Routh Order Reduction Method of Relativistic Birkhoffian Systems

Routh order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic Birkhoffian system, the cyclic integrals can be found by using the perfect differential method. Through these cyclic integrals, the order of the system can be reduced. If the relativistic Birkhoffian system has a cyclic integral, then the Birkhoffian equations can be reduced at least by two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics, and the relativistic Lagrangian mechanics are discussed, and the Routh order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.

Simplified Method and Improved Solution for Deriving Fifth Order Stokes Wave

As the solution of the two equations for determining the existing fifth order Stokes wave derived by Skjelbreia is complex and tedious, the two equations are simplified into one equation for determining d / L, i. e., f(H, T, d / L) = 0. According to this simplified method, three cases of the solution for the Skjelbreia equations have been found: one accurate solution; more than one accurate solution and no accurate solution (but there exists the optimum approximate solution in the area of satisfying Skjelbreia equations). As to the case of more than one accurate solution, the reasonable solution can be judged from the method of variational principle, by means elf which an optimum solution improved from the solution of Skjelbreia equations in the area of satisfying the original mathematical equations of non-vortex and nonlinear wave theory, i. e., the optimum fifth order Stokes wave, is given.

State space solution to 3D multilayered elastic soils based on order reduction method

Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.

Methods in Model Order Reduction(MOR) field

Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industry requirements,analytically tractable and computationally cheap models must be designed.This is the essence task of Model Order Reduction(MOR).This article describes the basics of MOR optimization,various way of designing MOR,and gives the conclusion about existing methods.In addition,it proposed some heuristic footpath.

轴向流作用下均布非线性弹簧支承二维壁板的复杂响应

考虑刚性导流段和尾流段对流场的影响,建立轴向流作用下二维板的非线性流固耦合运动控制方程,用有限差分法对控制方程进行离散。为了克服差分网格较多时带来的计算规模较大的问题,对控制方程用主模态缩减法缩减自由度,然后对离散方程进行数值积分,得到系统的复杂响应,分析其分岔和混沌特性。计算结果表明,以来流流速幅值和阻尼参数为可变参数时,系统具有极其复杂的动态响应,通过分岔图、相图和庞加莱截面图等方法判断了系统多种形式的周期、拟周期和混沌运动,在以来流流速幅值为可变参数时,系统一开始经由周期倍化分岔的方式进入混沌;在以阻尼系数为可变参数时,经由倒周期倍化分岔的方式从混沌运动退回到周期振动。

一个解特定二阶驻定方程的新方法——特征伴随方程法

本文对文献[1]中提出的一类二阶驻定方程G″/G=∑^(m)_(j=0)P_(j)(G′/G)^(j)的求法进行探讨,提出了全新的求解方法——特征伴随方程法,通过该求法得到这类方程当m取不同非负整数(本文仅讨论m=2)时的通解,并相应给出该方程作为求解非线性偏微分方程的辅助方程时所需要的G′/G的解析表达式;同时给出一个作为常微分方程中驻定方程的应用实例,以及该方程作为非线性偏微分方程的辅助方程时利用扩展G′/G展开法的求解例子,通过该实例给出方程的精确行波解。

基于POD-αATS的油浸变压器瞬态温升降阶自适应变步长计算方法

针对油浸式电力变压器瞬态温升计算效率过低的问题,该文提出本征正交分解-αATS(proper orthogonal decomposition-adaptive time stepping based onαfactor,POD-αATS)降阶自适应变步长瞬态计算方法。首先,推导变压器绕组瞬态温升计算的有限元离散方程;其次,采用POD降阶算法改善传统瞬态计算中存在的条件数过大及方程阶数过高的问题;同时对于瞬态计算中的时间步长选择问题,提出适用于非线性问题的αATS变步长策略;然后,为验证方法的有效性,基于110 kV油浸式电力变压器绕组的基本结构建立二维八分区数值计算模型,同时将计算结果与基于110 kV绕组的温升实验结果进行对比。数值计算及实验结果表明,所提算法与全阶定步长算法在流场和温度场中的精度几乎相同,且流场计算效率提升约45倍,温度场计算效率提升约38倍,计算速度得到显著提高。这一点在温升实验中同样得到验证,说明该文所提算法的准确性、高效性及一定的工程实用性。

不确定转子系统动力学降阶模型构建与模型散度参数辨识

在航空、航天、船舶等领域的实际工程转子系统中,广泛存在高维复杂的非线性系统。在航空发动机转子系统、燃气轮机转子系统等重点研究领域,通常还难以对高维复杂非线性系统进行直接的数据处理和分析统计。针对不确定性转子系统的模型维度较高等问题,提出了一种模型不确定性动力学降阶计算模型构建和模型散度参数辨识方法。首先,根据确定性动力学模型和静态矩阵降阶方法,完善了确定性动力学降阶模型;然后,基于随机矩阵理论和非参数动力学建模方法,提出了不确定性动力学降阶模型;最后,利用系统确定性模型的一阶临界转速、振型和实验数据,对不确定性动力学模型的散度参数进行了辨识;为了验证散度参数辨识方法的有效性,笔者又在转子实验平台上进行了实验验证。研究结果表明:实验结果与降阶之后振动响应均值的差异性较小,且与不确定性动力学模型相差不超过10%,表明所采用的理论模型在描述转子系统行为方面具备了较高的准确性和可靠性,该模型可以为深入研究模型不确定性转子系统提供参考。

实时周跳探测与修复的MGF周跳解算方法的改进

周跳的探测和修复是基于载波相位高精度定位的关键技术之一。基于改进的几何无关相位组合MGF方法具有直接分离不同频率上的周跳,对高频数据中较小的周跳实现有效探测,探测速度远快于TurboEdit法等优点。但MGF法无法探测4周以上的周跳,并对低采样率和低卫星高度角下的数据进行周跳探测时,会选取错误的周跳备选值作为周跳检验量从而造成周跳的误判。针对MGF法所存在的问题,通过联合相位减伪距法PRP法,构建新的周跳备选值判断方程,并对MGF法的周跳检验量进行二次历元间差分STMGF,组成PRP-STMGF周跳探测组合。PRP-STMGF周跳探测组合能够探测任意周的周跳,与TurboEdit法相比,修复时无需分离周跳,直接对PRP-STMGF法的周跳检验量进行四舍五入即可确定出正确的周跳值,且适用于低采样率和低卫星高度角下的实时周跳探测与修复。最后通过北斗双频实测数据进行实验验证,结果表明,PRP-STMGF周跳探测组合,避免了MGF法选取错误周跳备选值的问题,相较于TurboEdit法不仅低延时,准确率高,且适用于不同采样率和低卫星高度角下周跳探测与修复。

基于等效线性化隔震结构设计周期折减系数研究

《建筑隔震设计标准》提出的隔震设计是基于复振型分解反应谱等效线性化的一体化直接设计方法,但未提及隔震结构周期折减系数如何取值。基于此,根据刚度串联关系推导等效单自由度隔震体系周期折减系数简化计算公式,探讨隔震结构周期折减系数因素的影响规律,建立不同填充材料、不同填充率的有限元数值模型,并利用数值模拟结果验证隔震结构周期折减系数简化计算公式。结果表明:隔震结构周期折减系数与名义周期比、非隔震结构周期折减系数存在函数关系;墙体开洞与通高墙体的隔震结构的周期折减系数均随着填充率的增大而减小,当填充率相同时,呈现出随填充材料弹性模量增大而减小的趋势,墙体开洞会增大隔震结构周期折减系数,且隔震结构的周期折减系数的取值范围相对较窄,为0.915~0.965;数值有限元模拟与理论结果偏差小于3%,吻合度高,以验证隔震结构周期折减系数简化计算公式的正确性,说明该简化计算方法对隔震工程设计具有一定指导意义。

Second-order difference scheme for a nonlinear model of wood drying process

A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.

Exact Solutions to Nonlinear Schr(?)dinger Equation and Higher-Order Nonlinear Schr(?)dinger Equation

We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.

Precise integration method for solving singular perturbation problems

This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.

Reducing the ordering temperature of FePt nanoparticles by Cu additive and alternate reduction method

(FePt)85Cu15 nanoparticles were successfully prepared by alternate reduction of metal salts in aqueous medium.Detailed investigations on the correlation between the magnetic and structural properties of these nanoparticles are presented as a function of annealing temperature.Both the X-ray diffraction patterns and the magnetic hysteresis loop measurements show the existence of L10-FePt phase at a relative low annealing temperature.It is proved that the Cu additive and alternate reduction are very effective methods in reducing the ordering temperature of FePt nanoparticles.

A New Method for Predicting the UL of Circular CFST Columns

Concrete filled steel tube structures have gained booming development in recent decades, especially in China. Simplified methods have been proposed in design codes, such as the Eurocode 4 (EC4) and the China engineering and construction specification (CECS). In EC4, the confinement effect is reasonably related to slenderness and load eccentricity. The CECS method is much straight forward in that the slenderness ratio and load eccentricity are treated as independent reduction factors. To make use of the advantages of both the CECS and the EC4 methods, the CECS method is modified to consider the confinement effect associated with slenderness and load eccentricity. It is shown that the proposed method can predict well the ultimate load capacity of circular section concrete filled steel tube columns.

基于交叉降阶取样的改进响应面方法

针对经典响应面法和加权响应面法存在的计算精度不高和稳定性不强的问题,提出一种新的样本点选择策略,即交叉降阶思想,并基于此发展出一种新的改进响应面方法。该方法以均值点加上0.5倍的标准差作为初始迭代点。在Bucher试验设计的基础之上,将n维坐标系降阶为n个一维坐标系。然后,依据样本点的重要性,筛选出n+1个靠近真实失效面的优秀样本点,并用这些样本点去拟合线性响应面函数。最后依据样本中心间的距离与上一次迭代得到的设计点的范数之商作为其收敛准则。通过5个数值算例与工程算例,验证了交叉降阶响应面法具有较高的精度、效率、稳定性和一定的工程适用性。

非比例阻尼结构谐响应分析的自适应模型降阶方法

针对非比例阻尼结构谐响应分析效率低的问题,开展了基于二阶Arnoldi算法的模型降阶方法研究,提出一种基于二分法和交叉验证策略自适应确定展开频点数目和标准正交基阶数的方法,以较少计算量建立了高保真降阶模型,实现非比例阻尼结构响应的高精度计算。通过阻尼涂层板和网格加筋筒壳的谐响应分析算例验证了自适应降阶策略的有效性;数值结果表明,自适应降阶模型预测结构动柔顺度相对误差较小,相比模态叠加法和模态加速度法具有更高的计算精度和效率。

基于降阶模型和数据驱动的动态结构数字孪生方法

针对受动载荷作用的结构,提出了一种基于降阶模型库和机器学习数据驱动的数字孪生构建方法.首先根据物理结构服役过程中可能出现的损伤状态,采用有限单元法建立高保真有限元模型.其次采用Krylov子空间模型降阶方法对模型进行降阶,建立了物理结构各种状态下的降阶模型,形成模型库.最后利用随机森林机器学习算法训练获得模型选择器,通过物理结构上传感器的数据推断当前物理结构的状态,驱动数字孪生体跟随物理结构一同演化.设计制作了一个框架结构物理模型,模拟了结构不同位置损伤及不同损伤程度,验证了提出的数字孪生构建方法.

基于自适应降阶滑模算法的受约束多机械臂力/位混合控制

针对多机械臂系统末端受环境约束而产生的力/位混合控制问题,提出一种基于自适应降阶滑模算法的受约束多机械臂力/位混合控制方法。通过运用多个坐标系建立受约束多机械臂系统动力学模型,并将位置控制、约束力控制以及内力控制引入同一控制器中。将自适应滑模算法与降阶方法相结合,对动力学模型中的未知扰动进行了补偿。基于李雅普诺夫方法,证明系统的稳定性。经仿真验证,该方法不仅提高了控制器的控制精度和系统的响应速度,同时还能保证约束力误差及内力误差均稳定在极小的范围内。