Galerkin Method for Numerical Solution of Volterra Integro-Differential Equations with Certain Orthogonal Basis Function

This paper concerns the implementation of the orthogonal polynomials using the Galerkin method for solving Volterra integro-differential and Fredholm integro-differential equations. The constructed orthogonal polynomials are used as basis functions in the assumed solution employed. Numerical examples for some selected problems are provided and the results obtained show that the Galerkin method with orthogonal polynomials as basis functions performed creditably well in terms of absolute errors obtained.

Selecting the Technology of Sodium Silicate Modified Poplar with the Highest Performance by Fuzzy Orthogonal Method

Sodium silicate modification can improve the overall performance of wood.The modification process has a great influence on the properties of modified wood.In this study,a new method was introduced to analyze the wood modification process,and the properties of modified wood were studied.Poplar wood was modified with sodium silicate by vacuum-pressure impregnation.After screening using single-factor experiments,an orthogonal experiment was carried out with solution concentration,impregnation time,impregnation pressure,and the cycle times as experimental factors.The modified poplar with the best properties was selected by fuzzy mathematics and characterized by SEM,FT-IR,XRD and TG.The results showed that some lignin and hemicellulose were removed from the wood due to the alkaline action of sodium silicate,and the orderly crystal area of poplar became disorderly,resulting in the reduction of crystallinity of the modified poplar wood.FT-IR analysis showed that sodium silicate was hydrolyzed to form polysilicic acid in wood,and structural analysis revealed the formation of Si-O-Si and Si-O-C,indicating that sodium silicate reacted with fibers on the wood cell wall.TG-DTG curves showed that the final residual mass of modified poplar wood increased from 25%to 67%,and the temperature of the maximum loss rate decreased from 343℃ to 276℃.The heat release and smoke release of modified poplar wood decreased obviously.This kind of material with high strength and fire resistance can be used in the outdoor building and indoor furniture.

Finite Element Orthogonal Collocation Approach for Time Fractional Telegraph Equation with Mamadu-Njoseh Polynomials

Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.

The proper orthogonal decomposition method for the Navier-Stokes equations

The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.

Numerical Solutions of Volterra Equations Using Galerkin Method with Certain Orthogonal Polynomials

This work is aim at providing a numerical technique for the Volterra integral equations using Galerkin method. For this purpose, an effective matrix formulation is proposed to solve linear Volterra integral equations of the first and second kind respectively using orthogonal polynomials as trial functions which are constructed in the interval [-1,1] with respect to the weight function w(x)=1+x2. The efficiency of the proposed method is tested on several numerical examples and compared with the analytic solutions available in the literature.

Fully Discrete Orthogonal Collocation Method of Sobolev Equations

In this paper, the fully discrete orthogonal collocation method for Sobolev equations is considered, and the equivalence for discrete Garlerkin method is proved. Optimal order error estimate is obtained.

Solution of Electrohydrodynamic Flow Equation Using an Orthogonal Collocation Method Based on Mixed Interpolation

In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction terms given in the form of sine and cosine function. By these correction terms, we can control the error in the solution. We have applied this approach to a non-linear boundary value problem (BVP) in ODE which governs the electrohydrodynamic flow in a cylindrical conduit. The solution profiles shown in the figures are in good agreement with the work of Paullet (1999) and Ghasemi et al. (2014). Our solution is monotonic decreasing and satisfies , where, α governs the strength of non-linearity and for large values of α solutions are . The residual errors are given in Table 1 and Table 2 which are significantly small. Comparison of residual errors between our proposed method, Least square method and Homotopy analysis method is also given and shown via the Table 3 where as the profiles of the residual error are depicted in Figures 4-8. Table and graphs show that efficiency of the proposed method. The error bound and its L2-norm with relevant theorems for mixed interpolation are also given.

基于自适应短时傅里叶变换的品质因子Q值估算方法

品质因子Q是描述地下介质对地震波吸收衰减强弱程度的参数,同时也是地层含油气性的重要标志。在地震资料Q估算中,常用的方法是短时傅里叶变换方法,当窗函数被选定以后,其时频分辨率就固定了。针对该问题,提出一种自适应窗短时傅里叶变换的方法,以获得更准确的瞬时中心频率,并利用峰值频移法来估算品质因子Q。首先,利用固定窗长的短时傅里叶变换来提取信号的瞬时中心频率作为初始频率;然后,根据初始频率自适应计算不同频率的窗长,并利用自适应窗长短时傅里叶变换来求取瞬时中心频率;最后,结合峰值频移法得到高分辨率的品质因子Q值。利用合成数据和实际数据进行了测试,结果表明,相比于固定时窗短时傅里叶变换方法,自适应短时傅里叶变换方法具有更好的时间和频率分辨率,可以获得更高分辨率的品质因子Q值。该结果可以为地下介质的研究提供更准确、可靠的工具,有助于更好地了解地下结构和油气资源分布情况。

收益率服从q-高斯分布的二叉树期权定价模型及实证分析

以股票价格收益率服从q-高斯分布为基础,使用二叉树定价方法,得到收益率符合q-高斯分布的新型二叉树期权定价模型及数值解法;以部分2023年中证1000和上证50的股指期权价格数据为样本,利用MATLAB进行参数估计、模拟计算股指期权看涨期权价格,并进行图像拟合;最后,对一般二叉树模型、新型二叉树模型所求价格与实际期权价格进行比较,得出收益率服从q-高斯分布的新型二叉树期权定价模型更优的结论,为收益率具有尖峰厚尾特征的相关股指期权定价问题提供了一定的方法和依据.

基于Dueling-DQN的异构无线网络垂直切换算法研究

针对当前异构无线网络中切换算法考虑的服务质量指标较少,用户频繁切换愈加严重的问题,提出了基于主客观加权与改进的深度强化学习相结合的异构无线网络垂直切换方法。首先,提出了一种支持异构无线网络的软件定义网络架构;其次,提出了主客观加权相结合的属性加权算法;最后,将网络选择问题利用改进的Dueling-DQN方法解决。仿真结果表明,本文所提算法在不同用户类型网络下切换次数分别减少了11.25%,13.34%,18.76%,13.75%,吞吐量提升了16.64%。因此本文所提算法有效避免了乒乓切换,减少切换次数并且提升了吞吐量。

包含快照选择策略的POD-QDEIM油浸式变压器绕组瞬态温升降阶算法研究及其实验验证

为了提高采用有限元方法对油浸式电力变压器绕组瞬态温升进行仿真的计算速度,该文提出一种包含快照选择策略的本征正交分解(proper orthogonal decomposition,POD)-基于列主元QR分解的离散经验插值(QR factorization-discrete empirical interpolation method,Q-DEIM)(POD-QDEIM)算法。首先,文章基于最小二乘有限元法与迎风有限元法推导绕组流热耦合计算方程;其次,通过引入POD方法,降低有限元方程阶数提高求解效率;同时提出POD自适应快照选择策略,在保证降阶模型精度的前提下,减小快照矩阵规模;随后,为了改善POD方法求解非线性问题时效率不高的劣势,文章结合基于Q-DEIM方法,通过插值的方法形成方程中的非线性项,从而提高每一时步非线性项的形成效率;最后,基于110 kV油浸式电力变压器绕组基本结构,建立了八分区分匝绕组传热模型以及绕组温升试验装置对所提算法进行验证,仿真及实验结果表明POD-QDEIM降阶算法的计算精度在工程上属于可接受范围,其计算效率较全阶计算提升了近11.72倍,说明该算法在油浸式电力变压器绕组瞬态温升快速仿真领域的工程应用价值。

Application of orthogonal experimental design and Tikhonov regularization method for the identification of parameters in the casting solidification process

The inverse heat conduction method is one of methods to identify the casting simulation parameters. A new inverse method was presented according to the Tikhonov regularization theory. One appropriate regularized functional was established, and the functional was solved by the sensitivity coefficient and Newtonaphson iteration method. Moreover, the orthogonal experimental design was used to estimate the appropriate initial value and variation domain of each variable to decrease the number of iteration and improve the identification accuracy and efficiency. It illustrated a detailed case of AlSiTMg sand mold casting and the temperature measurement experiment was done. The physical properties of sand mold and the interracial heat transfer coefficient were identified at the meantime. The results indicated that the new regularization method was efficient in overcoming the ill-posedness of the inverse heat conduction problem and improving the stability and accuracy of the solutions.

Optimizing casting parameters of steel ingot based on orthogonal method

The influence and signification of casting parameters on the solidification process of steel ingot were discussed based on the finite element method (FEM) results by orthogonal experiment method. The range analysis, analysis of variance (ANOVA) and optimization project were used to investigate the FEM results. In order to decrease the ingot riser head and improve the utilization ratio of ingot, the casting parameters involved casting temperature, pouring velocity and interface heat transfer were optimized to decrease shrinkage pore and microporosity. The results show that the heat transfer coefficient between melt and heated board is a more sensitive factor. It is favor to decrease the shrinkage pore and microporosity under the conditions of low temperature, high pouring velocity and high heat transfer between melt and mold. If heat transfer in the ingot body is quicker than that in the riser, the position of shrinkage pore and microporosity will be closer to riser top. The results of optimization project show that few of shrinkage pore and microporosity reach into ingot body with the rational parameters, so the riser size can be reduced.

铁路隧道BQ法、Q值法、RMR法相互关系研究

研究目的:围岩等级是铁路隧道设计和施工需确定的关键参数,随着中国铁路“走出去”战略的深入实施,我国设计工程师与国际咨询在隧道围岩分级方法的选取和应用上往往难以达成共识,从而影响海外工程的顺利开展。为研究围岩分级国标BQ法与国际主流Q值法和RMR法间的相互关系,总结对比BQ法、Q值法、RMR法三种围岩分级方法间差异,选取国内外多座代表性铁路隧道,对同一里程掌子面分别采用上述三种方法进行围岩分级,并结合其他文献研究成果,对分级结果进行对比分析。研究结论:(1)Q值法、RMR法在实际工程应用中均存在利弊,现场围岩等级的确定宜结合国标BQ法相互校核得出结论;(2)[BQ]值和Q值间关系符合指数函数,[BQ]值和RMR值间符合线性关系,Q值和RMR值间关系符合对数函数;(3)不同文献在BQ法、Q值法、RMR法间相互关系研究成果差异性大小方面,Q值和RMR值关系最小,也最为成熟,[BQ]值和RMR值关系次之,[BQ]值和Q值关系最大;(4)本文建立了国标BQ法与国际Q值法和RMR法间围岩等级划分对应关系表,在无法应用BQ法划分围岩级别情况下,可通过查表帮助国内设计人员理解和选择围岩支护体系,研究成果将有利于国标BQ法与国际Q值法和RMR法间的相互借鉴和融合,对海外隧道工程设计和施工具有一定指导意义。

Influence of radial forging process on strain inhomogeneity of hollow gear shaft using finite element method and orthogonal design

Due to the current trend towards lightweight design in automotive industry,hollow stepped gear shafts for automobile and its radial forging process are widely investigated.Utilizing coupled finite element thermo-mechanical model,radial forging process of a hollow stepped gear shaft for automobile was simulated.The optimal combination of three process parameters including initial temperature,rotation rate and radial reduction was also selected using orthogonal design method.To examine the strain inhomogeneity of the forging workpiece,the strain inhomogeneity factor was introduced.The results reveal that the maximum effective strain and the minimum effective strain appeared in the outermost and innermost zones of different cross sections for the hollow stepped gear shaft,respectively.Optimal forging parameters are determined as a combination of initial temperature of 780°C,rotation rate of 21°/stroke and radial reduction of 3 mm.

STRESS INTENSITY FACTORS CALCULATION IN ANTI-PLANE FRACTURE PROBLEM BY ORTHOGONAL INTEGRAL EXTRACTION METHOD BASED ON FEMOL

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eigenfunctions） of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors （SIFs）, so any order SIF can be extracted based on a certain known solution of displacement （an analytic result or a numerical result）. Many numerical examples based on the finite element method of lines （FEMOL） show that the present method is very powerful and efficient.

基于UPLC-Q-Exactive-Orbitrap-MS分析马齿苋炒炭前后化学成分变化

目的:分析马齿苋炒炭前后化学成分变化,筛选差异性止血成分。方法:采用UPLC-Q-Exactive-Orbitrap-MS技术检测,选择Waters BEH C_(18)(100 mm×2.1 mm,1.7μm)色谱柱;流速为0.2 mL/min;进样量为1μL;柱温为35℃;流动相为水-乙腈,梯度洗脱;采用电喷雾离子源,正、负离子扫描模式,质量扫描范围m/z 50~1500,根据相对分子质量和碎片信息,结合文献及数据库鉴定化学成分。应用SIMCA 14.1软件对质谱数据进行主成分分析和正交偏最小二乘判别分析,通过查阅相关文献筛选马齿苋炒炭前后差异性止血活性成分。结果:在正、负离子模式下,马齿苋及其炭品共鉴定出41个成分,含黄酮9个、苷类6个、有机酸12个、脂肪酸4个、氨基酸3个、生物碱4个、萜类1个、其他成分2个,通过VIP值结合文献筛选出6个差异性止血成分,其中没食子酸、5,7,4′-三羟基黄酮、大豆苷元含量增加。结论:马齿苋炭主要含黄酮类和有机酸类等成分,上述研究结果可为马齿苋炒炭后止血作用增强提供物质基础依据。

Reduced-order method for nuclear reactor primary circuit calculation

Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.

Factors influencing HPAM solution viscosity prepared by produced water using orthogonal method

The effect of temperature and metal ion components on the viscosity of HPAM solution was studied by means of orthogonal method.Five factors and 4 levels were considered for the orthogonal design.The five factors included temperature,contents of Na+,Mg2+,Ca2+ and S2-,and the four levels mainly considered the level of produced water components in main oilfields in China.The experiment results show that temperature is the most important factor to control HPAM solution viscosity prepared by produced water.The effect of ions was in order of Na+>S2->Mg2+>Ca2+.The mechanism of each factor influencing viscosity was also discussed.Based on the actual condition of Nanyang oilfield,the desulfurization was used to improve the solution viscosity,and satisfactory result was obtained.

Plasma shape optimization for EAST tokamak using orthogonal method

It is necessary to reduce the currents of poloidal field(PF) coils as small as possible, during the static equilibrium design procedure of Experimental Advanced Superconductive Tokamak(EAST). The quasi-snowflake(QSF) divertor configuration is studied in this paper. Starting from a standard QSF plasma equilibrium, a new QSF equilibrium with 300 kA total plasma current is designed. In order to reduce the currents of PF6 and PF14, the influence of plasma shape on PF coil current distribution is analyzed. A fixed boundary equilibrium solver based on a non-rigid plasma model is used to calculate the flux distribution and PF coil current distribution. Then the plasma shape parameters are studied by the orthogonal method. According to the result, the plasma shape is redefined, and the calculated equilibrium shows that the currents of PF6 and PF14 are reduced by 3.592 kA and 2.773 kA, respectively.