Analytical derivation and numerical experiment of degenerate scale by using the degenerate kernel of the bipolar coordinates

2017 ◽  
Vol 85 ◽  
pp. 70-86 ◽  
Author(s):  
Jeng-Tzong Chen ◽  
Shing-Kai Kao ◽  
Jia-Wei Lee
Keyword(s):  
Numerical Experiment ◽  
Degenerate Kernel ◽  
Bipolar Coordinates ◽  
Analytical Derivation ◽  
Degenerate Scale

Analytical derivation and numerical experiments of degenerate scale for an ellipse in BEM

2012 ◽  
Vol 36 (9) ◽  
pp. 1397-1405 ◽  
Author(s):  
Jeng-Tzong Chen ◽  
Ying-Te Lee ◽  
Shyh-Rong Kuo ◽  
Yi-Wei Chen
Keyword(s):  
Numerical Experiments ◽  
Analytical Derivation ◽  
Degenerate Scale

Degenerate-scale problem of the boundary integral equation method/boundary element method for the bending plate analysis

2017 ◽  
Vol 34 (5) ◽  
pp. 1527-1550 ◽  
Author(s):  
Jeng-Tzong Chen ◽  
Shyh-Rong Kuo ◽  
Yu-Lung Chang ◽  
Shing-Kai Kao
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Arbitrary Shape ◽  
Boundary Integral ◽  
Degenerate Kernel ◽  
Content Type ◽  
Degenerate Scale ◽  
Circular Case ◽  
Plate Analysis

Purpose The purpose of this paper is to detect the degenerate scale of a 2D bending plate analytically and numerically. Design/methodology/approach To avoid the time-consuming scheme, the influence matrix of the boundary element method (BEM) is reformulated to an eigenproblem of the 4 by 4 matrix by using the scaling transform instead of the direct-searching scheme to find degenerate scales. Analytical degenerate scales are derived from the boundary integral equation (BIE) by using the degenerate kernel only for the circular case. Numerical results of the direct-searching scheme and the eigen system for the arbitrary shape are also considered. Findings Results using three methods, namely, analytical derivation, the direct-searching scheme and the 4 by 4 eigen system, are also given for the circular case and arbitrary shapes. Finally, addition of a constant for the kernel function makes original eigenvalues (2 real roots and 2 complex roots) of the 4 by 4 matrix to be all real. This indicates that a degenerate scale depends on the kernel function. Originality/value The analytical derivation for the degenerate scale of a 2D bending plate in the BIE is first studied by using the degenerate kernel. Through the reformed eigenproblem of a 4 by 4 matrix, the numerical solution for the plate of an arbitrary shape can be used in the plate analysis using the BEM.

scholarly journals An indirect BIE free of degenerate scales

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jeng-Tzong Chen ◽  
Shing-Kai Kao ◽  
Jeng-Hong Kao ◽  
Wei-Chen Tai
Keyword(s):  
Unique Solution ◽  
External Source ◽  
Wave Number ◽  
Degenerate Kernel ◽  
Influence Matrix ◽  
Boundary Density ◽  
Numerical Tests ◽  
Degenerate Scale ◽  
Similar Idea ◽  
Laplace Problem

<p style='text-indent:20px;'>Thanks to the fundamental solution, both BIEs and BEM are effective approaches for solving boundary value problems. But it may result in rank deficiency of the influence matrix in some situations such as fictitious frequency, spurious eigenvalue and degenerate scale. First, the nonequivalence between direct and indirect method is analytically studied by using the degenerate kernel and examined by using the linear algebraic system. The influence of contaminated boundary density on the field response is also discussed. It's well known that the CHIEF method and the Burton and Miller approach can solve the unique solution for exterior acoustics for any wave number. In this paper, we extend a similar idea to avoid the degenerate scale for the interior two-dimensional Laplace problem. One is the external source similar to the null-field BIE in the CHIEF method. The other is the Burton and Miller approach. Two analytical examples, circle and ellipse, were analytically studied. Numerical tests for general cases were also done. It is found that both two approaches can yield an unique solution for any size.</p>

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

Microwave Field Distribution Uniformity Coefficient in the Grain Mass

2020 ◽  
Vol 67 (2) ◽  
pp. 87-92
Author(s):  
Dmitriy A. Budnikov
Keyword(s):  
Electromagnetic Field ◽  
Numerical Experiment ◽  
Microwave Field ◽  
Research Purpose ◽  
Coefficient Of Determination ◽  
Material Research ◽  
Dense Layer ◽  
Uniformity Coefficient ◽  
Average Value ◽  
Processed Material

The article considers the microwave electromagnetic fields as one of the options for improving the thermal drying of grain. Their application is limited by the high unevenness of the field propagation in the layer of the processed material. (Research purpose) The research purpose is in justifying the uniformity of distribution of microwave field in the layer of the processed grain. (Materials and methods) The article presents the scheme of computer models of microwave processing zones and waveguides, properties of materials for conducting a numerical experiment. (Results and discussion) A numerical experiment was performed to determine the uniformity coefficient of propagation of the microwave field in a layer of grain material. The article presents the dependencies. (Conclusions) It was found that the results of modeling the distribution of the electromagnetic field in the zone of microwave convective influence of the installation containing two sources of microwave power for processing the grain layer indicate a high level of its unevenness in the volume of the product pipeline. To assess the uniformity of the distribution of the electromagnetic field in the working area of a laboratory installation, there used a coefficient that is the ratio of the average value of the intensity in the zone of microwave convective action to its average value of the wave strength passing through the output of the waveguide. The values of the uniformity coefficient in the considered implementation options are in the range of 0.1757-0.4946 for a dense layer of wheat. To ensure a sufficient level of uniformity of the electromagnetic wave distribution in the volume of the microwave convective zone, the uniformity coefficient must be higher than 0.37. The article presents the dependence of the uniformity coefficient of the electromagnetic field on the humidity of the processed material by a third-degree polynomial with a coefficient of determination higher than 0.98.

scholarly journals Unsupervised Offline Changepoint Detection Ensembles

2021 ◽  
Vol 11 (9) ◽  
pp. 4280
Author(s):  
Iurii Katser ◽  
Viacheslav Kozitsin ◽  
Victor Lobachev ◽  
Ivan Maksimov
Keyword(s):  
Numerical Experiment ◽  
Failure Time ◽  
Cost Functions ◽  
Technical Diagnostics ◽  
Classification Problems ◽  
Tennessee Eastman Process ◽  
Changepoint Detection ◽  
Aggregation Functions ◽  
The Individual ◽  
Ensemble Algorithms

Offline changepoint detection (CPD) algorithms are used for signal segmentation in an optimal way. Generally, these algorithms are based on the assumption that signal’s changed statistical properties are known, and the appropriate models (metrics, cost functions) for changepoint detection are used. Otherwise, the process of proper model selection can become laborious and time-consuming with uncertain results. Although an ensemble approach is well known for increasing the robustness of the individual algorithms and dealing with mentioned challenges, it is weakly formalized and much less highlighted for CPD problems than for outlier detection or classification problems. This paper proposes an unsupervised CPD ensemble (CPDE) procedure with the pseudocode of the particular proposed ensemble algorithms and the link to their Python realization. The approach’s novelty is in aggregating several cost functions before the changepoint search procedure running during the offline analysis. The numerical experiment showed that the proposed CPDE outperforms non-ensemble CPD procedures. Additionally, we focused on analyzing common CPD algorithms, scaling, and aggregation functions, comparing them during the numerical experiment. The results were obtained on the two anomaly benchmarks that contain industrial faults and failures—Tennessee Eastman Process (TEP) and Skoltech Anomaly Benchmark (SKAB). One of the possible applications of our research is the estimation of the failure time for fault identification and isolation problems of the technical diagnostics.

scholarly journals Research on feeder network design: a case study of feeder service for the port of Kotka

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Yisong Lin ◽  
Xuefeng Wang ◽  
Hao Hu ◽  
Hui Zhao
Keyword(s):  
Control System ◽  
Numerical Experiment ◽  
Network Design ◽  
Evaluation System ◽  
Real Life ◽  
Objective Evaluation ◽  
Multi Objective Optimization ◽  
Real Life Data ◽  
The Mathematical Model

Abstract By exemplifying the feeder service for the port of Kotka, this study proposed a multi-objective optimization model for feeder network design. Innovative for difference from the single-objective evaluation system, the objective of feeder network design was proposed to include single allocation cost, intra-Europe cargo revenue, equipment balance, sailing cycle, allocation utilization, service route competitiveness, and stability. A three-stage control system was presented, and numerical experiment based on container liner’s real life data was conducted to verify the mathematical model and the control system. The numerical experiment revealed that the three-stage control system is effective and practical, and the research ideas had been applicable with satisfactory effect.

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