Boundary Nodes Research Articles

Characterization of the Response Maps of Alternating-Current Networks

In an alternating-current network, each edge has a complex conductance with positive real part. The response map is the linear map from the vector of voltages at a subset of boundary nodes to the vector of currents flowing into the network through these nodes. In this paper, it is proved that the known necessary conditions for a linear map to be a response map are sufficient, and we show how to construct an appropriate network for a given response map.

Online Equivalent Method of External Network Based on Measurement Information

How to acquire the accurate equivalent network of external system in the interconnected power grid has always been a challenging issue in the fields of both academic and engineering. This paper proposes a new method for online equivalence of the external network based on the measurement information of the internal network. Firstly, it builds an equivalent network of the external system, including the coupled branches between each of the boundary node, the equivalent generators and the equivalent lines from corresponding boundary nodes to them. Then, based on the SCADA (Supervisory Control and Data Acquisition) measurement information, an optimization model to estimate the parameters of the equivalent network is constructed, with the minimization of the mismatch between the boundary’s measurement and the calculation value of the equivalent network being the objective and the parameters of each line of the equivalent network within the reasonable range being the constraints. In order to reduce the calculation scale, measure is adopted to remove the coupled lines whose electrical distances (or impedances) are larger than a relative big threshold. The impedance range of each line in the equivalent network is determined by ward equivalent method under the condition of maximum and minimum operation mode. The model is solved by interior point method, which owns the satisfactory convergency performance. The solution of the model makes each of the calculated value of the equivalent network at the boundary node closest to the measured value, while all the parameters of the equivalent network within a practical range. The results of an example demonstrate the validity and effectiveness of the model and method proposed in the paper.

Research on Modeling of New Energy Power Plant Interface Characteristics Based on Computer Power Flow Calculation Model

In view of the adverse effects of wind power and photovoltaics as the representative of new energy power stations’ active power output fluctuations on the security and stability of the grid, a solution to smooth the active power output of intermittent power sources using energy storage systems is presented. In this paper, the boundary coordination equation in the form of implicit function is used to model the coordinated solution of dynamic power flow equations in the whole network. This model can uniformly consider the reasonable distribution of boundary node power balance and unbalanced power among the district grids.

Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates

An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution.

Finite Difference Implicit Structural Modeling of Geological Structures

We introduce a new method for implicit structural modeling. The main developments in this paper are the new regularization operators we propose by extending inherent properties of the classic one-dimensional discrete second derivative operator to higher dimensions. The proposed regularization operators discretize naturally on the Cartesian grid using finite differences, owing to the highly symmetric nature of the Cartesian grid. Furthermore, the proposed regularization operators do not require any special treatment on boundary nodes, and their generalization to higher dimensions is straightforward. As a result, the proposed method has the advantage of being simple to implement. Numerical examples show that the proposed method is robust and numerically efficient.

A novel localized collocation solver based on Trefftz basis for potential-based inverse electromyography

This paper introduces a novel localized collocation Trefftz method (LCTM) for potential-based inverse electromyography (PIE). PIE is a noninvasive technique to calculate the internal electrical potentials from measured body surface electromyographic data, which can be considered as an inverse Cauchy problem with potential equation. In the proposed LCTM, the electrical potential at every node is expressed as a linear combination of 3D Trefftz basis in each stencil support, and the sparse linear system is yield by satisfying governing equation at interior nodes and boundary conditions at boundary nodes. The proposed LCTM inherits the properties of easy-to-use and meshless from the collocation Trefftz method (CTM), and mitigates the ill-conditioning resultant matrix encountered in the CTM. Numerical efficiency of the proposed method is investigated in comparison with the CTM and experimental data.

A Dominating Tree Based Leader Election Algorithm for Smart Cities IoT Infrastructure

In wireless sensor and IoT networks dedicated to smart-cities, a leader node performs critical tasks such as generating encryption/decryption keys. In this paper, the leader is the node situated at the extreme left of the network. It is the node which starts the algorithm of searching the boundary nodes. These nodes will be used to monitor any sensitive, dangerous or inaccessible site. For this type of application, the used algorithm must be robust and fault-tolerant because it is difficult or even impossible to intervene in the presence of node failures. If this node is the leader, such a situation can be catastrophic. In this article, we present a new algorithm called DoTRo, which is based on a tree routing protocol. It starts with local leaders which will launch the flooding process to determine a spanning tree. During this process, their values will be forwarded. If two spanning trees meet, the tree that routes the best value continues its process while the other tree stops. The remaining tree root will be the leader. This algorithm is low energy consuming with reduction rates that can exceed 85% with respect to the classical minium finding algorithm. It is efficient and fault-tolerant since it works even in the presence of node failures and communication disconnectivity. Additionally, the energy consumption is well balanced between nodes. Finally, the complexity and the proof of convergence of the proposed algorithm is presented.

Localized Boundary Knot Method for Solving Two-Dimensional Laplace and Bi-Harmonic Equations

In this paper, a localized boundary knot method is proposed, based on the local concept in the localized method of fundamental solutions. The localized boundary knot method is formed by combining the classical boundary knot method and the localization approach. The localized boundary knot method is truly free from mesh and numerical quadrature, so it has great potential for solving complicated engineering applications, such as multiply connected problems. In the proposed localized boundary knot method, both of the boundary nodes and interior nodes are required, and the algebraic equations at each node represent the satisfaction of the boundary condition or governing equation, which can be derived by using the boundary knot method at every subdomain. A sparse system of linear algebraic equations can be yielded using the proposed localized boundary knot method, which can greatly reduce the computer time and memory required in computer calculations. In this paper, several cases of simply connected domains and multi-connected domains of the Laplace equation and bi-harmonic equation are demonstrated to evidently verify the accuracy, convergence and stability of this proposed meshless method.

The Erdogan fundamental solution-based hybrid boundary node method for fracture problems

Based on the Erdogan fundamental solutions for infinite cracked plates, a new hybrid boundary node method for linear fracture problems is proposed in this paper. The origin singular intensity factor for the Erdogan fundamental solutions is developed to overcome the singular when the field points are coincided with the source points, and no virtual source points are needed, a new scheme for calculating the origin singular intensity factor for the Erdogan fundamental solutions is developed. Based on the Erdogan fundamental solutions, the zero traction boundary condition on crack surfaces is naturally and strictly satisfied in this method, and no nodes are arranged on the crack surface in the entire calculation process. Based on the Erdogan fundamental solution of stress intensity factor for the mixed mode crack, the stress intensity factor of the present method can be easily interpolated by the Erdogan fundamental solutions. As a result, no complex scheme for calculating stress intensity factor is needed. Based on those theories and methods, the proposed method is further applied to analyze some linear crack problems, and the computational accuracy, convergence rate and the versatility of the present method are demonstrated in details.

Factorized wave propagation model in tree-type pipe networks and its application to leak localization

In a leaky tree-structured pipe network, transient head and discharge at a measurement location arise from a superposition of the waves along the set of pipes linking the measurement location to each boundary node. Moreover, the solution can be split into a leak-free part and a term that accounts for the scattering from the leak, the latter varies linearly with leak size and nonlinearly with leak location. It is then shown that if the head adjacent to each boundary node is measured, any reasonably-sized leak can be uniquely and efficiently identified by the matched-field processing approach. The efficiency of the leak identification scheme stems from the linear dependence of wave scattering on leak size. The proposed method is successfully applied both numerically and to pilot data from a tree-structured system of viscoelastic pipes.

Practical Application of the Galerkin Finite Element Method with a Mass Conservation Scheme under Dirichlet Boundary Conditions to Solve Groundwater Problems

The Galerkin finite element method (FEM) has long been used to solve groundwater flow equations and compute the mass balance in a region. In this study, we proposed a simple, new computational FEM procedure for global mass balance computations that can simultaneously obtain boundary fluxes at Dirichlet boundary nodes and finite element hydraulic heads at all nodes in only one step, whereas previous approaches usually require two steps. In previous approaches, the first step obtains the Galerkin finite element hydraulic heads at all nodes, and then, the boundary fluxes are calculated using the obtained Galerkin finite element hydraulic heads in a second step. Comparisons between the new approach proposed in this study and previous approaches, such as Yeh’s approach and a conventional differential approach, were performed using two practical groundwater problems to illustrate the improved accuracy and efficiency of the new approach when computing the global mass balance or boundary fluxes. From the results of the numerical experiments, it can be concluded that the new approach provides a more efficient mass balance computation scheme and a much more accurate mass balance computation compared to previous approaches that have been widely used in commercial and public groundwater software.

The osteopontin expression and microvascular density in thyroid cancer, comparison of CT and ultrasound in diagnosis of thyroid cancer and correlations of CT features and thyroid cancer.

The aim of this study was to explore the osteopontin expression and microvascular density in thyroid cancer, compare computed tomography (CT) and ultrasound in diagnosis of thyroid cancer and investigate the correlations of CT Features and thyroid cancer. A total of 80 patients with thyroid masses admitted to our hospital from April 2017 to August 2019 were selected, of which there were 40 with benign tumor and 40 with malignant tumor. All patients with thyroid cancer confirmed by pathological tissue biopsy were examined by ultrasound (ultrasound group) and CT (CT group). The expression of osteopontin was detected by PCR while microvascular density was tested by immunohistochemistry. Then univariate analysis and multivariate logistic regression analysis of risk factors were carried out for CT imaging diagnosis of thyroid cancer. The levels of osteopontin and microvascular density in malignant group were significantly higher than those in benign group. The incidence rates of unclear boundary and peripheral lymph node enlargement in CT group were remarkably higher than those in ultrasound group. The diagnostic rate of masses ≥1 cm in diameter was notably higher than that of masses <1 cm in diameter in thyroid cancer patients in CT group and ultrasound group (P<0.05). In addition, the diagnostic rates of follicular carcinoma and papillary carcinoma were higher, whereas those of medullary carcinoma and undifferentiated carcinoma were lower in CT group and ultrasound group. There was no significant difference in the accuracy of thyroid cancer diagnosis between CT group and ultrasound group. Moreover, diameter ≥1 cm, irregular shape, unclear boundary, calcified foci, uneven density/echo and peripheral lymph node enlargement were related risk factors for the CT imaging diagnosis of thyroid cancer, in which irregular shape, unclear boundary, calcified foci and uneven density/echo were independent risk factors for the CT imaging diagnosis of thyroid cancer. The levels of osteopontin and microvascular density were increased in thyroid cancer. CT examination may be of higher diagnostic value in diagnosis of thyroid cancer compared with ultrasound. Irregular shape, unclear boundary, calcified foci and uneven density/echo were independent risk factors for the CT imaging diagnosis of thyroid cancer.

An efficient and accurate hybrid weak-form meshless method for transient nonlinear heterogeneous heat conduction problems

Our purpose is to establish a numerical method meeting the requirements of efficiency, stability, accuracy and easy-using. Faced with these demands, in this paper, a hybrid method combining the advantages of 2 weak-form meshless methods is proposed for solving steady and transient heat conduction problems with temperature-dependent thermophysical properties in heterogeneous media. In the process of the calculation for an arbitrary model discretized by the hybrid method, two different weak-form methods are used for the nodes categorized as: (1) boundary nodes, (2) near boundary interior nodes and (3) interior nodes. A Galerkin free element method (GFREM) is proposed for the interior nodes of the Cartesian grid; and the local radial point interpolation method (LRPIM) is used for the other two types of nodes. The GFREM using the Cartesian grid can greatly improve the accuracy and efficiency of the hybrid scheme. Special decomposition technology to determine the irregular integral domain for LRPIM can increase the flexibility for complex models. In addition, the full implicit finite difference scheme and Newton–Raphson method are used for solving transient nonlinear problems. And non-crossing interface integral domain and support domain are employed for heterogeneous media. Compared with other methods, numerical results show better accuracy, stability and efficiency from the numerical experiments.

Modified curved boundary scheme for two-phase lattice Boltzmann simulations

The lattice Boltzmann (LB) method has gained much success in a variety of fields involving fluid flow and/or heat transfer. In this method, the bounce-back scheme is a popular technique for the treatment of nonslip boundaries. However, this scheme leads to a staircase representation of curved walls. Therefore many curved boundary schemes have been proposed, but mostly have detrimental effects such as mass leakage. Several correction schemes have been suggested for simulating single-phase flows, but very few discussions or studies have been made for two-phase LB simulations with curved boundaries. In this paper, the performances of three well-known schemes for dealing with curved boundaries in two-phase LB simulations are investigated through modeling a droplet resting on a circular cylinder. For all of the investigated schemes, the results show that the simulated droplet rapidly “evaporates” under the nonslip and isothermal condition, owing to the imbalance between the mass streamed out of the system by outgoing distribution functions and the mass streamed into the system by incoming distribution functions at each boundary node. Based on the numerical investigation, we formulate two modified mass-conservative curved boundary schemes for two-phase LB simulations. The accuracy of the modified curved boundary schemes and their capability of conserving mass in two-phase LB simulations are numerically demonstrated.

Numerical and Experimental Study of Classical Hydraulic Jump

The present work is an effort to simulate numerically a classical hydraulic jump in a horizontal open channel with a rectangular cross-section, as far as the jump location and free surface elevation is concerned, and compare the results to experiments with Froude numbers in the range 2.44 to 5.38. The governing equations describing the unsteady one-dimensional rapidly varied flow have been solved with the assumption of non-hydrostatic pressure distribution. Two finite difference schemes were used for the discretization of the mass and momentum conservation equations, along with the appropriate initial and boundary conditions. The method of specified intervals has been employed for the calculation of the velocity at the downstream boundary node. Artificial viscosity was required for damping the oscillations near the steep gradients of the jump. An iterative algorithm was used to minimize the difference of flow depth between two successive iterations that must be less than a threshold value, for achieving steady state solution. The time interval varied in each iteration as a function of the Courant number for stability reasons. Comparison of the numerical results with experiments showed the validity of the computations. The numerical codes have been implemented in house using a Matlab® environment.

Pipe Hydraulic Resistances Identification of District Heating Networks Based on Matrix Analysis

District heating networks (DHNs) are essential municipal infrastructure in the north of China. Obtaining accurate resistance characteristics is a critical step to improve the operating regulation level of DHNs. In this paper, pipe hydraulic resistances (PHRs) are introduced to express the resistance characteristics. A hydraulic model of a DHN can be established by using observed data of pressures and discharges. The boundary nodes are taken as observed sites. After establishing a matrix equation and analyzing the rank of its coefficient matrix, the authors propose a method to determine all the PHRs uniquely, by using a small number of observed sites and operating conditions. Furthermore, when observed errors are introduced, the adverse impact can be weakened by increasing the number of operating conditions and the accuracy of observed devices. When the observed error ranges are 1% and 0.5%, the results show that the average relative errors of identified PHRs are 2.4% and 1.1% respectively, which can be acceptable in engineering. Then, a loop DHN can be transformed into several branch DHNs, which are identified individually.

A fast reduced-order model for radial integral boundary element method based on proper orthogonal decomposition in nonlinear transient heat conduction problems

In order to efficiently solve nonlinear transient heat conduction problem, a method combining the radial integration boundary element method (RIBEM) and the proper orthogonal decomposition (POD) is proposed to establish the nonlinear reduced-order model, and the implementation of the reduced-order model makes fast numerical simulation possible in engineering field. Transient heat conduction problems with temperature-dependent and temperature-independent thermal conductivity are firstly solved by the RIBEM respectively, and two types of snapshots are composed of these solved transient temperature fields. Subsequently, the POD is applied in the analysis of the snapshots, and then a set of optimal orthogonal basis can be obtained. In the procedure of establishing the reduced-order model, we need to redistribute the nonlinear equations. The strategy is to separate the boundary nodes defined as Dirichlet condition, and then the orthogonal basis is used to derive a reduced-order expression for the remaining unknowns. Therefore, the degree of freedom that needs to be solved can be greatly reduced. Numerical examples show that different reduced-order models based on nonlinear basis and linear basis are all consistent with the full-order model. What is more, the computational efficiency is greatly improved due to the introduction of the reduced-order model.

A dynamic distributed boundary node detection algorithm for management zone delineation in Precision Agriculture

Dividing a larger area into smaller subregions is a well addressed problem in Precision Agriculture (PA) where the existing application specific solutions (laboratory based) require human intervention and result in static region demarcation schemes. However, the boundary of a subregion is subject to change with various soil and environmental parameters. On the other hand, Wireless Sensor Networks (WSNs), a potential candidate to produce dynamic subregions due to its real-time decision making capability, are utilized as merely a data collection unit for PA.In an attempt to introduce the in-network decision making feature of WSN in PA, design of a novel three layered WSN-CPS architecture is presented in this work and at layer-I the distributed mechanism for region demarcation is proposed. The proposed scheme identifies nodes based on data values and position information, that serve as the boundary of a subregion and data transmitters to the base station for final decision making. Existing methods for boundary node detection identify network boundary nodes (not designed to demarcate the interior boundary), coverage hole boundary nodes (identifies boundary nodes of a smaller portion in network), and event boundary nodes (not able to identify outer boundary). The proposed work identifies network boundary nodes, coverage hole boundary nodes, and the subregion boundary nodes accurately. It takes various critical situations into account while labelling of nodes and shows its reliability in node failure conditions. Impact of varying transmission range and number of nodes is analyzed on proposed mechanism via simulation. In a comparative study with recent network boundary node detection scheme, decrease of 32% and 30% is seen at 200 and 300 nodes respectively in terms of energy consumption.

Simulation of 3D grinding temperature field by using an improved finite difference method

3D grinding temperature field can be simulated by the finite difference method. When the finite difference method is used to calculate the temperature field, the boundary conditions need to be considered. Unfortunately, the difference equations for internal nodes and boundary nodes are not the same. For cuboid computing domains, there are twenty-six types of boundary nodes. This reduces the calculation efficiency to a certain extent. An improved finite difference method for the 3D grinding temperature field was proposed to solve this problem in this paper. By adding auxiliary nodes, the boundary nodes are converted into internal nodes, and the difference equations of the boundary nodes and internal nodes are unified. In this paper, the improved algorithm was used to simulate the 3D grinding temperature field. The temperature distribution characteristics of the grinding temperature field were analyzed. Then, the effects of heat source type, space step size, and convective heat transfer coefficient on the temperature field were studied. The results show that the improved algorithm can well simulate the 3D grinding temperature field. Finally, compared with the original algorithm, the calculation results were completely consistent, and the efficiency is improved by about 20%.

Boundary Nodes and Interior Nodes in Bipolar Fuzzy Graphs

Boundary Nodes and Interior Nodes in Bipolar Fuzzy Graphs