Singular Method Research Articles

A Novel Coupled Meshless Model for Simulation of Acoustic Wave Propagation in Infinite Domain Containing Multiple Heterogeneous Media

This study presents a novel coupled meshless model for simulating acoustic wave propagation in heterogeneous media, based on the singular boundary method (SBM) and Kansa’s method (KS). In the proposed approach, the SBM was used to model the homogeneous part of the propagation domain, while KS was employed to model a heterogeneity. The interface compatibility conditions associated with velocities and pressures were imposed to couple the two methods. The proposed SBM–KS coupled approach combines the respective advantages of the SBM and KS. The SBM is especially suitable for solving external sound field problems, while KS is attractive for nonlinear problems in bounded non-homogeneous media. Moreover, the new methodology completely avoids grid generation and numerical integration compared with the finite element method and boundary element method. Numerical experiments verified the accuracy and effectiveness of the proposed scheme.

Post-emergency reconfiguration of a distribution network as a method for restoring power supply to consumers

The work is aimed at solving the problem of using reconfiguration and additional reactive power sources to restore power to consumers of the medium-voltage distribution network in the case of emergency disconnections of connections by bus section circuit breakers. The reconfiguration problem for a 118-node test distribution network is solved using a high-speed algorithm involving the construction of a maximum spanning tree on a network graph as the basis for determining information about the composition of branches and chords of independent circuits necessary to restore power following disconnection. To ensure acceptable voltage levels following power restoration, additional reactive power sources determined using singular Jacobian matrix analysis methods are installed in the sensor nodes of the network. For the test circuit, the modes for single disconnections of individual sectional switches, including in dead-end sections, are analysed. By optimally reconfiguring the network in the normal mode, it is possible to reduce voltage deviations from 13% to 7%. For the modes caused by disconnections of individual bus section circuit breakers that lead to unacceptable voltage deviations, the set-down locations and reactive power of additional sources are selected. In the most severe of the considered disconnection scenarios, the installation of additional sources provided a reduction in voltage deviations from 18 to 8%. Thus, the methods proposed by the authors make it possible to restore the test network mode following emergency disconnections and ensure that the voltages in the network nodes are maintained within acceptable limits, both in normal and in post-emergency modes.

Induction Motor Bearing Fault Diagnosis Based on Singular Value Decomposition of the Stator Current

Among the most widespread systems in industrial plants are automated drive systems, the key and most common element of which is the induction motor. In view of challenging operating conditions of equipment, the task of fault detection based on the analysis of electrical parameters is relevant. The authors propose the identification of patterns characterizing the occurrence and development of the bearing defect by the singular analysis method as applied to the stator current signature. As a result of the decomposition, the time series of the three-phase current are represented by singular triples ordered by decreasing contribution, which are reconstructed into the form of time series for subsequent analysis using a Hankelization of matrices. Experimental studies with bearing damage imitation made it possible to establish the relationship between the changes in the contribution of the reconstructed time series and the presence of different levels of bearing defects. By using the contribution level and tracking the movement of the specific time series, it became possible to observe both the appearance of new components in the current signal and the changes in the contribution of the components corresponding to the defect to the overall structure. The authors verified the clustering results based on a visual assessment of the component matrices’ structure similarity using scattergrams and hierarchical clustering. The reconstruction of the time series from the results of the component grouping allows the use of these components for the subsequent prediction of faults development in electric motors.

Green NOMA based MU-MIMO transmission for MEC in 6G Networks

Mobile edge computing (MEC) is a distributed computing paradigm that brings computing and data storage closer to the network’s edge. This paper considers a multiple-input multiple-output (MIMO) uplink scenario where non-orthogonal multiple access (NOMA) users partially offload their data to a MEC server. The objective of this study is to minimize the total energy consumption during local computing, task offloading, and MEC computing. To this end, the base station optimizes power allocation vectors and task assignment coefficients under time and power constraints. The generalized singular value decomposition-based linear beamforming method integrates NOMA, MIMO, and MEC technologies. Due to the non-convex nature of the problem, a successive convex optimization (SCA) and alternation optimization (AO) based low-complex solution is proposed. The impact of the delay tolerance, the size of the offloaded task, and the distance of the users are investigated concerning energy consumption. The simulation results show that the proposed method achieves better energy performance than the orthogonal multiple access (OMA) schemes. More importantly, the performance gap increases when the data size is large, and the delay requirement is stringent, as 6G networks require.

On exact wave propagation analysis in a beach volleyball ball

Wave propagation and vibration state in the sports balls have important effects on the stability in movement and accuracy of hits. In some sports, similar to football and volleyball, the balls are subjected to continuous strong hits from players. In the current study, the wave propagation in a beach volleyball ball under the effect of temperature change, different material characteristics, different thicknesses, and the total mass is investigated. In this regard, the ball is modeled using a spherical shell structure and a higher-order displacement field is considered. The classical theory of elasticity is employed along with Hamilton’s principle for the spherical shell. The outcome equations with different boundary conditions are solved by engaging the discrete singular convolution method (DSCM). In addition, the finite element method is used to obtain the modal shape and natural frequency. The formulations and solution method are utilized in different steps of convergence examination, validation, and parametric study to acquire a comprehensive insight into the behavior of beach volleyball balls under the effect of the dynamic loading conditions. In specific, we are more interested in the phase velocity of the ball. The results are presented for different temperature changes and geometrical and material properties.

Prediction method of pipe joint opening-closing deformation of immersed tunnel based on singular spectrum analysis and SSA-SVR

In order to predict the joint opening-closing deformation of immersed tunnel in operation, a comprehensive prediction model combining time series decomposition, least square method, sparrow search algorithm (SSA) and support vector regression (SVR) is proposed, which is verified by the monitoring data of E13-E14 and E17-E18 joints opening-closing deformation of immersed tunnel in Hong Kong-Zhuhai-Macao Bridge. Firstly, on the basis of summarizing and analyzing the characteristics of joint opening-closing deformation, the monitoring sequence of joint opening-closing is decomposed into trend component, periodic component and residual component by using time series decomposition singular spectrum analysis method, which clearly shows the composition of each component. Secondly, the least square method is used to fit and predict the trend component; Combining the commonly used RBF kernel function, Sigmoid kernel function and Ploy kernel function with SVR respectively, the SSA algorithm is used to globally optimize the penalty factors and kernel function parameters of the three models, and the optimized three coupling models are used to predict the periodic component and residual component. The results show that the prediction effect of the SVR model optimized by SSA algorithm is better than that of the traditional SVR model, The prediction result of SSA-SVR model constructed by RBF kernel function is the best. Finally, the time series addition model is applied to superimpose the optimal predicted values to obtain the predicted opening-closing amount. The mean square errors of the total predicted values of the opening-closing amount of the two joints are 0.1900mm and 0.2291mm respectively, the average errors are 0.1587mm and 0.2156mm respectively, and the correlation coefficients are 0.9792 and 0.9695 respectively. A satisfactory prediction effect is obtained, which proves the reliability and accuracy of this method, and provides a new way for the prediction of the opening-closing deformation of the pipe joint of immersed tunnel during the operation period.

:Neither the Time nor the Place: The New Nineteenth-Century American Studies

:<i>Neither the Time nor the Place: The New Nineteenth-Century American Studies</i>

Investigating the Improvement of Recurrent Forecasting of Singular Spectrum Analysis Method in Structural Time Series Models Using Data Filtration and Weighting Algorithm

Investigating the Improvement of Recurrent Forecasting of Singular Spectrum Analysis Method in Structural Time Series Models Using Data Filtration and Weighting Algorithm

Dynamic Drifting Control for General Path Tracking of Autonomous Vehicles

Taking full advantage of tire saturation in high sideslip drifting maneuvers can substantially improve the handling limits of autonomous vehicles. However, most singular motion control methods in conventional drifting controllers have been conducted, which cannot meet general driving needs. In this paper, a hierarchical dynamic drifting controller (HDDC) is designed under both drifting maneuvers and typical cornering maneuvers to uniformly track the general path within and beyond stability limits. Specifically, the HDDC includes the path tracking layer, vehicle motion control layer, and actuator regulating layer. The first layer is designed to achieve accurate path tracking and generate the desired states, and it is algorithmically adaptable and confirmed by MPC and LQR. The second layer is proposed to integrate drifting and typical cornering control by the dynamic drifting inverse model. The third layer can achieve the steering system and wheel speed control to satisfy corresponding commands. Ultimately, the real-time performance of the controller is verified by the ECU hardware-in-the-loop platform. The results with MPC-HDDC and LQR-HDDC show that the HDDC can achieve integrated control of drifting and typical cornering maneuvers and possess high tracking accuracy.

Optimization of human gait using singular-value decomposition-based design variables

Age, walking speed, the presence of walking problems, the slope of the ground, and many other parameters affect human gait. Understanding gait variations and obtaining a reference behavior under different conditions is important for identifying abnormal walking behaviors and designing walking assistive devices, orthoses, and prostheses. Predictive dynamics can be used to determine a reference motion for a given task. In the predictive dynamics approach, the motion of a human is generated using design variables, and the equation of motion is considered a constraint. Several design variables were used to generate the motion, and the biological limits of the joints were considered additional constraints in previous studies. A foot-ground contact model was used to generate vertical and horizontal ground reaction forces using the nonlinear spring-damper model. This study proposed a singular value decomposition-based joint angle generation method to reduce the number of design variables and additional constraints. First, the joint angles were calculated using the motion capture data of 225 participants. Then, a joint angle matrix containing the joint angles of all participants in the experiments was created. The modes of the joint angles were extracted using singular-value decomposition. The joint angles were generated by summing the multiplication of the first nine modes of the joint angles and their corresponding design variables. Therefore, the number of design variables was significantly reduced. Moreover, the constraints related to the joint angle limits were intrinsically satisfied. Joint angles, moments, and power were obtained for the optimal energy and moment square cases at different walking speeds. The optimal results were found to be consistent with experimental results in the literature.

Recovering Corrupted Data in Wind Farm Measurements: A Matrix Completion Approach

Availability of reliable and extended datasets of recorded power output from renewables is nowadays seen as one of the key drivers to improve the design and control of smart energy systems. In particular, these datasets are needed to train artificial intelligence methods. Very often, however, datasets can be corrupted due to lack of records connected to failures of the acquisition system, maintenance downtime periods, etc. Several recovery (imputation) methods have been used to guess and replace missing data. In this paper, we exploit the matrix completion approach. The available measures of several variables referring to a real onshore wind farm are organized into a matrix in a daily range and the Singular Value Thresholding method is used to carry out the matrix completion process. Numerical results show that matrix completion is a reliable and parameter-free tuning tool to impute missing data in these applications.

Modified 2.5D singular boundary methods to deal with spurious eigensolutions in exterior acoustic problems

This paper studies the problem of spurious eigensolutions in the context of the singular boundary method (SBM) formulated in the two-and-a-half-dimensional (2.5D) domain and proposes two numerical schemes to overcome this numerical difficulty. The SBM can be seen as a version of the method of fundamental solutions where the source points are located at the physical boundary. Similar to other boundary-type discretization schemes, the SBM also encounters the non-uniqueness problem at the vicinity of the eigensolutions of the corresponding interior problem. In the 2.5D domain framework, the so-called fictitious eigenfrequencies appearing in 3D problems arise in the form of spurious dispersion curves associated with propagation modes of the corresponding interior problem. The two enhanced 2.5D SBM approaches proposed in this work, based on the Burton–Miller method in one case and the dual surface method in the other, are designed to filter out the spurious eigenvalues from the simulation results and deliver accurate solutions along the wavenumber-frequency spectrum. Three benchmark examples including the radiation problems of an infinitely long cylinder under Dirichlet and Neumann boundary conditions and the radiation problem of a longitudinally infinite object with a constant star-like cross section subjected to a Dirichlet boundary condition are considered to study the proposed methods. The results demonstrate the capability of the proposed numerical schemes to successfully avoid the non-uniqueness problem when the 2.5D SBM is employed.

A 2.5D automatic FEM-SBM method for the evaluation of free-field vibrations induced by underground railway infrastructures

This paper presents an efficient method to predict underground railway-induced vibrations. The method uses the finite element method (FEM) to model the railway tunnel structure and the singular boundary method (SBM) to model the wave propagation in the surrounding soil. The FEM mesh and the distribution of SBM collocation points at the tunnel/soil interface are generated using an automatic meshing strategy. The presented method is one of the main components of VIBWAY, a user-friendly prediction tool to address railway-induced vibration problems. This paper presents three calculation examples in which the soil response due to forces applied on the tunnel structure are computed in terms of transfer functions. The results obtained for each one of the calculation examples are compared with those computed using a model based on a 2.5D FEM-BEM approach. The presented comparisons show that the proposed approach is a suitable strategy for predicting underground railway-induced vibrations, both in terms of accuracy and computational efficiency. Moreover, the use of an automatic meshing strategy and the SBM formulation not only eases the implementation of the approach but it also makes it easier to use, which is one of the key features of the VIBWAY tool.

An inverse nano-cavity/-inhomogeneity problem with surface/interface effects in terahertz frequency range

In nondestructive evaluation, the maximum wavelength of the incident wave must be smaller than twice the perceptible obstacle size. Hence, in order to be able to detect a nanosize fiber of radius about a few nanometer, the frequency of the incident elastic wave should be in the order of 1012 Hz, i.e., in the terahertz frequency range. The present work addresses the possibility of application of elastic waves in terahertz frequency range to detect embedded circular nanosize inhomogeneity or nanocavity for which, respectively, the interface and surface effects are remarkable. Traditionally, singular sources method (SSM) and linear sampling method (LSM) have been utilized to treat inverse problems in the context of classical elasticity theory, where the surface/interface effects are not important. In the present paper these methods are extended to operate in the mathematical framework of surface/interface elasticity theory, suitable for capturing the surface/interface effects. In this framework the boundary conditions in contrast to the common Dirichlet and Neumann types involve the second derivative of the displacement field. The validity and uniqueness of the extended LSM and SSM in this framework will be established. An exact analysis emphasizing the importance of the consideration of surface/interface effects will also be given for the direct problem of SH waves scattering. In this work, the scatterer will be reconstructed solely based on data from the incident waves and the far-field pattern. Using the proposed theory, the size and location of the embedded nano-size cavity and nano-size inhomogeneity are detected. The surface effects of a nano-size cavity within a silver plate are more significant than the copper–silver interface effects in the case of a nano-size copper inhomogeneity embedded in a silver plate.

Fuzzy Algorithmic Modeling of Economics and Innovation Process Dynamics Based on Preliminary Component Allocation by Singular Spectrum Analysis Method

In this article, the authors propose an algorithmic approach to building a model of the dynamics of economic and, in particular, innovation processes. The approach under consideration is based on a complex algorithm that includes (1) decomposition of the time series into components using singular spectrum analysis; (2) recognition of the optimal component model based on fuzzy rules, and (3) creation of statistical models of individual components with their combination. It is shown that this approach corresponds to the high uncertainty characteristic of the tasks of the dynamics of innovation processes. The proposed algorithm makes it possible to create effective models that can be used both for analysis and for predicting the future states of the processes under study. The advantage of this algorithm is the possibility to expand the base of rules and components used for modeling. This is an important condition for improving the algorithm and its applicability for solving a wide range of problems.

KOMPUTE: imputing summary statistics of missing phenotypes in high-throughput model organism data.

The International Mouse Phenotyping Consortium (IMPC) is striving to build a comprehensive functional catalog of mammalian protein-coding genes by systematically producing and phenotyping gene-knockout mice for almost every protein-coding gene in the mouse genome and by testing associations between gene loss-of-function and phenotype. To date, the IMPC has identified over 90 000 gene-phenotype associations, but many phenotypes have not yet been measured for each gene, resulting in largely incomplete data; ∼75.6% of association summary statistics are still missing in the latest IMPC summary statistics dataset (IMPC release version 16). To overcome these challenges, we propose KOMPUTE, a novel method for imputing missing summary statistics in the IMPC dataset. Using conditional distribution properties of multivariate normal, KOMPUTE estimates the association Z-scores of unmeasured phenotypes for a particular gene as a conditional expectation given the Z-scores of measured phenotypes. Our evaluation of the method using simulated and real-world datasets demonstrates its superiority over the singular value decomposition matrix completion method in various scenarios. An R package for KOMPUTE is publicly available at https://github.com/statsleelab/kompute, along with usage examples and results for different phenotype domains at https://statsleelab.github.io/komputeExamples.

A Modified Formulation of Singular Boundary Method for Exterior Acoustics

This paper proposes a modified formulation of the singular boundary method (SBM) by introducing the combined Helmholtz integral equation formulation (CHIEF) and the self-regularization technique to exterior acoustics. In the SBM, the concept of the origin intensity factor (OIF) is introduced to avoid the singularities of the fundamental solutions. The SBM belongs to the meshless boundary collocation methods. The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently. Consequently, by using the SBM coupled with the CHIEF scheme and the self-regularization technique, the accuracy of the numerical solution can be improved, especially near the corresponding internal characteristic frequencies. Several numerical examples of two-dimensional and three-dimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method. The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods.

Continuous Monitoring of Hyperthermia Treatment of Breast Tumors With Singular Sources Method

Qualitative microwave imaging methods provide a fast and accurate reconstruction of the shapes of the targets from scattered electric field measurements. In this paper, a qualitative imaging method, the singular sources method (SSM), is analyzed for two-dimensional transverse magnetic electromagnetic (2D-TM EM) inverse scattering scenarios. The contribution of the paper can be briefly summarized as: (i) The SSM was previously proposed for the far-field scenario, here we extend the SSM in the near field - inhomogeneous background setup. While making the extension each step (which includes an integral equation) is explained by exploiting the linearity and reciprocity principles to give physical insights. (ii) The relation between the electrical parameters of the scatterers and the indicator of SSM is derived. (iii) To analyze the performance of SSM in real-world problems, the proposed method is tested for monitoring hyperthermia treatment problems with a realistic breast model. Obtained results show that the SSM can handle realistic breast phantoms for monitoring hyperthermia problems.

Hopf bifurcation problems near double positive equilibrium points for a class of quartic Kolmogorov model

&lt;abstract&gt;&lt;p&gt;The Kolmogorov model is a class of significant ecological models and is initially introduced to describe the interaction between two species occupying the same ecological habitat. Limit cycle bifurcation problem is close to Hilbertis 16th problem. In this paper, we focus on investigating bifurcation of limit cycle for a class of quartic Kolmogorov model with two positive equilibrium points. Using the singular values method, we obtain the Lyapunov constants for each positive equilibrium point and investigate their limit cycle bifurcations behavior. Furthermore, based on the analysis of their Lyapunov constants' structure and Hopf bifurcation, we give the condition that each one positive equilibrium point of studied model can bifurcate 5 limit cycles, which include 3 stable limit cycles.&lt;/p&gt;&lt;/abstract&gt;

EXACT SOLUTION OF CONTACT PROBLEMS IN A FINITE-WIDTH BAND ON A MULTILAYER MEDIUM

In this paper, for the first time, an exact solution of contact problems for rigid or deformable stamps in a strip of finite width is obtained. It is assumed that the strip is located on a multilayer base of finite thickness. The universal modeling method previously developed by the authors is used. With its help, the solutions of complex boundary value problems for systems of partial differential equations are reduced, using the Galerkin transform, to solving individual differential equations, among which the Helmholtz equations are the simplest. In an earlier work of the authors published, when studying the problem for a deformable stamp in a strip, we had to limit ourselves to an asymptotic solution that is valid only for strips of large relative width. The solution for a strip of any finite size was constrained by the impossibility of constructing an exact solution to the contact problem for a rigid stamp in a strip of any finite width. As a result of the exact solution of the Wiener-Hopf integral equation in a finite-width band for the case of a multilayer medium, this contact problem was solved. The approach applied to the solution consists in constructing an exact operator equation of an infinite system of algebraic equations for large-width bands, using the operator formula of functions from matrices and investigating the constructed solution in the range of small relative bandwidth. The solution obtained in this way coincides with the solution obtained another method, namely, the singular integral method for the case of a small relative bandwidth. The constructed solution brings closer to the problems of research for materials of complex rheologies of contact problems with a deformable stamp, the description of cracks of a new type in limited bodies, modeling of nano particles, the study of tectonic plates of limited dimensions.