wavelength of the #3FBG is almost constant, which means that the temperature rem stable (ΔT = 0). Thus, it is reasonable to ignore the temperature effect when testin function of the proposed structure.  According to the center wavelength variations obtained by #1FBG and #2FBG, the strain values on the proposed sensitization structure and pipeline wall can be obtained and shown in Figure 15. As shown in Figure 15, it can be seen that the center wavelength shift of #1FBG (black line) shows a linear relationship with the change of the pipeline's inner pressure as the pressure increasing, the center wavelength gradually increases. By using linear fitting, the slope of the black line is about 757.27. This means that the strain on the sensitization structure can increase to 757.27 µε/MPa (757.27/1.20 = 631.06 pm/MPa) when the pressure increases by 1.0 MPa. From #2FBG (red line), it can be seen that there also exists a significant linear correlation between the pipeline's wall strain and inner pressure. The slope of the red line is about 65.80 µε/MPa. The related fitting coefficients R 2 are 0.9914 and 0.9993, respectively. It can be concluded that the strain value is obviously expanded by the sensitization structure compared with the wall strain. The sensitivity of the proposed sensitization structure is approximately 9.59 pm/µε, and the strain on the proposed sensitization structure is 11.51 (757.27/65.80 = 11.51) times the strain on the pipeline's outside surface.
Materials 2022, 15, x FOR PEER REVIEW 14 According to the center wavelength variations obtained by #1FBG and #2FBG strain values on the proposed sensitization structure and pipeline wall can be obta and shown in Figure 15. As shown in Figure 15, it can be seen that the center wavelen shift of #1FBG (black line) shows a linear relationship with the change of the pipeli inner pressure as the pressure increasing, the center wavelength gradually increases using linear fitting, the slope of the black line is about 757.27. This means that the st on the sensitization structure can increase to 757.27 με/MPa (757.27/1.20 = 63 pm/MPa) when the pressure increases by 1.0 MPa. From #2FBG (red line), it can be that there also exists a significant linear correlation between the pipeline's wall strain inner pressure. The slope of the red line is about 65.80 με/MPa. The related fitting co cients R 2 are 0.9914 and 0.9993, respectively. It can be concluded that the strain valu obviously expanded by the sensitization structure compared with the wall strain. sensitivity of the proposed sensitization structure is approximately 9.59 pm/με, and strain on the proposed sensitization structure is 11.51 (757.27/65.80 = 11.51) times strain on the pipeline's outside surface.
This shows that the structure has a high sensitivity for pipeline pressure monitor Meanwhile, FBG can establish a distributed measurement system, and multiple sen can be connected in series or parallel. Therefore, multiple FBG sensors can be arran along the pipeline to monitor the pressure in different positions.

Conclusions
This study presented a strain amplifying structure based on FBG. The structure w combinations of flexure hinge and mechanical lever, mainly includes two parts: a fle hinge sheet and a pipe-clip. Firstly, the principle of FBG and stress-state of the pipe This shows that the structure has a high sensitivity for pipeline pressure monitoring. Meanwhile, FBG can establish a distributed measurement system, and multiple sensors can be connected in series or parallel. Therefore, multiple FBG sensors can be arranged along the pipeline to monitor the pressure in different positions.

Conclusions
This study presented a strain amplifying structure based on FBG. The structure with combinations of flexure hinge and mechanical lever, mainly includes two parts: a flexure hinge sheet and a pipe-clip. Firstly, the principle of FBG and stress-state of the pipeline are introduced. Then, a novel structure is designed, and the strain amplification effect is conducted by mechanical analyses. Subsequently, the parameter optimization for the designed structure is operated by FEM, and the optimal size is obtained. Finally, the sensitivity of the structure is confirmed through experiments and the results are analyzed, and the experimental results are consistent with the simulation results. The results demonstrate that this structure can obviously magnify the strain on the pipeline's walls. It has a strain sensitivity of 9.59 pm/µε, which is 11.51 times than the pipeline surface strain. In short, the proposed structure can achieve non-intrusive detection and has a good application prospect in structural health monitoring. Moreover, it has a small size and high sensitivity and has very high practical value.