Arbitrary Shape Research Articles

Particle Tracking of Orientation and Velocity Of Arbitrary Shape

Dispersions or particulate systems are prevalent in numerous natural and practical applications. Characterisation of such multiphase systems usually involves measuring size, spatial location, velocity and number density, which is usually non-trivial. The 'Depth from Defocus' (DFD) technique provides an imaging-based volumetric approach for estimating the size and position of dispersed spherical particles using the blurring information from a shadowgraph image. The two-image DFD approach involves two cameras to capture simultaneous images at different degrees of blur, which, although simpler, requires a mandatory calibration procedure. This study proposes a single-image DFD technique that provides a calibration-free size estimation using theoretical functions while evaluating position requires a simple calibration. The efficacy of this technique is demonstrated for various sparse spherical dispersions, including target dots, dispersed glass beads, liquid droplets in sprays and surface bubble rupture, and pollen grains. The method further enables precise determination of the measurement volume, which is crucial, allowing for bias-free estimates of the size distribution and volume concentration. The simple optical configuration and semi-automatic calibration procedure make this method easily deployable and accessible for diverse applications. The pixelation effect on the limiting value of the degree of blur is also estimated theoretically and compared with experiments. This effect is of interest concerning any typical discrete sensor imaging system in general.

A point cloud segmentation framework for image-based spatial transcriptomics

Recent progress in image-based spatial RNA profiling enables to spatially resolve tens to hundreds of distinct RNA species with high spatial resolution. It presents new avenues for comprehending tissue organization. In this context, the ability to assign detected RNA transcripts to individual cells is crucial for downstream analyses, such as in-situ cell type calling. Yet, accurate cell segmentation can be challenging in tissue data, in particular in the absence of a high-quality membrane marker. To address this issue, we introduce ComSeg, a segmentation algorithm that operates directly on single RNA positions and that does not come with implicit or explicit priors on cell shape. ComSeg is applicable in complex tissues with arbitrary cell shapes. Through comprehensive evaluations on simulated and experimental datasets, we show that ComSeg outperforms existing state-of-the-art methods for in-situ single-cell RNA profiling and in-situ cell type calling. ComSeg is available as a documented and open source pip package at https://github.com/fish-quant/ComSeg.

Semi-analytical method for calculating ground vibrations from a tunnel in a homogeneous half-space with an irregular surface

This paper proposes a novel two-dimensional (2D) semi-analytical method for calculating ground vibrations from a tunnel situated in a homogeneous half-space with an irregular surface. The circular tunnel is conceptualized as an elastic solid, while the soil is modelled as an elastic, isotropic, and homogeneous half-space with an irregular surface. A virtual horizontal interface is introduced to divide the soil domain into an irregular region with an arbitrary-shaped surface and a half-space with a circular hollow. The wavefield scattered by the irregular surface is simulated by the boundary integral equation. Through the application of the discrete wavenumber approach and expansion of wavefield on the irregular surface, the boundary integral equation is transformed into a set of simultaneous matrix equations containing unknown expansion coefficients. By utilizing the transformation between cylindrical and plane waves, the boundary conditions on soil-tunnel interface are satisfied, yielding a solution for a harmonic point load acting on the tunnel in a half-space with an irregular surface. The proposed method can simulate topographies with arbitrary shapes and only requires the discretization of the irregular part of the ground surface, which provides a highly efficient tool to investigate the propagation characteristics of train-induced vibrations in complex topographies. The proposed method is verified through comparisons with the existing analytical methods and the finite element method. The dynamic responses of a tunnel embedded in a half-space with a Gaussian-shaped surface are meticulously investigated. A case study involving a site for the Shenzhen metro line 5 is performed. The numerical results demonstrate that the presence of irregular topography alters the distribution of ground vibrations, leading to significant differences in responses within the irregular region and certain disparities in the regular region. The effect of the location, size, and undulating direction of the irregular topography on ground vibrations is frequency-dependent.

Virtual fit assessment of U.S. army body armor using NASA spacesuit techniques

Fit and accommodation are critical design goals for a body armor system to maximize Soldiers’ protection, comfort, mobility, and performance. The aim of this study is to assess fit and accommodation of body armor plates for the US Army. A virtual fit assessment technique, developed, validated, and deployed by NASA for spacesuit design, was adopted for this work. Specifically, 3D manikins of the Soldier population were overlaid virtually with geometrically similar surrogates of the armor plates. Trained subject matter experts with the US Army and NASA manually assessed the fit of the armor plates to manikins using a computer visualization tool and selected the appropriate plate size and position. A prediction model was built from the assessment data to predict the plate size from an arbitrary body shape and the resultant patterns of body-to-plate contact were quantified. The outcome indicated a unique trend of the plate sizes covarying with anthropometry. More pronouncedly, when the overlap between the body tissue and armor plate was quantified, female Soldiers are likely to experience a 25 times larger body-to-plate contact volume and 6.5 times larger contact depth than males on average, due to sex-based anthropometric differences. Overall, the prediction model and contact patterns provided key metrics for virtual body armor fit assessments, of which the locations, patterns, and magnitudes can help to improve sizing and fit of body armor systems, as previously demonstrated for NASA spacesuit design.

Optical torque calculations and measurements for DNA torsional studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As a further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

An optimal control strategy to design passive thermal cloaks of arbitrary shape

In this paper, we describe a numerical framework for achieving passive thermal cloaking of arbitrary shapes in both static and transient regimes. The design strategy is cast as the solution of an optimal control problem (OCP) for the heat equation where the coefficients of the thermal diffusivity matrix take the role of control functions, and the distance between the uncloaked and the cloaked field is minimized in a suitable observation domain. The control actions enter bilinearly in the heat equation, thus making the resulting OCP nonlinear, and its analysis non-trivial. We show that optimal diffusivity coefficients exist both for the static and the transient case; we derive a system of first-order necessary optimality conditions; finally, we carry out their numerical approximation using the finite-element method. A series of numerical test cases assess the capability of our strategy to tackle passive thermal cloaking of arbitrarily complex two-dimensional objects.

Prediction of directivity characteristics of piezoelectric macro-fiber composite interdigital transducers: a semi-analytical approach

The employment of guided waves for structural health monitoring applications has attracted substantial attention in recent years. Piezoelectric transducers are frequently employed in these systems for elastic wave generation and acquisition. Their dynamic properties, i.e., direction-dependent frequency characteristics, are an important feature for designing a reliable monitoring strategy. Although analysis of the transducer directivity pattern can be performed using finite element models, these usually tend to be computationally very expensive, especially, for parametric and optimization studies. In this paper, a semi-analytical methodology is proposed that can predict the far-field responses of complex transducers of arbitrary shape and structure mounted on elastic plates. The approach reported here couples analytical far-field predictions with a local FE model evaluating the traction field generated by the transducer. Thus, the FE model captures the near-field responses, while the analytical part predicts the far-field responses. The implementation of this semi-analytical method requires development of analytical and numerical frameworks. The former includes computation of dispersion curves of the inspected plate, the stress and displacement profiles of wave modes and the excitability curves, while the latter includes estimation of the traction field between the transducer and the plate using the FE model. Owing to the popularity of piezoelectric macro-fiber composite (MFC) interdigital transducers, in this paper, we apply the proposed method to simulate the directivity patterns of the MFC IDTs of different configurations. To validate the reliability of the proposed method the simulated patterns are compared with experimental results obtained using Laser Doppler Vibrometer (LDV).

(HTBNet)Arbitrary Shape Scene Text Detection with Binarization of Hyperbolic Tangent and Cross-Entropy.

The existing segmentation-based scene text detection methods mostly need complicated post-processing, and the post-processing operation is separated from the training process, which greatly reduces the detection performance. The previous method, DBNet, successfully simplified post-processing and integrated post-processing into a segmentation network. However, the training process of the model took a long time for 1200 epochs and the sensitivity to texts of various scales was lacking, leading to some text instances being missed. Considering the above two problems, we design the text detection Network with Binarization of Hyperbolic Tangent (HTBNet). First of all, we propose the Binarization of Hyperbolic Tangent (HTB), optimized along with which the segmentation network can expedite the initial convergent speed by reducing the number of epochs from 1200 to 600. Because features of different channels in the same scale feature map focus on the information of different regions in the image, to better represent the important features of all objects in the image, we devise the Multi-Scale Channel Attention (MSCA). Meanwhile, considering that multi-scale objects in the image cannot be simultaneously detected, we propose a novel module named Fused Module with Channel and Spatial (FMCS), which can fuse the multi-scale feature maps from channel and spatial dimensions. Finally, we adopt cross-entropy as the loss function, which measures the difference between predicted values and ground truths. The experimental results show that HTBNet, compared with lightweight models, has achieved competitive performance and speed on Total-Text (F-measure:86.0%, FPS:30) and MSRA-TD500 (F-measure:87.5%, FPS:30).

Unsupervised learning-enabled pulsed infrared thermographic microscopy of subsurface defects in stainless steel

Metallic structures produced with laser powder bed fusion (LPBF) additive manufacturing method (AM) frequently contain microscopic porosity defects, with typical approximate size distribution from one to 100 microns. Presence of such defects could lead to premature failure of the structure. In principle, structural integrity assessment of LPBF metals can be accomplished with nondestructive evaluation (NDE). Pulsed infrared thermography (PIT) is a non-contact, one-sided NDE method that allows for imaging of internal defects in arbitrary size and shape metallic structures using heat transfer. PIT imaging is performed using compact instrumentation consisting of a flash lamp for deposition of a heat pulse, and a fast frame infrared (IR) camera for measuring surface temperature transients. However, limitations of imaging resolution with PIT include blurring due to heat diffusion, sensitivity limit of the IR camera. We demonstrate enhancement of PIT imaging capability with unsupervised learning (UL), which enables PIT microscopy of subsurface defects in high strength corrosion resistant stainless steel 316 alloy. PIT images were processed with UL spatial–temporal separation-based clustering segmentation (STSCS) algorithm, refined by morphology image processing methods to enhance visibility of defects. The STSCS algorithm starts with wavelet decomposition to spatially de-noise thermograms, followed by UL principal component analysis (PCA), fine-tuning optimization, and neural learning-based independent component analysis (ICA) algorithms to temporally compress de-noised thermograms. The compressed thermograms were further processed with UL-based graph thresholding K-means clustering algorithm for defects segmentation. The STSCS algorithm also includes online learning feature for efficient re-training of the model with new data. For this study, metallic specimens with calibrated microscopic flat bottom hole defects, with diameters in the range from 203 to 76 µm, were produced using electro discharge machining (EDM) drilling. While the raw thermograms do not show any material defects, using STSCS algorithm to process PIT images reveals defects as small as 101 µm in diameter. To the best of our knowledge, this is the smallest reported size of a sub-surface defect in a metal imaged with PIT, which demonstrates the PIT capability of detecting defects in the size range relevant to quality control requirements of LPBF-printed high-strength metals.

Intrinsic Optimum Thermodynamic Shapes of Zincblende‐ and Diamond‐Structure Nanowire Cross‐Sections

AbstractCrystalline nanowire (NWire) cross‐section shapes are known to vary considerably in experiment; an accurate analytic evaluation of NWire cross‐sections from a thermodynamic perspective is still missing. Building on previous work, analytic descriptions are given for zincblende (zb) NWire cross‐section morphing to arbitrary convex hexagonal shapes in order to evaluate the crystallographic‐structural stability of experimental NWire cross‐sections. The maximum of the ratio of NWire‐internal bonds per NWire atom describes the most stable crystallographic and thermodynamic shape of the NWire as far as internal forces are concerned. This maximum occurs when the first derivative of the above ratio , with presenting respective optimum morphing indices to obtain . The stability evaluation is then carried out by comparing derived from the experimental image over the complete morphing range of the NWire cross‐section represented by . This user‐friendly analytic approach allows to calculate the optimum morphing indices and thus all follow‐on parameters, such as , , the number of interface bonds and the NWire cross‐section area . Three examples with experimental data demonstrate the versatility and detailed insight the stability evaluation provides to any zb‐ and diamond‐lattice NWire cross‐section.

Visually encoding orthogonal planar graph drawings as graph mazes: An eye tracking study

There are various styles to visually represent relational data in the form of node-link diagrams. In particular, for planar graphs we can find orthogonal node-link diagrams consisting of links bending only at ninety degrees a successful and prominent variant. One of the benefits of such drawings is the tracking of longer paths through a network with the eyes due to their limited number of link orientations, changes, and variations, but on the negative side the links can have arbitrary bending shapes. In this article we developed a novel way to visualize such orthogonal planar drawings by making use of mazes that look more natural to the human eye due to the street-like visual metaphor that many people are familiar with. Tracking paths is one of the major tasks in such graph visualizations, similar to orthogonal node-link diagrams, however, we argue that mazes are a more natural way to find paths. To get insights in the visual scanning behavior when reading graph mazes we conducted a comparative eye tracking study with 26 male versus female participants of different experience levels while also alternating between orthogonal node-link drawings and graph mazes as well as different graph size levels. The major result of this comparative study is that the participants can track paths in both representation styles, including a geodesic path tendency in their visual search behavior, but typically have a longer fixation duration at branching nodes and locations in the mazes that lead to opposite directions to the geodesic path tendency, maybe the viewers had to start a reorientation phase in their visual scanning behavior. We also found out that the size, that is the number of graph vertices has an impact on the visual scanning behavior for both orthogonal node-link diagrams as well as street-like maze representations, but for the mazes we found this impact to be less strong (in terms of the eye movement data metrics fixation durations and saccade lengths) compared to the node-link diagrams. To conclude the article, we discuss limitations and scalability issues of our approach. Moreover, we give an outlook and future work for possible extensions.

Environmental protection after civil war: A difference-in-geographic-discontinuity approach

Although civil war devastates the environment, we still do not understand the role of environmental policies in post-war countries and often have a pessimistic view without empirical evidence. This study challenges this view by arguing that the introduction of independent monitoring mechanisms can make environmental regulations effective even in post-war countries and also by exploiting analytical opportunities in the Democratic Republic of the Congo (DRC). In 2011–2013, the government implemented independent monitoring mechanisms to lessen the side effects of mining activities on deforestation. The reform, however, only applied to mining permit zones, which had arbitrary grid-based shapes. This allows combining a geographic regression discontinuity and difference-in-differences to a difference-in-geographic-discontinuity (DiGD) design. With satellite-based data available at every 30 metres for over 40 million cells in the DRC, the analysis indicates that the 2011–2013 reform decreased deforestation rates immediately inside the mining permit zones. The effect existed even in the areas of continuing armed conflicts. Further analysis of causal mechanisms suggests that the 2011–2013 reform facilitated the compliance of existing operators and also screened out incompliant operators. Overall, these findings imply that the environmental effects of civil war can depend on post-war policies — a missing link in the literature on environmental security.

Topological derivative based sensitivity analysis for three-dimensional discrete variable topology optimization

This study introduces a novel Topological Derivative-based Sensitivity Analysis (TDSA) methodology for three-dimensional (3D) discrete variable topology optimization. Recently, the authors pointed out that the discrete variable sensitivity can be related to the topological derivative, and thus can be rationally approximated by the specially customized topological derivative for plane stress problems. However, the 3D discrete variable sensitivity requires the 3D topological derivative with element-shaped (e.g., unit cube) domain perturbation, whose analytical solution is not available in the literature. This paper proposes a unified parameter fitting framework to calculate the 3D topological derivative with arbitrary shape 3D domain perturbation. The formula for spherical hole perturbation obtained through this parameter fitting framework is identical to the well-known analytical topological derivative formula. Further, the 3D discrete variable sensitivity can be easily obtained through element-shaped domain perturbation. With the recently proposed Sequential Approximate Integer Programming (SAIP), numerical examples demonstrate that TDSA is precise not only for the self-adjoint 3D minimum compliance problems but also for the non-adjoint 3D compliant mechanism design problems. In sum, numerical examples have been conducted by feeding the derived sensitivity to the SAIP optimization algorithms, and the correctness of the sensitivity information has been well demonstrated. This research further solidifies the foundation of rational discrete variable sensitivity analysis in 3D topology optimization.

Reactive Collision Avoidance Control for Nonholonomic Vehicles and Obstacles of Arbitrary Shape

Abstract Potential field-based collision avoidance algorithms for mobile robots frequently assume vehicles and obstacles to have circular or spherical shapes. This assumption not only simplifies the analysis but also limits the mobility of agents in confined spaces, particularly for vehicles with elongated or irregular shapes. To increase mobility, this letter presents a decentralized collision avoidance framework for nonholonomic systems of unicycle type that considers the non-circular shape and relative orientation of vehicles and obstacles. The framework builds on the concepts of potential field and avoidance functions. However, it proposes using a non-constant minimum safe distance radius that changes based on the shape, relative position, and relative orientation of agents. The control framework is proven to guarantee collision avoidance at all times and is shown, via simulation, to increase the ability of agents to navigate through narrow spaces safely.

FLIPEC, an ideal MHD free-boundary axisymmetric equilibrium solver in the presence of macroscopic flows

The most relevant features of FLIPEC (Free fLow Iterative Plasma Equilibrium Code) are presented. This new code iteratively calculates free-boundary, axisymmetric ideal MHD equilibria with arbitrary poloidal and toroidal plasma flows. FLIPEC is a mature code that has emerged from a complete overhaul of a previous version (F-Torija Daza 2022 et al Nucl. Fusion 62 126044). It uses a (inverse) curvilinear coordinate representation for the Grad–Shafranov–Bernoulli equation system, which allows FLIPEC to extend its free-boundary capabilities to arbitrary plasma shapes and removes many limitations with regards to the distance between plasma and external coils. Run-time stabilization of vertical modes has also been implemented by means of artificial feedback coils. Finally, active targeting schemes have also been included. These capabilities are illustrated on two very different cases: the ITER tokamak baseline configuration and a NSTX spherical tokamak equilibrium.

Rope–sheave contact transient analysis in hoisting operations with a bristle model and an arbitrary Lagrangian–Eulerian approach

AbstractThis paper describes the development of a computational model for the rope–sheave contact interaction in reeving systems when the ropes are modeled with an arbitrary Lagrangian–Eulerian approach. This discretization approach has been developed in previous publications as a general and systematic method for the modeling and simulation of reeving systems. However, the rope–sheave contact model was avoided assuming the no-slip contact condition. The contact model developed in this paper introduces specialized ALE-ANCF-cubic rope contact elements that are used to discretize the rope segment winded at the sheave. The contact is modeled using a set of virtual discrete bristles attached to material points in the mid-line of the rope in one end and in contact with the sheave in the other end. Therefore, a second Lagrangian mesh, apart of the ALE mesh used to discretize the rope, is used to define the fixed ends of the bristles. The kinematics and dynamics used to calculate the normal and tangential contact forces are described in detail. The contact model is 3D and can be used to analyze the contact with a sheave groove with arbitrary shape. The tangential contact force model can be used to describe stick and slip contact conditions and, to improve the simulation performance of the model, an LuGre regularization tangential contact force model is used. The rope-sheave contact model is used to analyze the behavior of a simple elevator system. The numerical results show that the static rope-sheave contact interaction agrees well with an analytical solution of the problem. Finally, the same elevator system is analyzed dynamically for a cabin ride of 8 meters with a steady velocity of 1 m/s. Results show that the normal and tangential contact forces during the steady velocity period are not so different from the static solution, but very different from the classical Creep Theory and Firbank’s Theory.

Experimental Realization of a One‐Directional Broadband Transmissive Cloak in Microwaves

AbstractHiding an isolated object in free space using a transmissive invisibility cloak has become a significant research area, propelled by advancements in metamaterials and transformation optics over the past decade. Despite the availability of various simplified methods for implementing transmissive cloaks, issues such as impedance mismatches and narrow working bandwidths often arise, posing challenges. Achieving a broadband transmissive cloak in free space has proven to be particularly arduous. This study presents a near‐perfect one‐directional broadband transmissive cloak constructed from multilayer metasurfaces of arbitrary shapes, showcasing superior performance across a broadband frequency range. The phase distribution of the metasurfaces and the efficacy of the transmissive cloak are assessed using the generalized Snell's law. An experimental near‐perfect broadband transmissive cloak is successfully demonstrated to operate within the frequency range of 8.5 to 11.2 GHz. This study contributes to reducing the density and mass of cloaks, thereby facilitating the expansion of cloaking capabilities in various directions and across different frequency bands.

G2-SCANN: Gaussian-kernel graph-based SLD clustering algorithm with natural neighbourhood

For most clustering methods, not only the number of clusters must be set in advance, but also various hyperparameters such as initial centroids, number of nearest neighbours, the minimum number of points, neighbourhood radius, and cutoff distance all require pre-specification. As one of the most promising unsupervised learning methods in machine intelligence, existing clustering methods cannot simultaneously handle datasets with arbitrary shapes, different densities, distinct sizes, and overlapping. Background outliers and high dimensionality make clustering problems more challenging. In this paper, we propose a novel universal clustering methodology, called G2-SCANN, which yields the best clustering performance for all 30 synthetic and real datasets without any hyperparameter tuning if the exact number of clusters is known. Firstly, the shortest path length (SPL) in complex network or graph-based geodesic distance is used to give a locally backbone-structured description of graph vertex similarity. Accordingly, SPL-weighted local degree (SLD) is defined as vertex attributes of a SPL-weighted graph expressed by G2-SPL adjacency matrix with ε-natural neighbourhood. Secondly, the process of calculating SLD for every data point in a bottom-up way directly leads to division from a complete graph constituted by all data points to a group of SLD trees. This brings the interpretability and the elimination of lone trees. Thirdly, contrastive learning of largest SLD values for finding root vertices of each divisive tree is conducted and top-down category message is then transmitted from the root vertices to all the leaf ones of a SLD tree. It eventually produces tree-like clusters. Totally, the proposed G2-SCANN method leverages both local neighbouring similarity of data points and global information about data distribution and makes it perform better than other methods.

Efficient and robust clustering based on backbone identification

Clustering is the process of grouping similar data objects into different subsets based on their similarities. Inspired by the concept of the popularity of individuals in a community, we rate the popularity of each sample which reflects the centrality of that sample in the dataset. With the aim of identifying clusters with arbitrary shapes and varying densities, we propose a clustering approach that divides samples into separate population groups. This approach is based on identifying the backbone of data, characterized by a set of popular points surrounded by less popular points. To distinguish poorly separated clusters, a proximity measure is defined based on the popularity of samples. We also use the popularity of samples to assign halo points to clusters and calculate cohesion between clusters. The proposed clustering method can detect arbitrary-shaped clusters with varying densities without requiring to specify the number of clusters. Outliers are also identified according to popularity. We demonstrate the effectiveness of the approach on synthetic and real-world datasets.

Dispersion characteristics of arc-axis waveguides

Ultrasonic single mode excitation methods, mode separation algorithms and damage detection applications all require the calculation of the dispersion characteristics of the waveguide. However, existing dispersion calculation methods are mainly applicable to straight-axis waveguides. Therefore, in this paper, a novel semi-analytical finite element method in cylindrical coordinates (SAFEM-CC) is established and we focus on the dispersion characteristics of arc-axis waveguides. The cross-section of the waveguide can have arbitrary complex shapes, and the correctness of this method is verified by the finite element eigenfrequency method. At the same time, this paper takes the example of an arc-axis structure with a square cross-section and investigates the convergence of SAFEM-CC under different numbers of elements, element types, and element orders. This paper also establishes a finite element simulation model to study the waveform transmission law over a wide frequency range and the wave amplitude distribution law within the cross-section of arc-axis waveguides. The dispersion characteristics of arc-axis waveguides at different radii are also investigated. Finally, the correctness of the proposed method and the dispersion characteristics of arc-axis waveguides are verified by a large number of experiments. The main conclusions are as follows: the waveform transmission laws of the guided wave in arc-axis waveguides at each frequency agree with the dispersion curve; the theoretical wavestructure gives the distribution law of the amplitude within the cross-section; when the axis is arc, the displacement of the wavestructure on the inner and outer sides does not have symmetry, and the difference between the left and right sides gradually increases as the radius decreases.