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A Continuous Finite Element Method with Homotopy VanishingViscosity for Solving the Static Eikonal Equation

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Communications in Computational Physics 2022年第5期31卷 1402-1433页

作者： Yong Yang wenrui hao Yong-Tao Zhang College of Science Nanjing University of Aeronautics and AstronauticsNanjing 210016China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106China Department of Mathematics Pennsylvania State UniversityUniversity ParkPennsylvaniaUSA Department of Applied and Computational Mathematics and Statistics University of Notre DameNotre DameIN 46556USA

We develop a second-order continuousfinite element method for solving the static Eikonal *** is based on the vanishing viscosity approach with a homotopy method for solving the discretized nonlinear *** specifically,the homotopy method is utilized to decrease the viscosity coefficient gradually,while Newton’s method is applied to compute the solution for each viscosity ***’s method alone converges for just big enough viscosity coefficients on very coarse grids and for simple 1D examples,but the proposed method is much more robust and guarantees the convergence of the nonlinear solver for all viscosity coefficients and for all examples over all *** experiments from 1D to 3D are presented to confirm the second-order convergence and the effectiveness of the proposed method on both structured or unstructured meshes.

关键词： Eikonal equation finite element method homotopy method

Predict Blood Pressure by Photoplethysmogram with the Fluid-Structure Interaction Modeling

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Communications in Computational Physics 2022年第4期31卷 1114-1133页

作者： Jianhong Chen wenrui hao Pengtao Sun Lian Zhang Wilshire Advisors LLC Los AngelesCaliforniaUSA Department of Mathematics Pennsylvania State UniversityUniversity ParkPennsylvaniaUSA Department of Mathematical Sciences University of Nevada Las VegasLas VegasNevadaUSA In-Chao Institute Ltd ShenzhenChina

Blood pressure(BP)has been identified as one of the main factors in cardiovascular disease and other related *** how to accurately and conveniently measure BP is important to monitor BP and to prevent *** paper proposes an efficient BP measurement model by integrating a fluid-structure interaction model with the photoplethysmogram(PPG)signal and developing a data-driven computational approach to fit two optimization parameters in the proposedmodel for each *** developed BPmodel has been validated on a public BP dataset and has shown that the average prediction errors among the root mean square error(RMSE),the mean absolute error(MAE),the systolic blood pressure(SBP)error,and the diastolic blood pressure(DBP)error are all below 5mmHg for normal BP,stage I,and stage II hypertension groups,and,prediction accuracies of the SBP and the DBP are around 96%among those three groups.

关键词： Blood pressure prediction fluid-structure interaction PPG

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基于相关变量分解的重要性测度分析新方法

西北工业大学学报 2012年第1期30卷 88-93页

作者：郝文锐吕震宙田龙飞西北工业大学航空学院陕西西安710072

为了清晰地掌握相关输入变量情况下响应量方差的来源,有必要将重要性测度分离为相关部分和独立部分。通过将相关变量构造为独立变量的线性组合,相关输入变量对功能响应的方差贡献可被分离为相关部分和非相关部分,提出线性响应量情况下... 详细信息

为了清晰地掌握相关输入变量情况下响应量方差的来源,有必要将重要性测度分离为相关部分和独立部分。通过将相关变量构造为独立变量的线性组合,相关输入变量对功能响应的方差贡献可被分离为相关部分和非相关部分,提出线性响应量情况下基于相关变量分解的重要性测度分析方法。所提方法不仅能将某一相关变量对响应的方差贡献分解为独立部分和相关部分,还可将其相关贡献分离为其与每一相关变量间的相关贡献分量。在此基础上针对非线性响应量的情况建立了基于迭代一阶泰勒展开的重要性求解方法,该方法可在响应的一阶泰勒展开式的方差与原响应方差基本一致的情况下对相关变量进行重要性测度求解。采用所提方法,对文中数值算例和工程应用算例中各相关输入变量的相关部分和独立部分的重要性测度指标进行了求解,证明了文中提出的基于相关变量分解的重要性测度方法是合理、可行的。

关键词：灵敏度分析重要性测度相关变量分解泰勒展开多项式

基于方差的相关输入变量重要性测度分析新方法

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航空学报 2011年第9期32卷 1637-1643页

作者：郝文锐吕震宙田龙飞西北工业大学航空学院陕西西安710072

为了清晰地掌握相关输入变量情况下响应量方差的来源,非常有必要将基于方差的重要性测度(VBIM)分离为相关部分和独立部分。为此,在二阶非线性回归的基础上,提出了一种适用于非线性响应量的相关变量重要性分析的新方法。一个输入变量对... 详细信息

为了清晰地掌握相关输入变量情况下响应量方差的来源,非常有必要将基于方差的重要性测度(VBIM)分离为相关部分和独立部分。为此,在二阶非线性回归的基础上,提出了一种适用于非线性响应量的相关变量重要性分析的新方法。一个输入变量对响应量方差的相关贡献由该变量与每一个剩余变量两两相关的贡献分量组成,所以又进一步提出了一种概念简单有效的求解相关贡献分量的方法,并在此基础上定义了重要性矩阵,以便清晰地表达相关变量对响应量方差贡献的各个分量。数值算例和工程应用算例中,各相关输入变量的重要性测度分析的结果表明:本文方法可以在二次非线性响应量情况下合理分解相关变量的相关贡献和独立贡献;对于更复杂的非线性响应量情况,通过将所提方法中的二次非线性回归扩展为更合理的近似模型,可以得到重要性分析的高精度结果。

关键词：灵敏度分析重要性测度相关变量方差分解回归分析重要性矩阵

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高自由度双足机器人数学模型及步行控制研究

力学与实践 2006年第6期28卷 69-72页

作者：郝文瑞刘畅南开大学数学学院天津300071 密歇根科技大学密歇根霍顿市美国49931

基于ZMP理论及位姿矩阵,采用了相对重心以及相对坐标系的数学描述方法,对17自由度双足机器人步行稳定性控制进行数学建模研究．所建立的数学模型能够描述机器人稳定性控制．并经过Matlab数学计算和仿真研究,验证了所建立的模型可以描述... 详细信息

基于ZMP理论及位姿矩阵,采用了相对重心以及相对坐标系的数学描述方法,对17自由度双足机器人步行稳定性控制进行数学建模研究．所建立的数学模型能够描述机器人稳定性控制．并经过Matlab数学计算和仿真研究,验证了所建立的模型可以描述双足机器人的步行规律,在理论上达到了双足机器人步行稳定性的控制目的．最后通过VC++把整个模型封装成一个可视化系统,便于将所研究的模型应用到实际的控制中,为未来机器人的实时控制的研究提供了技术支持．

关键词：步行控制数学建模零力矩点遗传算法

Enhancing SAEAs with unevaluated solutions:a case study of relation model for expensive optimization

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Science China(Information Sciences) 2024年第2期67卷 41-58页

作者： hao hao Xiaoqun ZHANG Aimin ZHOU Institute of Natural Sciences Shanghai Jiao Tong University Shanghai Frontiers Science Center of Molecule Intelligent Syntheses School of Computer Science and Technology East China Normal University

Surrogate-assisted evolutionary algorithms(SAEAs) hold significant importance in resolving expensive optimization problems. Extensive efforts have been devoted to improving the efficiency of SAEAs through the development of proficient model-assisted solution selection methods, which, however, first requires generating high-quality solutions. The fundamental paradigm of evaluating a limited number of solutions in each generation within SAEAs reduces the variance of adjacent populations, thereby affecting the quality of offspring solutions. This is a frequently encountered issue yet receives little attention. To address the issue, this paper presents a framework using unevaluated solutions to enhance the efficiency of *** surrogate model is employed to identify high-quality solutions for the direct generation of new solutions without evaluation. To ensure dependable selection, we have introduced two tailored relation models to select the optimal solution and the unevaluated population. A comprehensive experimental analysis is performed on two test suites, which showcases the superiority of the relation model over regression and classification models in the solution selection phase. Furthermore, the surrogate-selected unevaluated solutions with high potential have been shown to enhance the efficiency of the algorithm significantly.

关键词： expensive optimization unevaluated solutions relation model surrogate-assisted evolutionary algorithm

Nonclassical correlations in two-dimensional graphene lattices

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Communications in Theoretical Physics 2024年第4期76卷 72-79页

作者： hao Wang Shanghai Normal University Tianhua College ShangHai 201815China

We investigate nonclassical correlations via negativity,local quantum uncertainty(LQU)and local quantum Fisher information(LQFI)for two-dimensional graphene *** explicitly analytical expressions for negativity,LQU and LQFI are *** close forms of LQU and LQFI confirm the inequality between the quantum Fisher information and skew information,where the LQFI is always greater than or equal to the LQU,and both show very similar behavior with different ***,the effects of the different system parameters on the quantified quantum correlation are *** LQFI reveals more nonclassical correlations than LQU in a two-dimensional graphene lattice system.

关键词： negativity local quantum uncertainty(LQU) local quantum Fisher information(LQFI) graphene lattices nonclassical correlations

A Global Optimality Principle for Fully Coupled Mean-field Control Systems

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 379-413页

作者： Tao hao School of Statistics and Mathematics Shandong University of Finance and EconomicsJinan 250014China

This paper concerns a global optimality principle for fully coupled mean-field control *** the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Y^(ε) that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The comparison with the stochastic maximum principle for controlled mean-field stochastic differential equations is supplied.

关键词： optimal control global maximum principle fully coupled general mean-field FBSDE adjoint equation recursive utility

Machine learning-assisted smart epitaxy ofⅢ-Ⅴsemiconductors

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Science China Materials 2024年第9期67卷 3041-3042页

作者： Yue hao Key Laboratory of Wide Band Gap Semiconductor Technology School of MicroelectronicsXidian UniversityXi’an710071China

Semiconductor epitaxial growth is the front-end process for manufacturing microelectronic and optoelectronic *** beam epitaxy(MBE),capable of precisely controlling atomic layer deposition,has emerged as a crucial technique in chip atomic-level manufacturing[1].However,in semiconductor epitaxy,the heterogeneous nature of materials is complicated,and the growth condition fluctuations poses significant challenges in defect suppression[2],substantially impacting chip performance and yield.

关键词： optoelectronic smart semiconductors