Displacement measurement is of great significance to monitor the crack variation and ensure the health of building structures. Aiming at the problems of low sensitivity and high temperature error of fiber Bragg grating (FBG) displacement sensors in displacement monitoring, this paper presents an adjustable cantilever beam displacement sensor with the FBGs as the sensing element. The sensor adds double FBGs on the relative surfaces of the equal-strength cantilever beam, which increases the bending deformation on the FBG of the beam surface to improve the sensitivity and realize the temperature compensation of the sensor. By adding an adjustable external rod structure between a flexible spring and a fixed foot stand, the sensor can regulate the range of initial crack width for different occasions. A theoretical analysis of the displacement sensor is performed, and the simulation analysis and optimization design for the structural parameters of the cantilever beam elastic sensitive element are implemented by adopting SolidWorks and ANSYS software. Finally, a displacement testing platform is constructed to test its performance. Experimental results show that this design has a high sensitivity coefficient of 39.47 pm/mm and a temperature coefficient of 1.04 pm/°C in the range of initial crack width from 0 to 110 mm or from 0 to 130 mm depending on different monitoring situations. Furthermore, good linearity, hysteresis delay, repeatability, and temperature compensation performance have also been demonstrated.
Structural health monitoring equipment has been widely used in the fields of building construction, civil tunneling, aeronautics and space, navigational shipbuilding, and national defense installation.1–5 It exploits sensors to gather dynamic information of structural cracks and assess their health status, which prevents financial losses and casualties caused by building collapses. Displacement is an important physical quantity in structural health monitoring. The dynamic variation of cracks can be determined by measuring the change in displacement. Displacement sensors can measure the variation of cracks in building structures. The ability of displacement sensors has an essential practice foundation for further improvement in the health evaluation level of critical engineering structures.6,7 The existing electrical displacement sensor is susceptible to electromagnetic interference and will lead to low precision and large power loss. It is not suitable for long-term monitoring in harsh environments. The fiber Bragg grating (FBG) sensing element has the advantages of small size, high precision, anti-electromagnetic interference, and electrical insulation in signal transmission processing, distributed measurement, and low transmission loss, which can improve the ability of long-time structural monitoring and make it to replace the electrical displacement sensor in harsh environments.8–10
In recent years, several studies on FBG displacement sensing technologies based on different sensitive elastomer structures and different detection principles have been developed by researchers at home and abroad. Sensors were designed by using pre-stretching fiber subjected to displacement, which induced deformation directly by Li et al. and Xiong et al. It has a high sensitivity, but it is easyily damaged because FBG is exposed to air.11,12 A cantilever beam is widely used as a classic displacement sensing mechanism. The deflection of the free end of a cantilever beam can be applied as the displacement input. Wang et al. designed a FBG displacement sensor based on a tape measure structure using a micro-structure elastic transition body, with a sensitivity of 6.33 pm/mm and a range of 500 mm. The sensor chip had a large measuring range and high sensitivity with small size.13 Lv et al. presented a displacement sensor based on two wedge-shaped sliding surfaces and an integrated equal-strength beam structure, with a sensitivity of 11.92 pm/mm in a range of −100–100 mm, and the correlation coefficient of the fitted curve reaches above 0.9996.14 Thomas et al. proposed a FBG displacement sensor for long-range measurement using a mechanical transfer structure, with a displacement sensitivity of 23.80 pm/mm in a measurement range of 0–150 mm.15 A high precision FBG displacement sensor with an embedded spring was developed to monitor structural displacement by Li et al., with a sensitivity coefficient of 23.96 pm/mm and a static relative error of 4.94%.16 Guo et al. proposed a sensor using two pairs of FBG-cantilever-wedge shaped slider structures for detecting displacement, with a measurement range of ±50 mm and a sensitivity of 29.373 pm/mm.17 Guo et al. designed a FBG displacement sensor that adopted a conversion mechanism structure with a wedge-shaped sliding block and an equal-strength beam, with a sensitivity of 34.32 pm/mm in a range of 0–90 mm.18 The displacement sensor consists of a FBG, a thin-walled ring, a steel-spring, and a linear bearing for increasing stability and measurement capabilities designed by Li et al., with a sensitivity of 36.36 pm/mm.19 Zhu et al. invented a displacement sensor with a user-configurable triangle-geometry as a displacement transfer mechanism, with a resolution of 0.270 μm over a wide measurement range of 2.0 cm.20 However, these displacement sensors are not suitable for structural health monitoring due to the low sensitivity, high temperature error, and uncontrollable range of initial crack width.
To overcome the above-mentioned limitations, we report a novel dual-FBG displacement sensor based on an adjustment structure for structural health monitoring. The sensor adds double FBGs on the relative surfaces of the equal-strength cantilever beam, which increases the bending deformation on the FBG of the beam surface to improve the sensitivity and realize the temperature compensation of the sensor. By adding an adjustable external rod structure connecting between a flexible spring and a fixed foot stand, the sensor can regulate the range of initial crack width for different occasions. A theoretical analysis of the displacement sensor is performed, and the simulation analysis and optimization design for the structural parameters of the cantilever beam elastic sensitive element are implemented by adopting SolidWorks and ANSYS software. According to the simulation results, the prototype sensor is developed, and its performance is tested.
II. PRINCIPLE AND STRUCTURE OF SENSOR
A. Structure design of sensor
The displacement sensor mainly consists of equal-strength cantilever beam pasted FBGs, a flexible spring, a drive rod, an external rod, and fixed foot stands. The structural model of the displacement sensor is shown in Fig. 1. The cantilever beam and flexible spring of the sensor are made of stainless steel and spring steel, respectively. The center wavelength of the optical fiber is 1550 ± 0.3 nm. Other parts of the sensor are made of aluminum.
When the displacement sensor is working, the left and right foot stands are fixed at the building surfaces of the measured structural crack. Fixed foot stand 1 connects the housing and the building surface, and fixed foot stand 2 connects the external rod and the building surface. An adjustable external rod structure connects between a flexible spring and a fixed foot stand, so the sensor can regulate the range of initial crack width for different occasions. The crack width variation affects the displacement, transferring through the fixed foot stand and external rod, and the flexible spring is stretched. The spring force generates deformation of the equal-strength cantilever beam. The shift of the central wavelength of the FBGs pasted on the cantilever beam is changed. There is a linear relationship between the output shift of the central wavelength and the measured displacement. Finally, the crack width variation can carry out real-time monitoring.
B. Working principle of sensor
It can be seen that there is a linear relationship between the output shift of the central wavelength and the measured displacement.
III. FINITE ELEMENT MODEL AND ANALYSIS OF STRUCTURAL PARAMETER
A. Finite element model of sensor
In order to analyze the influence parameters of the cantilever beam of the sensor, a finite element analysis using ANSYS Workbench 19.0 is conducted. Model the sensor with Solidworks software, import it into ANSYS software for simulation analysis, set the model material properties, and classify the mesh of the model. Set the cantilever beam model material properties as the stainless steel, with the elasticity modulus of 199 GPa, a density of 7930 kg/m3, and a Poisson’s ratio of 0.29. Set the flexible spring model material properties as the spring steel with an elasticity modulus of 196 GPa, a density of 7810 kg/m3, and the Poisson’s ratio of 0.28. In addition, set the optical fiber model with an elasticity modulus of 72 GPa and a center wavelength of 1550 ± 0.3 nm. Classify the mesh of the model to match the shape and size, and the fixed foot stand and the rod block are set to the tetrahedrons method with a 1.0 mm size of patch conforming unit. The flexible spring block is set to sweep method with a 1.0 mm size of default unit. The cantilever beam block is set to the automatic meshing method with a 1.0 mm size of quad/tri unit. The housing block is set to the automatic meshing method with the default unit. The finite element model of the displacement sensor is described in Fig. 3.
B. Parameter analysis of sensor
As shown in formulas (7) of the theoretical analysis, the length a, the width b, and the thickness h of the cantilever beam are the critical parameters that affect the sensitivity of the displacement sensor. A certain parameter condition is given, and the parameter enumeration method is used, modeling for different key parameters and finite element analysis is implemented. The bottom end of the cantilever beam of the sensor is fixed, and the top end is used as the free end. A tensile force of 0.5 N in the z-direction is applied to the free end of the cantilever beam of the sensor. It can be reached in the stress nephogram of the sensor in the z-direction, as shown in Fig. 4.
The range of parameters a is from 35 to 45 mm with a step of 1 mm, b is from 15 to 25 mm with a step of 1 mm, and h is from 0.05 to 0.6 mm with a step of 0.05 mm. The simulation results are shown in Fig. 5. As shown in Fig. 5, the stress output increases with an increase in a and decreases with an increase in b, while the stress output presents a rapidly decreasing and then slowly decreasing with an increase in 1.5 mm.
In order to analyze the stress distribution of the cantilever beam under the tensile force, the stress nephogram of an equal-strength cantilever beam under different forces of 0.5, 1, 1.5, and 2 N are shown in Fig. 6. It can be seen that the stress distribution of the intermediate zone is equal, and the FBGs should be fixed at the symmetrical position.
IV. EXPERIMENT AND DISCUSSION
The displacement sensor experimental test system is mainly composed of a FBG demodulator, displacement test ruler, temperature control chamber, console, and upper computer. The FBG demodulator adopts the MW4E03A model of Wuhan Maxwell Technology Co., with a built-in laser light source and a sampling frequency of 1–3 Hz; demodulation accuracy is 1 pm, and spectral resolution is less than 1 pm. The center wavelength of FBG is 1550 ± 0.3 nm, the reflectivity is higher than 90%, and the grating length is 10 mm. The displacement ruler has a range of 0–300 mm, and its accuracy is 1 mm. The temperature control chamber is the MQTH1000F model of Zhongkemeiqi Technology Co., with a temperature range of −70 to 150 °C, an resolution of 0.1 °C, an accuracy of 1 °C, a heating rate of 2 °C per minute, and a cooling rate of 2 °C per minute. The displacement sensor test system is established by using the above equipment in Hebei key laboratory of seismic disaster instrument and monitoring technology, as shown in Fig. 7. After studying the displacement measurement characteristics and temperature compensation of the sensor with the system, it can be achieved the performance.
A. Displacement characteristics test
In order to research the displacement characteristics of linearity, sensitivity, repeatability, and hysteresis delay for the sensor, the displacements test is performed from 0 to full range 100 mm with a step of 10 mm, maintaining each displacement point for 10 s and recording the experimental data of stable center wavelength. In addition, the unloading of displacement is back to 0 with the same interval of 10 mm, and the experimental data are recorded. Experimental data are collected at a frequency of 1 Hz by the FBG demodulator. The displacement loading and unloading test process is repeated three times to obtain the relationship curve of the FBG center wavelength shift with the displacement in the loading and unloading process, as shown in Figs. 8 and 9.
According to the fitting curves of averaged displacement experimental results in Fig. 9, it can be found that the displacement measurement sensitivity of the FBG1 on the left surface of the cantilever beam is 19.68 pm/mm, with a fitting determination coefficient of R2 = 0.9999; while the displacement measurement sensitivity of the FBG2 on the right surface of the cantilever beam is 19.79 pm/mm, with a fitting determination coefficient of R2 = 0.9999. Combined with the effects of FBG1 and FBG2, the displacement measurement sensitivity of the displacement sensor is 39.47 pm/mm with a linearity error of 0.5%. In addition, according to the measurement data of the three cycle tests, the maximum center wavelength is 1551.92 nm, the maximum hysteresis ΔHmax is 0.07 nm, which appeared at the displacement of 60 mm in the third cycle test, and the maximum deviation error ΔRmax is 0.14 nm, which appeared at the displacement of 10 mm during the unloading/loading test. Therefore, the maximum hysteresis delay γH in the three cycle tests is calculated γH = ΔHmax/YFS = 0.07%, and the repeatability error γR of the six experimental curves is calculated γR = ΔRmax/YFS = 0.14%. The experimental results show that the designed FBG displacement sensor can meet the engineering needs of a large range and high sensitivity with good stability.
B. Temperature compensation test
When the FBG displacement sensor is used to measure, the center wavelength shift of the FBG will be affected by temperature. To evaluate the temperature compensation performance of the FBG sensor, the variation of center wavelength shift vs temperature change has been tested. The displacement FBG sensor is placed in the temperature control chamber, and the temperature is changed from −20 to 50 °C with a sampling interval of 5 °C. Maintaining each temperature point for 10 min and recording the experimental data of stable center wavelength. The variation curves of the center wavelength shift of FBGs with temperature are shown in Fig. 10.
As seen in Fig. 10, the center wavelength shifts of two FBGs have almost the same temperature sensitivity. The experimental results show that the temperature sensitivities of FBG1 and FBG2 are 13.93 and 14.97 pm/°C, respectively. The dual FBGs can be compensated by subtracting the wavelength shifts of FBG1 and FBG2 during the displacement measurement, and the temperature sensitivity of the displacement sensor is 1.04pm/°C. The maximum temperature effect value is only 0.41 nm (occurring at −15 °C), and the temperature compensation effect of the FBG sensor is significant. If the thermal expansion coefficients of the two fiber gratings are nearly close, the temperature compensation has more obvious effectiveness.
This paper describes a dual-FBG displacement sensor based on an adjustment structure with a cantilever beam sensitive element. The displacement external rod is combined with the spring to regulate the range of the initial crack width. The optimization design and performance test are conducted for the designed sensor through the study method combining simulation analysis and experimental verification. The proposed sensor has a high sensitivity coefficient of 39.47 pm/mm and a low temperature coefficient of 1.04 pm/°C in the flexible displacement range from 0 to 130 mm or from 0 to 110 mm depending on different monitoring situations. Compared with other FBG displacement sensors, the sensor proposed in this paper has the advantages of high sensitivity, good repeatability, and a good temperature compensation coefficient. However, it still has a large promotion space. The sensor has not yet presented a unit of stepless adjustment of the measurement range. In the real experiment, the sensor range is affected because of the high sensitivity. Therefore, the original scheme can be further improved so that it can be used in online monitoring of real field building and other fields as soon as possible.
This work was funded by Langfang Science and Technology Support Plan Project (Grant No. 2022011007), the Open Fund of Hebei Key Laboratory of Seismic Disaster Instrument and Monitoring Technology (Grant No. FZ224106), the Special Fund of Fundamental Scientific Research Business Expense for Higher School of Central Government (Projects for creation teams) (Grant No. ZY20215101), and the National Natural Science Foundation of China (Grant No. 60475028). The research work of this paper was performed at the Hebei Key Laboratory of Seismic Disaster Instrument and Monitoring Technology.
Conflict of Interest
The authors have no conflicts to disclose.
Zhenjing Yao: Methodology (lead); Supervision (lead); Writing – review & editing (lead). Mingyang Li: Conceptualization (equal); Data curation (equal); Writing – original draft (equal). Guangmin Li: Data curation (equal); Formal analysis (equal); Investigation (equal). Mengtao Xing: Investigation (equal); Software (equal); Validation (equal). Ning Chen: Investigation (equal); Software (equal); Validation (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request.