Hybrid group search optimiser with quadratic interpolation method and its application

2011 ◽  
Vol 5 (1) ◽  
pp. 98 ◽  
Author(s):  
Jian Yao ◽  
Zhihua Cui ◽  
Zhanhong Wei ◽  
Ying Tan
Keyword(s):  
Interpolation Method ◽  
Quadratic Interpolation ◽  
Quadratic Interpolation Method ◽  
Group Search ◽  
Hybrid Group

An Immersed Boundary Method for Calculating the Relative Viscosity of a Suspension of Rigid Particles

2014 ◽  
Author(s):  
Mohsen Daghooghi ◽  
Iman Borazjani
Keyword(s):  
Interpolation Method ◽  
Relative Viscosity ◽  
Immersed Boundary ◽  
Rigid Particles ◽  
Bulk Stress ◽  
Quadratic Interpolation ◽  
Background Grid ◽  
Triangular Elements ◽  
Quadratic Interpolation Method ◽  
Good Agreement

In this paper, we provide a numerical framework to calculate the relative viscosity of a suspension of rigid particles. A high-resolution background grid is used to solve the flow around the particles. In order to generate infinite number of particles in the suspension, a particle is placed in the center of a cubic cell and periodic boundary conditions are imposed in two directions. The flow around the particle is solved using the second-order accurate curvilinear immersed boundary (CURVIB) method [1]. The particle is discretized with triangular elements, and is treated as a sharp interface immersed boundary by reconstructing the velocities on the fluid nodes adjacent to interface using a quadratic interpolation method. Hydrodynamic torque on the particle has been calculated, to solve the equation of motion for the particle and obtain its angular velocity. Finally, relative viscosity of the suspension has been calculated based on two different methods: (1) the rate of the energy consumption and (2) bulk stress-bulk strain method. The framework has been validated by simulating a suspension of spheres, and comparing the numerical results with the corresponding analytical ones. Very good agreement has been observed between the analytical and the calculated relative viscosities using both methods. This framework is then used to model a suspension with arbitrary complex particles, which demonstrates the effect of shape on the effective viscosity.

scholarly journals Solving fractional differential equations by the ultraspherical integration method

2021 ◽  
Vol 40 ◽  
pp. 1-14
Author(s):  
Ali Khani ◽  
S. Panahi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Optimization Problem ◽  
Integration Method ◽  
Interpolation Method ◽  
Constrained Optimization Problem ◽  
Quadratic Interpolation ◽  
Fractional Differential ◽  
Quadratic Interpolation Method ◽  
Linear Fractional Differential Equations

In this paper, we present a numerical method to solve a linear fractional differential equations. This new investigation is based on ultraspherical integration matrix to approximate the highest order derivatives to the lower order derivatives. By this approximation the problem is reduced to a constrained optimization problem which can be solved by using the penalty quadratic interpolation method. Numerical examples are included to confirm the efficiency and accuracy of the proposed method.

Efficient hybrid group search optimizer for assembling printed circuit boards

2018 ◽  
Vol 33 (03) ◽  
pp. 259-274
Author(s):  
Cheng-Jian Lin ◽  
Mei-Ling Huang
Keyword(s):  
Printed Circuit Boards ◽  
Population Diversity ◽  
Nearest Neighbor Search ◽  
Circuit Boards ◽  
Research Attention ◽  
Assembly Time ◽  
Printed Circuit ◽  
Pick And Place ◽  
Group Search ◽  
Hybrid Group

AbstractAssembly optimization of printed circuit boards (PCBs) has received considerable research attention because of efforts to improve productivity. Researchers have simplified complexities associated with PCB assembly; however, they have overlooked hardware constraints, such as pick-and-place restrictions and simultaneous pickup restrictions. In this study, a hybrid group search optimizer (HGSO) was proposed. Assembly optimization of PCBs for a multihead placement machine is segmented into three problems: the (1) auto nozzle changer (ANC) assembly problem, (2) nozzle setup problem, and (3) component pick-and-place sequence problem. The proposed HGSO proportionally applies a modified group search optimizer (MGSO), random-key integer programming, and assigned number of nozzles to an ANC to solve the component picking problem and minimize the number of nozzle changes, and the place order is treated as a traveling salesman problem. Nearest neighbor search is used to generate an initial place order, which is then improved using a 2-opt method, where chaos local search and a population manager improve efficiency and population diversity to minimize total assembly time. To evaluate the performance of the proposed HGSO, real-time PCB data from a plant were examined and compared with data obtained by an onsite engineer and from other related studies. The results revealed that the proposed HGSO has the lowest total assembly time, and it can be widely employed in general multihead placement machines.

scholarly journals The Deviation Analysis and Application of Correlation Tracking Algorithm

2018 ◽  
Vol 232 ◽  
pp. 03006
Author(s):  
Qinyong Zeng ◽  
Zhengzhong Huang ◽  
Kaiyu Qin ◽  
Xiangcheng Tang
Keyword(s):  
Interpolation Method ◽  
Tracking Algorithm ◽  
Positioning Error ◽  
Tracking Accuracy ◽  
Error Sources ◽  
Deviation Analysis ◽  
Quadratic Interpolation ◽  
Fitting Method ◽  
Correlation Tracking ◽  
Set Up

Correlation tracking algorithm is the most widely used image tracking algorithm . Its main error sources include processing error and positioning error. In order to improve the accuracy of correlation tracking algorithm, a mathematical model of positioning error based on the theory of random walk and martingale is set up, and the average time of positioning error exceeds the range is presented. The image-interpolation method and surfaces-fitting method are put forward to suppress the positioning error and improve the accuracy. Simulation results show that: compared with the whole pixel tracking, quadratic interpolation tracking can double the accuracy, and quartic interpolation and surfaces-fitting can improve the tracking accuracy of about 4 times.

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