Furnace Temperature Curve Optimization Model Based on Differential Evolution Algorithm

When soldering electronic components onto circuit boards,the temperature curves of the reflow ovens across different zones and the conveyor belt speed significantly influence the product quality.This study focuses on optimizing the furnace temperature curve under varying settings of reflow oven zone temperatures and conveyor belt speeds.To address this,the research sequentially develops a heat transfer model for reflow soldering,an optimization model for reflow furnace conditions using the differential evolution algorithm,and an evaluation and decision model combining the differential evolution algorithm with the Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)method.This approach aims to determine the optimal furnace temperature curve,zone temperatures of the reflow oven,and the conveyor belt speed.

Relocation of the 1998 Zhangbei-Shangyi earthquake sequence using the double difference earthquake location algorithm

On January 10, 1998, at 11h50min Beijing Time (03h50min UTC), an earthquake of ML=6.2 occurred in the border region between the Zhangbei County and Shangyi County of Hebei Province. This earthquake is the most significant event to have occurred in northern China in the recent years. The earthquake-generating structure of this event was not clear due to no active fault capable of generating a moderate earthquake was found in the epicentral area, nor surface ruptures with any predominate orientation were observed, no distinct orientation of its aftershock distribution given by routine earthquake location was shown. To study the seismogenic structure of the Zhangbei- Shangyi earthquake, the main shock and its aftershocks with ML3.0 of the Zhangbei-Shangyi earthquake sequence were relocated by the authors of this paper in 2002 using the master event relative relocation technique. The relocated epicenter of the main shock was located at 41.145癗, 114.462癊, which was located 4 km to the NE of the macro-epicenter of this event. The relocated focal depth of the main shock was 15 km. Hypocenters of the aftershocks distributed in a nearly vertical plane striking 180~200 and its vicinity. The relocated results of the Zhangbei-Shangyi earthquake sequence clearly indicated that the seismogenic structure of this event was a NNE-SSW-striking fault with right-lateral and reverse slip. In this paper, a relocation of the Zhangbei-Shangyi earthquake sequence has been done using the double difference earthquake location algorithm (DD algorithm), and consistent results with that obtained by the master event technique were obtained. The relocated hypocenters of the main shock are located at 41.131癗, 114.456癊, which was located 2.5 km to the NE of the macro-epicenter of the main shock. The relocated focal depth of the main shock was 12.8 km. Hypocenters of the aftershocks also distributed in a nearly vertical N10E-striking plane and its vicinity. The relocated results using DD algorithm clearly indicated that the seismogenic structure of this event was a NNE-striking fault again.

A Finite Difference Method and Effective Modification of Gradient Descent Optimization Algorithm for MHD Fluid Flow Over a Linearly Stretching Surface

Present contribution is concerned with the construction and application of a numerical method for the fluid flow problem over a linearly stretching surface with the modification of standard Gradient descent Algorithm to solve the resulted difference equation.The flow problem is constructed using continuity,and Navier Stoke equations and these PDEs are further converted into boundary value problem by applying suitable similarity transformations.A central finite difference method is proposed that gives third-order accuracy using three grid points.The stability conditions of the present proposed method using a Gauss-Seidel iterative procedure is found using Von-Neumann stability criteria and order of the finite difference method is proved by applying the Taylor series on the discretised equation.The comparison of the presently modified optimisation algorithm with the Gauss-Seidel iterative method and standard Newton’s method in optimisation is also made.It can be concluded that the presently modified optimisation Algorithm takes a few iterations to converge with a small value of the parameter contained in it compared with the standard descent algorithm that may take millions of iterations to converge.The present modification of the steepest descent method converges faster than Gauss-Seidel method and standard steepest descent method,and it may also overcome the deficiency of singular hessian arise in Newton’s method for some of the cases that may arise in optimisation problem(s).

Optimization of the seismic processing phase-shift plus finite-difference migration operator based on a hybrid genetic and simulated annealing algorithm

Although the phase-shift seismic processing method has characteristics of high accuracy, good stability, high efficiency, and high-dip imaging, it is not able to adapt to strong lateral velocity variation. To overcome this defect, a finite-difference method in the frequency-space domain is introduced in the migration process, because it can adapt to strong lateral velocity variation and the coefficient is optimized by a hybrid genetic and simulated annealing algorithm. The two measures improve the precision of the approximation dispersion equation. Thus, the imaging effect is improved for areas of high-dip structure and strong lateral velocity variation. The migration imaging of a 2-D SEG/EAGE salt dome model proves that a better imaging effect in these areas is achieved by optimized phase-shift migration operator plus a finite-difference method based on a hybrid genetic and simulated annealing algorithm. The method proposed in this paper is better than conventional methods in imaging of areas of high-dip angle and strong lateral velocity variation.

Research on Kalman Filtering Algorithmfor Deformation Information Series ofSimilar Single-Difference Model

Using similar single-difference methodology(SSDM) to solve the deformation values of the monitoring points, there is unstability of the deformation information series, at sometimes.In order to overcome this shortcoming, Kalman filtering algorithm for this series is established,and its correctness and validity are verified with the test data obtained on the movable platform in plane. The results show that Kalman filtering can improve the correctness, reliability and stability of the deformation information series.

Relocation of the M_S≥2.0 Earthquakes in the Northern Tianshan Region, Xinjiang, Using the Double-Difference Earthquake Relocation Algorithm

We applied the double-difference earthquake rdocation algorithm to 1348 earthquakes with Ms ≥2.0 that occurred in the northern Tianshan region, Xinjiang, from April 1988 to June 2003, using a total of 28701 P- and S-wave arrival times recorded by 32 seismic stations in Xinjiang. Aiming to obtain most of these Ms ≥ 2.0 earthquakes relocations, and considering the requirements of the DD method and the condition of data, we added the travel time data of another 437 earthquakes with 1.5 ≤ Ms 〈 2.0. Finally, we obtained the relocation results for 1253 earthquakes with Ms ≥2.0, which account for 93 % of all the 1348 earthquakes with Ms ≥ 2.0 and includes all the Ms ≥ 3.0 earthquakes. The reason for not relocating the 95 earthquakes with 2.0 ≤ Ms 〈 3.0 is analyzed in the paper. After relocation, the RMS residual decreased from 0.83s to 0.14s, the average error is 0.993 km in E-W direction, 1.10 km in N- S direction, and 1.33 km in vertical direction. The hypocenter depths are more convergent than before and distributed from 5 km to 35 kin, with 94% being from 5km to 35 kin, 68.2% from 10 km to 25 kin. The average hypocenter depth is 19 kin.

Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm

A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method

A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.

High Accurate Fourth-Order Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate

In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.

Efficient BTCS + CTCS Finite Difference Scheme for General Linear Second Order PDE

This work deals with a second order linear general equation with partial derivatives for a two-variable function. It covers a wide range of applications. This equation is solved with a finite difference hybrid method: BTCS + CTCS. This scheme is simple, precise, and economical in terms of time and space occupancy in memory.

Finite Difference Method of Modelling Groundwater Flow

In this study, finite difference method is used to solve the equations that govern groundwater flow to obtain flow rates, flow direction and hydraulic heads through an aquifer. The aim therefore is to discuss the principles of Finite Difference Method and its applications in groundwater modelling. To achieve this, a rectangular grid is overlain an aquifer in order to obtain an exact solution. Initial and boundary conditions are then determined. By discretizing the system into grids and cells that are small compared to the entire aquifer, exact solutions are obtained. A flow chart of the computational algorithm for particle tracking is also developed. Results show that under a steady-state flow with no recharge, pathlines coincide with streamlines. It is also found that the accuracy of the numerical solution by Finite Difference Method is largely dependent on initial particle distribution and number of particles assigned to a cell. It is therefore concluded that Finite Difference Method can be used to predict the future direction of flow and particle location within a simulation domain.

Solution of 1D Poisson Equation with Neumann-Dirichlet and Dirichlet-Neumann Boundary Conditions, Using the Finite Difference Method

An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.

Two Energy-Preserving Compact Finite Difference Schemes for the Nonlinear Fourth-Order Wave Equation

In this paper,two fourth-order compact finite difference schemes are derived to solve the nonlinear fourth-order wave equation which can be viewed as a generalized model from the nonlinear beam equation.Differing from the existing compact finite difference schemes which preserve the total energy in a recursive sense,the new schemes are proved to per-fectly preserve the total energy in the discrete sense.By using the standard energy method and the cut-off function technique,the optimal error estimates of the numerical solutions are established,and the convergence rates are of O(h^(4)+τ^(2))with mesh-size h and time-step τ.In order to improve the computational efficiency,an iterative algorithm is proposed as the outer solver and the double sweep method for pentadiagonal linear algebraic equations is introduced as the inner solver to solve the nonlinear difference schemes at each time step.The convergence of the iterative algorithm is also rigorously analyzed.Several numerical results are carried out to test the error estimates and conservative properties.

Multi-strategy Differential Evolution Algorithm for QoS Multicast Routing

This paper studies the difference algorithm parameters characteristic of the multicast routing problem, and to compare it with genetic algorithms. The algorithm uses the path of individual coding, combined with the differential cross-choice strategy and operations optimization. Finally, we simulated 30 node networks, and compared the performance of genetic algorithm and differential evolution algorithm. Experimental results show that multi-strategy Differential Evolution algorithm converges faster and better global search ability and stability.

SAR Change Detection Algorithm Combined with FFDNet Spatial Denoising

Objectives:When detecting changes in synthetic aperture radar(SAR)images,the quality of the difference map has an important impact on the detection results,and the speckle noise in the image interferes with the extraction of change information.In order to improve the detection accuracy of SAR image change detection and improve the quality of the difference map,this paper proposes a method that combines the popular deep neural network with the clustering algorithm.Methods:Firstly,the SAR image with speckle noise was constructed,and the FFDNet architecture was used to retrain the SAR image,and the network parameters with better effect on speckle noise suppression were obtained.Then the log ratio operator is generated by using the reconstructed image output from the network.Finally,K-means and FCM clustering algorithms are used to analyze the difference images,and the binary map of change detection results is generated.Results:The experimental results have high detection accuracy on Bern and Sulzberger’s real data,which proves the effectiveness of the method.

基于免疫选择和自适应权重的鲸鱼优化定位算法

针对鲸鱼优化算法(WOA)在到达时间差和到达角度混合定位中存在后期迭代种群多样性减小,容易导致局部最优、定位精确度降低的问题,提出一种基于免疫选择和自适应权重的鲸鱼优化算法(IM-WOA).由最大似然估计法得到目标定位函数,为丰富种群多样性引入免疫机制,能够有效产生新的个体,从而避免种群陷入局部最优.通过将自适应惯性权重应用于个体位置的更新公式,实现算法全局探索能力和局部开发能力的平衡和协调,对经典基准函数和目标定位函数进行求解.结果表明,与WOA、AWOA、CSSOA、PIO、CASSA算法相比,IM-WOA算法对绝大多数基准函数的求解具有更高的精度、稳定性和定位精度.

基于深度神经网络的7065铝合金厚板应力检测模型

针对工业生产中传统超声应力检测法对铝合金厚板在不同拉伸率和不同温度条件下存在的测量误差的问题,以7065铝合金厚板为实验对象,提出一种在不同拉伸率和不同温度条件下的基于树突神经网络的应力预测模型与传统超声检测法融合的应力检测模型,然后使用改进的GSA-GRNN对该应力检测模型进行温度补偿。以南南铝公司生产的7065铝合金厚板为研究对象,使用恒温槽为超声检测提供恒温环境,分别对不同拉伸率、不同温度下的7065铝合金厚板进行超声检测,将声时差、拉伸率作为输入参数,应力作为输出参数,创建一个基于树突神经网络的应力检测模型,然后将应力检测模型的输出作为输入,使用改进的GSA-GRNN建立温度补偿模型对应力检测模型进行温度补偿。研究结果表明:融合了传统超声声时差的检测模型均方根误差为0.84636,相关系数为0.99743,和其他神经网络模型对比,该模型拥有更好的精度;在对该模型进行温度补偿后,模型的应力均方根误差和相关系数分别可以达到0.78848和0.99844,模型的精度得到了进一步的提升。证明基于数据驱动的神经网络融合传统超声检测可以有效降低检测误差,同时省去传统检测方法人工计算应力的时间,提高了检测效率。研究结果可以为基于数据驱动的应力检测模型提供进一步的优化参考。

基于多目标遗传算法的8×8 S盒的优化设计方法

混沌系统具有非线性、伪随机性、初始值敏感等特性,为基于动力系统构造性能良好的S盒提供了基础,进一步保证了分组加密算法安全性.目前,基于混沌构造S盒的方法大多数针对单个性能指标进行优化,难以获得全面的性能提升.针对此问题,结合混沌映射与多目标遗传算法,提出了一种新的S盒设计方法.首先,利用混沌映射的特性产生初始S盒种群;然后,以S盒的非线性度和差分均匀性为优化目标,基于遗传算法框架对上述两指标进行优化.针对S盒的特点,在优化算法中引入了交换操作,设计了新的变异操作以及非支配序集计算,有效提升了S盒的非线性度和差分均匀性.实验结果表明该算法产生的S盒其差分均匀度为6,非线性度值至少为110,有效提升了S盒的综合性能.