A Real-Time Transient Analysis of a Functionally Graded Material Plate Using Reduced-Basis Methods

Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients

A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved.

H^1-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis Ⅱ

Abstract. Let （R＋,＊,A） be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley g function and the Lusin area function for the Jacobi hypergroup and consider their （H^1, L^1 ） boundedness. Although the g operator for （R＋,＊,A） possesses better property than the classical g operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the （H^1,L^1） estimate for the Lusin area operator, a slight modification in its form is required.

Comparative Study of Radial Basis Functions for PDEs with Variable Coefficients

The radial basis functions(RBFs)play an important role in the numerical simulation processes of partial differential equations.Since the radial basis functions are meshless algorithms,its approximation is easy to implement and mathematically simple.In this paper,the commonly⁃used multiquadric RBF,conical RBF,and Gaussian RBF were applied to solve boundary value problems which are governed by partial differential equations with variable coefficients.Numerical results were provided to show the good performance of the three RBFs as numerical tools for a wide range of problems.It is shown that the conical RBF numerical results were more stable than the other two radial basis functions.From the comparison of three commonly⁃used RBFs,one may obtain the best numerical solutions for boundary value problems.

Sensitivity Analysis of Radial Basis Function Networks for River Stage Forecasting

Sensitivity analysis of neural networks to input variation is an important research area as it goes some way to addressing the criticisms of their black-box behaviour. Such analysis of RBFNs for hydrological modelling has previously been limited to exploring perturbations to both inputs and connecting weights. In this paper, the backward chaining rule that has been used for sensitivity analysis of MLPs, is applied to RBFNs and it is shown how such analysis can provide insight into physical relationships. A trigonometric example is first presented to show the effectiveness and accuracy of this approach for first order derivatives alongside a comparison of the results with an equivalent MLP. The paper presents a real-world application in the modelling of river stage shows the importance of such approaches helping to justify and select such models.

Concurrent Two-Scale Topology Optimization of Thermoelastic Structures Using a M-VCUT Level Set Based Model of Microstructures

By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.

Diatoms as indicators of environmental change in coastal areas:a case study in Lianjiang coast of East China Sea

Owing to the significant differences in environmental characteristics and explanatory factors among estuarine and coastal regions,research on diatom transfer functions and database establishment remains incomplete.This study analysed diatoms in surface sediment samples and a sediment core from the Lianjiang coast of the East China Sea,together with environmental variables.Principal component analysis of the environmental variables showed that sea surface salinity(SSS)and sea surface temperature were the most important factors controlling hydrological conditions in the Lianjiang coastal area,whereas canonical correspondence analysis indicated that SSS and pH were the main environmental factors affecting diatom distribution.Based on the modern diatom species–environmental variable database,we developed a diatom-based SSS transfer function to quantitatively reconstruct the variability in SSS between 1984 and 2021 for sediment core HK3 from the Lianjiang coastal area.The agreement between the reconstructed SSS and instrument SSS data from 1984 to 2021 suggests that diatombased SSS reconstruction is reliable for studying past SSS variability in the Lianjiang coastal area.Three low SSS events in AD 2019,2013,and 1999,together with an increased relative concentration of freshwater diatom species and coarser sediment grain sizes,corresponded to two super-typhoon events and a catastrophic flooding event in Lianjiang County.Thus,a diatom-based SSS transfer function for reconstructing past SSS variability in the estuarine and coastal areas of the East China Sea can be further used to reflect the paleoenvironmental events in this region.

Customized Optimization for Vehicle Acoustic Statistical Energy Analysis

Statistical Energy Analysis(SEA) is one of the conventional tools for predicting vehicle high-frequency acoustic responses.This study proposes a new method that can provide customized optimization solutions to meet NVH targets based on the specific needs of different project teams during the initial project stages.This approach innovatively integrates dynamic optimization,Radial Basis Function(RBF),and Fuzzy Design Variables Genetic Algorithm(FDVGA) into the optimization process of Statistical Energy Analysis(SEA),and also takes vehicle sheet metal into account in the optimization of sound packages.In the implementation process,a correlation model is established through Python scripts to link material density with acoustic parameters,weight,and cost.By combining Optimus and VaOne software,an optimization design workflow is constructed and the optimization design process is successfully executed.Under various constraints related to acoustic performance,weight and cost,a globally optimal design is achieved.This technology has been effectively applied in the field of Battery Electric Vehicle(BEV).

Situation Awareness and Sensitivity Analysis for Absorption of Grid-connected Renewable Energy Power Generation Integrating Robust Optimization and Radial Basis Function Neural Network

The significance of situation awareness(SA) in power systems has increased to enhance the utilization of gridconnected renewable energy power generation(REPG). This paper proposes a real-time calculation architecture based on the integration of robust optimization(RO) and artificial intelligence. First, the time-series simulation of the REPG consumption capacity is carried out under the current grid operating conditions. RO is employed in this simulation, given the randomness of the REPG output and the grid load. Then, the radial basis function neural network(RBFNN) is trained with the results under different parameters using the artificial fish swarm algorithm(AFSA), enabling the neural network(NN) to be the replacement for the time-series simulation model. The trained NN can quickly perceive the REPG absorption situation within the predefined grid structure and period. Moreover, the Sobol' method is adopted to conduct the global sensitivity analysis for different parameters based on the input-output samples obtained by the trained NN. Finally, the simulation experiments based on the modified IEEE 14-bus system prove the real-time performance and accuracy of the proposed SA architecture.

An isogeometric approach to free vibration analysis of bi-directional functionally graded porous doubly-curved shallow microshells with variable length-scale parameters

This study uses iso-geometric investigation,which is based on the non-uniform rational B-splines(NURBS)basis function,to investigate natural oscillation of bi-directional functionally graded porous(BFGP)doublycurved shallow microshells placed on Pasternak foundations with any boundary conditions.The characteristics of the present material vary in both thickness and axial directions along the x-axis.To be more specific,a material length-scale coefficient of the microshell varies in both thickness and length directions as the material's mechanical properties.One is able to develop a differential equation system with varying coefficients that regulate the motion of BFGP double-curved shallow microshells by using Hamilton principle,Kirchhoff-Love hypothesis,and modified couple stress theory.The numerical findings are reported for thin microshells that are spherical,cylindrical,and hyperbolic paraboloidal,with a variety of planforms,including rectangles and circles.The validity and effectiveness of the established model are shown by comparing the numerical results given by the proposed formulations with previously published findings in many specific circumstances.In addition,influences of length scale parameters,power-law indexes,thickness-to-side ratio,and radius ratio on natural oscillation responses of BFGP microshells are investigated in detail.

The Interannual Variability of Summer Rainfall in the Arid and Semiarid Regions of Northern China and Its Association with the Northern Hemisphere Circumglobal Teleconnection

Using the latest daily observational rainfall datasets for the period 1961–2008, the present study investigates the interannual variability of June–September （JJAS） mean rainfall in northern China. The regional characteristics of JJAS mean rainfall are revealed by a rotated empirical orthogonal function （REOF） analysis. The analysis identifies three regions of large interannual variability of JJAS rainfall： North China （NC）, Northeast China （NEC）, and the Taklimakan Desert in Northwest China （TDNWC）. Summer rainfall over NC is shown to have displayed a remarkable dry period from the late 1990s; while over NEC, decadal-scale variation with a significant decreasing trend in the last two decades is found, and over TDNWC, evidence of large interannual variability is revealed. Results also show that the interannual variability of JJAS rainfall in northern China is closely associated with the Northern Hemisphere circumglobal teleconnection （CGT）. Correlation coefficients between the CGT index and regional-averaged JJAS mean rainfall over NC and NEC were calculated, revealing values of up to 0.50 and 0.53, respectively, both of which exceeded the 99% confidence level.

Detection Performance Analysis of Spectrum Sensing in Cognitive Radio Networks with Mobile Secondary Users

The majority of existing papers about spectrum sensing have the assumption that secondary users(SUs) are stationary. However,mobility is an essential feature of mobile communications networks. In this paper,the detection performance of spectrum sensing by mobile SUs was analyzed. Three performance metrics,i.e.,detection probability,miss detection probability and false alarm probability,were thoroughly investigated. In our analysis,a critical variable was the real-time received primary user signal power by a mobile SU. Its probability distribution and mathematical expectation were analytically derived. Moreover,the three performance metrics in single-node spectrum sensing and multi-node collaborative spectrum sensing systems were also derived. Extensive simulations were performed. The results are consistent with the theoretical analysis. And it is concluded that SU mobility has a significant impact on the detection probability and the miss detection probability,but not on the false alarm probability.

Trends and Interannual Variability of Winds and Turbulent Heat Flux in the Indian Ocean Sector of Southern Ocean during 2000-2009

Using satellite-based wind and sea surface temperature (SST) observations, linear trend and inter-annual variability of wind stress, turbulent heat flux (Q) and wind stress curl are addressed for the Indian Ocean sector of the Southern Ocean (ISO, 0°E - 155°E) for the period 2000-2009. The analysis reveals that spatial mean of Q varies between 70 and 73 Wm-2 in the austral summer and winter, respectively, while the mean wind stress is nearly same at 0.22 Nm-2 for both seasons. The anticyclonic curl dominates the ISO, which increases from 0.15 × 10-7 to 0.35 × 10-7 Nm-3 during the austral summer. The detrended box-mean time series of Q, wind stress, and wind stress curl exhibits a decreasing trend of –6.3 ± 1.6 Wm-2·decade-1, -0.012 ± 0.004 Nm-2·decade-1 and -0.48 ± 0.6 × 10-8 Nm-3·decade-1, respectively. The Empirical Orthogonal Function (EOF) analysis was carried out to study inter-annual variability. EOF-1 of Q captures 25% of the total variance, which mimics the austral summer pattern;its time coefficient is highly and negatively correlated with a 2-month lagged Nino3.4 SST index (r =-0.8 at 95% confidence). EOF-1 of wind stress accounts for 35% of the total variance and its time coefficient is strongly correlated with the Antarctic Oscillation (r= 0.86 at 95% confidence). EOF-1 of wind stress curl captures 15% of the total variance;its time coefficient is correlated to the Nino3.4 SST index (r= 0.65 at 95% confidence) with the former lagging the latter by two years. The repercussions of the weakening trends of the climatic parameters on the air-sea interaction and ocean circulation are highlighted.

Isogeometric Analysis for Linear and Nonlinear Cantilever in CAD

A novel method for the mechanical simulation of linear and nonlinear Timoshenko-beams has been presented.The beam strains are based on a kinematic assumption where the shear deformation and rotational are considered.Applying the isoparametric concept the kinematic quantities are approximated using NURBS(non-uniform Rational B-spline)functions.This numerical simulation can be called as isogeometric analysis,which can improve the efficiency in CAD(computer aided design).Furthermore,an efficient Code has been developed and the results for two numerical applications are given in the end.

海域重力异常模型的多尺度分析

不同于传统的重力异常模型精度分析方法,本文以马里亚纳海沟区域(140°E—150°E,10°N—20°N)为例,利用DOG球面小波提取了DTU10、DTU17和SIO V32.1模型在不同波段内的重力异常信号,对模型间的差异进行了深入分析,并对基于径向基函数的不同深度、不同分辨率的多尺度分析进行了尝试。利用DOG球面小波对各模型多尺度分析的结果表明,随着尺度变小,模型间的差异在变大;DTU10、DTU17模型间的差异主要集中在10.9~43.6 km的波段内,分布在海岸、海沟、海底山附近,体现了Cryosat-2、Jason-1/GM观测数据和FES2014海潮模型的贡献;受模型构建方法不同、观测数据增多和波形重跟踪的影响,DTU17、SIO V32.1模型的差异大于DTU10、DTU17之间的差异。对传统径向基函数进行了改进,实现了多深度、多空间分辨率情况下径向基函数多尺度分析,结果略优于单一深度、单一空间分辨率径向基函数构建结果,有望应用于多源数据的重力场模型构建。

基于SSA-RBF神经网络的煤自然发火预测模型

为解决传统煤自燃预测模型预测状态单一和预测精度不高的问题,提出基于麻雀搜索算法(SSA)优化的径向基(RBF)神经网络煤自然发火预测模型。首先,采用程序升温试验分析煤样指标气随温度的变化特征,将煤自然发火过程按煤温分为缓慢(80≤t_(i)<120℃)、加速(120≤t_(i)<160℃)和激烈(t_(i)≥160℃)3个氧化阶段,同时分析这3个阶段指标气与煤温的灰色关联度;其次通过不同维度测试函数检验粒子群算法(PSO)、灰狼算法(GWO)和SSA算法性能;最后利用6个矿区数据验证基于SSA-RBF神经网络的煤自燃预测模型的优越性。结果显示,缓慢氧化阶段CO/ΔO_(2)、CO、C_(2)H_(4)这3种指标气体与煤温的灰色关联系数最大;而加速氧化阶段C_(2)H_(4)/C_(2)H_(6)、CO/ΔO_(2)、CO_(2)/CO_(3)种指标与煤温的灰色关联系数最大。3种不同维度函数的测试结果表明:SSA与PSO、GWO相比具有更好的全局搜索能力和稳定性,其收敛速度更快;神经元数量为5个、迭代次数为300次时,SSA-RBF神经网络预测模型对缓慢氧化和加速氧化阶段的预测准确性分别达到了99%和93%。

数模—动模混合仿真系统的接口建模与稳定性分析

为满足现代电力系统实时仿真的发展需求,数模-动模混合仿真系统结合实时数字仿真和物理动态模拟仿真的优点,成为现代电力系统研究的重要仿真方法。接口系统是混合仿真系统设计中的核心与难点。为了深入分析混合仿真系统的稳定性,对接口系统各个组成环节进行建模得到系统开环传递函数,分别根据劳斯判据和奈奎斯特判据研究开环传递函数中不同参数对系统稳定性的影响。理论推导表明接口系统中滤波器截止频率、接口延时和阻抗模拟比对系统的稳定性影响较大,并通过所搭建的混合仿真系统进行实验,实验结果表明不同参数对系统的稳定性影响与理论推导一致。

实变函数中简单函数的研究

实变函数较之数学分析更加抽象复杂,是近代数学的重要基础。简单函数是实变函数中非常基础且具体的重要函数类。围绕简单函数与可测函数间的联系,及其在Lebesgue积分中的运用等问题开展研究,探讨简单函数在实变函数教学中的广泛应用,以期实现降低学习的难度提升实变函数的教学效果目的。

论高职院校房产管理系统设计实现

以包头职业技术学院为例,重点分析了房产系统的业务需求,设计系统总体功能模块及数据库表单,明确数据表逻辑关系,提出采用先进的前后端分离的体系架构模式,给出了系统主要功能的现实代码,总结了系统设计的特色。本文将为高职类院校房产管理实现信息化建设提供参考。