Discontinuous Problems Research Articles

On Improving Bounding Box Representations for Oriented Object Detection

Detecting objects in remote sensing images (RSIs) using oriented bounding boxes (OBBs) is flourishing but challenging, wherein the design of OBB representations is the key to achieving accurate detection. In this article, we focus on two issues that hinder the performance of the two-stage oriented detectors: 1) the notorious boundary discontinuity problem, which would result in significant loss increases in boundary conditions, and 2) the inconsistency in regression schemes between the two stages. We propose a simple and effective bounding box representation by drawing inspiration from the polar coordinate system and integrate it into two detection stages to circumvent the two issues. The first stage specifically initializes four quadrant points as the starting points of the regression for producing high-quality oriented candidates without any postprocessing. In the second stage, the final localization results are refined using the proposed novel bounding box representation, which can fully release the capabilities of the oriented detectors. Such consistency brings a good trade-off between accuracy and speed. With only flipping augmentation and single-scale training and testing, our approach with ResNet-50-FPN harvests 76.25% mAP on the DOTA dataset with a speed of up to 16.5 frames/s, achieving the best accuracy and the fastest speed among the mainstream two-stage oriented detectors. Additional results on the DIOR-R and HRSC2016 datasets also demonstrate the effectiveness and robustness of our method. The source code is publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/yanqingyao1994/QPDet</uri> .

Diffusive Regularization Inverse PINN Solutions to Discontinuous Problems

It is of great importance to numerically capture discontinuities for the numerical solutions to hyperbolic conservation laws equations. The PINN (physics-informed neural networks) was used to solve the forward problem of the hyperbolic conservation laws equations, with the diffusion term added, which is difficult to determine and needs to be obtained through high-cost trial calculation. To capture the discontinuous solutions and save calculation costs, the equation was regularized through addition of diffusive terms. Then the regularized equation was incorporated into the loss function, and the exact solutions or reference solutions to the conservation laws equations were used as the training set to learn the diffusion coefficients, and the solutions at different moments were predicted. Compared with that of the PINN method for solving forward problems, the resolution of discontinuous solutions was improved, and the trouble of massive trial calculation was avoided. Finally, the feasibility of the algorithm was verified by 1D and 2D numerical experiments. The numerical results show that, the new algorithm has better ability to capture discontinuities, produces no spurious oscillations and no screed phenomena. Additionally, the diffusive coefficients obtained with the new algorithm make a reference to construct the classic numerical scheme.

İki Rijit Dikdörtgen Blok ile Yüklenen Elastik İki Tabakanın Süreksiz Temas Problemi

In this study, unlike the literature, the discontinuous contact problem of two elastic layers resting on a loaded elastic semi-infinite plane with two rigid rectangular blocks is analyzed analytically.P and Q loads are.transferred to the layers through blocks. Sheet weights were included in the problem. When the load value λ applied to the system exceeds the critical load value λcr, discontinuities occur on the contact surfaces. The problem is reduced to a singular integral equation using Fourier integral transform techniques in case of discontinuous contact. Singular integral equation is solve using Gauss-Chebyshev integral formulation. These discontinuities have been examined for the change in distance between blocks, block widths and changes in load ratios. Moreover, the swelling rates occurring during the separations are presented in graphics. In addition, the results obtained have been solved and compared with the help of ANSYS package program using the Finite Element Method.

Refined three-dimensional simulation of ribbed bar pull-out tests based on an enhanced peridynamic model

Peridynamic (PD) theory can effectively model discontinuous problems, but it remains a challenging task for refined three-dimensional (3D) simulation of bond-slip behaviors in pull-out tests, particularly when the rib of rebar is considered. The mesh size of the model needs to be small enough (e.g., decimillimetre or 0.1 mm) to simulate various shapes of ribs. Therefore, the scale of the PD model is usually significantly large and the computational efficiency is low. This paper proposes an enhanced bond-based PD (BPD) model to perform a refined 3D simulation of bond-slip behaviors in the ribbed bar pull-out test. In order to reduce the computation scale and improve efficiency, a practical 3D coupled element is developed to couple the fine PD model and coarse finite element (FE) model, where the PD is used to model the regions in concrete and rebar that are close to the interface, while FE model is used to simulate the regions far away from the interface. A computational framework is developed for implicit and static analyses of the coupled PD-FE model. A parallel computing strategy is adopted to improve the computational efficiency, and enhanced concrete and steel BPD models are presented to accurately simulate the nonlinear behaviors and damage of concrete and ribbed rebars. The enhanced PD modeling approach is implemented in an open-source finite element software framework, OpenSees, and verified by a cantilever beam under uniaxial loading conditions and a pushover analysis of an RC column. Based on the enhanced PD, a refined 3D simulation of ribbed rebar pull-out tests is performed. The bond-slip behaviors are studied in detail, e.g., the crack propagation with different types of ribs, concrete strengths, and rebar properties. The enhanced PD modeling approach provides an effective tool for refined simulation of the complicated bond-slip behaviors in RC structures.

Multi‐view side information‐incorporated tensor completion

AbstractTensor completion originates in numerous applications where data utilized are of high dimensions and gathered from multiple sources or views. Existing methods merely incorporate the structure information, ignoring the fact that ubiquitous side information may be beneficial to estimate the missing entries from a partially observed tensor. Inspired by this, we formulate a sparse and low‐rank tensor completion model named SLRMV. The ‐norm instead of its relaxation is used in the objective function to constrain the sparseness of noise. The CP decomposition is used to decompose the high‐quality tensor, based on which the combination of Schatten ‐norm on each latent factor matrix is employed to characterize the low‐rank tensor structure with high computation efficiency. Diverse similarity matrices for the same factor matrix are regarded as multi‐view side information for guiding the tensor completion task. Although SLRMV is a nonconvex and discontinuous problem, the optimality analysis in terms of Karush‐Kuhn‐Tucker (KKT) conditions is accordingly proposed, based on which a hard‐thresholding based alternating direction method of multipliers (HT‐ADMM) is designed. Extensive experiments remarkably demonstrate the efficiency of SLRMV in tensor completion.

An innovative approach to measure multidimensional poverty: A synthesis method

This paper presents a new approach to measure multidimensional poverty, combining the strengths of the Fuzzy Set method and the Alkire and Foster method, and addresses some of their limitations. The approach applies the Fuzzy Set method to resolve the discontinuity problem that arises when the latter is used in the Alkire and Foster method to identify the multidimensionally poor people. The resultant process satisfies poverty axioms of a good poverty measure. It also incorporates some s statistical techniques in selecting indicators and computing weights for the membership function. The empirical assessment is done to primary data, collected from the Uva province of Sri Lanka, an economically, neglected comprising of people representing various socio-economic backgrounds. This study examines poverty under three main dimensions; material, social dimensions and human capital. The results reveal that, 42.3 percent of people in the Uva province have a propensity to poverty. The incidence of multidimensional poverty is 56 percent and the intensity is 48.6 percent. The adjusted fuzzy headcount index is 27.2 percent. Interestingly, the highest contribution to overall poverty comes from deprivation by social dimensions. The application of the this method undoubtedly would encourage the analysis of further research on multidimensional poverty.

A fast-convolution based space–time Chebyshev spectral method for peridynamic models

AbstractPeridynamics is a nonlocal generalization of continuum mechanics theory which addresses discontinuous problems without using partial derivatives and replacing them by an integral operator. As a consequence, it finds applications in the framework of the development and evolution of fractures and damages in elastic materials.In this paper we consider a one-dimensional nonlinear model of peridynamics and propose a suitable two-dimensional fast-convolution spectral method based on Chebyshev polynomials to solve the model. This choice allows us to gain the same accuracy both in space and time. We show the convergence of the method and perform several simulations to study the performance of the spectral scheme.

Reducing thermodynamics to Boltzmannian statistical mechanics: the case of macro values

Thermodynamic macro variables, such as the temperature or volume macro variable, can take on a continuum of allowable values, called thermodynamic macro values. Although referring to the same macro phenomena, the macro variables of Boltzmannian Statistical Mechanics (BSM) differ from thermodynamic macro variables in an important respect: within the framework of BSM the evolution of macro values of systems with finite available phase space is invariably modelled as discontinuous, due to the method of partitioning phase space into macro regions with sharp, fixed boundaries. Conceptually, this is at odds with the continuous evolution of macro values as described by thermodynamics, as well as with the continuous evolution of the micro state assumed in BSM. This discrepancy I call the discontinuity problem. I show how it arises from BSM’s framework and demonstrate its consequences, in particular for the foundational project of reducing thermodynamics to BSM: thermodynamic macro values are shown to not supervene on the corresponding BSM macro values. With supervenience being a conditio sine qua non for the kind of reduction envisaged by the foundational project, the latter is in jeopardy.

Cyclic Behavior and Modeling of Reinforced Concrete Shear Walls Based on Enhanced Bond-Based Peridynamics

Peridynamics (PD) has gained increasing usage in simulating the nonlinear damage behavior of reinforced concrete (RC) structures due to its extraordinary capacity in solving discontinuous problems. This paper presents an enhanced bond-based peridynamic (BPD) modeling method for simulating the complex nonlinear behavior of RC shear walls, such as strength deterioration and cracking propagation, under cyclic loading conditions. In the proposed BPD method, a novel concrete bond model is presented that can consider the stiffness degradation, strength deterioration, and residual plastic deformation. A steel model and a coupled axial-shear model are adopted to simulate the nonlinear behavior of rebar and reinforcement-concrete interaction. The enhanced PD is implemented in an open-source finite element software framework, OpenSees, and can perform implicit or explicit, dynamic or static analyses in a parallel manner. Two RC shear walls under cyclic loading conditions are used as verification examples. The nonlinear damage behavior is studied in detail for the RC shear walls, e.g. the strength deterioration, pinch effect, and cracking behavior. The results demonstrate that the enhanced BPD modeling approach is capable of simulating the nonlinear damage behavior of RC shear walls under cyclic loading conditions.

Continuous and discontinuous contact problems of a functionally graded piezoelectric layer resting on a homogeneous piezoelectric half plane

In this study, the plane continuous and discontinuous contact problems between a graded piezoelectric layer and a homogeneous piezoelectric half plane are considered. The layer is pressed by a rigid conducting flat punch with an electrical load. The problem is converted using Fourier integral transform into a singular integral equation. This equation is then solved numerically by applying the Gauss-Chebychev integration formula. The primary objective of this article is to investigate the effect of varying several parameters including the contact length, the mechanical and electrical loads, and the graded layer non-homogeneity parameter on the contact stresses and on the normal electric displacement.

A Convolutional Dynamic-Jerk-Planning Algorithm for Impedance Control of Variable-Stiffness Cable-Driven Manipulators.

Cable-driven manipulators, characterized by slender arms, dexterous motion, and controllable stiffness, have great prospects for application to capture on-orbit satellites. However, it is difficult to achieve effective motion planning and stiffness control of cable-driven manipulators because of the coupled relationships between cable lengths, joint angles, and reaction forces. Therefore, a convolutional dynamic-jerk-planning algorithm is devised for impedance control of variable-stiffness cable-driven manipulators. First, a variable-stiffness cable-driven manipulator with universal modules and rotary quick-change modules is designed to overcome difficulties related to disassembly, installation, and maintenance. Second, a convolutional dynamic-jerk-planning algorithm is devised to overcome the discontinuity and shock problems of the manipulator's velocity during intermittent control processes. The algorithm can also make acceleration smooth by setting jerk dynamically, reducing acceleration shock and ensuring the stable movement of the cable-driven manipulator. Third, the stiffness of the cable-driven manipulator is further optimized by compensating for the position and velocity of drive cables by employing position-based impedance control. Finally, the prototype of the variable-stiffness cable-driven manipulator is developed and tested. The convolutional dynamic-jerk-planning algorithm is used to plan the desired velocity curves for velocity control experiments of the cable-driven manipulator. The results verify that the algorithm can improve the acceleration smoothness, thereby making movement smooth and reducing vibrations. Furthermore, stiffness control experiments verify that the cable-driven manipulator has ideal variable stiffness capabilities.

BÉZIER BASE EXTENDED ISOGEOMETRIC NUMERICAL METHOD FOR THERMO ELASTIC-PLASTIC ANALYSIS OF CRACK PROPAGATION IN CRACKED PLATE UNDER WELDING RESIDUAL STRESS AND THERMAL LOAD

A new procedure in the field of Bézier base extended isogeometric method (XIGA) has been introduced to analyze the effect of welding residual stress and thermal load on crack propagation rate and fatigue life. This new procedure is based on the constitutive thermoelastic plastic equation. The main parts of this procedure are using the B´ezier base XIGA method to calculate the redistribution of welding residual stress due to crack growth and to compute the value of stress intensity factor (SIF) in the welding residual stress field. For this purpose, the grid points of Bézier elements (with C0-continuity) around the crack line and the crack tip are identified by the level set representation. Then, discontinuous enrichment functions are added to the isogeometric analysis approximation. Thus, this method does not require the re-meshing process. The results show that there is a good agreement between the results of proposed numerical method and the Hole-Drilling Strain-Gage method. The interaction integral method has been used to extract SIF. The effects of welding residual stress and thermal load on the SIF are considered using the superposition method. Also, the Walker equation has been modified to calculate the fatigue life caused by thermal loading and welding residual stress. The results display a good agreement between the proposed method and the finite element method. Due to the advantages of the Bézier based XIGA method, which eliminates parametric space and allows the precise addition of enrichment functions to the basis functions of cracked elements (crack line or crack tip), the obtained results are highly accurate that shows this method is effective for analyzing discontinuous problems.

Application of the Godunov-Type Corrective Smoothed Particle Method to Impulsive Load Studies

The smoothed particle hydrodynamics (SPH) method is based on the kernel particle approximation, which is sensitive to the uniformity of the SPH particle distribution in the computational domain; that is, all SPH particles must be distributed evenly in the computational domain. These factors significantly influence the practical application of the SPH method. Meanwhile, calculating the sum near the boundaries of the computational domain may cause boundary defect problems since there are insufficient particles in the support domain, thus often resulting in relatively high errors in numerical simulation results near boundaries. To address these problems, the kernel particle approximation discrete process was corrected based on the traditional SPH method, and the corrected SPH method, the Godunov-type corrective smoothed particle method (CSPM), was formulated by introducing Riemann decomposition. In this study, the traditional SPH method and Godunov-type CSPM method were applied in a comparative study of discontinuous function problems, 1D shock tubes and 1D detonation waves. According to the analysis results, the Godunov-type CSPM method can not only effectively improve the calculation accuracy and compatibility of the traditional SPH method in discontinuous shock wave problems but also increase the accuracy of the traditional SPH method in capturing strong discontinuities.

Oriented Vehicle Detection in Aerial Images Based on YOLOv4.

CNN-based object detectors have achieved great success in recent years. The available detectors adopted horizontal bounding boxes to locate various objects. However, in some unique scenarios, objects such as buildings and vehicles in aerial images may be densely arranged and have apparent orientations. Therefore, some approaches extend the horizontal bounding box to the oriented bounding box to better extract objects, usually carried out by directly regressing the angle or corners. However, this suffers from the discontinuous boundary problem caused by angular periodicity or corner order. In this paper, we propose a simple but efficient oriented object detector based on YOLOv4 architecture. We regress the offset of an object's front point instead of its angle or corners to avoid the above mentioned problems. In addition, we introduce the intersection over union (IoU) correction factor to make the training process more stable. The experimental results on two public datasets, DOTA and HRSC2016, demonstrate that the proposed method significantly outperforms other methods in terms of detection speed while maintaining high accuracy. In DOTA, our proposed method achieved the highest mAP for the classes with prominent front-side appearances, such as small vehicles, large vehicles, and ships. The highly efficient architecture of YOLOv4 increases more than 25% detection speed compared to the other approaches.

GCCINet: Global feature capture and cross-layer information interaction network for building extraction from remote sensing imagery

• Our GCCINet can effectively solve the current building extraction problems. • GCCINet performs state-of-the-art compared with eleven methods in recent studies. • The sufficient comparative experiments and analysis are implemented. • An efficient plug and play CAFE module is proposed. The extraction of buildings from remote sensing images is a challenging task. However, existing methods are insufficiently accurate because of the diverse types of buildings, large-scale variability, and complex backgrounds in remote sensing images. There are many deficiencies of the extraction results, such as small building omission, building internal discontinuity, blurred boundary, and irregular building appearance extraction. To solve these problems, a global feature capture and cross-layer information interaction network (GCCINet) is proposed, in which the continuous atrous convolution feature enhancement module is designed to capture a larger range of multiscale building feature information by using continuous atrous convolution to generate different sizes of receptive fields, thus alleviating the problem of discontinuities and the overall appearance of irregular buildings. The global high-low feature cross-fusion module reduces the loss of local information to enhance the ability to identify small buildings through the effective cross-fusion of high-low features. The cross-layer refined fusion and boundary refinement module adopts a unique fusion method to form information fusion between different layers, obtain multiscale context information, and further refine boundaries, thus improving the capability of boundary extraction. The WHU Building Dataset and Inria Dataset are selected for validation. The results show that GCCINet performs state-of-the-art (SOTA) compared with other existing methods, and the performance of GCCINet is verified in terms of usability, interference resistance, robustness, and ablation study. Furthermore, a plug-and-play CAFE module is designed, which can introduce a few parameters to other models while improving their performance.

Parametric Modeling Incorporating Joint Polynomial-Transfer Function With Neural Networks for Microwave Filters

This article proposes a novel parametric modeling technique incorporating a joint polynomial-transfer function with neural networks (short for neuro-PTF) for electromagnetic (EM) behaviors of microwave filters. In the proposed technique, the polynomial function is introduced together with the pole-residue-based transfer function to represent the EM responses. The pole-residue-based transfer function is used to represent the whole EM response at the beginning and is subsequently divided into multiple subtransfer functions where each subtransfer function contains one pair of pole/residue. A novel smoothness-discriminating algorithm is proposed to judge the smoothness of each subtransfer function response and separate the pole/residue pairs whose subtransfer function response is determined to be smooth. The proposed method introduces low nonlinear polynomial functions to re-fit the smooth parts of subresponse and remains the nonsmooth parts of subresponse for the highly nonlinear transfer functions to represent. By this way, the proposed method avoids the discontinuity problems of nonunique parameter extraction caused by fitting smooth curves using the highly nonlinear transfer function. Neural networks are proposed to learn the relationship between the polynomial coefficients/poles/residues and the geometrical parameters. Utilizing both advantages of the polynomial functions and transfer functions, the proposed method can produce more accurate models than the existing neuro-TF methods, especially with large geometrical variations. The accuracy and robustness of the proposed technique are demonstrated using three EM application examples of microwave filters.

General analysis method for global revisit characteristics of satellite constellation with repeating ground tracks

Coverage analysis is an essential process when designing a satellite constellation, and the variations of global revisit characteristics are usually elusive in discontinuous coverage problems. In dealing with this, a general method for analyzing the global revisit characteristics of constellations with repeating ground track orbits is proposed in this paper. Firstly, a two-dimensional map based analytical model for the point coverage of constellations is introduced. Then, the variations of revisit characteristics along both the parallel and meridian are analyzed based on the presented analytical model. Finally, numerical examples are carried out. On the one hand, the proposed analytical model for point coverage is demonstrated to be of high precision. On the other hand, all possible positions where the discontinuous changes of revisit characteristics occur can be analytically obtained, which can reveal the discontinuous variations of revisit characteristics along both the parallel and meridian, and can also ensure that all possible global or regional revisit characteristics are counted for a given constellation. The proposed method can contribute to constellation design and coverage performance analysis.

Distributed adaptive formation tracking using quantized feedback communication for networked mobile robots with unknown wheel slippage

In this study, we consider a quantized-feedback-communication-based control design problem for the distributed adaptive formation tracking of multiple nonholonomic mobile robots with unknown slippage constraints under capacity-limited network control environments. Uniform-hysteretic quantizers are employed to quantize all the inputs and states of robots and the quantized position information of each robot is only transmitted to neighboring robots through directed networks. Compared with existing literature related to the robot formation, the primary contribution of this paper lies in establishing a novel local adaptive control design methodology to deal with the discontinuity problem caused by using the quantized states of each follower and the quantized position communication of neighboring robots. In the proposed strategy, the communication of the orientations and velocities of neighboring robots is not required for the local control design of follower robots. Moreover, quantized-states-based adaptive compensation schemes are constructed for the effects of signal quantization and wheel slippage. Based on the analysis of quantization errors, the practical stability strategy of the overall closed-loop formation system is derived with the convergence of local tracking errors. Simulation results clarify the proposed formation strategy.

Microfluidic Manufacture of Lipid-Based Nanomedicines.

Nanoparticulate technologies have revolutionized drug delivery allowing for passive and active targeting, altered biodistribution, controlled drug release (temporospatial or triggered), enhanced stability, improved solubilization capacity, and a reduction in dose and adverse effects. However, their manufacture remains immature, and challenges exist on an industrial scale due to high batch-to-batch variability hindering their clinical translation. Lipid-based nanomedicines remain the most widely approved nanomedicines, and their current manufacturing methods remain discontinuous and face several problems such as high batch-to-batch variability affecting the critical quality attributes (CQAs) of the product, laborious multistep processes, need for an expert workforce, and not being easily amenable to industrial scale-up involving typically a complex process control. Several techniques have emerged in recent years for nanomedicine manufacture, but a paradigm shift occurred when microfluidic strategies able to mix fluids in channels with dimensions of tens of micrometers and small volumes of liquid reagents in a highly controlled manner to form nanoparticles with tunable and reproducible structure were employed. In this review, we summarize the recent advancements in the manufacturing of lipid-based nanomedicines using microfluidics with particular emphasis on the parameters that govern the control of CQAs of final nanomedicines. The impact of microfluidic environments on formation dynamics of nanomaterials, and the application of microdevices as platforms for nanomaterial screening are also discussed.

A spectrum improved peridynamic model for shock wave problems

Most previous peridynamics (PD) based shock wave modeling focuses on the field discontinuity problem but neglects the temporal discontinuous feature. Considering it is of vital importance to reproduce the shock jumps, the spectral properties of PD are studied and improved in this paper. A systematic theoretical analysis is firstly conducted and reveals the overly-dispersive behavior of PD model, including the oscillatory dispersion relation and zero energy modes. To suppress the consequent spurious oscillation, the dissipation effect is nonlocally introduced by viscosity as a minimum variation of conventional PD. Rather than applying the existing viscosities directly, the spectral balance is considered for the good control of both the oscillation and shock width, leading to the proposal of polynomial and force-limited viscous force states. The proposed model is then verified by several impact and explosion cases. The quantification of spectral balance is established and is employed for parameter calibration. The results suggest that the model shows good performance in shock wave modeling, with which both the suppression of oscillation and control of shock width near the shock jump are well achieved.