Point Constraints Research Articles

Second order splitting of a class of fourth order PDEs with point constraints

We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with point constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments.

Critical Points for Variable Length Elastica With a Fixed Point Constraint Under Displacement Control

Abstract This paper studies a variable length elastica with a fixed point constraint by an assembly method that regards the whole elastica as an assembly of two components, i.e., pinned-clamped elasticas. The pinned-clamped elastica is obtained based on the post-buckled deformed shape with one internal inflection point. Thus, multiple coexisting solutions can be located accurately, which reveals three distinct equilibrium paths for the complete load–displacement curves. Under displacement control, two critical points on two equilibrium paths are found at saddle-node bifurcations. Interestingly, a new critical point is located at the boundary point of one equilibrium path, where the shapes of two pinned-clamped elasticas are two different post-buckled deformed shapes. Changing the location of the fixed point constraint allows the position of the boundary point to be easily manipulated, and the associated snap-through phenomenon can occur on different equilibrium paths. This flexible generation of the snap-through phenomenon is useful for designing engineering systems that require controllable snap-through.

High-Efficiency Determination of Coastline by Combination of Tidal Level and Coastal Zone DEM from UAV Tilt Photogrammetry

To meet the needs of coastline efficient extraction and dynamic monitoring, this paper proposes a new method for coastline extraction by combining the tidal level and the digital elevation model (DEM) of the coastal zone from tilt photography. Firstly, the DEM of coastal zone was obtained by using unmanned aerial vehicle (UAV) tilt photography; at the same time, the accuracy of aerial triangulation(AT) is improved referencing to the constraint of water boundary points, and then the mean high water spring tide was obtained by combining tidal harmonic analysis and Global Navigation Satellite System (GNSS) tidal level. Finally, the coastline and the dynamic water-surface line are extracted from the DEM of the coastal zone by tracking the contour lines with the elevation of the mean high water springs (MHWS) and the instantaneous sea-surface elevation, respectively. The experiments carried out in the coastal zones of Liaoning Province, China, proved the proposed method and achieved better than 0.2 m of horizontal position accuracy and 0.1 m of the vertical accuracy.

Strong Local Optimality for a Bang–Bang–Singular Extremal: General Constraints

The paper provides second-order sufficient conditions for the strong local optimality of bang–bang–singular extremals in a Mayer problem with general end point constraints. The sufficient conditions are expressed as a strengthening of the necessary ones plus the coerciveness of a suitable quadratic form related to a sub-problem of the given one. The sufficiency of the given conditions is proven via Hamiltonian methods.

Penalty function method for imposing nonlinear multi freedom and multi node constraints in finite element analysis of frame systems

This paper focuses on the treatment of nonlinear multi-freedom and multi-point boundary condition in finite element analysis of frame systems. The treatment of boundary constraints is required to produce modified system of equations based on master stiffness equations considering nonlinear constraints. For imposing nonlinear multi freedom and multi point constraints, the Penalty Augmentation method and Lagrange Multiplier Adjunction method are better in many applications. In present paper, the Penalty Augmentation method is using for implementation of nonlinear boundary constraints. The nonlinear relationship considerably increases the difficulty in constructing and solving the modified system of equations. The Newton Raphson method, have been the most powerful and popular method for solution of nonlinear equations, is used for solving studied problem. Using the Newton Raphson technique, this paper develops the incremental-iterative algorithm to solve the nonlinear modified system of equations. Based on the presented algorithm, the paper proposed calculation procedure and established programs for determining internal forces and displacements of frames having nonlinear multi freedom and multi point constrains boundary. The numerical test results using the proposed method show the efficiency and reliability of proposed algorithm.

Image stitching with positional relationship constraints of feature points and lines

The elimination of parallax and the processing of natural issue in complex scenes are challenging tasks for image stitching. In this paper, an image stitching method with positional relationship constraints of feature points and lines, which can accomplish accurate alignment and reduce projection distortion, is proposed. At first, to reduce the computational cost and the number of outliers on subsequent feature matching, we combine the template matching to propose a quick way for detecting overlapping regions. Then, the appropriate reference image is determined to mitigate the projection distortion that the image warping is in the cases of non-planar geometry of the scenes. Furthermore, a local mesh model based on dual features is established to guide the mesh deformation. And an energy function is designed to refine alignment. In addition to alignment error terms, a novel positional relationship constraint term is proposed to improve quality of naturalness of final stitching results. Finally, experimental results demonstrate that our approach is superior to the existing image stitching algorithms in improving quality of the stitched image naturalness.

A fast calibration method of the robot’s 3D vision system

Calibration accuracy and convenience are very important for the rapid production of vision-based robots. Although there are many calibration methods for the 3D vision system, the convenience of calibration cannot meet the needs of industrial sites. In this paper, we propose a fast calibration method based on a 3D calibration block. Its key point is to complete the calibration process through multiple space point constraints, and the space points used are jointly solved by multiple planes obtained by local point cloud fitting. The experimental results show that the proposed method can quickly complete the calibration of the robot’s 3D vision system, and the calibration accuracy can meet low precision occasions.

Sub-pixel mapping with point constraints

Remote sensing images contain abundant land cover information. Due to the complex nature of land cover, however, mixed pixels exist widely in remote sensing images. Sub-pixel mapping (SPM) is a technique for predicting the spatial distribution of land cover classes within mixed pixels. As an ill-posed inverse problem, the uncertainty of prediction cannot be eliminated and hinders the production of accurate sub-pixel maps. In contrast to conventional methods that use continuous geospatial information (e.g., images) to enhance SPM, in this paper, a SPM method with point constraints into SPM is proposed. The method of fusing point constraints is implemented based on the pixel swapping algorithm (PSA) and utilizes the auxiliary point information to reduce the uncertainty in the SPM process and increase map accuracy. The point data are incorporated into both the initialization and optimization processes of PSA. Experiments were performed on three images to validate the proposed method. The influences of the performances were also investigated under different numbers of point data, different spatial characters of land cover and different zoom factors. The results show that by using the point data, the proposed SPM method can separate more small-sized targets from aggregated artifacts and the accuracies are increased obviously. The proposed method is also more accurate than the advanced radial basis function interpolation-based method. The advantage of using point data is more evident when the point data size and scale factor are large and the spatial autocorrelation of the land cover is small. As the amount of point data increases, however, the increase in accuracy becomes less noticeable. Furthermore, the SPM accuracy can still be increased even if the point data and coarse proportions contain errors.

A measurement method for calibrating kinematic parameters of industrial robots with point constraint by a laser displacement sensor

This paper proposes a novel calibration method for robot kinematic parameters by constraining a command point. At first, the profile errors derived from measuring the sphere surface by a laser displacement sensor are estimated and analyzed. A three-step measurement procedure is performed around a command point with only one single laser displacement sensor. Then, a kinematic error model including both the robot parameter errors and the errors between the robot base frame and the measurement frame is established. An identification algorithm comprising the least square method and the particle swarm optimization algorithm is developed. Comparison simulations are carried out with the proposed method, a least square method, and the traditional identified method. Experiments show that the estimated compensation results are significant, with the mean reduced from 10.259 mm to 0.845 mm. A verification experiment shows the mean of the relative deviations is decreased from 1.674 mm to 0.538 mm.

Optimal Capacity Allocation of Energy Storage System considering Uncertainty of Load and Wind Generation

Energy storage systems (ESSs) are promising solutions for the mitigation of power fluctuations and the management of load demands in distribution networks (DNs). However, the uncertainty of load demands and wind generations (WGs) may have a significant impact on the capacity allocation of ESSs. To solve the problem, a novel optimal ESS capacity allocation scheme for ESSs is proposed to reduce the influence of uncertainty of both WG and load demands. First, an optimal capacity allocation model is established to minimize the ESS investment costs and the network power loss under constraints of DN and ESS operating points and power balance. Then, the proposed method reduces the uncertainty of load through a comprehensive demand response system based on time-of-use (TOU) and incentives. To predict the output of WGs, we combined particle swarm optimization (PSO) and backpropagation neural network to create a prediction model of the wind power. An improved simulated annealing PSO algorithm (ISAPSO) is used to solve the optimization problem. Numerical studies are carried out in a modified IEEE 33-node distribution system. Simulation results demonstrate that the proposed model can provide the optimal capacity allocation and investment cost of ESSs with minimal power losses.

Data-driven streamline stiffener path optimization (SSPO) for sparse stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures

The homogenization-based streamline stiffener path optimization (SSPO) method was previously proposed by the authors for stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures. The applications are limited to densely distributed stiffeners with no significant scale effect in the homogenization process, which is revealed in this work. A data-driven SSPO method, which is inspired by the popular principal component analysis (PCA) in data processing, is proposed for sparse stiffener layout design. With several referential layouts as input, the PCA generates a sequence of principal layouts. Together with weighting factors and distortion techniques, using only a small number of dominant principal layouts is enough to represent most possible synthesized layouts, which significantly reduces the number of design variables while preserving and extending a large design space. This strategy is further enhanced with a detailed modeling technique based on multiple point constraints (MPCs) to automate the modeling process. The data-driven SSPO method can be integrated with either gradient-based or artificial intelligence (AI) algorithms due to the small number of design variables. A flexible objective target, to maximize the critical buckling load or minimize the structural weight, can be used since the structural responses are evaluated on the detailed model. Numerical examples demonstrate the effectiveness of the proposed method in optimizing the layout of sparsely distributed stiffeners.

A Semianalytical Solution for In-Plane Vibration Analysis of Annular Panels with Arbitrary Distribution of Internal Point Constraints

In this paper, a semianalytical solution for the in-plane vibration analysis of annular panel with arbitrary distribution of internal point constraints is established for the first time. In-plane dynamic behavior of such panel structure is described via energy principle. A modified version of Fourier series is constructed for the in-plane vibration displacement expansion supplemented with the boundary smoothed terms, and the arbitrarily concentrated constraint in each field point is described in conjunction with Dirac delta function. A standard matrix eigenvalue problem containing various in-plane modal information of such annular panel is derived and solved through Rayleigh–Ritz procedure. Several numerical examples are presented to demonstrate the correctness and effectiveness of the proposed model by comparing the results with those from other approaches. Three representative types of point constraints, including point, line, and area configurations, are considered by collection of point constraints, and it is shown that the current model can make an accurate and efficient modal parameter prediction for annular panel with such most general case of point constraints.

A point and distance constraint based 6R robot calibration method through machine vision

Abstract This paper proposes a 6R robot closed-loop kinematic calibration method to improve absolute position accuracy with point and distance constraints though machine vision. In the calibration process, a camera attached to the mounting plate of the robot is used to capture a fixed reference sphere as a point constraint and to record robot joint angles and gauge block lengths that are used as a distance constraint. A first-order difference quotient is used to calculate the Jacobian matrix in the joint parameter identification process. The Staubli TX60 robot is successfully calibrated using the proposed method. After calibration, the average distance error of robot motion is decreased from 2.05 mm to 0.24 mm.

An OD Flow Clustering Method Based on Vector Constraints: A Case Study for Beijing Taxi Origin-Destination Data

Origin-destination (OD) flow pattern mining is an important research method of urban dynamics, in which OD flow clustering analysis discovers the activity patterns of urban residents and mine the coupling relationship of urban subspace and dynamic causes. The existing flow clustering methods are limited by the spatial constraints of OD points, rely on the spatial similarity of geographical points, and lack in-depth analysis of high-dimensional flow characteristics, and therefore it is difficult to find irregular flow clusters. In this paper, we propose an OD flow clustering method based on vector constraints (ODFCVC), which defines OD flow event point and OD flow vector to express the spatial location relationship and geometric flow behavior characteristics of OD flow. First, the OD flow vector coordinate system is normalized by the Euclidean distance-based OD flow event point spatial clustering, and then the OD flow clusters with similar flow patterns are mined using adjusted cosine similarity-based OD flow vector feature clustering. The transformation of OD data from point set space to vector space is realized by constraining the vector coordinate system and vector similarity through two-step clustering, which simplifies the calculation of high-dimensional similarity of OD flow and helps mining representative OD flow clusters in flow space. Due to the OD flow cluster property, the k-means algorithm is selected as the basic clustering logic in the two-step clustering method, and a sum of squared error perceptually important points algorithm considering silhouette coefficients (SSEPIP) is adopted to automatically extract the optimal cluster number without defining any parameters. Tested by origin-destination flow data in Beijing, China, new traffic flow communities based on traffic hubs are obtained by using the ODFCVC method, and irregular traffic flow clusters (including cluster mode, divergence mode, and convergence mode) with representative travel trends are found.

Power Compensation of Network Losses in a Microgrid With BESS by Distributed Consensus Algorithm

In this article, by using distributed consensus algorithm, the power compensation problem of network losses in a microgrid is considered with battery energy storage systems (BESSs). At first, the battery storage unit (BSU) is assembled at each node to maintain the power supply demand balance of the microgrid, then the power constraint is considered, which demands each BSU must run between its upper and lower bounds, otherwise, the upper or lower bounds will be used to replace the real power of the BSU. In order to keep the power balance of microgrid when network losses exist, a novel distributed consensus algorithm is proposed to compensate the missing power through the discharging process of BSUs, and the state of charge (SOC) of BESS is also considered. Besides, the case of battery faults is also considered, where the minimum layout point constraint is presented to ensure the completely compensation of the whole transmission losses. Finally, the test results of IEEE 14-bus and IEEE 57-bus microgrid systems are provided to verify the effectiveness and validity of the proposed method, respectively.

Partially-Coupled d–q–0 Components of Magnetically-Isolated FSCW IPM Machines With Open-End-Winding Drives

Fractional-slot concentrated winding interior permanent magnet (FSCW-IPM) machines have been designed with very low winding mutual inductance for magnetic isolation features required for improving their fault-tolerant capabilities. These magnetically-isolated FSCW-IPM machines no longer adhere to the preconditions required for a conventional abc-to-dq0 transformation. As a result, it is found in this article that d-, q-axes could couple with 0-axis in magnetically-isolated FSCW-IPM machines. Considering the second-order reluctance component, this phenomenon leads to third-harmonic injection in phase voltages during normal operation, which can be cancelled out in terms of line-to-line voltage for Y-connected three-phase system. However, for open-end-winding machine drives without winding neutral point constraint, these voltage harmonics will show up in the winding voltage waveforms. Study shows that the amplitudes of these extra harmonics are determined by both saliency ratio and zero-axis current. The bandwidth of the proportional integral (PI) current regulator as well as switching frequency should be carefully determined to be able to take into account the major harmonics injected in phase voltages. Experimental verification on a 12-slot/10-pole prototype machine with spoke PMs has been carried out to show the impact of this phenomenon.

A Point Constrained Boundary Reconstruction Framework for Ultrasound Guided Electrical Impedance Tomography

As a non-invasive and radiation-free imaging modality, electrical impedance tomography (EIT) has attracted much attention in the field of industrial measurement. However, image reconstruction with EIT is a non-linear and ill-posed inverse problem, causing it to suffer from low spatial resolution and high noise sensitivity. To overcome this problem, a point-constrained framework is proposed to guide inclusion boundary reconstruction in EIT with ultrasound point detection. The boundary reconstruction problem is formulized with an energy minimization approach. The energy function consists of the residual, point constraint, geometric and re-parameterisation terms. The residual term fits the actual EIT data by adjusting the inclusion shape and conductivity with a computable forward model. The point constraint term drags the estimated boundary toward the ultrasound detected ‘at-boundary’ points and pushes it away from the ultrasound detected ‘outside-inclusion’ points. The geometric and re-parameterisation terms regularize the boundary reconstruction problem and diffuse the point constraint energy along the inclusion boundary. According to the numerical results, the proposed method is robust to measurement noise, as well as the super parameter and initial boundary guess issues. An experimental phantom study with a water tank model further proved that the dual-modality shape reconstruction method outperforms the single-modality shape reconstruction method in both single-phase and multiphase conductivity cases.

A Spatial Flow Clustering Method Based on the Constraint of Origin-Destination Points’ Location

With the development of mobile positioning technology, a large number of Origin-Destination (OD) flow data with spatial and temporal details have been produced. These OD flow could give us a great opportunity to research geographical phenomena such as spatial interaction and mobility patterns. The OD flow clustering approach is an effective way to explore the main mobility patterns of the objects. At the same time, similarity measurement plays a key role in OD flow clustering. However, most of the previous OD flow similarity measurement methods failed to make full use of the spatial information of the flow including spatial proximity and geometric similarity. In this paper, we considered both position information and geometric properties of OD flow and propose a new method to measure the spatial similarity between OD flows. Specifically, the proposed method sets the neighbor threshold with the length of OD flows and the parameter $\alpha $ dynamically. Based on the constraint of the OD points’ location, the directions of the flows are implicitly restricted. The sole-parameter $\alpha $ has a practical value as it determines the maximum length difference and the maximum directional difference that can be tolerated between similar flows. The proposed method passed a simulation experiment with synthetic flows and a case study with 283,008 taxi trips in Beijing in one day. The results show that the proposed method can discover the dominant mobility pattern from a large number of flow data effectively. In the case study, the dominant flow clusters reveal the taxi mobility patterns of residents at different distances in Beijing.

A real-time semantic visual SLAM approach with points and objects

Visual simultaneously localization and mapping (SLAM) is important for self-localization and environment perception of service robots, where semantic SLAM can provide a more accurate localization result and a map with abundant semantic information. In this article, we propose a real-time PO-SLAM approach with the combination of both point and object measurements. With point–point association in ORB-SLAM2, we also consider point–object association based on object segmentation and object–object association, where the object segmentation is employed by combining object detection with depth histogram. Also, besides the constraint of feature points belonging to an object, a semantic constraint of relative position invariance among objects is introduced. Accordingly, two semantic loss functions with point and object information are designed and added to the bundle adjustment optimization. The effectiveness of the proposed approach is verified by experiments.

Parallel computing proximal method for nonsmooth convex optimization with fixed point constraints of quasi-nonexpansive mappings

Parallel computing proximal method for nonsmooth convex optimization with fixed point constraints of quasi-nonexpansive mappings