Legendre-Weighted Residual Methods for System of Fractional Order Differential Equations

The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.

Method of Semi Analytic Perturbation Weighted Residuals for Nonlinear Bending of Shallow Shells

The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.

A WEIGHTED RESIDUAL METHOD FOR ELASTIC-PLASTIC ANALYSIS NEAR A CRACK TIP AND THE CALCULATION OF THE PLASTIC STRESS INTENSITY FACTORS

In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plastic solutions of the crack lip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field, to calculate the plastic stress intensity factors, are also developed. Therefore, a complete analvsis based on the calculation both for the crack tip field and for the whole crack body field is provided.

Weighted residual method for diffraction of plane P-waves in a 2-D elastic half-spaceⅢ:on an almost circular arbitrary-shaped alluvial valley

Scattering and diffraction of elastic in-plane P- and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong motion seismologists for over forty years. The case of out-of- plane SH-waves on the same elastic canyon that is semicircular in shape on the half-space surface is the first such problem that was solved by analytic closed-form solutions over forty years ago by Trifunac. The corresponding case of in-plane P- and SV- waves on the same circular canyon is a much more complicated problem because the in-plane P- and SV- scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by Lee and Liu. This paper uses their technique of defining these stress-free scattered waves, which Brandow and Lee previously used to solve the problem of the scattering and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape, to the study of the scattering and diffraction of these in-plane waves on an almost circular arbitrary-shaped alluvial valley.

Utilizing Water Treatment Residuals for Phosphorus Removal:Batch Trials,Column Trials and Effects of Three Low-Molecular-Weight Organic Acids

Phosphorus( P) has been recognized as a major limited nutrient responsible for the eutrophication of surface waters. Water treatment residuals( WTRs) are safe by-products of water treatment plants and are cost-efficient adsorbents. In this study, batch experiments and column experiments based on WTRs were employed to study the characteristics of P adsorption and the effects of lowmolecular-weight organic acids( LMWOAs)( citric acid, oxalic acid,and tartaric acid) on P adsorption. Different models of adsorption were used to describe equilibrium and kinetic data. The adsorption data were fitted well by a pseudo-second order kinetic model. The adsorption process was determined to be controlled by three steps of diffusion mechanisms through the intra-particle model.The adsorption equilibrium was well described by the Langmuir,Freundlich,Redlich-Peterson,and Sips isotherm models. Batch and continuous flow experiments indicated that the LMWOAs exhibited inhibitory action,and as pH increased,the inhibitory action became weaker for all the three acids. The effect of LMWOAs concentration was not significant on inhibition. The effects of LMWOAs were closely related to reaction time.

AN ASSESSMENT OF THE MESHLESS WEIGHTED LEAST-SQUARE METHOD

The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, the coe?cient matrix obtained is symmetric and semi- positive de?nite. In this paper, the method is further examined critically. The e?ects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an in?nite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more e?cient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equi- librium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense.

Effects of Pleurotus eryngii Residue on Weight Gain of Chick and Duck

In the present study, Pleurotus eryngii residue was added into conventional feed of Chai chicks and meat-type ducks at different ratios to measure its effects on the production performance of chicks and ducks. The results revealed that the growth performance of chicks and ducks was the best when 20% Pleurotus eryngii residue was added into the feed. Under such condition, the daily weight gain of 8 - 11 and 12 - 15-week-old Chai chicks was increased by 6.8% and 13.5%, and that of 8 - 11 and 12 - 15-week-old ducks was increased by 11.5% and 19.3%, respectively.

Generalized Weighted Exponential-Gompertez Distribution

Statistical analysis of lifetime data is a significant topic in social sciences, engineering, reliability, biomedical and others. We use the generalized weighted exponential distribution, as a generator to introduce a new family called generalized weighted exponential-G family, and apply this new generator to provide a new distribution called generalized weighted exponential gombertez distribution. We investigate some of its properties, moment generating function, moments, conditional moments, mean residual lifetime, mean inactivity time, strong mean inactivity time, Rényi entropy, Lorenz curves and Bonferroni. Furthermore, in this model, we estimate the parameters by using maximum likelihood method. We apply this model to a real data-set to show that the new generated distribution can produce a better fit than other classical lifetime models.

Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual

In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

受试者测试状态对卡尔曼加权平均ABR测试残余噪声的影响

目的探讨采用卡尔曼加权平均(Kalman-weighted averaging,KWA)的听性脑干反应(ABR)测试中,受试者不同测试状态对残余噪声及ABR波V振幅的影响。方法选取21例(42耳)18~34岁听力正常成年人,分别在安静诊室内三种不同的状态下(安静平卧、坐位、写字)使用卡尔曼加权平均的新型ABR系统(vivosonic integrity system)进行ABR测试,同时使用传统ABR测试系统(interacoustics,IA)在隔声屏蔽室内进行ABR测试,记录各状态下受试者ABR反应的残余噪声水平和波V幅值并进行比较。结果①传统ABR和卡尔曼加权平均ABR三种不同测试状态(平卧、坐位、写字)下波V振幅没有显著差异(P>0.05);②卡尔曼加权平均ABR安静平卧和坐位两种状态下的残余噪声水平较传统ABR低,但无统计学差异(P>0.05);卡尔曼加权平均ABR在写字状态下的残余噪声水平显著高于其他三种状态(P<0.05);③写字状态下卡尔曼加权平均ABR的残余噪声、波V振幅在左右耳之间没有显著差异(P>0.05)。结论与传统ABR相比,卡尔曼加权平均ABR在写字状态下的残余噪声显著升高,但安静平卧和坐位状态下的残余噪声水平与传统ABR无显著差异,受试者的不同测试状态对残余噪声水平有一定影响。

An approach for optimization of the wall thickness (weight) of a thick-walled cylinder under axially non-uniform internal service pressure distribution

Today, improving the weight/load carrying capacity ratio of a part is the matter of studies in most of the scientific and industrial areas.Autofrettage dimensions, the amount of material removed from outer and inner radius while manufacturing and the service pressure applied affect the residual stress distribution throughout the wall thickness and hence the load-bearing capacity of a thick-walled cylinder. Calculation of residual stresses after autofrettage process and optimization of autofrettage outline dimensions by using the amount of service pressures applied are common issues in literature.In this study, mandrel-cylinder tube interference dimensions were renovated by using traditional methods for swage autofrettage process of a gun barrel. Also, the residual stresses in the cylinder after autofrettage process, inside and outside material removal process and the variable service pressure throughout the cylinder applied were taken into consideration and incorporated into the design. By using the constrained optimization method, wall thickness(thus the weight) was optimized(minimized)to achieve the specified safety factor along the length of the cylinder. For the same cylinder, the results of the suggested analytical/with residual stress calculation approach were compared to analytical/without residual stress calculation results and numerical topology optimization method calculation results. Since the experimental measurement results are not yet available, it was not possible to compare them with the calculation results.The suggested approach enabled 22.9% extra weight reduction in proportion to numerical topology optimization and enabled 4.2% extra weight reduction in proportion to analytical/without residual stress optimization.Using this approach, the gain from residual stresses after autofrettage operation, the loss of residual stresses after material removal, and the effects of service pressures can be taken into account for each stage of design.

加权核范数最小化和改进小波阈值函数的图像去噪算法

针对加权核范数最小化算法存在结构残余噪声以及无法较好地保持图像边缘结构的问题,提出基于加权核范数最小化和改进小波阈值函数的图像去噪算法。利用全变分模型对噪声图像进行初步去噪,使用噪声图像与初步去噪后的图像进行差分运算,对差分后得到的噪声残差图像使用改进的小波阈值函数去噪,将小波去噪后的残差图像与初步去噪图像叠加,将叠加后的图像使用基于残余噪声水平迭代的加权核范数最小化算法进行二次去噪。相较于当下主流去噪算法,经该算法处理后的图像的PSNR和SSIM值均有所提升,能够更好地保持图像的纹理结构,且在高噪声环境下效果更佳。

Box-Behnken响应面法优化复合益生菌发酵三七药渣工艺及体外抗氧化活性研究

目的以三七药渣为原料,通过益生菌发酵比较不同益生菌以及复合益生菌对各指标成分影响的差异,探究最佳发酵工艺。方法采用单因素、Box-Behnken响应面法优化发酵工艺,并通过体外抗氧化实验评价发酵产物的抗氧化能力。结果最佳发酵工艺为有氧发酵48 h、厌氧发酵36 h,嗜热链球菌、两歧双歧杆菌、嗜酸乳杆菌的比例为2∶3∶1,料液比0.14 g·mL^(-1),接菌量5%,温度33℃。在最佳发酵工艺条件下,三七药渣中性多糖、酸性多糖、总黄酮的含量分别提高了105.64%、96.98%、123.83%,相较于单菌发酵均显著升高。发酵产物清除DPPH、ABTS自由基的IC 50值分别为1.774、3.065 mg·mL^(-1),还原Fe^(3+)的能力为0.138 mmol FeSO_(4)·g^(-1),较未发酵药渣显著增强。结论最佳发酵工艺能显著提高三七药渣中各指标成分含量,显著增强其抗氧化能力,相较单菌发酵各指标成分含量均显著提高,提示上述益生菌之间没有明显的拮抗作用。研究结果为三七药渣的资源化利用提供了科学依据和数据支撑。

基于GIS的灌区土壤投入品残留污染监测预警系统

为了解决工业发展导致的灌区土壤投入品残留污染问题,给出一种基于地理信息系统(geographic information system,GIS)的土壤污染监测预警系统。该系统结合VOC-PF1型传感器、STM32主控芯片和GSM通信模块,实现了高效的数据采集和通信功能。通过反距离加权(inverse distance weighted,IDW)插值法进行空间分析,并设立预警阈值,实现对灌区土壤投入品残留污染的实时监测和预警。实验结果表明:该系统的监测精度高达98%,监测时长最高为49 s,具有很高的实用性和效率。研究结果不仅为灌区土壤投入品残留污染监测提供了有效手段,也为环境保护和农业可持续发展提供有力支持。

MBRNet:融合残差连接的多分支手写字符识别网络

脱机手写中文字符识别(handwritten Chinese character recognition,HCCR)在计算机视觉领域一直是一个巨大的挑战。相比传统方法,基于深度学习的网络通过训练大量数据在识别任务中取得了差异化的效果,但识别效果依旧处于发展过程中。基于此,结合DW卷积和残差连接设计了一种多分支残差模块,该模块通过DW卷积以较小的内存和参数量为代价来加深网络深度,增强网络的特征提取能力;再通过残差连接抑制网络梯度问题和退化问题;另外,提出了一种多分支权重算法,来改善多分支残差模块中各分支的权重分配问题;并将六个以多分支残差模块为主的结构线性连接,组成HCCR识别网络。该模型在CASIA-HWDB1.0、CASIA-HWDB1.1、ICDAR2013数据集上的识别准确率分别达到了97.77%、97.30%、97.64%,表现出高精度的识别效果。

基于自适应红外多波段联合光谱分析的高精度气体浓度反演研究

本文提出一种自适应多波段联合浓度反演算法,结合透过率稳定区间与谱宽阈值自适应选择待测气体的有效波段;采用非线性最小二乘拟合方法对各有效波段进行浓度反演及残差分析,获得各有效波段的浓度反演结果及其权重,通过加权平均实现待测气体浓度的精确定量分析。设计并进行实验验证,结果表明,自适应多波段联合浓度反演算法的稳定系数达到了0.9976,与传统的单波段及多波段浓度反演算法相比,该反演结果的均方根误差分别降低了64.44%和41.52%,平均相对误差分别降低了65.97%和46.72%,平均绝对误差分别降低了66.32%和47.74%,反演精度与稳定性得到了明显提升。

基于MCABResnet的二维滚动轴承故障诊断新方法

针对时域信号冗余度大及滚动轴承故障诊断效果和强噪声环境下诊断正确率低和泛化能力差的问题,提出一种新的基于多联合注意力机制和多残差卷积块的多尺度进化故障诊断方法。采用宽、窄核卷积的跃迁块和多联合注意机制对深层卷积进行特征补充,减少特征流失,保证特征图的质量。通过通道和空间注意力权重的分配,为卷积层提供不同的权重参数,进行自适应特征细化。将提出的方法分别在凯斯西储大学轴承数据集和东南大学轴承数据集进行试验验证及分析。结果显示:所提方法的分类正确率超过99.75%,即使在强噪声环境下,分类正确率也超过98.5%;在变工况下,平均分类正确率超过了90%。因此,所提方法具有良好的故障诊断效果、泛化能力和抗噪声性能。

基于智慧路灯云平台的动态权重负载均衡算法

大规模路灯向云平台发送数据会导致服务器在高并发情况下的各节点出现负载失衡、引起通信故障。针对该问题,文中基于微服务提出了一种基于智慧路灯云平台的动态权重负载均衡算法。该算法在初始化时根据各个服务器的硬件性能计算出各自的权重系数及各节点的初始权值,并在请求过程中结合CPU(Central Processing Unit)和网络带宽的空闲率动态地调节服务器权重,实现负载的优化。通过设定最低阈值与计算出的剩余负载率进行比较,将到达负载上限的服务器权值置为0,防止服务器出现过载情况。测试结果表明,在实验环境下,文中算法相比于最小连接数算法和平滑加权轮询算法具有更优的负载均衡效果,相比于动态权重算法,平均响应时间和实际并发连接数也有所提升。

考虑地震事件内空间相关性的区域概率地震危险性分析

一次地震事件不同地点的地震动强度参数与结构响应参数之间是空间相关的,相关的地震效应将导致地震损失急剧集中与积累,从而造成灾难性事件,但是现有的区域尺度地震风险评估并没有考虑地震动的空间相关性。该文采用地统计学方法表征地震事件内地震动强度参数的空间相关性,提出了理论半变异函数的几何稳健估计方法,并采用加权最小二乘法实现对短距离空间相关性的准确高效评估。以新潟越冲地震为例,基于指数半变异函数模型,采用加权最小二乘法对几何稳健估计半变异函数值进行拟合,得到了PGA、PGV和0 s~10 s谱加速度的空间相关性函数,提出了变程b值的预测模型,结果表明:相比于短周期谱加速度,长周期谱加速度的空间相关性衰减速率更小,且在T=0.45 s处存在拐点。将所开发的空间相关性模型应用于区域概率地震危险性分析,采用Monte Carlo方法实现了空间相关随机场的区域地震动强度参数的模拟,改进了传统区域地震危险性分析的方法,发现绝大多数情况下考虑空间相关性的年超越概率大于未考虑空间相关性的年超越概率,表明考虑空间相关性对于建筑群落及基础设施风险评估、韧性城市建设等具有重要的指导意义。

物理信息神经网络的一种自适应配置点算法

物理信息神经网络(PINN)能够将方程模型融入到损失最小化训练中,能同时学习输入数据分布和物理规律,大多数PINN是通过均匀采样配置点来覆盖整个求解区域,且各个配置点间都同等发挥作用,其配置点策略简便易行,但也使得PINN增加了部分不必要的配置点,且对部分复杂规律的学习能力不足.文章提出一种配置点自适应设置策略,以提高PINN学习能力和学习效率.首先通过损失函数残差及梯度联合分布确定配置点选择概率,同时在迭代一定次数后进行重采样,避免过早陷入局部最优,这样可以使一部分配置点分布在损失较高或变化较明显处,从而改善配置点的分布情况,达到以较少的配置点也能准确反映方程模型的效果,提升学习效率;其次引入配置点的变权重设定,使每个配置点对方程残差的影响有所侧重,在网络迭代训练中自动提高损失值较高部分配置点的权重,从而使PINN更专注于损失较大的部分,即复杂规律的学习.最后通过Burgers方程、Schrodinger方程、Helmholtz方程和Navier-Stokes方程4种典型算例与传统PINN及其各种改进方法进行比较实验.数值结果表明,该算法可以在较少的配置点数量和迭代次数设定下,有效提升求解精度和计算效率.