Fiber Bragg Grating Strain Sensors Research Articles

Particle Filter for temperature compensation of FBG strain sensors for event segmentation

Structural Health Monitoring (SHM) plays a crucial role in assessing the integrity and performance of structures. Fibre-Bragg-Grating (FBG) technology has emerged as a valuable tool for strain measurements in SHM applications. However, FBG strain sensors are susceptible to temperature variations that can confound accurate strain measurements, potentially leading to errors in fatigue damage calculations and event detection. This research addresses the challenge of temperature compensation in FBG-based SHM setups. Instead of the traditional approach of placing temperature sensors near every strain sensor, which can escalate costs and complexity with a growing number of sensors, we propose a filter-based alternative. The proposed approach leverages the slower strain changes induced by temperature effects compared to those caused by external loads, e.g. a passing train. The key innovation lies in a filtering method that isolates temperature-induced strain variations as filtered data while treating load-induced strain as process noise. We explore the application of state-based filters such as the Kalman Filter (KF) and Particle Filter (PF). While the KF is limited to normally distributed noise, which does not represent load-induced strain effectively, the PF can handle various, adjustable noise distributions, that can be tailored to specific requirements. The research showcases the PF's ability for temperature compensation on multiple structures, such as a pedestrian bridge equipped with only 8 temperature sensors for 82 strain sensors loaded either in tension or compression. This novel approach enables more reliable strain measurements of events for detection and analysis in SHM systems.

Assessment of Tunnel Lining Stability through Integrated Monitoring of Fiber Bragg Grating Strain and Structural Deformation.

Tunnel excavation induces the stress redistribution of the surrounding rock. Structural cracks may develop in the secondary lining due to this stress redistribution and bias pressure, consequently affecting the overall construction safety of the tunnel. This paper aims to achieve real-time monitoring of the excavation stability of the lining structure by integrating two monitoring technologies: structural deformation monitoring and fiber grating strain monitoring. Additionally, it proposes a method to simultaneously measure the thermal strain and applied stress-strain of the structure. By analyzing the displacement and deformation of the lining structure, its stability can be preliminarily evaluated in the short term. To achieve long-term real-time monitoring and a more accurate assessment of the tunnel structure's stability, the paper introduces fiber Bragg grating (FBG) strain sensor monitoring technology. First, based on the geological stratigraphy information obtained from the exploration, a simulation model of the tunnel under different section bias angles is established. The displacement and stress concentration areas of the lining structure are then analyzed to optimize the sensor deployment array and provide a theoretical basis for the sensor arrangement. FBG strain sensors are installed on the surface of the structure to measure thermal strain and loading stress-strain, whereas FBG temperature sensors measure local temperature. The findings indicate that following tunnel excavation, the maximum daily strain differences at K107+043 and K107+240 were 126.87 µε and 209.38 µε, respectively. After a period of rock disturbance, the average daily strain differences due to applied stress-strain were 16.8 µε and 12.65 µε, respectively. The thermal strain was close to the daily strain difference. Therefore, after the rock disturbance subsided, the strain fluctuations in the lining structure were mainly caused by local temperature changes, and the surrounding rock tended to stabilize. This offers a viable method for evaluating structural stability post-tunnel excavation.

Structural damage detection based on structural macro-strain mode shapes extracted from non-stationary output responses

Abstract Long-gauge fiber Bragg grating strain sensors have been widely employed because of their broader measuring range and higher sensitivity. However, current structural damage detection methods using macro-strain modal parameters are based on structural frequency response function or stationary power spectrum density, which are not applicable to non-stationary responses. To overcome this limitation, an improved method is proposed in this paper for structural damage detection based on structural macro-strain responses under unknown multi-point non-stationary excitations. First, a new concept of macro-strain energy spectrum transmissibility (MEST) is proposed using structural non-stationary macro-strain responses, and it is derived that MEST at a certain system pole equals the ratio of macro-strain mode shape. Then, the singular value decomposition technique is adopted for the MEST matrix to identify structural natural frequencies and macro-strain mode shapes. Finally, two damage detection indicators are constructed based on the identified normalized macro-strain mode shape (NMMS). The first indicator is the difference in structural NMMS before and after structural damage. The second one is based on the curvatures of structural NMMS, which can be used for structures without intact baseline. Numerical verifications are conducted to identify beam-type structural damage under multi-point non-stationary excitations or vehicle loads. Five damage scenarios with different measurement noise levels are investigated, and damage detection results validate the effectiveness of the proposed method.

Discontinuous Deformation Monitoring of Smart Aerospace Structures Based on Hybrid Reconstruction Strategy and Fiber Bragg Grating.

A hybrid enhanced inverse finite element method (E-iFEM) is proposed for real-time intelligent sensing of discontinuous aerospace structures. The method can improve the flight performance of intelligent aircrafts by feeding back the structural shape information to the control system. Initially, the presented algorithm combines rigid kinematics with the classical iFEM to discretize the aerospace structures into elastic parts and rigid parts, which will effectively overcome structural complexity due to fluctuating bending stiffness and a special aerodynamic section. Subsequently, the rigid parts provide geometric constraints for the iFEM in the shape reconstruction method. Meanwhile, utilizing the Fiber Bragg grating (FBG) strain sensor to obtain real-time strain information ensures lightweight and anti-interference of the monitoring system. Next, the strain data and the geometric constraints are processed by the iFEM for monitoring the full-field elastic deformation of the aerospace structures. The whole procedure can be interpreted as a piecewise sensing technology. Overall, the effectiveness and reliability of the proposed method are validated by employing a comprehensive numerical simulation and experiment.

Rotation angle sensor based on magnetostrictive materials and fiber Bragg gratings

We present a sensor concept for measuring rotation angle based on magnetostrictive materials and fiber Bragg grating strain sensors. The fiber optic strain sensors are used to measure strain in developed in the magnetostrictive rods due to the rotating permanent magnets. The measured strain is related to the angle of rotation. Numerical modeling was performed to investigate the response of magnetostrictive rods due to different angular orientation of magnets. A prototype based on a pendulum was designed to measure the angle with respect to the direction of gravity. Experimental evaluation of its performance revealed a large amount of hysteresis present in the strain data. Finally, we provide some suggestions for further improvement of the design to improve performance and reduce the amount of hysteresis.

Dual-parameter combined measurement sensor based on tri-metal structure

Simultaneous measurement of strain and temperature in vibrating environments has always been a key technical issue in the field of structural health monitoring. To address the bottleneck of inadequate dual-parameter measurement performance in existing Fiber Bragg Grating (FBG) strain and temperature sensors, a new type of fiber optic grating sensor with anti-vibration capabilities for the measurement of both strain and temperature is proposed. The sensor utilizes a flexible hinge structure made of 304 steel with high elastic modulus for strain sensitization and a bimetallic structure composed of 7075 aluminum and 4 J36 Invar alloy for temperature sensitization, integrating both types of sensors. Theoretical analysis of the sensor was conducted, followed by the fabrication of a prototype and the establishment of a testing system for performance evaluation. The results show that the designed dual-parameter FBG sensor has a strain sensitivity of approximately 3.06 pm/µε, about 2.62 times that of a bare FBG, and a temperature sensitivity of about 50.2 pm/℃, roughly 4.97 times that of a bare FBG. In anti-vibration performance tests between 5–100 Hz, the wavelength drift of the strain and temperature sections of the FBG in the sensor were both within 1 pm, meeting the requirements for simultaneous measurement of strain and temperature in vibrating environments. These findings provide a reference for the development of similar sensors and further improvement of the measurement performance of FBG strain and temperature sensors.

Temperature-Compensated Fiber Bragg Grating Strain Sensor Based on a Two-Tap Microwave Photonic Filter

Temperature-Compensated Fiber Bragg Grating Strain Sensor Based on a Two-Tap Microwave Photonic Filter

Diagnosis and Monitoring of Tunnel Lining Defects by Using Comprehensive Geophysical Prospecting and Fiber Bragg Grating Strain Sensor.

Tunnel excavation induces the stress redistribution of surrounding rock. In this excavation process, the elastic strain in the rock is quickly released. When the maximum stress on the tunnel lining exceeds the concrete's load-bearing capacity, it causes cracking of the lining. Comprehensive geophysical exploration methods, including seismic computerized tomography, the high-density electrical method, and the ultrasonic single-plane test, indicated the presence of incomplete distribution of broken rock along the tunnel axis. Based on the geophysical exploration results, a carbon-fiber-strengthened tunnel simulation model was established to analyze the mechanical characteristics of the structure and provide a theoretical basis for sensor deployment. Fiber Bragg grating (FBG) strain sensors were used to measure the stress and strain changes in the second lining concrete after carbon reinforcement. Meanwhile, one temperature sensor was installed in each section to enable temperature compensation. The monitoring results demonstrated that the stress-strain of the second lining fluctuated within a small range, and the lining did not show any crack expansion behavior, which indicated that carbon-fiber-reinforced polymer (CFRP) played an effective role in controlling the structural deformation. Therefore, the combined detection of physical exploration and FBG sensors for the structure provided an effective monitoring method for evaluating tunnel stability.

A monitoring method of rail fastener reaction force based on iron pad strain

This research has successfully explored a monitoring method that does not necessitate modifications to the current structure of the fastening system and ensures that the intrinsic force distribution remains undisturbed, which is the pioneering use of Fiber Bragg Grating (FBG) strain sensors to test the strain of iron pads to reflect the force of fastener support points. Then, through the laboratory single-point loading test and finite element simulation, the feasibility of the monitoring method has been confirmed, and the resolution is higher than the traditional method. Subsequently, based on the experimental environment of high-speed railway commissioning, dynamic long-term monitoring research was conducted, and relevant calibration experiments and finite element simulation analyses were carried out. The experimental research and finite element simulation analysis revealed the superior ability of the method in capturing intricate data details, with the field experiment verifying a high resolution markedly surpassing other existing methods. Furthermore, by monitoring the same train, the data were found to be highly repeatable, which confirmed the ability of the monitoring method to stably reflect the dynamic behavior of the train. Overall, the monitoring method provided in this research could monitor the fastener reaction force in real time for an extended period and accurately record its periodic dynamic loading cycle pattern, which provides important data support for the structural health condition of the ballastless track and the safe operation assessment of trains.

A study on fiber Bragg grating (FBG) strain sensor based on symmetrical lever structure.

Thin-walled structure deformation detection technology is one of the key technologies for structural health monitoring and fault diagnosis of high-end mechanical equipment. Aiming at the problem that the existing Fiber Bragg Grating (FBG) strain sensor is difficult to effectively measure the deformation of thin-walled structures, an FBG strain sensor based on a symmetrical lever structure is proposed. The sensitivity of the sensor is analyzed theoretically, and the sensor is simulated and analyzed by the SOLIDWORKS and Abaqus software, and then, the structural parameters are optimized. According to the simulation results, the sensor is developed and a strain testing system is set up to test the performance of the sensor. The results indicate that the sensor sensitivity is ∼6.6 pm/με, which is about 5.5 times that of bare FBG. Its strain measurement sensitivity and stability are much higher than those of bare FBG, thus meeting the strain detection requirements of thin-walled structural parts during deformation. Moreover, the linearity is more than 99%, which enables the accurate measurement of tiny strains caused by the deformation and reconstruction of the thin-walled structure by the strain sensor. The results of this study provide a reference for the development of like sensors and a further improvement in the sensitivity of the optic-fiber strain sensor.

Novel measurement method for full-field bridge strain and displacement with limited long-gauge strain sensors

In efforts to resolve the limitations of incomplete bridge measurements in accurately identifying structural parameters, this study introduces a novel approach for precise measurement of full-field bridge strain and displacement using a limited number of long-gauge fibre Bragg grating strain sensors. This method consists of two algorithms: a double reconstruction algorithm for strain reconstruction and an improved conjugate beam algorithm (ICBA) for displacement identification. The dual reconstruction algorithm exploits proper orthogonal decomposition to establish a comprehensive mapping relationship between units, thereby achieving precise strain estimation. This intricate mapping process enables the algorithm to accurately compute strain responses. By leveraging the derived full-field strain data, the ICBA effectively captures complete displacement responses. The conventional sensor placement configuration monitors only a limited number of units. To enhance full-field measurement accuracy, this method categorizes unmonitored units into two levels based on sensor placement. The double reconstruction algorithm then estimates the strain response sequentially, contributing to enhanced precision. Numerical simulations validate the proposed method (PM), which is demonstrated to be efficient and robust under various vehicle loads, impact loads, and noised levels. A physical experiment further demonstrates the efficacy of the PM in practice. The results underscore the potency of the PM as powerful theoretical and practical approach for full-field strain and displacement measurement.

Embedded Fiber Bragg Grating Sensors for Monitoring Temperature and Thermo-Elastic Deformations in a Carbon Fiber Optical Bench.

A composite optical bench made up of Carbon Fiber Reinforced Polymer (CFRP) skin and aluminum honeycomb has been developed for the Tunable Magnetograph instrument (TuMag) for the SUNRISE III mission within the NASA Long Duration Balloon Program. This optical bench has been designed to meet lightweight and low sensitivity to thermal gradient requirements, resulting in a low Coefficient of Thermal Expansion (CTE). In addition to the flight model, a breadboard model identical to the flight one has been manufactured, including embedded fiber Bragg temperature and strain sensors. The aim of this is to explore if the use of distributed fiber Bragg gratings (FBGs) can provide valuable information for strain and temperature mapping of an optical instrument on board a space mission during its operation as well as its on-ground testing. Furthermore, surface-mounted strain FBG sensors and thermocouples have been installed in the optical bench for intercomparison purposes. This paper presents the results obtained from a thermal vacuum test consisting of three thermal cycles with stabilization steps at 100 °C, 60 °C, 20 °C and -20 °C. Experimental results provide information about how FBG embedded temperature sensors can provide a proper and quick response to the temperature changes of the optical bench and that embedded FBG strain sensors are able to measure micro-deformation induced in a close-to-zero CTE optical bench.

Experimental study on wayside monitoring method of train dynamic load based on strain of ballastless track slab

In the long-term service of ballastless track, which constantly bears the cyclic load from high-speed trains, it is important to obtain the long-term mechanical behavior of train dynamic load on the ballastless track. In this paper, a novel wayside monitoring method of train dynamic load is proposed, which takes CRTS III ballastless track as the research object and embeds Fiber Bragg grating (FBG) strain sensors into the track slab. The traditional wayside method installing strain gauges on the rail is used to compared with the sensors embedded in the track slab, which was tested in the field. Then, the time domain and frequency domain information of rail strain and slab strain are analyzed in detail, and the correlation analysis of signals is carried out. Finally, the calculation method of the running trains information and dynamic load is proposed. The results show that the vertical strain level of track slab is low under the action of high-speed train dynamic load. The time history curve shows that the adjacent wheel has obvious coupling effect on the slab strain signal, rather than rail strain. The frequency domain analysis of the signals indicates that the low-frequency components of the rail strain and slab strain have a strong correlation. However, the high-frequency components of train dynamic load are buffered out due to the effect of the fastener system. The mapping relationship between the track slab strain and the dynamic load can be found through calibration test, which provide a novel monitoring method of dynamic train load. The monitoring method can realize the real-time monitoring of train running information and record the long-term train dynamic load cycle law, and provide important parameters for the ballastless track boundary condition model.

Fiber Bragg grating (FBG) strain sensor based on positive and negative double strain body structure

Fiber Bragg grating (FBG) strain sensor based on positive and negative double strain body structure

Laboratory Test Study on Pile Jacking Penetration Mechanism Considering Different Diameter and Length Based on Photoelectric Integration Technology

Model tests are carried out on the jacked single piles of different diameters and pile lengths under the model pile of different diameters and pile lengths in clayey soil, which aims to investigate the penetration mechanical mechanism. How to accurately test the pile end resistance and pile side resistance during jacked pile sinking is particularly important. In this paper, a full-section spoke-type pressure sensor, a double diaphragm temperature self-compensating fiber Bragg grating (FBG) earth pressure sensor and a sensitized miniature FBG strain sensor are jointly applied to a single pile penetration model test to test a single pile driving force, pile end resistance and pile body stress during penetration. The test results show that the load transfer performance of test piles will be affected by different diameters, and the axial force transfer capability of a large diameter in the depth direction is better than that of a small diameter since the compacting effect is more obvious. The unit skin friction of the pile increases gradually as the depth increases, which is larger due to the lateral extrusion force increasing as the diameter increases. At the same depth, the unit skin friction of two different diameter piles demonstrates “friction fatigue”, which also decreases obviously as the depth increases. Under the conditions of this test, the maximum frictional resistance of the pile TP1 pile side is about 27.7% higher than that of the test pile TP2. In the static pile sinking process of three test piles in cohesive soil, 50% is end bearing; therefore, there is 50% friction, and the diameter influences the end bearing and the length influences the friction.

Investigation of real-time strain responses of the insulating system of superconducting magnets by using fiber Bragg grating sensors

The normal operation of various superconducting magnets is greatly influenced by the thermal stress of the insulating system, commonly made of epoxy resins with vacuum pressure impregnation (VPI) technology, throughout the curing and cooling processes. In this work, we developed a Fiber Bragg Grating (FBG) strain measurement method to monitor the real-time strain responses of an epoxy resin IR-3 and its glass fiber-reinforced composite during both curing and cooling processes. Then, we also monitored the same process of a Nb–Ti superconducting magnet coil prepared by VPI technology. With the help of FBG strain sensors, the residual strains of the coil at various positions and directions were investigated. The results show that the large residual strain occurred near the end of the coil in the axial direction. In addition, the interlaminar shear stress properties were measured at both room temperature and liquid nitrogen temperature. The strain characteristics of the epoxy resin IR-3 and the insulating system can provide useful guidance for the design and construction of high-field Nb–Ti superconducting magnets.

Monitoring shear deformation of sliding zone via fiber Bragg grating and particle image velocimetry

Monitoring shear deformation of sliding zones is of great significance for understanding the landslide evolution mechanism, in which fiber optic strain sensing has shown great potential. However, the correlation between strain measurements of quasi-distributed fiber Bragg grating (FBG) sensing arrays and shear displacements of surrounding soil remains elusive. In this study, a direct shear model test was conducted to simulate the shear deformation of sliding zones, in which the soil internal deformation was captured using FBG strain sensors and the soil surface deformation was measured by particle image velocimetry (PIV). The test results show that there were two main slip surfaces and two secondary ones, developing a spindle-shaped shear band in the soil. The formation of the shear band was successfully captured by FBG sensors. A sinusoidal model was proposed to describe the fiber optic cable deformation behavior. On this basis, the shear displacements and shear band widths were calculated by using strain measurements. This work provides important insight into the deduction of soil shear deformation using soil-embedded FBG strain sensors.

Design and characteristic research of smart rod based on optical fiber grating for strain monitoring of power transmission tower.

The safety of the power transmission towers is the basis for the reliable operation of the power grid. Real-time monitoring of the strain of the key rods of the power transmission tower can reflect the safety status of the power transmission tower. In this paper, a smart rod equipped with fiber Bragg grating with strain sensitivity enhanced structure is proposed to detect the strain of key rods of large-span power transmission towers on the southeast coast of the Yangtze River. The smart rod can be connected with the power transmission tower rod through the foot nails and the force on the tower can be transformed effectively. This structure has the advantages of convenient installation and no damage to the power transmission tower. Prestress can be applied to fiber Bragg grating equipped in the smart rod through the prestressed sleeve and can be continuously and accurately adjusted, sensitivity of the fiber Bragg grating was enhanced by strain sensitivity enhanced structure. The relationship between force and strain of fiber Bragg grating installed in the smart rod was analyzed by ANSYS software. Experimental results show that the sensitivity of the fiber Bragg grating strain sensor in the smart rod is 13 times that of the conventional structure fiber Bragg grating strain sensor, and the linearity between the fiber Bragg grating wavelength change and force is as high as 0.999. Temperature compensation was realized through temperature measurement fiber Bragg grating installed in the smart rod. This structure can be used to measure the strain of a large-span power transmission tower from 0 to 2000 με with an accuracy of 0.1 με with good repeatability.

Advantageous Strain Sensing Performances of FBG Strain Sensors Equipped with Planar UV-Curable Resin.

The existing optical strain sensors based on fiber Bragg grating (FBG) have limitations, such as a complex structure, a limited strain range (±200 με) and poor linearity performance (R-squared value < 0.9920); these limitations affect their potential practical applications. Here, four FBG strain sensors equipped with planar UV-curable resin are investigated. The proposed FBG strain sensors have a simple structure, a large strain range (±1800 με) and excellent linearity performance (R-squared value ≥ 0.9998); they further produce the following performances: (1) good optical properties, including an undistorted Bragg peak shape, narrow bandwidth (-3 dB bandwidth ≤ 0.65 nm) and a high side mode suppression ratio (SMSR, the absolute value of SMSR ≥ 15 dB); (2) good temperature sensing properties with high temperature sensitivities (≥47.7 pm/°C) and a good linearity performance (R-squared value ≥ 0.9990); and (3) excellent strain sensing properties with no hysteresis behavior (hysteresis error ≤ 0.058%) and excellent repeatability (repeatability error ≤ 0.045%). Based on their excellent properties, the proposed FBG strain sensors are expected to be applied as high-performance strain sensing devices.

Thermal Strain Detection for Concrete Structure Cold Shrinkage under Stress Constraint with FBG.

Additional strain increments occur in concrete subject to stress constraints during cold shrinkage, resulting in irregular deformation and reducing the concrete structure's stability. When an annular concrete structure is subjected to radial pressure, two tensile stress concentration zones will appear at the intersection of the inner wall and the diameter along the pressure direction. When exposed to low temperatures, the total strain in the tensile stress concentration zones is caused by the combined effect of applied stress strain and thermal strain. Then, the thermal strain of the structure can be obtained from the difference between the total strain and the applied stress strain. Gradient cooling was performed after applying radial pressure to the annular concrete using a counterforce device. The applied stress strain and total strain of the tensile stress concentration zones are measured by fiber Bragg grating (FBG) strain sensors fixed along the stress direction. According to the measurement results, the thermal strains of the concrete structure under the stress constraint are extracted to analyze the influence of the tensile stress constraint on the thermal strain of the concrete structure. In the temperature range of -40∘C∼20∘C, the thermal strains of the structure under radial pressures of 1500 N, 2000 N, and 3000 N are extracted, respectively. The thermal expansion coefficients are calculated based on the thermal strain of the structure. The free thermal expansion coefficient of concrete structures fluctuates around 11×10-6/∘C. When the temperature is reduced to 10∘C, the difference between the thermal expansion coefficient under the stress constraint and the free thermal expansion coefficient is the largest. When the temperature is reduced to -20∘C, the thermal expansion coefficients under each stress condition are close to the same. The results show that the stress confinement significantly inhibits the cold shrinkage of the concrete structure, and the inhibitory effect is gradually weakened when the temperature decreases.