Local Coordinate System Research Articles

Study on the potential of UAV scanning for measuring complex technical infrastructure

Laser scanning surveys conducted on complex technical infrastructure with a horizontal structure often encounter the issue of mutual obscuration of elements. This problem can be addressed by utilizing UAV surveys, provided that the necessary accuracy is maintained. Photogrammetric drones are susceptible to disturbances such as shading, lighting, and reflections, which can impact survey accuracy. Scanning drones offer more stable accuracy in such scenarios. The research aimed to determine if a scanning drone could generate point clouds of technical infrastructure with geometry accuracy comparable to terrestrial scanning. Previous studies on scanning drones have primarily focused on absolute measurement accuracy, typically within a few centimeters. However, for determining the geometric shape of installation elements in a local coordinate system, internal measurement consistency is crucial. The research demonstrated that by integrating point clouds from multiple drone flight paths effectively, consistency within a few to several millimeters can be achieved. A comparison with terrestrial laser scanning results indicated the ability to detect deformations at a level of approximately 5–10 mm.

An efficient method of moments for analysis of electromagnetic scattering from a multilayered arbitrary‐shape anisotropic dielectric object

AbstractThis paper introduces an efficient method of moments (MoM) designed to explore electromagnetic scattering in multilayered anisotropic structures. Each layer is made up of a dielectric anisotropic material characterised by a generalised tensor for permittivity, which is unrestricted in its geometrical configuration. The authors’ approach analyses each layer independently, employing the surface equivalence theorem to substitute the interfaces between layers with suitable equivalent electric and magnetic surface current densities. The authors derive the necessary surface integral equations (SIEs) for each interface by implementing the proper boundary conditions. The analysis utilises rotated dyadic Green's functions that populate the infinite space with the material properties specific to each anisotropic layer. The rotation angle corresponds to the deviation between the local principal coordinate system of the material and the global coordinate system, which is determined by diagonalising the full dielectric tensor of the respective anisotropic material given in the global coordinate system. To address the SIEs for determining the unknown equivalent electric and magnetic surface current densities, Galerkin's MoM is applied. This involves expanding the unknown surface currents using suitable basis functions, simplifying the issue to a matrix equation solved through the inversion of a block‐tridiagonal impedance matrix. The diagonal nature and sparse structure of the impedance matrix, along with an effective block‐inversion method, significantly boost computational efficiency and reduce memory demands. To demonstrate the feasibility of the proposed method, the authors present a detailed derivation of the impedance matrix for the case of non‐magnetic uniaxial anisotropic media for which the Green's functions are available in closed form. The validity and efficiency of the proposed SIE‐MoM scheme are demonstrated by comparing the results of several case studies against those found in literature and results obtained via commercial numerical codes.

АНАЛІЗ НАПРУЖЕНОГО СТАНУ ШАРУ З ДВОМА ЦИЛІНДРИЧНИМИ ВРІЗАНИМИ ОПОРАМИ ТА ЦИЛІНДРИЧНИМИ ВТУЛКАМИ

The spatial problem of the theory of elasticity for a layer on cylindrical embedded supports with cylindrical sleeves (thick-walled pipes) located between each support and the layer is solved. Smooth contact conditions are set at the interface between the layer and the pipes. Stresses are specified on the surfaces of the layer, and displacements are specified on the inner surface of the pipe (rigidly conjugated to the support). The analytical and numerical solution of the problem is based on the Lamé equations written for the layer and each pipe. When the boundary conditions and the conditions of conjugation of the layer with the pipes are met, a system of integro-algebraic equations is created, which reduces to a system of linear algebraic equations. Each equation is written in its local coordinate system. For this purpose, the transition formulas of the generalized Fourier method are applied to the basic solutions of the Lamé equation. After solving the system of equations and finding the unknowns, the stress-strain state in the body of the layer and pipes was obtained. The reduction method was used to obtain numerical results. Fulfillment of the boundary conditions showed high convergence of the results, the accuracy of which depends on the order of the system of equations. The analysis of the stress-strain state of the layer and the pipe was carried out for different sleeve materials in places of stress concentration. The results indicate an increase in the stresses sφ and sz on cylindrical surfaces in the case of using polyamide bushings. The proposed method makes it possible to analyze the stress-strain state of a wide range of pipe structures. It also provides an opportunity to assess how changes in material and geometric parameters affect the stress distribution in such systems, which allows optimizing structures and ensuring their reliability. In the further development of this research topic, it is necessary to consider models where bushings are combined with other types of inhomogeneities (cavities, reinforcement) and other boundary conditions.

Low-cost 3D vision-based triangulation system for ultrasonic probe positioning

Abstract Introduction: In ultrasonic imaging, such as echocardiography, accurately positioning the probe in relation to the patient’s body or an external coordinate system is typically done manually. However, when developing speckle-tracking methods for echocardiology, ensuring consistency in probe positioning is essential for reliable data interpretation. To address this challenge, we present a vision-based system and method for probe positioning in this study. Materials and Methods: Our system comprises two cameras, a calibration frame with eight markers of known coordinates in the frames’ local coordinate system, and a probe holder with four markers. The calibration process involves image segmentation via region growing and extraction of the camera projection matrices. Subsequently, our positioning method also utilises marker segmentation, followed by estimating the markers’ positions using triangulation. Results: To evaluate the system’s performance, we conducted tests using a validation plate with five coplanar circular markers. The distances between each pair of points were calculated, and their errors compared to the true distances were found to be within a maximum of 0.7 mm. This level of accuracy is comparable to ultrasonic imaging resolution and thus deemed sufficient for the intended purpose. Conclusion: For those interested in replicating or modifying our methods, the supplementary material includes the complete design of the calibration frame and the Matlab code.

Calibration accuracy evaluation method for multi-camera measurement systems

To address the limitations of Digital Image Correlation (DIC) technology in terms of single-view and resolution capabilities, multi-camera systems have emerged, expanding the measurement area by increasing the number of cameras. However, traditional multi-camera systems continue to face challenges in the calibration of global external parameters and error control, particularly when uniform calibration between camera subsystems is not achieved, making the calibration results difficult to evaluate and analyze. In response, this paper systematically investigates the sources of error in multi-camera system calibration and proposes a novel precision evaluation method. This method qualitatively analyzes the registration results of subsystems by examining the determinant of the rotation matrix used to transform local coordinate systems to the global coordinate system and quantitatively assesses the registration accuracy based on the alignment error of targets after registration. Furthermore, a series of experiments were conducted to validate the proposed evaluation method, with results demonstrating that the method not only offers high effectiveness in precision evaluation but also provides reliable technical support in complex engineering measurements.

Biomechanical conditions of subtalar joint arthrodesis with calcaneal locking nail: A probabilistic numerical study.

Subtalar joint arthrodesis is primarily indicated for advanced osteoarthritis, hindfoot deformity, and/or instability. During the first 6-10 weeks after surgery, there is an intermediary structurally weaker state before complete bony fusion of the calcaneus and talus occurs. Loading of the foot can lead to mechanical stresses and relative movements in the former joint gap, which can impede the fusion process. The objective of this study was to examine the mechanical healing conditions for a subtalar arthrodesis with a calcaneal locking nail. A probabilistic finite element model of the subtalar joint with a calcaneal locking nail was created to represent the foot post-surgery that accounts for the uncertainty of the material properties. The model differentiates between cortical and cancellous bone and includes non-linear contact definitions in the subtalar joint. Multiple loading scenarios, including hindfoot inversion/eversion, were simulated to determine bone and implant stresses. Utilizing local articular coordinate systems, a displacement analysis was established to separate normal and tangential components and account for their separate effects. The loading of the locking nail was assessed through section moments. Under inversion/eversion loading, the area near the locking screws and upper end of the nail experienced the highest stresses. The maximum stresses in cortical and cancellous bone were 112±8.3 MPa and 2.1±0.2 MPa, respectively. The comparison of the von Mises and maximum principal stresses for the bones showed a load case dependency with strong effect on tensile loading states. The proposed method for the analysis of relative displacement in the local articular coordinate systems showed joint regions exhibiting normal and tangential movements that changed with the considered loading states. It was found that tangential displacements of up to 0.19 mm are related to the torsional loading of the calcaneal locking nail, which is connected to the corresponding torsional stiffness of the implant and its fixation in the calcaneus and talus. Normal displacements in the joint gap of up to -0.18 mm can be shown to be governed by the bending moments acting on the calcaneal locking nail, which are linked to the nail's bending stiffness. The ratio of tangential and normal displacement in the critical inversion configuration was determined to be -1.1. Inversion and eversion loads can lead to significant mechanical loading of the bones and to bending and torsional loading of the locking nail. The bending leads to normal displacements in the articular gap. Torsions can lead to significant tangential displacements that have been shown to promote non-union instead of bony fusion.

Simulating and Verifying a 2D/3D Laser Line Sensor Measurement Algorithm on CAD Models and Real Objects.

The increasing adoption of 2D/3D laser line sensors in industrial and research applications necessitates accurate and efficient simulation tools for tasks such as surface inspection, dimensional verification, and quality control. This paper presents a novel algorithm developed in MATLAB for simulating the measurements of any 2D/3D laser line sensor on STL CAD models. The algorithm uses a modified fast-ray triangular intersection method, addressing challenges such as overlapping triangles in assembly models and incorporating sensor resolution to ensure realistic simulations. Quantitative analysis shows a significant reduction in computation time, enhancing the practical utility of the algorithm. The simulation results exhibit a mean deviation of 0.42 mm when compared to real-world measurements. Notably, the algorithm effectively handles complex geometric features, such as holes and grooves, and offers flexibility in generating point cloud data in both local and global coordinate systems. This work not only reduces the need for physical prototyping, thereby contributing to sustainability, but also supports AI training by generating accurate synthetic data. Future work should aim to further optimize the simulation speed and explore noise modeling to enhance the realism of simulated measurements.

General Three-Body Problem in Conformal-Euclidean Space: New Properties of a Low-Dimensional Dynamical System

Despite the huge number of studies of the three-body problem in physics and mathematics, the study of this problem remains relevant due to both its wide practical application and taking into account its fundamental importance for the theory of dynamical systems. In addition, one often has to answer the cognitive question: is irreversibility fundamental for the description of the classical world? To answer this question, we considered a reference classical dynamical system, the general three-body problem, formulating it in conformal Euclidean space and rigorously proving its equivalence to the Newtonian three-body problem. It has been proven that a curved configuration space with a local coordinate system reveals new hidden symmetries of the internal motion of a dynamical system, which makes it possible to reduce the problem to a sixth-order system instead of the eighth order. An important consequence of the developed representation is that the chronologizing parameter of the motion of a system of bodies, which we call internal time, differs significantly from ordinary time in its properties. In particular, it more accurately describes the irreversible nature of multichannel scattering in a three-body system and other chaotic properties of a dynamical system. The paper derives an equation describing the evolution of the flow of geodesic trajectories, with the help of which the entropy of the system is constructed. New criteria for assessing the complexity of a low-dimensional dynamical system and the dimension of stochastic fractal structures arising in three-dimensional space are obtained. An effective mathematical algorithm is developed for the numerical simulation of the general three-body problem, which is traditionally a difficult-to-solve system of stiff ordinary differential equations.

Hypercyclicity and universality phenomena with atlas-smooth and atlas-holomorphic sequences

Smooth manifolds often require one to account for multiple local coordinate systems. On a smooth manifold like real n-dimensional space, we typically work within a single global coordinate system. Consequently, it is not hard to define partial differentiation operators, for example, and show that they are hypercyclic. However, defining a partial differentiation operator on smooth functions defined globally on general smooth manifolds is difficult due to the multiple local coordinate systems. We introduce the concepts of atlas-smooth and atlas-holomorphic sequences, which we use to study hypercyclicity and universality on spaces of functions defined both locally and globally on manifolds. We focus on partial differentiation operators acting on smooth functions defined on smooth manifolds, and we also consider complex manifolds as well. In 1941, Seidel and Walsh [5] showed that a certain sequence is universal on the space of holomorphic functions defined on the open unit disk. We use the ideas developed here to extend this result to certain complex manifolds.

Grad B Drifts of Heavy Ions Solar Energetic Particles at Solar Corona Region

The objective of this research study the Grad B drifts velocity of the heavy ion of the solar wind (C+4, C+5 (at corona region with distance (1 to 15) * 6.69*108m for two varied angles (Ɵ= 90ᵒ, 180ᵒ). It has been studied, that grad B drifts velocity, in the model of Parker spiral. within single particle dynamics model, in a spherical coordinate system (local coordinate system with an axis aligned with the magnetic field). This work result shown that, azimuthal grad B drift velocity, V∇Bφ` takes maximum value at polar zone for (C+4, C+5) for both velocities of solar wind. Also, there is no azimuthal grad B drifts V∇Bφ` at equators zone. And as for colatitude grad B drift velocity, V∇Bθ` takes high value at most of regions and the highest value at polar zone for fast and slow solar winds. And noting that the slow solar winds have higher values than fast solar wind at the equator region.

A High-Precision Inverse Finite Element Method for Shape Sensing and Structural Health Monitoring

In the contemporary era, the further exploitation of deep-sea resources has led to a significant expansion of the role of ships in numerous domains, such as in oil and gas extraction. However, the harsh marine environments to which ships are frequently subjected can result in structural failures. In order to ensure the safety of the crew and the ship, and to reduce the costs associated with such failures, it is imperative to utilise a structural health monitoring (SHM) system to monitor the ship in real time. Displacement reconstruction is one of the main objectives of SHM, and the inverse finite element method (iFEM) is a powerful SHM method for the full-field displacement reconstruction of plate and shell structures. However, existing inverse shell elements applied to curved shell structures with irregular geometry or large curvature may result in element distortion. This paper proposes a high-precision iFEM for curved shell structures that does not alter the displacement mode of the element or increase the mesh and node quantities. In reality, it just modifies the methods of calculation. This method is based on the establishment of a local coordinate system on the Gaussian integration point and the subsequent alteration of the stiffness integration. The results of numerical examples demonstrate that the high-precision iFEM is capable of effectively reducing the displacement difference resulting from inverse finite element method reconstruction. Furthermore, it performs well in practical engineering applications.

Segmental vertebral three-dimensional motion in patients with L4 isthmic spondylolisthesis under weight-bearing conditions

ObjectiveTo investigate in vivo 6-degree-of-freedom (DOF) vertebral motion in patients with isthmic spondylolisthesis (IS) during various functional weight-bearing activities.MethodsFifteen asymptomatic volunteers (mean age 54.8 years) and fourteen patients with IS at L4-5 (mean age 53.4 years) were recruited. The positions of the vertebrae (L4-L5) in the supine, standing, flexion–extension, left–right twisting and left–right bending positions were determined using previously described CT-based models and dual fluoroscopic imaging techniques. Local coordinate systems were established at the center of the anterior vertebra of L4 isthmic spondylolisthesis (AIS), the posterior lamina of L4 isthmic spondylolisthesis (PIS) and the center of the L5 vertebra to obtain the 6DOF range of motion (ROM) at L4-L5 and the range of motion (ROM) between the AIS and the PIS.ResultsThe translation along the anteroposterior axis at L4-L5 during flexion–extension, left–right bending and left–right twisting was significantly greater than that of the healthy participants. However, the translation along the mediolateral axis at L4-L5 presented paradoxical motion under different positions: the ROM increased in the supine-standing and flexion–extension positions but decreased in the left–right bending and left–right twisting positions. The separation along the anteroposterior axis during flexion was significantly greater than that during standing, on average, reaching more than 1 mm. The separation along the mediolateral axis during standing, flexion and extension was significantly greater than that in the supine position.ConclusionsThis study revealed the occurrence of displacement between the AIS and PIS, primarily in the form of separation during flexion. Symptomatic patients with isthmic spondylolisthesis exhibit intervertebral instability, which might be underestimated by flexion–extension radiographs.

Effects of Analog Modeling Materials on Topographic Photogrammetry (SfM) Reconstructions

AbstractAccurate topographic data are essential for quantitative structural analysis, both in natural settings and in the laboratory. The selection of modeling materials (with appropriate rheological properties) is known to be fundamental for the success of scaled physical analog experiments. However, the optical properties of analog materials and their impact on the reliability and precision of high‐resolution topographic reconstructions have not (to our knowledge) previously been assessed. Here we evaluate the effects of material composition, color, and grain size on Structure‐from‐Motion (SfM) photogrammetry reconstruction efficacy for deformed and undeformed model configurations in the laboratory. Image collections for photogrammetry are acquired from multiple camera positions with a handheld digital camera, and reconstructions are registered using ground control points in a local coordinate system. Static experiments show that low reflectivity granular materials (e.g., silica sand, volcanic ash, pumice, and Al2O3) yield relatively reliable photogrammetry data for a wide range of grain sizes (44–2,400 μm) but larger grain sizes (≥250 μm) provide more robust results. Reflective materials (e.g., glass beads, wet clay) yield less reliable point‐clouds but the addition of low‐reflectivity granular materials (e.g., Al2O3 grains) on the surface of wet clay improves reconstruction results, with higher grain densities typically yielding lower point‐cloud residuals. SfM‐photogrammetry reconstruction of deformed clay analog models tends to improve at higher extension magnitudes because of fault and associated texture development on model surfaces. We anticipate that our results will help practitioners to improve the precision and reliability of photogrammetric data acquired in the analog modeling laboratory.

Geometric descriptors for beta turns.

Beta turns, in which the protein backbone abruptly changes direction over four amino acid residues, are the most common type of protein secondary structure after alpha helices and beta sheets and play key structural and functional roles. Previous work has produced classification systems for turn geometry at multiple levels of precision, but these operate in backbone dihedral-angle (Ramachandran) space, and the absence of a local Euclidean-space coordinate system and structural alignment for turns, or of any systematic Euclidean-space characterization of turn backbone shape, presents challenges for the visualization, comparison and analysis of the wide range of turn conformations and the design of turns and the structures that incorporate them. This work derives a turn-local coordinate system that implicitly aligns turns, together with a set of geometric descriptors that characterize the bulk BB shapes of turns and describe modes of structural variation not explicitly captured by existing systems. These modes are shown to be meaningful by the demonstration of clear relationships between descriptor values and the electrostatic energy of the beta-turn H-bond, the overrepresentations of key side-chain motifs, and the structural contexts of turns. Geometric turn descriptors complement Ramachandran-space classifications, and they can be used to select turn structures for compatibility with particular side-chain interactions or contexts. Potential applications include protein design and other tasks in which an enhanced Euclidean-space characterization of turns may improve understanding or performance. The web-based tools ExploreTurns, MapTurns, and ProfileTurn, available at www.betaturn.com, incorporate turn-local coordinates and turn descriptors and demonstrate their utility.

The effect of (not) applying symmetry constraints during refinement and using different local coordinate systems on local symmetry of atoms and atom types in the MATTS data bank

The effect of (not) applying symmetry constraints during refinement and using different local coordinate systems on local symmetry of atoms and atom types in the MATTS data bank

Validation in X-Plane of Control Schemes for Taking off and Landing Manoeuvres of Quadrotors

This paper shows the results obtained by using MATLAB/Simulink and X-Plane as co-simulation tools for the comparison of control schemes for takeoff and landing maneuvers of a quadrotor. Two control schemes based on nested saturations are compared to ensure the convergence of θ and ϕ angles to the equilibrium point, each with its own specific characteristics in its design and tuning procedure. Furthermore, in both proposals, a Generalized Proportional Integral (GPI) control is used for the height part, while a feedforward PID control is used for the ψ angle. The control schemes are proposed from a local geodetic coordinate system East, North, Up (ENU). Feedback data for the control schemes are obtained from X-Plane via User Datagram Protocol (UDP)-based interface; they are used in MATLAB/Simulink for the calculation of the control actions; the control actions are then entered into a transformation matrix that converts the actions into rotor angular velocities, which are sent to X-Plane. Several numerical simulations are presented to demonstrate the effectiveness and robustness of the proposed schemes, considering the presence of disturbances mainly due to wind speed. Finally, different performance indices are used to evaluate the schemes based on error; in this way, the use of X-Plane as a Model-in-Loop (MIL) environment is validated, which helps to identify errors or problems of the proposed controllers before their coding and physical implementation.

Méary's angle decoded: 3D analysis of first ray plantarflexion deformity in Charcot-marie-tooth disease

BackgroundThe typical cavovarus deformity seen in patients with Charcot-Marie-Tooth (CMT) involves plantarflexion of the first ray. The exact apex of the deformity has never been proven, although it is presumed to be within the medial cuneiform. The aim of this study was to utilize weight-bearing computed tomography (WBCT) to localize and quantify first ray plantarflexion deformity in CMT patients. MethodsWBCTs of 16 CMT patients with lateral Méary’s angle > 20 degrees were compared to controls utilizing semi-automated analysis software. A local coordinate system based on the first metatarsal was used to avoid bias of proximal deformity. The tarsometatarsal angle was subdivided into components (cuneiform-cuneiform joint normal, tarsometatarsal joint and metatarsal-metatarsal joint normal) and compared between CMT and controls. CMT patient’s first, second and third rays were also compared. Means were compared with a 2-sample t test (p < .05). ResultsCMT patients had significantly more plantarflexion of the first ray than controls (16.4 versus 8.8 degrees respectively(p < 0.001)). The largest difference of was found at the medial cuneiform with 20.6 degrees of plantarflexion in CMT patients versus 14.8 degrees in controls (p < .0001). There was also approximately 2 degrees of plantarflexion at the TMT joint (p < .001). ConclusionsPlantarflexion deformity in CMT patients is primarily an osseous deformity at the level of the medial cuneiform with a lesser contribution from the tarsometatarsal joint. Level of evidenceIII Retrospective comparative study

A novel isogeometric coupling approach for assembled thin-walled structures

In the aerospace field, there are numerous assembled thin-walled structures with complex geometric continuity conditions. This makes isogeometric analysis (IGA) inevitably meet multi-patch issues. In previous work on 5-DOFs shell, when encountering G0 continuity or kinks, the approach often involved converting two local coordinate system rotations into three global coordinate system rotations to achieve multi-patch coupling. This often introduces additional DOFs and may destabilize the stiffness matrix. In this study, inspired by the concept of solid coupling, a new shell coupling approach is proposed, developing a 5-DOFs shell coupling framework suitable for different geometric continuities, providing a more efficient and simpler framework. When calculating the coupling stiffness matrix, there is no need for prior classification of the control points. Within this framework, the Nitsche, Penalty, and Mortar methods based on IGA are implemented. To demonstrate the effectiveness of the proposed framework in static and linear buckling analyzes, four different numerical examples were constructed, including G1, G0 continuity, and kinks. Under different continuity conditions, the results are sensitive to the parameter selection of the Nitsche and Penalty methods. Appropriate parameter selection can lead to better results for them. Compared to others, the Mortar method avoids this problem, making it easier to apply in engineering. The core codes are publicly available at https://github.com/tasteofbbq/ICA4ATWS.

Конечно-элементное моделирование нелинейных задач упругости в абсолютных узловых координатах на неструктурированных шестигранных сетках

We consider a finite element approach to solving the problem of elasticity theory in terms of absolute nodal coordinate formulation (ANCF), in which large body displacements are described in a global reference frame without using any local coordinate system. The main feature of the method is the absence of gyroscopic effects and, as a result, constancy of the mass matrix and the vector of the generalized force of gravity. In contrast to the traditional ANCF approach, the sets of nodal degrees of freedom of the finite element are formed only on the basis of absolute coordinates of nodes, which allows us to solve the problem using, in particular, unstructured hexahedral meshes. To construct the stiffness matrix, we apply a second-order automatic differentiation algorithm, which ensures its symmetrical form (Hessian matrix) and is analytically accurate in calculating the derivative. This approach also makes it possible to carry out calculations for models of hyperelastic materials without the corresponding Piola-Kirchhoff tensor. It has been shown that within the framework of discretization of the equation of motion, along with the well-known Newmark numerical integration scheme, it is possible to use the HTT-α scheme, which is unconditionally stable, second-order accurate and dissipative for high frequencies. We present several examples of solving static and dynamic elasticity problems for compressible and incompressible models of hyperelastic materials, in which the functions of internal energy density of the body are specified in terms of the deformation gradient.

Theoretical and experimental investigation into detection of early-stage propagation of double cracks with distributed fiber optic sensor

A strain transfer model is developed to describe the transfer of crack opening displacement (COD) of double cracks in a structural substrate to the distributed fiber optic sensor (DFOS). Global and local coordinate systems are set up to aid in the deduction of the transfer of CODs of the double cracks to the DFOS. The analytical model of strain transfer is first derived in the local coordinate system and then is transformed into the global coordinate system. Analytical results show that the DFOS fiber strain induced by CODs of the double cracks in the structural substrate is affected by both the spacing and the CODs of the double cracks, and the strain peak is suppressed as the crack spacing is less than the characteristic length which is defined as the range of influence of the COD of the individual crack. The influences of the material properties of the DFOS, the fiber coating, the bonding adhesive, and the DFOS-fiber coating interfacial stiffness are discussed. The developed model is also experimentally validated by monitoring CODs of double cracks in aluminum alloy plates with optical frequency domain reflectometer (OFDR) DFOSs. Experimental results show that the strain distribution measured by the OFDR DFOSs agree well with the analytical results of the developed model. The limitations of the developed model and future work anticipated are then discussed.