Displacement-strain Transformation Research Articles

Full-field static and dynamic strain measurement by an inverse conjugate beam method with two-type sensor placement

This paper presents a novel inverse conjugate beam method (ICBM) to full-field static and dynamic strain measurement using long-gauge fiber Bragg grating (FBG) and vision sensors. By applying reverse analysis of conjugate beam theory, the ICBM establishes a displacement–strain transformation model that effectively explains the correlation between displacement, distributed strain and desired strain. The static and dynamic strain can be reconstructed directly by combining the monitored displacement and strain responses at the displacement monitoring locations. The vision sensor is employed to complement the installed long-gauge strain sensor for monitoring the displacement of the location without a long-gauge sensor. This method helps overcome the difficulty of monitoring the full-bridge strain due to insufficient sensors or inaccessible monitoring positions. At the same time, according to this method, it is necessary to use the displacement from the visual sensor to determine the residual stiffness of each unit as prior information for the ICBM. Both numerical studies and laboratory tests are carried out on a simply supported beam for conceptual verification. The results demonstrate that the proposed ICBM successfully achieves static and dynamic strain response reconstruction at displacement monitoring locations.

Coarse and Fine Two-Stage Calibration Method for Enhancing the Accuracy of Inverse Finite Element Method.

The inverse finite element method (iFEM) is a novel method for reconstructing the full-field displacement of structures by discrete measurement strain. In practical engineering applications, the accuracy of iFEM is reduced due to the positional offset of strain sensors during installation and errors in structural installation. Therefore, a coarse and fine two-stage calibration (CFTSC) method is proposed to enhance the accuracy of the reconstruction of structures. Firstly, the coarse calibration is based on a single-objective particle swarm optimization algorithm (SOPSO) to optimize the displacement-strain transformation matrix related to the sensor position. Secondly, as selecting different training data can affect the training effect of self-constructed fuzzy networks (SCFN), this paper proposes to screen the appropriate training data based on residual analysis. Finally, the experiments of the wing-integrated antenna structure verify the efficiency of the method on the reconstruction accuracy of the structural body displacement field.

Displacement–strain transformation for a variable cross-section beam based on hypergeometric and Meijer-G functions

The modal-learning displacement–strain transformation has been proved to be able to predict the strain of the typical uniform beam. However, as the complexity of the structure increases, for example, the shape of the beam cross-section changes. The typical displacement–strain transformation is no longer applicable due to the unknown mode function. To further explore this issue, the hypergeometric and Meijer-G functions are used to establish the mode shape function with good structural adaptability. A displacement–strain transformation method based on the hypergeometric and Meijer-G functions is proposed to predict the dynamic strain of the variable cross-section beam. Experiment results demonstrate that the proposed method can solve the problem of full-field strain prediction for beams with variable sections and boost the displacement–strain transformation’s theoretical calculation accuracy. Under sinusoidal excitation and random excitation, the strain prediction accuracy reaches 99.69% and 99.25%, respectively. This approach simplifies the preprocessing of the structure, and provides a welcome boost to developing the displacement–strain transformation method in full-field strain measurement.

Displacement, Strain and Failure Estimation for Multi-Material Structure Using the Displacement-Strain Transformation Matrix

In this study, we propose a method to estimate structural deformation and failure by using displacement-strain transformation matrices, i.e., strain-to-displacement transformation (SDT) and displacement-to-strain transformation (DST). The proposed SDT method can be used to estimate the complete structural deformation where it is not possible to apply deformation measurement sensors, and the DST method can be used for to estimate structural failures where strain and stress sensors cannot be applied. We applied the SDT matrix to a 1D beam, a 2D plate, rotating structures and real wind turbine blades, and successfully estimated the deformation in the structures. However, certain difficulties were encountered while estimating the displacement of brittle material such as an alumina beam. The study aims at estimating the displacement and stress to predict the failure of the structure. We also explored applying the method to multi-material structures such as a two-beam bonded structure. In the study, we used alumina–aluminum bonded structures because alumina is bonded to the substrate to protect the structure from heat in many cases. Finally, we present the results of the displacement and failure estimation for the alumina–aluminum structure.

Modal learning displacement-strain transformation.

The displacement-strain transformation is essential for revealing the internal mechanics of structures and developing strain measurement methods. This transformation typically depends on the environment of the structure. In contrast to the traditional invariant transformation, this paper proposes a method to obtain a variable displacement-strain transformation by self-learning of the modal parameters of the structure in operation. The beam experimental results demonstrate that the transformation is able to take account of different forms of excitation and to obtain strain measurements under sinusoidal and random excitation with up to 99.82% and 99.70% accuracy, respectively. Moreover, these results indicate that the proposed displacement-strain transformation is able to take account of the environmental conditions encountered in practical situations more consistently than conventional approaches. The introduction of a modal-learning displacement-strain transformation in the proposed approach provides a welcome boost to the development of strain measurement methods.

3D beam shape estimation based on distributed coaxial cable interferometric sensor

We present a coaxial cable interferometer based distributed sensing system for 3D beam shape estimation. By making a series of reflectors on a coaxial cable, multiple Fabry–Perot cavities are created on it. Two cables are mounted on the beam at proper locations, and a vector network analyzer (VNA) is connected to them to obtain the complex reflection signal, which is used to calculate the strain distribution of the beam in horizontal and vertical planes. With 6 GHz swept bandwidth on the VNA, the spatial resolution for distributed strain measurement is 0.1 m, and the sensitivity is 3.768 MHz mε−1 at the interferogram dip near 3.3 GHz. Using displacement-strain transformation, the shape of the beam is reconstructed. With only two modified cables and a VNA, this system is easy to implement and manage. Comparing to optical fiber based sensor systems, the coaxial cable sensors have the advantage of large strain and robustness, making this system suitable for structure health monitoring applications.

Development of a wireless pilot arm–wearable haptic interface for unmanned aerial vehicle wing deflection sensing

When the flight of an unmanned aerial vehicle is controlled by a ground pilot, a wing deflection monitoring is required to avoid overload wing structural failures. Therefore, integrated structural health monitoring technologies are being developed to transfer such information to the pilot. In general, this information can be monitored visually by the ground pilot. In this study, a haptic interface enables human–machine communication through tactile sense and provides synchronized information exchange between a pilot and an unmanned aerial vehicle. In other words, we propose not a vision interface but a haptic interface to transfer the wing deflection information to the ground pilot; this interface is named “Fly-by-haptic,” which is beneficial because the vision of the ground pilot is already performing multiple tasks. For a proof of concept, four integrated fiber Bragg grating sensors were installed on a half wing specimen to measure dynamic strains. The wing deflection information was estimated by the displacement–strain transformation matrix. The wing deflection information was wirelessly transferred to actuate vibro-haptic motors installed in a pilot arm–wearable haptic interface. Finally, a human test was performed using the developed haptic interface; the test results determined that the 15 participants, who are novices, showed 100% accuracy for wing deflection.

Measurement of strain and bending deflection of a wind turbine tower using arrayed FBG sensors

This paper introduces a fiber Bragg grating (FBG) based arrayed sensor system for use in the measurement of strain and bending deflection of an 1.5 MW wind turbine tower, and describes the results of field tests of structural monitoring of turbine start and feathering load conditions. A wavelength division multiplexing (WDM) FBG interrogator was developed with a spectrometer-type demodulator based on a linear photo detector for high-speed strain sensing. Real-time shape estimation of the wind turbine tower was accomplished using strain data gathered by surface mounted fiber Bragg grating sensors. The finite element model of the wind turbine tower was created and the displacement-strain transformation (DST) matrix on the basis of the modal approach was obtained. To monitor the dynamic structural behavior of the wind turbine, 10 FBG sensors were arrayed and installed on the inner surface of the tower located at the primary wind direction. The time histories of the strain were gathered using the FBG sensors and the deflections of the tower top position were simultaneously transformed using the DST matrix. Finally, the full deflection shapes of the tower were successfully estimated using arrayed FBG sensors.

Shape estimation with distributed fiber Bragg grating sensors for rotating structures

This study investigates shape estimation of rotating structures using displacement–strainrelationships and strain data measured with distributed fiber Bragg grating (FBG) sensors.A displacement–strain transformation based on a modal approach is applied to a beammodel, and the locations of the strain sensors are optimized by minimizing thecondition number of the displacement–strain transformation matrix. In a numericalsimulation of a rotating beam, the beam shapes are successfully estimated using theproposed displacement–strain transformation. Experimental validations for transientand steady rotations of the beam are also performed. The estimated shapes ofthe rotating beam on the basis of FBG signals are compared with the directlycaptured shapes from photographs taken with a high-speed camera. The resultsshow very close agreement, demonstrating the potential of the proposed shapeestimation technique based on displacement–strain transformation using FBG sensors.

광섬유 변형률 센서를 이용한 구조물의 동적 변형 추정

In this study, structural deformation estimation using displacement-strain relationship is investigated. When displacements of a structure cannot be measured directly, estimation of displacements using strain data can be an alternative solution. Additionally, the deformation of the whole structure as well as the displacement at the point of interest can be estimated. Strain signals are obtained front Fiber Bragg Grating(FBG) sensors that have an excellent multiplexing ability. Some experiments were performed on two beams and a plate to which FBG sensors were attached in the laboratory. Strain signals from FBG sensors along a single strand of optical fiber were obtained through wavelength division multiplexing(WDM) method. The beams and the plate structures were subjected to various loading conditions, and deformed shapes were reconstructed from the displacement-strain transformation relationship. The results show good agreements with those measured directly from laser sensors. Moreover, the whole structural shapes of the beams and the plate were estimated using only some strain sensors.