Development of a High-Sensitivity and Adjustable FBG Strain Sensor for Structural Monitoring

. In this paper, a new fber Bragg grating (FBG) strain sensor with adjustable sensitivity is invented. Te sensitivity adjustment, strain sensing, and temperature compensation principles of the sensor and the corresponding formulae are developed. Te prototype sensor specimen is developed, and a series of tests are performed to investigate its strain sensitivity and temperature compensation characteristics. Te results show that the strain sensitivity of the sensor can be adjusted efectively by the cor-respondent L/L FBG parameter, with an acceptable discrepancy within ± 5% of the theoretical value. Te linearity, repeatability, and hysteresis were analyzed, and the errors were 0.98%, 1.15%, and 0.09%, respectively, with excellent performance. When the temperature diference was 20 ° C, through temperature compensation calibration, the error between the monitored strain and the actual strain was within 5% after temperature compensation correction, showing that this new type of FBG strain sensor can meet the strain monitoring needs of various engineering structures and provide reliable data acquisition.


Introduction
With the rapid development of structural health monitoring (SHM) [1][2][3][4][5], the application of new materials and advanced processes, the structural system becomes increasingly complex, and the traditional structural monitoring sensors can hardly meet the long-term monitoring needs.However, due to its small size, light weight, good stability, strong antiinterference, long-distance transmission, and other signifcant advantages of fber Bragg grating (FBG) [6][7][8][9][10][11], it applies for health monitoring of structural performance widely and in-depth, for example, online monitoring of transformers [12], sliding warning of slopes [13], long-term health monitoring of roads [14], corrosion rate monitoring of prestressed structures [15], and real-time monitoring of the full corrosion process of reinforcement in concrete structures [16], monitoring of bridge structures during proof load testing (PLT) [17], and other structural health monitoring studies [18][19][20][21].Strain is an important performance parameter of engineering structures and is closely related to the internal forces and deformation of the structure, so strain monitoring is one of the most important means of obtaining the health status of engineering structures.As a sensor for strain monitoring, the strain sensitivity of a fber Bragg grating is an important indicator of its performance, and the larger the coefcient, the higher the monitoring accuracy.By improving the material properties of fber Bragg gratings, their sensitivity coefcients can be improved.Sridevi et al. [22] developed an etched sensor with a strain sensitivity of 5.5 pm/με by coating graphene on fber Bragg gratings; also for etched sensors, Oliveira et al. [23] fused polymer ZEONEX-480R fber Bragg gratings with silicon fbers as a coating for FBGs, increasing their strain sensitivity to 13.4 pm/με.In addition, some scholars have investigated FBG strain sensors etched with diferent material coatings [24,25], all achieving high sensitivity.Tese etching techniques mainly involve coating the fber Bragg grating, which in turn improves the strain sensitivity of the sensor by changing the efective refractive index of the fber Bragg grating, but the difculty and accuracy of the material fabrication limit their prevalence for monitoring engineering structures.A simple and straightforward way to monitor strain in fber Bragg gratings is to adhere the bare fber Bragg grating to the structure to be measured or to embed the fber Bragg grating in a polymer composite to achieve intelligent monitoring of the structure [26,27], at which point the strain sensitivity of the bare fber Bragg grating is approximately 1.21 pm/με, as the resolution and accuracy of commonly used demodulators are 1 pm and ±5 pm, respectively, the resolution and accuracy of the bare fber Bragg grating strain sensor are 0.8 με and ±4 με, which is difcult to apply to the monitoring of small strains (less than 20 με).Changing the mechanical structure of the sensor can also improve its sensitivity coefcient.Li et al. [28] used an adhesive to fx the fber Bragg grating to the substrate and used the lever principle to amplify the deformation of the measured component sensed by the fber Bragg grating to increase the strain sensitivity of the sensor to 6.2 pm/με; [29] applied the principle of concentrated sensitivity enhancement and developed a sensor with a strain sensitivity of 10.84 pm/με based on a fexible hinge structure; Peng's team combined the above two sensitivity enhancement principles and developed a FBG sensor with a strain sensitivity of 11.49 pm/με [30].Te FBG sensor developed by Nawrot et al. [31] based on the symmetrical double cantilever structure increases the strain sensitivity by more than 30 times and can be used for small strain monitoring of structures.Due to the strain-temperature cross-sensitivity of fber Bragg gratings, the necessary temperature compensation should be applied to FBG strain sensors when there is a temperature change [32][33][34][35][36].
Building structures are subjected to harsh service environments such as wind, vehicles, seismic, sun, and rain.When strain monitoring is carried out by means of direct paste [26,27] or indirect paste [28], the fber Bragg grating is prone to fall of after a long period of environmental action, making it difcult to achieve long-term health monitoring, and direct paste [26,27] is more difcult to produce and install, while indirect paste [28] has a certain impact on the structural force itself due to the greater stifness of the sensor itself.Te use of the hinge [29,30] method for sensors in complex and vibrating engineering structures presents a challenge due to the thin and fragile nature of the hinge, resulting in a low survival rate.Such structures, including bridge engineering and long-span space engineering, are comprised of various components, each with diferent stress states and strain ranges.Te use of a sensor with a fxed and nonadjustable sensitivity coefcient [26][27][28][29][30] is not feasible for monitoring diferent structural parts simultaneously, as it would require an excessive number of sensors and afect mass production and application.In order to improve the production efciency and meet the static and dynamic measurement of multiple parts of the structure, as well as to avoid excessive sensor stifness afecting structural forces, long-term monitoring, and other factors, this paper proposes a high-sensitivity and adjustable FBG strain sensor, and the structure of the sensor is designed based on the principles of strain monitoring and temperature compensation: the stifness of the sensor is close to that of the fber grating itself, which is low and avoids afecting the force of the measured structure and improves the monitoring accuracy; it adopts the screw fxing method, which is easy to be installed on all kinds of structural components in the harsh service environment; it adjusts the ratio between the distance L of the two support fxing tubes and the distance L FBG of the grating pasting point, i.e., L/L FBG , so as to realize the sensitivity adjustability, which applies to the large amount of ranges as well as the monitoring of high accuracy; and it adopts the reference grating method to carry out the temperature compensation of the sensor to eliminate the temperature changes in the harsh service environment on the sensor monitoring performance.On the basis of theoretical and structural design, a series of verifcation tests were designed to verify the performance of the sensor, such as sensitivity adjustment, linearity, repeatability, hysteresis, and temperature compensation.Te excellent sensitivityadjustable FBG strain sensor proposed in this paper can provide fexible monitoring means and technical support for various complex engineering structures and their various components.

Algorithm of FBG Monitoring
A FBG is an optical fber in which the index of refraction within the core of the fber changes along its length, from high-index to low-index.Te modulation of the refractive index causes an FBG to act like a mirror that refects certain wavelengths and transmits others.According to the coupled mode theory, its central wavelength λ B is determined by the refractive index n eff of the core and the grating period Λ is expressed as follows: It can be seen from equation (1) that the variation of the center wavelength of the grating is positively correlated with the refractive index of the core and the grating period.In practical engineering applications, the strain sensor based on FBG is only afected by stress and temperature, which cause the center wavelength of the fber Bragg grating to change.

FBG Strain Monitoring.
When the fber Bragg grating is subjected to axial strain at a constant temperature, the axial strain will change its period and the photoelastic efect will change its core refractive index.At this point, the relationship between the central wavelength shift ∆λ B of the fber Bragg grating and its strain ε FBG is [37,38]: where p e is the efective elasto-optic coefcient, which is generally 0.22 for common quartz fber; and λ B is the center wavelength of the grating.
2 Structural Control and Health Monitoring 2.2.FBG Temperature Compensation.Te main reasons for the change in the center wavelength of the fber Bragg grating are caused by the temperature variations, including the thermal expansion efect of the fber material, the thermo-optical efect, and the photoelastic efect caused by the thermal stress inside the fber.Among them, the thermal expansion will cause the grating period to change, the thermo-optical efect will cause the efective refractive index of the grating to change, and the photoelastic efect coefcient is neglected because it is much smaller than the thermal expansion efect and the thermo-optical efect coefcient.
When the bare fber Bragg grating is only afected by the temperature change, the central wavelength shift of the fber Bragg grating is as follows [39] ∆λ B � ξ F + α F λ B ∆T. ( When the bare fber Bragg grating is afected by strain and temperature at the same time, the central wavelength shifts ∆λ B of the FBG obtained by simultaneous (2) and ( 3) is where ∆T is the temperature variation and ξ F and α F are the coefcients of thermal-optic and thermal expansion for optical fbers, with values of approximately ξ F � 6.55 × 10 − 6 and α F � 0.55 × 10 − 6 , respectively.
When the fber Bragg grating is pasted on the substrate material, as the thermal expansion coefcient of the substrate material is diferent from that of the fber Bragg grating, the fber Bragg grating will be stretched or compressed simultaneously by the thermal expansion efect of the substrate material.If this force due to the diferent thermal expansion coefcients is approximated as an axial force, then the axial strain of the fber Bragg grating by this force is ε FBG � (α M − α F )∆T.
When the fber Bragg grating is pasted onto the substrate material and subjected to temperature variation, only, the center wavelength shift of the fber Bragg grating can be obtained from equation (4) as follows: where α M is the coefcient of thermal expansion of the substrate.
When the fber Bragg grating is bonded to the substrate material and is afected by the strain and temperature at the same time, the central wavelength shift of the fber Bragg grating is obtained from equations (4) and (5).
As can be seen from equation (6), when coupling a fber Bragg grating to a substrate to measure its strain, the change in temperature and the diference in the coefcient of thermal expansion between the fber Bragg grating and the substrate material should be excluded from the amount of change in the central wavelength, otherwise it will result a large error in the measured strain.Terefore, the temperature compensation of the FBG is needed.Te FBG strain sensor in question is made of stainless steel and has a coefcient of thermal expansion of α M � 1.5 × 10 − 5 .

Design of the New FBG Strain Sensor with Adjustable Sensitivity
Te section view of the new FBG strain sensor with adjustable sensitivity is shown in Figure 1.Te sensor consists of two fxed tubes, two clamping rods, springs, protective tubes, and an optical fber engraved with strain gratings and temperature-compensated gratings.Considering the infuence of the stifness and paste of the fber grating on the sensitivity and the deviation of the temperature on the strain monitoring, the strain grating on the optical fber is placed in the middle of the two clamping rods, and the temperaturecompensated grating is placed in the clamping rod at one end.Among them, the L segment is covered with a bare fber protection tube.After the two ends of the L segment are sealed, the optical fber and the temperature-compensated grating are attached in the groove of the clamping rod using an adhesive, and then the optical fber is extended to the outside of the fxed tube.Ten the spring protected with a protective sleeve is assembled, both ends are sleeved outside the clamping rod, and the spring needs to be preloaded during assembly to make the optical fber in a tightening position; the assembly of the clamping rod and the bearing fxed tube at both ends is connected by internal and external threads; fnally, the optical fbers at both ends run through the clamping rod and the support fxed tube in turn.Among them, the optical fber jumper protection tube is set outside the two support fxed tubes to protect the optical fber and install it on the measured object through the support.After the processing of the whole structure is completed, the suspended part of the fber Bragg grating is protected by glue.Te stifness of this FBG strain sensor is very small and is essentially equivalent to that of a fber Bragg grating.When the sensor is installed on the specimens, the support fxed tube slides with the displacement of the specimens, causing the wavelength of the strain grating changes, and the wavelength change of the temperature compensation grating is only afected by temperature.
Let the distance between the optical fbers at the two ends of the strain grating at the attachment point of the clamping rod be L FBG , and the distance between the midpoints of the two fxed tubes be L.When the fxed tubes slide with the strain of the specimens to be measured, the stifness of the optical fbers is much less than that of the clamping rod and the fxed tube, so the elongation of the optical fbers and the fxed tube can be presumed to be the same, i.e., ∆L � ∆L FBG .Let the strain of the object to be measured be ε, and the strain of the strain grating be ε FBG .Te ratio between the two is Structural Control and Health Monitoring From the above equation, the ratio of the strain ε FBG of the strain grating to the strain ε of the object to be measured is equal to the ratio of the distance between the midpoints of the two fxed tubes and the distance between the attachment points of the fbers at the ends of the strain grating.
Te relationship between the shift of the central wavelength of the fber Bragg grating and the strain ε of the measured object without the infuence of temperature can be obtained by combining equations ( 2) and ( 7) as follows: From equation ( 2), the strain sensitivity coefcient of the bare grating is K ε � (1 − P e )λ B for universal FBG sensors from equation (8) for the new sensor, the strain sensitivity coefcient of the strain sensor is Comparing the two sensitivity coefcients, it can be seen that changing the ratio between L and L FBG can adjust the sensitivity of the strain sensor.When the strain ε of the measured object is less than the limit strain ε FBG of the strain grating, the sensitivity needs to be increased to make L > L FBG ; when the strain ε of the measured object is greater than the limit strain ε FBG of the strain grating, it is necessary to expand the monitoring range and reduce the sensitivity.By extending the clamping rod, the distance between the two fxed tubes is reduced, and the two sticking points of the optical fber in the groove of the clamping rod are moved outward, so that L < L FBG can be achieved.In practice, L can be determined according to the installation space of the measured object and the required range.According to equation (8), L FBG can be determined theoretically to determine the distance between the two clamping rods; this is the principle of the sensor with adjustable sensitivity.
When the sensor is afected by both strain and temperature, the relationship between the two can be obtained by combining equations ( 6) and ( 7) as follows: Let the temperature sensitivity coefcient of the strain grating be 9) can be simplifed as follows: where the temperature variation ∆T can be obtained by the temperature compensation grating.Let the initial central wavelength of the temperature compensation grating be λ B,T , the central wavelength shift be ∆λ B,T , and the temperature sensitivity coefcient be From equation ( 5): ∆T � ∆λ B,T /K T−T , substitute into equation (10): where the strain sensitivity coefcient K ε−S and the temperature sensitivity coefcient K T−S of the strain grating and the temperature sensitivity coefcient K T−T of the temperature compensated grating can be obtained by the calibration of the sensor.Tis is the principle of temperature compensation of the strain sensor using the temperature reference grating method.At present, the key efort in this paper is to enhance the strain sensitivity coefcient by reducing the stifness of the fber Bragg grating paste section of the conventional FBG strain sensor, but the degree of stifness reduction is limited, and once the sensor is processed, the sensitivity coefcient is fxed.Te stifness of the FBG strain sensor developed in this paper has been reduced to be equal to the stifness of the fber Bragg grating.Te stifness of the fber Bragg grating is almost negligible compared to the stifness of the measured structure, and the sensitivity adjustment can therefore be  It can be seen from equation ( 8) that the theoretical strain sensitivity coefcient K ε−S of the FBG strain sensor is positively correlated with L/L FBG , so the sensitivity coefcient can be adjusted by controlling the value of L/L FBG .In order to verify the reliability of this method, the distance L between the midpoint of the fxed tube and the distance L FBG between the optical fber sticking points is taken as the change parameter.According to the fact that the total length of the specimen is 137 mm, L is 70 mm∼80 mm, and L FBG is 40 mm∼50 mm, the specifc parameters are shown in Table 2: Based on the above materials and parameters, the physical diagram of the developed FBG sensor is shown in Figure 2.

Strain sensitivity Test of Strain Grating.
Sensitivity is an important performance index of the sensor, refecting its sensitivity to external stress and strain.In general, there is a serious constraint relationship between sensitivity and monitoring range.According to practical engineering applications, the sensitivity should be improved as much as possible when a certain monitoring range is guaranteed.Te specifc steps of the strain sensitivity test of the FBG strain sensor are as follows: (1) In the constant ambient temperature of 20 °C, the strain sensor is fxed on the displacement platform, and the fber grating demodulator is connected with the jumper.(2) Use the vernier caliper to check L, clear the displacement meter, and read the initial center wavelength value λ B of the strain grating from the software system; (3) Increase from 0 με to 3000 με at a rate of 600 με per step displacement and perform the grading test.Te displacement of each step is held for 5 minutes and the central wavelength reading λ i of each step strain grating is recorded.(4) Te strain unloading is carried out with a displacement of 600 με per stage, and the unloading process is the same as that of (3), forming a cycle; (5) Repeat steps (3)∼(4) twice.Te accuracy of the displacement meter used in the test is 0.001 mm, the accuracy of the displacement table is 0.69 × 10 −3 mm, and the wavelength resolution of the fber grating demodulator is 0.1 pm.Te device is shown in Figure 3. Taking the central wavelength shift ∆λ of each level of the strain grating as the vertical coordinate and the strain value as the horizontal coordinate, the diagram is drawn and linearly ftted.Te experimental results are shown in Figure 4.
Figure 4 shows that the wavelength shift ∆λ of the strain grating is positively correlated with the strain ε during loading and unloading, with a linear correlation coefcient of 99.97% or more.Te slope of the curve is the strain sensitivity coefcient K ε−S .Te average value of the strain sensitivity coefcient for the six positive and reverse itineraries was taken as the test value of the strain sensitivity coefcient K ε−S,M and compared with its theoretical value, and the data were compiled as shown in Table 3.
According to Table 3, as the L/L FBG value increases, the strain sensitivity coefcient of the sensor increases proportionally, and the error of its theoretical value is very small, all within 5%.Te error between the experimental value and the theoretical value of the sensitivity coefcient of S 1 , S 2 , and S 3 sensors is −2.08%, 0.10%, and −4.84%, respectively.Te experimental results show that the sensitivity coefcient can be adjusted by changing the value of L/L FBG .
In order to verify the real performance of FBG strain sensors, the linearity, repeatability, and hysteresis of the strain sensitivity coefcients are analyzed using the S 2 sensor as an example.

Linearity analysis of the Strain Sensitivity Coefcient
Te linearity of the FBG sensor strain sensitivity refects the degree of linear correlation between the test value and the linear ftting curve value during the sensitivity calibration.Te smaller the linear error, the greater the correlation, indicating better linearity.
Let the wavelength shift corresponding to each strain level be the average value ∆λ i of the three repeated test values, where i � 1 ∼ 6; the least square method is used to linearly ft the ∆λ i of the positive and reverse itineraries, and the ftting curve is shown in Figure 5.
Te ∆λ i and its ftting value ∆λ i,m and the error ∆λ i − ∆λ i,m between them are obtained under the 6 levels of strain for positive and reverse itineraries, as shown in Table 4.
Assuming that ∆λ i corresponding to the maximum strain 3000 με is ∆λ max and ∆λ i corresponding to the minimum strain 0 με is ∆λ min , the sensitivity linear error can be expressed as follows: Structural Control and Health Monitoring Table 1: Comparison of the characteristics of the FBG strain sensors designed in this paper with those of conventional FBG strain sensors.

Comparative items
Te FBG strain sensors designed in this paper

Conventional FBG strain sensors
Accuracy of monitoring Te structure has low stifness and is easily deformed.Whether monitoring large or small strains, the monitoring sensitivity and measurement accuracy are high When used for small strain measurements, the monitoring accuracy is low Measurement range Te adjustable range is large, which is not only suitable for strain monitoring with a smaller limit strain than the fber grating itself, but also suitable for strain monitoring with a larger limit strain than the fber grating itself It is difcult for the range of the external sensor to exceed the ultimate strain of the fber grating itself Whether or not it afects the forces on the member under test Te stifness of the sensor is very small, close to the stifness of the fber grating itself, and does not change the stress state of the measured component Sensors are used for the monitoring of small stress components, which afect the stress state of the measured components Quality of installation Te support can be fxed with a small force when it is installed.It can be clamped or welded.Te installation is convenient and reliable, and the quality is easy to guarantee As the sensor has a certain stifness, it is possible to produce deformation or cracks in the support after use Initial error Tere is a pretension after fabrication of the fber Bragg grating, and there is no initial error for fabrication and installation It is possible to produce initial errors 6 Structural Control and Health Monitoring It can be seen from the data in Table 4 that max(∆λ i − ∆λ i,m ) � 56.35 pm, ∆λ max � 5759.2 pm, and ∆λ min � 0.67 pm, and the sensitivity linearity error δ � 0.98% can be obtained by substituting it into equation (12), indicating that the FBG strain sensor has good linearity.

Repeatability analysis of the Strain Sensitivity Coefcient K ε−S .
Te repeatability of the FBG sensor strain sensitivity determines whether it can complete the monitoring task and ensure the accuracy of the monitoring data.It refects the degree of deviation in wavelength shift caused by the same strain in diferent paths during sensitivity calibration.Te smaller the repeatability error is, the higher the stability of the monitoring will be.
Assuming that the three repeated test values of the wavelength variation corresponding to the same strain in diferent orders are ∆λ R−mn and the average value is ∆λ R−n , where m � 1 ∼ 3, n � 1 ∼ 6, plot the sensor strain grating K versus time, as shown in Figure 6.
From Figure 6, ∆λ R−mn and ∆λ R−n can be obtained, then the standard deviation of the sensitivity value of the sensor for three repeated tests can be expressed as follows:

Structural Control and Health Monitoring
Combined with the data in Figure 6 and equation ( 13), the standard deviation of the sensitivity repeatability of the sensor at each strain level can be obtained, as shown in Table 5.
Te equation for the sensitivity repeatability error is as follows: Combined with Tables 4 and 5, the maximum standard deviation is ∆σ n,max � 22.036 pm; ∆λ max − ∆λ min � 5758.53 pm when the confdence probability is 99.7%, the confdence       15% can be obtained by substituting it into formula (14), indicating that the FBG strain sensor has good stability.

Hysteresis Analysis of the Strain Sensitivity Coefcient
Te hysteresis of the FBG sensor strain sensitivity is mainly caused by the sensor material and the fxed condition of the support, which refects the degree of error between the wavelength changes of diferent paths corresponding to the same strain level when the sensitivity calibration is the full range output, i.e., the maximum diference between the forward and reverse strokes at the same strain is analyzed against the full range output value.Te smaller the hysteresis error, the higher the monitoring accuracy.
Let the wavelength shift of the positive and reverse itinerary corresponding to each level of strain is the average value ∆λ pi and ∆λ ri of the three repeated test values, where i � 1 ∼ 6.Based on Table 4, the hysteresis error analysis data are shown in Table 6.
Assuming that ∆λ pi and ∆λ ri corresponding to the maximum strain 3000 με are ∆λ p,max and ∆λ r,max , respectively, and ∆λ pi and ∆λ ri corresponding to the minimum strain 0 με are ∆λ p,min and ∆λ r,min , respectively, then the sensitivity hysteresis error can be expressed as follows: It can be seen from the data in Table 6 that max(∆λ pi − ∆λ ri ) � 5.23 pm, max(∆λ p,max − ∆λ p,min , ∆λ r,max − ∆λ r,min ) � 5758.53 pm, and the sensitivity hysteresis error c d � 0.09% can be obtained by substituting it into equation (15), indicating that the FBG strain sensor has high monitoring accuracy.

Calibration Test of Temperature Sensitivity Coefcients K T−S and K T−T of Strain and Temperature Compensated
Grating.Te S 2 sensor is selected to calibrate the temperature sensitivity coefcient.Te initial center wavelength of the strain grating is 1543.6654nm, and the initial center wavelength of the temperature grating is 1535.4299nm.By theoretical calculation, K T−S � 28.359pm/ °C, and K T−T � 28.207 pm/ °C.Te strain grating and the temperature compensation grating on the strain sensor are recorded as FBG ε and FBG T , respectively.Te calibration test steps for the temperature sensitivity coefcient are as follows: (1) Te strain sensor is put into a heating vessel flled with pure water, and the fber grating demodulator is connected to a jumper.(2) Te initial temperature of the water is set to 20 °C, and the temperature gradually increased to 70 °C with an increment of 10 °C e.At the same time, a thermometer is used to measure whether the water temperature is consistent with the indication of the thermostatic bath to avoid reading errors.During the period, the FBG ε and FBG T center wavelength readings corresponding to the demodulator are recorded by the software system.(3) cooling to 20 °C at a rate of 10 °C per stage; the process is the same as (2), forming a cycle; (4) Repeat steps (2)∼(3) twice.Te accuracy of the thermostat vessel used in the experiment is 0.001 °C, the accuracy of the thermometer is 0.1 °C, and the wavelength resolution of the fber grating demodulator is 0.1 pm.Te device is shown in Figure 7.
Taking the drift ∆λ of the central wavelength of each level of the grating relative to the initial central wavelength as the vertical coordinate and the temperature variation ∆T as the horizontal coordinate, the diagram is drawn and linearly ftted.Te test results are shown in Figures 8 and 9.
As it can be seen from Figures 8 and 9, the wavelength shifts ∆λ of the two gratings is positively correlated with the temperature variation ∆T, with a linear correlation coefcient of 99.97% or more.Te slope of the linear ftting curve is the temperature sensitivity coefcients K T−S and K T−T of the FBG strain sensor.Te average value of the temperature sensitivity coefcients of the six positive and reverse itineraries was taken as the test values K T−S,M and K T−T,M of the strain sensitivity coefcients of the sensor and compared with their theoretical values, and the compiled data are shown in Table 7.
From Table 7, the temperature sensitivity coefcient of this FBG sensor has a small error with its theoretical values of −0.79% and 0.29%, respectively.
To further verify the performance of the two gratings of the FBG strain sensor when the temperature changes, the linearity, repeatability, and hysteresis of the temperature sensitivity coefcients K T−S and K T−T of the strain grating and the temperature-compensated grating of the sensor are examined with reference to Section 4.2.1-4.2.3.Te corresponding errors of K T−S are −0.92%,1.13% and 0.45%, respectively.For K T−T , the values are −0.91%,1.15%, and −0.23%, respectively.Te analysis results show that the Structural Control and Health Monitoring strain performance of the two gratings is excellent when the temperature changes.

Temperature compensation Validation Test.
To verify the accuracy of strain monitoring of the FBG strain sensor under diferent temperature environments, the temperature in the constant temperature chamber was increased to 40 °C (i.e., 20 °C higher than the temperature when K ε−S was calibrated).Te FBG strain sensor was loaded and unloaded at all strain levels according to the calibration process of K ε−S in Section 4.2, and the central wavelength changes of the strain grating and the temperature grating under each level of strain were recorded and compared.
According to equation (11), when the FBG strain sensor is subjected to both temperature and axial force, its strain due to axial force can be expressed as follows:    where ∆λ B is the diference between the center wavelength of the strain grating at all strain levels at the validation test room temperature of 40 °C and the center wavelength at zero strain at the strain calibration test room temperature of 20 °C.∆λ B,T is the diference between the center wavelength of the temperature-compensated grating at the validation test room temperature of 40 °C and the center wavelength at the strain calibration test room temperature of 20 °C.Te coefcients K ε−S , K T−S , and K T−T are taken from the calibrated test values and are 1.928 pm/με, 28.135 pm/με, and 28.126 pm/με, respectively.Te initial center wavelengths of the strain grating and temperature-compensated grating for the strain calibration were 1543.6654nm and 1535.4299nm, respectively.Te experimental data are listed in Table 8.
Te strain ε S in Table 8 represents the strain values at all levels, which is also the actual strain of the FBG sensor; ε T is based on the measured data in equation ( 16) to calculate the strain of the sensor monitored by the strain grating after temperature compensation.From the analysis results, it can be seen that the errors at all levels of strain are positive values, which means the test monitoring value after temperature compensation is greater than the real strain.Te reason may be caused by the structure of the sensor itself.Because the temperature compensation grating is bonded to the clamping rod of stainless steel, the actual temperature may be greater than the temperature of the strain grating suspended in the spring, so the compensated strain is slightly larger, but the error is within 5%.Tis indicates that the temperature reference grating method can be used to compensate for the strain due to temperature in the FBG sensor in the presence of both temperature and stress, thus accurately monitoring the strain due to stress and providing accurate strain monitoring data for the test object.
According to the test results in Sections 4.2 and 4.3, the performance of the FBG strain sensor developed in this paper is further compared with the conventional ones, as shown in Table 9.As can be seen from the table, the FBG strain sensor developed in this paper realizes adjustable sensitivity and temperature compensation, and a series of tests and quantitative analysis are carried out on the linearity, repeatability, and hysteresis performance of its sensitivity, which provides fexible monitoring means and technical support for diferent complex engineering structures and their various components.

Conclusions
In this paper, a new sensitivity adjustable FBG strain sensor is designed, its strain sensing algorithm and temperature compensation algorithm are theoretically and experimentally investigated, and the following conclusions are reached: (1) Te strain sensitivity of the strain sensor is adjusted to meet the monitoring requirements of diferent engineering structures by adjusting the ratio of the distance between the midpoint of the two fxed tubes and the distance between the paste points at the two ends of the grating, i.e., the value of L/L FBG .In the calibration test, the strain sensitivity test value was within ±5% of the theoretical value, and its linearity, repeatability, and hysteresis were less than 1.2%, indicating excellent strain performance.(2) Further temperature compensation verifcation tests were carried out on the sensor, and when the temperature diference was 20 °C, the error between the monitored strain and the actual strain was within 5% after correction by temperature compensation.Tis FBG strain sensor can meet the needs of different engineering structures for strain monitoring and provides reliable data acquisition.(3) Te temperature sensitivity coefcients of the strain grating and temperature-compensated grating of the FBG sensor were calibrated, and the error between the test value and the theoretical value of the two grating temperature sensitivity coefcients was within ±1%, and their linearity, repeatability, and hysteresis were less than 1.2%, indicating their excellent temperature performance.(4) Te temperature compensation equation was derived based on the temperature reference grating method, and a temperature compensation verifcation test was carried out at a temperature diference of 20 °C.Te analysis results showed that the error between the monitored strain and the actual strain was within 5% at all strain levels, indicating that the temperature reference grating method can compensate well for the strain generated by temperature, thus providing reliable monitoring data for the analysis of the internal force of the structure under the coupling efect of force and temperature.

Figure 6 :
Figure 6: Wavelength shift-time curve for three repetitions of the sensor.

Figure 8 :
Figure 8: Fitting curves for temperature sensitivity K T−S .

Figure 9 :
Figure 9: Fitting curves for temperature sensitivity K T−T .

4
Structural Control and Health Monitoring achieved by changing the ratio between L and L FBG .Even after the sensor is processed, the distance L can be changed to achieve the sensitivity adjustment.Due to the essential diference in structural design, the FBG strain sensor developed in this paper has the following remarkable characteristics compared with the conventional FBG strain sensor, as shown in

Table 1 : 4. Prototype Testing of the New FBG Strain Sensor 4
[40]ensor Material and Structural Parameters.According to the structure diagram in Figure1, the material selection for each part of the sensor is as follows: Te clamping rod is an important part of the fber Bragg grating.Based on the research results of the team on the bonding performance of optical fber, the spacing should not be less than 40 mm[40], the diameter is 4∼8 mm, and considering the monitoring condition, the material selected was 304 stainless steel.Te support fxed tube is fxed to the measured component by clamping or welding methods.Combined with the size of the common support, the length of 25 mm, the wall thickness of 3 mm, and the substrate of 304 stainless steel pipes are selected and its inner diameter is matched with the clamping rod.Te compression spring adopts 65 Mn spring steel with good elasticity and high fatigue strength.Te protective tube is made of stainless steel circular tube adapted to support the fxed tubes; the optical fber jumper protection tube is made of 304 stainless steel circular tubes, 25 mm in length, 2 mm in wall thickness, and 7 mm in outer diameter.

Table 2 :
FBG sensor number and parameters.

Table 3 :
Strain sensitivity K

Table 4 :
Linearity error analysis of the strain sensitivity coefcient K ε−S .

Table 6 :
Hysteresis error analysis of the strain sensitivity coefcient K ε−S .

Table 5 :
Standard deviation analysis of the strain sensitivity coefcient K ε−S .

Table 7 :
Temperature sensitivity coefcients K T−S and K T−T .

Table 8 :
Error analysis for all levels of strain after temperature compensation.

Table 9 :
Comparison of the performance of FBG strain sensors developed in this paper with conventional FBG strain sensors.