Fiber Bragg Grating Strain Sensors Research Articles

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.

High-sensitivity fiber Bragg grating strain sensor of the substrate type.

Strain measurement has important applications in mechanical engineering, civil engineering, aerospace, earthquake monitoring, and other fields. Aiming at the problem of low sensitivity of existing fiber Bragg grating (FBG) strain sensors, a high-sensitivity FBG strain sensor of the substrate type with a sensitization structure is proposed. The sensitivity of the sensor is analyzed theoretically, the sensor is simulated by Solidworks and ANSYS software, and the structural parameters are optimized. According to the simulation results, the real sensor is developed, and the strain test system is built to test the performance of the sensor. The results show that the strain sensitivity of the sensor is 3.21p m/µε, which is about 2.7 times that of the bare FBG strain sensor, which is basically in line with the theoretical value. The fitting linear correlation coefficient is 0.9999, and the repeatability error is 3.9%FS. The research results provide a reference for developing the same type of sensors and further improving the sensitivity of fiber strain sensors.

Evaluation of thermal-drift effect on strain measurement of energy pile

Fiber Bragg grating (FBG) strain sensors and electrical resistance strain (ERS) gauges are typically utilized to monitor the internal deformation of structures. However, a common problem inherent in these sensors is the unwanted thermal drift in the measurement results. This study first investigated factors influencing the thermal strain measurements of FBG strain sensors and ERS gauges through a series of calibration experiments. The results demonstrate that the relative error caused by the thermal output of the heated connection cables was as high as 90 %. Then a correction method for the thermal drift of the strain measurement was proposed. This correction method reduced the relative difference between the strain readings of bonded ERS gauges and FBG sensors from 82.6 % to around 10–20 %. Finally, FBG strain sensors and ERS gauges were employed to monitor the strain of the energy piles under cooling and heating cycles. The difference between the corrected readings from FBG strain sensors and ERS gauges was less than ± 10 %. The experimental results also reveal that the monitoring reliability of the FBG strain sensors was higher than the ERS gauges.

Real-Time Virtual Sensing for Dynamic Vibration of Flexible Structure via Fiber Bragg Grating Sensors

Real-time monitoring of the dynamic vibrations of beam-type structures indicates important implications in aerospace engineering applications, in which the additional sensing information about vibration parameters, including displacements, rotational angles, angular rates, as well as accelerations, facilitates the improvement of the system’s safety. This article proposed a virtual sensing method with the usage of fiber Bragg grating (FBG) strain sensors to directly estimate the vibration parameters from the measured strains. The algebraic relationships of displacement–strain and rotation–strain on the sensor’s installing points as well as the boundary points are obtained based on the Birkhoff interpolation method, and meanwhile, the explicit expressions on angular rates and accelerations are derived. Furthermore, a tracking differentiator is used to recover the strain signals and their first- and second-order derivatives from the noisy measurements in order to real-time estimate the angular rates and accelerations of the vibrating beam. Differing from the classical modal-based method, complex modal decomposition is not required in the proposed method. The comparison of numerical simulation results reveals that the proposed method has advantages over the modal-based method in accuracy and efficiency. Furthermore, the laboratory experiments indicate that the proposed method is effective for real-time estimating vibration parameters from the noisy measured strains.

On the study of vortex-induced vibration of a straked pipe in bidirectionally sheared flow

Helical strakes are widely used to suppress vortex-induced vibration (VIV) in ocean engineering. However, the VIV response and suppression efficiency of the straked pipe are unclear under the recently discovered bidirectionally sheared flow field. Experiments on vortex-induced vibration for a flexible pipe with three kinds of helical strakes were carried out in an ocean basin. The bare pipe model was 28.41mm in diameter and 7.64m in length. Three kinds of helical strakes with different pitch/height (17.5D/0.15D, 17.5D/0.25D,and 17.5D/0.35D) were applied. The test was performed on a rotating test rig to simulate bidirectionally sheared flow conditions. Fiber Bragg Grating (FBG) strain sensors were arranged along the test pipe to measure bending strains, and the modal analysis approach was used to determine the VIV response. The reduced velocities based on the tested first natural frequency of the bare pipe in water reached 30.79. The cross-flow and in-line VIV amplitudes, VIV suppression efficiency, and fatigue damage are presented in this article. The results showed that the helical strakes can suppress bidirectionally sheared flow-induced VIV significantly at a high reduced velocity regime with fatigue damage suppression efficiency over 99% in the CF and IL directions, but cannot suppress the in-line initial displacement, which was also found in previous studies as a drawback of helical strakes.

Biomechanical assessment and quantification of femur healing process using fibre Bragg grating strain sensors

Femur diaphysis fractures almost always require surgery to heal. The femur recovery process may take 3–6 months or even longer. The current femur recovery assessment methods are qualitative and mainly rely on physicians' clinical experience. A better methodology to quantify the healing status will help the physicians counsel their patients on the appropriate load-bearing activities accordingly. This paper numerically and experimentally demonstrates a femur healing assessment methodology using fibre Bragg grating (FBG) sensors. Finite Element (FE) analysis was conducted to confirm the feasibility of the used epoxies. For the experiments, a fourth-generation composite femur (4GCF) sample fixated with an implant plate was prepared. The sample was instrumented with a total of six FBGs on the proximal and distal posterior, mid-shaft, and implant surfaces. The prepared sample was then subjected to cyclic loading on a hydraulic tensile machine in various situations including (1) intact, (2) fractured (mid-shaft transverse and wedge), and (3) epoxy-healed. Epoxies with different curing times were applied on the fractured femur to mimic bone regeneration stages as they harden. FBGs were used to monitor the alterations in the strain values during the healing stages. The results demonstrated that the strain values measured by FBGs were able to justify the non-union, mal-union, delayed union, and fully union conditions on the femur shaft compared to the intact and fractured conditions. The proposed assessment technique can potentially be used on long bones with various fracture types and for patients of different ages and recovery rates. • Fractured femur healing process was quantitatively monitored and assessed. • Epoxies were applied on fractured femur to mimic bone regeneration stages as they cure. • Finite element analysis was used to investigate the utilised epoxies feasibility. • The healing extent of the femur is shown at each stage during the recovery time period.

Influence of frost and local stiffness variations on the strain mode shapes of a steel arch bridge

Natural frequencies are probably the most widely used modal characteristics in vibration-based monitoring. However, they can be highly influenced by temperature and this influence can completely mask the effect of even severe damage. This translates into a necessity for time-consuming data-normalization techniques to remove the influence of temperature and identify damage. Displacement mode shapes of homogeneous material structures are less influenced by temperature, but obtaining them in a dense grid, which is required for damage localization, is cumbersome due to the large number of sensors needed. Strain mode shapes on the other hand can be insensitive to temperature variations, while obtaining them in a dense grid is possible when fiber-optic sensors such as fiber-Bragg gratings (FBG) are used. This work presents the results of the continuous monitoring of a steel railway bridge for a period of almost two years, where modal data were collected for a wide temperature range. The bridge is instrumented with eighty FBG strain sensors, multiplexed in four fibers. The natural frequencies and strain mode shapes of ten modes have been automatically identified from operational strain time histories, on an hourly basis. A clear influence of temperature on the natural frequency of most modes is identified, especially during frost periods. On the contrary, the strain mode shapes are mostly insensitive to temperature changes and only these of some higher-order modes are slightly and uniformly influenced when frost occurs. This behavior is confirmed also by a finite element model (FE) of the bridge. Furthermore, the FE model is used to investigate the influence of local stiffness changes on the modal characteristics. A clear and local change of the modal strain amplitude is observed at the location of the reduced stiffness, especially when information from all modes is combined in a sensitive damage index.

High-Speed and High-Resolution Optical Fiber Sensor Interrogation Based on Optical Injection in Semiconductor Laser and Microwave Filtering

Real-time and high-speed interrogation of optical fiber sensors normally requires sophisticated detection systems. Here a novel microwave photonic approach for interrogation of high-speed and high-resolution optical fiber sensors based on optical injection in a semiconductor laser and simple passive microwave frequency filtering is proposed and experimentally demonstrated. An intensity-modulated master laser is injected into a semiconductor laser to produce a wavelength scanning optical sideband. A fiber Bragg grating (FBG) sensor is embedded into a fiber ring laser. Beating of the scanning optical sideband and the fiber ring laser wavelength at a photodetector generates a linearly frequency-chirped microwave signal. The real-time wavelength shift of the FBG sensor is converted into the change of the microwave center frequency. After a simple passive microwave bandpass filter, two electrical pulses are obtained corresponding to positive and negative frequency sweeping. The FBG wavelength can be retrieved from the time interval of the two pulses. A proof-of-concept experiment to measure an FBG strain sensor has been carried out. A high interrogation speed of 1 MHz and measurement sensitivity of 17.3 ns/μϵ have been achieved.

Design and experimental study of a fiber Bragg grating strain sensor with enhanced sensitivity.

A novel high-sensitivity fiber Bragg grating (FBG) strain sensor is reported, to the best of our knowledge. The sensitivity of the sensor is improved by fixing the FBG on an elastic substrate with a sensitization function. The sensitization principle of the designed sensor is introduced, and the mathematical model of the sensor is established. In the static and dynamic experiments of the sensor, the effect of adhesive between the sensor and the measured structure on the sensitivity of the FBG strain sensor is experimentally investigated. The experimental results show that the adhesive with high shear strength is beneficial to the realization of a high-sensitivity sensor. The sensor fixed with planting bar glue can achieve a sensitivity of 9.42 pm/µε, a repeatability error of 4.79%, and a hysteresis error of 3.36%, which is consistent with theoretical and simulation results. The designed high-sensitivity strain sensor has a simple structure, small size, and convenient installation, so it has a good application prospect in micro-strain monitoring.

Experimental investigation of vortex-induced vibration of a flexible pipe in bidirectionally sheared flow

The existence of a bidirectionally sheared flow field caused by internal solitary waves has recently been confirmed according to a field survey in the South China Sea. A model test of a tensioned flexible pipe in bidirectionally sheared flow was performed in an ocean basin. The model was 28.41mm in diameter and 7.64m in length. The purpose of the model test was to understand the response performance and obtain benchmark data of vortex-induced vibration (VIV) in bidirectionally sheared flow. The test was performed on a rotating test rig to simulate bidirectionally sheared flow conditions. Fiber Bragg Grating (FBG) strain sensors were arranged along the test pipe to measure bending strains, and the modal analysis approach was used to determine the VIV response. Reduced velocities based on the tested first natural frequency in water reached 30.79. The cross-flow and in-line VIV amplitudes, response frequencies in statistics and time-domain analysis, traveling wave characteristics, phase synchronization and trajectories are presented in this article. The maximum root mean square (RMS) VIV amplitudes in the test reached 0.51 diameters and 0.18 diameters in the cross-flow and in-line directions, respectively. A relative low Strouhal number of 0.10 was found in the CF direction.

Realization of an ultra-high pressure dynamic calibrate system by drop hammer based on fiber Bragg grating strain sensor.

In this letter, we propose a novel technique for dynamic ultra-high pressure calibration that measured pressure by FBG based strain sensor. Generally, the traditional method of dynamic ultra-high pressure calibration by standard sensor is costly and it is difficult to improve the accuracy. Therefore, we prefer FBG strain sensor to replace the standard sensor to calibrate the ultra-high pressure. In this proposal, the calibration process is that the central wavelength of the FBG attached to the elastic element changes rapidly with the strain of the elastic element during the drop hammer impact, synchronously. This allows the calibration accuracy to be easily increased to 0.02% and the cost to be reduced by 1/100 compared to traditional calibration techniques. The experiment results show that coefficient of linear correlation between the strain waveform and the pressure signal reaches 0.999. The strain calibration based on FBG is of great significance to the measurement and calibration of dynamic ultra-high pressure sensors.

Study on strain sensing property of fiber Bragg grating based on surface strain measurement of mechanical structure.

Strain monitoring is of great significance to identify the failure of key mechanical components and ensure the good operation of mechanical equipment. In terms of the common issue of the low sensitivity of fiber Bragg grating (FBG) strain sensor in strain measurement on the mechanical structure surface, this paper describes a flexible hinge strain sensor with the FBG as the sensitive element. A theoretical analysis of the sensitivity of the sensor is performed, a copper alloy material with a large elastic modulus is selected, the simulation analysis and optimization design for the structural parameters of the sensor are carried out by using ANSYS and Solidworks software, then the object of the sensor is developed according to the simulation results, and finally, the performance of the sensor is tested. The results show that the maximum deformation the sensor can measure is 0.5299 µε, the sensitivity of the sensor is ∼1.8870 pm/µε, which is approximately twice that of the bare FBG sensor, the linearity is greater than 99%, and the relative standard deviation of the repeatability is 0.9%. The results of the study provide a reference for developing the optical fiber strain sensor and further improving its sensitivity.

Strain sensor based on FBG in fiber loop ring down system

AbstractIn this paper, a strain sensor with a high resolution based on fiber Bragg grating (FBG) is proposed by combining a fiber loop ring down (FLRD) technology. When a light pulse enters and circulates in the fiber loop, it experiences a little loss each time as it paases through the sensor head. The ring‐dong time of the system would be altered by intensity loss near the sensor head, which is related to the size of the strain. The experimental results show that the FBG strain sensor with a high resolution is achieved by monitoring the ring‐down time, due to the more precision time measurement compared with the wavelength measurement. In the 0–1250 με strain range, the sensitivity ranged from 5.82&amp;nbsp;to 20.82 ns/με, and the theoretical best resolution is obtained as 0.24 με. The system has the advantages of simple structure, low cost, reflective sensor head, and high resolution.

Applied Quasi-Distributed Fibre Bragg Grating Strain Sensors in Structural Damage Sensing of a Bridge Structure

Bridge structural decay is a prevalent problem around the world. Consequently, most structurally deficient bridges are characterized by unknown levels of damage, which impose high socio-economic risks to society. To address these concerns, this study is aimed at determining how to accurately sense the damage present in a bridge structure. Owing to the pitfalls of conventional sensing technologies and the complexities associated with civil structure instrumentation, the use of fibre optics sensors is found to be relevant for this study. While the employment of quasi distributed fibre Bragg grating strain sensors is not a relatively new concept, research is still necessary for their effective deployment in structural damage monitoring systems. A proof of concept for the developed sensing system is primarily simulated and thereafter demonstrated in the laboratory through a series of strain measurements tests conducted on a reinforced concrete slab. The experimental set-up consisted of a serial array of five wavelength division multiplexed fibre Bragg grating sensors, which were coupled with swept wavelength laser scanning technology. The experimental sensing resolution of less than 0.5 &#x03BC;&#x03B5; was achieved. Structural damage information was extracted from the measured multipoint flexural strains, using our developed macro-modal strain ratio cross correlation algorithm. Alternatively, to simulate our sensor system response, vibration field tests, and finite element analysis were conducted on the Beatrice Bridge in Zimbabwe. Therefore, this paper presents the simulation and experimental results of a simulated and designed structural damage sensing system, based on quasi-distributed fibre Bragg grating strain sensors.

Characterization of carbon dioxide leakage process along faults in the laboratory

It is important to understand the process of multiphase carbon dioxide (CO 2 ) leakage in faults for the risk assessment of carbon capture and storage (CCS). To quantitatively characterize the CO 2 leakage process in the fault, pressure sensors, fiber Bragg grating (FBG) temperature and strain sensors were simultaneously used to monitor CO 2 leakage in the fault. Ten experiments were carried out, including five groups of gaseous CO 2 leakage tests with initial pressures of 1–5 MPa and five groups of liquid CO 2 leakage tests with initial pressures of 6–10 MPa. The results indicate that when liquid CO 2 leaked with an initial pressure of 7–10 MPa, the pressure and temperature of CO 2 dropped rapidly in the first few seconds and then remained unchanged. The behavior that CO 2 continues to leak while maintaining temperature and pressure unchanged is defined as “temporary pseudo-sealing (TPS)” behavior, which continues for the first 1/3 of the leakage period. However, this TPS behavior did not occur in gaseous CO 2 leakage. If only the pressure and temperature data were used to evaluate whether CO 2 leakage occurred, we would misjudge the risk of leakage in CCS projects during the TPS period. The causes and conditions of TPS behavior were further studied experimentally. The results show that: (1) TPS behavior is caused by the phase transition energy generated when liquid CO 2 leaks. (2) The condition for TPS behavior is a small leak aperture (0.2 mm). Only a small leakage rate can make the phase transition energy and pressure change from a dynamic equilibrium, and (3) The compression zone caused by the Bernoulli effect and fault “barrier” could reduce the CO 2 leakage rate and further promote the occurrence of TPS behavior. This study provides technical and theoretical support for the quantitative characterization of the CO 2 leakage process in faults of CCS projects.

Integration of an optical FBG sensor into a nuclear magnetic resonance core flooding system

A new platen was designed and developed for a nuclear magnetic resonance (NMR) core flooding cell for the integratation of fibre Bragg grating (FBG) strain sensors. The platen is made from carbon fibre material with a special channel to insert the FBG inside the cell, and it is compatible with an NMR overburden system (i.e. no metal, and also resistant to pressure, temperature and reactive chemicals) to allow, for example, advanced chemical experiments. This development has allowed us to acquire both fluid dynamics behaviour, from NMR, and deformation/elastic properties, from FBG sensors, during NMR core flooding experiments for advanced hydro-mechanical-chemical coupling characterisation. Generally, pore fluid redistribution occurs while changing the surrounding stress and/or temperature conditions of the tested material, and will generate elastic and geomechanical responses. The impact of rock–fluid interactions during NMR core flooding has not been evaluated until now, mainly due to technical limitations. Fortunately, the FBG sensing technique is a localised/discreet micro-strain gauge (8 mm long and 125 micro thick), and it is applicable to the monitoring of pseudo-tomography during core flooding experiments. We recently managed to attach eight FBG sensors on a carbonate rock plug to monitor strain alteration during brine imbibition under 800 psi confining pressure. The results validate the ability of the FBG sensors to track mechanical strength alterations due to pore pressure changes and also to detect waterfront velocity during injection. The integration of FBG sensors into the NMR core flooding system has added a new capability to the NMR overburden system, enabling it to simultaneously monitor material deformation with FBG sensors during pressure/temperature alterations as a first basic application.

An experimental investigation on interfering VIVs of double and triple unequal-diameter flexible cylinders in tandem

Many unequal-diameter risers have been widely applied to satisfy different operational requirements in ocean oil and gas drilling engineering, and adjacent tandem risers can undergo complex vibration responses and even collisions under ocean flow conditions. To investigate the wake interference responses for multiple risers in tandem configuration, an experiment of double and triple unequal-diameter flexible cylinders was conducted under uniform flow with Reynolds numbers Re ranging from 2832 to 11,328 for the larger cylinder and from 1805 to 7220 for the smaller cylinder. The two cylinders were 8 m in length with aspect ratios equal to 282.49 and 443.21, respectively, and the corresponding diameter ratio was 0.64. Two different tandem configurations were arranged with a large cylinder upstream and downstream, and the wall spacing between adjacent cylinders was fixed at 4D, where D is the diameter of small cylinders. Fiber Bragg grating strain sensors were used to measure both in-line (IL) and cross-flow (CF) strain responses. The modal superposition method was applied to reconstruct displacement responses based on measured strains, and drag forces were further inversely identified from the mean IL displacements. Equivalent wake velocities were calculated from drag force reductions. The results show that the downstream large cylinder in a triple-cylinder system endures a stronger wake interference effect than that in a double-cylinder system. Wake interference can decrease the dominant mode of downstream cylinders and increase the vibration amplitudes due to the reduction in the local wake velocity. In addition, a downstream cylinder undergoing wake-induced vibrations has the same dominant frequency in the CF and IL directions, and its CF frequency is identical to that of the upstream cylinder.

Experimental Investigation of Low-Frequency Distributed Acoustic Strain-Rate Responses to Propagating Fractures

Summary Low-frequency distributed acoustic sensing (LF-DAS) responds to strain changes due to far-field fracture propagation. To better understand the LF-DAS response to fracture propagation, we performed laboratory-scale hydraulic fracture experiments with embedded optical strain sensors. The objectives of this research are to generate hydraulic fractures of known geometry, measure the strain response along the embedded fiber-optic cable comparable to LF-DAS measurements, and use the results to inform the interpretation of field-derived LF-DAS data. The experiments were conducted in unconfined transparent cubic blocks with a dimension of 8 in. on each side. The block was made of transparent epoxy to visualize the fracture propagation. Fiber-optic sensing cables were embedded in the block at different distances to the source of injection. We injected dyed water through an injection tubing to generate a transverse, radial fracture along an initial flaw. An optical interrogator recorded the response of offset fiber Bragg grating (FBG) strain sensors normal to the plane of the fracture. The strain data were visualized on a waterfall plot, akin to visualizations of field-derived LF-DAS data. Dimensional analysis was used to scale the laboratory results to field conditions. We compared the evolution of the strain response at the fiber-optic cable, injection pressure, and rate with known fracture geometry. The measured strains were compared with Sneddon’s (1946) linear elastic solution for a penny-shaped crack and found to follow this behavior. The generated radial fractures in transparent media can be modeled with Sneddon’s linear elastic radial fracture model and a Mode I critical stress intensity factor. The LF-DAS characteristic response of a narrowing region of extension surrounded by compression was exhibited as a fracture that approached and intersected the fiber-optic cable. The experimentally derived strain and strain-rate waterfall plots with known fracture geometry, injection rate, and pressure response provide insight in understanding LF-DAS responses in the field. Furthermore, we developed a method to estimate fracture geometry evolution from the fiber-optic strain data and validated the method against the experimental data.

Wide-range fiber Bragg grating strain sensor for load testing of aircraft landing gears

The impact load borne by landing gear during the take-off and landing of aircraft is an important parameter in structural health monitoring. A wide-range fiber Bragg grating (FBG) strain sensor with a surface-attached carbon fiber matrix is designed to measure the strain and load of aircraft landing gear structures for monitoring requirements. The sensor's performance was tested, and its strain sensitivity is 1.14 pm/μɛ. In addition, a multivariate linear load regression method was proposed, which can simultaneously monitor and predict the three-way load of landing gear, and the ground static loading test was carried out to verify the feasibility of this method. The result shows that the regression load error calculated by this method is within 5%, which meets the actual engineering requirements.